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2017-07-11 | Stability of partially locked states in the Kuramoto model through Landau damping with Sobolev regularity | The Kuramoto model is a mean-field model for the synchronisation behaviour of
oscillators, which exhibits Landau damping. In a recent work, the nonlinear
stability of a class of spatially inhomogeneous stationary states was shown
under the assumption of analytic regularity. This paper proves the nonlinear
Landau damping under the assumption of Sobolev regularity. The weaker
regularity required the construction of a different more robust bootstrap
argument, which focuses on the nonlinear Volterra equation of the order
parameter. | 1707.03475v2 |
2017-12-04 | Graviton-mediated dark matter model explanation the DAMPE electron excess and search at $e^+e^-$ colliders | The very recent result of the DAMPE cosmic ray spectrum of electrons shows a
narrow bump above the background at around 1.4 TeV. We attempt to explain the
DAMPE electron excess in a simplified Kaluza-Klein graviton-mediated dark
matter model, in which the graviton only interacts with leptons and dark
matter. The related phenomenological discussions are given and this simplified
graviton-mediated dark matter model has the potential to be cross-tested in
future lepton collider experiments. | 1712.01143v1 |
2017-12-13 | On nonlinear damped wave equations for positive operators. I. Discrete spectrum | In this paper we study a Cauchy problem for the nonlinear damped wave
equations for a general positive operator with discrete spectrum. We derive the
exponential in time decay of solutions to the linear problem with decay rate
depending on the interplay between the bottom of the operator's spectrum and
the mass term. Consequently, we prove global in time well-posedness results for
semilinear and for more general nonlinear equations with small data. Examples
are given for nonlinear damped wave equations for the harmonic oscillator, for
the twisted Laplacian (Landau Hamiltonian), and for the Laplacians on compact
manifolds. | 1712.05009v1 |
2018-05-29 | Asymptotic profile of solutions for strongly damped Klein-Gordon equations | We consider the Cauchy problem in the whole space for strongly damped
Klein-Gordon equations. We derive asymptotic profles of solutions with weighted
initial data by a simple method introduced by R. Ikehata. The obtained results
show that the wave effect will be weak because of the mass term, especially in
the low dimensional case (n = 1,2) as compared with the strongly damped wave
equations without mass term (m = 0), so the most interesting topic in this
paper is the n = 1,2 cases. | 1805.11975v1 |
2019-02-27 | Forward Discretely Self-Similar Solutions of the MHD Equations and the Viscoelastic Navier-Stokes Equations with Damping | In this paper, we prove the existence of forward discretely self-similar
solutions to the MHD equations and the viscoelastic Navier-Stokes equations
with damping with large weak $L^3$ initial data. The same proving techniques
are also applied to construct self-similar solutions to the MHD equations and
the viscoelastic Navier-Stokes equations with damping with large weak $L^3$
initial data. This approach is based on [Z. Bradshaw and T.-P. Tsai, Ann. Henri
Poincar'{e}, vol. 18, no. 3, 1095-1119, 2017]. | 1902.10771v3 |
2019-03-11 | The effect of magnetic twist on resonant absorption of slow sausage waves in magnetic flux tubes | Observations show that twisted magnetic flux tubes are present throughout the
sun's atmosphere. The main aim of this work is to obtain the damping rate of
sausage modes in the presence of magnetic twist. Using the connection formulae
obtained by Sakurai et al. (1991), we investigate resonant absorption of the
sausage modes in the slow continuum under photosphere conditions. We derive the
dispersion relation and solve it numerically and consequently obtain the
frequencies and damping rates of the slow surface sausage modes. We conclude
that the magnetic twist can result in strong damping in comparison with the
untwisted case. | 1903.04171v1 |
2019-03-14 | Endpoint Strichartz estimate for the damped wave equation and its application | Recently, the Strichartz estimates for the damped wave equation was obtained
by the first author except for the wave endpoint case. In the present paper, we
give the Strichartz estimate in the wave endpoint case. We slightly modify the
argument of Keel--Tao. Moreover, we apply the endpoint Strichartz estimate to
the unconditional uniqueness for the energy critical nonlinear damped wave
equation. This problem seems not to be solvable as the perturbation of the wave
equation. | 1903.05891v2 |
2019-04-02 | Linear inviscid damping in Gevrey spaces | We prove linear inviscid damping near a general class of monotone shear flows
in a finite channel, in Gevrey spaces. It is an essential step towards proving
nonlinear inviscid damping for general shear flows that are not close to the
Couette flow, which is a major open problem in 2d Euler equations. | 1904.01188v2 |
2019-04-16 | Damping modes of harmonic oscillator in open quantum systems | Through a set of generators that preserves the hermiticity and trace of
density matrices, we analyze the damping of harmonic oscillator in open quantum
systems into four modes, distinguished by their specific effects on the
covariance matrix of position and momentum of the oscillator. The damping modes
could either cause exponential decay to the initial covariance matrix or shift
its components. They have to act together properly in actual dynamics to ensure
that the generalized uncertainty relation is satisfied. We use a few quantum
master equations to illustrate the results. | 1904.07452v2 |
2019-05-20 | Stabilization of two strongly coupled hyperbolic equations in exterior domains | In this paper we study the behavior of the total energy and the $L^2$-norm of
solutions of two coupled hyperbolic equations by velocities in exterior
domains. Only one of the two equations is directly damped by a localized
damping term. We show that, when the damping set contains the coupling one and
the coupling term is effective at infinity and on captive region, then the
total energy decays uniformly and the $L^2$-norm of smooth solutions is
bounded. In the case of two Klein-Gordon equations with equal speeds we deduce
an exponential decay of the energy. | 1905.08370v1 |
2019-11-26 | Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping | The aim of this paper is to analyze the long-time dynamical behavior of the
solution for a degenerate wave equation with time-dependent damping term
$\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded
domain $\Omega\subset\mathbb{R}^N$ with Dirichlet boundary conditions. Under
some restrictions on $\beta(t)$ and critical growth restrictions on the
nonlinear term $f$, we will prove the local and global well-posedness of the
solution and derive the existence of a pullback attractor for the process
associated with the degenerate damped hyperbolic problem. | 1911.11432v1 |
2019-12-18 | Blow-up criteria for linearly damped nonlinear Schrödinger equations | We consider the Cauchy problem for linearly damped nonlinear Schr\"odinger
equations
\[ i\partial_t u + \Delta u + i a u= \pm |u|^\alpha u, \quad (t,x) \in
[0,\infty) \times \mathbb{R}^N, \] where $a>0$ and $\alpha>0$. We prove the
global existence and scattering for a sufficiently large damping parameter in
the energy-critical case. We also prove the existence of finite time blow-up
$H^1$ solutions to the focusing problem in the mass-critical and
mass-supercritical cases. | 1912.08752v2 |
2020-01-17 | Bounding the Classical Capacity of Multilevel Damping Quantum Channels | A recent method to certify the classical capacity of quantum communication
channels is applied for general damping channels in finite dimension. The
method compares the mutual information obtained by coding on the computational
and a Fourier basis, which can be obtained by just two local measurement
settings and classical optimization. The results for large representative
classes of different damping structures are presented. | 2001.06486v2 |
2020-01-27 | Robustness of polynomial stability of damped wave equations | In this paper we present new results on the preservation of polynomial
stability of damped wave equations under addition of perturbing terms. We in
particular introduce sufficient conditions for the stability of perturbed
two-dimensional wave equations on rectangular domains, a one-dimensional weakly
damped Webster's equation, and a wave equation with an acoustic boundary
condition. In the case of Webster's equation, we use our results to compute
explicit numerical bounds that guarantee the polynomial stability of the
perturbed equation. | 2001.10033v3 |
2020-02-09 | Fujita modified exponent for scale invariant damped semilinear wave equations | The aim of this paper is to prove a blow up result of the solution for a
semilinear scale invariant damped wave equation under a suitable decay
condition on radial initial data. The admissible range for the power of the
nonlinear term depends both on the damping coefficient and on the pointwise
decay order of the initial data. In addition we give an upper bound estimate
for the lifespan of the solution, in terms of the power of the nonlinearity,
size and growth of initial data. | 2002.03418v2 |
2020-02-16 | Blow up results for semi-linear structural damped wave model with nonlinear memory | This article is to study the nonexistence of global solutions to semi-linear
structurally damped wave equation with nonlinear memory in $\R^n$ for any space
dimensions $n\ge 1$ and for the initial arbitrarily small data being subject to
the positivity assumption. We intend to apply the method of a modified test
function to establish blow-up results and to overcome some difficulties as well
caused by the well-known fractional Laplacian $(-\Delta)^{\sigma/2}$ in
structural damping terms. | 2002.06582v1 |
2020-05-24 | A transmission problem for the Timoshenko system with one local Kelvin-Voigt damping and non-smooth coefficient at the interface | In this paper, we study the indirect stability of Timoshenko system with
local or global Kelvin-Voigt damping, under fully Dirichlet or mixed boundary
conditions. Unlike the results of H. L. Zhao, K. S. Liu, and C. G. Zhang and of
X. Tian and Q. Zhang, in this paper, we consider the Timoshenko system with
only one locally or globally distributed Kelvin-Voigt damping. Indeed, we prove
that the energy of the system decays polynomially and that the obtained decay
rate is in some sense optimal. The method is based on the frequency domain
approach combining with multiplier method. | 2005.12756v1 |
2020-06-09 | Lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity | This paper is devoted to the lifespan of solutions to a damped fourth-order
wave equation with logarithmic nonlinearity $$u_{tt}+\Delta^2u-\Delta
u-\omega\Delta u_t+\alpha(t)u_t=|u|^{p-2}u\ln|u|.$$ Finite time blow-up
criteria for solutions at both lower and high initial energy levels are
established, and an upper bound for the blow-up time is given for each case.
Moreover, by constructing a new auxiliary functional and making full use of the
strong damping term, a lower bound for the blow-up time is also derived. | 2006.05006v1 |
2020-07-05 | Oscillation of damped second order quasilinear wave equations with mixed arguments | Following the previous work [1], we investigate the impact of damping on the
oscillation of smooth solutions to some kind of quasilinear wave equations with
Robin and Dirichlet boundary condition. By using generalized Riccati
transformation and technical inequality method, we give some sufficient
conditions to guarantee the oscillation of all smooth solutions. From the
results, we conclude that positive damping can ``hold back" oscillation. At
last, some examples are presented to confirm our main results. | 2007.02284v1 |
2020-07-08 | A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term | In this paper, we investigate blow-up of solutions to semilinear wave
equations with scale-invariant damping and nonlinear memory term in
$\mathbb{R}^n$, which can be represented by the Riemann-Liouville fractional
integral of order $1-\gamma$ with $\gamma\in(0,1)$. Our main interest is to
study mixed influence from damping term and the memory kernel on blow-up
conditions for the power of nonlinearity, by using test function method or
generalized Kato's type lemma. We find a new competition, particularly for the
small value of $\gamma$, on the blow-up range between the effective case and
the non-effective case. | 2007.03954v2 |
2020-09-10 | Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime | We prove by using an iteration argument some blow-up results for a semilinear
damped wave equation in generalized Einstein-de Sitter spacetime with a
time-dependent coefficient for the damping term and power nonlinearity. Then,
we conjecture an expression for the critical exponent due to the main blow-up
results, which is consistent with many special cases of the considered model
and provides a natural generalization of Strauss exponent. In the critical
case, we consider a non-autonomous and parameter-dependent Cauchy problem for a
linear ODE of second-order, whose explicit solutions are determined by means of
special functions' theory. | 2009.05372v1 |
2020-09-11 | Asymptotic profiles for a wave equation with parameter dependent logarithmic damping | We study a nonlocal wave equation with logarithmic damping which is rather
weak in the low frequency zone as compared with frequently studied strong
damping case. We consider the Cauchy problem for this model in the whole space
and we study the asymptotic profile and optimal estimates of the solutions and
the total energy as time goes to infinity in L^{2}-sense. In that case some
results on hypergeometric functions are useful. | 2009.06395v1 |
2020-09-17 | Sensitivity of steady states in a degenerately-damped stochastic Lorenz system | We study stability of solutions for a randomly driven and degenerately damped
version of the Lorenz '63 model. Specifically, we prove that when damping is
absent in one of the temperature components, the system possesses a unique
invariant probability measure if and only if noise acts on the convection
variable. On the other hand, if there is a positive growth term on the vertical
temperature profile, we prove that there is no normalizable invariant state.
Our approach relies on the derivation and analysis of non-trivial Lyapunov
functions which ensure positive recurrence or null-recurrence/transience of the
dynamics. | 2009.08429v1 |
2021-01-23 | Oscillation time and damping coefficients in a nonlinear pendulum | We establish a relationship between the normalized damping coefficients and
the time that takes a nonlinear pendulum to complete one oscillation starting
from an initial position with vanishing velocity. We establish some conditions
on the nonlinear restitution force so that this oscillation time does not
depend monotonically on the viscosity damping coefficient. | 2101.09400v2 |
2021-02-20 | Lifespan estimates for semilinear wave equations with space dependent damping and potential | In this work, we investigate the influence of general damping and potential
terms on the blow-up and lifespan estimates for energy solutions to power-type
semilinear wave equations. The space-dependent damping and potential functions
are assumed to be critical or short range, spherically symmetric perturbation.
The blow up results and the upper bound of lifespan estimates are obtained by
the so-called test function method. The key ingredient is to construct special
positive solutions to the linear dual problem with the desired asymptotic
behavior, which is reduced, in turn, to constructing solutions to certain
elliptic "eigenvalue" problems. | 2102.10257v1 |
2021-02-24 | Attractors for locally damped Bresse systems and a unique continuation property | This paper is devoted to Bresse systems, a robust model for circular beams,
given by a set of three coupled wave equations. The main objective is to
establish the existence of global attractors for dynamics of semilinear
problems with localized damping. In order to deal with localized damping a
unique continuation property (UCP) is needed. Therefore we also provide a
suitable UCP for Bresse systems. Our strategy is to set the problem in a
Riemannian geometry framework and see the system as a single equation with
different Riemann metrics. Then we perform Carleman-type estimates to get our
result. | 2102.12025v1 |
2021-03-09 | Global weak solution of 3D-NSE with exponential damping | In this paper we prove the global existence of incompressible Navier-Stokes
equations with damping $\alpha (e^{\beta |u|^2}-1)u$, where we use Friedrich
method and some new tools. The delicate problem in the construction of a global
solution, is the passage to the limit in exponential nonlinear term. To solve
this problem, we use a polynomial approximation of the damping part and a new
type of interpolation between $L^\infty(\mathbb{R}^+,L^2(\mathbb{R}^3))$ and
the space of functions $f$ such that $(e^{\beta|f|^2}-1)|f|^2\in
L^1(\mathbb{R}^3)$. Fourier analysis and standard techniques are used. | 2103.05388v1 |
2021-05-31 | Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition | It has been established that solutions to the inviscid Proudman-Johnson
equation subject to a homogeneous three-point boundary condition can develop
singularities in finite time. In this paper, we consider the possibility of
singularity formation in solutions of the generalized, inviscid
Proudman-Johnson equation with damping subject to the same homogeneous
three-point boundary condition. In particular, we derive conditions the initial
data must satisfy in order for solutions to blowup in finite time with either
bounded or unbounded smooth damping term. | 2106.00068v1 |
2021-06-16 | Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations | The dependence of the fractal dimension of global attractors for the damped
3D Euler--Bardina equations on the regularization parameter $\alpha>0$ and
Ekman damping coefficient $\gamma>0$ is studied. We present explicit upper
bounds for this dimension for the case of the whole space, periodic boundary
conditions, and the case of bounded domain with Dirichlet boundary conditions.
The sharpness of these estimates when $\alpha\to0$ and $\gamma\to0$ (which
corresponds in the limit to the classical Euler equations) is demonstrated on
the 3D Kolmogorov flows on a torus. | 2106.09077v1 |
2021-06-23 | Damping of the Franz-Keldysh oscillations in the presence of disorder | Franz-Keldysh oscillations of the optical absorption in the presence of
short-range disorder are studied theoretically. The magnitude of the effect
depends on the relation between the mean-free path in a zero field and the
distance between the turning points in electric field. Damping of the
Franz-Keldysh oscillations by the disorder develops at high absorption
frequency. Effect of damping is amplified by the fact that, that electron and
hole are most sensitive to the disorder near the turning points. This is
because, near the turning points, velocities of electron and hole turn to zero. | 2106.12691v1 |
2021-06-25 | Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems | In Hilbert space, we propose a family of primal-dual dynamical system for
affine constrained convex optimization problem. Several damping coefficients,
time scaling coefficients, and perturbation terms are thus considered. By
constructing the energy functions, we investigate the convergence rates with
different choices of the damping coefficients and time scaling coefficients.
Our results extend the inertial dynamical approaches for unconstrained convex
optimization problems to affine constrained convex optimization problems. | 2106.13702v1 |
2021-07-01 | Event-triggering mechanism to damp the linear wave equation | This paper aims at proposing a sufficient matrix inequality condition to
carry out the global exponential stability of the wave equation under an
event-triggering mechanism that updates a damping source term. The damping is
distributed in the whole space but sampled in time. The wellposedness of the
closed-loop event-triggered control system is shown. Furthermore, the avoidance
of Zeno behavior is ensured provided that the initial data are more regular.
The interest of the results is drawn through some numerical simulations. | 2107.00292v1 |
2022-01-28 | Quantum metrology with a non-linear kicked Mach-Zehnder interferometer | We study the sensitivity of a Mach-Zehnder interferometer that contains in
addition to the phase shifter a non-linear element. By including both elements
in a cavity or a loop that the light transverses many times, a non-linear
kicked version of the interferometer arises. We study its sensitivity as
function of the phase shift, the kicking strength, the maximally reached
average number of photons, and damping due to photon loss for an initial
coherent state. We find that for vanishing damping Heisenberg-limited scaling
of the sensitivity arises if squeezing dominates the total photon number. For
small to moderate damping rates the non-linear kicks can considerably increase
the sensitivity as measured by the quantum Fisher information per unit time. | 2201.12255v1 |
2022-02-27 | The time asymptotic expansion for the compressible Euler equations with time-dependent damping | In this paper, we study the compressible Euler equations with time-dependent
damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We propose a time asymptotic
expansion around the self-similar solution of the generalized porous media
equation (GPME) and rigorously justify this expansion as $\lambda \in
(\frac17,1)$. In other word, instead of the self-similar solution of GPME, the
expansion is the best asymptotic profile of the solution to the compressible
Euler equations with time-dependent damping. | 2202.13385v1 |
2022-03-12 | Stability for nonlinear wave motions damped by time-dependent frictions | We are concerned with the dynamical behavior of solutions to semilinear wave
systems with time-varying damping and nonconvex force potential. Our result
shows that the dynamical behavior of solution is asymptotically stable without
any bifurcation and chaos. And it is a sharp condition on the damping
coefficient for the solution to converge to some equilibrium. To illustrate our
theoretical results, we provide some numerical simulations for dissipative
sine-Gordon equation and dissipative Klein-Gordon equation. | 2203.06312v1 |
2022-03-30 | A Toy Model for Damped Water Waves | We consider a toy model for a damped water waves system in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$. The toy model is based on the
paradifferential water waves equation derived in the work of
Alazard-Burq-Zuily. The form of damping we utilize we utilize is a modified
sponge layer proposed for the three-dimensional water waves system by Clamond,
et. al. We show that, in the case of small Cauchy data, solutions to the toy
model exhibit a quadratic lifespan. This is done via proving energy estimates
with the energy being constructed from appropriately chosen vector fields. | 2203.16645v1 |
2022-05-10 | Global attractor for the weakly damped forced Kawahara equation on the torus | We study the long time behaviour of solutions for the weakly damped forced
Kawahara equation on the torus. More precisely, we prove the existence of a
global attractor in $L^2$, to which as time passes all solutions draw closer.
In fact, we show that the global attractor turns out to lie in a smoother space
$H^2$ and be bounded therein. Further, we give an upper bound of the size of
the attractor in $H^2$ that depends only on the damping parameter and the norm
of the forcing term. | 2205.04642v1 |
2022-06-07 | Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data | We study the large time behavior of solutions to the semilinear wave equation
with space-dependent damping and absorbing nonlinearity in the whole space or
exterior domains. Our result shows how the amplitude of the damping
coefficient, the power of the nonlinearity, and the decay rate of the initial
data at the spatial infinity determine the decay rates of the energy and the
$L^2$-norm of the solution. In Appendix, we also give a survey of basic results
on the local and global existence of solutions and the properties of weight
functions used in the energy method. | 2206.03218v2 |
2022-10-24 | The time asymptotic expansion for the compressible Euler equations with damping | In 1992, Hsiao and Liu \cite{Hsiao-Liu-1} firstly showed that the solution to
the compressible Euler equations with damping time-asymptotically converges to
the diffusion wave $(\bar v, \bar u)$ of the porous media equation. In
\cite{Geng-Huang-Jin-Wu}, we proposed a time-asymptotic expansion around the
diffusion wave $(\bar v, \bar u)$, which is a better asymptotic profile than
$(\bar v, \bar u)$. In this paper, we rigorously justify the time-asymptotic
expansion by the approximate Green function method and the energy estimates.
Moreover, the large time behavior of the solution to compressible Euler
equations with damping is accurately characterized by the time asymptotic
expansion. | 2210.13157v1 |
2022-12-18 | Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions | We establish the decay of the solutions of the damped wave equations in one
dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions
where the damping coefficient is a function of space and time. The analysis is
based on the study of the corresponding hyperbolic systems associated with the
Riemann invariants. The key ingredient in the study of these systems is the use
of the internal dissipation energy to estimate the difference of solutions with
their mean values in an average sense. | 2212.09164v1 |
2023-02-09 | A remark on the logarithmic decay of the damped wave and Schrödinger equations on a compact Riemannian manifold | In this paper we consider a compact Riemannian manifold (M, g) of class C 1
$\cap$ W 2,$\infty$ and the damped wave or Schr\"odinger equations on M , under
the action of a damping function a = a(x). We establish the following fact: if
the measure of the set {x $\in$ M ; a(x) = 0} is strictly positive, then the
decay in time of the associated energy is at least logarithmic. | 2302.04498v1 |
2023-03-02 | Using vibrating wire in non-linear regime as a thermometer in superfluid $^3$He-B | Vibrating wires are common temperature probes in $^3$He experiments. By
measuring mechanical resonance of a wire driven by AC current in magnetic field
one can directly obtain temperature-dependent viscous damping. This is easy to
do in a linear regime where wire velocity is small enough and damping force is
proportional to velocity. At lowest temperatures in superfluid $^3$He-B a
strong non-linear damping appears and linear regime shrinks to a very small
velocity range. Expanding measurements to the non-linear area can significantly
improve sensitivity. In this note I describe some technical details useful for
analyzing such temperature measurements. | 2303.01189v1 |
2023-04-06 | A turbulent study for a damped Navier-Stokes equation: turbulence and problems | In this article we consider a damped version of the incompressible
Navier-Stokes equations in the whole three-dimensional space with a
divergence-free and time-independent external force. Within the framework of a
well-prepared force and with a particular choice of the damping parameter, when
the Grashof numbers are large enough, we are able to prove some estimates from
below and from above between the fluid characteristic velocity and the energy
dissipation rate according to the Kolmogorov dissipation law. Precisely, our
main contribution concerns the estimate from below which is not often studied
in the existing literature. Moreover, we address some remarks which open the
door to a deep discussion on the validity of this theory of turbulence. | 2304.03134v1 |
2023-05-03 | Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions | We establish the exponential decay of the solutions of the damped wave
equations in one-dimensional space where the damping coefficient is a
nowhere-vanishing function of space. The considered PDE is associated with
several dynamic boundary conditions, also referred to as Wentzell/Ventzel
boundary conditions in the literature. The analysis is based on the
determination of appropriate Lyapunov functions and some further analysis. This
result is associated with a regulation problem inspired by a real experiment
with a proportional-integral control. Some numerical simulations and additional
results on closed wave equations are also provided. | 2305.01969v2 |
2023-05-13 | Global existence for a 3D Tropical Climate Model with damping and small initial data in $\dot H^{1/2}(\mathbb{R}^3)$ | We consider a 3D Tropical Climate Model with damping terms in the equation of
the barotropic mode $u$ and in the equation of the first baroclinic mode $v$ of
the velocity. The equation for the temperature $\theta$ is free from dampings.
We prove global existence in time for this system assuming the initial data
$(u_0, v_0,\theta_0)$ small, in terms of the homogeneous space $\dot
H^{1/2}(\mathbb{R}^3)$. | 2305.07964v1 |
2023-06-21 | The effect of singularities and damping on the spectra of photonic crystals | Understanding the dispersive properties of photonic crystals is a fundamental
and well-studied problem. However, the introduction of singular permittivities
and damping complicates the otherwise straightforward theory. In this paper, we
study photonic crystals with a Drude-Lorentz model for the permittivity,
motivated by halide perovskites. We demonstrate how the introduction of
singularities and damping affects the spectral band structure and show how to
interpret the notion of a "band gap" in this setting. We present explicit
solutions for a one-dimensional model and show how integral operators can be
used to handle multi-dimensional systems. | 2306.12254v1 |
2023-07-12 | Asymptotic behavior of solutions to the Cauchy problem for 1-D p-system with space dependent damping | We consider the Cauchy problem for one-dimensional p-system with damping of
space-dependent coefficient. This system models the compressible flow through
porous media in the Lagrangean coordinate. Our concern is an asymptotic
behavior of solutions, which is expected to be the diffusion wave based on the
Darcy law. To show this expectation, the problem is reformulated to the Cauchy
problem for the second order quasilinear hyperbolic equation with space
dependent damping, which is analyzed by the energy method. | 2307.05865v1 |
2023-07-12 | Parabolic-elliptic Keller-Segel's system | We study on the whole space R d the compressible Euler system with damping
coupled to the Poisson equation when the damping coefficient tends towards
infinity. We first prove a result of global existence for the Euler-Poisson
system in the case where the damping is large enough, then, in a second step,
we rigorously justify the passage to the limit to the parabolic-elliptic
Keller-Segel after performing a diffusive rescaling, and get an explicit
convergence rate. The overall study is carried out in 'critical' Besov spaces,
in the spirit of the recent survey [16] by R. Danchin devoted to partially
dissipative systems. | 2307.05981v1 |
2023-07-25 | Asymptotic behavior and life-span estimates for the damped inhomogeneous nonlinear Schrödinger equation | We are interested in the behavior of solutions to the damped inhomogeneous
nonlinear Schr\"odinger equation $ i\partial_tu+\Delta
u+\mu|x|^{-b}|u|^{\alpha}u+iau=0$, $\mu \in\mathbb{C} $, $b>0$, $a \in
\mathbb{C}$ such that $\Re \textit{e}(a) \geq 0$, $\alpha>0$. We establish
lower and upper bound estimates of the life-span. In particular for $a\geq 0$,
we obtain explicit values $a_*,\; a^*$ such that if $a<a_*$ then blow up
occurs, while for $a>a^*,$ global existence holds. Also, we prove scattering
results with precise decay rates for large damping. Some of the results are new
even for $b=0.$ | 2307.13495v1 |
2023-07-26 | On nonlinear Landau damping and Gevrey regularity | In this article we study the problem of nonlinear Landau damping for the
Vlasov-Poisson equations on the torus. As our main result we show that for
perturbations initially of size $\epsilon>0$ and time intervals
$(0,\epsilon^{-N})$ one obtains nonlinear stability in regularity classes
larger than Gevrey $3$, uniformly in $\epsilon$. As a complementary result we
construct families of Sobolev regular initial data which exhibit nonlinear
Landau damping. Our proof is based on the methods of Grenier, Nguyen and
Rodnianski. | 2307.14271v1 |
2023-08-18 | Damping for fractional wave equations and applications to water waves | Motivated by numerically modeling surface waves for inviscid Euler equations,
we analyze linear models for damped water waves and establish decay properties
for the energy for sufficiently regular initial configurations. Our findings
give the explicit decay rates for the energy, but do not address
reflection/transmission of waves at the interface of the damping. Still for a
subset of the models considered, this represents the first result proving the
decay of the energy of the surface wave models. | 2308.09288v1 |
2023-08-30 | Optimal decay for one-dimensional damped wave equations with potentials via a variant of Nash inequality | The optimality of decay properties of the one-dimensional damped wave
equations with potentials belonging to a certain class is discussed. The
typical ingredient is a variant of Nash inequality which involves an invariant
measure for the corresponding Schr\"odinger semigroup. This enables us to find
a sharp decay estimate from above. Moreover, the use of a test function method
with the Nash-type inequality provides the decay estimate from below. The
diffusion phenomena for the damped wave equations with potentials are also
considered. | 2308.15680v1 |
2023-09-15 | Explicit solutions and linear inviscid damping in the Euler-Boussinesq equation near a stratified Couette flow in the periodic strip | This short note provides explicit solutions to the linearized Boussinesq
equations around the stably stratified Couette flow posed on
$\mathbb{T}\times\mathbb{R}$. We consider the long-time behavior of such
solutions and prove inviscid damping of the perturbed density and velocity
field for any positive Richardson number, with optimal rates. The explicit
solution is obtained through the limiting absorption principle whereas the
inviscid damping is proved using oscillatory integral methods. | 2309.08419v2 |
2023-09-21 | Beyond Qubits : An Extensive Noise Analysis for Qutrit Quantum Teleportation | The four quantum noises Bit Flip, Phase Flip, Depolarization, and Amplitude
Damping as well as any potential combinations of them are examined in this
papers investigation of quantum teleportation using qutrit states. Among the
above mentioned noises, we observed phase flip has highest fidelity. Compared
to uncorrelated Amplitude Damping, we find that correlated Amplitude Damping
performs two times better. Finally, we agreed that, for better fidelity, it is
preferable to provide the same noise in channel state if noise is unavoidable. | 2309.12163v1 |
2023-12-22 | Soliton resolution for the energy critical damped wave equations in the radial case | We consider energy-critical damped wave equation \begin{equation*}
\partial_{tt}u-\Delta u+\alpha \partial_t u=\left|u\right|^{\frac{4}{D-2}}u
\end{equation*} with radial initial data in dimensions $D\geq 4$. The equation
has a nontrivial radial stationary solution $W$, called the ground state, which
is unique up to sign and scale. We prove that any bounded energy norm solution
behaves asymptotically as a superposition of the modulated ground states and a
radiation term. In the global case, particularly, the solution converges to a
pure multi-bubble due to the damping effect. | 2401.04115v2 |
2024-02-18 | Sharp lifespan estimate for the compressible Euler system with critical time-dependent damping in $\R^2$ | This paper concerns the long time existence to the smooth solutions of the
compressible Euler system with critical time dependent damping in $\R^2$. We
establish the sharp lifespan estimate from below, with respect to the small
parameter of the initial perturbation. For this end, the vector fields
$\widehat{Z}$ (defined below) are used instead of the usual one $Z$, to get
better decay for the linear error terms. This idea may also apply to the long
time behavior study of nonlinear wave equations with time-dependent damping. | 2402.11516v1 |
2024-02-28 | Linear inviscid damping in the presence of an embedding eigenvalue | In this paper, we investigate the long-time dynamics of the linearized 2-D
Euler equations around a hyperbolic tangent flow $(\tanh y,0)$. A key
difference compared to previous results is that the linearized operator has an
embedding eigenvalue, which has a significant impact on the dynamics of the
linearized system. For the first mode, the dynamics consists of there parts:
non-decay part related to the eigenspace associated with the embedding
eigenvalue, slow decay part due to the resolvent singularity, and fast decay
part related to the inviscid damping. For higher modes, the dynamics is similar
to the inviscid damping phenomena in the case without embedding eigenvalues. | 2402.18229v1 |
2024-03-19 | Improved decay results for micropolar flows with nonlinear damping | We examine the long-time behavior of solutions (and their derivatives) to the
micropolar equations with nonlinear velocity damping. Additionally, we get a
speed-up gain of $ t^{1/2} $ for the angular velocity, consistent with
established findings for classic micropolar flows lacking nonlinear damping.
Consequently, we also obtain a sharper result regarding the asymptotic
stability of the micro-rotational velocity $\ww(\cdot,t)$. Related results of
independent interest are also included. | 2403.12885v1 |
2024-03-26 | On a class of nonautonomous quasilinear systems with general time-gradually-degenerate damping | In this paper, we study two systems with a time-variable coefficient and
general time-gradually-degenerate damping. More explicitly, we construct the
Riemann solutions to the time-variable coefficient Zeldovich approximation and
time-variable coefficient pressureless gas systems both with general
time-gradually-degenerate damping. Applying the method of similar variables and
nonlinear viscosity, we obtain classical Riemann solutions and delta shock wave
solutions. | 2403.17732v1 |
2002-09-30 | The Cosmic Microwave Background & Inflation, Then & Now | Boomerang, Maxima, DASI, CBI and VSA significantly increase the case for
accelerated expansion in the early universe (the inflationary paradigm) and at
the current epoch (dark energy dominance), especially when combined with data
on high redshift supernovae (SN1) and large scale structure (LSS). There are
``7 pillars of Inflation'' that can be shown with the CMB probe, and at least
5, and possibly 6, of these have already been demonstrated in the CMB data: (1)
a large scale gravitational potential; (2) acoustic peaks/dips; (3) damping due
to shear viscosity; (4) a Gaussian (maximally random) distribution; (5)
secondary anisotropies; (6) polarization. A 7th pillar, anisotropies induced by
gravity wave quantum noise, could be too small. A minimal inflation parameter
set, \omega_b,\omega_{cdm}, \Omega_{tot}, \Omega_Q,w_Q,n_s,\tau_C, \sigma_8},
is used to illustrate the power of the current data. We find the CMB+LSS+SN1
data give \Omega_{tot} =1.00^{+.07}_{-.03}, consistent with (non-baroque)
inflation theory. Restricting to \Omega_{tot}=1, we find a nearly scale
invariant spectrum, n_s =0.97^{+.08}_{-.05}. The CDM density, \Omega_{cdm}{\rm
h}^2 =.12^{+.01}_{-.01}, and baryon density, \Omega_b {\rm h}^2 =
>.022^{+.003}_{-.002}, are in the expected range. (The Big Bang nucleosynthesis
estimate is 0.019\pm 0.002.) Substantial dark (unclustered) energy is inferred,
\Omega_Q \approx 0.68 \pm 0.05, and CMB+LSS \Omega_Q values are compatible with
the independent SN1 estimates. The dark energy equation of state, crudely
parameterized by a quintessence-field pressure-to-density ratio w_Q, is not
well determined by CMB+LSS (w_Q < -0.4 at 95% CL), but when combined with SN1
the resulting w_Q < -0.7 limit is quite consistent with the w_Q=-1 cosmological
constant case. | 0210007v1 |
2003-06-17 | Kinetic equilibrium of iron in the atmospheres of cool stars III. The ionization equilibrium of selected reference stars | Non-LTE line formation calculations of Fe I are performed for a small number
of reference stars to investigate and quantify the efficiency of neutral
hydrogen collisions. Using the atomic model that was described in previous
publications, the final discrimination with respect to hydrogen collisions is
based on the condition that the surface gravities as determined by the Fe I/Fe
II ionization equilibria are in agreement with their astrometric counterparts
obtained from HIPPARCOS parallaxes. Depending on the choice of the hydrogen
collision scaling factor S_H, we find deviations from LTE in Fe I ranging from
0.00 (S_H = infinity) to 0.46 dex (S_H = 0 for HD140283) in the logarithmic
abundances while Fe II follows LTE.
With the exception of Procyon, for which a mild temperature correction is
needed to fulfil the ionization balance, excellent consistency is obtained for
the metal-poor reference stars if Balmer profile temperatures are combined with
S_H = 3. The correct choice of collisional damping parameters ("van-der-Waals"
constants) is found to be generally more important for these little evolved
metal-poor stars than considering departures from LTE. For the Sun the
calibrated value for S_H leads to average Fe I non-LTE corrections of 0.02 dex
and a mean abundance from Fe I lines of log epsilon(Fe) = 7.49 \pm 0.08.
We confront the deduced stellar parameters with comparable spectroscopic
analyses by other authors which also rely on the iron ionization equilibrium as
a gravity indicator. On the basis of the HIPPARCOS astrometry our results are
shown to be an order of magnitude more precise than published data sets, both
in terms of offset and star-to-star scatter. | 0306337v1 |
2003-10-08 | Signatures of Relativistic Neutrinos in CMB Anisotropy and Matter Clustering | We present a detailed analytical study of ultra-relativistic neutrinos in
cosmological perturbation theory and of the observable signatures of
inhomogeneities in the cosmic neutrino background. We note that a modification
of perturbation variables that removes all the time derivatives of scalar
gravitational potentials from the dynamical equations simplifies their solution
notably. The used perturbations of particle number per coordinate, not proper,
volume are generally constant on superhorizon scales. In real space an
analytical analysis can be extended beyond fluids to neutrinos.
The faster cosmological expansion due to the neutrino background changes the
acoustic and damping angular scales of the cosmic microwave background (CMB).
But we find that equivalent changes can be produced by varying other standard
parameters, including the primordial helium abundance. The low-l integrated
Sachs-Wolfe effect is also not sensitive to neutrinos. However, the gravity of
neutrino perturbations suppresses the CMB acoustic peaks for the multipoles
with l>~200 while it enhances the amplitude of matter fluctuations on these
scales. In addition, the perturbations of relativistic neutrinos generate a
*unique phase shift* of the CMB acoustic oscillations that for adiabatic
initial conditions cannot be caused by any other standard physics. The origin
of the shift is traced to neutrino free-streaming velocity exceeding the sound
speed of the photon-baryon plasma. We find that from a high resolution, low
noise instrument such as CMBPOL the effective number of light neutrino species
can be determined with an accuracy of sigma(N_nu) = 0.05 to 0.09, depending on
the constraints on the helium abundance. | 0310198v3 |
2004-09-22 | First stars VI - Abundances of C, N, O, Li, and mixing in extremely metal-poor giants. Galactic evolution of the light elements | We have investigated the poorly-understood origin of nitrogen in the early
Galaxy by determining N abundances in 35 extremely metal-poor halo giants (22
stars have [Fe/H]<-3.0) using the C and O abundances determined in Paper V.
Because any dredge-up of CNO processed material to the surface may complicate
the interpretation of CNO abundances in giants, we have also measured the
surface abundance of lithium. Our sample shows a clear dichotomy between two
groups of stars. The first group shows evidence of C to N conversion through CN
cycling and strong Li dilution, a signature of mixing. The second group shows
no evidence for C to N conversion, and Li is only moderately diluted, and we
conclude that their C and N abundances are very close to those of the gas from
which they formed in the early Galaxy. These "unmixed" stars reflect the
abundances in the early Galaxy: the [C/Fe] ratio is constant (about +0.2 dex)
and the [C/Mg] ratio is close to solar at low metallicity, favouring a high C
production by massive zero-metal supernovae. The [N/Fe] and [N/Mg] ratios
scatter widely. The larger values of these ratios define a flat upper plateau
([N/Mg]= 0.0, [N/Fe]= +0.1), which could reflect higher values within a wide
range of yields of zero-metal Sne II. Alternatively, by analogy with the DLA's,
the lower abundances ([N/Mg]= -1.1, [N/Fe]= -0.7) could reflect generally low
yields from the first Sne II, the other stars being N enhanced by winds of
massive Asymptotic Giant Branch (AGB) stars. At present it cannot be decided
whether primary N is produced primarily in SNe II or in massive AGB stars, or
in both. The stellar N abundances and [N/O] ratios are compatible with those
found in Damped Lyman-alpha (DLA) systems. | 0409536v3 |
2005-09-15 | Damped Lyman Alpha Systems at z<1.65: The Expanded SDSS HST Sample | We present results of our HST Cycle 11 Survey for low-redshift (z<1.65) DLAs
in the UV spectra of quasars selected from the SDSS Early Data Release. These
quasars have strong intervening MgII-FeII systems which are known signatures of
high column density neutral gas. In total, UV observations of Ly-alpha
absorption in 197 MgII systems with z<1.65 and rest equivalent width (REW)
W2796 \ge 0.3A have now been obtained. The main results are: (1) 36(+/- 6)% of
systems with W2796 \ge 0.5 A and FeII W2600 \ge 0.5 A are DLAs. This increases
to 42(+/- 7)% for systems with W2796/W2600 < 2 and MgI W2852 > 0.1 A. (2) The
mean N(HI) of MgII systems with 0.3 A \le W2796 < 0.6 A is a factor of ~36
lower than that of systems with W2796 \ge 0.6 A. (3) The DLA incidence per unit
redshift is consistent with no evolution for z <~ 2 (Omega_L=0.7, Omega_M =
0.3), but exhibits significant evolution for z >~ 2. (4) Omega_{DLA} is
constant for 0.5<z<5.0 to within the uncertainties. This is larger than
Omega_{gas}(z=0) by a factor of ~2. (5) The slope of the N(HI) distribution
does not change significantly with redshift. However, the low redshift
distribution is marginally flatter due to the higher fraction of high N(HI)
systems in our sample. (6) Finally, using the precision of MgII survey
statistics, we find that there may be evidence of a decreasing Omega_{DLA} from
z=0.5 to z=0. We reiterate the conclusion of Hopkins, Rao, & Turnshek that very
high columns of neutral gas might be missed by DLA surveys because of their
very small cross sections, and therefore, that Omega_{DLA} might not include
the bulk of the neutral gas mass in the Universe. (Abridged) | 0509469v1 |
2007-01-03 | HI 21cm absorption at $z \sim 3.39$ towards PKS 0201+113 | We report the GMRT detection of HI 21cm absorption from the $z \sim 3.39$
damped Lyman-$\alpha$ absorber (DLA) towards PKS 0201+113, the highest redshift
at which 21cm absorption has been detected in a DLA. The absorption is spread
over $\sim 115$ km s$^{-1}$ and has two components, at $z = 3.387144 (17)$ and
$z = 3.386141 (45)$. The stronger component has a redshift and velocity width
in agreement with the tentative detection of Briggs et al. (1997), but a
significantly lower optical depth. The core size and DLA covering factor are
estimated to be $\lesssim 100$ pc and $f \sim 0.69$, respectively, from a VLBA
328 MHz image. If one makes the conventional assumption that the HI column
densities towards the optical and radio cores are the same, this optical depth
corresponds to a spin temperature of $\ts \sim [(955 \pm 160) \times (f/0.69)]
$ K. However, this assumption may not be correct, given that no metal-line
absorption is seen at the redshift of the stronger 21cm component, indicating
that this component does not arise along the line of sight to the optical QSO,
and that there is structure in the 21cm absorbing gas on scales smaller than
the size of the radio core. We model the 21cm absorbing gas as having a
two-phase structure with cold dense gas randomly distributed within a diffuse
envelope of warm gas. For such a model, our radio data indicate that, even if
the optical QSO lies along a line-of-sight with a fortuitously high ($\sim
50$%) cold gas fraction, the average cold gas fraction is low, ($\lesssim
17%$), when averaged over the the spatial extent of the radio core. Finally,
the large mismatch between peak 21cm and optical redshifts and the complexity
of both profiles makes it unlikely that the $z \sim 3.39$ DLA will be useful in
tests of fundamental constant evolution. | 0701074v2 |
2004-10-24 | Field theory of the inverse cascade in two-dimensional turbulence | A two-dimensional fluid, stirred at high wavenumbers and damped by both
viscosity and linear friction, is modeled by a statistical field theory. The
fluid's long-distance behavior is studied using renormalization-group (RG)
methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732
(1977)]. With friction, which dissipates energy at low wavenumbers, one expects
a stationary inverse energy cascade for strong enough stirring. While such
developed turbulence is beyond the quantitative reach of perturbation theory, a
combination of exact and perturbative results suggests a coherent picture of
the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is
derived from a generalized time-reversal symmetry and implies zero anomalous
dimension for the velocity even when friction is present. Thus the Kolmogorov
scaling of the inverse cascade cannot be explained by any RG fixed point. The
beta function for the dimensionless coupling ghat is computed through two
loops; the ghat^3 term is positive, as already known, but the ghat^5 term is
negative. An ideal cascade requires a linear beta function for large ghat,
consistent with a Pad\'e approximant to the Borel transform. The conjecture
that the Kolmogorov spectrum arises from an RG flow through large ghat is
compatible with other results, but the accurate k^{-5/3} scaling is not
explained and the Kolmogorov constant is not estimated. The lack of scale
invariance should produce intermittency in high-order structure functions, as
observed in some but not all numerical simulations of the inverse cascade. When
analogous RG methods are applied to the one-dimensional Burgers equation using
an FDT-preserving dimensional continuation, equipartition is obtained instead
of a cascade--in agreement with simulations. | 0410050v2 |
2004-09-20 | Effect of the Vacuum Energy Density on Graviton Propagation | It is known that the value L of the vacuum energy density affects the
propagation equation for gravitons: A mass term appears in the propagation
equation, such that m^2=-L. As a consequence, the polarization states of
gravitons also change. This effect of the L-term has been confirmed by recent
calculations in a curved background, which is the only proper setting, since
solutions of the classical Einstein equations in the presence of a L-term
represent a space with constant curvature. A real value for the mass (when L<0)
will show up as a slight exponential damping in the gravitational potential,
which is however strongly constrained by astronomical data. The consequences of
an imaginary mass (for L>0) are still unclear; on general grounds, one can
expect the onset of instabilities in this case. This is also confirmed by
numerical simulations of quantum gravity which became recently available. These
properties gain a special interest in consideration of the following. (1) The
most recent cosmological data indicate that L is positive and of the order of
0.1 J/m^3. Is this value compatible with a stable propagation of gravitons? (2)
The answer to the previous question lies perhaps in the scale dependence of the
effective value of L. L may be negative at the small distance/large energy
scale at which the quantum behavior of gravitational fields and waves becomes
relevant. Furthermore, local contributions to the vacuum energy density (in
superconductors in certain states, and in very strong static electromagnetic
fields) can change locally the sign of L, and so affect locally the propagation
and the properties of gravitons. The graviton wavefunction, for different
values of the parameters, may be characterized by superluminal phase velocity
or by unitarity only in imaginary valued time. | 0409098v1 |
2006-07-02 | Physics of Flow Instability and Turbulent Transition in Shear Flows | In this paper, the physics of flow instability and turbulent transition in
shear flows is studied by analyzing the energy variation of fluid particles
under the interaction of base flow with a disturbance. For the first time, a
model derived strictly from physics is proposed to show that the flow
instability under finite amplitude disturbance leads to turbulent transition.
The proposed model is named as "energy gradient method." It is demonstrated
that it is the transverse energy gradient that leads to the disturbance
amplification while the disturbance is damped by the energy loss due to
viscosity along the streamline. It is also shown that the threshold of
disturbance amplitude obtained is scaled with the Reynolds number by an
exponent of -1, which exactly explains the recent modern experimental results
by Hof et al. for pipe flow. The mechanism for velocity inflection and hairpin
vortex formation are explained with reference to analytical results. Following
from this analysis, it can be demonstrated that the critical value of the so
called energy gradient parameter Kmax is constant for turbulent transition in
wall bounded parallel flows, and this is confirmed by experiments and is about
370-389. The location of instability initiation in the flow field accords well
with the experiments for both pipe Poiseuille flow (r/R=0.58) and plane
Poiseuille flow (y/h=0.58). It is also inferred from the proposed method that
the transverse energy gradient can serve as the power for the self-sustaining
process of wall bounded turbulence. Finally, the relation of "energy gradient
method" to the classical "energy method" based on Rayleigh-Orr equation is
discussed. | 0607004v5 |
2007-06-25 | Toward faithful templates for non-spinning binary black holes using the effective-one-body approach | We present an accurate approximation of the full gravitational radiation
waveforms generated in the merger of non-eccentric systems of two non-spinning
black holes. Utilizing information from recent numerical relativity simulations
and the natural flexibility of the effective-one-body (EOB) model, we extend
the latter so that it can successfully match the numerical relativity waveforms
during the last stages of inspiral, merger and ringdown. By ``successfully''
here, we mean with phase differences < 8% of a gravitational-wave cycle
accumulated by the end of the ringdown phase, maximizing only over time of
arrival and initial phase. We obtain this result by simply adding a
4-post-Newtonian order correction in the EOB radial potential and determining
the (constant) coefficient by imposing high-matching performances with
numerical waveforms of mass ratios m1/m2 = 1, 3/2, 2 and 4, m1 and m2 being the
individual black-hole masses. The final black-hole mass and spin predicted by
the numerical simulations are used to determine the ringdown frequency and
decay time of three quasi-normal-mode damped sinusoids that are attached to the
EOB inspiral-(plunge) waveform at the EOB light-ring. The EOB waveforms might
be tested and further improved in the future by comparison with extremely long
and accurate inspiral numerical-relativity waveforms. They may already be
employed for coherent searches and parameter estimation of gravitational waves
emitted by non-spinning coalescing binary black holes with ground-based
laser-interferometer detectors. | 0706.3732v3 |
2007-08-06 | Ejection of Supermassive Black Holes from Galaxy Cores | [Abridged] Recent numerical relativity simulations have shown that the
emission of gravitational waves during the merger of two supermassive black
holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as
4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks
and the effects on the stellar distribution using high-accuracy direct N-body
simulations. Following the kick, the motion of the SMBH exhibits three distinct
phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via
dynamical friction each time it passes through the core. Chandrasekhar's theory
accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda <
3 and if the changing core density is taken into account. (2) When the
amplitude of the motion has fallen to roughly the core radius, the SMBH and
core begin to exhibit oscillations about their common center of mass. These
oscillations decay with a time constant that is at least 10 times longer than
would be predicted by naive application of the dynamical friction formula. (3)
Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate
the time for the SMBH's oscillations to damp to the Brownian level in real
galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection
of SMBHs also results in a lowered density of stars near the galaxy center;
mass deficits as large as five times the SMBH mass are produced for kick
velocities near the escape velocity. We compare the N-body density profiles
with luminosity profiles of early-type galaxies in Virgo and show that even the
largest observed cores can be reproduced by the kicks, without the need to
postulate hypermassive binary SMBHs. Implications for displaced AGNs and
helical radio structures are discussed. | 0708.0771v2 |
2007-11-19 | Effect of the intergalactic environment on the observability of Ly-alpha emitters during reionization | Observations of high-redshift Ly-alpha sources are a major tool for studying
the high-redshift Universe. We discuss the effect of the reionizing
intergalactic medium on the observability of Ly-alpha sources based on large
simulations of early structure formation with radiative transfer. This takes
into account self-consistently the reionization history, density, velocity and
ionization structures and nonlinear source clustering. We find that all fields
are highly anisotropic and as a consequence there are very large variations in
opacity among the different lines-of-sight. The velocity effects, from both
infall and source peculiar velocity are most important for the luminous
sources, affecting the line profile and depressing the bright end of the
luminosity function. The line profiles are generally asymmetric and the line
centers of the luminous sources are always absorbed due to the high density of
the local IGM. For both luminous and average sources the damping wing effects
are of similar magnitude and remain significant until fairly late.
The ionizing flux in the ionized patch surrounding a high density peak is
generally strongly dominated, particularly at late times, by the cluster of
faint sources, rather than the central massive galaxy. The IGM absorption does
not change appreciably the correlation function of sources at high redshift.
Our derived luminosity function assuming constant mass-to-light ratio provides
an excellent match to the shape of the observed luminosity function at z=6.6
with faint-end slope of alpha=-1.5. The resulting mass-to-light ratio implies
that the majority of sources responsible for reionization are too faint to be
observed by the current surveys. (abridged) | 0711.2944v2 |
2007-12-17 | The Nitrogen and Oxygen abundances in the neutral gas at high redshift | We study the Oxygen and Nitrogen abundances in the interstellar medium of
high-redshift galaxies. We use high resolution and high signal-to-noise ratio
spectra of Damped Lyman-alpha (DLA) systems detected along the line-of-sight to
quasars to derive robust abundance measurements from unsaturated metal
absorption lines. We present results for a sample of 16 high-redshift DLAs and
strong sub-DLAs (log N(HI)>19.5, 2.4<zabs<3.6) including 13 new measurements.
We find that the Oxygen to Iron abundance ratio is pretty much constant with
[O/Fe]=+0.32+-0.10 for -2.5<[O/H]<-1.0 with a small scatter around this value.
The Oxygen abundance follows quite well the Silicon abundance within 0.2dex
although the Silicon abundance could be slightly smaller for [O/H]<-2. The
distribution of the [N/O] abundance ratio, measured from components that are
detected in both species, is somehow double peaked: five systems have [N/O]>-1
and nine systems have [N/O]<-1.15. In the diagram [N/O] versus [O/H], a loose
plateau is possibly present at [N/O]=-0.9 that is below the so-called primary
plateau as seen in local metal-poor dwarf galaxies ([N/O] in the range -0.57 to
-0.74). No system is seen above this primary plateau whereas the majority of
the systems lie well below with a large scatter. All this suggests a picture in
which DLAs undergo successive star-bursts. During such an episode, the [N/O]
ratio decreases sharply because of the rapid release of Oxygen by massive stars
whereas inbetween two bursts, Nitrogen is released by low and intermediate-mass
stars with a delay and the [N/O] ratio increases. | 0712.2760v1 |
2008-10-26 | Non-linear Study of Bell's Cosmic Ray Current-driven Instability | The cosmic ray current-driven (CRCD) instability, predicted by Bell (2004),
consists of non-resonant, growing plasma waves driven by the electric current
of cosmic rays (CRs) that stream along the magnetic field ahead of both
relativistic and non-relativistic shocks. Combining an analytic, kinetic model
with one-, two-, and three-dimensional particle-in-cell simulations, we confirm
the existence of this instability in the kinetic regime and determine its
saturation mechanisms. In the linear regime, we show that, if the background
plasma is well magnetized, the CRCD waves grow exponentially at the rates and
wavelengths predicted by the analytic dispersion relation. The magnetization
condition implies that the growth rate of the instability is much smaller than
the ion cyclotron frequency. As the instability becomes non-linear, significant
turbulence forms in the plasma. This turbulence reduces the growth rate of the
field and damps the shortest wavelength modes, making the dominant wavelength,
\lambda_d, grow proportional to the square of the field. At constant CR
current, we find that plasma acceleration along the motion of CRs saturates the
instability at the magnetic field level such that v_A ~ v_{d,cr}, where v_A is
the Alfven velocity in the amplified field, and v_{d,cr} is the drift velocity
of CRs. The instability can also saturate earlier if CRs get strongly deflected
by the amplified field, which happens when their Larmor radii get close to
\lambda_d. We apply these results to the case of CRs in the upstream medium of
supernova remnants. Considering only the most energetic CRs that escape from
the shock, we obtain that the field amplification factor of ~10 can be reached.
This confirms the CRCD instability as a potentially important component of
magnetic amplification process in astrophysical shocks. | 0810.4565v1 |
2008-10-27 | Determination of the neutron star mass-radii relation using narrow-band gravitational wave detector | The direct detection of gravitational waves will provide valuable
astrophysical information about many celestial objects. The most promising
sources of gravitational waves are neutron stars and black holes. These objects
emit waves in a very wide spectrum of frequencies determined by their
quasi-normal modes oscillations. In this work we are concerned with the
information we can extract from f and p$_I$-modes when a candidate leaves its
signature in the resonant mass detectors ALLEGRO, EXPLORER, NAUTILUS, MiniGrail
and SCHENBERG. Using the empirical equations, that relate the gravitational
wave frequency and damping time with the mass and radii of the source, we have
calculated the radii of the stars for a given interval of masses $M$ in the
range of frequencies that include the bandwidth of all resonant mass detectors.
With these values we obtain diagrams of mass-radii for different frequencies
that allowed to determine the better candidates to future detection taking in
account the compactness of the source. Finally, to determine which are the
models of compact stars that emit gravitational waves in the frequency band of
the mass resonant detectors, we compare the mass-radii diagrams obtained by
different neutron stars sequences from several relativistic hadronic equations
of state (GM1, GM3, TM1, NL3) and quark matter equations of state (NJL, MTI bag
model). We verify that quark stars obtained from MIT bag model with bag
constant equal to 170 MeV and quark of matter in color-superconductivity phase
are the best candidates for mass resonant detectors. | 0810.4848v4 |
2009-02-17 | 21-cm absorbers at intermediate redshifts | Damped Lyman-alpha systems (DLAs) seen in the spectra of high-z QSOs allow us
to probe the physical conditions in protogalaxies. Our understanding of
physical conditions in DLAs at high-z is primarily based on the absorption
lines of H_2 molecules and fine-structure transitions. Another important way of
probing the thermal state of interstellar medium in these systems is by
studying the 21-cm absorption in the spectra of background quasars. Here we
report the main results of our GMRT survey to search for 21-cm absorption in a
representative and unbiased sample of 35 DLA candidates at 1.10<z<1.45. Our
sample of DLA candidates is drawn from the strong MgII systems in SDSS DR5 and
has resulted in discovery of 9 new 21-cm absorbers. Prior to our survey only
one 21-cm absorber was known in the redshift range: 0.7<z<2. This survey has
allowed us to investigate the dependence of detectability of 21-cm absorption
on the properties of UV absorption lines detected in SDSS spectra and estimate
the number per unit redshift of 21-cm absorbers. Our GMRT survey provides a
representative sample of systems that can be used in combination with various
follow-up observations: (1) for investigating the physical conditions in the
absorbing gas using spin temperature measurements, (2) for investigating the
effect of metallicity and dust content on the detectability of 21-cm
absorption, (3) for studying the morphology of the absorbing gas and (4) for
probing the time evolution of various fundamental constants. Results from the
first phase of our survey are presented in Gupta et al. (2007). Detailed
description of the entire sample and results from the survey are presented in
Gupta et al. (2009). | 0902.3016v1 |
2009-08-27 | Very Light Magnetized Jets on Large Scales - I. Evolution and Magnetic Fields | Magnetic fields, which are undoubtedly present in extragalactic jets and
responsible for the observed synchrotron radiation, can affect the morphology
and dynamics of the jets and their interaction with the ambient cluster medium.
We examine the jet propagation, morphology and magnetic field structure for a
wide range of density contrasts, using a globally consistent setup for both the
jet interaction and the magnetic field. The MHD code NIRVANA is used to evolve
the simulation, using the constrained-transport method. The density contrasts
are varied between \eta = 10^{-1} and 10^{-4} with constant sonic Mach number
6. The jets are supermagnetosonic and simulated bipolarly due to the low jet
densities and their strong backflows. The helical magnetic field is largely
confined to the jet, leaving the ambient medium nonmagnetic. We find magnetic
fields with plasma \beta \sim 10 already stabilize and widen the jet head.
Furthermore they are efficiently amplified by a shearing mechanism in the jet
head and are strong enough to damp Kelvin-Helmholtz instabilities of the
contact discontinuity. The cocoon magnetic fields are found to be stronger than
expected from simple flux conservation and capable to produce smoother lobes,
as found observationally. The bow shocks and jet lengths evolve self-similarly.
The radio cocoon aspect ratios are generally higher for heavier jets and grow
only slowly (roughly self-similar) while overpressured, but much faster when
they approach pressure balance with the ambient medium. In this regime,
self-similar models can no longer be applied. Bow shocks are found to be of low
excentricity for very light jets and have low Mach numbers. Cocoon turbulence
and a dissolving bow shock create and excite waves and ripples in the ambient
gas. Thermalization is found to be very efficient for low jet densities. | 0908.4055v1 |
2009-10-12 | Average luminosity distance in inhomogeneous universes | The paper studies the correction to the distance modulus induced by
inhomogeneities and averaged over all directions from a given observer. The
inhomogeneities are modeled as mass-compensated voids in random or regular
lattices within Swiss-cheese universes. Void radii below 300 Mpc are
considered, which are supported by current redshift surveys and limited by the
recently observed imprint such voids leave on CMB. The averaging over all
directions, performed by numerical ray tracing, is non-perturbative and
includes the supernovas inside the voids. Voids aligning along a certain
direction produce a cumulative gravitational lensing correction that increases
with their number. Such corrections are destroyed by the averaging over all
directions, even in non-randomized simple cubic void lattices. At low
redshifts, the average correction is not zero but decays with the peculiar
velocities and redshift. Its upper bound is provided by the maximal average
correction which assumes no random cancelations between different voids. It is
described well by a linear perturbation formula and, for the voids considered,
is 20% of the correction corresponding to the maximal peculiar velocity. The
average correction calculated in random and simple cubic void lattices is
severely damped below the predicted maximal one after a single void diameter.
That is traced to cancellations between the corrections from the fronts and
backs of different voids. All that implies that voids cannot imitate the effect
of dark energy unless they have radii and peculiar velocities much larger than
the currently observed. The results obtained allow one to readily predict the
redshift above which the direction-averaged fluctuation in the Hubble diagram
falls below a required precision and suggest a method to extract the background
Hubble constant from low redshift data without the need to correct for peculiar
velocities. | 0910.2611v3 |
2009-12-22 | Rest-frame ultraviolet spectrum of the gravitationally lensed galaxy `the 8 o'clock arc': stellar and interstellar medium properties | We present the first detailed analysis of the rest-frame UV spectrum of the
gravitationally lensed Lyman break galaxy (LBG), the `8 o'clock arc'. The
spectrum of the 8 o'clock arc is rich in stellar and interstellar medium (ISM)
features, and presents several similarities to the well-known MS1512-cB58 LBG.
The stellar photospheric absorption lines allowed us to constrain the systemic
redshift, z_sys = 2.7350+/-0.0003, of the galaxy, and derive its stellar
metallicity, Z=0.82 Z_sol. With a total stellar mass of ~4.2x10^{11} M_sol, the
8 o'clock arc agrees with the mass-metallicity relation found for z>2
star-forming galaxies. The 31 ISM absorption lines detected led to the
abundance measurements of 9 elements. The metallicity of the ISM, Z=0.65 Z_sol
(Si), is very comparable to the metallicity of stars and ionized gas, and
suggests that the ISM of the 8 o'clock arc has been rapidly polluted and
enriched by ejecta of OB stars. The ISM lines extend over ~1000 km/s and have
their peak optical depth blueshifted relative to the stars, implying gas
outflows of about -120 km/s. The Ly-alpha line is dominated by a damped
absorption profile on top of which is superposed a weak emission, redshifted
relative to the ISM lines by about +690 km/s and resulting from multiply
backscattered Ly-alpha photons emitted in the HII region surrounded by the
cold, expanding ISM shell. A homogeneous spherical radiation transfer shell
model with a constant outflow velocity, determined by the observations, is able
to reproduce the observed Ly-alpha line profile and dust content. These results
fully support the scenario proposed earlier, where the diversity of Ly-alpha
line profiles in LBGs and Ly-alpha emitters, from absorption to emission, is
mostly due to variations of HI column density and dust content (abridged). | 0912.4384v1 |
2010-07-19 | The Evolution of Lyman Limit Absorption Systems to Redshift Six | We have measured the redshift evolution of the density of Lyman limit systems
(LLS) in the intergalactic medium over the redshift range 0 < z < 6. We have
used two new quasar samples to (1) improve coverage at z ~ 1, with GALEX grism
spectrograph observations of 50 quasars with 0.8 < z_em < 1.3, and (2) extend
coverage to z ~ 6, with Keck ESI spectra of 25 quasars with 4.17 < z_em < 5.99.
Using these samples together with published data, we find that the number
density of LLS per unit redshift, n(z), can be well fit by a simple evolution
of the form n(z) = n_3.5 [(1+z)/4.5]^gamma, with n_3.5 = 2.80 +/- 0.33 and
gamma = 1.94^(+0.36)_(-0.32) for the entire range 0 < z < 6. We have also
reanalyzed the evolution of damped Lyman alpha systems (DLAs) in the redshift
range 4 < z < 5 using our high-redshift quasar sample. We find a total of 17
DLAs and sub-DLAs, which we have analyzed in combination with published data.
The DLAs with log (HI column density) > 20.3 show the same redshift evolution
as the LLS. When combined with previous results, our DLA sample is also
consistent with a constant Omega_DLA= 9 x 10^(-4) from z = 2 to z = 5. We have
used the LLS number density evolution to compute the evolution in the mean free
path of ionizing photons. We find a smooth evolution to z ~ 6, very similar in
shape to that of Madau, Haardt & Rees (1999) but about a factor of two higher.
Recent theoretical models roughly match to the z < 6 data but diverge from the
measured power law at z > 6 in different ways, cautioning against extrapolating
the fit to the mean free path outside the measured redshift range. | 1007.3262v2 |
2010-11-01 | A Model for Thermal Phase Variations of Circular and Eccentric Exoplanets | We present a semi-analytic model atmosphere for close-in exoplanets that
captures the essential physics of phase curves: orbital and viewing geometry,
advection, and re-radiation. We calibrate the model with the well-characterized
transiting planet, HD 189733b, then compute light curves for seven of the most
eccentric transiting planets. We present phase variations for a variety of
different radiative times and wind speeds. In the limit of instant
re-radiation, the light curve morphology is entirely dictated by the planet's
eccentricity and argument of pericenter: the light curve maximum leads or
trails the eclipse depending on whether the planet is receding from or
approaching the star at superior conjunction, respectively. For a planet with
non-zero radiative timescales, the phase peak occurs early for super- rotating
winds, and late for sub-rotating winds. We find that for a circular orbit, the
timing of the phase variation maximum with respect to superior conjunction
indicates the direction of the dominant winds, but cannot break the degeneracy
between wind speed and radiative time. For circular planets the phase minimum
occurs half an orbit away from the phase maximum -despite the fact that the
coolest longitudes are always near the dawn terminator- and therefore does not
convey any additional information. In general, increasing the advective
frequency or the radiative time has the effect of reducing the peak-to-trough
amplitude of phase variations, but there are interesting exceptions to these
trends. Lastly, eccentric planets with orbital periods significantly longer
than their radiative time exhibit "ringing" whereby the hot spot generated at
periastron rotates in and out of view. The existence of ringing makes it
possible to directly measure the wind speed (the frequency of the ringing) and
the radiative time constant (the damping of the ringing). | 1011.0428v1 |
2010-12-16 | Constraints on coronal turbulence models from source sizes of noise storms at 327 MHz | We seek to reconcile observations of small source sizes in the solar corona
at 327 MHz with predictions of scattering models that incorporate refractive
index effects, inner scale effects and a spherically diverging wavefront. We
use an empirical prescription for the turbulence amplitude $C_{N}^{2}(R)$ based
on VLBI observations by Spangler and coworkers of compact radio sources against
the solar wind for heliocentric distances $R \approx$ 10--50 $R_{\odot}$. We
use the Coles & Harmon model for the inner scale $l_{i}(R)$, that is presumed
to arise from cyclotron damping. In view of the prevalent uncertainty in the
power law index that characterizes solar wind turbulence at various
heliocentric distances, we retain this index as a free parameter. We find that
the inclusion of spherical divergence effects suppresses the predicted source
size substantially. We also find that inner scale effects significantly reduce
the predicted source size. An important general finding for solar sources is
that the calculations substantially underpredict the observed source size.
Three possible, non-exclusive, interpretations of this general result are
proposed. First and simplest, future observations with better angular
resolution will detect much smaller sources. Consistent with this, previous
observations of small sources in the corona at metric wavelengths are limited
by the instrument resolution. Second, the spatially-varying level of turbulence
$C_{N}^{2}(R)$ is much larger in the inner corona than predicted by
straightforward extrapolation Sunwards of the empirical prescription, which was
based on observations between 10--50 $R_{\odot}$. Either the functional form or
the constant of proportionality could be different. Third, perhaps the inner
scale is smaller than the model, leading to increased scattering. | 1012.3523v2 |
2011-01-25 | The Surprisingly Constant Strength of O VI Absorbers over Cosmic Time | O VI absorption is observed in a wide range of astrophysical environments,
including the Local ISM, the disk and halo of the Milky Way, high-velocity
clouds, the Magellanic clouds, starburst galaxies, the intergalactic medium,
damped Lyman-alpha systems, and gamma-ray-burst host galaxies. Here a new
compilation of 775 O VI absorbers drawn from the literature is presented, all
observed at high resolution (instrumental FWHM<20 km/s) and covering the
redshift range z=0-3. In galactic environments [log N(H I)>20], the mean O VI
column density is shown to be insensitive to metallicity, taking a value log
N(O VI)~14.5 for galaxies covering the range -1.6<[O/H]<0. In intergalactic
environments [log N(H I)<17], the mean O VI component column density measured
in datasets of similar sensitivity shows only weak evolution between z=0.2 and
z=2.3, but IGM O VI components are on average almost twice as broad at z=0.2
than at z=2.3. The existence of a characteristic value of log N(O VI) for
galactic O VI absorbers, and the lack of evolution in log N(O VI) for
intergalactic absorbers, lend support to the ``cooling-flow' model of Heckman
et al. (2002), in which all O VI absorbers are created in regions of
initially-hot shock-heated plasma that are radiatively cooling through coronal
temperatures. These regions could take several forms, including conductive,
turbulent, or shocked boundary layers between warm (~10^4 K) clouds and hot
(~10^6 K) plasma, although many such regions would have to be intersected by a
typical galaxy-halo sightline to build up the characteristic galactic N(O VI).
The alternative, widely-used model of single-phase photoionization for
intergalactic O VI is ruled out by kinematic evidence in the majority of IGM O
VI components at low and high redshift. | 1101.4766v1 |
2011-03-21 | A Groundbased Imaging Study of Galaxies Causing DLA, subDLA, and LLS Absorption in Quasar Spectra | We present results from a search for galaxies that give rise to damped Lyman
alpha (DLA), subDLA, and Lyman limit system (LLS) absorption at redshifts 0.1
~< z ~< 1 in the spectra of background quasars. The sample was formed from a
larger sample of strong MgII absorbers (W_0^(2796) >= 0.3 A) whose HI column
densities were determined by measuring the Ly-alpha line in HST UV spectra.
Photometric redshifts, galaxy colors, and proximity to the quasar sightline, in
decreasing order of importance, were used to identify galaxies responsible for
the absorption. Our sample includes 80 absorption systems for which the
absorbing galaxies have been identified, of which 54 are presented here for the
first time. The main results of this study are: (i) the surface density of
galaxies falls off exponentially with increasing impact parameter, b, from the
quasar sightline relative to a constant background of galaxies, with an
e-folding length of ~46 kpc. Galaxies with b >~ 100 kpc calculated at the
absorption redshift are statistically consistent with being unrelated to the
absorption system. (ii) log N(HI) is inversely correlated with b at the 3.0
sigma level of significance. DLA galaxies are found systematically closer to
the quasar sightline, by a factor of two, than are galaxies which give rise to
subDLAs or LLSs. The median impact parameter is 17.4 kpc for the DLA galaxy
sample, 33.3 kpc for the subDLA sample, and 36.4 kpc for the LLS sample. (iii)
Absorber galaxy luminosity relative to L*, L/L*, is not significantly
correlated with W_0^(2796), log N(HI), or b. (iv) DLA, subDLA, and LLS galaxies
comprise a mix of spectral types, but are inferred to be predominantly late
type galaxies based on their spectral energy distributions. The implications of
these results are discussed. (Abridged) | 1103.4047v3 |
2011-05-06 | Non-relativistic bound states in a moving thermal bath | We study the propagation of non-relativistic bound states moving at constant
velocity across a homogeneous thermal bath and we develop the effective field
theory which is relevant in various dynamical regimes. We consider values of
the velocity of the bound state ranging from moderate to highly relativistic
and temperatures at all relevant scales smaller than the mass of the particles
that form the bound state. In particular, we consider two distinct temperature
regimes, corresponding to temperatures smaller or higher than the typical
momentum transfer in the bound state. For temperatures smaller or of the order
of the typical momentum transfer, we restrict our analysis to the simplest
system, a hydrogen-like atom. We build the effective theory for this system
first considering moderate values of the velocity and then the relativistic
case. For large values of the velocity of the bound state, the separation of
scales is such that the corresponding effective theory resembles the soft
collinear effective theory (SCET). For temperatures larger than the typical
momentum transfer we also consider muonic hydrogen propagating in a plasma
which contains photons and massless electrons and positrons, so that the system
resembles very much heavy quarkonium in a thermal medium of deconfined quarks
and gluons. We study the behavior of the real and imaginary part of the static
two-body potential, for various velocities of the bound state, in the hard
thermal loop approximation. We find that Landau damping ceases to be the
relevant mechanism for dissociation from a certain "critical" velocity on in
favor of screening. Our results are relevant for understanding how the
properties of heavy quarkonia states produced in the initial fusion of partons
in the relativistic collision of heavy ions are affected by the presence of an
equilibrated quark-gluon plasma. | 1105.1249v2 |
2011-08-24 | Dynamical Tides in Compact White Dwarf Binaries: Tidal Synchronization and Dissipation | In compact white dwarf (WD) binary systems (with periods ranging from minutes
to hours), dynamical tides involving the excitation and dissipation of gravity
waves play a dominant role in determining the physical conditions of the WDs
prior to mass transfer or binary merger. We calculate the amplitude of the
tidally excited gravity waves as a function of the tidal forcing frequency
\omega=2(\Omega-\Omega_s) (where \Omega is the orbital frequency and \Omega_s
is the spin frequency) for several realistic carbon-oxygen WD models, assuming
that the waves are efficiently dissipated in the outer layer of the star by
nonlinear effects or radiative damping. The mechanism of wave excitation in WDs
is complex due to the sharp features associated with composition changes inside
the WD, and in our WD models gravity waves are launched just below the
helium-carbon boundary. We find that the tidal torque on the WD and the related
tidal energy transfer rate, \dot E_{\rm tide}, depend on \omega in an erratic
way. On average, \dot E_{\rm tide} scales approximately as \Omega^5\omega^5 for
a large range of tidal frequencies. We also study the effects of dynamical
tides on the long-term evolution of WD binaries. Above a critical orbital
frequency \Omega_c, corresponding to an orbital period of order one hour
(depending on WD models), dynamical tides efficiently drive \Omega_s toward
\Omega, although a small, almost constant degree of asynchronization
(\Omega-\Omega_s\sim {\rm constant}) is maintained even at the smallest binary
periods. While the orbital decay is always dominated by gravitational
radiation, the tidal energy transfer can induce significant phase error in the
low-frequency gravitational waveforms, detectable by the planned LISA project.
Tidal dissipation may also lead to significant heating of the WD envelope and
brightening of the system long before binary merger. | 1108.4910v5 |
2011-11-22 | Coronal heating in coupled photosphere-chromosphere-coronal systems: turbulence and leakage | Coronal loops act as resonant cavities for low frequency fluctuations that
are transmitted from the deeper layers of the solar atmosphere and are
amplified in the corona, triggering nonlinear interactions. However trapping is
not perfect, some energy leaks down to the chromosphere, thus limiting the
turbulence development and the associated heating. We consider the combined
effects of turbulence and leakage in determining the energy level and
associated heating rate in models of coronal loops which include the
chromosphere and transition region. We use a piece-wise constant model for the
Alfven speed and a Reduced MHD - Shell model to describe the interplay between
turbulent dynamics in the direction perpendicular to the mean field and
propagation along the field. Turbulence is sustained by incoming fluctuations
which are equivalent, in the line-tied case, to forcing by the photospheric
shear flows. While varying the turbulence strength, we compare systematically
the average coronal energy level (E) and dissipation rate (D) in three models
with increasing complexity: the classical closed model, the semi-open corona
model, and the corona-chromosphere (or 3-layer) model, the latter two models
allowing energy leakage. We find that:
(i) Leakage always plays a role (even for strong turbulence), E and D are
systematically lower than in the line-tied model. (ii) E is close to the
resonant prediction, i.e., assuming effective turbulent correlation time longer
than the Alfven coronal crossing time (Ta). (iii) D is close to the value given
by the ratio of photospheric energy divided by Ta (iv) The coronal spectra
exibits an inertial range with 5/3 spectral slope, and a large scale peak of
trapped resonant modes that inhibit nonlinear couplings. (v) In the realistic
3-layer model, the two-component spectrum leads to a damping time equal to the
Kolmogorov time reduced by a factor u_rms/Va_corona | 1111.5359v1 |
2012-06-22 | Cosmic Acceleration from Causal Backreaction with Recursive Nonlinearities | We revisit the causal backreaction paradigm, in which the need for Dark
Energy is eliminated via the generation of an apparent cosmic acceleration from
the causal flow of inhomogeneity information coming in towards each observer
from distant structure-forming regions. This second-generation formalism
incorporates "recursive nonlinearities": the process by which
already-established metric perturbations will then act to slow down all future
flows of inhomogeneity information. Here, the long-range effects of causal
backreaction are now damped, weakening its impact for models that were
previously best-fit cosmologies. Nevertheless, we find that causal backreaction
can be recovered as a replacement for Dark Energy via the adoption of larger
values for the dimensionless `strength' of the clustering evolution functions
being modeled -- a change justified by the hierarchical nature of clustering
and virialization in the universe, occurring on multiple cosmic length scales
simultaneously. With this, and with one new model parameter representing the
slowdown of clustering due to astrophysical feedback processes, an alternative
cosmic concordance can once again be achieved for a matter-only universe in
which the apparent acceleration is generated entirely by causal backreaction
effects. One drawback is a new degeneracy which broadens our predicted range
for the observed jerk parameter $j_{0}^{\mathrm{Obs}}$, thus removing what had
appeared to be a clear signature for distinguishing causal backreaction from
Cosmological Constant $\Lambda$CDM. As for the long-term fate of the universe,
incorporating recursive nonlinearities appears to make the possibility of an
`eternal' acceleration due to causal backreaction far less likely; though this
does not take into account gravitational nonlinearities or the large-scale
breakdown of cosmological isotropy, effects not easily modeled within this
formalism. | 1206.5056v1 |
2013-06-17 | GRB 130606A as a Probe of the Intergalactic Medium and the Interstellar Medium in a Star-forming Galaxy in the First Gyr After the Big Bang | We present high signal-to-noise ratio Gemini and MMT spectroscopy of the
optical afterglow of the gamma-ray burst (GRB) 130606A at redshift z=5.913,
discovered by Swift. This is the first high-redshift GRB afterglow to have
spectra of comparable quality to those of z~6 quasars. The data exhibit a
smooth continuum at near-infrared wavelengths that is sharply cut off blueward
of 8410 Angs due to absorption from Ly-alpha at redshift z~5.91, with some flux
transmitted through the Ly-alpha forest between 7000-7800 Angs. We use column
densities inferred from metal absorption lines to constrain the metallicity of
the host galaxy between a lower limit of [Si/H]>-1.7 and an upper limit of
[S/H]<-0.5 set by the non-detection of S II absorption. We demonstrate
consistency between the dramatic evolution in the transmission fraction of
Ly-alpha seen in this spectrum over the redshift range z=4.9 to 5.85 with that
previously measured from observations of high-redshift quasars. There is an
extended redshift interval of Delta-z=0.12 in the Ly-alpha forest at z=5.77
with no detected transmission, leading to a 3-sigma upper limit on the mean
Ly-alpha transmission fraction of <0.2% (or tau_eff(Ly-alpha) > 6.4). This is
comparable to the lowest-redshift Gunn-Peterson troughs found in quasar
spectra. We set a 2-sigma upper limit of 0.11 on the neutral fraction of the
IGM at the redshift of the GRB from the lack of a Ly-alpha red damping wing,
assuming a model with a constant neutral density. Some Ly-beta and Ly-gamma
transmission is detected in this redshift window, indicating that it is not
completely opaque, and hence that the IGM is nonetheless mostly ionized at
these redshifts. GRB 130606A thus for the first time realizes the promise of
GRBs as probes of the first galaxies and cosmic reionization. | 1306.3949v2 |
2013-11-29 | Continuous Emission of A Radiation Quantum | It is in accordance with such experiments as single photon self-interference
that a photon, conveying one radiation energy quantum "$ h \times$ frequency",
is spatially extensive and stretches an electromagnetic wave train. A wave
train, hence an energy quantum, can only be emitted by its source gradually. In
both the two processes the wave and "particle" attributes of the radiation
field are simultaneously prominent, where an overall satisfactory theory has
been lacking. This paper presents a first principles treatment, in a unified
framework of the classical and quantum mechanics, of the latter process, the
emission of a single radiation quantum based on the dynamics of the
radiation-emitting source, a charged oscillator which is itself extensive
across its confining potential well. During the emission of one single
radiation quantum, the extensive charged oscillator undergoes a continuous
radiation damping and is non-stationary. This process is in this work treated
using a quasi stationary approach, whereby the classical equation of motion,
which directly facilitates the correspondence principle for a particle
oscillator, and the quantum wave equation are established for each sufficiently
brief time interval. As an inevitable consequence of the division of the total
time for emitting one single quantum, a fractional Planck constant $h$ is
introduced. The solutions to the two simultaneous equations yield for the
charged oscillator a continuously exponentially decaying Hamiltonian that is at
the same time quantised with respect to the fractional-$h$ at any instant of
time; and the radiation wave field emitted over time stretches a wave train of
finite length. The total system of the source and radiation field maintains at
any time (integer $n$ times) one whole energy quantum, $h \times$ frequency, in
complete accordance with the notion of quantum mechanics and experiment. | 1312.0918v1 |
2014-02-06 | Dynamics of Order Parameters near Stationary States in Superconductors with a Charge-Density Wave | We consider a simple model of a quasi-one-dimensional conductor in which two
order parameters (OP) may coexist, i.e., the superconducting OP $\Delta$ and
the OP $W$ that characterizes the amplitude of a charge-density wave (CDW). In
the mean field approximation we present equations for the matrix Green's
functions $G_{ik}$, where $i$ relates to the one of the two Fermi sheets and
$k$, operates in the Gor'kov-Nambu space. Using the solutions of these
equations, we find stationary states for different values of the parameter
describing the curvature of the Fermi surface, $\mu$, which can be varied,
e.g., by doping. It is established that in the interval $\mu_1<\mu<\mu_2$ the
self-consistency equations have a solution for coexisting OPs $\Delta$ and $W$.
However, this solution corresponds to a saddle point in the energy functional
$\Phi(\Delta, W)$, i.e., it is unstable. Stable states are: 1)the state with
the CDW at $\mu < \mu_{2}$; and 2) the purely superconducting state at
$\mu_1<\mu$. At $\mu<\mu_0$, the state 1) corresponds to a global minimum, and
at $\mu_0<\mu$, the state 2) has a lower energy, i.e., only the superconducting
state survives at large $\mu$. We study the dynamics of the variations
$\delta\Delta$ and $\delta W$ from these states in the collisionless limit. It
is characterized by two modes of oscillations, the fast and the slow one. The
fast mode is analogous to damped oscillations in conventional superconductors.
The frequency of slow modes depends on the curvature $\mu$ and is much smaller
than $2\Delta$ if the coupling constants for superconductivity and CDW are
close to each other. The considered model can be applied to high-$T_c$
superconductors where the parts of the Fermi surface near the `hot' spots may
be regarded as the considered two Fermi sheets. We also discuss relation of the
considered model to the simplest model for Fe-based pnictides. | 1402.1411v4 |
2014-05-28 | GRB 140515A at z=6.33: Constraints on the End of Reionization From a Gamma-ray Burst in a Low Hydrogen Column Density Environment | We present the discovery and subsequent spectroscopy with Gemini-North of the
optical afterglow of the Swift gamma-ray burst (GRB) 140515A. The spectrum
exhibits a well-detected continuum at wavelengths longer than 8915 Angs with a
steep decrement to zero flux blueward of 8910 Angs due to Ly-alpha absorption
at redshift z~6.33. Some transmission through the Lyman-alpha forest is present
at 5.2<z<5.733, but none is detected at higher redshift, consistent with
previous measurements from quasars and GRB 130606A. We model the red damping
wing of Lyman-alpha in three ways that provide equally good fits to the data:
(a) a single host galaxy absorber at z=6.327 with log(N_HI)=18.62+/-0.08; (b)
pure intergalactic medium (IGM) absorption from z=6.0 to z=6.328 with a
constant neutral hydrogen fraction of x_HI=0.056+0.011-0.027; and (c) a hybrid
model with a host absorber located within an ionized bubble of radius 10
comoving Mpc in an IGM with x_HI=0.12+/-0.05 (x_HI<0.21 at the 2-sigma level).
Regardless of the model, the sharpness of the dropoff in transmission is
inconsistent with a substantial neutral fraction in the IGM at this redshift.
No narrow absorption lines from the host galaxy are detected, indicating a host
metallicity of [Z/H]<~ -0.8. Even if we assume that all of the hydrogen
absorption is due to the host galaxy, the column is unusually low for a GRB
sightline, similar to two out of the other three highest-redshift bursts with
measured log(N_HI). This is possible evidence that the escape fraction of
ionizing photons from normal star-forming galaxies increases at z>~6. | 1405.7400v1 |
2014-08-24 | Thickness dependence of dynamic and static magnetic properties of pulsed laser deposited La$_{0.7}$Sr$_{0.3}$MnO$_3$ films on SrTiO$_3$(001) | We present a comprehensive study of the thickness dependence of static and
magneto-dynamic magnetic properties of La$_{0.7}$Sr$_{0.3}$MnO$_3$. Epitaxial
pulsed laser deposited La$_{0.7}$Sr$_{0.3}$MnO$_3$ / SrTiO$_3$(001) thin films
in the range from 3 unit cells (uc) to 40 uc (1.2 - 16 nm) have been
investigated through ferromagnetic resonance spectroscopy (FMR) and SQUID
magnetometry at variable temperature. Magnetodynamically, three different
thickness, $d$, regimes are identified: 20 uc $\lesssim d$ uc where the system
is bulk like, a transition region 8 uc $\le d \lesssim 20$ uc where the FMR
line width and position depend on thickness and $d=6$ uc which displays
significantly altered magnetodynamic properties, while still displaying bulk
magnetization. Magnetization and FMR measurements are consistent with a
nonmagnetic volume corresponding to $\sim$ 4 uc. We observe a reduction of
Curie temperature ($T_C$) with decreasing thickness, which is coherent with a
mean field model description. The reduced ordering temperature also accounts
for the thickness dependence of the magnetic anisotropy constants and resonance
fields. The damping of the system is strongly thickness dependent, and is for
thin films dominated by thickness dependent anisotropies, yielding both a
strong 2-magnon scattering close to $T_c$ and a low temperature broadening. For
the bulk like samples a large part of the broadening can be linked to spread in
magnetic anisotropies attributed to crystal imperfections/domain boundaries of
the bulk like film. | 1408.5631v1 |
2015-01-27 | Comparative analysis of existing models for power-grid synchronization | The dynamics of power-grid networks is becoming an increasingly active area
of research within the physics and network science communities. The results
from such studies are typically insightful and illustrative, but are often
based on simplifying assumptions that can be either difficult to assess or not
fully justified for realistic applications. Here we perform a comprehensive
comparative analysis of three leading models recently used to study
synchronization dynamics in power-grid networks -- a fundamental problem of
practical significance given that frequency synchronization of all power
generators in the same interconnection is a necessary condition for a power
grid to operate. We show that each of these models can be derived from first
principles within a common framework based on the classical model of a
generator, thereby clarifying all assumptions involved. This framework allows
us to view power grids as complex networks of coupled second-order phase
oscillators with both forcing and damping terms. Using simple illustrative
examples, test systems, and real power-grid datasets, we study the inherent
frequencies of the oscillators as well as their coupling structure, comparing
across the different models. We demonstrate, in particular, that if the network
structure is not homogeneous, generators with identical parameters need to be
modeled as non-identical oscillators in general. We also discuss an approach to
estimate the required (dynamical) parameters that are unavailable in typical
power-grid datasets, their use for computing the constants of each of the three
models, and an open-source MATLAB toolbox that we provide for these
computations. | 1501.06926v2 |
2015-04-28 | A meeting point of entropy and bifurcations in cross-diffusion herding | A cross-diffusion system modeling the information herding of individuals is
analyzed in a bounded domain with no-flux boundary conditions. The variables
are the species' density and an influence function which modifies the
information state of the individuals. The cross-diffusion term may stabilize or
destabilize the system. Furthermore, it allows for a formal gradient-flow or
entropy structure. Exploiting this structure, the global-in-time existence of
weak solutions and the exponential decay to the constant steady state is proved
in certain parameter regimes. This approach does not extend to all parameters.
We investigate local bifurcations from homogeneous steady states analytically
to determine whether this defines the validity boundary. This analysis shows
that generically there is a gap in the parameter regime between the entropy
approach validity and the first local bifurcation. Next, we use numerical
continuation methods to track the bifurcating non-homogeneous steady states
globally and to determine non-trivial stationary solutions related to herding
behaviour. In summary, we find that the main boundaries in the parameter regime
are given by the first local bifurcation point, the degeneracy of the diffusion
matrix and a certain entropy decay validity condition. We study several
parameter limits analytically as well as numerically, with a focus on the role
of changing a linear damping parameter as well as a parameter controlling the
cross-diffusion. We suggest that our paradigm of comparing
bifurcation-generated obstructions to the parameter validity of
global-functional methods could also be of relevance for many other models
beyond the one studied here. | 1504.07555v4 |
2015-06-18 | Galaxy power spectrum in redshift space: combining perturbation theory with the halo model | Theoretical modeling of the redshift-space power spectrum of galaxies is
crucially important to correctly extract cosmological information from redshift
surveys. The task is complicated by the nonlinear biasing and redshift space
distortion effects, which change with halo mass, and by the wide distribution
of halo masses and their occupations by galaxies. One of the main modeling
challenges is the existence of satellite galaxies that have both radial
distribution and large virial velocities inside halos, a phenomenon known as
the Finger-of-God effect. We present a model for the galaxy power spectrum of
in which we decompose a given galaxy sample into central and satellite galaxies
and relate different contributions to 1- and 2-halo terms in a halo model. Our
primary goal is to ensure that any parameters that we introduce have physically
meaningful values, and are not just fitting parameters. For the 2-halo terms we
use the previously developed RSD modeling of halos in the context of
distribution function and perturbation theory approach. This term needs to be
multiplied by the effect of radial distances and velocities of satellites
inside the halo. To this one needs to add the 1-halo terms, which are
non-perturbative. We show that the real space 1-halo terms can be modeled as
almost constant, with the finite extent of the satellites inside the halo
inducing a small k^2R^2 term, where R is related to the size of the halo. We
adopt a similar model for FoG in redshift space, ensuring that FoG velocity
dispersion is related to the halo mass. For FoG k^2 type expansions do not work
and FoG resummation must be used instead. We test several damping functions to
model the velocity dispersion FoG effect. Applying the formalism to mock
galaxies modeled after the "CMASS" sample of the BOSS survey, we find that our
predictions for the redshift-space power spectra are accurate up to k~0.4Mpc/h. | 1506.05814v2 |
2015-10-25 | A class of chemotaxis systems with growth source and nonlinear secretion | In this paper, we are concerned with a class of parabolic-elliptic chemotaxis
systems encompassing the prototype $$\left\{\begin{array}{lll} &u_t =
\nabla\cdot(\nabla u-\chi u\nabla v)+f(u), & x\in \Omega, t>0, \\[0.2cm] &0=
\Delta v -v+u^\kappa, & x\in \Omega, t>0 \end{array}\right. $$ with nonnegative
initial condition for $u$ and homogeneous Neumann boundary conditions in a
smooth bounded domain $\Omega\subset \mathbb{R}^n(n\geq 2)$, where $\chi>0$,
$\kappa>0$ and $f$ is a smooth growth source satisfying $f(0)\geq 0$ and $$
f(s)\leq a-bs^\theta, \quad s\geq 0, \text{with some} a\geq 0, b>0, \theta>1.
$$ Firstly, it is shown, either $$ \kappa<\frac{2}{n}\quad \& \quad f\equiv 0,
$$ or $$\theta>\kappa+1, $$ or $$ \theta-\kappa=1, \ \ b\geq \frac{(\kappa
n-2)}{\kappa n}\chi, \eqno(*) $$
that the corresponding initial-value problem admits a unique classical
solution that is uniformly bounded in space and time. Our proof is elementary
and semigroup-free. Whilst, with the particular choices $\theta=2$ and
$\kappa=1$, Tello and Winkler \cite{TW07} use sophisticated estimates via the
Neumann heat semigroup to obtain the global boundedness under the strict
inequality in ($\ast$). Thereby, we improve their results to the "borderline"
case $b=(\kappa n-2)/(\kappa n)\chi$ in this regard. Next, for an unbounded
range of $\chi$, the system is shown to exhibit pattern formations, and, the
emerging patterns are shown to converge weakly in $ L^\theta(\Omega)$ to some
constants as $\chi\rightarrow \infty$. While, for small $\chi$ or large damping
$b$, precisely $b>2\chi$ if $f(u)=u(a-bu^\kappa)$ for some $a, b>0$, we show
that the system does not admit pattern formation and the large time behavior of
solutions is comparable to its associated ODE+algebraic system. | 1510.07204v1 |
2017-01-20 | On the Transition from Potential Flow to Turbulence Around a Microsphere Oscillating in Superfluid ^4He | The flow of superfluid $^4$He around a translationally oscillating sphere,
levitating without mechanical support, can either be laminar or turbulent,
depending on the velocity amplitude. Below a critical velocity $v_c$ that
scales as $\omega ^{1/2}$, and is temperature independent below 1 K, the flow
is laminar (potential flow). Below 0.5 K the linear drag force is caused by
ballistic phonon scattering that vanishes as T$^4$ until background damping,
measured in the empty cell, becomes dominant for T $<$ 0.1 K. Increasing the
velocity amplitude above $v_c$ leads to a transition from potential flow to
turbulence, where the large turbulent drag force varies as $(v^2 - v_c^2)$. In
a small velocity interval $\Delta v / v_c \le 3 \%$ above $v_c$, the flow is
unstable below 0.5 K, switching intermittently between both patterns. From time
series recorded at constant temperature and driving force, the lifetimes of
both phases are analyzed statistically. We observe metastable states of
potential flow which, after a mean lifetime of 25 minutes, ultimately break
down due to vorticity created by natural background radioactivity. The
lifetimes of the turbulent phases have an exponential distribution, and the
mean increases exponentially with $\Delta v^2$. We investigate the frequency at
which the vortex rings are shed from the sphere. Our results are compared with
recent data of other authors on vortex shedding by moving a laser beam through
a Bose-Einstein condensate. Finally, we show that our observed transition to
turbulence belongs to the class of "supertransient chaos" where lifetimes of
the turbulent states increase faster than exponentially. Peculiar results
obtained in dilute $^3$He - $^4$He mixtures are presented in the Appendix. | 1701.05733v2 |
2017-02-04 | Brightness Temperature of Radio Zebras and Wave Energy Densities in Their Sources | We estimated the brightness temperature of radio zebras (zebra pattern --
ZP), considering that ZPs are generated in loops having an exponential density
profile in their cross-section. We took into account that when in plasma there
is a source emitting in all directions, then in the escape process from the
plasma the emission obtains a directional character nearly perpendicular to the
constant-density profile. Owing to the high directivity of the plasma emission
the region from which the emission escapes can be very small. We estimated the
brightness temperature of three observed ZPs for two values of the density
scale height (1 and 0.21 Mm) and two values of the loop width (1 and 2 arcsec).
In all cases high brightness temperatures were obtained. For the higher value
of the density scale height, the brightness temperature was estimated as 1.1
$\times$ 10$^{15}$ - 1.3 $\times$ 10$^{17}$ K, and for the lower value as 4.7
$\times$ 10$^{13}$ - 5.6 $\times$ 10$^{15}$ K. We also computed the saturation
energy density of the upper-hybrid waves (which according to the double plasma
resonance model are generated in the zebra source) using a 3D particle-in-cell
model with the loss-cone type of distribution of hot electrons. We found that
this saturated energy is proportional to the ratio of hot electron and
background plasma densities. Thus, comparing the growth rate and collisional
damping of the upper-hybrid waves, we estimated minimal densities of hot
electrons as well as the minimal value of the saturation energy density of the
upper-hybrid waves. Finally, we compared the computed energy density of the
upper-hybrid waves with the energy density of the electromagnetic waves in the
zebra source and thus estimated the efficiency of the wave transformation. | 1702.01278v2 |
2017-10-05 | Cross section alignment of polycyclic aromatic hydrocarbons by anisotropic radiation | We study the effect of anisotropic radiation illumination on the alignment of
polycyclic aromatic hydrocarbons (PAHs) and report that cross-sectional
mechanism of alignment earlier considered in terms of gas-grain interactions
can also be efficient for the photon-grain interaction. We demonstrate this by
first calculating the angle-dependence rotational damping and excitation
coefficients by photon absorption followed by infrared emission. We then
calculate the degree of PAH alignment for the different environments and
physical parameters, including the illumination direction, ionization fraction,
and magnetic field strength. For the reflection nebula (RN) conditions with
unidirectional radiation field, we find that the degree of alignment tends to
increase with increasing the angle $\psi$ between the illumination direction
and the magnetic field, as a result of the decrease of the cross-section of
photon absorption with $\psi$. We calculate the polarization of spinning PAH
emission using the obtained degree of alignment for the different physical
parameters, assuming constant grain temperatures. We find that the polarization
of spinning PAH emission from RN can be large, between $5-20~\%$ at frequencies
$\nu > 20$ GHz, whereas the polarization is less than $3~\%$ for
photodissociation regions (PDRs). In realistic conditions, the polarization is
expected to be lower due to grain temperature fluctuations and magnetic field
geometry. The polarization for the diffuse cold neutral medium (CNM) is rather
low, below $1~\%$ at $\nu>20$ GHz, consistent with observations by WMAP and
Planck. Our results demonstrate that the RNe are the favored environment to
observe the polarization of spinning dust emission as well as polarized mid-IR
emission from PAHs. | 1710.01835v2 |
2018-07-27 | Phase spreading and temporal coherence of a pair-condensed Fermi gas at low temperature | A condensate of pairs in an isolated, homogeneous, unpolarised, finite-size
spin 1/2 Fermi gas at low nonzero temperature T, undergoes with time a phase
change with a random component, due to coupling to the gas thermal phonons.
With the quantum second Josephson relation relating the derivative of the
condensate phase operator to the phonon occupation numbers, and linearised
kinetic equations giving the evolution of occupation number fluctuations, we
access the behaviour of the phase change variance at times much longer than the
phonon collision time. The case of a convex phonon branch is similar to the
Bose gas case: the leading collisional processes are the Beliaev-Landau
3-phonons processes, and the variance is the sum of a ballistic term and of a
delayed diffusive term, whose analytical expressions are given in the
thermodynamic limit. The concave case is more exotic. It is analysed at time
scales $T^{-9}$, allowing one to restrict to 2 phonons $\rightarrow$ 2 phonons
small-angle Landau-Khalatnikov processes. The total number of phonons is
conserved and the phonon mean occupation numbers at equilibrium can exhibit a
negative chemical potential, assumed isotropic. The phase change variance is
then the sum of a ballistic term, of a diffusive term, of exotic subsubleading
terms and of a constant term. The analytic expression of some of the
corresponding coefficients is obtained, as well as the diverging leading
behavior of the other ones when the phonon chemical potential tends to 0. When
this chemical potential is 0, the variance sub-ballistic part becomes
superdiffusive, with an exponent 5/3 and an exactly-known coefficient. For a
nonzero infinitesimal phonon chemical potential, a law is found, interpolating
between superdiffusive and diffusive phase spreading. Also new results are
obtained on the phonon Landau-Khalatnikov damping rate, in particular at
negative phonon chemical potential. | 1807.10476v2 |
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