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2023-05-13
|
Global existence for a 3D Tropical Climate Model with damping and small initial data in $\dot H^{1/2}(\mathbb{R}^3)$
|
We consider a 3D Tropical Climate Model with damping terms in the equation of
the barotropic mode $u$ and in the equation of the first baroclinic mode $v$ of
the velocity. The equation for the temperature $\theta$ is free from dampings.
We prove global existence in time for this system assuming the initial data
$(u_0, v_0,\theta_0)$ small, in terms of the homogeneous space $\dot
H^{1/2}(\mathbb{R}^3)$.
|
2305.07964v1
|
2023-06-21
|
The effect of singularities and damping on the spectra of photonic crystals
|
Understanding the dispersive properties of photonic crystals is a fundamental
and well-studied problem. However, the introduction of singular permittivities
and damping complicates the otherwise straightforward theory. In this paper, we
study photonic crystals with a Drude-Lorentz model for the permittivity,
motivated by halide perovskites. We demonstrate how the introduction of
singularities and damping affects the spectral band structure and show how to
interpret the notion of a "band gap" in this setting. We present explicit
solutions for a one-dimensional model and show how integral operators can be
used to handle multi-dimensional systems.
|
2306.12254v1
|
2023-07-12
|
Asymptotic behavior of solutions to the Cauchy problem for 1-D p-system with space dependent damping
|
We consider the Cauchy problem for one-dimensional p-system with damping of
space-dependent coefficient. This system models the compressible flow through
porous media in the Lagrangean coordinate. Our concern is an asymptotic
behavior of solutions, which is expected to be the diffusion wave based on the
Darcy law. To show this expectation, the problem is reformulated to the Cauchy
problem for the second order quasilinear hyperbolic equation with space
dependent damping, which is analyzed by the energy method.
|
2307.05865v1
|
2023-07-12
|
Parabolic-elliptic Keller-Segel's system
|
We study on the whole space R d the compressible Euler system with damping
coupled to the Poisson equation when the damping coefficient tends towards
infinity. We first prove a result of global existence for the Euler-Poisson
system in the case where the damping is large enough, then, in a second step,
we rigorously justify the passage to the limit to the parabolic-elliptic
Keller-Segel after performing a diffusive rescaling, and get an explicit
convergence rate. The overall study is carried out in 'critical' Besov spaces,
in the spirit of the recent survey [16] by R. Danchin devoted to partially
dissipative systems.
|
2307.05981v1
|
2023-07-25
|
Asymptotic behavior and life-span estimates for the damped inhomogeneous nonlinear Schrödinger equation
|
We are interested in the behavior of solutions to the damped inhomogeneous
nonlinear Schr\"odinger equation $ i\partial_tu+\Delta
u+\mu|x|^{-b}|u|^{\alpha}u+iau=0$, $\mu \in\mathbb{C} $, $b>0$, $a \in
\mathbb{C}$ such that $\Re \textit{e}(a) \geq 0$, $\alpha>0$. We establish
lower and upper bound estimates of the life-span. In particular for $a\geq 0$,
we obtain explicit values $a_*,\; a^*$ such that if $a<a_*$ then blow up
occurs, while for $a>a^*,$ global existence holds. Also, we prove scattering
results with precise decay rates for large damping. Some of the results are new
even for $b=0.$
|
2307.13495v1
|
2023-07-26
|
On nonlinear Landau damping and Gevrey regularity
|
In this article we study the problem of nonlinear Landau damping for the
Vlasov-Poisson equations on the torus. As our main result we show that for
perturbations initially of size $\epsilon>0$ and time intervals
$(0,\epsilon^{-N})$ one obtains nonlinear stability in regularity classes
larger than Gevrey $3$, uniformly in $\epsilon$. As a complementary result we
construct families of Sobolev regular initial data which exhibit nonlinear
Landau damping. Our proof is based on the methods of Grenier, Nguyen and
Rodnianski.
|
2307.14271v1
|
2023-08-18
|
Damping for fractional wave equations and applications to water waves
|
Motivated by numerically modeling surface waves for inviscid Euler equations,
we analyze linear models for damped water waves and establish decay properties
for the energy for sufficiently regular initial configurations. Our findings
give the explicit decay rates for the energy, but do not address
reflection/transmission of waves at the interface of the damping. Still for a
subset of the models considered, this represents the first result proving the
decay of the energy of the surface wave models.
|
2308.09288v1
|
2023-08-30
|
Optimal decay for one-dimensional damped wave equations with potentials via a variant of Nash inequality
|
The optimality of decay properties of the one-dimensional damped wave
equations with potentials belonging to a certain class is discussed. The
typical ingredient is a variant of Nash inequality which involves an invariant
measure for the corresponding Schr\"odinger semigroup. This enables us to find
a sharp decay estimate from above. Moreover, the use of a test function method
with the Nash-type inequality provides the decay estimate from below. The
diffusion phenomena for the damped wave equations with potentials are also
considered.
|
2308.15680v1
|
2023-09-15
|
Explicit solutions and linear inviscid damping in the Euler-Boussinesq equation near a stratified Couette flow in the periodic strip
|
This short note provides explicit solutions to the linearized Boussinesq
equations around the stably stratified Couette flow posed on
$\mathbb{T}\times\mathbb{R}$. We consider the long-time behavior of such
solutions and prove inviscid damping of the perturbed density and velocity
field for any positive Richardson number, with optimal rates. The explicit
solution is obtained through the limiting absorption principle whereas the
inviscid damping is proved using oscillatory integral methods.
|
2309.08419v2
|
2023-09-21
|
Beyond Qubits : An Extensive Noise Analysis for Qutrit Quantum Teleportation
|
The four quantum noises Bit Flip, Phase Flip, Depolarization, and Amplitude
Damping as well as any potential combinations of them are examined in this
papers investigation of quantum teleportation using qutrit states. Among the
above mentioned noises, we observed phase flip has highest fidelity. Compared
to uncorrelated Amplitude Damping, we find that correlated Amplitude Damping
performs two times better. Finally, we agreed that, for better fidelity, it is
preferable to provide the same noise in channel state if noise is unavoidable.
|
2309.12163v1
|
2023-12-22
|
Soliton resolution for the energy critical damped wave equations in the radial case
|
We consider energy-critical damped wave equation \begin{equation*}
\partial_{tt}u-\Delta u+\alpha \partial_t u=\left|u\right|^{\frac{4}{D-2}}u
\end{equation*} with radial initial data in dimensions $D\geq 4$. The equation
has a nontrivial radial stationary solution $W$, called the ground state, which
is unique up to sign and scale. We prove that any bounded energy norm solution
behaves asymptotically as a superposition of the modulated ground states and a
radiation term. In the global case, particularly, the solution converges to a
pure multi-bubble due to the damping effect.
|
2401.04115v2
|
2024-01-22
|
Damping-Enhanced Magnon Transmission
|
The inevitable Gilbert damping in magnetization dynamics is usually regarded
as detrimental to spin transport. Here we demonstrate in a
ferromagnetic-insulator--normal-metal heterostructure that the strong momentum
dependence and chirality of the eddy-current-induced damping causes also
beneficial scattering properties. Here we show that a potential barrier that
reflects magnon wave packets becomes transparent in the presence of a metallic
cap layer, but only in one direction. We formulate the unidirectional
transmission in terms of a generalized group velocity with an imaginary
component and the magnon skin effect. This trick to turn presumably harmful
dissipation into useful functionalities should be useful for future quantum
magnonic devices.
|
2401.12022v1
|
2024-02-18
|
Sharp lifespan estimate for the compressible Euler system with critical time-dependent damping in $\R^2$
|
This paper concerns the long time existence to the smooth solutions of the
compressible Euler system with critical time dependent damping in $\R^2$. We
establish the sharp lifespan estimate from below, with respect to the small
parameter of the initial perturbation. For this end, the vector fields
$\widehat{Z}$ (defined below) are used instead of the usual one $Z$, to get
better decay for the linear error terms. This idea may also apply to the long
time behavior study of nonlinear wave equations with time-dependent damping.
|
2402.11516v1
|
2024-02-28
|
Linear inviscid damping in the presence of an embedding eigenvalue
|
In this paper, we investigate the long-time dynamics of the linearized 2-D
Euler equations around a hyperbolic tangent flow $(\tanh y,0)$. A key
difference compared to previous results is that the linearized operator has an
embedding eigenvalue, which has a significant impact on the dynamics of the
linearized system. For the first mode, the dynamics consists of there parts:
non-decay part related to the eigenspace associated with the embedding
eigenvalue, slow decay part due to the resolvent singularity, and fast decay
part related to the inviscid damping. For higher modes, the dynamics is similar
to the inviscid damping phenomena in the case without embedding eigenvalues.
|
2402.18229v1
|
2024-03-19
|
Improved decay results for micropolar flows with nonlinear damping
|
We examine the long-time behavior of solutions (and their derivatives) to the
micropolar equations with nonlinear velocity damping. Additionally, we get a
speed-up gain of $ t^{1/2} $ for the angular velocity, consistent with
established findings for classic micropolar flows lacking nonlinear damping.
Consequently, we also obtain a sharper result regarding the asymptotic
stability of the micro-rotational velocity $\ww(\cdot,t)$. Related results of
independent interest are also included.
|
2403.12885v1
|
2024-03-26
|
On a class of nonautonomous quasilinear systems with general time-gradually-degenerate damping
|
In this paper, we study two systems with a time-variable coefficient and
general time-gradually-degenerate damping. More explicitly, we construct the
Riemann solutions to the time-variable coefficient Zeldovich approximation and
time-variable coefficient pressureless gas systems both with general
time-gradually-degenerate damping. Applying the method of similar variables and
nonlinear viscosity, we obtain classical Riemann solutions and delta shock wave
solutions.
|
2403.17732v1
|
2024-04-09
|
Phase space contraction of degenerately damped random splittings
|
When studying out-of-equilibrium systems, one often excites the dynamics in
some degrees of freedom while removing the excitation in others through
damping. In order for the system to converge to a statistical steady state, the
dynamics must transfer the energy from the excited modes to the dissipative
directions. The precise mechanisms underlying this transfer are of particular
interest and are the topic of this paper. We explore a class of randomly
switched models introduced in [2,3] and provide some of the first results
showing that minimal damping is sufficient to stabilize the system in a fluids
model.
|
2404.06465v1
|
2002-09-30
|
The Cosmic Microwave Background & Inflation, Then & Now
|
Boomerang, Maxima, DASI, CBI and VSA significantly increase the case for
accelerated expansion in the early universe (the inflationary paradigm) and at
the current epoch (dark energy dominance), especially when combined with data
on high redshift supernovae (SN1) and large scale structure (LSS). There are
``7 pillars of Inflation'' that can be shown with the CMB probe, and at least
5, and possibly 6, of these have already been demonstrated in the CMB data: (1)
a large scale gravitational potential; (2) acoustic peaks/dips; (3) damping due
to shear viscosity; (4) a Gaussian (maximally random) distribution; (5)
secondary anisotropies; (6) polarization. A 7th pillar, anisotropies induced by
gravity wave quantum noise, could be too small. A minimal inflation parameter
set, \omega_b,\omega_{cdm}, \Omega_{tot}, \Omega_Q,w_Q,n_s,\tau_C, \sigma_8},
is used to illustrate the power of the current data. We find the CMB+LSS+SN1
data give \Omega_{tot} =1.00^{+.07}_{-.03}, consistent with (non-baroque)
inflation theory. Restricting to \Omega_{tot}=1, we find a nearly scale
invariant spectrum, n_s =0.97^{+.08}_{-.05}. The CDM density, \Omega_{cdm}{\rm
h}^2 =.12^{+.01}_{-.01}, and baryon density, \Omega_b {\rm h}^2 =
>.022^{+.003}_{-.002}, are in the expected range. (The Big Bang nucleosynthesis
estimate is 0.019\pm 0.002.) Substantial dark (unclustered) energy is inferred,
\Omega_Q \approx 0.68 \pm 0.05, and CMB+LSS \Omega_Q values are compatible with
the independent SN1 estimates. The dark energy equation of state, crudely
parameterized by a quintessence-field pressure-to-density ratio w_Q, is not
well determined by CMB+LSS (w_Q < -0.4 at 95% CL), but when combined with SN1
the resulting w_Q < -0.7 limit is quite consistent with the w_Q=-1 cosmological
constant case.
|
0210007v1
|
2003-06-17
|
Kinetic equilibrium of iron in the atmospheres of cool stars III. The ionization equilibrium of selected reference stars
|
Non-LTE line formation calculations of Fe I are performed for a small number
of reference stars to investigate and quantify the efficiency of neutral
hydrogen collisions. Using the atomic model that was described in previous
publications, the final discrimination with respect to hydrogen collisions is
based on the condition that the surface gravities as determined by the Fe I/Fe
II ionization equilibria are in agreement with their astrometric counterparts
obtained from HIPPARCOS parallaxes. Depending on the choice of the hydrogen
collision scaling factor S_H, we find deviations from LTE in Fe I ranging from
0.00 (S_H = infinity) to 0.46 dex (S_H = 0 for HD140283) in the logarithmic
abundances while Fe II follows LTE.
With the exception of Procyon, for which a mild temperature correction is
needed to fulfil the ionization balance, excellent consistency is obtained for
the metal-poor reference stars if Balmer profile temperatures are combined with
S_H = 3. The correct choice of collisional damping parameters ("van-der-Waals"
constants) is found to be generally more important for these little evolved
metal-poor stars than considering departures from LTE. For the Sun the
calibrated value for S_H leads to average Fe I non-LTE corrections of 0.02 dex
and a mean abundance from Fe I lines of log epsilon(Fe) = 7.49 \pm 0.08.
We confront the deduced stellar parameters with comparable spectroscopic
analyses by other authors which also rely on the iron ionization equilibrium as
a gravity indicator. On the basis of the HIPPARCOS astrometry our results are
shown to be an order of magnitude more precise than published data sets, both
in terms of offset and star-to-star scatter.
|
0306337v1
|
2003-10-08
|
Signatures of Relativistic Neutrinos in CMB Anisotropy and Matter Clustering
|
We present a detailed analytical study of ultra-relativistic neutrinos in
cosmological perturbation theory and of the observable signatures of
inhomogeneities in the cosmic neutrino background. We note that a modification
of perturbation variables that removes all the time derivatives of scalar
gravitational potentials from the dynamical equations simplifies their solution
notably. The used perturbations of particle number per coordinate, not proper,
volume are generally constant on superhorizon scales. In real space an
analytical analysis can be extended beyond fluids to neutrinos.
The faster cosmological expansion due to the neutrino background changes the
acoustic and damping angular scales of the cosmic microwave background (CMB).
But we find that equivalent changes can be produced by varying other standard
parameters, including the primordial helium abundance. The low-l integrated
Sachs-Wolfe effect is also not sensitive to neutrinos. However, the gravity of
neutrino perturbations suppresses the CMB acoustic peaks for the multipoles
with l>~200 while it enhances the amplitude of matter fluctuations on these
scales. In addition, the perturbations of relativistic neutrinos generate a
*unique phase shift* of the CMB acoustic oscillations that for adiabatic
initial conditions cannot be caused by any other standard physics. The origin
of the shift is traced to neutrino free-streaming velocity exceeding the sound
speed of the photon-baryon plasma. We find that from a high resolution, low
noise instrument such as CMBPOL the effective number of light neutrino species
can be determined with an accuracy of sigma(N_nu) = 0.05 to 0.09, depending on
the constraints on the helium abundance.
|
0310198v3
|
2004-09-22
|
First stars VI - Abundances of C, N, O, Li, and mixing in extremely metal-poor giants. Galactic evolution of the light elements
|
We have investigated the poorly-understood origin of nitrogen in the early
Galaxy by determining N abundances in 35 extremely metal-poor halo giants (22
stars have [Fe/H]<-3.0) using the C and O abundances determined in Paper V.
Because any dredge-up of CNO processed material to the surface may complicate
the interpretation of CNO abundances in giants, we have also measured the
surface abundance of lithium. Our sample shows a clear dichotomy between two
groups of stars. The first group shows evidence of C to N conversion through CN
cycling and strong Li dilution, a signature of mixing. The second group shows
no evidence for C to N conversion, and Li is only moderately diluted, and we
conclude that their C and N abundances are very close to those of the gas from
which they formed in the early Galaxy. These "unmixed" stars reflect the
abundances in the early Galaxy: the [C/Fe] ratio is constant (about +0.2 dex)
and the [C/Mg] ratio is close to solar at low metallicity, favouring a high C
production by massive zero-metal supernovae. The [N/Fe] and [N/Mg] ratios
scatter widely. The larger values of these ratios define a flat upper plateau
([N/Mg]= 0.0, [N/Fe]= +0.1), which could reflect higher values within a wide
range of yields of zero-metal Sne II. Alternatively, by analogy with the DLA's,
the lower abundances ([N/Mg]= -1.1, [N/Fe]= -0.7) could reflect generally low
yields from the first Sne II, the other stars being N enhanced by winds of
massive Asymptotic Giant Branch (AGB) stars. At present it cannot be decided
whether primary N is produced primarily in SNe II or in massive AGB stars, or
in both. The stellar N abundances and [N/O] ratios are compatible with those
found in Damped Lyman-alpha (DLA) systems.
|
0409536v3
|
2005-09-15
|
Damped Lyman Alpha Systems at z<1.65: The Expanded SDSS HST Sample
|
We present results of our HST Cycle 11 Survey for low-redshift (z<1.65) DLAs
in the UV spectra of quasars selected from the SDSS Early Data Release. These
quasars have strong intervening MgII-FeII systems which are known signatures of
high column density neutral gas. In total, UV observations of Ly-alpha
absorption in 197 MgII systems with z<1.65 and rest equivalent width (REW)
W2796 \ge 0.3A have now been obtained. The main results are: (1) 36(+/- 6)% of
systems with W2796 \ge 0.5 A and FeII W2600 \ge 0.5 A are DLAs. This increases
to 42(+/- 7)% for systems with W2796/W2600 < 2 and MgI W2852 > 0.1 A. (2) The
mean N(HI) of MgII systems with 0.3 A \le W2796 < 0.6 A is a factor of ~36
lower than that of systems with W2796 \ge 0.6 A. (3) The DLA incidence per unit
redshift is consistent with no evolution for z <~ 2 (Omega_L=0.7, Omega_M =
0.3), but exhibits significant evolution for z >~ 2. (4) Omega_{DLA} is
constant for 0.5<z<5.0 to within the uncertainties. This is larger than
Omega_{gas}(z=0) by a factor of ~2. (5) The slope of the N(HI) distribution
does not change significantly with redshift. However, the low redshift
distribution is marginally flatter due to the higher fraction of high N(HI)
systems in our sample. (6) Finally, using the precision of MgII survey
statistics, we find that there may be evidence of a decreasing Omega_{DLA} from
z=0.5 to z=0. We reiterate the conclusion of Hopkins, Rao, & Turnshek that very
high columns of neutral gas might be missed by DLA surveys because of their
very small cross sections, and therefore, that Omega_{DLA} might not include
the bulk of the neutral gas mass in the Universe. (Abridged)
|
0509469v1
|
2007-01-03
|
HI 21cm absorption at $z \sim 3.39$ towards PKS 0201+113
|
We report the GMRT detection of HI 21cm absorption from the $z \sim 3.39$
damped Lyman-$\alpha$ absorber (DLA) towards PKS 0201+113, the highest redshift
at which 21cm absorption has been detected in a DLA. The absorption is spread
over $\sim 115$ km s$^{-1}$ and has two components, at $z = 3.387144 (17)$ and
$z = 3.386141 (45)$. The stronger component has a redshift and velocity width
in agreement with the tentative detection of Briggs et al. (1997), but a
significantly lower optical depth. The core size and DLA covering factor are
estimated to be $\lesssim 100$ pc and $f \sim 0.69$, respectively, from a VLBA
328 MHz image. If one makes the conventional assumption that the HI column
densities towards the optical and radio cores are the same, this optical depth
corresponds to a spin temperature of $\ts \sim [(955 \pm 160) \times (f/0.69)]
$ K. However, this assumption may not be correct, given that no metal-line
absorption is seen at the redshift of the stronger 21cm component, indicating
that this component does not arise along the line of sight to the optical QSO,
and that there is structure in the 21cm absorbing gas on scales smaller than
the size of the radio core. We model the 21cm absorbing gas as having a
two-phase structure with cold dense gas randomly distributed within a diffuse
envelope of warm gas. For such a model, our radio data indicate that, even if
the optical QSO lies along a line-of-sight with a fortuitously high ($\sim
50$%) cold gas fraction, the average cold gas fraction is low, ($\lesssim
17%$), when averaged over the the spatial extent of the radio core. Finally,
the large mismatch between peak 21cm and optical redshifts and the complexity
of both profiles makes it unlikely that the $z \sim 3.39$ DLA will be useful in
tests of fundamental constant evolution.
|
0701074v2
|
2004-10-24
|
Field theory of the inverse cascade in two-dimensional turbulence
|
A two-dimensional fluid, stirred at high wavenumbers and damped by both
viscosity and linear friction, is modeled by a statistical field theory. The
fluid's long-distance behavior is studied using renormalization-group (RG)
methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732
(1977)]. With friction, which dissipates energy at low wavenumbers, one expects
a stationary inverse energy cascade for strong enough stirring. While such
developed turbulence is beyond the quantitative reach of perturbation theory, a
combination of exact and perturbative results suggests a coherent picture of
the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is
derived from a generalized time-reversal symmetry and implies zero anomalous
dimension for the velocity even when friction is present. Thus the Kolmogorov
scaling of the inverse cascade cannot be explained by any RG fixed point. The
beta function for the dimensionless coupling ghat is computed through two
loops; the ghat^3 term is positive, as already known, but the ghat^5 term is
negative. An ideal cascade requires a linear beta function for large ghat,
consistent with a Pad\'e approximant to the Borel transform. The conjecture
that the Kolmogorov spectrum arises from an RG flow through large ghat is
compatible with other results, but the accurate k^{-5/3} scaling is not
explained and the Kolmogorov constant is not estimated. The lack of scale
invariance should produce intermittency in high-order structure functions, as
observed in some but not all numerical simulations of the inverse cascade. When
analogous RG methods are applied to the one-dimensional Burgers equation using
an FDT-preserving dimensional continuation, equipartition is obtained instead
of a cascade--in agreement with simulations.
|
0410050v2
|
2004-09-20
|
Effect of the Vacuum Energy Density on Graviton Propagation
|
It is known that the value L of the vacuum energy density affects the
propagation equation for gravitons: A mass term appears in the propagation
equation, such that m^2=-L. As a consequence, the polarization states of
gravitons also change. This effect of the L-term has been confirmed by recent
calculations in a curved background, which is the only proper setting, since
solutions of the classical Einstein equations in the presence of a L-term
represent a space with constant curvature. A real value for the mass (when L<0)
will show up as a slight exponential damping in the gravitational potential,
which is however strongly constrained by astronomical data. The consequences of
an imaginary mass (for L>0) are still unclear; on general grounds, one can
expect the onset of instabilities in this case. This is also confirmed by
numerical simulations of quantum gravity which became recently available. These
properties gain a special interest in consideration of the following. (1) The
most recent cosmological data indicate that L is positive and of the order of
0.1 J/m^3. Is this value compatible with a stable propagation of gravitons? (2)
The answer to the previous question lies perhaps in the scale dependence of the
effective value of L. L may be negative at the small distance/large energy
scale at which the quantum behavior of gravitational fields and waves becomes
relevant. Furthermore, local contributions to the vacuum energy density (in
superconductors in certain states, and in very strong static electromagnetic
fields) can change locally the sign of L, and so affect locally the propagation
and the properties of gravitons. The graviton wavefunction, for different
values of the parameters, may be characterized by superluminal phase velocity
or by unitarity only in imaginary valued time.
|
0409098v1
|
2006-07-02
|
Physics of Flow Instability and Turbulent Transition in Shear Flows
|
In this paper, the physics of flow instability and turbulent transition in
shear flows is studied by analyzing the energy variation of fluid particles
under the interaction of base flow with a disturbance. For the first time, a
model derived strictly from physics is proposed to show that the flow
instability under finite amplitude disturbance leads to turbulent transition.
The proposed model is named as "energy gradient method." It is demonstrated
that it is the transverse energy gradient that leads to the disturbance
amplification while the disturbance is damped by the energy loss due to
viscosity along the streamline. It is also shown that the threshold of
disturbance amplitude obtained is scaled with the Reynolds number by an
exponent of -1, which exactly explains the recent modern experimental results
by Hof et al. for pipe flow. The mechanism for velocity inflection and hairpin
vortex formation are explained with reference to analytical results. Following
from this analysis, it can be demonstrated that the critical value of the so
called energy gradient parameter Kmax is constant for turbulent transition in
wall bounded parallel flows, and this is confirmed by experiments and is about
370-389. The location of instability initiation in the flow field accords well
with the experiments for both pipe Poiseuille flow (r/R=0.58) and plane
Poiseuille flow (y/h=0.58). It is also inferred from the proposed method that
the transverse energy gradient can serve as the power for the self-sustaining
process of wall bounded turbulence. Finally, the relation of "energy gradient
method" to the classical "energy method" based on Rayleigh-Orr equation is
discussed.
|
0607004v5
|
2007-06-25
|
Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
|
We present an accurate approximation of the full gravitational radiation
waveforms generated in the merger of non-eccentric systems of two non-spinning
black holes. Utilizing information from recent numerical relativity simulations
and the natural flexibility of the effective-one-body (EOB) model, we extend
the latter so that it can successfully match the numerical relativity waveforms
during the last stages of inspiral, merger and ringdown. By ``successfully''
here, we mean with phase differences < 8% of a gravitational-wave cycle
accumulated by the end of the ringdown phase, maximizing only over time of
arrival and initial phase. We obtain this result by simply adding a
4-post-Newtonian order correction in the EOB radial potential and determining
the (constant) coefficient by imposing high-matching performances with
numerical waveforms of mass ratios m1/m2 = 1, 3/2, 2 and 4, m1 and m2 being the
individual black-hole masses. The final black-hole mass and spin predicted by
the numerical simulations are used to determine the ringdown frequency and
decay time of three quasi-normal-mode damped sinusoids that are attached to the
EOB inspiral-(plunge) waveform at the EOB light-ring. The EOB waveforms might
be tested and further improved in the future by comparison with extremely long
and accurate inspiral numerical-relativity waveforms. They may already be
employed for coherent searches and parameter estimation of gravitational waves
emitted by non-spinning coalescing binary black holes with ground-based
laser-interferometer detectors.
|
0706.3732v3
|
2007-08-06
|
Ejection of Supermassive Black Holes from Galaxy Cores
|
[Abridged] Recent numerical relativity simulations have shown that the
emission of gravitational waves during the merger of two supermassive black
holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as
4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks
and the effects on the stellar distribution using high-accuracy direct N-body
simulations. Following the kick, the motion of the SMBH exhibits three distinct
phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via
dynamical friction each time it passes through the core. Chandrasekhar's theory
accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda <
3 and if the changing core density is taken into account. (2) When the
amplitude of the motion has fallen to roughly the core radius, the SMBH and
core begin to exhibit oscillations about their common center of mass. These
oscillations decay with a time constant that is at least 10 times longer than
would be predicted by naive application of the dynamical friction formula. (3)
Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate
the time for the SMBH's oscillations to damp to the Brownian level in real
galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection
of SMBHs also results in a lowered density of stars near the galaxy center;
mass deficits as large as five times the SMBH mass are produced for kick
velocities near the escape velocity. We compare the N-body density profiles
with luminosity profiles of early-type galaxies in Virgo and show that even the
largest observed cores can be reproduced by the kicks, without the need to
postulate hypermassive binary SMBHs. Implications for displaced AGNs and
helical radio structures are discussed.
|
0708.0771v2
|
2007-11-19
|
Effect of the intergalactic environment on the observability of Ly-alpha emitters during reionization
|
Observations of high-redshift Ly-alpha sources are a major tool for studying
the high-redshift Universe. We discuss the effect of the reionizing
intergalactic medium on the observability of Ly-alpha sources based on large
simulations of early structure formation with radiative transfer. This takes
into account self-consistently the reionization history, density, velocity and
ionization structures and nonlinear source clustering. We find that all fields
are highly anisotropic and as a consequence there are very large variations in
opacity among the different lines-of-sight. The velocity effects, from both
infall and source peculiar velocity are most important for the luminous
sources, affecting the line profile and depressing the bright end of the
luminosity function. The line profiles are generally asymmetric and the line
centers of the luminous sources are always absorbed due to the high density of
the local IGM. For both luminous and average sources the damping wing effects
are of similar magnitude and remain significant until fairly late.
The ionizing flux in the ionized patch surrounding a high density peak is
generally strongly dominated, particularly at late times, by the cluster of
faint sources, rather than the central massive galaxy. The IGM absorption does
not change appreciably the correlation function of sources at high redshift.
Our derived luminosity function assuming constant mass-to-light ratio provides
an excellent match to the shape of the observed luminosity function at z=6.6
with faint-end slope of alpha=-1.5. The resulting mass-to-light ratio implies
that the majority of sources responsible for reionization are too faint to be
observed by the current surveys. (abridged)
|
0711.2944v2
|
2007-12-17
|
The Nitrogen and Oxygen abundances in the neutral gas at high redshift
|
We study the Oxygen and Nitrogen abundances in the interstellar medium of
high-redshift galaxies. We use high resolution and high signal-to-noise ratio
spectra of Damped Lyman-alpha (DLA) systems detected along the line-of-sight to
quasars to derive robust abundance measurements from unsaturated metal
absorption lines. We present results for a sample of 16 high-redshift DLAs and
strong sub-DLAs (log N(HI)>19.5, 2.4<zabs<3.6) including 13 new measurements.
We find that the Oxygen to Iron abundance ratio is pretty much constant with
[O/Fe]=+0.32+-0.10 for -2.5<[O/H]<-1.0 with a small scatter around this value.
The Oxygen abundance follows quite well the Silicon abundance within 0.2dex
although the Silicon abundance could be slightly smaller for [O/H]<-2. The
distribution of the [N/O] abundance ratio, measured from components that are
detected in both species, is somehow double peaked: five systems have [N/O]>-1
and nine systems have [N/O]<-1.15. In the diagram [N/O] versus [O/H], a loose
plateau is possibly present at [N/O]=-0.9 that is below the so-called primary
plateau as seen in local metal-poor dwarf galaxies ([N/O] in the range -0.57 to
-0.74). No system is seen above this primary plateau whereas the majority of
the systems lie well below with a large scatter. All this suggests a picture in
which DLAs undergo successive star-bursts. During such an episode, the [N/O]
ratio decreases sharply because of the rapid release of Oxygen by massive stars
whereas inbetween two bursts, Nitrogen is released by low and intermediate-mass
stars with a delay and the [N/O] ratio increases.
|
0712.2760v1
|
2008-10-26
|
Non-linear Study of Bell's Cosmic Ray Current-driven Instability
|
The cosmic ray current-driven (CRCD) instability, predicted by Bell (2004),
consists of non-resonant, growing plasma waves driven by the electric current
of cosmic rays (CRs) that stream along the magnetic field ahead of both
relativistic and non-relativistic shocks. Combining an analytic, kinetic model
with one-, two-, and three-dimensional particle-in-cell simulations, we confirm
the existence of this instability in the kinetic regime and determine its
saturation mechanisms. In the linear regime, we show that, if the background
plasma is well magnetized, the CRCD waves grow exponentially at the rates and
wavelengths predicted by the analytic dispersion relation. The magnetization
condition implies that the growth rate of the instability is much smaller than
the ion cyclotron frequency. As the instability becomes non-linear, significant
turbulence forms in the plasma. This turbulence reduces the growth rate of the
field and damps the shortest wavelength modes, making the dominant wavelength,
\lambda_d, grow proportional to the square of the field. At constant CR
current, we find that plasma acceleration along the motion of CRs saturates the
instability at the magnetic field level such that v_A ~ v_{d,cr}, where v_A is
the Alfven velocity in the amplified field, and v_{d,cr} is the drift velocity
of CRs. The instability can also saturate earlier if CRs get strongly deflected
by the amplified field, which happens when their Larmor radii get close to
\lambda_d. We apply these results to the case of CRs in the upstream medium of
supernova remnants. Considering only the most energetic CRs that escape from
the shock, we obtain that the field amplification factor of ~10 can be reached.
This confirms the CRCD instability as a potentially important component of
magnetic amplification process in astrophysical shocks.
|
0810.4565v1
|
2008-10-27
|
Determination of the neutron star mass-radii relation using narrow-band gravitational wave detector
|
The direct detection of gravitational waves will provide valuable
astrophysical information about many celestial objects. The most promising
sources of gravitational waves are neutron stars and black holes. These objects
emit waves in a very wide spectrum of frequencies determined by their
quasi-normal modes oscillations. In this work we are concerned with the
information we can extract from f and p$_I$-modes when a candidate leaves its
signature in the resonant mass detectors ALLEGRO, EXPLORER, NAUTILUS, MiniGrail
and SCHENBERG. Using the empirical equations, that relate the gravitational
wave frequency and damping time with the mass and radii of the source, we have
calculated the radii of the stars for a given interval of masses $M$ in the
range of frequencies that include the bandwidth of all resonant mass detectors.
With these values we obtain diagrams of mass-radii for different frequencies
that allowed to determine the better candidates to future detection taking in
account the compactness of the source. Finally, to determine which are the
models of compact stars that emit gravitational waves in the frequency band of
the mass resonant detectors, we compare the mass-radii diagrams obtained by
different neutron stars sequences from several relativistic hadronic equations
of state (GM1, GM3, TM1, NL3) and quark matter equations of state (NJL, MTI bag
model). We verify that quark stars obtained from MIT bag model with bag
constant equal to 170 MeV and quark of matter in color-superconductivity phase
are the best candidates for mass resonant detectors.
|
0810.4848v4
|
2009-02-17
|
21-cm absorbers at intermediate redshifts
|
Damped Lyman-alpha systems (DLAs) seen in the spectra of high-z QSOs allow us
to probe the physical conditions in protogalaxies. Our understanding of
physical conditions in DLAs at high-z is primarily based on the absorption
lines of H_2 molecules and fine-structure transitions. Another important way of
probing the thermal state of interstellar medium in these systems is by
studying the 21-cm absorption in the spectra of background quasars. Here we
report the main results of our GMRT survey to search for 21-cm absorption in a
representative and unbiased sample of 35 DLA candidates at 1.10<z<1.45. Our
sample of DLA candidates is drawn from the strong MgII systems in SDSS DR5 and
has resulted in discovery of 9 new 21-cm absorbers. Prior to our survey only
one 21-cm absorber was known in the redshift range: 0.7<z<2. This survey has
allowed us to investigate the dependence of detectability of 21-cm absorption
on the properties of UV absorption lines detected in SDSS spectra and estimate
the number per unit redshift of 21-cm absorbers. Our GMRT survey provides a
representative sample of systems that can be used in combination with various
follow-up observations: (1) for investigating the physical conditions in the
absorbing gas using spin temperature measurements, (2) for investigating the
effect of metallicity and dust content on the detectability of 21-cm
absorption, (3) for studying the morphology of the absorbing gas and (4) for
probing the time evolution of various fundamental constants. Results from the
first phase of our survey are presented in Gupta et al. (2007). Detailed
description of the entire sample and results from the survey are presented in
Gupta et al. (2009).
|
0902.3016v1
|
2009-08-27
|
Very Light Magnetized Jets on Large Scales - I. Evolution and Magnetic Fields
|
Magnetic fields, which are undoubtedly present in extragalactic jets and
responsible for the observed synchrotron radiation, can affect the morphology
and dynamics of the jets and their interaction with the ambient cluster medium.
We examine the jet propagation, morphology and magnetic field structure for a
wide range of density contrasts, using a globally consistent setup for both the
jet interaction and the magnetic field. The MHD code NIRVANA is used to evolve
the simulation, using the constrained-transport method. The density contrasts
are varied between \eta = 10^{-1} and 10^{-4} with constant sonic Mach number
6. The jets are supermagnetosonic and simulated bipolarly due to the low jet
densities and their strong backflows. The helical magnetic field is largely
confined to the jet, leaving the ambient medium nonmagnetic. We find magnetic
fields with plasma \beta \sim 10 already stabilize and widen the jet head.
Furthermore they are efficiently amplified by a shearing mechanism in the jet
head and are strong enough to damp Kelvin-Helmholtz instabilities of the
contact discontinuity. The cocoon magnetic fields are found to be stronger than
expected from simple flux conservation and capable to produce smoother lobes,
as found observationally. The bow shocks and jet lengths evolve self-similarly.
The radio cocoon aspect ratios are generally higher for heavier jets and grow
only slowly (roughly self-similar) while overpressured, but much faster when
they approach pressure balance with the ambient medium. In this regime,
self-similar models can no longer be applied. Bow shocks are found to be of low
excentricity for very light jets and have low Mach numbers. Cocoon turbulence
and a dissolving bow shock create and excite waves and ripples in the ambient
gas. Thermalization is found to be very efficient for low jet densities.
|
0908.4055v1
|
2009-10-12
|
Average luminosity distance in inhomogeneous universes
|
The paper studies the correction to the distance modulus induced by
inhomogeneities and averaged over all directions from a given observer. The
inhomogeneities are modeled as mass-compensated voids in random or regular
lattices within Swiss-cheese universes. Void radii below 300 Mpc are
considered, which are supported by current redshift surveys and limited by the
recently observed imprint such voids leave on CMB. The averaging over all
directions, performed by numerical ray tracing, is non-perturbative and
includes the supernovas inside the voids. Voids aligning along a certain
direction produce a cumulative gravitational lensing correction that increases
with their number. Such corrections are destroyed by the averaging over all
directions, even in non-randomized simple cubic void lattices. At low
redshifts, the average correction is not zero but decays with the peculiar
velocities and redshift. Its upper bound is provided by the maximal average
correction which assumes no random cancelations between different voids. It is
described well by a linear perturbation formula and, for the voids considered,
is 20% of the correction corresponding to the maximal peculiar velocity. The
average correction calculated in random and simple cubic void lattices is
severely damped below the predicted maximal one after a single void diameter.
That is traced to cancellations between the corrections from the fronts and
backs of different voids. All that implies that voids cannot imitate the effect
of dark energy unless they have radii and peculiar velocities much larger than
the currently observed. The results obtained allow one to readily predict the
redshift above which the direction-averaged fluctuation in the Hubble diagram
falls below a required precision and suggest a method to extract the background
Hubble constant from low redshift data without the need to correct for peculiar
velocities.
|
0910.2611v3
|
2009-12-22
|
Rest-frame ultraviolet spectrum of the gravitationally lensed galaxy `the 8 o'clock arc': stellar and interstellar medium properties
|
We present the first detailed analysis of the rest-frame UV spectrum of the
gravitationally lensed Lyman break galaxy (LBG), the `8 o'clock arc'. The
spectrum of the 8 o'clock arc is rich in stellar and interstellar medium (ISM)
features, and presents several similarities to the well-known MS1512-cB58 LBG.
The stellar photospheric absorption lines allowed us to constrain the systemic
redshift, z_sys = 2.7350+/-0.0003, of the galaxy, and derive its stellar
metallicity, Z=0.82 Z_sol. With a total stellar mass of ~4.2x10^{11} M_sol, the
8 o'clock arc agrees with the mass-metallicity relation found for z>2
star-forming galaxies. The 31 ISM absorption lines detected led to the
abundance measurements of 9 elements. The metallicity of the ISM, Z=0.65 Z_sol
(Si), is very comparable to the metallicity of stars and ionized gas, and
suggests that the ISM of the 8 o'clock arc has been rapidly polluted and
enriched by ejecta of OB stars. The ISM lines extend over ~1000 km/s and have
their peak optical depth blueshifted relative to the stars, implying gas
outflows of about -120 km/s. The Ly-alpha line is dominated by a damped
absorption profile on top of which is superposed a weak emission, redshifted
relative to the ISM lines by about +690 km/s and resulting from multiply
backscattered Ly-alpha photons emitted in the HII region surrounded by the
cold, expanding ISM shell. A homogeneous spherical radiation transfer shell
model with a constant outflow velocity, determined by the observations, is able
to reproduce the observed Ly-alpha line profile and dust content. These results
fully support the scenario proposed earlier, where the diversity of Ly-alpha
line profiles in LBGs and Ly-alpha emitters, from absorption to emission, is
mostly due to variations of HI column density and dust content (abridged).
|
0912.4384v1
|
2010-07-19
|
The Evolution of Lyman Limit Absorption Systems to Redshift Six
|
We have measured the redshift evolution of the density of Lyman limit systems
(LLS) in the intergalactic medium over the redshift range 0 < z < 6. We have
used two new quasar samples to (1) improve coverage at z ~ 1, with GALEX grism
spectrograph observations of 50 quasars with 0.8 < z_em < 1.3, and (2) extend
coverage to z ~ 6, with Keck ESI spectra of 25 quasars with 4.17 < z_em < 5.99.
Using these samples together with published data, we find that the number
density of LLS per unit redshift, n(z), can be well fit by a simple evolution
of the form n(z) = n_3.5 [(1+z)/4.5]^gamma, with n_3.5 = 2.80 +/- 0.33 and
gamma = 1.94^(+0.36)_(-0.32) for the entire range 0 < z < 6. We have also
reanalyzed the evolution of damped Lyman alpha systems (DLAs) in the redshift
range 4 < z < 5 using our high-redshift quasar sample. We find a total of 17
DLAs and sub-DLAs, which we have analyzed in combination with published data.
The DLAs with log (HI column density) > 20.3 show the same redshift evolution
as the LLS. When combined with previous results, our DLA sample is also
consistent with a constant Omega_DLA= 9 x 10^(-4) from z = 2 to z = 5. We have
used the LLS number density evolution to compute the evolution in the mean free
path of ionizing photons. We find a smooth evolution to z ~ 6, very similar in
shape to that of Madau, Haardt & Rees (1999) but about a factor of two higher.
Recent theoretical models roughly match to the z < 6 data but diverge from the
measured power law at z > 6 in different ways, cautioning against extrapolating
the fit to the mean free path outside the measured redshift range.
|
1007.3262v2
|
2010-11-01
|
A Model for Thermal Phase Variations of Circular and Eccentric Exoplanets
|
We present a semi-analytic model atmosphere for close-in exoplanets that
captures the essential physics of phase curves: orbital and viewing geometry,
advection, and re-radiation. We calibrate the model with the well-characterized
transiting planet, HD 189733b, then compute light curves for seven of the most
eccentric transiting planets. We present phase variations for a variety of
different radiative times and wind speeds. In the limit of instant
re-radiation, the light curve morphology is entirely dictated by the planet's
eccentricity and argument of pericenter: the light curve maximum leads or
trails the eclipse depending on whether the planet is receding from or
approaching the star at superior conjunction, respectively. For a planet with
non-zero radiative timescales, the phase peak occurs early for super- rotating
winds, and late for sub-rotating winds. We find that for a circular orbit, the
timing of the phase variation maximum with respect to superior conjunction
indicates the direction of the dominant winds, but cannot break the degeneracy
between wind speed and radiative time. For circular planets the phase minimum
occurs half an orbit away from the phase maximum -despite the fact that the
coolest longitudes are always near the dawn terminator- and therefore does not
convey any additional information. In general, increasing the advective
frequency or the radiative time has the effect of reducing the peak-to-trough
amplitude of phase variations, but there are interesting exceptions to these
trends. Lastly, eccentric planets with orbital periods significantly longer
than their radiative time exhibit "ringing" whereby the hot spot generated at
periastron rotates in and out of view. The existence of ringing makes it
possible to directly measure the wind speed (the frequency of the ringing) and
the radiative time constant (the damping of the ringing).
|
1011.0428v1
|
2010-12-16
|
Constraints on coronal turbulence models from source sizes of noise storms at 327 MHz
|
We seek to reconcile observations of small source sizes in the solar corona
at 327 MHz with predictions of scattering models that incorporate refractive
index effects, inner scale effects and a spherically diverging wavefront. We
use an empirical prescription for the turbulence amplitude $C_{N}^{2}(R)$ based
on VLBI observations by Spangler and coworkers of compact radio sources against
the solar wind for heliocentric distances $R \approx$ 10--50 $R_{\odot}$. We
use the Coles & Harmon model for the inner scale $l_{i}(R)$, that is presumed
to arise from cyclotron damping. In view of the prevalent uncertainty in the
power law index that characterizes solar wind turbulence at various
heliocentric distances, we retain this index as a free parameter. We find that
the inclusion of spherical divergence effects suppresses the predicted source
size substantially. We also find that inner scale effects significantly reduce
the predicted source size. An important general finding for solar sources is
that the calculations substantially underpredict the observed source size.
Three possible, non-exclusive, interpretations of this general result are
proposed. First and simplest, future observations with better angular
resolution will detect much smaller sources. Consistent with this, previous
observations of small sources in the corona at metric wavelengths are limited
by the instrument resolution. Second, the spatially-varying level of turbulence
$C_{N}^{2}(R)$ is much larger in the inner corona than predicted by
straightforward extrapolation Sunwards of the empirical prescription, which was
based on observations between 10--50 $R_{\odot}$. Either the functional form or
the constant of proportionality could be different. Third, perhaps the inner
scale is smaller than the model, leading to increased scattering.
|
1012.3523v2
|
2011-01-25
|
The Surprisingly Constant Strength of O VI Absorbers over Cosmic Time
|
O VI absorption is observed in a wide range of astrophysical environments,
including the Local ISM, the disk and halo of the Milky Way, high-velocity
clouds, the Magellanic clouds, starburst galaxies, the intergalactic medium,
damped Lyman-alpha systems, and gamma-ray-burst host galaxies. Here a new
compilation of 775 O VI absorbers drawn from the literature is presented, all
observed at high resolution (instrumental FWHM<20 km/s) and covering the
redshift range z=0-3. In galactic environments [log N(H I)>20], the mean O VI
column density is shown to be insensitive to metallicity, taking a value log
N(O VI)~14.5 for galaxies covering the range -1.6<[O/H]<0. In intergalactic
environments [log N(H I)<17], the mean O VI component column density measured
in datasets of similar sensitivity shows only weak evolution between z=0.2 and
z=2.3, but IGM O VI components are on average almost twice as broad at z=0.2
than at z=2.3. The existence of a characteristic value of log N(O VI) for
galactic O VI absorbers, and the lack of evolution in log N(O VI) for
intergalactic absorbers, lend support to the ``cooling-flow' model of Heckman
et al. (2002), in which all O VI absorbers are created in regions of
initially-hot shock-heated plasma that are radiatively cooling through coronal
temperatures. These regions could take several forms, including conductive,
turbulent, or shocked boundary layers between warm (~10^4 K) clouds and hot
(~10^6 K) plasma, although many such regions would have to be intersected by a
typical galaxy-halo sightline to build up the characteristic galactic N(O VI).
The alternative, widely-used model of single-phase photoionization for
intergalactic O VI is ruled out by kinematic evidence in the majority of IGM O
VI components at low and high redshift.
|
1101.4766v1
|
2011-03-21
|
A Groundbased Imaging Study of Galaxies Causing DLA, subDLA, and LLS Absorption in Quasar Spectra
|
We present results from a search for galaxies that give rise to damped Lyman
alpha (DLA), subDLA, and Lyman limit system (LLS) absorption at redshifts 0.1
~< z ~< 1 in the spectra of background quasars. The sample was formed from a
larger sample of strong MgII absorbers (W_0^(2796) >= 0.3 A) whose HI column
densities were determined by measuring the Ly-alpha line in HST UV spectra.
Photometric redshifts, galaxy colors, and proximity to the quasar sightline, in
decreasing order of importance, were used to identify galaxies responsible for
the absorption. Our sample includes 80 absorption systems for which the
absorbing galaxies have been identified, of which 54 are presented here for the
first time. The main results of this study are: (i) the surface density of
galaxies falls off exponentially with increasing impact parameter, b, from the
quasar sightline relative to a constant background of galaxies, with an
e-folding length of ~46 kpc. Galaxies with b >~ 100 kpc calculated at the
absorption redshift are statistically consistent with being unrelated to the
absorption system. (ii) log N(HI) is inversely correlated with b at the 3.0
sigma level of significance. DLA galaxies are found systematically closer to
the quasar sightline, by a factor of two, than are galaxies which give rise to
subDLAs or LLSs. The median impact parameter is 17.4 kpc for the DLA galaxy
sample, 33.3 kpc for the subDLA sample, and 36.4 kpc for the LLS sample. (iii)
Absorber galaxy luminosity relative to L*, L/L*, is not significantly
correlated with W_0^(2796), log N(HI), or b. (iv) DLA, subDLA, and LLS galaxies
comprise a mix of spectral types, but are inferred to be predominantly late
type galaxies based on their spectral energy distributions. The implications of
these results are discussed. (Abridged)
|
1103.4047v3
|
2011-05-06
|
Non-relativistic bound states in a moving thermal bath
|
We study the propagation of non-relativistic bound states moving at constant
velocity across a homogeneous thermal bath and we develop the effective field
theory which is relevant in various dynamical regimes. We consider values of
the velocity of the bound state ranging from moderate to highly relativistic
and temperatures at all relevant scales smaller than the mass of the particles
that form the bound state. In particular, we consider two distinct temperature
regimes, corresponding to temperatures smaller or higher than the typical
momentum transfer in the bound state. For temperatures smaller or of the order
of the typical momentum transfer, we restrict our analysis to the simplest
system, a hydrogen-like atom. We build the effective theory for this system
first considering moderate values of the velocity and then the relativistic
case. For large values of the velocity of the bound state, the separation of
scales is such that the corresponding effective theory resembles the soft
collinear effective theory (SCET). For temperatures larger than the typical
momentum transfer we also consider muonic hydrogen propagating in a plasma
which contains photons and massless electrons and positrons, so that the system
resembles very much heavy quarkonium in a thermal medium of deconfined quarks
and gluons. We study the behavior of the real and imaginary part of the static
two-body potential, for various velocities of the bound state, in the hard
thermal loop approximation. We find that Landau damping ceases to be the
relevant mechanism for dissociation from a certain "critical" velocity on in
favor of screening. Our results are relevant for understanding how the
properties of heavy quarkonia states produced in the initial fusion of partons
in the relativistic collision of heavy ions are affected by the presence of an
equilibrated quark-gluon plasma.
|
1105.1249v2
|
2011-08-24
|
Dynamical Tides in Compact White Dwarf Binaries: Tidal Synchronization and Dissipation
|
In compact white dwarf (WD) binary systems (with periods ranging from minutes
to hours), dynamical tides involving the excitation and dissipation of gravity
waves play a dominant role in determining the physical conditions of the WDs
prior to mass transfer or binary merger. We calculate the amplitude of the
tidally excited gravity waves as a function of the tidal forcing frequency
\omega=2(\Omega-\Omega_s) (where \Omega is the orbital frequency and \Omega_s
is the spin frequency) for several realistic carbon-oxygen WD models, assuming
that the waves are efficiently dissipated in the outer layer of the star by
nonlinear effects or radiative damping. The mechanism of wave excitation in WDs
is complex due to the sharp features associated with composition changes inside
the WD, and in our WD models gravity waves are launched just below the
helium-carbon boundary. We find that the tidal torque on the WD and the related
tidal energy transfer rate, \dot E_{\rm tide}, depend on \omega in an erratic
way. On average, \dot E_{\rm tide} scales approximately as \Omega^5\omega^5 for
a large range of tidal frequencies. We also study the effects of dynamical
tides on the long-term evolution of WD binaries. Above a critical orbital
frequency \Omega_c, corresponding to an orbital period of order one hour
(depending on WD models), dynamical tides efficiently drive \Omega_s toward
\Omega, although a small, almost constant degree of asynchronization
(\Omega-\Omega_s\sim {\rm constant}) is maintained even at the smallest binary
periods. While the orbital decay is always dominated by gravitational
radiation, the tidal energy transfer can induce significant phase error in the
low-frequency gravitational waveforms, detectable by the planned LISA project.
Tidal dissipation may also lead to significant heating of the WD envelope and
brightening of the system long before binary merger.
|
1108.4910v5
|
2011-11-22
|
Coronal heating in coupled photosphere-chromosphere-coronal systems: turbulence and leakage
|
Coronal loops act as resonant cavities for low frequency fluctuations that
are transmitted from the deeper layers of the solar atmosphere and are
amplified in the corona, triggering nonlinear interactions. However trapping is
not perfect, some energy leaks down to the chromosphere, thus limiting the
turbulence development and the associated heating. We consider the combined
effects of turbulence and leakage in determining the energy level and
associated heating rate in models of coronal loops which include the
chromosphere and transition region. We use a piece-wise constant model for the
Alfven speed and a Reduced MHD - Shell model to describe the interplay between
turbulent dynamics in the direction perpendicular to the mean field and
propagation along the field. Turbulence is sustained by incoming fluctuations
which are equivalent, in the line-tied case, to forcing by the photospheric
shear flows. While varying the turbulence strength, we compare systematically
the average coronal energy level (E) and dissipation rate (D) in three models
with increasing complexity: the classical closed model, the semi-open corona
model, and the corona-chromosphere (or 3-layer) model, the latter two models
allowing energy leakage. We find that:
(i) Leakage always plays a role (even for strong turbulence), E and D are
systematically lower than in the line-tied model. (ii) E is close to the
resonant prediction, i.e., assuming effective turbulent correlation time longer
than the Alfven coronal crossing time (Ta). (iii) D is close to the value given
by the ratio of photospheric energy divided by Ta (iv) The coronal spectra
exibits an inertial range with 5/3 spectral slope, and a large scale peak of
trapped resonant modes that inhibit nonlinear couplings. (v) In the realistic
3-layer model, the two-component spectrum leads to a damping time equal to the
Kolmogorov time reduced by a factor u_rms/Va_corona
|
1111.5359v1
|
2012-06-22
|
Cosmic Acceleration from Causal Backreaction with Recursive Nonlinearities
|
We revisit the causal backreaction paradigm, in which the need for Dark
Energy is eliminated via the generation of an apparent cosmic acceleration from
the causal flow of inhomogeneity information coming in towards each observer
from distant structure-forming regions. This second-generation formalism
incorporates "recursive nonlinearities": the process by which
already-established metric perturbations will then act to slow down all future
flows of inhomogeneity information. Here, the long-range effects of causal
backreaction are now damped, weakening its impact for models that were
previously best-fit cosmologies. Nevertheless, we find that causal backreaction
can be recovered as a replacement for Dark Energy via the adoption of larger
values for the dimensionless `strength' of the clustering evolution functions
being modeled -- a change justified by the hierarchical nature of clustering
and virialization in the universe, occurring on multiple cosmic length scales
simultaneously. With this, and with one new model parameter representing the
slowdown of clustering due to astrophysical feedback processes, an alternative
cosmic concordance can once again be achieved for a matter-only universe in
which the apparent acceleration is generated entirely by causal backreaction
effects. One drawback is a new degeneracy which broadens our predicted range
for the observed jerk parameter $j_{0}^{\mathrm{Obs}}$, thus removing what had
appeared to be a clear signature for distinguishing causal backreaction from
Cosmological Constant $\Lambda$CDM. As for the long-term fate of the universe,
incorporating recursive nonlinearities appears to make the possibility of an
`eternal' acceleration due to causal backreaction far less likely; though this
does not take into account gravitational nonlinearities or the large-scale
breakdown of cosmological isotropy, effects not easily modeled within this
formalism.
|
1206.5056v1
|
2012-10-10
|
Bodily tides near the 1:1 spin-orbit resonance. Correction to Goldreich's dynamical model
|
Spin-orbit coupling is often described in the "MacDonald torque" approach
which has become the textbook standard. Within this method, a concise
expression for the additional tidal potential, derived by MacDonald (1964; Rev.
Geophys. 2, 467), is combined with an assumption that the Q factor is
frequency-independent (i.e., that the geometric lag angle is constant in time).
This makes the approach unphysical because MacDonald's derivation of the said
formula was implicitly based on keeping the time lag frequency-independent,
which is equivalent to setting Q to scale as the inverse tidal frequency. The
contradiction requires the MacDonald treatment of both non-resonant and
resonant rotation to be rewritten.
The non-resonant case was reconsidered by Efroimsky & Williams (2009; CMDA
104, 257), in application to spin modes distant from the major
commensurabilities. We continue this work by introducing the necessary
alterations into the MacDonald-torque-based model of falling into a 1:1
resonance. (For the original version of the model, see Goldreich 1966; AJ 71,
1.)
We also study the effect of the triaxiality on both circulating and librating
rotation near the synchronous state. Circulating rotation may evolve toward the
libration region or toward a spin rate larger than synchronous
(pseudosynchronous spin). Which behaviour depends on the eccentricity, the
triaxiality of the primary, and the mass ratio of the secondary and primary
bodies. The spin evolution will always stall for the oblate case. For
small-amplitude librations, expressions are derived for the libration
frequency, damping rate, and average orientation.
However, the stability of pseudosynchronous spin hinges upon the dissipation
model. Makarov and Efroimsky (2012; arXiv:1209.1616) have found that a more
realistic dissipation model than the corrected MacDonald torque makes
pseudosynchronous spin unstable.
|
1210.2923v3
|
2012-11-06
|
Tidal resonance locks in inspiraling white dwarf binaries
|
We calculate the tidal response of helium and carbon/oxygen (C/O) white dwarf
(WD) binaries inspiraling due to gravitational wave emission. We show that
resonance locks, previously considered in binaries with an early-type star,
occur universally in WD binaries. In a resonance lock, the orbital and spin
frequencies evolve in lockstep, so that the tidal forcing frequency is
approximately constant and a particular normal mode remains resonant, producing
efficient tidal dissipation and nearly synchronous rotation. We show that
analogous locks between the spin and orbital frequencies can occur not only
with global standing modes, but even when damping is so efficient that the
resonant tidal response becomes a traveling wave. We derive simple analytic
formulas for the tidal quality factor Q and tidal heating rate during a g-mode
resonance lock, and verify our results numerically. We find that Q ~ 10^7 for
orbital periods ~ 1 - 2 hr in C/O WDs, and Q ~ 10^9 for P_orb ~ 3 - 10 hr in
helium WDs. Typically tidal heating occurs sufficiently close to the surface
that the energy should be observable as surface emission. Moreover, near an
orbital period of ~ 10 min, the tidal heating rate reaches ~ 10^{-2} L_\sun,
rivaling the luminosities of our fiducial WD models. Recent observations of the
13-minute double-WD binary J0651 are roughly consistent with our theoretical
predictions. Tides naturally tend to generate differential rotation; however,
we show that the fossil magnetic field strength of a typical WD can maintain
solid-body rotation down to at least P_orb ~ 10 min even in the presence of a
tidal torque concentrated near the WD surface.
|
1211.1393v4
|
2013-06-17
|
GRB 130606A as a Probe of the Intergalactic Medium and the Interstellar Medium in a Star-forming Galaxy in the First Gyr After the Big Bang
|
We present high signal-to-noise ratio Gemini and MMT spectroscopy of the
optical afterglow of the gamma-ray burst (GRB) 130606A at redshift z=5.913,
discovered by Swift. This is the first high-redshift GRB afterglow to have
spectra of comparable quality to those of z~6 quasars. The data exhibit a
smooth continuum at near-infrared wavelengths that is sharply cut off blueward
of 8410 Angs due to absorption from Ly-alpha at redshift z~5.91, with some flux
transmitted through the Ly-alpha forest between 7000-7800 Angs. We use column
densities inferred from metal absorption lines to constrain the metallicity of
the host galaxy between a lower limit of [Si/H]>-1.7 and an upper limit of
[S/H]<-0.5 set by the non-detection of S II absorption. We demonstrate
consistency between the dramatic evolution in the transmission fraction of
Ly-alpha seen in this spectrum over the redshift range z=4.9 to 5.85 with that
previously measured from observations of high-redshift quasars. There is an
extended redshift interval of Delta-z=0.12 in the Ly-alpha forest at z=5.77
with no detected transmission, leading to a 3-sigma upper limit on the mean
Ly-alpha transmission fraction of <0.2% (or tau_eff(Ly-alpha) > 6.4). This is
comparable to the lowest-redshift Gunn-Peterson troughs found in quasar
spectra. We set a 2-sigma upper limit of 0.11 on the neutral fraction of the
IGM at the redshift of the GRB from the lack of a Ly-alpha red damping wing,
assuming a model with a constant neutral density. Some Ly-beta and Ly-gamma
transmission is detected in this redshift window, indicating that it is not
completely opaque, and hence that the IGM is nonetheless mostly ionized at
these redshifts. GRB 130606A thus for the first time realizes the promise of
GRBs as probes of the first galaxies and cosmic reionization.
|
1306.3949v2
|
2013-10-31
|
Spatially Resolved Emission of a High Redshift DLA Galaxy with the Keck/OSIRIS IFU
|
We present the first Keck/OSIRIS infrared IFU observations of a high redshift
damped Lyman-alpha (DLA) galaxy detected in the line of sight to a background
quasar. By utilizing the Laser Guide Star Adaptive Optics (LGSAO) to reduce the
quasar PSF to FWHM~0.15 arcsec, we were able to search for and map the
foreground DLA emission free from the quasar contamination. We present maps of
the H-alpha and [OIII] $\lambda \lambda$ 5007, 4959 emission of DLA 2222-0946
at a redshift of z ~ 2.35. From the composite spectrum over the H-alpha
emission region we measure a star formation rate of 9.5 $\pm$ 1.0 M$_{\odot}$
year$^{-1}$ and a dynamical mass, M$_{dyn}$ = 6.1 x 10$^9$ M$_{\odot}$. The
average star formation rate surface density is < \Sigma_{SFR} > = 0.55
M$_{\odot}$ yr$^{-1}$ kpc$^{-2}$, with a central peak of 1.7 M$_{\odot}$
yr$^{-1}$ kpc$^{-2}$. Using the standard Kennicutt-Schmidt relation, this
corresponds to a gas mass surface density of $\Sigma_{gas}$ = 243 M$_{\odot}$
pc$^{-2}$. Integrating over the size of the galaxy we find a total gas mass of
M$_{gas}$ = 4.2 x 10$^9$ M$_{\odot}$. We estimate the gas fraction of DLA
2222-0946 to be $f_{gas}$ ~ 40%. We detect [NII]$\lambda$6583 emission at 2.5
sigma significance with a flux corresponding to a metallicity of 75% solar.
Comparing this metallicity with that derived from the low-ion absorption gas ~6
kpc away, ~30% solar, indicates possible evidence for a metallicity gradient or
enriched in/outflow of gas. Kinematically, both H-alpha and [OIII] emission
show relatively constant velocity fields over the central galactic region.
While we detect some red and blueshifted clumps of emission, they do not
correspond with rotational signatures that support an edge-on disk
interpretation.
|
1311.0045v1
|
2013-11-29
|
Continuous Emission of A Radiation Quantum
|
It is in accordance with such experiments as single photon self-interference
that a photon, conveying one radiation energy quantum "$ h \times$ frequency",
is spatially extensive and stretches an electromagnetic wave train. A wave
train, hence an energy quantum, can only be emitted by its source gradually. In
both the two processes the wave and "particle" attributes of the radiation
field are simultaneously prominent, where an overall satisfactory theory has
been lacking. This paper presents a first principles treatment, in a unified
framework of the classical and quantum mechanics, of the latter process, the
emission of a single radiation quantum based on the dynamics of the
radiation-emitting source, a charged oscillator which is itself extensive
across its confining potential well. During the emission of one single
radiation quantum, the extensive charged oscillator undergoes a continuous
radiation damping and is non-stationary. This process is in this work treated
using a quasi stationary approach, whereby the classical equation of motion,
which directly facilitates the correspondence principle for a particle
oscillator, and the quantum wave equation are established for each sufficiently
brief time interval. As an inevitable consequence of the division of the total
time for emitting one single quantum, a fractional Planck constant $h$ is
introduced. The solutions to the two simultaneous equations yield for the
charged oscillator a continuously exponentially decaying Hamiltonian that is at
the same time quantised with respect to the fractional-$h$ at any instant of
time; and the radiation wave field emitted over time stretches a wave train of
finite length. The total system of the source and radiation field maintains at
any time (integer $n$ times) one whole energy quantum, $h \times$ frequency, in
complete accordance with the notion of quantum mechanics and experiment.
|
1312.0918v1
|
2014-02-06
|
Dynamics of Order Parameters near Stationary States in Superconductors with a Charge-Density Wave
|
We consider a simple model of a quasi-one-dimensional conductor in which two
order parameters (OP) may coexist, i.e., the superconducting OP $\Delta$ and
the OP $W$ that characterizes the amplitude of a charge-density wave (CDW). In
the mean field approximation we present equations for the matrix Green's
functions $G_{ik}$, where $i$ relates to the one of the two Fermi sheets and
$k$, operates in the Gor'kov-Nambu space. Using the solutions of these
equations, we find stationary states for different values of the parameter
describing the curvature of the Fermi surface, $\mu$, which can be varied,
e.g., by doping. It is established that in the interval $\mu_1<\mu<\mu_2$ the
self-consistency equations have a solution for coexisting OPs $\Delta$ and $W$.
However, this solution corresponds to a saddle point in the energy functional
$\Phi(\Delta, W)$, i.e., it is unstable. Stable states are: 1)the state with
the CDW at $\mu < \mu_{2}$; and 2) the purely superconducting state at
$\mu_1<\mu$. At $\mu<\mu_0$, the state 1) corresponds to a global minimum, and
at $\mu_0<\mu$, the state 2) has a lower energy, i.e., only the superconducting
state survives at large $\mu$. We study the dynamics of the variations
$\delta\Delta$ and $\delta W$ from these states in the collisionless limit. It
is characterized by two modes of oscillations, the fast and the slow one. The
fast mode is analogous to damped oscillations in conventional superconductors.
The frequency of slow modes depends on the curvature $\mu$ and is much smaller
than $2\Delta$ if the coupling constants for superconductivity and CDW are
close to each other. The considered model can be applied to high-$T_c$
superconductors where the parts of the Fermi surface near the `hot' spots may
be regarded as the considered two Fermi sheets. We also discuss relation of the
considered model to the simplest model for Fe-based pnictides.
|
1402.1411v4
|
2014-05-28
|
GRB 140515A at z=6.33: Constraints on the End of Reionization From a Gamma-ray Burst in a Low Hydrogen Column Density Environment
|
We present the discovery and subsequent spectroscopy with Gemini-North of the
optical afterglow of the Swift gamma-ray burst (GRB) 140515A. The spectrum
exhibits a well-detected continuum at wavelengths longer than 8915 Angs with a
steep decrement to zero flux blueward of 8910 Angs due to Ly-alpha absorption
at redshift z~6.33. Some transmission through the Lyman-alpha forest is present
at 5.2<z<5.733, but none is detected at higher redshift, consistent with
previous measurements from quasars and GRB 130606A. We model the red damping
wing of Lyman-alpha in three ways that provide equally good fits to the data:
(a) a single host galaxy absorber at z=6.327 with log(N_HI)=18.62+/-0.08; (b)
pure intergalactic medium (IGM) absorption from z=6.0 to z=6.328 with a
constant neutral hydrogen fraction of x_HI=0.056+0.011-0.027; and (c) a hybrid
model with a host absorber located within an ionized bubble of radius 10
comoving Mpc in an IGM with x_HI=0.12+/-0.05 (x_HI<0.21 at the 2-sigma level).
Regardless of the model, the sharpness of the dropoff in transmission is
inconsistent with a substantial neutral fraction in the IGM at this redshift.
No narrow absorption lines from the host galaxy are detected, indicating a host
metallicity of [Z/H]<~ -0.8. Even if we assume that all of the hydrogen
absorption is due to the host galaxy, the column is unusually low for a GRB
sightline, similar to two out of the other three highest-redshift bursts with
measured log(N_HI). This is possible evidence that the escape fraction of
ionizing photons from normal star-forming galaxies increases at z>~6.
|
1405.7400v1
|
2014-08-24
|
Thickness dependence of dynamic and static magnetic properties of pulsed laser deposited La$_{0.7}$Sr$_{0.3}$MnO$_3$ films on SrTiO$_3$(001)
|
We present a comprehensive study of the thickness dependence of static and
magneto-dynamic magnetic properties of La$_{0.7}$Sr$_{0.3}$MnO$_3$. Epitaxial
pulsed laser deposited La$_{0.7}$Sr$_{0.3}$MnO$_3$ / SrTiO$_3$(001) thin films
in the range from 3 unit cells (uc) to 40 uc (1.2 - 16 nm) have been
investigated through ferromagnetic resonance spectroscopy (FMR) and SQUID
magnetometry at variable temperature. Magnetodynamically, three different
thickness, $d$, regimes are identified: 20 uc $\lesssim d$ uc where the system
is bulk like, a transition region 8 uc $\le d \lesssim 20$ uc where the FMR
line width and position depend on thickness and $d=6$ uc which displays
significantly altered magnetodynamic properties, while still displaying bulk
magnetization. Magnetization and FMR measurements are consistent with a
nonmagnetic volume corresponding to $\sim$ 4 uc. We observe a reduction of
Curie temperature ($T_C$) with decreasing thickness, which is coherent with a
mean field model description. The reduced ordering temperature also accounts
for the thickness dependence of the magnetic anisotropy constants and resonance
fields. The damping of the system is strongly thickness dependent, and is for
thin films dominated by thickness dependent anisotropies, yielding both a
strong 2-magnon scattering close to $T_c$ and a low temperature broadening. For
the bulk like samples a large part of the broadening can be linked to spread in
magnetic anisotropies attributed to crystal imperfections/domain boundaries of
the bulk like film.
|
1408.5631v1
|
2015-01-27
|
Comparative analysis of existing models for power-grid synchronization
|
The dynamics of power-grid networks is becoming an increasingly active area
of research within the physics and network science communities. The results
from such studies are typically insightful and illustrative, but are often
based on simplifying assumptions that can be either difficult to assess or not
fully justified for realistic applications. Here we perform a comprehensive
comparative analysis of three leading models recently used to study
synchronization dynamics in power-grid networks -- a fundamental problem of
practical significance given that frequency synchronization of all power
generators in the same interconnection is a necessary condition for a power
grid to operate. We show that each of these models can be derived from first
principles within a common framework based on the classical model of a
generator, thereby clarifying all assumptions involved. This framework allows
us to view power grids as complex networks of coupled second-order phase
oscillators with both forcing and damping terms. Using simple illustrative
examples, test systems, and real power-grid datasets, we study the inherent
frequencies of the oscillators as well as their coupling structure, comparing
across the different models. We demonstrate, in particular, that if the network
structure is not homogeneous, generators with identical parameters need to be
modeled as non-identical oscillators in general. We also discuss an approach to
estimate the required (dynamical) parameters that are unavailable in typical
power-grid datasets, their use for computing the constants of each of the three
models, and an open-source MATLAB toolbox that we provide for these
computations.
|
1501.06926v2
|
2015-04-28
|
A meeting point of entropy and bifurcations in cross-diffusion herding
|
A cross-diffusion system modeling the information herding of individuals is
analyzed in a bounded domain with no-flux boundary conditions. The variables
are the species' density and an influence function which modifies the
information state of the individuals. The cross-diffusion term may stabilize or
destabilize the system. Furthermore, it allows for a formal gradient-flow or
entropy structure. Exploiting this structure, the global-in-time existence of
weak solutions and the exponential decay to the constant steady state is proved
in certain parameter regimes. This approach does not extend to all parameters.
We investigate local bifurcations from homogeneous steady states analytically
to determine whether this defines the validity boundary. This analysis shows
that generically there is a gap in the parameter regime between the entropy
approach validity and the first local bifurcation. Next, we use numerical
continuation methods to track the bifurcating non-homogeneous steady states
globally and to determine non-trivial stationary solutions related to herding
behaviour. In summary, we find that the main boundaries in the parameter regime
are given by the first local bifurcation point, the degeneracy of the diffusion
matrix and a certain entropy decay validity condition. We study several
parameter limits analytically as well as numerically, with a focus on the role
of changing a linear damping parameter as well as a parameter controlling the
cross-diffusion. We suggest that our paradigm of comparing
bifurcation-generated obstructions to the parameter validity of
global-functional methods could also be of relevance for many other models
beyond the one studied here.
|
1504.07555v4
|
2015-05-29
|
Microscopic Theory for Coupled Atomistic Magnetization and Lattice Dynamics
|
A coupled atomistic spin and lattice dynamics approach is developed which
merges the dynamics of these two degrees of freedom into a single set of
coupled equations of motion. The underlying microscopic model comprises local
exchange interactions between the electron spin and magnetic moment and the
local couplings between the electronic charge and lattice displacements. An
effective action for the spin and lattice variables is constructed in which the
interactions among the spin and lattice components are determined by the
underlying electronic structure. In this way, expressions are obtained for the
electronically mediated couplings between the spin and lattice degrees of
freedom, besides the well known inter-atomic force constants and spin-spin
interactions. These former susceptibilities provide an atomistic ab initio
description for the coupled spin and lattice dynamics. It is important to
notice that this theory is strictly bilinear in the spin and lattice variables
and provides a minimal model for the coupled dynamics of these subsystems and
that the two subsystems are treated on the same footing. Questions concerning
time-reversal and inversion symmetry are rigorously addressed and it is shown
how these aspects are absorbed in the tensor structure of the interaction
fields. By means of these results regarding the spin-lattice coupling, simple
explanations of ionic dimerization in double anti-ferromagnetic materials, as
well as, charge density waves induced by a non-uniform spin structure are
given. In the final parts, a set of coupled equations of motion for the
combined spin and lattice dynamics are constructed, which subsequently can be
reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations
for spin dynamics and damped driven mechanical oscillator for the ...
|
1505.08005v3
|
2015-06-18
|
Galaxy power spectrum in redshift space: combining perturbation theory with the halo model
|
Theoretical modeling of the redshift-space power spectrum of galaxies is
crucially important to correctly extract cosmological information from redshift
surveys. The task is complicated by the nonlinear biasing and redshift space
distortion effects, which change with halo mass, and by the wide distribution
of halo masses and their occupations by galaxies. One of the main modeling
challenges is the existence of satellite galaxies that have both radial
distribution and large virial velocities inside halos, a phenomenon known as
the Finger-of-God effect. We present a model for the galaxy power spectrum of
in which we decompose a given galaxy sample into central and satellite galaxies
and relate different contributions to 1- and 2-halo terms in a halo model. Our
primary goal is to ensure that any parameters that we introduce have physically
meaningful values, and are not just fitting parameters. For the 2-halo terms we
use the previously developed RSD modeling of halos in the context of
distribution function and perturbation theory approach. This term needs to be
multiplied by the effect of radial distances and velocities of satellites
inside the halo. To this one needs to add the 1-halo terms, which are
non-perturbative. We show that the real space 1-halo terms can be modeled as
almost constant, with the finite extent of the satellites inside the halo
inducing a small k^2R^2 term, where R is related to the size of the halo. We
adopt a similar model for FoG in redshift space, ensuring that FoG velocity
dispersion is related to the halo mass. For FoG k^2 type expansions do not work
and FoG resummation must be used instead. We test several damping functions to
model the velocity dispersion FoG effect. Applying the formalism to mock
galaxies modeled after the "CMASS" sample of the BOSS survey, we find that our
predictions for the redshift-space power spectra are accurate up to k~0.4Mpc/h.
|
1506.05814v2
|
2015-10-25
|
A class of chemotaxis systems with growth source and nonlinear secretion
|
In this paper, we are concerned with a class of parabolic-elliptic chemotaxis
systems encompassing the prototype $$\left\{\begin{array}{lll} &u_t =
\nabla\cdot(\nabla u-\chi u\nabla v)+f(u), & x\in \Omega, t>0, \\[0.2cm] &0=
\Delta v -v+u^\kappa, & x\in \Omega, t>0 \end{array}\right. $$ with nonnegative
initial condition for $u$ and homogeneous Neumann boundary conditions in a
smooth bounded domain $\Omega\subset \mathbb{R}^n(n\geq 2)$, where $\chi>0$,
$\kappa>0$ and $f$ is a smooth growth source satisfying $f(0)\geq 0$ and $$
f(s)\leq a-bs^\theta, \quad s\geq 0, \text{with some} a\geq 0, b>0, \theta>1.
$$ Firstly, it is shown, either $$ \kappa<\frac{2}{n}\quad \& \quad f\equiv 0,
$$ or $$\theta>\kappa+1, $$ or $$ \theta-\kappa=1, \ \ b\geq \frac{(\kappa
n-2)}{\kappa n}\chi, \eqno(*) $$
that the corresponding initial-value problem admits a unique classical
solution that is uniformly bounded in space and time. Our proof is elementary
and semigroup-free. Whilst, with the particular choices $\theta=2$ and
$\kappa=1$, Tello and Winkler \cite{TW07} use sophisticated estimates via the
Neumann heat semigroup to obtain the global boundedness under the strict
inequality in ($\ast$). Thereby, we improve their results to the "borderline"
case $b=(\kappa n-2)/(\kappa n)\chi$ in this regard. Next, for an unbounded
range of $\chi$, the system is shown to exhibit pattern formations, and, the
emerging patterns are shown to converge weakly in $ L^\theta(\Omega)$ to some
constants as $\chi\rightarrow \infty$. While, for small $\chi$ or large damping
$b$, precisely $b>2\chi$ if $f(u)=u(a-bu^\kappa)$ for some $a, b>0$, we show
that the system does not admit pattern formation and the large time behavior of
solutions is comparable to its associated ODE+algebraic system.
|
1510.07204v1
|
2017-01-20
|
On the Transition from Potential Flow to Turbulence Around a Microsphere Oscillating in Superfluid ^4He
|
The flow of superfluid $^4$He around a translationally oscillating sphere,
levitating without mechanical support, can either be laminar or turbulent,
depending on the velocity amplitude. Below a critical velocity $v_c$ that
scales as $\omega ^{1/2}$, and is temperature independent below 1 K, the flow
is laminar (potential flow). Below 0.5 K the linear drag force is caused by
ballistic phonon scattering that vanishes as T$^4$ until background damping,
measured in the empty cell, becomes dominant for T $<$ 0.1 K. Increasing the
velocity amplitude above $v_c$ leads to a transition from potential flow to
turbulence, where the large turbulent drag force varies as $(v^2 - v_c^2)$. In
a small velocity interval $\Delta v / v_c \le 3 \%$ above $v_c$, the flow is
unstable below 0.5 K, switching intermittently between both patterns. From time
series recorded at constant temperature and driving force, the lifetimes of
both phases are analyzed statistically. We observe metastable states of
potential flow which, after a mean lifetime of 25 minutes, ultimately break
down due to vorticity created by natural background radioactivity. The
lifetimes of the turbulent phases have an exponential distribution, and the
mean increases exponentially with $\Delta v^2$. We investigate the frequency at
which the vortex rings are shed from the sphere. Our results are compared with
recent data of other authors on vortex shedding by moving a laser beam through
a Bose-Einstein condensate. Finally, we show that our observed transition to
turbulence belongs to the class of "supertransient chaos" where lifetimes of
the turbulent states increase faster than exponentially. Peculiar results
obtained in dilute $^3$He - $^4$He mixtures are presented in the Appendix.
|
1701.05733v2
|
2017-02-04
|
Brightness Temperature of Radio Zebras and Wave Energy Densities in Their Sources
|
We estimated the brightness temperature of radio zebras (zebra pattern --
ZP), considering that ZPs are generated in loops having an exponential density
profile in their cross-section. We took into account that when in plasma there
is a source emitting in all directions, then in the escape process from the
plasma the emission obtains a directional character nearly perpendicular to the
constant-density profile. Owing to the high directivity of the plasma emission
the region from which the emission escapes can be very small. We estimated the
brightness temperature of three observed ZPs for two values of the density
scale height (1 and 0.21 Mm) and two values of the loop width (1 and 2 arcsec).
In all cases high brightness temperatures were obtained. For the higher value
of the density scale height, the brightness temperature was estimated as 1.1
$\times$ 10$^{15}$ - 1.3 $\times$ 10$^{17}$ K, and for the lower value as 4.7
$\times$ 10$^{13}$ - 5.6 $\times$ 10$^{15}$ K. We also computed the saturation
energy density of the upper-hybrid waves (which according to the double plasma
resonance model are generated in the zebra source) using a 3D particle-in-cell
model with the loss-cone type of distribution of hot electrons. We found that
this saturated energy is proportional to the ratio of hot electron and
background plasma densities. Thus, comparing the growth rate and collisional
damping of the upper-hybrid waves, we estimated minimal densities of hot
electrons as well as the minimal value of the saturation energy density of the
upper-hybrid waves. Finally, we compared the computed energy density of the
upper-hybrid waves with the energy density of the electromagnetic waves in the
zebra source and thus estimated the efficiency of the wave transformation.
|
1702.01278v2
|
2017-03-02
|
Pinch dynamics in a low-$β$ plasma
|
The relaxation of a helical magnetic field ${\bf B}({\bf x}, t)$ in a
high-conductivity plasma contained in the annulus between two perfectly
conducting coaxial cylinders is considered. The plasma is of low density and
its pressure is negligible compared with the magnetic pressure; the flow of the
plasma is driven by the Lorentz force and and energy is dissipated primarily by
the viscosity of the medium. The axial and toroidal fluxes of magnetic field
are conserved in the perfect-conductivity limit, as is the mass per unit axial
length. The magnetic field relaxes during a rapid initial stage to a force-free
state, and then decays slowly, due to the effect of weak resistivity $\eta$,
while constrained to remain approximately force-free. Interest centres on
whether the relaxed field may attain a Taylor state; but under the assumed
conditions with axial and toroidal flux conserved inside every cylindrical
Lagrangian surface, this is not possible. The effect of an additional
$\alpha$-effect associated with instabilities and turbulence in the plasma is
therefore investigated in exploratory manner. An assumed pseudo-scalar form of
$\alpha$ proportional to $q\,\eta\, ({\bf j}\cdot {\bf B})$ is adopted, where $
{\bf j}=\nabla\times {\bf B}$ and $q$ is an $\mathcal{O}(1)$ dimensionless
parameter. It is shown that, when $q$ is less that a critical value $q_c$, the
evolution remains smooth and similar to that for $q=0$; but that if $q>q_c$,
negative-diffusivity effects act on the axial component of $\bf B$, generating
high-frequency rapidly damped oscillations and an associated transitory
appearance of reversed axial field. However, the scalar quantity $\gamma={\bf
j}\cdot {\bf B}/B^2$ remains highly non-uniform, so that again the field shows
no sign of relaxing to a Taylor state for which $\gamma$ would have to be
constant.
|
1703.00708v1
|
2017-04-18
|
Outbursts of the intermediate-mass black hole HLX-1: a wind instability scenario
|
We model the intermediate-mass black hole HLX-1, using the Hubble Space
Telescope, XMM-Newton and Swift. We quantify the relative contributions of a
bluer component, function of X-ray irradiation, and a redder component,
constant and likely coming from an old stellar population. We estimate a black
hole mass of about (2^{+2}_{-1}) x 10^4 M_{sun}, a spin parameter a/M ~ 0.9 for
moderately face-on view, and a peak outburst luminosity of about 0.3 times the
Eddington luminosity. We discuss the discrepancy between the characteristic
sizes inferred from the short X-ray timescale (R ~ a few 10^{11} cm) and from
the optical emitter (R sqrt[cos theta] ~ 2.2 x 10^{13} cm). One possibility is
that the optical emitter is a circumbinary disk; however, we disfavour this
scenario because it would require a very small donor star. A more plausible
scenario is that the disk is large but only the inner annuli are involved in
the X-ray outburst. We propose that the recurrent outbursts are caused by an
accretion-rate oscillation driven by wind instability in the inner disk. We
argue that the system has a long-term-average accretion rate of a few percent
Eddington, just below the upper limit of the low/hard state; a wind-driven
oscillation can trigger transitions to the high/soft state, with a recurrence
period of ~1 year (much longer than the binary period, which we estimate as ~10
days). The oscillation that dominated the system in the last decade is now
damped such that the accretion rate no longer reaches the level required to
trigger a transition. Finally, we highlight similarities between disk winds in
HLX-1 and in the Galactic black hole V404 Cyg.
|
1704.05468v1
|
2017-07-04
|
Lattice symmetries and the topological protected transport of colloidal particles
|
The topologically protected transport of colloidal particles on top of
magnetic patterns of all possible single lattice constant two dimensional
magnetic point group symmetries is studied experimentally, theoretically, and
with numerical simulations. We examine the transport of colloidal particles in
response to modulation loops of the external field. We classify the modulation
loops into topologically distinct classes causing different transport. We show
that the lattice symmetry has a profound influence on the transport modes, the
accessibility of transport networks, and the individual addressability of
paramagnetic versus diamagnetic colloidal particles. We show how the transport
of colloidal particles above a two fold symmetric stripe pattern changes from
universal adiabatic transport at large elevations via a topologically protected
ratchet motion at intermediate elevations toward a non-transport regime at low
elevations. Transport above four fold symmetric patterns is closely related to
the transport above two fold symmetric patterns. There exists a family of three
fold symmetric patterns that vary as a function of the phase of the pattern. We
show how this family can be divided into two topologically distinct classes
supporting different transport modes and being protected by proper and improper
six fold symmetries. Both classes support individual control over the transport
of paramagnetic and diamagnetic particles. We discuss the topological
transition when moving the phase from one class of pattern to the other class.
The similarities and the differences in the lattice symmetry protected
transport of classical over-damped colloidal particles versus the topologically
protected transport in quantum mechanical systems are emphasized
|
1707.00861v1
|
2017-10-05
|
Cross section alignment of polycyclic aromatic hydrocarbons by anisotropic radiation
|
We study the effect of anisotropic radiation illumination on the alignment of
polycyclic aromatic hydrocarbons (PAHs) and report that cross-sectional
mechanism of alignment earlier considered in terms of gas-grain interactions
can also be efficient for the photon-grain interaction. We demonstrate this by
first calculating the angle-dependence rotational damping and excitation
coefficients by photon absorption followed by infrared emission. We then
calculate the degree of PAH alignment for the different environments and
physical parameters, including the illumination direction, ionization fraction,
and magnetic field strength. For the reflection nebula (RN) conditions with
unidirectional radiation field, we find that the degree of alignment tends to
increase with increasing the angle $\psi$ between the illumination direction
and the magnetic field, as a result of the decrease of the cross-section of
photon absorption with $\psi$. We calculate the polarization of spinning PAH
emission using the obtained degree of alignment for the different physical
parameters, assuming constant grain temperatures. We find that the polarization
of spinning PAH emission from RN can be large, between $5-20~\%$ at frequencies
$\nu > 20$ GHz, whereas the polarization is less than $3~\%$ for
photodissociation regions (PDRs). In realistic conditions, the polarization is
expected to be lower due to grain temperature fluctuations and magnetic field
geometry. The polarization for the diffuse cold neutral medium (CNM) is rather
low, below $1~\%$ at $\nu>20$ GHz, consistent with observations by WMAP and
Planck. Our results demonstrate that the RNe are the favored environment to
observe the polarization of spinning dust emission as well as polarized mid-IR
emission from PAHs.
|
1710.01835v2
|
2018-05-15
|
Nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors
|
Nonreciprocal charge transport phenomena are studied theoretically for
two-dimensional noncentrosymmetric superconductors under an external magnetic
field $B$. Rashba superconductors, surface superconductivity on the surface of
three-dimensional topological insulators, and transition metal dichalcogenides
(TMD) are representative systems, and the current-voltage $I$-$V$
characteristics, i.e., $V=V(I)$, for each of them is analyzed. $V(I)$ can be
expanded with respect to the current $I$ as $V(I)= \sum_{j=1,\infty} a_j(B,T)
I^j$, and the $(B,T)$-dependence of $a_j$ depends on the mechanism of the
charge transport. Above the mean field transition temperature $T_0$, the
fluctuation of the superconducting order parameter gives the additional
conductivity, i.e., paraconductivity. Extending the analysis to the nonlinear
response, we obtain the nonreciprocal charge transport expressed by $a_2(B,T) =
a_1(T) \gamma(T) B$, where $\gamma$ converges to a finite value at $T=T_0$.
Below $T_0$, the vortex motion is relevant to the voltage drop, and the
dependence of $a_j$ on $B,T$ is different depending on the system and
mechanisms. For the superconductors under the in-plane magnetic field, the
Kosterlitz-Thouless (KT) transition occurs at $T_{\rm KT}$. In this case
$\gamma$ has the characteristic temperature dependences such as $\gamma \sim
(T-T_{\rm KT})^{-3/2}$ near $T_{\rm KT}$. On the other hand, for TMD with
out-plane magnetic field, the KT transition is gone, and there are two possible
mechanisms for the nonreciprocal response. One is the anisotropy of the damping
constant for the motion of the vortex. In this case, $a_1(B) \sim B$ and
$a_2(B) \sim B^2$. The other one is the ratchet potential acting on the vortex
motion, which gives $a_1(B) \sim B$ and $a_2(B) \sim B$. Based on these
results, we propose the experiments to identify the mechanism of the
nonreciprocal charge transport.
|
1805.05735v1
|
2018-07-27
|
Phase spreading and temporal coherence of a pair-condensed Fermi gas at low temperature
|
A condensate of pairs in an isolated, homogeneous, unpolarised, finite-size
spin 1/2 Fermi gas at low nonzero temperature T, undergoes with time a phase
change with a random component, due to coupling to the gas thermal phonons.
With the quantum second Josephson relation relating the derivative of the
condensate phase operator to the phonon occupation numbers, and linearised
kinetic equations giving the evolution of occupation number fluctuations, we
access the behaviour of the phase change variance at times much longer than the
phonon collision time. The case of a convex phonon branch is similar to the
Bose gas case: the leading collisional processes are the Beliaev-Landau
3-phonons processes, and the variance is the sum of a ballistic term and of a
delayed diffusive term, whose analytical expressions are given in the
thermodynamic limit. The concave case is more exotic. It is analysed at time
scales $T^{-9}$, allowing one to restrict to 2 phonons $\rightarrow$ 2 phonons
small-angle Landau-Khalatnikov processes. The total number of phonons is
conserved and the phonon mean occupation numbers at equilibrium can exhibit a
negative chemical potential, assumed isotropic. The phase change variance is
then the sum of a ballistic term, of a diffusive term, of exotic subsubleading
terms and of a constant term. The analytic expression of some of the
corresponding coefficients is obtained, as well as the diverging leading
behavior of the other ones when the phonon chemical potential tends to 0. When
this chemical potential is 0, the variance sub-ballistic part becomes
superdiffusive, with an exponent 5/3 and an exactly-known coefficient. For a
nonzero infinitesimal phonon chemical potential, a law is found, interpolating
between superdiffusive and diffusive phase spreading. Also new results are
obtained on the phonon Landau-Khalatnikov damping rate, in particular at
negative phonon chemical potential.
|
1807.10476v2
|
2018-09-24
|
Laser cooling and magneto-optical trapping of molecules analyzed using optical Bloch equations and the Fokker-Planck-Kramers equation
|
We study theoretically the behavior of laser-cooled calcium monofluoride
(CaF) molecules in an optical molasses and magneto-optical trap (MOT), and
compare our results to recent experiments. We use multi-level optical Bloch
equations to estimate the force and the diffusion constant, followed by a
Fokker-Planck-Kramers equation to calculate the time-evolution of the velocity
distribution. The calculations are done in three-dimensions, and we include all
the relevant energy levels of the molecule and all the relevant frequency
components of the light. Similar to simpler model systems, the
velocity-dependent force curve exhibits Doppler and polarization-gradient
forces of opposite signs. We show that the temperature of the MOT is governed
mainly by the balance of these two forces. Our calculated MOT temperatures and
photon scattering rates are in broad agreement with those measured
experimentally over a wide range of parameters. In a blue-detuned molasses, the
temperature is determined by the balance of polarization gradient cooling, and
heating due to momentum diffusion, with no significant contribution from
Doppler heating. In the molasses, we calculate a damping rate similar to the
measured one, and steady-state temperatures that have the same dependence on
laser intensity and applied magnetic field as measured experimentally, but are
consistently a few times smaller than measured. We attribute the higher
temperatures in the experiments to fluctuations of the dipole force which are
not captured by our model. We show that the photon scattering rate is strongly
influenced by the presence of dark states in the system, but that the
scattering rate does not go to zero even for stationary molecules because of
the transient nature of the dark states.
|
1809.08833v4
|
2019-02-01
|
The Neutrino Puzzle: Anomalies, Interactions, and Cosmological Tensions
|
New physics in the neutrino sector might be necessary to address anomalies
between different neutrino oscillation experiments. Intriguingly, it also
offers a possible solution to the discrepant cosmological measurements of $H_0$
and $\sigma_8$. We show here that delaying the onset of neutrino free-streaming
until close to the epoch of matter-radiation equality can naturally accommodate
a larger value for the Hubble constant $H_0=72.3 \pm 1.4$ km/s/Mpc and a lower
value of the matter fluctuations $\sigma_8=0.786\pm 0.020$, while not degrading
the fit to the cosmic microwave background (CMB) damping tail. We achieve this
by introducing neutrino self-interactions in the presence of a non-vanishing
sum of neutrino masses. This strongly interacting neutrino cosmology prefers
$N_{\rm eff} = 4.02 \pm 0.29$, which has interesting implications for particle
model-building and neutrino oscillation anomalies. We show that the absence of
the neutrino free-streaming phase shift on the CMB can be compensated by
shifting the value of other cosmological parameters, hence providing an
important caveat to the detections made in the literature. Due to their impact
on the evolution of the gravitational potential at early times,
self-interacting neutrinos and their subsequent decoupling leave a rich
structure on the matter power spectrum. In particular, we point out the
existence of a novel localized feature appearing on scales entering the horizon
at the onset of neutrino free-streaming. While the interacting neutrino
cosmology provides a better global fit to current cosmological data, we find
that traditional Bayesian analyses penalize the model as compared to the
standard cosmological. Our analysis shows that it is possible to find radically
different cosmological models that nonetheless provide excellent fits to the
data, hence providing an impetus to thoroughly explore alternate cosmological
scenarios.
|
1902.00534v2
|
2019-01-31
|
Analysis and active control of geometrically nonlinear responses of smart FG porous plates with graphene nanoplatelets reinforcement based on Bézier extraction of NURBS
|
In this paper, we propose an effective computational approach to analyze and
active control of geometrically nonlinear responses of functionally graded (FG)
porous plates with graphene nanoplatelets (GPLs) reinforcement integrated with
piezoelectric layers. The key concept behind this work is to utilize
isogeometric analysis (IGA) based on B\'ezier extraction technique and
$C^0$-type higher-order shear deformation theory ($C^0$-HSDT). By applying
B\'ezier extraction, the original Non-Uniform Rational B-Spline (NURBS) control
meshes can be transformed into B\'ezier elements which allow us to inherit the
standard numerical procedure like the standard finite element method (FEM). In
this scenario, the approximation of mechanical displacement field is calculated
via $C^0$-HSDT whilst the electric potential field is considered as a linear
function across the thickness of each piezoelectric sublayer. The FG plate
includes internal pores and GPLs dispersed into metal matrix either uniformly
or non-uniformly along plate's thickness. To control responses of structures,
the top and bottom surfaces of FG plate are firmly bonded with piezoelectric
layers which are considered as sensor and actuator layers. The geometrically
nonlinear equations are solved by Newton-Raphson iterative procedure and
Newmark's integration. The influence of porosity coefficient, weight fraction
of GPLs as well as external electrical voltage on geometrically nonlinear
behaviors of plate structures with various distributions of porosity and GPLs
are thoroughly investigated. A constant displacement and velocity feedback
control approaches are then adopted to actively control geometrically nonlinear
static and dynamic responses, where structural damping effect is taken into
account, based on a closed-loop control with sensor and actuator layers.
|
1902.10806v2
|
2019-03-19
|
Phase mixing of nonlinear Alfven waves
|
Aims: This paper presents 2.5D numerical experiments of Alfv\'en wave phase
mixing and aims to assess the effects of nonlinearities on wave behaviour and
dissipation. In addition, this paper aims to quantify how effective the model
presented in this work is at providing energy to the coronal volume.
Methods: The model is presented and explored through the use of several
numerical experiments which were carried out using the Lare2D code. The
experiments study footpoint driven Alfv\'en waves in the neighbourhood of a
two-dimensional x-type null point with initially uniform density and plasma
pressure. A continuous sinusoidal driver with a constant frequency is used.
Each experiment uses different driver amplitudes to compare weakly nonlinear
experiments with linear experiments.
Results: We find that the wave trains phase-mix owing to variations in the
length of each field line and variations in the field strength. The
nonlinearities reduce the amount of energy entering the domain, as they reduce
the effectiveness of the driver, but they have relatively little effect on the
damping rate (for the range of amplitudes studied). The nonlinearities produce
density structures which change the natural frequencies of the field lines and
hence cause the resonant locations to move. The shifting of the resonant
location causes the Poynting flux associated with the driver to decrease.
Reducing the magnetic diffusivity increases the energy build-up on the resonant
field lines, however, it has little effect on the total amount of energy
entering the system. From an order of magnitude estimate, we show that the
Poynting flux in our experiments is comparable to the energy requirements of
the quiet Sun corona. However a (possibly unphysically) large amount of
magnetic diffusion was used however and it remains unclear if the model is able
to provide enough energy under actual coronal conditions.
|
1903.08093v1
|
2019-07-30
|
Rapid Reionization by the Oligarchs: The Case for Massive, UV-Bright, Star-Forming Galaxies with High Escape Fractions
|
The protagonists of cosmic reionization remain elusive. Faint star-forming
galaxies are leading candidates because they are numerous and may have
significant ionizing photon escape fractions ($f_{esc}$). Here we update this
picture via an empirical model that successfully predicts latest observations
(e.g., the drop in star-formation density at z>8). We generate an ionizing
spectrum for each galaxy in our model and constrain $f_{esc}$ using latest
measurements of the reionization timeline (e.g., Ly$\alpha$ damping of quasars
and galaxies at z>7). Assuming a constant $f_{esc}$, we find $M_{UV}$<-13.5
galaxies need $f_{esc}=0.21^{+0.06}_{-0.04}$ to complete reionization. The
inferred IGM neutral fraction is [0.9, 0.5, 0.1] at z=[8.2, 6.8, 6.2]$\pm$0.2,
i.e., the bulk of reionization transpires in 300 Myrs. Inspired by the emergent
sample of Lyman Continuum (LyC) leakers that overwhelmingly displays
higher-than-average star-formation surface density ($\Sigma$), we propose a
model relating $f_{esc}$ to $\Sigma$ and find
$f_{esc}\propto\Sigma^{0.4\pm0.1}$. Since $\Sigma$ falls by ~2.5 dex between
z=8 and z=0, our model explains the humble upper limits on $f_{esc}$ at lower
redshifts and its required evolution to ~0.2 at z>6. Within this model,
strikingly, <5% of galaxies with $M_{UV}$<-18 (the `oligarchs') account for
>80% of the reionization budget. In fact, faint sources ($M_{UV}$>-16) must be
relegated to a limited role to ensure high neutral fractions at z=7-8. Shallow
faint-end slopes of the UV luminosity function ($\alpha$>-2) and/or $f_{esc}$
distributions skewed toward bright galaxies produce the required late and rapid
reionization. We predict LyC leakers like COLA1 (z=6.6, $f_{esc}$~30%,
$M_{UV}$=-21.5) become increasingly common towards z~6 and that the drivers of
reionization do not lie hidden across the faint-end of the luminosity function,
but are already known to us. (abridged)
|
1907.13130v2
|
2019-09-13
|
Multi-Particle Collisions in Microgravity: Coefficient of Restitution and Sticking Threshold for Systems of Mm-Sized Particles
|
The current model of planet formation lacks a good understanding of the
growth of dust particles inside the protoplanetary disk beyond mm sizes. In
order to investigate the low-velocity collisions between this type of
particles, the NanoRocks experiment was flown on the International Space
Station (ISS) between September 2014 and March 2016. We present the results of
this experiment. We quantify the damping of energy in systems of multiple
particles in the 0.1 to 1 mm size range while they are in the bouncing regime,
and study the formation of clusters through sticking collisions between
particles. We developed statistical methods for the analysis of the large
quantity of collision data collected by the experiment. We measured the average
motion of particles, the moment of clustering, and the cluster size formed. In
addition, we ran simple numerical simulations in order to validate our
measurements. We computed the average coefficient of restitution (COR) of
collisions and find values ranging from 0.55 for systems including a population
of fine grains to 0.94 for systems of denser particles. We also measured the
sticking threshold velocities and find values around 1 cm/s, consistent with
the current dust collision models based on independently collected experimental
data. Our findings have the following implications that can be useful for the
simulation of particles in PPDs and planetary rings: (1) The average COR of
collisions between same-sized free-floating particles at low speeds (< 2 cm/s)
is not dependent on the collision velocity; (2) The simplified approach of
using a constant COR value will accurately reproduce the average behavior of a
particle system during collisional cooling; (3) At speeds below 5 mm/s, the
influence of particle rotation becomes apparent on the collision behavior; (4)
Current dust collision models predicting sticking thresholds are robust.
|
1909.06417v1
|
2019-10-14
|
A search for optical AGN variability in 35,000 low-mass galaxies with the Palomar Transient Factory
|
We present an analysis of the long-term optical variability for $\sim50,000$
nearby (z<0.055) galaxies from the NASA-Sloan Atlas, $35,000$ of which are
low-mass ($M_{\ast}<10^{10}~M_{\odot}$). We use difference imaging of Palomar
Transient Factory (PTF) R-band observations to construct light curves with
typical baselines of several years. We then search for subtle variations in the
nuclear light output. We determine whether detected variability is AGN-like by
assessing the fit quality to a damped random walk model. We identify 424
variability-selected AGN, including 244 with stellar masses between $10^{7}$
and $10^{10}~M_{\odot}$. 75% of low-mass galaxies with AGN-like variability
have narrow emission lines dominated by star formation. After controlling for
nucleus magnitude, the fraction of variable AGN is constant down to
$M_{\ast}=10^{9}~M_{\odot}$, suggesting no drastic decline in the BH occupation
fraction down to this stellar mass regime. Combining our NASA-Sloan Atlas
sample with samples of nearby galaxies with broad H$\alpha$ emission, we find
no dependence of variability properties with black hole mass. However, we
caution that the variable AGN fraction is strongly dependent on baseline. For
baselines less than two years, the variable fraction for the full sample is
0.25%, compared to 1.0% for baselines longer than two years. Finally, comparing
Stripe 82 light curves (Baldassare et al. 2018) to PTF light curves, we find
populations of changing-look AGN: 8 galaxies that are variable in Stripe 82,
but quiescent in PTF, and 15 galaxies where the reverse is true. Our PTF work
demonstrates the promise of long-term optical variability searches in low-mass
galaxies for finding AGNs missed by other selection techniques.
|
1910.06342v1
|
2019-10-30
|
A priori bounds for the $Φ^4$ equation in the full sub-critical regime
|
We derive a priori bounds for the $\Phi^4$ equation in the full sub-critical
regime using Hairer's theory of regularity structures. The equation is formally
given by \begin{equation} \label{e}(\partial_t-\Delta)\phi = -\phi^3 + \infty
\phi +\xi, \tag{$\star$} \end{equation} where the term $+\infty \phi$
represents infinite terms that have to be removed in a renormalisation
procedure. We emulate fractional dimensions $d<4$ by adjusting the regularity
of the noise term $\xi$, choosing $\xi \in C^{-3+\delta}$. Our main result
states that if $\phi$ satisfies this equation on a space-time cylinder $P=
(0,1) \times \{ |x| \leq 1 \}$, then away from the boundary $\partial P$ the
solution $\phi$ can be bounded in terms of a finite number of explicit
polynomial expressions in $\xi$, and this bound holds uniformly over all
possible choices of boundary data for $\phi$. The derivation of this bound
makes full use of the super-linear damping effect of the non-linear term
$-\phi^3$. A key part of our analysis consists of an appropriate re-formulation
of the theory of regularity structures in the specific context of \eqref{e},
which allows to couple the small scale control one obtains from this theory
with a suitable large scale argument. Along the way we make several new
observations and simplifications. Instead of a model $(\Pi_x)_x$ and the family
of translation operators $(\Gamma_{x,y})_{x,y}$ we work with just a single
object $(\mathbb{X}_{x, y})$ which acts on itself for translations, very much
in the spirit of Gubinelli's theory of branched rough paths. Furthermore, we
show that in the specific context of \eqref{e} the hierarchy of continuity
conditions which constitute Hairer's definition of a \emph{modelled
distribution} can be reduced to the single continuity condition on the
"coefficient on the constant level".
|
1910.13854v2
|
2019-10-31
|
One-point probability distribution function from spherical collapse: Early Dark Energy (EDE) vs. $Λ$CDM
|
We compute the one-point PDF of an initially Gaussian dark matter density
field using spherical collapse (SC). We compare the results to other forms
available in the literature and also compare the PDFs in the $\Lambda$CDM model
with an early dark energy (EDE) model. We find that the skewed log-normal
distribution provides the best fit to the non-linear PDF from SC for both
cosmologies, from $a=0.1$ to 1 and for scales characterized by the comoving
width of the Gaussian: $\sigma_G = 0.5, 1, 2$. To elucidate the effect of
cosmology, we examine the linear and non-linear growth rates through test
cases. For overdensities, when the two models have the same initial density
contrast, the differences due to cosmology are amplified in the non-linear
regime, whereas, if the two models have the same linear density contrast today,
then the differences in cosmology are damped in the non-linear regime. This
behaviour is in contrast with voids, where the non-linear growth becomes
`self-regulatory' and is less sensitive to cosmology and initial conditions. To
compare the PDFs, we examine the difference of the PDFs and evolution of the
width of the PDF. The trends with scale and redshift are as expected. A
tertiary aim of this paper was to check if the fitting form for the non-linear
density-velocity divergence relation, derived for constant equation of state
($w$) models by Nadkarni-Ghosh holds for the EDE model. We find that it does
with an accuracy of 4\%, thus increasing its range of validity.
|
1910.14347v3
|
2019-11-04
|
Planet-disk interaction in disks with cooling: basic theory
|
Gravitational coupling between young planets and their parent disks is often
explored using numerical simulations, which typically treat the disk
thermodynamics in a highly simplified manner. In particular, many studies adopt
the locally isothermal approximation, in which the disk temperature is a fixed
function of the stellocentric distance. We explore the dynamics of
planet-driven density waves in disks with more general thermodynamics, in which
the temperature is relaxed towards an equilibrium profile on a finite cooling
timescale $t_{\rm c}$. We use both linear perturbation theory and direct
numerical simulations to examine the global structure of density waves launched
by planets in such disks. A key diagnostic used in this study is the behavior
of the wave angular momentum flux (AMF), which directly determines the
evolution of the underlying disk. The AMF of free waves is constant for slowly
cooling (adiabatic) disks, but scales with the disk temperature for rapidly
cooling (and locally isothermal) disks. However, cooling must be extremely
fast, with $\beta = \Omega t_{\rm c} \lesssim 10^{-3}$ for the locally
isothermal approximation to provide a good description of density wave dynamics
in the linear regime (relaxing to $\beta \lesssim 10^{-2}$ when nonlinear
effects are important). For intermediate cooling timescales, density waves are
subject to a strong linear damping. This modifies the appearance of
planet-driven spiral arms and the characteristics of axisymmetric structures
produced by massive planets: in disks with $\beta \approx 0.1$ -- $1$, a
near-thermal mass planet opens only a single wide gap around its orbit, in
contrast to the several narrow gaps produced when cooling is either faster or
slower.
|
1911.01428v2
|
2019-11-18
|
Wave measurements from ship mounted sensors in the Arctic marginal ice zone
|
Increased research interest and economic activity in the Arctic raise the
need for new observations of sea ice dynamics. Remote sensing as well as
mathematical and numerical models of wave propagation in sea ice would benefit
from more in situ data for validation. This study presents wave measurements in
the marginal ice zone (MIZ) obtained from ship mounted sensors. The system
combines altimeter readings from the ship bow with ship motion correction data
to provide estimated single point ocean surface elevation. Significant wave
height and mean wave period, as well as one-dimensional wave spectra are
derived from the combined measurements. The results are compared with
integrated parameters from a spectral wave model over a period of eight days in
the open ocean, and with spectra and integrated parameters derived from motion
detecting instruments placed on ice floes inside the MIZ. Mean absolute errors
of the integrated parameters are in the range 15.0-18.9% when comparing with
the spectral wave model and 1.0-9.6% when comparing with valid motion detecting
instruments. The spatial wave damping coefficient is estimated by looking at
the change in spectral wave amplitude found at discrete frequency values as the
ship was moving along the longitudinal direction of the MIZ within time
intervals where the wave field is found to be approximately constant in time.
As expected from theory, high frequency waves are effectively dampened by the
presence of sea ice. The observed wave attenuation rates compare favourably
with a two-layer dissipation model. Our methodology can be regarded as a simple
and reliable way to collect more waves-in-ice data as it can be easily added to
any ship participating to ice expeditions, at little extra cost.
|
1911.07612v2
|
2019-11-29
|
Convection-dominated dissolution for single and multiple immersed sessile droplets
|
We numerically investigate both single and multiple droplet dissolution with
droplets consisting of lighter liquid dissolving in a denser host liquid. The
significance of buoyancy is quantified by the Rayleigh number Ra which is the
buoyancy force over the viscous damping force. In this study, Ra spans almost
four decades from 0.1 to 400. We focus on how the mass flux, characterized by
the Sherwood number Sh, and the flow morphologies depend on Ra. For single
droplet dissolution, we first show the transition of the Sh(Ra) scaling from a
constant value to $Sh\sim Ra^{1/4}$, which confirms the experimental results by
Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45--67). The two distinct
regimes, namely the diffusively- and the convectively-dominated regime, exhibit
different flow morphologies: when Ra>=10, a buoyant plume is clearly visible
which contrasts sharply to the pure diffusion case at low Ra. For multiple
droplet dissolution, the well-known shielding effect comes into play at low Ra
so that the dissolution rate is slower as compared to the single droplet case.
However, at high Ra, convection becomes more and more dominant so that a
collective plume enhances the mass flux, and remarkably the multiple droplets
dissolve faster than a single droplet. This has also been found in the
experiments by Laghezza et al. (Soft Matter, vol. 12, 2016, pp. 5787--5796). We
explain this enhancement by the formation of a single, larger plume rather than
several individual plumes. Moreover, there is an optimal Ra at which the
enhancement is maximized, because the single plume is narrower at larger Ra,
which thus hinders the enhancement. Our findings demonstrate a new mechanism in
collective droplet dissolution, which is the merging of the plumes, that leads
to non-trivial phenomena, contrasting the shielding effect.
|
1911.13040v1
|
2020-02-26
|
The Magnetized Vlasov-Ampère system and the Bernstein-Landau paradox
|
We study the Bernstein-Landau paradox in the collisionless motion of an
electrostatic plasma in the presence of a constant external magnetic field. The
Bernstein-Landau paradox consists in that in the presence of the magnetic
field, the electric field and the charge density fluctuation have an
oscillatory behavior in time. This is radically different from Landau damping,
in the case without magnetic field, where the electric field tends to zero for
large times. We consider this problem from a new point of view. Instead of
analyzing the linear magnetized Vlasov-Poisson system, as it is usually done,
we study the linear magnetized Vlasov-Amp\`ere system. We formulate the
magnetized Vlasov-Amp\`ere system as a Schr\"odinger equation with a
selfadjoint magnetized Vlasov-Amp\`ere operator in the Hilbert space of states
with finite energy. The magnetized Vlasov-Amp\`ere operator has a complete set
of orthonormal eigenfunctions, that include the Bernstein modes. The expansion
of the solution of the magnetized Vlasov-Amp\`ere system in the eigenfunctions
shows the oscillatory behavior in time. We prove the convergence of the
expansion under optimal conditions, assuming only that the initial state has
finite energy. This solves a problem that was recently posed in the literature.
The Bernstein modes are not complete. To have a complete system it is necessary
to add eigenfunctions that are associated with eigenvalues at all the integer
multiples of the cyclotron frequency. These special plasma oscillations
actually exist on their own, without the excitation of the other modes. In the
limit when the magnetic fields goes to zero the spectrum of the magnetized
Vlasov-Amp\`ere operator changes drastically from pure point to absolutely
continuous in the orthogonal complement to its kernel, due to a sharp change on
its domain. This explains the Bernstein-Landau paradox.
|
2002.11380v3
|
2020-07-24
|
Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity
|
Turbulent convection is thought to act as an effective viscosity ($\nu_E$) in
damping tidal flows in stars and giant planets. However, the efficiency of this
mechanism has long been debated, particularly in the regime of fast tides, when
the tidal frequency ($\omega$) exceeds the turnover frequency of the dominant
convective eddies ($\omega_c$). We present the results of hydrodynamical
simulations to study the interaction between tidal flows and convection in a
small patch of a convection zone. These simulations build upon our prior work
by simulating more turbulent convection in larger horizontal boxes, and here we
explore a wider range of parameters. We obtain several new results: 1) $\nu_E$
is frequency-dependent, scaling as $\omega^{-0.5}$ when $\omega/\omega_c
\lesssim 1$, and appears to attain its maximum constant value only for very
small frequencies ($\omega/\omega_c \lesssim 10^{-2}$). This
frequency-reduction for low frequency tidal forcing has never been observed
previously. 2) The frequency-dependence of $\nu_E$ appears to follow the same
scaling as the frequency spectrum of the energy (or Reynolds stress) for low
and intermediate frequencies. 3) For high frequencies ($\omega/\omega_c\gtrsim
1-5$), $\nu_E\propto \omega^{-2}$. 4) The energetically-dominant convective
modes always appear to contribute the most to $\nu_E$, rather than the resonant
eddies in a Kolmogorov cascade. These results have important implications for
tidal dissipation in convection zones of stars and planets, and indicate that
the classical tidal theory of the equilibrium tide in stars and giant planets
should be revisited. We briefly touch upon the implications for planetary
orbital decay around evolving stars.
|
2007.12624v1
|
2020-10-05
|
Cryogenic suspension design for a kilometer-scale gravitational-wave detector
|
We report the mirror suspension design for Large-scale Cryogenic
Gravitational wave Telescope, KAGRA, during bKAGRA Phase 1. Mirror thermal
noise is one of the fundamental noises for room-temperature gravitational-wave
detectors such as Advanced LIGO and Advanced Virgo. Thus, reduction of thermal
noise is required for further improvement of their sensitivity. One effective
approach for reducing thermal noise is to cool the mirrors. There are many
technical challenges that must be overcome to cool the mirrors, such as
cryocooler induced vibrations, thermal drift in suspensions, and reduction in
duty cycling due to the increased number of potential failure mechanisms. Our
mirror suspension has a black coating that makes radiative cooling more
efficient. For conduction cooling, we developed ultra high purity aluminum heat
links, which yield high thermal conductivity while keeping the spring constant
sufficiently small. A unique inclination adjustment system, called moving mass,
is used for aligning the mirror orientation in pitch. Photo-reflective
displacement sensors, which have a large range, are installed for damping
control on marionette recoil mass and intermediate recoil mass. Samarium cobalt
magnets are used for coil-magnet actuators to prevent significant change of
magnetism between room temperature and cryogenic temperature. In this paper,
the design of our first cryogenic payload and its performance during bKAGRA
Phase 1 are discussed.
|
2010.01889v2
|
2021-01-21
|
A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations
|
Magnetization dynamics in magnetic materials is often modeled by the
Landau-Lifshitz equation, which is solved numerically in general. In
micromagnetic simulations, the computational cost relies heavily on the
time-marching scheme and the evaluation of stray field. Explicit marching
schemes are efficient but suffer from severe stability constraints, while
nonlinear systems of equations have to be solved in implicit schemes though
they are unconditionally stable. A better compromise between stability and
efficiency is the semi-implicit scheme, such as the Gauss-Seidel projection
method (GSPM) and the second-order backward differentiation formula scheme
(BDF2). At each marching step, GSPM solves several linear systems of equations
with constant coefficients and updates the stray field several times, while
BDF2 updates the stray field only once but solves a larger linear system of
equations with variable coefficients and a nonsymmetric structure. In this
work, we propose a new method, dubbed as GSPM-BDF2, by combing the advantages
of both GSPM and BDF2. Like GSPM, this method is first-order accurate in time
and second-order accurate in space, and is unconditionally stable with respect
to the damping parameter. However, GSPM-BDF2 updates the stray field only once
per time step, leading to an efficiency improvement of about $60\%$ than the
state-of-the-art GSPM for micromagnetic simulations. For Standard Problem \#4
and \#5 from National Institute of Standards and Technology, GSPM-BDF2 reduces
the computational time over the popular software OOMMF by $82\%$ and $96\%$,
respectively. Thus, the proposed method provides a more efficient choice for
micromagnetic simulations.
|
2101.08574v1
|
2021-01-29
|
Radiative Poincare type eon and its follower
|
We consider two consecutive eons $\hat{M}$ and $\check{M}$ from Penrose's
Conformal Cyclic Cosmology and study how the matter content of the past eon
($\hat{M}$) determines the matter content of the present eon ($\check{M}$) by
means of the reciprocity hypothesis. We assume that the only matter content in
the final stages of the past eon is a spherical wave described by Einstein's
equations with the pure radiation energy momentum tensor $$\hat{T}^{ij} =
\hat{\Phi}K^iK^j, \quad \hat{g}_{ij} K^iK^j = 0,$$ and with cosmological
constant $\hat{\Lambda}$ . We solve these Einstein's equations associating to
$\hat{M}$ the metric $\hat{g}=t^{-2}\big(-d t^2+h_t\big)$, which is a
Lorentzian analog of the Poincar\'e-Einstein metric known from the theory of
conformal invariants. The solution is obtained under the assumption that the
3-dimensional conformal structure $[h]$ on the $\mathscr{I}^+$ of $\hat{M}$ is
flat, that the metric $\hat{g}$ admits a power series expansion in the time
variable $t$, and that $h_0\in [h]$. Such solution depends on one real
arbitrary function of the radial variable $r$. Applying the reciprocal
hypothesis, $\hat{g}\to \check{g}=t^4\hat{g}$, we show that the new eon
$(\check{M},\check{g})$ created from the one containing a single spherical
wave, is filled at its initial state with three types of radiation: (i) the
damped spherical wave which continues its life from the previous eon, (ii) the
in-going spherical wave obtained as a result of a collision of the wave from
the past eon with the Bang hypersurface and (3) randomly scattered waves that
could be interpreted as perfect fluid with the energy density $\check{\rho}$
and the isotropic pressure $\check{p}$ such that
$\check{p}=\tfrac13\check{\rho}$.
|
2101.12670v2
|
2021-03-24
|
Magnetism and Spin Dynamics in Room-Temperature van der Waals Magnet Fe$_5$GeTe$_2$
|
Two-dimensional (2D) van der Waals (vdWs) materials have gathered a lot of
attention recently. However, the majority of these materials have Curie
temperatures that are well below room temperature, making it challenging to
incorporate them into device applications. In this work, we synthesized a
room-temperature vdW magnetic crystal Fe$_5$GeTe$_2$ with a Curie temperature
T$_c = 332$ K, and studied its magnetic properties by vibrating sample
magnetometry (VSM) and broadband ferromagnetic resonance (FMR) spectroscopy.
The experiments were performed with external magnetic fields applied along the
c-axis (H$\parallel$c) and the ab-plane (H$\parallel$ab), with temperatures
ranging from 300 K to 10 K. We have found a sizable Land\'e g-factor difference
between the H$\parallel$c and H$\parallel$ab cases. In both cases, the Land\'e
g-factor values deviated from g = 2. This indicates contribution of orbital
angular momentum to the magnetic moment. The FMR measurements reveal that
Fe$_5$GeTe$_2$ has a damping constant comparable to Permalloy. With reducing
temperature, the linewidth was broadened. Together with the VSM data, our
measurements indicate that Fe$_5$GeTe$_2$ transitions from ferromagnetic to
ferrimagnetic at lower temperatures. Our experiments highlight key information
regarding the magnetic state and spin scattering processes in Fe$_5$GeTe$_2$,
which promote the understanding of magnetism in Fe$_5$GeTe$_2$, leading to
implementations of Fe$_5$GeTe$_2$ based room-temperature spintronic devices.
|
2103.13433v2
|
2021-07-25
|
High-overtone fits to numerical relativity ringdowns: beyond the dismissed n=8 special tone
|
In general relativity, the remnant object originating from an uncharged black
hole merger is a Kerr black hole. The approach to this final state is reached
through the emission of a late train of radiation known as the black hole
ringdown. The ringdown morphology is described by a countably infinite set of
damped sinusoids, whose complex frequencies are solely determined by the final
black hole's mass and spin. Recent results advocate that ringdown waveforms
from numerical relativity can be fully described from the peak of the strain
onwards if quasi-normal mode models with $N_{max}=7$ overtones are used. In
this work we extend this analysis to models with $N_{max}\geq 7$ up to
$N_{max}=16$ overtones by exploring the parameter bias on the final mass and
final spin obtained by fitting the nonprecessing binary black hole simulations
from the SXS catalogue. To this aim, we have computed the spin weight $-2$
quasi-normal mode frequencies and angular separation constants for the special
$(l=m=2, n=8,9)$ overtones for the Kerr spacetime. We find that a total of
$N_{max}\sim 6$ overtones are on average sufficient to model the ringdown
starting at the peak of the strain, although about $21\%$ of the cases studied
require at least $N_{max}\sim 12$ overtones to reach a comparable accuracy on
the final state parameters. Considering the waveforms from an earlier or later
point in time, we find that a very similar maximum accuracy can be reached in
each case, occurring at a different number of overtones $N_{max}$. We provide
new error estimates for the SXS waveforms based on the extrapolation and the
resolution uncertainties of the gravitational wave strain. Finally, we observe
substantial instabilities on the values of the best-fit amplitudes of the tones
beyond the fundamental mode and the first overtone, that, nevertheless, do not
impact significantly the mass and spin estimates.
|
2107.11829v2
|
2021-12-23
|
Real-time methods for spectral functions
|
In this paper we develop and compare different real-time methods to calculate
spectral functions. These are classical-statistical simulations, the Gaussian
state approximation (GSA), and the functional renormalization group (FRG)
formulated on the Keldysh closed-time path. Our test-bed system is the quartic
anharmonic oscillator, a single self-interacting bosonic degree of freedom,
coupled to an external heat bath providing dissipation analogous to the
Caldeira-Leggett model. As our benchmark we use the spectral function from
exact diagonalization with constant Ohmic damping. To extend the GSA for the
open system, we solve the corresponding Heisenberg-Langevin equations in the
Gaussian approximation. For the real-time FRG, we introduce a novel general
prescription to construct causal regulators based on introducing
scale-dependent fictitious heat baths. Our results explicitly demonstrate how
the discrete transition lines of the quantum system gradually build up the
broad continuous structures in the classical spectral function as temperature
increases. At sufficiently high temperatures, classical, GSA and
exact-diagonalization results all coincide. The real-time FRG is able to
reproduce the effective thermal mass, but overestimates broadening and only
qualitatively describes higher excitations, at the present order of our
combined vertex and loop expansion. As temperature is lowered, the GSA follows
the ensemble average of the exact solution better than the classical spectral
function. In the low-temperature strong-coupling regime, the qualitative
features of the exact result are best captured by our real-time FRG
calculation, with quantitative improvements to be expected at higher truncation
orders.
|
2112.12568v3
|
2022-01-03
|
Exact scalar (quasi-)normal modes of black holes and solitons in gauged SUGRA
|
In this paper we identify a new family of black holes and solitons that lead
to the exact integration of scalar probes, even in the presence of a
non-minimal coupling with the Ricci scalar which has a non-trivial profile. The
backgrounds are planar and spherical black holes as well as solitons of
$SU\left( 2\right) \times SU\left( 2\right) $ $\mathcal{N}=4$ gauged
supergravity in four dimensions. On these geometries, we compute the spectrum
of (quasi-)normal modes for the non-minimally coupled scalar field. We find
that the equation for the radial dependence can be integrated in terms of
hypergeometric functions leading to an exact expression for the frequencies.
The solutions do not asymptote to a constant curvature spacetime, nevertheless
the asymptotic region acquires an extra conformal Killing vector. For the black
hole, the scalar probe is purely ingoing at the horizon, and requiring that the
solutions lead to an extremum of the action principle we impose a Dirichlet
boundary condition at infinity. Surprisingly, the quasinormal modes do not
depend on the radius of the black hole, therefore this family of geometries can
be interpreted as isospectral in what regards to the wave operator
non-minimally coupled to the Ricci scalar. We find both purely damped modes, as
well as exponentially growing unstable modes depending on the values of the
non-minimal coupling parameter. For the solitons we show that the same
integrability property is achieved separately in a non-supersymmetric solutions
as well as for the supersymmetric one. Imposing regularity at the origin and a
well defined extremum for the action principle we obtain the spectra that can
also lead to purely oscillatory modes as well as to unstable scalar probes,
depending on the values of the non-minimal coupling.
|
2201.00438v1
|
2022-06-02
|
Axion dark matter from frictional misalignment
|
We study the impact of sphaleron-induced thermal friction on the axion
dark-matter abundance due to the interaction of an axion-like particle (ALP)
with a dark non-abelian gauge sector in a secluded thermal bath. Thermal
friction can either enhance the axion relic density by delaying the onset of
oscillations or suppress it by damping them. We derive an analytical formula
for the \emph{frictional adiabatic invariant}, which remains constant along the
axion evolution and which allows us to compute the axion relic density in a
general set-up. Even in the most minimal scenario, in which a single gauge
group is responsible for both the generation of the ALP mass and the friction
force, we find that the resulting dark-matter abundance from the misalignment
mechanism deviates from the standard scenario for axion masses $m_a\gtrsim 100
\; {\rm eV}$. We also generalize our analysis to the case where the gauge field
that induces friction and the gauge sector responsible for the ALP mass are
distinct and their couplings to the axion have a large hierarchy as can be
justified by means of alignment or clockwork scenarios. We find that it is easy
to open up the ALP parameter space where the resulting axion abundance matches
the observed dark-matter relic density both in the traditionally over- and
underabundant regimes. This conclusion also holds for the QCD axion.
|
2206.01129v3
|
2022-06-11
|
Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
|
We report on the results of 23Na NMR in the honeycomb lattice magnet
Na2Co2TeO6 which has been nominated as a Kitaev material. Measurements of
magnetic shift and width of the NMR line as functions of temperature and
magnetic field show that a spin-disordered phase does not appear up to a field
of 9 T. In the antiferromagnetic phase just below the Neel temperature TN, we
find a temperature region extending down to ~TN/2 where the nuclear
spin-lattice relaxation rate 1/T1 remains enhanced and is further increased by
a magnetic field. This region crosses over to a low temperature region
characterized by the rapidly decreasing 1/T1 which is less field-sensitive.
These observations suggest incoherent spin excitations with a large spectral
weight at low energies in the intermediate temperature region transforming to
more conventional spin-wave excitations at low temperatures. The drastic change
of the low-energy spin dynamics is likely caused by strong damping of spin
waves activated only in the intermediate temperature region, which may be
realized for triple-q magnetic order possessing partially-disordered moments as
scattering centers of spin waves. In the paramagnetic phase near TN, dramatic
field suppression of 1/T1 is observed. From analysis of the temperature
dependence of 1/T1 based on the renormalized-classical description of a
two-dimensional quantum antiferromagnet, we find the field-dependent spin
stiffness constant that scales with TN as a function of magnetic field. This
implies field suppression of the energy scale characterizing both
two-dimensional spin correlations and three-dimensional long-range order, which
may be associated with an increasing effect of frustration in magnetic fields.
|
2206.05409v3
|
2022-07-05
|
Emergence of a new HI 21-cm absorption component at z~1.1726 towards the gamma-ray blazar PKS~2355-106
|
We report the emergence of a new HI 21-cm absorption at z_abs = 1.172635 in
the damped Lyman-alpha absorber (DLA) towards the gamma-ray blazar PKS 2355-106
(z_em~1.639) using science verification observations (June 2020) from the
MeerKAT Absorption Line Survey (MALS). Since 2006, this DLA is known to show a
narrow HI 21-cm absorption at z_abs = 1.173019 coinciding with a distinct metal
absorption line component. We do not detect significant HI 21-cm optical depth
variations from this known HI component. A high resolution optical spectrum
(August 2010) shows a distinct Mg I absorption at the redshift of the new HI
21-cm absorber. However, this component is not evident in the profiles of
singly ionized species. We measure the metallicity ([Zn/H] = -(0.77\pm0.11) and
[Si/H]= -(0.96\pm0.11)) and depletion ([Fe/Zn] = -(0.63\pm0.16)) for the full
system. Using the apparent column density profiles of Si II, Fe II and Mg I we
show that the depletion and the N(Mg I)/N(Si II) column density ratio
systematically vary across the velocity range. The region with high depletion
tends to have slightly larger N(Mg I)/N(Si II) ratio. The two HI 21-cm
absorbers belong to this velocity range. The emergence of z_abs = 1.172635 can
be understood if there is a large optical depth gradient over a length scale of
~0.35 pc. However, the gas producing the z_abs = 1.173019 component must be
nearly uniform over the same scale. Systematic uncertainties introduced by the
absorption line variability has to be accounted for in experiments measuring
the variations of fundamental constants and cosmic acceleration even when the
radio emission is apparently compact as in PKS 2355-106.
|
2207.01807v1
|
2022-07-29
|
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum
|
We consider the initial-boundary value problem (IBVP) for the isentropic
compressible Navier-Stokes equations (\textbf{CNS}) in the domain exterior to a
ball in $\mathbb R^d$ $(d=2\ \text{or} \ 3)$. When viscosity coefficients are
given as a constant multiple of the mass density $\rho$, based on some analysis
of the nonlinear structure of this system, we prove the global existence of the
unique spherically symmetric classical solution for (large) initial data with
spherical symmetry and far field vacuum in some inhomogeneous Sobolev spaces.
Moreover, the solutions we obtained have the conserved total mass and finite
total energy. $\rho$ keeps positive in the domain considered but decays to zero
in the far field, which is consistent with the facts that the total mass is
conserved, and \textbf{CNS} is a model of non-dilute fluids where $\rho$ is
bounded away from the vacuum. To prove the existence, on the one hand, we
consider a well-designed reformulated structure by introducing some new
variables, which, actually, can transfer the degeneracies of the time evolution
and the viscosity to the possible singularity of some special source terms. On
the other hand, it is observed that, for the spherically symmetric flow, the
radial projection of the so-called effective velocity $\boldsymbol{v} =U+\nabla
\varphi(\rho)$ ($U$ is the velocity of the fluid, and $\varphi(\rho)$ is a
function of $\rho$ defined via the shear viscosity coefficient $\mu(\rho)$:
$\varphi'(\rho)=2\mu(\rho)/\rho^2$), verifies a damped transport equation which
provides the possibility to obtain its upper bound. Then combined with the BD
entropy estimates, one can obtain the required uniform a priori estimates of
the solution. It is worth pointing out that the frame work on the
well-posedness theory established here can be applied to the shallow water
equations.
|
2207.14494v1
|
2022-10-13
|
The Planck clusters in the LOFAR sky. III. LoTSS-DR2: Dynamic states and density fluctuations of the intracluster medium
|
The footprint of LoTSS-DR2 covers 309 PSZ2 galaxy clusters, 83 of which host
a radio halo and 26 host a radio relic(s). It provides us an excellent
opportunity to statistically study the properties of extended cluster radio
sources, especially their connection with merging activities. We aim to
quantify cluster dynamic states to investigate their relation with the
occurrence of extended radio sources. We also search for connections between
intracluster medium (ICM) turbulence and nonthermal characteristics of radio
halos in the LoTSS-DR2. We analyzed XMM-Newton and Chandra archival X-ray data
and computed concentration parameters and centroid shifts that indicate the
dynamic states of the clusters. We also performed a power spectral analysis of
the X-ray surface brightness (SB) fluctuations to investigate large-scale
density perturbations and estimate the turbulent velocity dispersion. The power
spectral analysis results in a large scatter density fluctuation amplitude. We
therefore only found a marginal anticorrelation between density fluctuations
and cluster relaxation state, and we did not find a correlation between density
fluctuations and radio halo power. Nevertheless, the injected power for
particle acceleration calculated from turbulent dissipation is correlated with
the radio halo power, where the best-fit unity slope supports the turbulent
(re)acceleration scenario. Two different acceleration models, transit-time
damping and adiabatic stochastic acceleration, cannot be distinguished due to
the large scatter of the estimated turbulent Mach number. We introduced a new
quantity $[kT\cdot Y_X]_{r_\mathrm{RH}}$, which is proportional to the
turbulent acceleration power assuming a constant Mach number. This quantity is
strongly correlated with radio halo power, where the slope is also unity.
|
2210.07284v1
|
2022-11-03
|
Skyrmion Jellyfish in Driven Chiral Magnets
|
Chiral magnets can host topological particles known as skyrmions, which carry
an exactly quantised topological charge $Q=-1$. In the presence of an
oscillating magnetic field ${\bf B}_1(t)$, a single skyrmion embedded in a
ferromagnetic background will start to move with constant velocity ${\bf
v}_{\text{trans}}$. The mechanism behind this motion is similar to the one used
by a jellyfish when it swims through water. We show that the skyrmion's motion
is a universal phenomenon, arising in any magnetic system with translational
modes. By projecting the equation of motion onto the skyrmion's translational
modes and going to quadratic order in ${\bf B}_1(t)$, we obtain an analytical
expression for ${\bf v}_{\text{trans}}$ as a function of the system's linear
response. The linear response and consequently ${\bf v}_{\text{trans}}$ are
influenced by the skyrmion's internal modes and scattering states, as well as
by the ferromagnetic background's Kittel mode. The direction and speed of ${\bf
v}_{\text{trans}}$ can be controlled by changing the polarisation, frequency
and phase of the driving field ${\bf B}_1(t)$. For systems with small Gilbert
damping parameter $\alpha$, we identify two distinct physical mechanisms used
by the skyrmion to move. At low driving frequencies, the skyrmion's motion is
driven by friction, and $v_{\text{trans}}\sim\alpha$, whereas at higher
frequencies above the ferromagnetic gap, the skyrmion moves by magnon emission,
and $v_{\text{trans}}$ becomes independent of $\alpha$.
|
2211.01714v5
|
2022-12-12
|
Modified propagation of gravitational waves from the early radiation era
|
We study the propagation of cosmological gravitational wave (GW) backgrounds
from the early radiation era until the present day in modified theories of
gravity. Comparing to general relativity (GR), we study the effects that
modified gravity parameters, such as the GW friction $\alpha_{\rm M}$ and the
tensor speed excess $\alpha_{\rm T}$, have on the present-day GW spectrum. We
use both the WKB estimate, which provides an analytical description but fails
at superhorizon scales, and numerical simulations that allow us to go beyond
the WKB approximation. We show that a constant $\alpha_{\rm T}$ makes
relatively insignificant changes to the GR solution, especially taking into
account the constraints on its value from GW observations by the LIGO--Virgo
collaboration, while $\alpha_{\rm M}$ can introduce modifications to the
spectral slopes of the GW energy spectrum in the low-frequency regime depending
on the considered time evolution of $\alpha_{\rm M}$. The latter effect is
additional to the damping or growth occurring equally at all scales that can be
predicted by the WKB approximation. In light of the recent observations by
pulsar timing array (PTA) collaborations, and the potential observations by
future detectors such as SKA, LISA, DECIGO, BBO, or ET, we show that, in most
of the cases, constraints cannot be placed on the effects of $\alpha_{\rm M}$
and the initial GW energy density $\mathcal{E}_{\rm GW}^*$ separately, but only
on the combined effects of the two, unless the signal is observed at different
frequency ranges. In particular, we provide some constraints on the combined
effects from the reported PTA observations.
|
2212.06082v3
|
2023-02-01
|
Post-dynamical inspiral phase of common envelope evolution: Binary orbit evolution and angular momentum transport
|
After the companion dynamically plunges through the primary's envelope, the
two cores remain surrounded by a common envelope and the decrease of the
orbital period $P_\text{orb}$ stalls. The subsequent evolution has never been
systematically explored with multidimensional simulations. For this study, we
performed 3D hydrodynamical simulations of an envelope evolving under the
influence of a central binary star using an adaptively refined spherical grid.
We followed the evolution over hundreds of orbits of the central binary to
characterize the transport of angular momentum by advection, gravitational
torques, turbulence, and viscosity. We find that local advective torques from
the mean flow and Reynolds stresses associated with the turbulent flow dominate
the angular momentum transport, which occurs outward in a disk-like structure
about the orbital plane and inward along the polar axis. Turbulent transport is
less efficient, but can locally significantly damp or enhance the net angular
momentum radial transport and may even reverse its direction. Short-term
variability in the envelope is remarkably similar to circumbinary disks,
including the formation and destruction of lump-like overdensities, which
enhance mass accretion and contribute to the outward transport of eccentricity
generated in the vicinity of the binary. If the accretion onto the binary is
allowed, the orbital decay timescale settles to a nearly constant value
$\tau_\text{b} \sim 10^3$ to $10^4\,P_\text{orb}$, while preventing accretion
leads to a slowly increasing $\tau_\text{b} \sim 10^5\,P_\text{orb}$ at the end
of our simulations. Our results suggest that the post-dynamical orbital
contraction and envelope ejection will slowly continue while the binary is
surrounded by gas and that $\tau_\text{b}$ is often much shorter than the
thermal timescale of the envelope.
|
2302.00691v2
|
2023-04-05
|
Threshold current of field-free perpendicular magnetization switching using anomalous spin-orbit torque
|
Spin-orbit torque (SOT) is a candidate technique in next generation magnetic
random-access memory (MRAM). Recently, experiments show that some material with
low-symmetric crystalline or magnetic structures can generate anomalous SOT
that has an out-of-plane component, which is crucial in switching perpendicular
magnetization of adjacent ferromagnetic (FM) layer in the field-free condition.
In this work, we analytically derive the threshold current of field-free
perpendicular magnetization switching using the anomalous SOT. And we
numerically calculate the track of the magnetic moment in a FM free layer when
an applied current is smaller and greater than the threshold current. After
that, we study the applied current dependence of the switching time and the
switching energy consumption, which shows the minimum energy consumption
decreases as out-of-plane torque proportion increases. Then we study the
dependences of the threshold current on anisotropy strength, out-of-plane
torque proportion, FM free layer thickness and Gilbert damping constant, and
the threshold current shows negative correlation with the out-of-plane torque
proportion and positive correlation with the other three parameters. Finally,
we demonstrate that when the applied current is smaller than the threshold
current, although it cannot switch the magnetization of FM free layer, it can
still equivalently add an effective exchange bias field H_{bias} on the FM free
layer. The H_{bias} is proportional to the applied current J_{SOT}, which
facilitates the determination of the anomalous SOT efficiency. This work helps
us to design new spintronic devices that favor field-free switching
perpendicular magnetization using the anomalous SOT, and provides a way to
adjust the exchange bias field, which is helpful in controlling FM layer
magnetization depinning.
|
2304.02248v2
|
2023-04-24
|
Magnetic levitation by rotation
|
A permanent magnet can be levitated simply by placing it in the vicinity of
another permanent magnet that rotates in the order of 200 Hz. This surprising
effect can be easily reproduced in the lab with off-the-shelf components. Here
we investigate this novel type of magnetic levitation experimentally and
clarify the underlying physics. Using a 19 mm diameter spherical NdFeB magnet
as rotor magnet, we capture the detailed motion of levitating, spherical NdFeB
magnets, denoted floater magnets. We find that as levitation occurs, the
floater magnet frequency-locks with the rotor magnet, and, noticeably, that the
magnetization of the floater is oriented close to the axis of rotation and
towards the like pole of the rotor magnet. This is in contrast to what might be
expected by the laws of magnetostatics as the floater is observed to align its
magnetization essentially perpendicular to the magnetic field of the rotor.
Moreover, we find that the size of the floater has a clear influence on the
levitation: the smaller the floater, the higher the rotor speed necessary to
achieve levitation, and the further away the levitation point shifts. We verify
that magnetostatic interactions between the rotating magnets are responsible
for creating the equilibrium position of the floater. Hence, this type of
magnetic levitation does not rely on gravity as a balancing force to achieve an
equilibrium position. Based on theoretical arguments and a numerical model, we
show that a constant, vertical field and eddy-current enhanced damping is
sufficient to produce levitation from rest. This enables a gyroscopically
stabilised counter-intuitive steady-state moment orientation, and the resulting
magnetostatically stable, mid-air equilibrium point. The numerical model
display the same trends with respect to rotation speed and the floater magnet
size as seen in the experiments.
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2305.00812v3
|
2023-07-26
|
Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-accelerated Computer Architectures
|
We present the development and implementation of the relativistic coupled
cluster linear response theory (CC-LR) which allows the determination of
molecular properties arising from time-dependent or time-independent electric,
magnetic, or mixed electric-magnetic perturbations (within a common gauge
origin), and take into account the finite lifetime of excited states via damped
response theory. We showcase our implementation, which is capable to offload
intensive tensor contractions onto graphical processing units (GPUs), in the
calculation of: \textit{(a)} frequency-(in)dependent dipole-dipole
polarizabilities of IIB atoms and selected diatomic molecules, with a emphasis
on the calculation of valence absorption cross-sections for the I$_2$
molecule;\textit{(b)} indirect spin-spin coupling constants for benchmark
systems such as the hydrogen halides (HX, X = F-I) as well the H$_2$Se-H$_2$O
dimer as a prototypical system containing hydrogen bonds; and \textit{(c)}
optical rotations at the sodium D line for hydrogen peroxide analogues
(H$_{2}$Y$_{2}$, Y=O, S, Se, Te). Thanks to this implementation, we are able
show the similarities in performance--but often the significant
discrepancies--between CC-LR and approximate methods such as density functional
theory (DFT). Comparing standard CC response theory with the equation of motion
formalism, we find that, for valence properties such as polarizabilities, the
two frameworks yield very similar results across the periodic table as found
elsewhere in the literature; for properties that probe the core region such as
spin-spin couplings, we show a progressive differentiation between the two as
relativistic effects become more important. Our results also suggest that as
one goes down the periodic table it may become increasingly difficult to
measure pure optical rotation at the sodium D line, due to the appearance of
absorbing states.
|
2307.14296v2
|
2023-09-22
|
Challenges in Quasinormal Mode Extraction: Perspectives from Numerical solutions to the Teukolsky Equation
|
The intricacies of black hole ringdown analysis are amplified by the absence
of a complete set of orthogonal basis functions for quasinormal modes. Although
damped sinusoids effectively fit the ringdown signals from binary black hole
mergers, the risk of overfitting remains, due to initial transients and
nonlinear effects. In light of this challenge, we introduce two methods for
extracting quasinormal modes in numerical simulations and qualitatively study
how the transient might affect quasinormal mode fitting. In one method, we
accurately fit quasinormal modes by using their spatial functional form at
constant time hypersurfaces, while in the other method, we exploit both spatial
and temporal aspects of the quasinormal modes. Both fitting methods leverage
the spatial behavior of quasinormal eigenfunctions to enhance accuracy,
outperforming conventional time-only fitting techniques at null infinity. We
also show that we can construct an inner product for which the quasinormal
eigenfunctions form an orthonormal (but not complete) set. We then conduct
numerical experiments involving linearly perturbed Kerr black holes in horizon
penetrating, hyperboloidally compactified coordinates, as this setup enables a
more precise isolation and examination of the ringdown phenomenon. From
solutions to the Teukolsky equation, describing scattering of an ingoing
gravitational wave pulse, we find that the contributions from early-time
transients can lead to large uncertainties in the fit to the amplitudes of
higher overtones ($n\geq 3$). While the methods we discuss here cannot be
applied directly to data from merger observations, our findings underscore the
persistence of ambiguities in interpreting ringdown signals, even with access
to both temporal and spatial information.
|
2309.13204v3
|
2023-09-25
|
Influence of density and viscosity on deformation, breakage, and coalescence of bubbles in turbulence
|
We investigate the effect of density and viscosity differences on a swarm of
large and deformable bubbles dispersed in a turbulent channel flow. For a given
shear Reynolds number, Re=300, and a constant bubble volume fraction, Phi=5.4%,
we perform a campaign of direct numerical simulations of turbulence coupled
with a phase-field method accounting for interfacial phenomena. For each
simulation, we vary the Weber number (We, ratio of inertial to surface tension
forces), the density ratio (r, ratio of bubble density to carrier flow density)
and the viscosity ratio (e, ratio of bubble viscosity to carrier flow
viscosity). Specifically, we consider two Weber numbers, We=1.50 and We=3.00,
four density ratios, from r=1 down to r=0.001, and five viscosity ratios, from
e=0.01 up to e=100. Our results show that density differences have a negligible
effect on breakage and coalescence phenomena, while a much stronger effect is
observed when changing the viscosity of the two phases. Increasing the bubble
viscosity with respect to the carrier fluid viscosity damps turbulence
fluctuations, makes the bubble more rigid, and strongly prevents large
deformations, thus reducing the number of breakage events. Local deformations
of the interface, on the contrary, depend on both density and viscosity ratios.
The opposite effect is observed for increasing bubble viscosities. We report
that these effects are mostly visible for larger Weber numbers, where surface
forces are weaker. Finally, we characterize the flow inside the bubbles; as the
bubble density is increased, we observe, as expected, an increase in the
turbulent kinetic energy (TKE) inside the bubble, while as the bubble viscosity
is increased, we observe a mild reduction of the TKE inside the bubble and a
strong suppression of turbulence.
|
2309.13995v1
|
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