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2004-03-16
|
The SDSS Damped Lya Survey: Data Release 1
|
We present the results from an automated search for damped Lya (DLA) systems
in the quasar spectra of Data Release 1 from the Sloan Digital Sky Survey
(SDSS-DR1). At z~2.5, this homogeneous dataset has greater statistical
significance than the previous two decades of research. We derive a statistical
sample of 71 damped Lya systems (>50 previously unpublished) at z>2.1 and
measure HI column densities directly from the SDSS spectra. The number of DLA
systems per unit redshift is consistent with previous measurements and we
expect our survey has >95% completeness. We examine the cosmological baryonic
mass density of neutral gas Omega_g inferred from the damped Lya systems from
the SDSS-DR1 survey and a combined sample drawn from the literature. Contrary
to previous results, the Omega_g values do not require a significant correction
from Lyman limit systems at any redshift. We also find that the Omega_g values
for the SDSS-DR1 sample do not decline at high redshift and the combined sample
shows a (statistically insignificant) decrease only at z>4. Future data
releases from SDSS will provide the definitive survey of DLA systems at z~2.5
and will significantly reduce the uncertainty in Omega_g at higher redshift.
|
0403391v2
|
2006-06-28
|
Neutral gas density in Damped Lyman Alpha systems
|
We estimate the intrinsic neutral gas density in Damped Lyman Alpha systems
($\Omega_{HI}^{(DLA)}$) in the redshift range $ 2.2 \lesssim z \lesssim 5$ from
the DLA SDSS DR_3 sample of optically selected quasars. We take into account
self-consistently the obscuration on background quasars due to the dust present
in Damped Lyman Alpha systems. We model the column density and redshift
distribution of these systems by using both a non-parametric and a parametric
approach. Under conservative assumptions on the dust content of Damped Lyman
$\alpha$ systems, we show that selection effects lead to underestimating the
intrinsic neutral gas density by at least $15\%$ with respect to the observed
neutral gas density. Over the redshift range $[2.2;5.5]$ we find
$\Omega_{HI}^{(DLA)}=0.97^{+0.08+0.28}_{-0.06-0.15} \cdot 10^{-3}$, where the
first set of error bars gives the $1\sigma$ random errors and the second set
gives the modeling uncertainty dependent on the fraction of metals in dust -
from 0\% to 50\%. This value compares with
$\Omega_{HI}^{(DLA)}=0.82^{+0.05}_{-0.05}$ ($1\sigma$ error bars), which is
obtained when no correction for dust is introduced. In the model with half of
the metals mass in dust we cannot constraint $\Omega_{HI}^{(DLA)}$ at a
confidence level higher than $90\%$. In this case there is indeed a probability
of about $10\%$ that the intrinsic column density distribution of DLA systems
is a power law $f(N_{HI}) \propto 1/N_{HI}^{~1.95}$. In contrast, with $25 \%$
of the metals in dust - the most realistic estimate - a power law is ruled out
at $99.5\%$ of confidence level.
|
0606693v1
|
2006-09-06
|
Sun-as-a-star observations: evidence for degree dependence of changes in damping of low-l p modes along the solar cycle
|
We use 9.5-yr of BiSON Sun-as-a-star data to search for dependence of
solar-cycle parameter changes on the angular degree, l, of the data. The nature
of the Sun-as-a-star observations is such that for changes measured at fixed
frequency, or for changes averaged across the same range in frequency, any l
dependence present carries information on the latitudinal distribution of the
agent (i.e., the activity) responsible for those changes. We split the 9.5-yr
timeseries into contiguous 108-d pieces, and determine mean changes in the
damping of, power in, and energy supplied to the modes through the solar cycle.
We also apply a careful correction to account for the deleterious effects of
the ground-based BiSON window function on the results. From our full analysis
we obtain a marginally significant result for the damping parameter, where the
mean change is found to be weakest at l=0. The other parameters show hints of
some dependence in l. Our main conclusion is that the mean fractional
solar-cycle change in the l=0 damping rates is approximately 50 % smaller than
was previously assumed. It had been common practice to use an average over all
low-l modes; our downward revision of the radial-mode value has implications
for comparisons with models of the global solar cycle changes, which are
usually based on a spherically symmetric geometry.
|
0609156v2
|
1997-08-12
|
Coherence in the Quasi-Particle 'Scattering' by the Vortex Lattice in Pure Type-II Superconductors
|
The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the
de-Haas van-Alphen oscillations in a pure type-II superconductor is
investigated within mean field,asymptotic perturbation theory. Using a 2D
electron gas model it is shown that, due to a strict phase coherence in the
many-particle correlation functions, the 'scattering' effect in the asymptotic
limit ($\sqrt{E_F/\hbar\omega_c}\gg 1$) is much weaker than what is predicted
by the random vortex lattice model proposed by Maki and Stephen, which destroys
this coherence . The coherent many particle configuration is a collinear array
of many particle coordinates, localized within a spatial region with size of
the order of the magnetic length. The amplitude of the magnetization
oscillations is sharply damped just below $% H_{c2}$ because of strong
$180^{\circ}$ out of phase magnetic oscillations in the superconducting
condensation energy ,which tend to cancel the normal electron oscillations.
Within the ideal 2D model used it is found, however, that because of the
relative smallness of the quartic and higher order terms in the expansion, the
oscillations amplitude at lower fields does not really damp to zero, but only
reverses sign and remains virtually undamped well below $H_{c2}$. This
conclusion may be changed if disorder in the vortex lattice, or vortex lines
motion will be taken into account. The reduced QP 'scattering' effect may be
responsible for the apparent crossover from a strong damping of the dHvA
oscillations just below $H_{c2}$ to a weaker damping at lower fields observed
experimentally in several 3D superconductors.
|
9708088v1
|
1999-08-27
|
Electron Correlations in an Electron Bilayer at Finite Temperature: Landau Damping of the Acoustic Plasmon
|
We report angle-resolved Raman scattering observations of the temperature
dependent Landau damping of the acoustic plasmon in an electron bilayer system
realised in a GaAs double quantum well structure. Corresponding calculations of
the charge-density excitation spectrum of the electron bilayer using forms of
the random phase approximation (RPA), and the static local field formalism of
Singwi, Tosi, Land and Sj\"{o}lander (STLS) extended to incorporate non-zero
electron temperature $T_{\rm e}$ and phenomenological damping, are also
presented. The STLS calculations include details of the temperature dependence
of the intra- and inter-layer local field factors and pair-correlation
functions. Good agreement between experiment and the various theories is
obtained for the acoustic plasmon energy and damping for $T_{\rm e} \lesssim
T_{\rm F}/2$, the Fermi temperature. However, contrary to current expectations,
all of the calculations show significant departures from our experimental data
for $T_{\rm e} \gtrsim T_{\rm F}/2$. From this, we go on to demonstrate
unambiguously that real local field factors fail to provide a physically
accurate description of exchange correlation behaviour in low dimensional
electron gases. Our results suggest instead that one must resort to a
{\em{dynamical}} local field theory, characterised by a {\em{complex}} field
factor to provide a more accurate description.
|
9908408v1
|
2000-10-02
|
Comment on "Magnetic Breakdown at High Fields: Semiclassical and Quantum Treatments"
|
We comment on the study of the spin-damping factor on the de Haas-van Alphen
(dHvA) discussed by Han et al. (Phys. Rev. Lett. 85, 1500 (2000)).
|
0010018v1
|
2002-03-11
|
Shubnikov - de Haas effect in the quantum vortex liquid state of the organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$
|
We report the Shubnikov-de Haas (SdH) oscillations observed in the vortex
liquid state of the quasi two dimensional organic superconductor
$\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$. The SdH oscillations can be observed
down to about 5 T at 0.5 K, where the flux flow resistivity becomes as small as
about 30 % of the normal state value. Below the upper critical field $H_{\rm
c2}$ of about 7 T, the additional damping of the SdH oscillation amplitude
appears, as well as that of the de Haas-van Alphen (dHvA) oscillations, with
respect to the normal state one which is described with the standard
Lifshitz-Kosevich formula. The magnitude of the additional damping near $H_{\rm
c2}$ is the same with that observed in the dHvA oscillations and well explained
by the theoretical predictions in consideration of fluctuations in the thermal
vortex liquid state. In the quantum fluctuation region at lower temperature,
however, only SdH effect shows the stronger damping than that of the dHvA
oscillations. The different magnetic field dependence of the additional damping
of the oscillation amplitude between the SdH and dHvA effects is discussed in
connection with the effect of the transport current on the short-range order of
vortices in the quantum vortex slush state reported at the same temperature and
magnetic field region.
|
0203228v2
|
2004-09-03
|
Weyl equation for temperature fields induced by attosecond laser pulses
|
In this paper the Weyl equation for temperature field induced by laser beam
interaction with matter is proposed and solved. Depending on the scattering
mechanism the temperature field oscillate or is damped.
Key words: Thermal processes, Weyl equation
|
0409076v1
|
2004-12-08
|
Spectroscopy of a driven solid-state qubit coupled to a structured environment
|
We study the asymptotic dynamics of a driven spin-boson system where the
environment is formed by a broadened localized mode. Upon exploiting an exact
mapping, an equivalent formulation of the problem in terms of a quantum
two-state system (qubit) coupled to a harmonic oscillator which is itself
Ohmically damped, is found. We calculate the asymptotic population difference
of the two states in two complementary parameter regimes. For weak damping and
low temperature, a perturbative Floquet-Born-Markovian master equation for the
qubit-oscillator system can be solved. We find multi-photon resonances
corresponding to transitions in the coupled quantum system and calculate their
line-shape analytically. In the complementary parameter regime of strong
damping and/or high temperatures, non-perturbative real-time path integral
techniques yield analytic results for the resonance line shape. In both
regimes, we find very good agreement with exact results obtained from a
numerical real-time path-integral approach. Finally, we show for the case of
strong detuning between qubit and oscillator that the width of the $n$-photon
resonance scales with the $n$-th Bessel function of the driving strength in the
weak-damping regime.
|
0412194v2
|
1995-03-08
|
A NEW NUMERICAL APPROACH TO THE OSCILLATION MODES OF RELATIVISTIC STARS
|
The oscillation modes of a simple polytropic stellar model are studied. Using
a new numerical approach (based on integration for complex coordinates) to the
problem for the stellar exterior we have computed the eigenfrequencies of the
highly damped w-modes. The results obtained agree well with recent ones of
Leins, Nollert and Soffel (1993) Specifically, we are able to explain why
several modes in this regime of the complex frequency plane could not be
identified within the WKB approach of Kokkotas and Schutz (1992). Furthermore,
we have established that the ``kink'' that was a prominent feature of the
spectra of Kokkotas and Schutz, but did not appear in the results of Leins {\em
et al.}, was a numerical artefact. Using our new numerical code we are also
able to compute, for the first time, several of the slowly damped (p) modes for
the considered stellar models. For very compact stars we find, somewhat
surprisingly, that the damping of these modes does not decrease monotonically
as one proceeds to higher oscillation frequencies. The existence of low-order
modes that damp away much faster than anticipated may have implications for
questions regarding stellar stability and the lifetime of gravitational-wave
sources. The present results illustrate the accuracy and reliability of the
complex-coordinate method and indicate that the method could prove to be of
great use also in problems involving rotating stars. There is no apparent
reason why the complex-coordinate approach should not extend to rotating stars,
whereas it is accepted that all previous methods will fail to do so.
|
9503014v1
|
1998-01-29
|
On the gravitational, dilatonic and axionic radiative damping of cosmic strings
|
We study the radiation reaction on cosmic strings due to the emission of
dilatonic, gravitational and axionic waves. After verifying the (on average)
conservative nature of the time-symmetric self-interactions, we concentrate on
the finite radiation damping force associated with the half-retarded minus
half-advanced ``reactive'' fields. We revisit a recent proposal of using a
``local back reaction approximation'' for the reactive fields. Using
dimensional continuation as convenient technical tool, we find, contrary to
previous claims, that this proposal leads to antidamping in the case of the
axionic field, and to zero (integrated) damping in the case of the
gravitational field. One gets normal positive damping only in the case of the
dilatonic field. We propose to use a suitably modified version of the local
dilatonic radiation reaction as a substitute for the exact (non-local)
gravitational radiation reaction. The incorporation of such a local
approximation to gravitational radiation reaction should allow one to complete,
in a computationally non-intensive way, string network simulations and to give
better estimates of the amount and spectrum of gravitational radiation emitted
by a cosmologically evolving network of massive strings.
|
9801105v3
|
2004-10-15
|
A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars II. Dynamics
|
Two mechanisms for nonlinear mode saturation of the r-mode in neutron stars
have been suggested: the parametric instability mechanism involving a small
number of modes and the formation of a nearly continuous Kolmogorov-type
cascade. Using a network of oscillators constructed from the eigenmodes of a
perfect fluid incompressible star, we investigate the transition between the
two regimes numerically. Our network includes the 4995 inertial modes up to n<=
30 with 146,998 direct couplings to the r-mode and 1,306,999 couplings with
detuning< 0.002 (out of a total of approximately 10^9 possible couplings).
The lowest parametric instability thresholds for a range of temperatures are
calculated and it is found that the r-mode becomes unstable to modes with
13<n<15. In the undriven, undamped, Hamiltonian version of the network the rate
to achieve equipartition is found to be amplitude dependent, reminiscent of the
Fermi-Pasta-Ulam problem. More realistic models driven unstable by
gravitational radiation and damped by shear viscosity are explored next. A
range of damping rates, corresponding to temperatures 10^6K to 10^9K, is
considered. Exponential growth of the r-mode is found to cease at small
amplitudes, approximately 10^-4. For strongly damped, low temperature models, a
few modes dominate the dynamics. The behavior of the r-mode is complicated, but
its amplitude is still no larger than about 10^-4 on average. For high
temperature, weakly damped models the r-mode feeds energy into a sea of
oscillators that achieve approximate equipartition. In this case the r-mode
amplitude settles to a value for which the rate to achieve equipartition is
approximately the linear instability growth rate.
|
0410072v1
|
1997-02-20
|
Numerical study of plasmon properties in the SU(2)-Higgs model
|
Using the (effective) classical approximation, we compute numerically
time-dependent correlation functions in the SU(2)-Higgs model around the
electroweak phase transition, for $m_H \approx m_W$. The parameters of the
classical model have been determined previously by the dimensional reduction
relations for time-independent correlators. The $H$ and $W$ correlation
functions correspond to gauge invariant fields. They show damped oscillatory
behavior from which we extract frequencies $\om$ and damping rates $\gm$. In
the Higgs phase the damping rates have roughly the values obtained in analytic
calculations in the quantum theory. In the plasma phase (where analytic
estimates for gauge invariant fields are not available), the damping rate
associated with $H$ is an order of magnitude larger than in the Higgs phase,
while the $W$ correlator appears to be overdamped, with a small rate. The
frequency $\om_H$ shows a clear dip at the transition. The results are
approximately independent of the lattice spacing, but this appears to be
compatible with the lattice spacing dependence expected from perturbation
theory.
|
9702017v2
|
2003-12-15
|
Nonequilibrium pion dynamics near the critical point in a constituent quark model
|
We study static and dynamical critical phenomena of chiral symmetry breaking
in a two-flavor Nambu--Jona-Lasinio constituent quark model. We obtain the
low-energy effective action for scalar and pseudoscalar degrees of freedom to
lowest order in quark loops and to quadratic order in the meson fluctuations
around the mean field. The \emph{static} limit of critical phenomena is shown
to be described by a Ginzburg-Landau effective action including \emph{spatial}
gradients. Hence \emph{static} critical phenomena is described by the
universality class of the O(4) Heisenberg ferromagnet. \emph{Dynamical}
critical phenomena is studied by obtaining the equations of motion for pion
fluctuations. We find that for $T<T_c$ the are stable long-wavelength pion
excitations with dispersion relation $\omega_{\pi}(k)=k$ described by isolated
pion poles. The residue of the pion pole vanishes near $T_c$ as $Z \propto
1/|\ln(1-T/T_c)|$ and long-wavelength fluctuations are damped out by Landau
damping on a time scale $t_\mathrm{rel}(k)\propto 1/k$, reflecting
\emph{critical slowing down} of pion fluctuations near the critical point. At
the critical point, the pion propagator features mass shell logarithmic
divergences which we conjecture to be the harbinger of a (large) dynamical
anomalous dimension. We find that while the \emph{classical spinodal} line
coincides with that of the Ginzburg-Landau theory, the growth rate of
long-wavelength spinodal fluctuations has a richer wavelength dependence as a
consequence of Landau damping. We argue that Landau damping prevents a
\emph{local} low energy effective action in terms of a derivative expansion in
real time.
|
0312185v2
|
2001-11-16
|
Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves
|
We investigate the role weakly damped modes play in the selection of Faraday
wave patterns forced with rationally-related frequency components m*omega and
n*omega. We use symmetry considerations to argue for the special importance of
the weakly damped modes oscillating with twice the frequency of the critical
mode, and those oscillating primarily with the "difference frequency"
|n-m|*omega and the "sum frequency" (n+m)*omega. We then perform a weakly
nonlinear analysis using equations of Zhang and Vinals (1997, J. Fluid Mech.
336) which apply to small-amplitude waves on weakly inviscid, semi-infinite
fluid layers. For weak damping and forcing and one-dimensional waves, we
perform a perturbation expansion through fourth order which yields analytical
expressions for onset parameters and the cubic bifurcation coefficient that
determines wave amplitude as a function of forcing near onset. For stronger
damping and forcing we numerically compute these same parameters, as well as
the cubic cross-coupling coefficient for competing waves travelling at an angle
theta relative to each other. The resonance effects predicted by symmetry are
borne out in the perturbation results for one spatial dimension, and are
supported by the numerical results in two dimensions. The difference frequency
resonance plays a key role in stabilizing superlattice patterns of the SL-I
type observed by Kudrolli, Pier and Gollub (1998, Physica D 123).
|
0111039v2
|
2002-02-01
|
Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with Applications to Multitone Interaction in Hearing
|
A nonlinear nonlocal cochlear model of the transmission line type is studied
in order to capture the multitone interactions and resulting tonal suppression
effects. The model can serve as a module for voice signal processing, it is a
one dimensional (in space) damped dispersive nonlinear PDE based on mechanics
and phenomenology of hearing. It describes the motion of basilar membrane (BM)
in the cochlea driven by input pressure waves. Both elastic damping and
selective longitudinal fluid damping are present. The former is nonlinear and
nonlocal in BM displacement, and plays a key role in capturing tonal
interactions. The latter is active only near the exit boundary (helicotrema),
and is built in to damp out the remaining long waves. The initial boundary
value problem is numerically solved with a semi-implicit second order finite
difference method. Solutions reach a multi-frequency quasi-steady state.
Numerical results are shown on two tone suppression from both high-frequency
and low-frequency sides, consistent with known behavior of two tone
suppression. Suppression effects among three tones are demonstrated by showing
how the response magnitudes of the fixed two tones are reduced as we vary the
third tone in frequency and amplitude. We observe qualitative agreement of our
model solutions with existing cat auditory neural data. The model is thus
simple and efficient as a processing tool for voice signals.
|
0202004v3
|
2003-12-22
|
Intermittency is a consequence of turbulent transport in nonlinear systems
|
Intermittent high-amplitude structures emerge in a damped and driven discrete
nonlinear Schroedinger equation whose solutions transport both energy and
particles from sources to sinks. These coherent structures are necessary for
any solution that has statistically stationary transport properties.
|
0312059v1
|
2004-06-17
|
Multi-frequency control of Faraday wave patterns
|
We show how pattern formation in Faraday waves may be manipulated by varying
the harmonic content of the periodic forcing function. Our approach relies on
the crucial influence of resonant triad interactions coupling pairs of critical
standing wave modes with damped, spatio-temporally resonant modes. Under the
assumption of weak damping and forcing, we perform a symmetry-based analysis
that reveals the damped modes most relevant for pattern selection, and how the
strength of the corresponding triad interactions depends on the forcing
frequencies, amplitudes, and phases. In many cases, the further assumption of
Hamiltonian structure in the inviscid limit determines whether the given triad
interaction has an enhancing or suppressing effect on related patterns.
Surprisingly, even for forcing functions with arbitrarily many frequency
components, there are at most five frequencies that affect each of the
important triad interactions at leading order. The relative phases of those
forcing components play a key role, sometimes making the difference between an
enhancing and suppressing effect. In numerical examples, we examine the
validity of our results for larger values of the damping and forcing. Finally,
we apply our findings to one-dimensional periodic patterns obtained with
impulsive forcing and to two-dimensional superlattice patterns and
quasipatterns obtained with multi-frequency forcing.
|
0406034v1
|
1997-01-22
|
Shell Model for Warm Rotating Nuclei
|
In order to provide a microscopic description of levels and E2 transitions in
rapidly rotating nuclei with internal excitation energy up to a few MeV, use is
made of a shell model which combines the cranked Nilsson mean-field and the
residual surface delta two-body force. The damping of collective rotational
motion is investigated in the case of a typical rare-earth nucleus, namely \Yb.
It is found that rotational damping sets in at around 0.8 MeV above the yrast
line, and the levels which form rotational band structures are thus limited. We
predict at a given rotational frequency existence of about 30 rotational bands
of various lengths, in overall agreement with the experimental findings. The
onset of the rotational damping proceeds quite gradually as a function of the
internal excitation energy. The transition region extends up to around 2 MeV
above yrast and it is characterized by the presence of scars of discrete
rotational bands which extend over few spin values and stand out among the
damped transitions, and by a two-component profile in the $E_\gamma -E_\gamma$
correlation. The important role played by the high-multipole components of the
two-body residual interaction is emphasized.
|
9701044v1
|
2005-04-21
|
Enhanced optical cooling of particle beams in storage rings
|
The problem of enhanced optical cooling (EOC) of particle beams in storage
rings beyond the Robinson's damping criterion is discussed.
|
0504145v1
|
1999-06-09
|
Quantum dynamics of a damped deformed oscillator
|
The interaction of a quantum deformed oscillator with the environment is
studied deriving a master equation whose form strongly depends on the type of
deformation.
|
9906031v1
|
2007-04-29
|
Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks: Electron-Positron Plasmas
|
We study the long term evolution of magnetic fields generated by a
collisionless relativistic $e^+e^-$ shock which is initially unmagnetized. Our
2D particle-in-cell numerical simulations show that downstream of such a
Weibel-mediated shock, particle distributions are close to isotropic,
relativistic Maxwellians, and the magnetic turbulence is highly intermittent
spatially, with the non-propagating magnetic fields forming relatively isolated
regions with transverse dimension $\sim 10-20$ skin depths. These structures
decay in amplitude, with little sign of downstream merging. The fields start
with magnetic energy density $\sim (0.1-0.2)$ of the upstream kinetic energy
within the shock transition, but rapid downstream decay drives the fields to
much smaller values, below $10^{-3}$ of equipartition after $10^3$ skin depths.
In an attempt to construct a theory that follows field decay to these smaller
values, we explore the hypothesis that the observed damping is a variant of
Landau damping in an unmagnetized plasma. The model is based on the small value
of the downstream magnetic energy density, which suggests that particle orbits
are only weakly perturbed from straight line motion, if the turbulence is
homogeneous. Using linear kinetic theory applied to electromagnetic fields in
an isotropic, relativistic Maxwellian plasma, we find a simple analytic form
for the damping rates, $\gamma_k$, in two and three dimensions for small
amplitude, subluminous electromagnetic fields. We find that magnetic energy
does damp due to phase mixing of current carrying particles as $(\omega_p
t)^{-q}$ with $q \sim 1$. (abridged)
|
0704.3832v2
|
2007-06-21
|
Production of a sterile species via active-sterile mixing: an exactly solvable model
|
The production of a sterile species via active-sterile mixing in a thermal
medium is studied in an exactly solvable model. The \emph{exact} time evolution
of the sterile distribution function is determined by the dispersion relations
and damping rates $\Gamma_{1,2}$ for the quasiparticle modes. These depend on
$\wtg = \Gamma_{aa}/2\Delta E$, with $\Gamma_{aa}$ the interaction rate of the
active species in absence of mixing and $\Delta E$ the oscillation frequency in
the medium without damping. $\wtg \ll1,\wtg \gg 1$ describe the weak and strong
damping limits respectively. For $\wtg\ll1$, $\Gamma_1 = \Gamma_{aa}\cos^2\tm ;
\Gamma_{2}=\Gamma_{aa}\sin^2\tm$ where $\tm$ is the mixing angle in the medium
and the sterile distribution function \emph{does not} obey a simple rate
equation. For $\wtg \gg 1$, $\Gamma_1= \Gamma_{aa}$ and $\Gamma_2 = \Gamma_{aa}
\sin^22\tm/4\wtg^2$, is the sterile production rate. In this regime sterile
production is suppressed and the oscillation frequency \emph{vanishes} at an
MSW resonance, with a breakdown of adiabaticity. These are consequences of
quantum Zeno suppression. For active neutrinos with standard model interactions
the strong damping limit is \emph{only} available near an MSW resonance
\emph{if} $\sin\theta \lesssim \alpha_w$ with $\theta$ the vacuum mixing angle.
The full set of quantum kinetic equations for sterile production for arbitrary
$\wtg$ are obtained from the quantum master equation. Cosmological resonant
sterile neutrino production is quantum Zeno suppressed relieving potential
uncertainties associated with the QCD phase transition.
|
0706.3167v2
|
2007-08-02
|
Eccentricity evolution of giant planet orbits due to circumstellar disk torques
|
The extrasolar planets discovered to date possess unexpected orbital
elements. Most orbit their host stars with larger eccentricities and smaller
semi-major axes than similarly sized planets in our own solar system do. It is
generally agreed that the interaction between giant planets and circumstellar
disks (Type II migration) drives these planets inward to small radii, but the
effect of these same disks on orbital eccentricity, e, is controversial.
Several recent analytic calculations suggest that disk-planet interactions can
excite eccentricity, while numerical studies generally produce eccentricity
damping. This paper addresses this controversy using a quasi-analytic approach,
drawing on several preceding analytic studies. This work refines the current
treatment of eccentricity evolution by removing several approximations from the
calculation of disk torques. We encounter neither uniform damping nor uniform
excitation of orbital eccentricity, but rather a function de/dt that varies in
both sign and magnitude depending on eccentricity and other solar system
properties. Most significantly, we find that for every combination of disk and
planet properties investigated herein, corotation torques produce negative
values of de/dt for some range in e within the interval [0.1, 0.5]. If
corotation torques are saturated, this region of eccentricity damping
disappears, and excitation occurs on a short timescale of less than 0.08 Myr.
Thus, our study does not produce eccentricity excitation on a timescale of a
few Myr -- we obtain either eccentricity excitation on a short time scale, or
eccentricity damping on a longer time scale. Finally, we discuss the
implications of this result for producing the observed range in extrasolar
planet eccentricity.
|
0708.0335v1
|
2007-10-10
|
HE 0515-4414 - an unusual sub-damped Ly alpha system revisited
|
Using STIS and VLT UVES observations we have examined the ionization,
abundances, and differential dust depletion of metals, the kinematic structure,
and the physical conditions in the molecular hydrogen-bearing sub-damped Ly
alpha system toward HE 0515-4414 at z = 1.15. The velocity interval of
associated metal lines extends for 700 km/s. In addition, saturated H I
absorption is detected in the blue damping wing of the main component. The
column density ratios of associated Al II, Al III, and Fe II lines indicate
that the absorbing material is ionized. 19 of in total 31 detected metal line
components are formed within peripheral H II regions, while only 12 components
are associated with the predominantly neutral main absorber. For the main
absorber the observed abundance ratios of refractory elements to Zn range from
Galactic warm disk [Si/Zn] = - 0.40, [Fe/Zn] = -1.10 to halo-like and
essentially undepleted patterns. The dust-corrected metal abundances indicate a
nucleosynthetic odd-even effect and might imply an anomalous depletion of Si
relative to Fe for two components, but otherwise do correspond to solar ratios.
The intrinsic average metallicity is almost solar [Fe/H] = -0.08, whereas the
uncorrected average is [Zn/H] = -0.38. The ion abundances in the periphery
conform with solar element composition. The detection of H II as well as the
large variation in dust depletion for this sight line raises the question
whether in future studies of damped Ly alpha systems ionization and depletion
effects have to be considered in further detail. Ionization effects, for
instance, may pretend an enrichment of alpha elements. An empirical recipe for
detecting H II regions is provided.
|
0710.3560v1
|
2008-06-05
|
Viscous damping of r-mode oscillations in compact stars with quark matter
|
We determine characteristic timescales for the viscous damping of r-mode
oscillations in rapidly rotating compact stars that contain quark matter. We
present results for the color-flavor-locked (CFL) phase of dense quark matter,
in which the up, down and strange quarks are gapped, as well as the normal
(ungapped) quark phase. While the ungapped quark phase supports a temperature
window between 10^8 K and 5x10^9 K where the r-mode is damped even for rapid
rotation, the r-mode in a rapidly rotating pure CFL star is not damped in the
temperature range 10^10 K - 10^11 K. Rotating hybrid stars with quark matter
cores display an instability window whose width is determined by the amount of
quark matter present, and they can have large spin frequencies outside this
window. Except at high temperatures T > 10^10 K, the presence of a quark phase
allows for larger critical frequencies and smaller spin-periods compared to
rotating neutron stars. If low-mass X-ray binaries contain a large amount of
ungapped or CFL quark matter, then our estimates of the r-mode instability
suggest that there should be a population of rapidly rotating binaries at
frequencies greater than 1000 Hz which have not yet been observed.
|
0806.1005v2
|
2008-06-18
|
Imaging method for interface rheological characterization
|
The present work investigates free damped oscillations of an oil drop in
water after its release from a capillary tube. Both pure heptane drops and
diluted crude oil drops are considered (in the second case the interface is
covered by amphiphilic species, natural components of crude oil). Shadowgraph
images of the drops are taken by means of a high speed camera and the drop
contour is detected by image processing. The axisymmetric drop shape is then
decomposed into spherical harmonics, which constitute the eigenmodes of
oscillations predicted by the Rayleigh-Lamb theory. Time evolution of each mode
is then obtained. The frequency and the damping rate of the principal mode
(n=2) are accurately determined and compared with theoretical values for an
immobile clean drop oscillating around spherical shape. For pure heptane drops,
theoretical value of the frequency agrees well with experiments whereas the
damping rate is significantly underestimated by theory. The experimental
results clearly show that the different modes are coupled. Energy is thus
transfered from mode n=2 to n=3, which probably explains the observed
enhancement of the damping rate. The effect of the interface viscoelastic
behaviour, induced by adsorbed amphiphilic species on the free oscillations was
examined. No significant effect was observed in the experiments conditions
(small amplitude oscillations and moderate aging).
|
0806.3030v1
|
2008-06-27
|
Klein - Gordon equation for market wealth operations
|
In this paper the modified Klein - Gordon equation for market processes is
proposed and solved. It is argued that the oscillations in market propagate
with the light velocity. The initial pulse in the market is damped and for very
large time diffused according to the Fourier law.
|
0806.4466v1
|
2008-10-22
|
Mean Motion Resonances in Extrasolar Planetary Systems with Turbulence, Interactions, and Damping
|
This paper continues previous work on the effects of turbulence on mean
motion resonances in extrasolar planetary systems. Turbulence is expected to
arise in the disks that form planets, and these fluctuations act to compromise
resonant configurations. This paper extends previous work by considering how
interactions between the planets and possible damping effects imposed by the
disk affect the outcomes. These physical processes are studied using three
approaches: numerical integrations of the 3-body problem with additional
forcing due to turbulence, model equations that reduce the problem to
stochastically driven oscillators, and Fokker-Planck equations that describe
the time evolution of an ensemble of systems. With this combined approach, we
elucidate the physics of how turbulence can remove extrasolar planetary systems
from mean motion resonance. As expected, systems with sufficiently large
damping (dissipation) can maintain resonance, in spite of turbulent forcing. In
the absence of strong damping, ensembles of these systems exhibit two regimes
of behavior, where the fraction of the bound states decreases as a power-law or
as an exponential. Both types of behavior can be understood through the model
developed herein. For systems with weak interactions between planets, the model
reduces to a stochastic pendulum, and the fraction of bound states decreases as
a power-law. For highly interactive systems, the dynamics are more complicated
and the fraction of bound states decreases exponentially. We show how planetary
interactions lead to drift terms in the Fokker-Planck equation and account for
this exponential behavior. In addition to clarifying the physical processes
involved, this paper strengthens the finding that turbulence implies that mean
motions resonances should be rare.
|
0810.4076v1
|
2009-01-11
|
On the derivation of structural models with general thermomechanical prestress
|
The vibrating behaviour of thin structures is affected by prestress states.
Hence, the effects of thermal prestress are important research subjects in view
of ambient vibration monitoring of civil structures. The interaction between
prestress, geometrically non-linear behaviour, as well as damping and its
coupling with the aforementioned phenomena has to be taken into account for a
comprehensive understanding of the structural behaviour. Since the literature
on this subject lacks a clear procedure to derive models of thin prestressed
and damped structures from 3D continuum mechanics, this paper presents a new
derivation of models for thin structures accounting for generic prestress,
moderate rotations and viscous damping. Although inspired by classical
approaches, the proposed procedure is quite different, because of (i) the
definition of a modified Hu-Washizu (H-W) functional, accounting for stress
constraints associated with Lagrange multipliers, in order to derive
lower-dimensional models in a convenient way; (ii) an original definition of a
(mechanical and thermal) strain measure and a rotation measure enabling one to
identify the main terms in the strain energy and to derive a cascade of
lower-dimensional models (iii) a new definition of "strain-rotation domains"
providing a clear interpretation of the classical assumptions of "small
perturbations" and "small strains and moderate rotations"; (iv) the
introduction of a pseudo-potential with stress constraints to account for
viscous damping. The proposed procedure is applied to thin beams.
|
0901.1446v1
|
2009-04-17
|
On Landau damping
|
Going beyond the linearized study has been a longstanding problem in the
theory of Landau damping. In this paper we establish exponential Landau damping
in analytic regularity. The damping phenomenon is reinterpreted in terms of
transfer of regularity between kinetic and spatial variables, rather than
exchanges of energy; phase mixing is the driving mechanism. The analysis
involves new families of analytic norms, measuring regularity by comparison
with solutions of the free transport equation; new functional inequalities; a
control of nonlinear echoes; sharp scattering estimates; and a Newton
approximation scheme. Our results hold for any potential no more singular than
Coulomb or Newton interaction; the limit cases are included with specific
technical effort. As a side result, the stability of homogeneous equilibria of
the nonlinear Vlasov equation is established under sharp assumptions. We point
out the strong analogy with the KAM theory, and discuss physical implications.
|
0904.2760v5
|
2009-07-27
|
Parameter exploration of optically trapped liquid aerosols
|
When studying the motion of optically trapped particles on the $\mu s$ time
scale, in low viscous media such as air, inertia cannot be neglected.
Resolution of unusual and interesting behaviour not seen in colloidal trapping
experiments is possible. In attempt to explain the phenomena we use power
spectral methods to perform a parameter study of the Brownian motion of
optically trapped liquid aerosol droplets concentrated around the critically
damped regime. We present evidence that the system is suitably described by a
simple harmonic oscillator model which must include a description of
Fax\'{e}n's correction, but not necessarily frequency dependent hydrodynamic
corrections to Stokes' law. We also provide results describing how the system
behaves under several variables and discuss the difficulty in decoupling the
parameters responsible for the observed behaviour. We show that due to the
relatively low dynamic viscosity and high trap stiffness it is easy to transfer
between over- and under-damped motion by experimentally altering either trap
stiffness or damping. Our results suggest stable aerosol trapping may be
achieved in under-damped conditions, but the onset of deleterious optical
forces at high trapping powers prevents the probing of the upper stability
limits due to Brownian motion.
|
0907.4582v2
|
2009-10-09
|
One-way coupled Van der Pol system
|
The equation of the Van der Pol oscillator, being characterized by a
dissipative term, is non-Lagrangian. Appending an additional degree of freedom
we bring the equation in the frame of action principle and thus introduce a
one-way coupled system. As with the Van der Pol oscillator, the coupled system
also involves only one parameter that controls the dynamics. The response
system is described by a linear differential equation coupled nonlinearly to
the drive system. In the linear approximation the equations of our coupled
system coincide with those of the Bateman dual system (a pair of damped and
anti-damped harmonic oscillators). The critical point of damped and anti-damped
oscillators are stable and unstable for all physical values of the frictional
coefficient $\mu$. Contrarily, the critical points of the drive- (Van der Pol)
and response systems depend crucially on the values of $\mu$. These points are
unstable for $\mu > 0$ while the critical point of the drive system is stable
and that of the response system is unstable for $\mu < 0$. The one-way coupled
system exhibits bifurcations which are different from those of the uncoupled
Van der Pol oscillator. Our system is chaotic and we observe phase
synchronization in the regime of dynamic chaos only for small values of $\mu$.
|
0910.1700v1
|
2010-02-17
|
Measurement of Gilbert damping parameters in nanoscale CPP-GMR spin-valves
|
In-situ, device level measurement of thermal mag-noise spectral linewidths in
60nm diameter CPP-GMR spin-valve stacks of IrMn/ref/Cu/free, with reference and
free layer of similar CoFe/CoFeGe alloy, are used to simultaneously determine
the intrinsic Gilbert damping for both magnetic layers. It is shown that
careful alignment at a "magic-angle" between free and reference layer static
equilibrium magnetization can allow direct measurement of the broadband
intrinsic thermal spectra in the virtual absence of spin-torque effects which
otherwise grossly distort the spectral line shapes and require linewidth
extrapolations to zero current (which are nonetheless also shown to agree well
with the direct method). The experimental magic-angle spectra are shown to be
in good qualitative and quantitative agreement with both macrospin calculations
and micromagnetic eigenmode analysis. Despite similar composition and
thickness, it is repeatedly found that the IrMn exchange pinned reference layer
has ten times larger intrinsic Gilbert damping (alpha ~ 0.1) than that of the
free-layer (alpha ~ 0.01). It is argued that the large reference layer damping
results from strong, off -resonant coupling to to lossy modes of an IrMn/ref
couple, rather than commonly invoked two-magnon processes.
|
1002.3295v1
|
2010-06-19
|
On the saturation amplitude of the f-mode instability
|
We investigate strong nonlinear damping effects which occur during high
amplitude oscillations of neutron stars, and the gravitational waves they
produce. For this, we use a general relativistic nonlinear hydrodynamics code
in conjunction with a fixed spacetime (Cowling approximation) and a polytropic
equation of state (EOS). Gravitational waves are estimated using the quadrupole
formula. Our main interest are l=m=2 f modes subject to the CFS (Chandrasekhar,
Friedman, Schutz) instability, but we also investigate axisymmetric and
quasiradial modes. We study various models to determine the influence of
rotation rate and EOS. We find that axisymmetric oscillations at high
amplitudes are predominantly damped by shock formation, while the
nonaxisymmetric f modes are mainly damped by wave breaking and, for rapidly
rotating models, coupling to nonaxisymmetric inertial modes. From the observed
nonlinear damping, we derive upper limits for the saturation amplitude of
CFS-unstable f modes. Finally, we estimate that the corresponding gravitational
waves for an oscillation amplitude at the upper limit should be detectable with
the advanced LIGO and VIRGO interferometers at distances above 10 MPc. This
strongly depends on the stellar model, in particular on the mode frequency.
|
1006.3885v2
|
2010-07-06
|
Magneto-elastic oscillations and the damping of crustal shear modes in magnetars
|
In a realistic model of magneto-elastic oscillations in magnetars, we find
that crustal shear oscillations, often invoked as an explanation of
quasi-periodic oscillations (QPOs) seen after giant flares in soft gamma-ray
repeaters (SGRs), are damped by resonant absorption on timescales of at most
0.2s, for a lower limit on the dipole magnetic field strength of 5 x 10^13 G.
At higher magnetic field strengths (typical in magnetars) the damping timescale
is even shorter, as anticipated by earlier toy-models. We have investigated a
range of equations of state and masses and if magnetars are dominated by a
dipole magnetic field, our findings exclude torsional shear oscillations of the
crust from explaining the observed low-frequency QPOs. In contrast, we find
that the Alfv\'en QPO model is a viable explanation of observed QPOs, if the
dipole magnetic field strength exceeds a minimum strength of about several
times 10^14 G to 10^15 G. Then, Alfv\'en QPOs are no longer confined to the
fluid core, but completely dominate in the crust region and have a maximum
amplitude at the surface of the star.
|
1007.0856v2
|
2010-08-16
|
Orbital evolution of eccentric planets in radiative discs
|
With an average eccentricity of about 0.29, the eccentricity distribution of
extrasolar planets is markedly different from the solar system. Among other
scenarios considered, it has been proposed that eccentricity may grow through
planet-disc interaction. Recently, it has been noticed that the thermodynamical
state of the disc can significantly influence the migration properties of
growing protoplanets. However, the evolution of planetary eccentricity in
radiative discs has not been considered yet. In this paper we study the
evolution of planets on eccentric orbits that are embedded in a
three-dimensional viscous disc and analyse the disc's effect on the orbital
evolution of the planet. We use the three-dimensional hydrodynamical code
NIRVANA that includes full tensor viscosity and implicit radiation transport in
the flux-limited diffusion approximation. The code uses the FARGO-algorithm to
speed up the simulations. First we measure the torque and power exerted on the
planet by the disc for fixed orbits, and then we let the planet start with
initial eccentricity and evolve it in the disc. For locally isothermal we
confirm previous results and find eccentricity damping and inward migration for
planetary cores. In the case of radiative discs, the planets experience an
inward migration as long as its eccentricity lies above a certain threshold.
After the damping of eccentricity cores with masses below 33 Earthmasses begin
to migrate outward in radiative discs, while higher mass cores always migrate
inward. For all planetary masses studied (up to 200 Earthmasses) we find
eccentricity damping. In viscous discs the orbital eccentricity of embedded
planets is damped during the evolution independent of the mass. Hence,
planet-disc interaction does not seem to be a viable mechanism to explain the
observed high eccentricity of exoplanets.
|
1008.2656v1
|
2010-11-02
|
A Carbon-enhanced Metal-poor Damped Lyman alpha System: Probing Gas from Population III Nucleosynthesis?
|
We present high resolution observations of an extremely metal-poor damped
Lyman-alpha system, at z_abs = 2.3400972 in the spectrum of the QSO J0035-0918,
exhibiting an abundance pattern consistent with model predictions for the
supernova yields of Population III stars. Specifically, this DLA has [Fe/H] =
-3.04, shows a clear `odd-even' effect, and is C-rich with [C/Fe] = +1.53, a
factor of about 20 greater than reported in any other damped Lyman-alpha
system. In analogy to the carbon-enhanced metal-poor stars in the Galactic halo
(with [C/Fe] > +1.0), this is the first reported case of a carbon-enhanced
damped Lyman-alpha system. We determine an upper limit to the mass of 12C,
M(12C) < 200 solar masses, which depends on the unknown gas density n(H); if
n(H) > 1 atom per cubic cm (which is quite likely for this DLA given its low
velocity dispersion), then M(12C) < 2 solar masses, consistent with pollution
by only a few prior supernovae. We speculate that DLAs such as the one reported
here may represent the `missing link' between the yields of Pop III stars and
their later incorporation in the class of carbon-enhanced metal-poor stars
which show no enhancement of neutron-capture elements (CEMP-no stars).
|
1011.0733v2
|
2010-11-08
|
Exponential stabilization without geometric control
|
We present examples of exponential stabilization for the damped wave equation
on a compact manifold in situations where the geometric control condition is
not satisfied. This follows from a dynamical argument involving a topological
pressure on a suitable uncontrolled set.
|
1011.1699v1
|
2010-11-11
|
Damping of longitudinal magneto-acoustic oscillations in slowly varying coronal plasma
|
We investigate the propagation of MHD waves in a homogenous, magnetized
plasma in a weakly stratified atmosphere, representing hot coronal loops. In
most of earlier studies a time-independent equilibrium is considered. Here we
abandon this restriction and allow the equilibrium to develop as function of
time. In particular, the background plasma is assumed to be cooling due to
thermal conduction. The cooling is assumed to be on a time scale greater than
the characteristic travel times of the perturbations. We investigate the
influence of cooling of the background plasma on the properties of
magneto-acoustic waves. The MHD equations are reduced to a 1-D system modelling
magneto-acoustic modes progressing along a dynamically cooling coronal loop. A
time dependent dispersion relation which describes the propagation of the
magneto-acoustic waves is derived by using the WKB theory. An analytic solution
for the time-dependent amplitude of waves is obtained and the method of
characteristics is used to find an approximate analytical solution. Numerical
calculations are applied to the analytically derived solutions to obtain
further insight into the behavior of the MHD waves in a system with variable,
time-dependent background. The results show that there is a strong damping of
MHD waves that can be linked to the widely observed damping of hot coronal loop
oscillations. The damping also appears to be independent of position along the
loop. Studies of MHD wave behaviour in time-dependent background seem to be a
fundamental and very important next step in developing MHD wave theory
applicable to a wide range in solar physics.
|
1011.2617v1
|
2010-12-17
|
Optimal switching of a nanomagnet assisted by microwaves
|
We develop an efficient and general method for optimizing the microwave field
that achieves magnetization switching with a smaller static field. This method
is based on optimal control and renders an exact solution for the 3D microwave
field that triggers the switching of a nanomagnet with a given anisotropy and
in an oblique static field. Applying this technique to the particular case of
uniaxial anisotropy, we show that the optimal microwave field, that achieves
switching with minimal absorbed energy, is modulated both in frequency and in
magnitude. Its role is to drive the magnetization from the metastable
equilibrium position towards the saddle point and then damping induces the
relaxation to the stable equilibrium position. For the pumping to be efficient,
the microwave field frequency must match at the early stage of the switching
process the proper precession frequency of the magnetization, which depends on
the magnitude and direction of the static field. We investigate the effect of
the static field (in amplitude and direction) and of damping on the
characteristics of the microwave field. We have computed the switching curves
in the presence of the optimal microwave field. The results are in qualitative
agreement with micro-SQUID experiments on isolated nanoclusters. The strong
dependence of the microwave field and that of the switching curve on the
damping parameter may be useful in probing damping in various nanoclusters.
|
1012.3901v1
|
2010-12-22
|
PageRank for ranking authors in co-citation networks
|
Google's PageRank has created a new synergy to information retrieval for a
better ranking of Web pages. It ranks documents depending on the topology of
the graphs and the weights of the nodes. PageRank has significantly advanced
the field of information retrieval and keeps Google ahead of competitors in the
search engine market. It has been deployed in bibliometrics to evaluate
research impact, yet few of these studies focus on the important impact of the
damping factor (d) for ranking purposes. This paper studies how varied damping
factors in the PageRank algorithm can provide additional insight into the
ranking of authors in an author co-citation network. Furthermore, we propose
weighted PageRank algorithms. We select 108 most highly cited authors in the
information retrieval (IR) area from the 1970s to 2008 to form the author
co-citation network. We calculate the ranks of these 108 authors based on
PageRank with damping factor ranging from 0.05 to 0.95. In order to test the
relationship between these different measures, we compare PageRank and weighted
PageRank results with the citation ranking, h-index, and centrality measures.
We found that in our author co-citation network, citation rank is highly
correlated with PageRank's with different damping factors and also with
different PageRank algorithms; citation rank and PageRank are not significantly
correlated with centrality measures; and h-index is not significantly
correlated with centrality measures.
|
1012.4872v1
|
2011-01-20
|
Magnetohydrodynamic waves in solar partially ionized plasmas: two-fluid approach
|
We derive the dynamics of magnetohydrodynamic waves in two-fluid partially
ionized plasmas and to compare the results with those obtained under
single-fluid description. Two-fluid magnetohydrodynamic equations are used,
where ion-electron plasma and neutral particles are considered as separate
fluids. Dispersion relations of linear magnetohydrodynamic waves are derived
for simplest case of homogeneous medium. Frequencies and damping rates of waves
are obtained for different parameters of background plasma. We found that two-
and single-fluid descriptions give similar results for low frequency waves.
However, the dynamics of MHD waves in two-fluid approach is significantly
changed when the wave frequency becomes comparable or higher than ion-neutral
collision frequency. Alfven and fast magneto-acoustic waves attain their
maximum damping rate at particular frequencies (for example, the peak frequency
equals 2.5 ion-neutral collision frequency for 50 % of neutral Hydrogen) in
wave spectrum. The damping rates are reduced for higher frequency waves. The
new mode of slow magneto-acoustic wave appears for higher frequency branch,
which is connected to neutral hydrogen fluid. The single-fluid approach
perfectly deals with slow processes in partially ionized plasmas, but fails for
time-scales smaller than ion-neutral collision time. Therefore, two-fluid
approximation should be used for the description of relatively fast processes.
Some results of single-fluid description, for example the damping of
high-frequency Alfven waves in the solar chromosphere due to ion-neutral
collisions, should be revised in future.
|
1101.3913v1
|
2011-08-25
|
Characterizing Multi-planet Systems with Classical Secular Theory
|
Classical secular theory can be a powerful tool to describe the qualitative
character of multi-planet systems and offer insight into their histories. The
eigenmodes of the secular behavior, rather than current orbital elements, can
help identify tidal effects, early planet-planet scattering, and dynamical
coupling among the planets, for systems in which mean-motion resonances do not
play a role. Although tidal damping can result in aligned major axes after all
but one eigenmode have damped away, such alignment may simply be fortuitous. An
example of this is 55 Cancri (orbital solution of Fischer et al., 2008) where
multiple eigenmodes remain undamped. Various solutions for 55 Cancri are
compared, showing differing dynamical groupings, with implications for the
coupling of eccentricities and for the partitioning of damping among the
planets. Solutions for orbits that include expectations of past tidal evolution
with observational data, must take into account which eigenmodes should be
damped, rather than expecting particular eccentricities to be near zero.
Classical secular theory is only accurate for low eccentricity values, but
comparison with other results suggests that it can yield useful qualitative
descriptions of behavior even for moderately large eccentricity values, and may
have advantages for revealing underlying physical processes and, as large
numbers of new systems are discovered, for triage to identify where more
comprehensive dynamical studies should have priority.
|
1108.5149v2
|
2011-09-12
|
Nonlinear spectroscopy of superconducting anharmonic resonators
|
We formulate a model for the steady state response of a nonlinear quantum
oscillator structure, such as those used in a variety of superconducting qubit
experiments, when excited by a steady, but not necessarily small, ac tone. We
show that this model can be derived directly from a circuit description of some
recent qubit experiments in which the state of the qubit is read out directly,
without a SQUID magnetometer. The excitation profile has a rich structure
depending on the detuning of the tone from the small-signal resonant frequency,
on the degree of damping, and on the excitation amplitude. We explore two
regions in detail: First, at high damping there is a trough in the excitation
response as a function of detuning, near where the classical Duffing
bifurcation occurs. This trough has been understood as a classical interference
between two metastable responses with opposite phase. We use Wigner function
studies to show that while this picture is roughly correct, there are also more
quantum mechanical aspects to this feature. Second, at low damping we study the
emergence of sharp, discrete spectral features from a continuum response. We
show that these the structures, associated with discrete transitions between
different excited-state eigenstates of the oscillator, provide an interesting
example of a quantum Fano resonance. The trough in the Fano response evolves
continuously from the "classical" trough at high damping.
|
1109.2490v1
|
2011-11-09
|
Stabilization by switching control methods
|
In this paper we consider some stabilization problems for the wave equation
with switching. We prove exponential stability results for appropriate damping
coefficients. The proof of the main results is based on D'Alembert formula and
some energy estimates.
|
1111.2171v1
|
2012-04-09
|
The Kato Smoothing Effect for Regularized Schrödinger Equations in Exterior Domains
|
We prove, under the exterior geometric control condition, the Kato smoothing
effect for solutions of an inhomogenous and damped Schr\"odinger equation on
exterior domains.
|
1204.1904v1
|
2012-04-26
|
Well-posedness and long time behavior in nonlinear dissipative hyperbolic-like evolutions with critical exponents
|
These lectures present the analysis of stability and control of long time
behavior of PDE models described by nonlinear evolutions of hyperbolic type.
Specific examples of the models under consideration include: (i) nonlinear
systems of dynamic elasticity: von Karman systems, Berger's equations,
Kirchhoff - Boussinesq equations, nonlinear waves (ii) nonlinear flow -
structure and fluid - structure interactions, (iii) and nonlinear
thermo-elasticity. A characteristic feature of the models under consideration
is criticality or super-criticality of sources (with respect to Sobolev's
embeddings) along with super-criticality of damping mechanisms which, in
addition, may be also geometrically constrained.
Our aim is to present several methods relying on cancelations, harmonic
analysis and geometric analysis, which enable to handle criticality and also
super-criticality in both sources and the damping of the underlined nonlinear
PDE. It turns out that if carefully analyzed the nonlinearity can be taken
"advantage of" in order to produce implementable damping mechanism.
Another goal of these lectures is the understanding of control mechanisms
which are geometrically constrained. The final task boils down to showing that
appropriately damped system is "quasi-stable" in the sense that any two
trajectories approach each other exponentially fast up to a compact term which
can grow in time. Showing this property- formulated as quasi-stability estimate
-is the key and technically demanding issue that requires suitable tools. These
include: weighted energy inequalities, compensated compactness, Carleman's
estimates and some elements of microlocal analysis.
|
1204.5864v1
|
2012-06-15
|
Comment on "Anisotropic Critical Magnetic Fluctuations in the Ferromagnetic Superconductor UCoGe"
|
We have presented the potential explanation of nonvanishing at q=0 Landau
damping measured experimentally in ferromagnetic compounds UGe2 and UCoGe based
on possible intersection of the Fermi sheets corresponding different bands.
|
1206.3468v1
|
2012-06-21
|
Interaction between an Isotropic Nanoparticle and Drifting Electrons in a Quantum Well
|
A hybrid system composed of an isotropic nanoparticle and a semiconductor
heterostructure with a quantum well has been considered. The nanoparticle is
supposed to be polarizable in an external electric field. A theoretical model
of the hybrid system is substantiated and formulated. Exact solutions of the
model equations are obtained. The frequencies of charge oscillations in the
hybrid system and their damping owing to the dipole--plasmon interaction are
found, the damping mechanism being similar to that of Landau damping. The
space-time behavior of concentration perturbations in the two-dimensional
electron gas is analyzed, and the polarization oscillations of a nanoparticle
are studied. The induced polarization of a nanoparticle at nonzero electron
drift velocities is found to have a complicated dynamics. In particular, the
polarization vector circulates along elliptic trajectories for two of three
frequency dispersion branches. If the electric current flows through the
quantum well due to an applied electric field, the damping of oscillations in
the hybrid system is replaced by their growth in time, which corresponds to the
electric instability of the system. New phenomena in hybrid systems can be used
to excite the emission of nanoparticles by an electric current and to
electrically stimulate the emission in the terahertz spectral range.
|
1206.4782v1
|
2012-10-11
|
Experimental estimations of viscoelastic properties of multilayer damped plates in broad-band frequency range
|
Regarding lightweighting structures for aeronautics, automotive or
construction applications, the level of performance of solutions proposed in
terms of damping and isolation is fundamental. Hence multilayered plate appears
as an interesting answer if damping performances are properly optimized. In
this paper, a novel modal analysis method (Ege et al, JSV 325 (4-5), 2009) is
used to identify viscoelastic properties (loss factors, Young's modulus) of
"polyethylene thermoplastic / aluminum" bilayer plates. The thermoplastic is
chosen for its high loss factors and relative low mass. The experimental method
consists in a high-resolution technique (ESPRIT algorithm) which allows precise
estimations of the viscoelastic properties even in frequency domains with high
modal overlap (high damping or modal density). Experimental loss factors
estimated from impact hammer excitations on the free-free plates highly
corresponds with two theoretical estimations. In the first model (Guyader &
Lesueur, JSV 58(1), 1978) the calculation is based on multilayered plates
equations and use wave propagation analysis ; in the second one (Laulagnet &
Guyader, JASA 96(1), 1994) the thickness deformation solving Navier's equations
is allowed. Results on several plates with several thicknesses of
thermoplastics are given and compared with the models, demonstrating the
validity of the approach.
|
1210.3333v3
|
2012-11-02
|
Damping of mechanical vibrations by free electrons in metallic nanoresonators
|
We investigate the effect of free electrons on the quality factor (Q) of a
metallic nanomechanical resonator in the form of a thin elastic beam. The
flexural and longitudinal modes of the beam are modeled using thin beam
elasticity theory, and simple perturbation theory is used to calculate the rate
at which an externally excited vibration mode decays due to its interaction
with free electrons. We find that electron-phonon interaction significantly
affects the Q of longitudinal modes, and may also be of significance to the
damping of flexural modes in otherwise high-Q beams. The finite geometry of the
beam is manifested in two important ways. Its finite length breaks translation
invariance along the beam and introduces an imperfect momentum conservation law
in place of the exact law. Its finite width imposes a quantization of the
electronic states that introduces a temperature scale for which there exists a
crossover from a high-temperature macroscopic regime, where electron-phonon
damping behaves as if the electrons were in the bulk, to a low-temperature
mesoscopic regime, where damping is dominated by just a few dissipation
channels and exhibits sharp non-monotonic changes as parameters are varied.
This suggests a novel scheme for probing the electronic spectrum of a nanoscale
device by measuring the Q of its mechanical vibrations.
|
1211.0450v1
|
2013-01-14
|
Two-qubit mixed states more entangled than pure states: Comparison of the relative entropy of entanglement for a given nonlocality
|
Amplitude damping changes entangled pure states into usually less-entangled
mixed states. We show, however, that even local amplitude damping of one or two
qubits can result in mixed states more entangled than pure states if one
compares the relative entropy of entanglement (REE) for a given degree of the
Bell-Clauser-Horne-Shimony-Holt inequality violation (referred to as
nonlocality). By applying Monte-Carlo simulations, we find the maximally
entangled mixed states and show that they are likely to be optimal by checking
the Karush-Kuhn-Tucker conditions, which generalize the method of Lagrange
multipliers for this nonlinear optimization problem. We show that the REE for
mixed states can exceed that of pure states if the nonlocality is in the range
(0,0.82) and the maximal difference between these REEs is 0.4. A former
comparison [Phys. Rev. A 78, 052308 (2008)] of the REE for a given negativity
showed analogous property but the corresponding maximal difference in the REEs
is one-order smaller (i.e., 0.039) and the negativity range is (0,0.53) only.
For appropriate comparison, we normalized the nonlocality measure to be equal
to the standard entanglement measures, including the negativity, for arbitrary
two-qubit pure states. We also analyze the influence of the phase-damping
channel on the entanglement of the initially pure states. We show that the
minimum of the REE for a given nonlocality can be achieved by this channel,
contrary to the amplitude damping channel.
|
1301.2969v2
|
2013-07-02
|
The ESO UVES Advanced Data Products Quasar Sample - I. Dataset and New N_HI Measurements of Damped Absorbers
|
We present here a dataset of quasars observed with the Ultraviolet Visual
Echelle Spectrograph (UVES) on the VLT and available in the ESO UVES Advanced
Data Products archive. The sample is made up of a total of 250 high resolution
quasar spectra with emission redshifts ranging from 0.191 < z_em <6.311. The
total UVES exposure time of this dataset is 1560 hours. Thanks to the high
resolution of UVES spectra, it is possible to unambiguously measure the column
density of absorbers with damping wings, down to N_HI > 10^{19} cm^{-2}, which
constitutes the sub-damped Lya absorber (sub-DLA) threshold. Within the
wavelength coverage of our UVES data, we find 150 damped Lya systems
(DLAs)/sub-DLAs in the range 1.5 < z_abs < 4.7. Of these 150, 93 are DLAs and
57 are sub-DLAs. An extensive search in the literature indicates that 6 of
these DLAs and 13 of these sub-DLAs have their N_HI measured for the first
time. Among them, 10 are new identifications as DLAs/sub-DLAs. For each of
these systems, we obtain an accurate measurement of the HI column density and
the absorber's redshift in the range 1.7 < z_abs < 4.2 by implementing a Voigt
profile-fitting algorithm. These absorbers are further confirmed thanks to the
detection of associated metal lines and/or lines from members of the Lyman
series. In our data, a few quasars' lines-of-sight are rich. An interesting
example is towards QSO J0133+0400 (z_em = 4.154) with six DLAs and sub-DLAs
reported.
|
1307.0678v2
|
2013-08-23
|
Stabilization of second-order evolution equations with time delay
|
We consider second-order evolution equations in an abstract setting with
damping and time delay and give sufficient conditions ensuring exponential
stability. Our abstract framework is then applied to the wave equation, the
elasticity system and the Petrovsky system.
|
1308.5106v1
|
2013-09-21
|
Bottomonium suppression at $\sqrt{s_{NN}}=2.76$ TeV using model based on color screening and gluonic dissociation with collisional damping
|
We present a model to explain the bottomonium suppression in Pb+Pb collisions
at mid rapidity obtained from Large Hadron Collider (LHC) energy,
$\sqrt{s_{NN}}=2.76$ TeV. The model consists of two decoupled mechanisms
namely, color screening during bottomonium production followed by gluon induced
dissociation along with collisional damping. The quasi-particle model (QPM) is
used as equation of state (EOS) for the Quark-Gluon Plasma (QGP) medium. The
feed-down from higher $\Upsilon$ states, such as $\Upsilon(1P)$, $\Upsilon(2S)$
and $\Upsilon(2P)$, dilated formation times for bottomonium states and viscous
effect of QGP medium are other ingredients included in the current formulation.
We further assume that the QGP is expanding according to (1+1)-dimensional
Bjorken's boost invariant scaling law. The net suppression (in terms of $p_T$
integrated survival probability) for bottomonium states at mid rapidity is
obtained as a function of centrality and the result is then compared both
quantitatively and qualitatively with the recent LHC experimental data in the
mid rapidity region recently published by CMS collaboration. We find that the
current model, based on the Debye color screening plus gluonic dissociation
along with collisional damping, better describes the centrality dependence of
bottomonium suppression at LHC energy as compared to color screening model
alone.
\vskip 0.5cm
{\nd \it Keywords} : Color screening, Gluonic dissociation, Collisional
damping, Survival probability {\nd \it PACS numbers} : 12.38.Mh, 12.38.Gc,
25.75.Nq, 24.10.Pa
|
1309.5467v2
|
2013-10-20
|
Nonequilibrium stationary state for a damped rotator
|
Perturbative construction of the nonequilibrium steady state of a rotator
under a stochastic forcing while subject to torque and friction
|
1310.5379v1
|
2013-11-07
|
Spin-Orbit Torques and Anisotropic Magnetization Damping in Skyrmion Crystals
|
The length scale of the magnetization gradients in chiral magnets is
determined by the relativistic Dzyaloshinskii-Moriya interaction. Thus, even
conventional spin-transfer torques are controlled by the relativistic
spin-orbit coupling in these systems, and additional relativistic corrections
to the current-induced torques and magnetization damping become important for a
complete understanding of the current-driven magnetization dynamics. We
theoretically study the effects of reactive and dissipative homogeneous
spin-orbit torques and anisotropic damping on the current-driven skyrmion
dynamics in cubic chiral magnets. Our results demonstrate that spin-orbit
torques play a significant role in the current-induced skyrmion velocity. The
dissipative spin-orbit torque generates a relativistic Magnus force on the
skyrmions, whereas the reactive spin-orbit torque yields a correction to both
the drift velocity along the current direction and the transverse velocity
associated with the Magnus force. The spin-orbit torque corrections to the
velocity scale linearly with the skyrmion size, which is inversely proportional
to the spin-orbit coupling. Consequently, the reactive spin-orbit torque
correction can be the same order of magnitude as the non-relativistic
contribution. More importantly, the dissipative spin-orbit torque can be the
dominant force that causes a deflected motion of the skyrmions if the torque
exhibits a linear or quadratic relationship with the spin-orbit coupling. In
addition, we demonstrate that the skyrmion velocity is determined by
anisotropic magnetization damping parameters governed by the skyrmion size.
|
1311.1778v1
|
2013-11-13
|
Recent progress in attractors for quintic wave equations
|
We report on new results concerning the global well-posedness, dissipativity
and attractors of the damped quintic wave equations in bounded domains of R^3.
|
1311.3290v1
|
2014-01-19
|
Analytical Solution of Mathieu Equation
|
The general solution of the homogeneous damped Mathieu equation in the
analytical form, allowing its practical using in many applications, including
superconductivity studies, without numerical calculations has been found.
|
1401.5348v1
|
2014-06-10
|
Wigner's Space-time Symmetries based on the Two-by-two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
|
The second-order differential equation for a damped harmonic oscillator can
be converted to two coupled first-order equations, with two two-by-two matrices
leading to the group $Sp(2)$. It is shown that this oscillator system contains
the essential features of Wigner's little groups dictating the internal
space-time symmetries of particles in the Lorentz-covariant world. The little
groups are the subgroups of the Lorentz group whose transformations leave the
four-momentum of a given particle invariant. It is shown that the damping modes
of the oscillator correspond to the little groups for massive and
imaginary-mass particles respectively. When the system makes the transition
from the oscillation to damping mode, it corresponds to the little group for
massless particles. Rotations around the momentum leave the four-momentum
invariant. This degree of freedom extends the $Sp(2)$ symmetry to that of
$SL(2,c)$ corresponding to the Lorentz group applicable to the four-dimensional
Minkowski space. The Poincar\'e sphere contains the $SL(2,c)$ symmetry. In
addition, it has a non-Lorentzian parameter allowing us to reduce the mass
continuously to zero. It is thus possible to construct the little group for
massless particles from that of the massive particle by reducing its mass to
zero. Spin-1/2 particles and spin-1 particles are discussed in detail.
|
1406.2403v1
|
2014-06-11
|
Quantum critical metals in $4-ε$ dimensions
|
We study the quantum theory of a Fermi surface coupled to a gapless boson
scalar in $D=4-\epsilon$ spacetime dimensions as a simple model for non-Fermi
liquids (NFL) near a quantum phase transition. Our analysis takes into account
the full backreaction from Landau damping of the boson, and obtains an RG flow
that proceeds through three distinct stages. Above the scale of Landau damping
the Fermi velocity flows to zero, while the coupling evolves according to its
classical dimension. Once damping becomes important, its backreaction leads to
a crossover regime where dynamic and static damping effects compete and the
fermion self-energy does not respect scaling. Below this crossover and having
tuned the boson to criticality, the theory flows to a $z=3$ scalar interacting
with a NFL. By increasing the number of bosonic flavors, the phase diagram near
the quantum critical point interpolates between a superconducting dome fully
covering the NFL behavior, and a phase where NFL effects become important
first, before the onset of superconductivity. A generic prediction of the
theory is that the Fermi velocity and quasiparticle residue vanish with a
power-law $\omega^\epsilon$ as the fixed point is approached. These features
may be useful for understanding some of the phenomenology of high $T_c$
materials in a systematic $\epsilon$--expansion.
|
1406.3029v2
|
2014-10-15
|
A comparison of weak-turbulence and PIC simulations of weak electron-beam plasma interaction
|
Quasilinear theory has long been used to treat the problem of a weak electron
beam interacting with plasma and generating Langmuir waves. Its extension to
weak-turbulence theory treats resonant interactions of these Langmuir waves
with other plasma wave modes, in particular ion-sound waves. These are strongly
damped in plasma of equal ion and electron temperatures, as sometimes seen in,
for example, the solar corona and wind. Weak turbulence theory is derived in
the weak damping limit, with a term describing ion-sound wave damping then
added. In this paper we use the EPOCH particle-in-cell code to numerically test
weak turbulence theory for a range of electron-ion temperature ratios. We find
that in the cold ion limit the results agree well, but increasing ion
temperature the three-wave resonance becomes broadened in proportion to the
ion-sound wave damping rate. This may be important in, for example, the theory
of solar radio bursts, where the spectrum of Langmuir waves is critical.
Additionally we establish lower limits on the number of simulation particles
needed to accurately reproduce the electron and wave distributions in their
saturated states, and to reproduce their intermediate states and time
evolution.
|
1410.4046v2
|
2015-03-31
|
Existence of the global attractor for the plate equation with nonlocal nonlinearity in R^{n}
|
We consider Cauchy problem for the semilinear plate equation with nonlocal
nonlinearity. Under mild conditions on the damping coefficient, we prove that
the semigroup generated by this problem possesses a global attractor.
|
1503.09123v1
|
2015-05-07
|
Theory for Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities
|
We construct a theory for Bose-Einstein condensation of light in
nano-fabricated semiconductor microcavities. We model the semiconductor by one
conduction and one valence band which consist of electrons and holes that
interact via a Coulomb interaction. Moreover, we incorporate screening effects
by using a contact interaction with the scattering length for a Yukawa
potential and describe in this manner the crossover from exciton gas to
electron-hole plasma as we increase the excitation level of the semiconductor.
We then show that the dynamics of the light in the microcavities is damped due
to the coupling to the semiconductor. Furthermore, we demonstrate that on the
electron-hole plasma side of the crossover, which is relevant for the
Bose-Einstein condensation of light, this damping can be described by a single
dimensionless damping parameter that depends on the external pumping.
Hereafter, we propose to probe the superfluidity of light in these
nano-fabricated semiconductor microcavities by making use of the differences in
the response in the normal or superfluid phase to a sudden rotation of the
trap. In particular, we determine frequencies and damping of the scissors modes
that are excited in this manner. Moreover, we show that a distinct signature of
the dynamical Casimir effect can be observed in the density-density
correlations of the excited light fluid.
|
1505.01732v2
|
2015-08-21
|
Which verification qubits perform best for secure communication in noisy channel?
|
In secure quantum communication protocols, a set of single qubits prepared
using 2 or more mutually unbiased bases or a set of $n$-qubit ($n\geq2$)
entangled states of a particular form are usually used to form a verification
string which is subsequently used to detect traces of eavesdropping. The qubits
that form a verification string are referred to as decoy qubits, and there
exists a large set of different quantum states that can be used as decoy
qubits. In the absence of noise, any choice of decoy qubits provides equivalent
security. In this paper, we examine such equivalence for noisy environment
(e.g., in amplitude damping, phase damping, collective dephasing and collective
rotation noise channels) by comparing the decoy-qubit assisted schemes of
secure quantum communication that use single qubit states as decoy qubits with
the schemes that use entangled states as decoy qubits. Our study reveals that
the single qubit assisted scheme perform better in some noisy environments,
while some entangled qubits assisted schemes perform better in other noisy
environments. Specifically, single qubits assisted schemes perform better in
amplitude damping and phase damping noisy channels, whereas a few
Bell-state-based decoy schemes are found to perform better in the presence of
the collective noise. Thus, if the kind of noise present in a communication
channel (i.e., the characteristics of the channel) is known or measured, then
the present study can provide the best choice of decoy qubits required for
implementation of schemes of secure quantum communication through that channel.
|
1508.05237v1
|
2015-08-30
|
Spin-transfer torque based damping control of parametrically excited spin waves in a magnetic insulator
|
The damping of spin waves parametrically excited in the magnetic insulator
Yttrium Iron Garnet (YIG) is controlled by a dc current passed through an
adjacent normal-metal film. The experiment is performed on a macroscopically
sized YIG(100nm)/Pt(10nm) bilayer of 4x2 mm^2 lateral dimensions. The spin-wave
relaxation frequency is determined via the threshold of the parametric
instability measured by Brillouin light scattering (BLS) spectroscopy. The
application of a dc current to the Pt film leads to the formation of a
spin-polarized electron current normal to the film plane due to the spin Hall
effect (SHE). This spin current exerts a spin transfer torque (STT) in the YIG
film and, thus, changes the spin-wave damping. Depending on the polarity of the
applied dc current with respect to the magnetization direction, the damping can
be increased or decreased. The magnitude of its variation is proportional to
the applied current. A variation in the relaxation frequency of +/-7.5% is
achieved for an applied dc current density of 5*10^10 A/m^2.
|
1508.07517v1
|
2015-09-08
|
Model comparison for the density structure across solar coronal waveguides
|
The spatial variation of physical quantities, such as the mass density,
across solar atmospheric waveguides governs the timescales and spatial scales
for wave damping and energy dissipation. The direct measurement of the spatial
distribution of density, however, is difficult and indirect seismology
inversion methods have been suggested as an alternative. We applied Bayesian
inference, model comparison, and model-averaging techniques to the inference of
the cross-field density structuring in solar magnetic waveguides using
information on periods and damping times for resonantly damped
magnetohydrodynamic (MHD) transverse kink oscillations. Three commonly employed
alternative profiles were used to model the variation of the mass density
across the waveguide boundary. Parameter inference enabled us to obtain
information on physical quantities such as the Alfv\'en travel time, the
density contrast, and the transverse inhomogeneity length scale. The inference
results from alternative density models were compared and their differences
quantified. Then, the relative plausibility of the considered models was
assessed by performing model comparison. Our results indicate that the evidence
in favor of any of the three models is minimal, unless the oscillations are
strongly damped. In such a circumstance, the application of model-averaging
techniques enables the computation of an evidence-weighted inference that takes
into account the plausibility of each model in the calculation of a combined
inversion for the unknown physical parameters.
|
1509.02340v1
|
2015-09-15
|
Resonance vibration of impact oscillator with biharmonic excitation
|
We consider a damped impact oscillator subject to the action of a biharmonic
force. The conditions for the existence and stability of almost periodic
resonance solutions are investigated.
|
1509.05381v1
|
2015-11-08
|
On 2d incompressible Euler equations with partial damping
|
We consider various questions about the 2d incompressible Navier-Stokes and
Euler equations on a torus when dissipation is removed from or added to some of
the Fourier modes.
|
1511.02530v1
|
2015-12-11
|
The Ping Pong Pendulum
|
Many damped mechanical systems oscillate with increasing frequency as the
amplitude decreases. One popular example is Euler's Disk, where the point of
contact rotates with increasing rapidity as the energy is dissipated. We study
a simple mechanical pendulum that exhibits this behaviour.
|
1512.03700v1
|
2016-01-26
|
Fast convex optimization via inertial dynamics with Hessian driven damping
|
We first study the fast minimization properties of the trajectories of the
second-order evolution equation $$\ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) +
\beta \nabla^2 \Phi (x(t))\dot{x} (t) + \nabla \Phi (x(t)) = 0,$$ where
$\Phi:\mathcal H\to\mathbb R$ is a smooth convex function acting on a real
Hilbert space $\mathcal H$, and $\alpha$, $\beta$ are positive parameters. This
inertial system combines an isotropic viscous damping which vanishes
asymptotically, and a geometrical Hessian driven damping, which makes it
naturally related to Newton's and Levenberg-Marquardt methods. For $\alpha\geq
3$, $\beta >0$, along any trajectory, fast convergence of the values
$$\Phi(x(t))- \min_{\mathcal H}\Phi =\mathcal O\left(t^{-2}\right)$$ is
obtained, together with rapid convergence of the gradients $\nabla\Phi(x(t))$
to zero. For $\alpha>3$, just assuming that $\Phi$ has minimizers, we show that
any trajectory converges weakly to a minimizer of $\Phi$, and $
\Phi(x(t))-\min_{\mathcal H}\Phi = o(t^{-2})$. Strong convergence is
established in various practical situations. For the strongly convex case,
convergence can be arbitrarily fast depending on the choice of $\alpha$. More
precisely, we have $\Phi(x(t))- \min_{\mathcal H}\Phi = \mathcal
O(t^{-\frac{2}{3}\alpha})$. We extend the results to the case of a general
proper lower-semicontinuous convex function $\Phi : \mathcal H \rightarrow
\mathbb R \cup \{+\infty \}$. This is based on the fact that the inertial
dynamic with Hessian driven damping can be written as a first-order system in
time and space. By explicit-implicit time discretization, this opens a gate to
new $-$ possibly more rapid $-$ inertial algorithms, expanding the field of
FISTA methods for convex structured optimization problems.
|
1601.07113v1
|
2016-03-28
|
Stabilization of gravity water waves
|
This paper is devoted to the stabilization of the incompressible Euler
equation with free surface. We study the damping of two-dimensional gravity
waves by an absorbing beach where the water-wave energy is dissipated by using
the variations of the external pressure.
|
1603.08541v1
|
2016-06-14
|
Precession Relaxation of Viscoelastic Oblate Rotators
|
Perturbations of all sorts destabilise the rotation of a small body and leave
it in a non-principal spin state. In such a state, the body experiences
alternating stresses generated by the inertial forces. This yields nutation
relaxation, i.e., evolution of the spin towards the principal rotation about
the maximal-inertia axis. Knowledge of the timescales needed to damp the
nutation is crucial in studies of small bodies' dynamics. In the literature
hitherto, nutation relaxation has always been described with aid of an
empirical quality factor $\,Q\,$ introduced to parameterise the energy
dissipation rate.
Among the drawbacks of this approach was its inability to describe the
dependence of the relaxation rate upon the current nutation angle. This
inability stemmed from our lack of knowledge of the quality factor's dependence
on the forcing frequency. In this article, we derive our description of
nutation damping directly from the rheological law obeyed by the material. This
renders us the nutation damping rate as a function of the current nutation
angle, as well as of the shape and the rheological parameters of the body. In
contradistinction from the approach based on an empirical $\,Q\,$-factor, our
development gives a zero damping rate in the spherical-shape limit. Our method
is generic and applicable to any shape and to any linear rheological law.
However, to simplify the developments, here we consider a dynamically oblate
rotator with a Maxwell rheology.
|
1606.04559v3
|
2016-09-07
|
Quasi-stability and Exponential Attractors for A Non-Gradient System---Applications to Piston-Theoretic Plates with Internal Damping
|
We consider a nonlinear (Berger or Von Karman) clamped plate model with a
{\em piston-theoretic} right hand side---which include non-dissipative,
non-conservative lower order terms. The model arises in aeroelasticity when a
panel is immersed in a high velocity linear potential flow; in this case the
effect of the flow can be captured by a dynamic pressure term written in terms
of the material derivative of the plate's displacement. The effect of
fully-supported internal damping is studied for both Berger and von Karman
dynamics. The non-dissipative nature of the dynamics preclude the use of strong
tools such as backward-in-time smallness of velocities and finiteness of the
dissipation integral. Modern quasi-stability techniques are utilized to show
the existence of compact global attractors and generalized fractal exponential
attractors. Specific results depending on the size of the damping parameter and
the nonlinearity in force. For the Berger plate, in the presence of large
damping, the existence of a proper global attractor (whose fractal dimension is
finite in the state space) is shown via a decomposition of the nonlinear
dynamics. This leads to the construction of a compact set upon which
quasi-stability theory can be implemented. Numerical investigations for
appropriate 1-D models are presented which explore and support the abstract
results presented herein.
|
1609.02211v1
|
2016-10-26
|
On the region of attraction of phase-locked states for swing equations on connected graphs with inhomogeneous dampings
|
We consider the synchronization problem of swing equations, a second-order
Kuramoto-type model, on connected networks with inhomogeneous dampings. This
was largely motivated by its relevance to the dynamics of power grids. We focus
on the estimate of the region of attraction of synchronous states which is a
central problem in the transient stability of power grids. In the recent
literature, D\"{o}rfler, Chertkov, and Bullo [Proc. Natl. Acad. Sci. USA, 110
(2013), pp. 2005-2010] found a condition for the synchronization in smart
grids. They pointed out that the region of attraction is an important unsolved
problem. In [SIAM J. Control Optim., 52 (2014), pp. 2482-2511], only a special
case was considered where the oscillators have homogeneous dampings and the
underlying graph has a diameter less than or equal to 2. There the analysis
heavily relies on these assumptions; however, they are too strict compared to
the real power networks. In this paper, we continue the study and derive an
estimate on the region of attraction of phase-locked states for lossless power
grids on connected graphs with inhomogeneous dampings. Our main strategy is
based on the gradient-like formulation and energy estimate. We refine the
assumptions by constructing a new energy functional which enables us to
consider such general settings.
|
1610.08437v1
|
2016-10-31
|
A quest for new physics inside the neutron
|
The lecture presents an overview of the quest for the new physics in low
energy neutron phenomena. In addition to the traditional topics the quantum
damping of $n$ $\bar{n}$ oscillations is discussed.
|
1610.10046v1
|
2016-12-19
|
Improving the efficiency of joint remote state preparation in noisy environment with weak measurement
|
Quantum secure communication provides a new way for protecting the security
of information. As an important component of quantum secure communication,
remote state preparation (RSP) can securely transmit a quantum state from a
sender to a remote receiver. The existence of quantum noise severely affects
the security and reliability of quantum communication system. In this paper, we
study the method for improving the efficiency of joint RSP (JRSP) subjected to
noise with the help of weak measurement and its reversal measurement. Taking a
GHZ based deterministic JRSP as an example, we utilize the technique of weak
measurement and its reversal to suppress the effect of the amplitude-damping
noise firstly. Our study shows that the fidelity of the output state can be
improved in the amplitude-damping noise. We also study the effect of weak
measurement and its reversal in other three types of noise usually encountered
in real-world, namely, the bit-flip, phase-flip (phase-damping) and
depolarizing noise. Our results show that the weak measurement has no effect
for suppressing the bit-flip and phase-flip (phase-damping) noise, while has
slight effect for suppressing the depolarizing noise. Our study is suitable for
JRSP and RSP, and will be helpful for improving the efficiency of multiparticle
entanglement based quantum secure communication in real implementation.
|
1612.06020v1
|
2017-02-27
|
Current Induced Damping of Nanosized Quantum Moments in the Presence of Spin-Orbit Interaction
|
Motivated by the need to understand current-induced magnetization dynamics at
the nanoscale, we have developed a formalism, within the framework of Keldysh
Green function approach, to study the current-induced dynamics of a
ferromagnetic (FM) nanoisland overlayer on a spin-orbit-coupling (SOC) Rashba
plane. In contrast to the commonly employed classical micromagnetic LLG
simulations the magnetic moments of the FM are treated {\it quantum
mechanically}. We obtain the density matrix of the whole system consisting of
conduction electrons entangled with the local magnetic moments and calculate
the effective damping rate of the FM. We investigate two opposite limiting
regimes of FM dynamics: (1) The precessional regime where the magnetic
anisotropy energy (MAE) and precessional frequency are smaller than the
exchange interactions, and (2) The local spin-flip regime where the MAE and
precessional frequency are comparable to the exchange interactions. In the
former case, we show that due to the finite size of the FM domain, the
\textquotedblleft Gilbert damping\textquotedblright does not diverge in the
ballistic electron transport regime, in sharp contrast to Kambersky's breathing
Fermi surface theory for damping in metallic FMs. In the latter case, we show
that above a critical bias the excited conduction electrons can switch the
local spin moments resulting in demagnetization and reversal of the
magnetization. Furthermore, our calculations show that the bias-induced
antidamping efficiency in the local spin-flip regime is much higher than that
in the rotational excitation regime.
|
1702.08408v2
|
2017-03-21
|
Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics
|
We resolve the thermal motion of a high-stress silicon nitride nanobeam at
frequencies far below its fundamental flexural resonance (3.4 MHz) using
cavity-enhanced optical interferometry. Over two decades, the displacement
spectrum is well-modeled by that of a damped harmonic oscillator driven by a
$1/f$ thermal force, suggesting that the loss angle of the beam material is
frequency-independent. The inferred loss angle at 3.4 MHz, $\phi = 4.5\cdot
10^{-6}$, agrees well with the quality factor ($Q$) of the fundamental beam
mode ($\phi = Q^{-1}$). In conjunction with $Q$ measurements made on higher
order flexural modes, and accounting for the mode dependence of stress-induced
loss dilution, we find that the intrinsic (undiluted) loss angle of the beam
changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the
impact of such "structural damping" on experiments in quantum optomechanics, in
which the thermal force acting on a mechanical oscillator coupled to an optical
cavity is overwhelmed by radiation pressure shot noise. As an illustration, we
show that structural damping reduces the bandwidth of ponderomotive squeezing.
|
1703.07134v2
|
2017-03-29
|
Comment on "Spreading widths of giant resonances in spherical nuclei: damped transient response" by Severyukhin et al. [arXiv:1703.05710]
|
We argue whether physics of universal approach of Severyukhin et al.
[arXiv:1703.05710] is approved.
|
1703.10003v1
|
2017-05-16
|
Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials
|
We address the problem of a front propagation in chains with a bi-stable
nondegenerate on-site potential and a nonlinear gradient coupling. For a
generic nonlinear coupling, one encounters a special regime of transitions,
characterized by extremely narrow fronts, far supersonic velocities of
propagation and long waves in the oscillatory tail. This regime can be
qualitatively associated with a shock wave. The front propagation can be
described with the help of a simple reduced-order model; the latter delivers a
kinetic law, which is almost not sensitive to fine details of the on-site
potential. Besides, it is possible to predict all main characteristics of the
transition front, including its shape and frequency and amplitude of the
oscillatory tail. The numerical results are in a good agreement with the
analytical predictions. The suggested approach allows one to consider the
effects of an external pre-load and on-site damping. When the damping is
moderate, the analysis remains in the frame of the reduced-order model. It is
possible to consider the solution for the front propagating in the damped chain
as a perturbation of the undamped dynamics. This approach yield reasonable
predictions. When the damping is high, the transition front enters a completely
different asymptotic regime. The gradient nonlinearity generically turns
negligible, and the propagating front converges to the exact solution obtained
from a simple linear continuous model.
|
1705.05555v1
|
2017-08-16
|
The Frequency-dependent Damping of Slow Magnetoacoustic Waves in a Sunspot Umbral Atmosphere
|
High spatial and temporal resolution images of a sunspot, obtained
simultaneously in multiple optical and UV wavelengths, are employed to study
the propagation and damping characteristics of slow magnetoacoustic waves up to
transition region heights. Power spectra are generated from intensity
oscillations in sunspot umbra, across multiple atmospheric heights, for
frequencies up to a few hundred mHz. It is observed that the power spectra
display a power-law dependence over the entire frequency range, with a
significant enhancement around 5.5 mHz found for the chromospheric channels.
The phase-difference spectra reveal a cutoff frequency near 3 mHz, up to which
the oscillations are evanescent, while those with higher frequencies propagate
upwards. The power-law index appears to increase with atmospheric height. Also,
shorter damping lengths are observed for oscillations with higher frequencies
suggesting frequency-dependent damping. Using the relative amplitudes of the
5.5 mHz (3 minute) oscillations, we estimate the energy flux at different
heights, which seems to decay gradually from the photosphere, in agreement with
recent numerical simulations. Furthermore, a comparison of power spectra across
the umbral radius highlights an enhancement of high-frequency waves near the
umbral center, which does not seem to be related to magnetic field inclination
angle effects.
|
1708.04835v1
|
2017-08-29
|
Spin wave damping arising from phase coexistence below $T_c$ in colossal magnetoresistive La$_{0.7}$Ca$_{0.3}$MnO$_3$
|
While the spin dynamics of La$_{0.7}$Ca$_{0.3}$MnO$_3$ in the ferromagnetic
phase are known to be unconventional, previous measurements have yielded
contradictory results regarding the damping of spin wave excitations. Neutron
spectroscopy measurements on a sample with a transition temperature of
$T_c$=257 K, higher than most single crystals, unambiguously reveal an
anomalous increase in spin wave damping for excitations approaching the
Brillouin zone boundary along the [$100$] direction that cannot be explained as
an artifact due to a noninteracting phonon branch. Spin waves throughout the
($HK0$) plane display a common trend where the spin wave damping is dependent
upon the excitation energy, increasing for energies above roughly 15 meV and
reaching a full width at half maximum of at least 20 meV. The results are
consistent with a model of intrinsic spatial inhomogeneity with phase separated
regions approximately 18 {\AA} in size persisting over a large range of
temperatures below $T_c$.
|
1708.08960v2
|
2017-09-08
|
Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems
|
In this paper, we study parameter-independent stability in qualitatively
heterogeneous passive networked systems containing damped and undamped nodes.
Given the graph topology and a set of damped nodes, we ask if output consensus
is achieved for all system parameter values. For given parameter values, an
eigenspace analysis is used to determine output consensus. The extension to
parameter-independent stability is characterized by a coloring problem, named
the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes
of the graph can be colored red, blue and black in such a way that (i) every
damped node is black, (ii) every black node has blue neighbors if and only if
it has red neighbors, and (iii) not all nodes in the graph are black. Such a
colored graph is referred to as a richly balanced colored graph.
Parameter-independent stability is guaranteed if there does not exist a richly
balanced coloring. The RBC problem is shown to cover another well-known graph
coloring scheme known as zero forcing sets. That is, if the damped nodes form a
zero forcing set in the graph, then a richly balanced coloring does not exist
and thus, parameter-independent stability is guaranteed. However, the full
equivalence of zero forcing sets and parameter-independent stability holds only
true for tree graphs. For more general graphs with few fundamental cycles an
algorithm, named chord node coloring, is proposed that significantly
outperforms a brute-force search for solving the NP-complete RBC problem.
|
1709.02629v1
|
2017-10-11
|
Collisional damping rates for plasma waves
|
The distinction between the plasma dynamics dominated by collisional
transport versus collective processes has never been rigorously addressed until
recently. A recent paper [Yoon et al., Phys. Rev. E 93, 033203 (2016)]
formulates for the first time, a unified kinetic theory in which collective
processes and collisional dynamics are systematically incorporated from first
principles. One of the outcomes of such a formalism is the rigorous derivation
of collisional damping rates for Langmuir and ion-acoustic waves, which can be
contrasted to the heuristic customary approach. However, the results are given
only in formal mathematical expressions. The present Brief Communication
numerically evaluates the rigorous collisional damping rates by considering the
case of plasma particles with Maxwellian velocity distribution function so as
to assess the consequence of the rigorous formalism in a quantitative manner.
Comparison with the heuristic ("Spitzer") formula shows that the accurate
damping rates are much lower in magnitude than the conventional expression,
which implies that the traditional approach over-estimates the importance of
attenuation of plasma waves by collisional relaxation process. Such a finding
may have a wide applicability ranging from laboratory to space and
astrophysical plasmas.
|
1710.03874v1
|
2017-10-20
|
Tidal dissipation in rotating fluid bodies: the presence of a magnetic field
|
We investigate effects of the presence of a magnetic field on tidal
dissipation in rotating fluid bodies. We consider a simplified model consisting
of a rigid core and a fluid envelope, permeated by a background magnetic field
(either a dipolar field or a uniform axial field). The wavelike tidal responses
in the fluid layer are in the form of magnetic-Coriolis waves, which are
restored by both the Coriolis force and the Lorentz force. Energy dissipation
occurs through viscous damping and Ohmic damping of these waves. Our numerical
results show that the tidal dissipation can be dominated by Ohmic damping even
with a weak magnetic field. The presence of a magnetic field smooths out the
complicated frequency-dependence of the dissipation rate, and broadens the
frequency spectrum of the dissipation rate, depending on the strength of the
background magnetic field. However, the frequency-averaged dissipation is
independent of the strength and structure of the magnetic field, and of the
dissipative parameters, in the approximation that the wave-like response is
driven only by the Coriolis force acting on the non-wavelike tidal flow.
Indeed, the frequency-averaged dissipation quantity is in good agreement with
previous analytical results in the absence of magnetic fields. Our results
suggest that the frequency-averaged tidal dissipation of the wavelike
perturbations is insensitive to detailed damping mechanisms and dissipative
properties.
|
1710.07690v2
|
2017-11-30
|
Implications of dark matter cascade decay from DAMPE, HESS, Fermi-LAT and AMS02 data
|
Recent high-energy cosmic $e^\pm$ measurement from the DArk Matter Particle
Explorer (DAMPE) satellite confirms the deviation of total cosmic ray electron
spectrum above 700-900 GeV from a simple power law. In this paper we
demonstrate that the cascade decay of dark matter (DM) can account for DAMPE's
TeV $e^+e^-$ spectrum. We select the least constraint DM decay channel into
four muons as the benchmark scenario, and perform an analysis with propagation
variance in both DM signal and the Milky Way's electron background. The
best-fit of the model is obtained for joint DAMPE, Fermi-Large Area Telescope
(Fermi-LAT), High Energy Stereoscopic System (HESS), high energy electron data
sets, and with an $\mathcal{O}(10^{26})$ second decay lifetime, which is
consistent with existing gamma ray and cosmic microwave background limits. We
compare the spectral difference between the cascade decay of typical
final-state channels. The least constrained $4\mu$ channels give good fits to
the electron spectrum's TeV scale down-turn, yet their low energy spectrum has
tension with sub-TeV positron data from AMS02. We also consider a three-step
cascade decay into eight muons, and also a gamma-ray constrained $4\mu,4b$
mixed channel, to demonstrate that a further softened cascade decay signal
would be required for the agreement with all the data sets.
|
1712.00370v3
|
2017-12-04
|
Scalar dark matter, Type II Seesaw and the DAMPE cosmic ray $e^+ + e^-$ excess
|
The DArk Matter Particle Explorer (DAMPE) has reported a measurement of the
flux of high energy cosmic ray electrons plus positrons (CREs) in the energy
range between $25$ GeV and $4.6$ TeV. With unprecedented high energy
resolution, the DAMPE data exhibit an excess of the CREs flux at an energy of
around $1.4$ TeV. In this letter, we discuss how the observed excess can be
understood in a minimal framework where the Standard Model (SM) is supplemented
by a stable SM singlet scalar as dark matter (DM) and type II seesaw for
generating the neutrino mass matrix. In our framework, a pair of DM particles
annihilates into a pair of the SM SU(2) triplet scalars ($\Delta$s) in type II
seesaw, and the subsequent $\Delta$ decays create the primary source of the
excessive CREs around $1.4$ TeV. The lepton flavor structure of the primary
source of CREs has a direct relationship with the neutrino oscillation data. We
find that the DM interpretation of the DAMPE excess determines the pattern of
neutrino mass spectrum to be the inverted hierarchy type, taking into account
the constraints from the Fermi-LAT observations of dwarf spheroidal galaxies.
|
1712.00869v2
|
2017-12-07
|
Nonlinear growth of structure in cosmologies with damped matter fluctuations
|
We investigate the nonlinear evolution of structure in variants of the
standard cosmological model which display damped density fluctuations relative
to cold dark matter (e.g. in which cold dark matter is replaced by warm or
interacting DM). Using N-body simulations, we address the question of how much
information is retained from different scales in the initial linear power
spectrum following the nonlinear growth of structure. We run a suite of N-body
simulations with different initial linear matter power spectra to show that,
once the system undergoes nonlinear evolution, the shape of the linear power
spectrum at high wavenumbers does not affect the non-linear power spectrum,
while it still matters for the halo mass function. Indeed, we find that linear
power spectra which differ from one another only at wavenumbers larger than
their half-mode wavenumber give rise to (almost) identical nonlinear power
spectra at late times, regardless of the fact that they originate from
different models with damped fluctuations. On the other hand, the halo mass
function is more sensitive to the form of the linear power spectrum. Exploiting
this result, we propose a two parameter model of the transfer function in
generic damped scenarios, and show that this parametrisation works as well as
the standard three parameter models for the scales on which the linear spectrum
is relevant.
|
1712.02742v2
|
2017-12-11
|
DAMPE excess from decaying right-handed neutrino dark matter
|
The flux of high-energy cosmic-ray electrons plus positrons recently measured
by the DArk Matter Particle Explorer (DAMPE) exhibits a tentative peak excess
at an energy of around $1.4$ TeV. In this paper, we consider the minimal gauged
$U(1)_{B-L}$ model with a right-handed neutrino (RHN) dark matter (DM) and
interpret the DAMPE peak with a late-time decay of the RHN DM into $e^\pm
W^\mp$. We find that a DM lifetime $\tau_{DM} \sim 10^{28}$ s can fit the DAMPE
peak with a DM mass $m_{DM}=3$ TeV. This favored lifetime is close to the
current bound on it by Fermi-LAT, our decaying RHN DM can be tested once the
measurement of cosmic gamma ray flux is improved. The RHN DM communicates with
the Standard Model particles through the $U(1)_{B-L}$ gauge boson ($Z^\prime$
boson), and its thermal relic abundance is controlled by only three free
parameters: $m_{DM}$, the $U(1)_{B-L}$ gauge coupling ($\alpha_{BL}$), and the
$Z^\prime$ boson mass ($m_{Z^\prime}$). For $m_{DM}=3$ TeV, the rest of the
parameters are restricted to be $m_{Z^\prime}\simeq 6$ TeV and $0.00807 \leq
\alpha_{BL} \leq 0.0149$, in order to reproduce the observed DM relic density
and to avoid the Landau pole for the running $\alpha_{BL}$ below the Planck
scale. This allowed region will be tested by the search for a $Z^\prime$ boson
resonance at the future Large Hadron Collider.
|
1712.03652v3
|
2017-12-11
|
A Statistical Study on The Frequency-Dependent Damping of Slow-mode Waves in Polar Plumes and Interplumes
|
We perform a statistical study on the frequency-dependent damping of slow
waves propagating along polar plumes and interplumes in the solar corona.
Analysis of a large sample of extreme ultraviolet (EUV) imaging data with high
spatial and temporal resolutions obtained from AIA/SDO suggests an inverse
power-law dependence of the damping length on the periodicity of slow waves
(i.e., the shorter period oscillations exhibit longer damping lengths), in
agreement with the previous case studies. Similar behavior is observed in both
plume and interplume regions studied in AIA 171 \AA\ and AIA 193 \AA\
passbands. It is found that the short-period (2--6 min) waves are relatively
more abundant than their long period (7--30 min) counterparts in contrast to
the general belief that the polar regions are dominated by the longer-period
slow waves. We also derived the slope of the power spectra ($\mathrm{\alpha}$,
the power-law index) statistically to better understand the characteristics of
turbulence present in the region. It is found that the $\mathrm{\alpha}$ values
and their distributions are similar in both plume and interplume structures
across the two AIA passbands. At the same time, the spread of these
distributions also indicates the complexity of the underlying turbulence
mechanism.
|
1712.03673v1
|
2018-08-05
|
Dispersion, damping, and intensity of spin excitations in the single-layer (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+δ}$ cuprate superconductor family
|
Using Cu-$L_3$ edge resonant inelastic x-ray scattering (RIXS) we measured
the dispersion and damping of spin excitations (magnons and paramagnons) in the
high-$T_\mathrm{c}$ superconductor (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+\delta}$
(Bi2201), for a large doping range across the phase diagram ($0.03\lesssim
p\lesssim0.21$). Selected measurements with full polarization analysis
unambiguously demonstrate the spin-flip character of these excitations, even in
the overdoped sample. We find that the undamped frequencies increase slightly
with doping for all accessible momenta, while the damping grows rapidly, faster
in the (0,0)$\rightarrow$(0.5,0.5) nodal direction than in the
(0,0)$\rightarrow$(0.5,0) antinodal direction. We compare the experimental
results to numerically exact determinant quantum Monte Carlo (DQMC)
calculations that provide the spin dynamical structure factor
$S(\textbf{Q},\omega)$ of the three-band Hubbard model. The theory reproduces
well the momentum and doping dependence of the dispersions and spectral weights
of magnetic excitations. These results provide compelling evidence that
paramagnons, although increasingly damped, persist across the superconducting
dome of the cuprate phase diagram; this implies that long range
antiferromagnetic correlations are quickly washed away, while short range
magnetic interactions are little affected by doping.
|
1808.01682v1
|
2018-09-19
|
Critical exponent for the semilinear wave equations with a damping increasing in the far field
|
We consider the Cauchy problem of the semilinear wave equation with a damping
term \begin{align*}
u_{tt} - \Delta u + c(t,x) u_t = |u|^p, \quad (t,x)\in (0,\infty)\times
\mathbb{R}^N,\quad
u(0,x) = \varepsilon u_0(x), \ u_t(0,x) = \varepsilon u_1(x), \quad x\in
\mathbb{R}^N, \end{align*} where $p>1$ and the coefficient of the damping term
has the form \begin{align*}
c(t,x) = a_0 (1+|x|^2)^{-\alpha/2} (1+t)^{-\beta} \end{align*} with some $a_0
> 0$, $\alpha < 0$, $\beta \in (-1, 1]$. In particular, we mainly consider the
cases $ \alpha < 0, \beta =0$ or $\alpha < 0, \beta = 1$, which imply $\alpha +
\beta < 1$, namely, the damping is spatially increasing and effective. Our aim
is to prove that the critical exponent is given by $ p = 1+
\frac{2}{N-\alpha}$. This shows that the critical exponent is the same as that
of the corresponding parabolic equation $c(t,x) v_t - \Delta v = |v|^p$. The
global existence part is proved by a weighted energy estimates with an
exponential-type weight function and a special case of the
Caffarelli-Kohn-Nirenberg inequality. The blow-up part is proved by a
test-function method introduced by Ikeda and Sobajima (arXiv:1710.06780v1). We
also give an upper estimate of the lifespan.
|
1809.06994v1
|
2018-09-28
|
Isotropic non-local Gilbert damping driven by spin currents in epitaxial Pd/Fe/MgO(001) films
|
Although both theoretical predications and experimental observations
demonstrated that the damping factor is anisotropic at
ferromagnet/semiconductor interface with robust interfacial spin-orbit
coupling, it is not well understood whether non-local Gilbert damping driven by
spin currents in heavy metal/ferromagnetic metal (HM/FM) bilayers is
anisotropic or not. Here, we investigated the in-plane angular- and frequency-
dependence of magnetic relaxation of epitaxial Fe/MgO(001) films with different
capping layers of Pd and Cu. After disentangling the parasitic contributions,
such as two-magnon scattering (TMS), mosaicity, and field-dragging effect, we
unambiguously observed that both local and non-local Gilbert damping are
isotropic in Fe(001) plane, suggesting that the pure spin currents absorption
is independent of Fe magnetization orientation in the epitaxial Pd/Fe
heterostructure. First principles calculation reveals that the effective spin
mixing conductance of Pd/Fe interface is nearly invariant for different
magnetization directions in good agreement with the experimental observations.
These results offer a valuable insight into the transmission and absorption of
pure spin currents, and facilitate us to utilize next-generation spintronic
devices.
|
1809.11020v1
|
2018-10-16
|
Dark matter gets DAMPE
|
The DArk Matter Particle Explorer (DAMPE) recently reported an excess of
electrons/positrons above expected background fluxes even when a double
power-law background spectrum is assumed. Several dark matter models that
involve TeV-scale leptophilic WIMPs have been suggested in the literature to
account for this excess. All of these models are associated with the presence
of a nearby dark matter clump/over-density.
In this work we set out to explore how current constraints from observational
data impact the suggested parameter space for a dark matter explanation of the
DAMPE excess, as well as make projections of the capacity of LOFAR and the
up-coming SKA to observe indirect radio emissions from the nearby dark matter
over-density.
We show that LOFAR is incapable of probing the parameter space for DAMPE
excess models, unless the dark matter clump is in the form of an ultra-compact
mini halo. Fermi-LAT limits on dark matter annihilation are unable to probe
these models in all cases. Limits derived from diffuse Coma cluster radio
emission can probe a substantial portion of the parameter space and muon
neutrino limits inferred from galactic centre gamma-ray fluxes heavily restrict
muon coupling for the proposed WIMPs. The SKA is shown to able to fully probe
the parameter space of all the studied models using indirect emissions from the
local dark matter over-density.
|
1810.07176v2
|
2018-12-16
|
Nonlinear Dynamics of Spherical Shells Buckling under Step Pressure
|
Dynamic buckling is addressed for complete elastic spherical shells subject
to a rapidly applied step in external pressure. Insights from the perspective
of nonlinear dynamics reveal essential mathematical features of the buckling
phenomena. To capture the strong buckling imperfection-sensitivity, initial
geometric imperfections in the form of an axisymmetric dimple at each pole are
introduced. Dynamic buckling under the step pressure is related to the
quasi-static buckling pressure. Both loadings produce catastrophic collapse of
the shell for conditions in which the pressure is prescribed. Damping plays an
important role in dynamic buckling because of the time-dependent nonlinear
interaction among modes, particularly the interaction between the spherically
symmetric 'breathing' mode and the buckling mode. In this paper we argue that
the precise frequency dependence of the damping does not matter as most of the
damping happens at a single frequency (the breathing frequency). In general,
there is not a unique step pressure threshold separating responses associated
with buckling from those that do not buckle. Instead there exists a cascade of
buckling thresholds, dependent on the damping and level of imperfection,
separating pressures for which buckling occurs from those for which it does not
occur. For shells with small and moderately small imperfections the dynamic
step buckling pressure can be substantially below the quasi-static buckling
pressure.
|
1812.06526v2
|
2018-12-18
|
Thermal gradient driven domain wall dynamics
|
The issue of whether a thermal gradient acts like a magnetic field or an
electric current in the domain wall (DW) dynamics is investigated. Broadly
speaking, magnetization control knobs can be classified as energy-driving or
angular-momentum driving forces. DW propagation driven by a static magnetic
field is the best-known example of the former in which the DW speed is
proportional to the energy dissipation rate, and the current-driven DW motion
is an example of the latter. Here we show that DW propagation speed driven by a
thermal gradient can be fully explained as the angular momentum transfer
between thermally generated spin current and DW. We found DW-plane rotation
speed increases as DW width decreases. Both DW propagation speed along the wire
and DW-plane rotation speed around the wire decrease with the Gilbert damping.
These facts are consistent with the angular momentum transfer mechanism, but
are distinct from the energy dissipation mechanism. We further show that
magnonic spin-transfer torque (STT) generated by a thermal gradient has both
damping-like and field-like components. By analyzing DW propagation speed and
DW-plane rotation speed, the coefficient ( \b{eta}) of the field-like STT
arising from the non-adiabatic process, is obtained. It is found that \b{eta}
does not depend on the thermal gradient; increases with uniaxial anisotropy
K_(||) (thinner DW); and decreases with the damping, in agreement with the
physical picture that a larger damping or a thicker DW leads to a better
alignment between the spin-current polarization and the local magnetization, or
a better adiabaticity.
|
1812.07244v2
|
2019-01-09
|
Turbulent dynamo in a weakly ionized medium
|
The small-scale turbulent dynamo is an important process contributing to the
cosmic magnetization. In partially ionized astrophysical plasmas, the dynamo
growth of magnetic energy strongly depends on the coupling state between ions
and neutrals and the ion-neutral collisional damping effect. A new damping
stage of turbulent dynamo in a weakly ionized medium was theoretically
predicted by Xu \& Lazarian (2016). By carrying out a 3D two-fluid dynamo
simulation, here we for the first time numerically confirmed the physical
conditions and the linear-in-time growth of magnetic field strength of the
damping stage of dynamo. The dynamo-amplified magnetic field has a
characteristic length as the damping scale, which increases with time and can
reach the injection scale of turbulence after around eight largest
eddy-turnover times given sufficiently low ionization fraction and weak initial
magnetic field. Due to the weak coupling between ions and neutrals, most
turbulent energy carried by neutrals cannot be converted to the magnetic
energy, resulting in a relatively weak magnetic field at the end of dynamo.
This result has important implications for the growth of magnetic fields in the
partially ionized interstellar medium and shock acceleration of Galactic cosmic
rays.
|
1901.02893v1
|
2019-01-25
|
Quantum speed limit time for correlated quantum channel
|
Memory effects play a fundamental role in the dynamics of open quantum
systems. There exist two different views on memory for quantum noises. In the
first view, the quantum channel has memory when there exist correlations
between successive uses of the channels on a sequence of quantum systems. These
types of channels are also known as correlated quantum channels. In the second
view, memory effects result from correlations which are created during the
quantum evolution. In this work we will consider the first view and study the
quantum speed limit time for a correlated quantum channel. Quantum speed limit
time is the bound on the minimal time which is needed for a quantum system to
evolve from an initial state to desired states. The quantum evolution is fast
if the quantum speed limit time is short. In this work, we will study the
quantum speed limit time for some correlated unital and correlated non-unital
channels. As an example for unital channels we choose correlated dephasing
colored noise. We also consider the correlated amplitude damping and correlated
squeezed generalized amplitude damping channels as the examples for non-unital
channels. It will be shown that the quantum speed limit time for correlated
pure dephasing colored noise is increased by increasing correlation strength,
while for correlated amplitude damping and correlated squeezed generalized
amplitude damping channels quantum speed limit time is decreased by increasing
correlation strength.
|
1901.08917v4
|
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