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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
|
2020-08-02
|
Quantum capacity analysis of multi-level amplitude damping channels
|
The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced
as a generalization of the standard qubit Amplitude Damping Channel to quantum
systems of finite dimension $d$. In the special case of $d=3$, by exploiting
degradability, data-processing inequalities, and channel isomorphism, we
compute the associated quantum and private classical capacities for a rather
wide class of maps, extending the set of solvable models known so far. We
proceed then to the evaluation of the entanglement assisted, quantum and
classical, capacities.
|
2008.00477v3
|
2020-08-11
|
An inverse spectral problem for a damped wave operator
|
This paper proposes a new and efficient numerical algorithm for recovering
the damping coefficient from the spectrum of a damped wave operator, which is a
classical Borg-Levinson inverse spectral problem. The algorithm is based on
inverting a sequence of trace formulas, which are deduced by a recursive
formula, bridging geometrical and spectrum information explicitly in terms of
Fredholm integral equations. Numerical examples are presented to illustrate the
efficiency of the proposed algorithm.
|
2008.04523v1
|
2020-08-17
|
Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I
|
In this paper, we are interested in the Cauchy problem for the viscoelastic
damped wave equation with memory of type I. By applying WKB analysis and
Fourier analysis, we explain the memory's influence on dissipative structures
and asymptotic profiles of solutions to the model with weighted $L^1$ initial
data. Furthermore, concerning standard energy and the solution itself, we
establish singular limit relations between the Moore-Gibson-Thompson equation
with memory and the viscoelastic damped wave equation with memory.
|
2008.07151v1
|
2020-08-18
|
A class of Finite difference Methods for solving inhomogeneous damped wave equations
|
In this paper, a class of finite difference numerical techniques is presented
to solve the second-order linear inhomogeneous damped wave equation. The
consistency, stability, and convergences of these numerical schemes are
discussed. The results obtained are compared to the exact solution, ordinary
explicit, implicit finite difference methods, and the fourth-order compact
method (FOCM). The general idea of these methods is developed by using the
C0-semigroups operator theory. We also showed that the stability region for the
explicit finite difference scheme depends on the damping coefficient.
|
2008.08043v2
|
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
|
2021-05-03
|
Enhanced and unenhanced dampings of Kolmogorov flow
|
In the present study, Kolmogorov flow represents the stationary sinusoidal
solution $(\sin y,0)$ to a two-dimensional spatially periodic Navier-Stokes
system, driven by an external force. This system admits the additional
non-stationary solution $(\sin y,0)+e^{-\nu t} (\sin y,0)$, which tends
exponentially to the Kolmogorov flow at the minimum decay rate determined by
the viscosity $\nu$. Enhanced damping or enhanced dissipation of the problem is
obtained by presenting higher decay rate for the difference between a solution
and the non-stationary basic solution. Moreover, for the understanding of the
metastability problem in an explicit manner, a variety of exact solutions are
presented to show enhanced and unenhanced dampings.
|
2105.00730v2
|
2021-05-06
|
On Linear Damping Around Inhomogeneous Stationary States of the Vlasov-HMF Model
|
We study the dynamics of perturbations around an inhomogeneous stationary
state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized
stability criterion (Penrose criterion). We consider solutions of the
linearized equation around the steady state, and prove the algebraic decay in
time of the Fourier modes of their density. We prove moreover that these
solutions exhibit a scattering behavior to a modified state, implying a linear
Landau damping effect with an algebraic rate of damping.
|
2105.02484v1
|
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
|
1994-05-02
|
Damped Lyman Alpha Systems vs. Cold + Hot Dark Matter
|
Although the Cold + Hot Dark Matter (CHDM) cosmology provides perhaps the
best fit of any model to all the available data at the current epoch, CHDM
produces structure at relatively low redshifts and thus could be ruled out if
there were evidence for formation of massive objects at high redshifts. Damped
Ly$\alpha$ systems are abundant in quasar absorption spectra and thus provide
possibly the most significant evidence for early structure formation, and thus
perhaps the most stringent constraint on CHDM. Using the numbers of halos in
N-body simulations to normalize Press-Schechter estimates of the number
densities of protogalaxies as a function of redshift, we find that CHDM with
$\Omega_c/\Omega_\nu/\Omega_b = 0.6/0.3/0.1$ is compatible with the damped
Ly$\alpha$ data at $\le 2.5$, but that it is probably incompatible with the
limited $z>3$ damped Ly$\alpha$ data. The situation is uncertain because there
is very little data for $z>3$, and also it is unclear whether all damped
Ly$\alpha$ systems are associated with collapsed protogalaxies. The predictions
of CHDM are quite sensitive to the hot (neutrino) fraction, and we find that
$\Omega_c/\Omega_\nu/\Omega_b = 0.675/0.25/0.075$ is compatible even with the
$z>3$ data. This corresponds to lowering the neutrino mass from 6.8 to 5.7 eV,
for $H_0=50\kmsMpc$. In CHDM, the higher redshift damped Ly$\alpha$ systems are
predicted to have lower masses, which can be checked by measuring the velocity
widths of the associated metal line systems.
|
9405003v1
|
1995-03-24
|
High Redshift Lyman Limit and Damped Lyman-Alpha Absorbers
|
We have obtained high signal:to:noise optical spectroscopy at 5\AA\
resolution of 27 quasars from the APM z$>$4 quasar survey. The spectra have
been analyzed to create new samples of high redshift Lyman-limit and damped
Lyman-$\alpha$ absorbers. These data have been combined with published data
sets in a study of the redshift evolution and the column density distribution
function for absorbers with $\log$N(HI)$\ge17.5$, over the redshift range 0.01
$<$ z $<$ 5. The main results are: \begin{itemize} \item Lyman limit systems:
The data are well fit by a power law $N(z) = N_0(1 + z)^{\gamma}$ for the
number density per unit redshift. For the first time intrinsic evolution is
detected in the product of the absorption cross-section and comoving spatial
number density for an $\Omega = 1$ Universe. We find $\gamma = 1.55$ ($\gamma =
0.5$ for no evolution) and $N_0 = 0.27$ with $>$99.7\% confidence limits for
$\gamma$ of 0.82 \& 2.37. \item Damped \lya systems: The APM QSOs provide a
substantial increase in the redshift path available for damped surveys for
$z>3$. Eleven candidate and three confirmed damped Ly$\alpha$ absorption
systems, have been identified in the APM QSO spectra covering the redshift
range $2.8\le z \le 4.4$ (11 with $z>3.5$). Combining the APM survey confirmed
and candidate damped \lya absorbers with previous surveys, we find evidence for
a turnover at z$\sim$3 or a flattening at z$\sim$2 in the cosmological mass
density of neutral gas, $\Omega_g$. \end{itemize} The Lyman limit survey
results are published in Storrie-Lombardi, et~al., 1994, ApJ, 427, L13. Here we
describe the results for the DLA population of absorbers.
|
9503089v1
|
1997-05-15
|
Cosmological Constraints from High-Redshift Damped Lyman-Alpha Systems
|
Any viable cosmological model must produce enough structure at early epochs
to explain the amount of gas associated with high-redshift damped Ly$\alpha$
systems. We study the evolution of damped Ly$\alpha$ systems at redshifts $z\ge
2$ in cold dark matter (CDM) and cold+hot dark matter (CDM+HDM) models using
both N-body and hydrodynamic simulations. Our approach incorporates the effects
of gas dynamics, and we find that all earlier estimates which assumed that all
the baryons in dark matter halos would contribute to damped Ly$\alpha$
absorption have overestimated the column density distribution $f(N)$ and the
fraction of neutral dense gas $\Omega_g$ in damped Ly$\alpha$ systems. The
differences are driven by ionization of hydrogen in the outskirts of galactic
halos and by gaseous dissipation near the halo centers, and they tend to
exacerbate the problem of late galaxy formation in CDM+HDM models. We only
include systems up to the highest observed column density $N\sim 10^{21.8}$
cm$^{-2}$ in the estimation of $\Omega_g$ for a fair comparison with data. If
the observed $f(N)$ and $\Omega_g$ inferred from a small number of confirmed
and candidate absorbers are robust, the amount of gas in damped Ly$\alpha$
systems at high redshifts in the $\Omega_\nu=0.2$ CDM+HDM model falls well
below the observations.
|
9705113v1
|
2001-01-03
|
Galactic Chemical Abundances at z>3 I: First Results from the Echellette Spectrograph and Imager
|
We present the first results from an ongoing survey to discover and measure
the metallicity of z>3 damped Lya systems with the Echellette Spectrograph and
Imager (ESI) on the Keck II telescope. Our motivation arises from a recent
study on the damped Lya systems suggesting only mild evolution in the cosmic
metallicity from z~2 to 4. The Echellette Spectrograph and Imager, which
provides two complementary spectroscopic modes, is the ideal instrument for a
z>3 damped Lya survey. We describe our observing strategy and report on the
discovery and analysis of 5 new z>3 damped Lya systems acquired in a single
night of observing. These observations further support the principal
conclusions of the previous study: (1) the cosmic metallicity in neutral gas
inferred from the damped Lya systems does not evolve significantly from z~2 to
4; (2) the unweighted metallicity exhibits a statistically significant decrease
with increasing redshift; and (3) not a single damped Lya system has a
metallicity below [Fe/H]=-3. We discuss the implications of these results and
comment on recent theoretical studies which attempt to explain the
observations.
|
0101029v1
|
2002-01-17
|
Self-shielding Effects on the Column Density Distribution of Damped Lyman Alpha Systems
|
We calculate the column density distribution of damped Lyman alpha systems,
modeled as spherical isothermal gaseous halos ionized by the external cosmic
background. The effects of self-shielding introduce a hump in this
distribution, at a column density N_{HI} \sim 1.6x10^{17} X^{-1} cm^{-2}, where
X is the neutral fraction at the radius where self-shielding starts being
important. The most recent compilation of the column density distribution by
Storrie-Lombardi & Wolfe shows marginal evidence for the detection of this
feature due to self-shielding, suggesting a value X \sim 10^{-3}. Assuming a
photoionization rate \Gamma \sim 10^{-12} s^{-1} from the external ionizing
background, the radius where self-shielding occurs is inferred to be about
3.8kpc. If damped Lyman alpha systems consist of a clumpy medium, this should
be interpreted as the typical size of the gas clumps in the region where they
become self-shielding. Clumps of this size with typical column densities N_H
\sim 3x10^{20} cm^{-2} would be in hydrostatic equilibrium at the
characteristic photoionization temperature \sim 10^4 K if they do not contain
dark matter. Since this size is similar to the overall radius of damped \lya
systems in Cold Dark Matter models, where all halos are assumed to contain
similar gas clouds producing damped absorbers, this suggests that the gas in
damped absorbers is in fact not highly clumped.
|
0201275v2
|
2002-04-30
|
Two-phase equilibrium and molecular hydrogen formation in damped Lyman-alpha systems
|
Molecular hydrogen is quite underabundant in damped Lyman-alpha systems at
high redshift, when compared to the interstellar medium near the Sun. This has
been interpreted as implying that the gas in damped Lyman-alpha systems is
warm. like the nearby neutral intercloud medium, rather than cool, as in the
clouds which give rise to most H I absorption in the Milky Way. Other lines of
evidence suggest that the gas in damped Lyman-alpha systems -- in whole or part
-- is actually cool; spectroscopy of neutral and ionized carbon, discussed
here, shows that the damped Lyman-alpha systems observed at lower redshift z
$<$ 2.3 are largely cool, while those seen at z $>$ 2.8 are warm (though not
devoid of H2). To interpret the observations of carbon and hydrogen we
constructed detailed numerical models of H2 formation under the conditions of
two-phase thermal equilibrium, like those which account for conditions near the
Sun, but with varying metallicity, dust-gas ratio, $etc$. We find that the low
metallicity of damped Lyman-alpha systems is enough to suppress H2 formation by
many orders of magnitude even in cool diffuse clouds, as long as the ambient
optical/uv radiation field is not too small. For very low metallicity and under
the most diffuse conditions, H2 formation will be dominated by slow gas-phase
processes not involving grains, and a minimum molecular fraction in the range
$10^{-8}-10^{-7}$ is expected.
|
0204515v1
|
2003-05-12
|
Ordinary and Viscosity-Damped MHD Turbulence
|
We compare the properties of ordinary strong magnetohydrodynamic (MHD)
turbulence in a strongly magnetized medium with the recently discovered
viscosity-damped regime. We focus on energy spectra, anisotropy, and
intermittency. Our most surprising conclusion is that in ordinary strong MHD
turbulence the velocity and magnetic fields show different high-order structure
function scalings. Moreover this scaling depends on whether the intermittency
is viewed in a global or local system of reference. This reconciles seemingly
contradictory earlier results. On the other hand, the intermittency scaling for
viscosity-damped turbulence is very different, and difficult to understand in
terms of the usual phenomenological models for intermittency in turbulence. Our
remaining results are in reasonable agreement with expectations. First, we find
that our high resolution simulations for ordinary MHD turbulence show that the
energy spectra are {\it compatible} with a Kolmogorov spectrum, while
viscosity-damped turbulence shows a shallow $k^{-1}$ spectrum for the magnetic
fluctuations. Second, a new numerical technique confirms that ordinary MHD
turbulence exhibits Goldreich-Sridhar type anisotropy, while viscosity-damped
MHD turbulence shows extremely anisotropic eddy structures. Finally, we show
that many properties of incompressible turbulence for both the ordinary and
viscosity-damped regimes carry over to the case of compressible turbulence.
|
0305212v2
|
2003-09-17
|
Observational Tests of Damping by Resonant Absorption in Coronal Loop Oscillations
|
One of the proposed damping mechanisms of coronal (transverse) loop
oscillations in the kink-mode is resonant absorption as a result of the Alfven
speed variation at the outer boundary of coronal loops. Analytical expressions
for the period and damping time exist for loop models with thin non-uniform
boundaries. Here we measure the thickness of the non-uniform layer in
oscillating loops for 11 events, by forward-fitting of the cross-sectional
density profile and line-of-sight integration to the cross-sectional fluxes
observed with TRACE 171 A. This way we model the internal and external electron
density of the coronal plasma in oscillating loops. This allows us to test the
theoretically predicted damping rates for thin boundaries as function of the
density ratio. We find that the density ratio predicted by the damping time is
higher than the density ratio estimated from the background fluxes. The lower
densities modeled from the background fluxes are likely to be a consequence of
the neglected hotter plasma that is not detected with the TRACE 171 A filter.
Taking these correction into account, resonant absorption predicts damping
times of kink-mode oscillations that are commensurable with the observed ones
and provides a new diagnostic of the density contrast of oscillating loops.
|
0309470v1
|
2005-03-01
|
Metal Abundances in a Damped Lyman-alpha System Along Two Lines of Sight at z=0.93
|
We study metal abundances in the z=0.9313 damped Lya system observed in the
two lines-of-sight, A and B, toward the gravitationally-lensed double QSO
HE0512-3329. Spatially resolved STIS spectra constrain the neutral-gas column
density to be LogN(HI)=20.5 in both Aand B. UVES spectra (spectral resolution
FWHM=9.8 km/s) show, in contrast, significant line-of-sight differences in the
column densities of MnII and FeII; these are not due to observational
systematics. We find that [Mn/H]=-1.44 and [Fe/H]=-1.52 in damped Lya system A,
while [Mn/H]=-0.98 and [Fe/H]>-1.32, and possibly as high as [Fe/H] approx. -1
in damped Lya system B. A careful assessment of possible systematic errors
leads us to conclude that these transverse differences are significant at a 5
sigma level or greater. Although nucleosynthesis effects may also be at play,
we favor differential dust-depletion as the main mechanism producing the
observed abundance gradient. The transverse separation is 5 kpc at the redshift
of the absorber, which is also likely to be the lensing galaxy. The derived
abundances therefore probe two opposite sides of a single galaxy hosting both
damped Lya systems. This is the first time firm abundance constraints have been
obtained for a single damped system probed by two lines-of-sight. The
significance of this finding for the cosmic evolution of metals is discussed.
|
0503026v1
|
2000-08-26
|
Adsorbate aggregation and relaxation of low-frequency vibrations
|
We present a study of resonant vibrational coupling between adsorbates and an
elastic substrate at low macroscopic coverages. In the first part of the paper
we consider the situation when adsorbates form aggregates with high local
coverage. Based upon our previously published theory, we derive formulas
describing the damping rate of adsorbate vibrations for two cases of such
aggregation: (i) adsorbates attached to step edges and (ii) adsorbates forming
two-dimensional islands. We have shown that damping is governed by local
coverage. Particularly, for a wide range of resonant frequencies, the damping
rate of adsorbates forming well separated islands is described by the damping
rate formula for a periodic overlayer with the coverage equal to the local
coverage in the island. The second part of the paper is devoted to facilitating
the evaluation of damping rates for a disordered overlayer. The formula
describing the damping rate involves the parameter $\beta$ which is related to
the local density of phonon states at the substrate surface and does not allow
a closed-form representation. For substrates of isotropic and cubic symmetries,
we have developed a good analytical approximation to this parameter. For a vast
majority of cubic substrates the difference between the analytical
approximation and numerical calculation does not exceed 4%.
|
0008389v1
|
2004-10-26
|
Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice
|
We present a theoretical treatment of the surprisingly large damping observed
recently in one-dimensional Bose-Einstein atomic condensates in optical
lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB)
calculations can describe qualitatively the main features of the damping
observed over a range of lattice depths. We also derive a formula of the
fluctuation-dissipation type for the damping, based on a picture in which the
coherent motion of the condensate atoms is disrupted as they try to flow
through the random local potential created by the irregular motion of
noncondensate atoms. We expect this irregular motion to result from the
well-known dynamical instability exhibited by the mean-field theory for these
systems. When parameters for the characteristic strength and correlation times
of the fluctuations, obtained from the HFB calculations, are substituted in the
damping formula, we find very good agreement with the experimentally-observed
damping, as long as the lattice is shallow enough for the fraction of atoms in
the Mott insulator phase to be negligible. We also include, for completeness,
the results of other calculations based on the Gutzwiller ansatz, which appear
to work better for the deeper lattices.
|
0410677v4
|
1998-10-16
|
Fermion Damping in a Fermion-Scalar Plasma
|
In this article we study the dynamics of fermions in a fermion-scalar plasma.
We begin by obtaining the effective in-medium Dirac equation in real time which
is fully renormalized and causal and leads to the initial value problem. For a
heavy scalar we find the novel result that the decay of the scalar into fermion
pairs in the medium leads to damping of the fermionic excitations and their
in-medium propagation as quasiparticles. That is, the fermions acquire a width
due to the decay of the heavier scalar in the medium. We find the damping rate
to lowest order in the Yukawa coupling for arbitrary values of scalar and
fermion masses, temperature and fermion momentum. An all-order expression for
the damping rate in terms of the exact quasiparticle wave functions is
established. A kinetic Boltzmann approach to the relaxation of the fermionic
distribution function confirms the damping of fermionic excitations as a
consequence of the induced decay of heavy scalars in the medium. A
linearization of the Boltzmann equation near equilibrium clearly displays the
relationship between the damping rate of fermionic mean fields and the fermion
interaction rate to lowest order in the Yukawa coupling directly in real time.
|
9810393v2
|
2006-01-06
|
Wave energy localization by self-focusing in large molecular structures: a damped stochastic discrete nonlinear Schroedinger equation model
|
Wave self-focusing in molecular systems subject to thermal effects, such as
thin molecular films and long biomolecules, can be modeled by stochastic
versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott,
and this can be approximated by continuum limits in the form of stochastic
nonlinear Schroedinger equations.
Previous studies directed at the SNLS approximations have indicated that the
self-focusing of wave energy to highly localized states can be inhibited by
phase noise (modeling thermal effects) and can be restored by phase damping
(modeling heat radiation).
We show that the continuum limit is probably ill-posed in the presence of
spatially uncorrelated noise, at least with little or no damping, so that
discrete models need to be addressed directly. Also, as has been noted by other
authors, omission of damping produces highly unphysical results.
Numerical results are presented for the first time for the discrete models
including the highly nonlinear damping term, and new numerical methods are
introduced for this purpose. Previous conjectures are in general confirmed, and
the damping is shown to strongly stabilize the highly localized states of the
discrete models. It appears that the previously noted inhibition of nonlinear
wave phenomena by noise is an artifact of modeling that includes the effects of
heat, but not of heat loss.
|
0601017v1
|
2007-11-15
|
Effect of the steady flow on spatial damping of small-amplitude prominence oscillations
|
Aims. Taking account of steady flow in solar prominences, we study its
effects on spatial damping of small-amplitude non-adiabatic magnetoacoustic
waves in a homogeneous, isothermal, and unbounded prominence plasma. Methods.
We model the typical feature of observed damped oscillatory motion in
prominences, removing the adiabaticity assumption through thermal conduction,
radiation and heating. Invoking steady flow in MHD equations, we linearise them
under small-amplitude approximation and obtain a new general dispersion
relation for linear non-adiabatic magnetoacoustic waves in prominences Results.
The presence of steady flow breaks the symmetry of forward and backward
propagating MHD wave modes in prominences. The steady flow has dramatic
influence on the propagation and damping of magnetoacoustic and thermal waves.
Depending upon the direction and strength of flow the magnetoacoustic and
thermal modes can show both the features of wave amplification and damping. At
the wave period of 5 min where the photospheric power is maximum, the slow mode
shows wave amplification. However, in the absence of steady flow the slow mode
wave shows damping. Conclusions. For the wave period between 5 min and 15 min,
the amplification length for slow mode, in the case of prominence regime 1.1,
varies between 3.4*10^11 m to 2*10^12 m. Dramatic influence of steady flow on
small-amplitude prominence oscillations is likely to play an important role in
both wave detection and prominence seismology.
|
0711.2353v1
|
2008-02-07
|
Cascade and Damping of Alfvén-Cyclotron Fluctuations: Application to Solar Wind Turbulence Spectrum
|
With the diffusion approximation, we study the cascade and damping of
Alfv\'{e}n-cyclotron fluctuations in solar plasmas numerically. Motivated by
wave-wave couplings and nonlinear effects, we test several forms of the
diffusion tensor. For a general locally anisotropic and inhomogeneous diffusion
tensor in the wave vector space, the turbulence spectrum in the inertial range
can be fitted with power-laws with the power-law index varying with the wave
propagation direction. For several locally isotropic but inhomogeneous
diffusion coefficients, the steady-state turbulence spectra are nearly
isotropic in the absence of damping and can be fitted by a single power-law
function. However, the energy flux is strongly polarized due to the
inhomogeneity that leads to an anisotropic cascade. Including the anisotropic
thermal damping, the turbulence spectrum cuts off at the wave numbers, where
the damping rates become comparable to the cascade rates. The combined
anisotropic effects of cascade and damping make this cutoff wave number
dependent on the wave propagation direction, and the propagation direction
integrated turbulence spectrum resembles a broken power-law, which cuts off at
the maximum of the cutoff wave numbers or the $^4$He cyclotron frequency.
Taking into account the Doppler effects, the model can naturally reproduce the
broken power-law wave spectra observed in the solar wind and predicts that a
higher break frequency is aways accompanied with a greater spectral index
change that may be caused by the increase of the Alfv\'{e}n Mach number, the
reciprocal of the plasma beta, and/or the angle between the solar wind velocity
and the mean magnetic field. These predictions can be tested by future
observations.
|
0802.0910v1
|
2011-04-13
|
Evolution of inclined planets in three-dimensional radiative discs
|
While planets in the solar system only have a low inclination with respect to
the ecliptic there is mounting evidence that in extrasolar systems the
inclination can be very high, at least for close-in planets. One process to
alter the inclination of a planet is through planet-disc interactions. Recent
simulations considering radiative transport have shown that the evolution of
migration and eccentricity can strongly depend on the thermodynamic state of
the disc. We extend previous studies to investigate the planet-disc
interactions of fixed and moving planets on inclined and eccentric orbits. We
also analyse the effect of the disc's thermodynamic properties on the orbital
evolution of embedded planets in detail. The protoplanetary disc is modelled as
a viscous gas where the internally produced dissipation is transported by
radiation. For locally isothermal discs, we confirm previous results and find
inclination damping and inward migration for planetary cores. For low
inclinations i < 2 H/r, the damping is exponential, while di/dt is proportional
to i^-2 for larger i. For radiative discs, the planetary migration is very
limited, as long as their inclination exceeds a certain threshold. If the
inclination is damped below this threshold, planetary cores with a mass up to
approximately 33 Earth masses start to migrate outwards, while larger cores
migrate inwards right from the start. The inclination is damped for all
analysed planet masses. In a viscous disc an initial inclination of embedded
planets will be damped for all planet masses. This damping occurs on timescales
that are shorter than the migration time. If the inclination lies beneath a
certain threshold, the outward migration in radiative discs is not handicapped.
Outward migration is strongest for circular and non-inclined orbits.
|
1104.2408v1
|
2011-07-12
|
Mode conversion of radiatively damped magnetogravity waves in the solar chromosphere
|
Modelling of adiabatic gravity wave propagation in the solar atmosphere
showed that mode conversion to field guided acoustic waves or Alfv\'en waves
was possible in the presence of highly inclined magnetic fields. This work aims
to extend the previous adiabatic study, exploring the consequences of radiative
damping on the propagation and mode conversion of gravity waves in the solar
atmosphere. We model gravity waves in a VAL-C atmosphere, subject to a uniform,
and arbitrarily orientated magnetic field, using the Newton cooling
approximation for radiatively damped propagation. The results indicate that the
mode conversion pathways identified in the adiabatic study are maintained in
the presence of damping. The wave energy fluxes are highly sensitive to the
form of the height dependence of the radiative damping time. While simulations
starting from 0.2 Mm result in modest flux attenuation compared to the
adiabatic results, short damping times expected in the low photosphere
effectively suppress gravity waves in simulations starting at the base of the
photosphere. It is difficult to reconcile our results and observations of
propagating gravity waves with significant energy flux at photospheric heights
unless they are generated in situ, and even then, why they are observed to be
propagating as low as 70 km where gravity waves should be radiatively
overdamped.
|
1107.2208v1
|
2013-09-23
|
Phonon-mediated damping of mechanical vibrations in a finite atomic chain coupled to an outer environment
|
We study phonon-mediated damping of mechanical vibrations in a finite
quantum-mechanical atomic-chain model. Our study is motivated by the quest to
understand the quality factors (Q) of nanomechanical resonators and
nanoelectromechanical systems (NEMS), as well as actual experiments with
suspended atomic chains and molecular junctions. We consider a finite atomic
chain which is coupled to a zero-temperature outer environment, modeled as two
additional semi-infinite chains, thus inducing "clamping-losses". Weak coupling
to the outer environment ensures that the clamping losses are small, and that
the initially discrete nature of the phonon spectrum is approximately
maintained. We then consider a phonon damping process known as "Landau-Rumer
damping", where phonons in the excited mode of vibration decay into other modes
through anharmonic phonon-phonon interaction. The approximately discrete nature
of the phonon spectrum leads to sharp nonmonotonic changes in Q as parameters
are varied, and to the appearance of resonances in the damping. The latter
correspond to the existence of decay processes where the participating phonons
approximately conserve energy. We explore means to control the damping by
changing either the number of atoms in the chains or the ratio between the
longitudinal and transverse speeds of sound, thereby suggesting future
experiments to observe this resonance-like behavior.
|
1309.5772v1
|
2014-04-01
|
Stellar dynamics in gas: The role of gas damping
|
In this paper, we consider how gas damping affects the dynamical evolution of
gas-embedded star clusters. Using a simple three-component (i.e. one gas and
two stellar components) model, we compare the rates of mass segregation due to
two-body relaxation, accretion from the interstellar medium, and gas dynamical
friction in both the supersonic and subsonic regimes. Using observational data
in the literature, we apply our analytic predictions to two different
astrophysical environments, namely galactic nuclei and young open star
clusters. Our analytic results are then tested using numerical simulations
performed with the NBSymple code, modified by an additional deceleration term
to model the damping effects of the gas.
The results of our simulations are in reasonable agreement with our analytic
predictions, and demonstrate that gas damping can significantly accelerate the
rate of mass segregation. A stable state of approximate energy equilibrium
cannot be achieved in our model if gas damping is present, even if Spitzer's
Criterion is satisfied. This instability drives the continued dynamical
decoupling and subsequent ejection (and/or collisions) of the more massive
population. Unlike two-body relaxation, gas damping causes overall cluster
contraction, reducing both the core and half-mass radii. If the cluster is mass
segregated (and/or the gas density is highest at the cluster centre), the
latter contracts faster than the former, accelerating the rate of core
collapse.
|
1404.0379v1
|
2014-04-26
|
Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
|
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is
studied in an unmagnetized dusty negative-ion plasma in the extreme conditions
when the free electrons are absent. The cold massive charged dusts are
described by fluid equations, whereas the two-species of ions (positive and
negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries
(KdV) equation with Landau damping, governing the dynamics of weakly nonlinear
and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids
{\bf 12}, 2388 (1969)]. It is shown that for some typical laboratory and space
plasmas, the Landau damping (and the nonlinear) effects are more pronounced
than the finite Debye length (dispersive) effects for which the KdV soliton
theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of
the linear phase velocity, solitary wave amplitudes (in presence and absence of
the Landau damping) as well as the Landau damping rate are studied with the
effects of the positive ion to dust density ratio $(\mu_{pd})$ as well as the
ratios of positive to negative ion temperatures $(\sigma)$ and masses $(m)$.
|
1404.6623v3
|
2015-03-31
|
Damping of Confined Excitations Modes of 1D Condensates in an Optical Lattice
|
We study the damping of the collective excitations of Bose-Einstein
condensates in a harmonic trap potential loaded in an optical lattice. In the
presence of a confining potential the system is non-homogeneous and the
collective excitations are characterized by a set of discrete confined
phonon-like excitations. We derive a general convenient analytical description
for the damping rate, which takes into account, the trapping potential and the
optical lattice, for the Landau and Beliaev processes at any temperature, $T$.
At high temperature or weak spatial confinement, we show that both mechanisms
display linear dependence on $T$. In the quantum limit, we found that the
Landau damping is exponentially suppressed at low temperatures and the total
damping is independent of $T$. Our theoretical predictions for the damping rate
under thermal regime is in completely correspondence with the experimental
values reported for 1D condensate of sodium atoms. We show that the laser
intensity can tune the collision process, allowing a \textit{resonant effect}
for the condensate lifetime. Also, we study the influence of the attractive or
repulsive non-linear terms on the decay rate of the collective excitations. A
general expression of the renormalized Goldstone frequency has been obtained as
a function of the 1D non-linear self-interaction parameter, laser intensity and
temperature.
|
1503.08884v2
|
2015-08-06
|
On the spatial scales of wave heating in the solar chromosphere
|
Dissipation of magnetohydrodynamic (MHD) wave energy has been proposed as a
viable heating mechanism in the solar chromospheric plasma. Here, we use a
simplified one-dimensional model of the chromosphere to theoretically
investigate the physical processes and the spatial scales that are required for
the efficient dissipation of Alfv\'en waves and slow magnetoacoustic waves. We
consider the governing equations for a partially ionized hydrogen-helium plasma
in the single-fluid MHD approximation and include realistic wave damping
mechanisms that may operate in the chromosphere, namely Ohmic and ambipolar
magnetic diffusion, viscosity, thermal conduction, and radiative losses. We
perform an analytic local study in the limit of small amplitudes to
approximately derive the lengthscales for critical damping and efficient
dissipation of MHD wave energy. We find that the critical dissipation
lengthscale for Alfv\'en waves depends strongly on the magnetic field strength
and ranges from 10~m to 1~km for realistic field strengths. The damping of
Alfv\'en waves is dominated by Ohmic diffusion for weak magnetic field and low
heights in the chromosphere, and by ambipolar diffusion for strong magnetic
field and medium/large heights in the chromosphere. Conversely, the damping of
slow magnetoacoustic waves is less efficient, and spatial scales shorter than
10~m are required for critical damping. Thermal conduction and viscosity govern
the damping of slow magnetoacoustic waves and play an equally important role at
all heights. These results indicate that the spatial scales at which strong
wave heating may work in the chromosphere are currently unresolved by
observations.
|
1508.01497v1
|
2015-11-11
|
A statistical study of decaying kink oscillations detected using SDO/AIA
|
Despite intensive studies of kink oscillations of coronal loops in the last
decade, a large scale statistically significant investigation of the
oscillation parameters has not been made using data from the Solar Dynamics
Observatory (SDO).
We carry out a statistical study of kink oscillations using Extreme
Ultra-Violet (EUV) imaging data from a previously compiled catalogue.
We analysed 58 kink oscillation events observed by the Atmospheric Imaging
Assembly (AIA) onboard SDO during its first four years of operation
(2010-2014). Parameters of the oscillations, including the initial apparent
amplitude, period, length of the oscillating loop, and damping are studied for
120 individual loop oscillations.
Analysis of the initial loop displacement and oscillation amplitude leads to
the conclusion that the initial loop displacement prescribes the initial
amplitude of oscillation in general. The period is found to scale with the loop
length, and a linear fit of the data cloud gives a kink speed of Ck
=(1330+/-50) km s-1 . The main body of the data corresponds to kink speeds in
the range Ck =(800-3300) km s-1. Measurements of 52 exponential damping times
were made, and it was noted that at least 22 of the damping profiles may be
better approximated by a combination of non-exponential and exponential
profiles, rather than a purely exponential damping envelope. There are an
additional 10 cases where the profile appears to be purely non-exponential, and
no damping time was measured. A scaling of the exponential damping time with
the period is found, following the previously established linear scaling
between these two parameters.
|
1511.03558v1
|
2016-03-01
|
A comparative study of protocols for secure quantum communication under noisy environment: single-qubit-based protocols versus entangled-state-based protocols
|
The effect of noise on various protocols of secure quantum communication has
been studied. Specifically, we have investigated the effect of amplitude
damping, phase damping, squeezed generalized amplitude damping, Pauli type as
well as various collective noise models on the protocols of quantum key
distribution, quantum key agreement,quantum secure direct quantum communication
and quantum dialogue. From each type of protocol of secure quantum
communication, we have chosen two protocols for our comparative study; one
based on single qubit states and the other one on entangled states. The
comparative study reported here has revealed that single-qubit-based schemes
are generally found to perform better in the presence of amplitude damping,
phase damping, squeezed generalized amplitude damping noises, while
entanglement-based protocols turn out to be preferable in the presence of
collective noises. It is also observed that the effect of noise entirely
depends upon the number of rounds of quantum communication involved in a scheme
of quantum communication. Further, it is observed that squeezing, a completely
quantum mechanical resource present in the squeezed generalized amplitude
channel, can be used in a beneficial way as it may yield higher fidelity
compared to the corresponding zero squeezing case.
|
1603.00178v1
|
2016-11-17
|
A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis
|
A stable partitioned algorithm is developed for fluid-structure interaction
(FSI) problems involving viscous incompressible flow and rigid bodies. This
{\em added-mass partitioned} (AMP) algorithm remains stable, without
sub-iterations, for light and even zero mass rigid bodies when added-mass and
viscous added-damping effects are large. The scheme is based on a generalized
Robin interface condition for the fluid pressure that includes terms involving
the linear acceleration and angular acceleration of the rigid body. Added-mass
effects are handled in the Robin condition by inclusion of a boundary integral
term that depends on the pressure. Added-damping effects due to the viscous
shear forces on the body are treated by inclusion of added-damping tensors that
are derived through a linearization of the integrals defining the force and
torque. Added-damping effects may be important at low Reynolds number, or, for
example, in the case of a rotating cylinder or rotating sphere when the
rotational moments of inertia are small. In this first part of a two-part
series, the properties of the AMP scheme are motivated and evaluated through
the development and analysis of some model problems. The analysis shows when
and why the traditional partitioned scheme becomes unstable due to either
added-mass or added-damping effects. The analysis also identifies the proper
form of the added-damping which depends on the discrete time-step and the
grid-spacing normal to the rigid body. The results of the analysis are
confirmed with numerical simulations that also demonstrate a second-order
accurate implementation of the AMP scheme.
|
1611.05711v1
|
2017-01-30
|
Torsional Alfvén resonances as an efficient damping mechanism for non-radial oscillations in red giant stars
|
Stars are self-gravitating fluids in which pressure, buoyancy, rotation and
magnetic fields provide the restoring forces for global modes of oscillation.
Pressure and buoyancy energetically dominate, while rotation and magnetism are
generally assumed to be weak perturbations and often ignored. However,
observations of anomalously weak dipole mode amplitudes in red giant stars
suggest that a substantial fraction of these are subject to an additional
source of damping localised to their core region, with indirect evidence
pointing to the role of a deeply buried magnetic field. It is also known that
in many instances the gravity-mode character of affected modes is preserved,
but so far no effective damping mechanism has been proposed that accommodates
this aspect. Here we present such a mechanism, which damps the oscillations of
stars harbouring magnetised cores via resonant interactions with standing
Alfv\'en modes of high harmonic index. The damping rates produced by this
mechanism are quantitatively on par with those associated with turbulent
convection, and in the range required to explain observations, for realistic
stellar models and magnetic field strengths. Our results suggest that magnetic
fields can provide an efficient means of damping stellar oscillations without
needing to disrupt the internal structure of the modes, and lay the groundwork
for an extension of the theory of global stellar oscillations that incorporates
these effects.
|
1701.08771v1
|
2018-03-30
|
Damping of gravitational waves in a viscous Universe and its implication for dark matter self-interactions
|
It is well known that a gravitational wave (GW) experiences the damping
effect when it propagates in a fluid with nonzero shear viscosity. In this
paper, we propose a new method to constrain the GW damping rate and thus the
fluid shear viscosity. By defining the effective distance which incorporates
damping effects, we can transform the GW strain expression in a viscous
Universe into the same form as that in a perfect fluid. Therefore, the
constraints of the luminosity distances from the observed GW events by LIGO and
Virgo can be directly applied to the effective distances in our formalism. We
exploit the lognormal likelihoods for the available GW effective distances and
a Gaussian likelihood for the luminosity distance inferred from the
electromagnetic radiation observation of the binary neutron star merger event
GW170817. Our fittings show no obvious damping effects in the current GW data,
and the upper limit on the damping rate with the combined data is $6.75 \times
10^{-4}\,{\rm Mpc}^{-1}$ at 95\% confidence level. By assuming that the dark
matter self-scatterings are efficient enough for the hydrodynamic description
to be valid, we find that a GW event from its source at a luminosity distance
$D\gtrsim 10^4\;\rm Mpc$ can be used to put a constraint on the dark matter
self-interactions.
|
1803.11397v1
|
2018-05-29
|
Basic microscopic plasma physics from N-body mechanics
|
Computing is not understanding. This is exemplified by the multiple and
discordant interpretations of Landau damping still present after seventy years.
For long deemed impossible, the mechanical N-body description of this damping,
not only enables its rigorous and simple calculation, but makes unequivocal and
intuitive its interpretation as the synchronization of almost resonant passing
particles. This synchronization justifies mechanically why a single formula
applies to both Landau growth and damping. As to the electrostatic potential,
the phase mixing of many beam modes produces Landau damping, but it is
unexpectedly essential for Landau growth too. Moreover, collisions play an
essential role in collisionless plasmas. In particular, Debye shielding results
from a cooperative dynamical self-organization process, where "collisional"
deflections due to a given electron diminish the apparent number of charges
about it. The finite value of exponentiation rates due to collisions is crucial
for the equivalent of the van Kampen phase mixing to occur in the N-body
system. The N-body approach incorporates spontaneous emission naturally, whose
compound effect with Landau damping drives a thermalization of Langmuir waves.
O'Neil's damping with trapping typical of initially large enough Langmuir waves
results from a phase transition. As to collisional transport, there is a smooth
connection between impact parameters where the two-body Rutherford picture is
correct, and those where a collective description is mandatory. The N-body
approach reveals two important features of the Vlasovian limit: it is singular
and it corresponds to a renormalized description of the actual N-body dynamics.
|
1805.11408v2
|
2018-08-22
|
Constructing a boosted, spinning black hole in the damped harmonic gauge
|
The damped harmonic gauge is important for numerical relativity computations
based on the generalized harmonic formulation of Einstein's equations, and is
used to reduce coordinate distortions near binary black hole mergers. However,
currently there is no prescription to construct quasiequilibrium binary black
hole initial data in this gauge. Instead, initial data are typically
constructed using a superposition of two boosted analytic single black hole
solutions as free data in the solution of the constraint equations. Then, a
smooth time-dependent gauge transformation is done early in the evolution to
move into the damped harmonic gauge. Using this strategy to produce initial
data in damped harmonic gauge would require the solution of a single black hole
in this gauge, which is not known analytically. In this work we construct a
single boosted, spinning, equilibrium BH in damped harmonic coordinates as a
regular time-independent coordinate transformation from Kerr-Schild
coordinates. To do this, we derive and solve a set of 4 coupled, nonlinear,
elliptic equations for this transformation, with appropriate boundary
conditions. This solution can now be used in the construction of damped
harmonic initial data for binary black holes.
|
1808.07490v3
|
2018-12-13
|
Neutrino damping in a fermion and scalar background
|
We consider the propagation of a neutrino in a background composed of a
scalar particle and a fermion using a simple model for the coupling of the form
$\lambda\bar f_R\nu_L\phi$. In the presence of these interactions there can be
damping terms in the neutrino effective potential and index of refraction. We
calculate the imaginary part of the neutrino self-energy in this case, from
which the damping terms are determined. The results are useful in the context
of Dark Matter-neutrino interaction models in which the scalar and/or fermion
constitute the dark-matter. The corresponding formulas for models in which the
scalar particle couples to two neutrinos via a coupling of the form
$\lambda^{(\nu\nu\phi)}\bar\nu^c_R\nu_L\phi$ are then obtained as a special
case, which can be important also in the context of neutrino collective
oscillations in a supernova and in the Early Universe hot plasma before
neutrino decoupling. A particular feature of our results is that the damping
term in a $\nu\phi$ background is independent of the antineutrino-neutrino
asymmetry in the background. Therefore, the relative importance of the damping
term may be more significant if the neutrino-antineutrino asymmetry in the
background is small, because the leading $Z$-exchange and $\phi$-exchange
contributions to the effective potential, which are proportional to the
neutrino-antineutrino asymmetry, are suppressed in that case, while the damping
term is not.
|
1812.05672v2
|
2019-04-25
|
High Spin-Wave Propagation Length Consistent with Low Damping in a Metallic Ferromagnet
|
We report ultra-low intrinsic magnetic damping in
Co$_{\text{25}}$Fe$_{\text{75}}$ heterostructures, reaching the low $10^{-4}$
regime at room temperature. By using a broadband ferromagnetic resonance
technique, we extracted the dynamic magnetic properties of several
Co$_{\text{25}}$Fe$_{\text{75}}$-based heterostructures with varying
ferromagnetic layer thickness. By estimating the eddy current contribution to
damping, measuring radiative damping and spin pumping effects, we found the
intrinsic damping of a 26\,nm thick sample to be $$\alpha_{\mathrm{0}} \lesssim
3.18\times10^{-4}$. Furthermore, using Brillouin light scattering microscopy we
measured spin-wave propagation lengths of up to $(21\pm1)\,\mathrm{\mu m}$ in a
26 nm thick Co$_{\text{25}}$Fe$_{\text{75}}$ heterostructure at room
temperature, which is in excellent agreement with the measured damping.
|
1904.11321v3
|
2019-11-02
|
Soft contribution to the damping rate of a hard photon in a weakly magnetized hot medium
|
We consider weakly magnetized hot QED plasma comprising electrons and
positrons. There are three distinct dispersive (longitudinal and two
transverse) modes of a photon in a thermo-magnetic medium. At lowest order in
coupling constant, photon is damped in this medium via Compton scattering and
pair creation process. We evaluate the damping rate of hard photon by
calculating the imaginary part of the each transverse dispersive modes in a
thermo-magnetic QED medium. We note that one of the fermions in the loop of
one-loop photon self-energy is considered as soft and the other one is hard.
Considering the resummed fermion propagator in a weakly magnetized medium for
the soft fermion and the Schwinger propagator for hard fermion, we calculate
the soft contribution to the damping rate of hard photon. In weak field
approximation the thermal and thermo-magnetic contributions to damping rate get
separated out for each transverse dispersive mode. The total damping rate for
each dispersive mode in presence of magnetic field is found to be reduced than
that of the thermal one. This formalism can easily be extended to QCD plasma.
|
1911.00744v2
|
2020-09-25
|
Temperature dependence of the damping parameter in the ferrimagnet Gd$_3$Fe$_5$O$_{12}$
|
The damping parameter ${\alpha}_{\text{FM}}$ in ferrimagnets defined
according to the conventional practice for ferromagnets is known to be strongly
temperature dependent and diverge at the angular momentum compensation
temperature, where the net angular momentum vanishes. However, recent
theoretical and experimental developments on ferrimagnetic metals suggest that
the damping parameter can be defined in such a way, which we denote by
${\alpha}_{\text{FiM}}$, that it is free of the diverging anomaly at the
angular momentum compensation point and is little dependent on temperature. To
further understand the temperature dependence of the damping parameter in
ferrimagnets, we analyze several data sets from literature for a ferrimagnetic
insulator, gadolinium iron garnet, by using the two different definitions of
the damping parameter. Using two methods to estimate the individual sublattice
magnetizations, which yield results consistent with each other, we found that
in all the used data sets, the damping parameter ${\alpha}_{\text{FiM}}$ does
not increase at the angular compensation temperature and shows no anomaly
whereas the conventionally defined ${\alpha}_{\text{FM}}$ is strongly dependent
on the temperature.
|
2009.12073v2
|
2020-09-25
|
A Complex Stiffness Human Impedance Model with Customizable Exoskeleton Control
|
The natural impedance, or dynamic relationship between force and motion, of a
human operator can determine the stability of exoskeletons that use
interaction-torque feedback to amplify human strength. While human impedance is
typically modelled as a linear system, our experiments on a single-joint
exoskeleton testbed involving 10 human subjects show evidence of nonlinear
behavior: a low-frequency asymptotic phase for the dynamic stiffness of the
human that is different than the expected zero, and an unexpectedly consistent
damping ratio as the stiffness and inertia vary. To explain these observations,
this paper considers a new frequency-domain model of the human joint dynamics
featuring complex value stiffness comprising a real stiffness term and a
hysteretic damping term. Using a statistical F-test we show that the hysteretic
damping term is not only significant but is even more significant than the
linear damping term. Further analysis reveals a linear trend linking hysteretic
damping and the real part of the stiffness, which allows us to simplify the
complex stiffness model down to a 1-parameter system. Then, we introduce and
demonstrate a customizable fractional-order controller that exploits this
hysteretic damping behavior to improve strength amplification bandwidth while
maintaining stability, and explore a tuning approach which ensures that this
stability property is robust to muscle co-contraction for each individual.
|
2009.12446v1
|
2020-11-26
|
On the stabilization of breather-type solutions of the damped higher order nonlinear Schrödinger equation
|
Spatially periodic breather solutions (SPBs) of the nonlinear Schr\"o\-dinger
(NLS) equation are frequently used to model rogue waves and are typically
unstable. In this paper we study the effects of dissipation and higher order
nonlinearities on the stabilization of both single and multi-mode SPBs in the
framework of a damped higher order NLS (HONLS) equation. We observe the onset
of novel instabilities associated with the development of critical states which
result from symmetry breaking in the damped HONLS system. We broaden the
Floquet characterization of instabilities of solutions of the NLS equation,
using an even 3-phase solution of the NLS as an example, to show instabilities
are associated with degenerate complex elements of both the periodic and
continuous Floquet spectrum. As a result the Floquet criteria for the
stabilization of a solution of the damped HONLS centers around the elimination
of all complex degenerate elements of the spectrum. For an initial SPB with a
given mode structure, a perturbation analysis shows that for short time only
the complex double points associated with resonant modes split under the damped
HONLS while those associated with nonresonant modes remain effectively closed.
The corresponding damped HONLS numerical experiments corroborate that
instabilities associated with nonresonant modes persist on a longer time scale
than the instabilities associated with resonant modes.
|
2011.13334v1
|
2020-12-22
|
Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators
|
The linear collisionless damping of zonal flows is calculated for
quasi-symmetric stellarator equilibria in flux-tube, flux-surface, and
full-volume geometry. Equilibria are studied from the quasi-helical symmetry
configuration of the Helically Symmetric eXperiment (HSX), a broken symmetry
configuration of HSX, and the quasi-axial symmetry geometry of the National
Compact Stellarator eXperiment (NCSX). Zonal flow oscillations and long-time
damping affect the zonal flow evolution, and the zonal flow residual goes to
zero for small radial wavenumber. The oscillation frequency and damping rate
depend on the bounce-averaged radial particle drift in accordance with theory.
While each flux tube on a flux surface is unique, several different flux tubes
in HSX or NCSX can reproduce the zonal flow damping from a flux-surface
calculation given an adequate parallel extent. The flux-surface or flux-tube
calculations can accurately reproduce the full-volume long-time residual for
moderate $k_x$, but the oscillation and damping time scales are longer in local
representations, particularly for small $k_x$ approaching the system size.
|
2012.12213v2
|
2020-12-31
|
Damping of slow surface kink modes in solar photospheric waveguides modeled by one-dimensional inhomogeneities
|
Given the recent interest in magnetohydrodynamic (MHD) waves in pores and
sunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) by
modeling solar photospheric waveguides with a cylindrical inhomogeneity
comprising a uniform interior, a uniform exterior, and a continuous transition
layer (TL) in between. Performing an eigen-mode analysis in linear, resistive,
gravity-free MHD, our approach is idealized in that, among other things, our
equilibrium is structured only in the radial direction. We can nonetheless
address two damping mechanisms simultaneously, one being the Ohmic resistivity,
and the other being the resonant absorption of SSKMs in the cusp and
Alfv$\acute{\rm e}$n continua. We find that the relative importance of the two
mechanisms depends sensitively on the magnetic Reynolds number ($R_{\rm m}$).
Resonant absorption is the sole damping mechanism for realistically large
values of $R_{\rm m}$, and the cusp resonance in general dominates the
Alfv$\acute{\rm e}$n one unless the axial wavenumbers are at the lower end of
the observationally relevant range. We also find that the thin-boundary
approximation holds only when the TL-width-to-radius ratios are much smaller
than nominally expected. The Ohmic resistivity is far more important for
realistically small $R_{\rm m}$. Even in this case, SSKMs are only marginally
damped, with damping-time-to-period-ratios reaching $\sim 10$ in the parameter
range we examine.
|
2012.15426v1
|
2021-02-24
|
Finding the mechanism of wave energy flux damping in solar pores using numerical simulations
|
Context. Solar magnetic pores are, due to their concentrated magnetic fields,
suitable guides for magnetoacoustic waves. Recent observations have shown that
propagating energy flux in pores is subject to strong damping with height;
however, the reason is still unclear. Aims. We investigate possible damping
mechanisms numerically to explain the observations. Methods. We performed 2D
numerical magnetohydrodynamic (MHD) simulations, starting from an equilibrium
model of a single pore inspired by the observed properties. Energy was inserted
into the bottom of the domain via different vertical drivers with a period of
30s. Simulations were performed with both ideal MHD and non-ideal effects.
Results. While the analysis of the energy flux for ideal and non-ideal MHD
simulations with a plane driver cannot reproduce the observed damping, the
numerically predicted damping for a localized driver closely corresponds with
the observations. The strong damping in simulations with localized driver was
caused by two geometric effects, geometric spreading due to diverging field
lines and lateral wave leakage.
|
2102.12420v1
|
2022-04-08
|
Damped Strichartz estimates and the incompressible Euler--Maxwell system
|
Euler--Maxwell systems describe the dynamics of inviscid plasmas. In this
work, we consider an incompressible two-dimensional version of such systems and
prove the existence and uniqueness of global weak solutions, uniformly with
respect to the speed of light $c\in (c_0,\infty)$, for some threshold value
$c_0>0$ depending only on the initial data. In particular, the condition
$c>c_0$ ensures that the velocity of the plasma nowhere exceeds the speed of
light and allows us to analyze the singular regime $c\to\infty$.
The functional setting for the fluid velocity lies in the framework of
Yudovich's solutions of the two-dimensional Euler equations, whereas the
analysis of the electromagnetic field hinges upon the refined interactions
between the damping and dispersive phenomena in Maxwell's equations in the
whole space. This analysis is enabled by the new development of a robust
abstract method allowing us to incorporate the damping effect into a variety of
existing estimates. The use of this method is illustrated by the derivation of
damped Strichartz estimates (including endpoint cases) for several dispersive
systems (including the wave and Schr\"odinger equations), as well as damped
maximal regularity estimates for the heat equation. The ensuing damped
Strichartz estimates supersede previously existing results on the same systems.
|
2204.04277v3
|
2022-05-11
|
A new look at the frequency-dependent damping of slow-mode waves in the solar corona
|
Being directly observed in the Doppler shift and imaging data and indirectly
as quasi-periodic pulsations in solar and stellar flares, slow magnetoacoustic
waves offer an important seismological tool for probing many vital parameters
of the coronal plasma. A recently understood active nature of the solar corona
for magnetoacoustic waves, manifested through the phenomenon of wave-induced
thermal misbalance, led to the identification of new natural mechanisms for the
interpretation of observed properties of waves. A frequency-dependent damping
of slow waves in various coronal plasma structures remains an open question, as
traditional wave damping theories fail to match observations. We demonstrate
that accounting for the back-reaction caused by thermal misbalance on the wave
dynamics leads to a modification of the relationship between the damping time
and oscillation period of standing slow waves, prescribed by the linear theory.
The modified relationship is not of a power-law form and has the equilibrium
plasma conditions and properties of the coronal heating/cooling processes as
free parameters. It is shown to readily explain the observed scaling of the
damping time with period of standing slow waves in hot coronal loops.
Functional forms of the unknown coronal heating process, consistent with the
observed frequency-dependent damping, are seismologically revealed.
|
2205.05346v1
|
2022-12-13
|
The Effect of Internal Damping on Locomotion in Frictional Environments
|
The gaits of undulating animals arise from a complex interaction of their
central nervous system, muscle, connective tissue, bone, and environment. As a
simplifying assumption, many previous studies have often assumed that
sufficient internal force is available to produce observed kinematics, thus not
focusing on quantifying the interconnection between muscle effort, body shape,
and external reaction forces. This interplay, however, is critical to
locomotion performance in crawling animals, especially when accompanied by body
viscoelasticity. Moreover, in bio-inspired robotic applications, the body's
internal damping is indeed a parameter that the designer can tune. Still, the
effect of internal damping is not well understood. This study explores how
internal damping affects the locomotion performance of a crawler with a
continuous, visco-elastic, nonlinear beam model. Crawler muscle actuation is
modeled as a traveling wave of bending moment propagating posteriorly along the
body. Consistent with the friction properties of the scales of snakes and
limbless lizards, environmental forces are modeled using anisotropic Coulomb
friction. It is found that by varying the crawler body's internal damping, the
crawler's performance can be altered, and distinct gaits could be achieved,
including changing the net locomotion direction from forward to back. We will
discuss this forward and backward control and identify the optimal internal
damping for peak crawling speed.
|
2212.06290v1
|
2023-01-19
|
Inverse Problems of Identifying the Unknown Transverse Shear Force in the Euler-Bernoulli Beam with Kelvin-Voigt Damping
|
In this paper, we study the inverse problems of determining the unknown
transverse shear force $g(t)$ in a system governed by the damped
Euler-Bernoulli equation $\rho(x)u_{tt}+\mu(x)u_t+ (r(x)u_{xx})_{xx}+
(\kappa(x)u_{xxt})_{xx}=0, ~(x,t)\in (0,\ell)\times(0,T],$ subject to the
boundary conditions $u(0,t) =0$, $u_{x}(0,t)=0$,
$\left[r(x)u_{xx}+\kappa(x)u_{xxt}\right]_{x=\ell} =0$,
$-\left[\big(r(x)u_{xx}+\kappa(x)u_{xxt}\big)_{x}\right]_{x=\ell}=g(t)$, $t\in
[0,T]$, from the measured deflection $\nu(t):=u(\ell,t)$, $t \in [0,T]$, and
from the bending moment $\omega(t):=-\left(
r(0)u_{xx}(0,t)+\kappa(0)u_{xxt}(0,t) \right)$, $t \in [0,T]$, where the terms
$(\kappa(x)u_{xxt})_{xx}$ and $\mu(x)u_t$ account for the Kelvin-Voigt damping
and external damping, respectively.
The main purpose of this study is to analyze the Kelvin-Voigt damping effect
on determining the unknown transverse shear force (boundary input) through the
given boundary measurements. The inverse problems are transformed into
minimization problems for Tikhonov functionals, and it is shown that the
regularized functionals admit unique solutions for the inverse problems. By
suitable regularity on the admissible class of shear force $g(t),$ we prove
that these functionals are Fr\'echet differentiable, and the derivatives are
expressed through the solutions of corresponding adjoint problems posed with
measured data as boundary data associated with the direct problem. The
solvability of these adjoint problems is obtained under the minimal regularity
of the boundary data $g(t)$, which turns out to be the regularizing effect of
the Kelvin-Voigt damping in the direct problem.
|
2301.07931v1
|
2023-03-28
|
Escape Kinetics of an Underdamped Colloidal Particle from a Cavity through Narrow Pores
|
It is often desirable to know the controlling mechanism of survival
probability of nano - or microscale particles in small cavities such as, e.g.,
confined submicron particles in fiber beds of high-efficiency filter media or
ions/small molecules in confined cellular structures. Here we address this
issue based on numerical study of the escape kinetics of inertial Brownian
colloidal particles from various types of cavities with single and multiple
pores. We consider both the situations of strong and weak viscous damping. Our
simulation results show that as long as the thermal length is larger than the
cavity size the mean exit time remains insensitive to the medium viscous
damping. On further increasing damping strength, a linear relation between
escape rate and damping strength emerges gradually. This result is in sharp
contrast to the energy barrier crossing dynamics where the escape rate exhibits
a turnover behavior as a function of the damping strength. Moreover, in the
ballistic regime, the exit rate is directly proportional to the pore width and
the thermal velocity. All these attributes are insensitive to the cavity as
well as the pore structures. Further, we show that the effects of pore
structure variation on the escape kinetics are conspicuously different in the
low damping regimes compared to the overdamped situation. Apart from direct
applications in biology and nanotechnology, our simulation results can
potentially be used to understand diffusion of living or artificial micro/nano
objects, such as bacteria, virus, Janus Particle etc. where memory effects play
dictating roles.
|
2303.16092v1
|
2023-06-05
|
Damping of coronal oscillations in self-consistent 3D radiative MHD simulations of the solar atmosphere
|
Oscillations are abundant in the solar corona. Coronal loop oscillations are
typically studied using highly idealised models of magnetic flux tubes. In
order to improve our understanding of coronal oscillations, it is necessary to
consider the effect of realistic magnetic field topology and density
structuring. We analyse the damping of coronal oscillations using a
self-consistent 3D radiation-MHD simulation of the solar atmosphere spanning
from the convection zone into the corona, the associated oscillation
dissipation and heating, and finally the physical processes responsible for the
damping and dissipation. The simulated corona formed in such a model does not
depend on any prior assumptions about the shape of the coronal loops. We find
that the bundle of magnetic loops shows damped transverse oscillations in
response to perturbations in two separate instances with oscillation periods of
177 s and 191 s, velocity amplitudes of 10 km/s and 16 km/s and damping times
of 176 s and 198 s, respectively. The coronal oscillations lead to the
development of velocity shear in the simulated corona resulting in the
formation of vortices seen in the velocity field caused by the Kelvin-Helmholtz
instability, contributing to the damping and dissipation of the transverse
oscillations. The oscillation parameters and evolution observed are in line
with the values typically seen in observations of coronal loop oscillations.
The dynamic evolution of the coronal loop bundle suggests the models of
monolithic and static coronal loops with constant lengths might need to be
re-evaluated by relaxing the assumption of highly idealised waveguides.
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2306.02770v1
|
2023-08-22
|
Investigating the characteristic shape and scatter of intergalactic damping wings during reionization
|
Ly$\alpha$ damping wings in the spectra of bright objects at high redshift
are a useful probe of the ionization state of the intergalactic medium during
the reionization epoch. It has recently been noted that, despite the
inhomogeneous nature of reionization, these damping wings have a characteristic
shape which is a strong function of the volume-weighted average neutral
hydrogen fraction of the intergalactic medium. We present here a closer
examination of this finding using a simulation of patchy reionization from the
Sherwood-Relics simulation suite. We show that the characteristic shape and
scatter of the damping wings are determined by the average neutral hydrogen
density along the line of sight, weighted by its contribution to the optical
depth producing the damping wing. We find that there is a redshift dependence
in the characteristic shape due to the expansion of the Universe. Finally, we
show that it is possible to differentiate between the shapes of damping wings
in galaxies and young (or faint) quasars at different points in the
reionization history at large velocity offsets from the point where the
transmission first reaches zero.
|
2308.11709v1
|
2023-10-02
|
Characterizing the Velocity-Space Signature of Electron Landau Damping
|
Plasma turbulence plays a critical role in the transport of energy from
large-scale magnetic fields and plasma flows to small scales, where the
dissipated turbulent energy ultimately leads to heating of the plasma species.
A major goal of the broader heliophysics community is to identify the physical
mechanisms responsible for the dissipation of the turbulence and to quantify
the consequent rate of plasma heating. One of the mechanisms proposed to damp
turbulent fluctuations in weakly collisional space and astrophysical plasmas is
electron Landau damping. The velocity-space signature of electron energization
by Landau damping can be identified using the recently developed field-particle
correlation technique. Here, we perform a suite of gyrokinetic turbulence
simulations with ion plasma beta values of 0.01, 0.1, 1, and 10 and use the
field-particle correlation technique to characterize the features of the
velocity-space signatures of electron Landau damping in turbulent plasma
conditions consistent with those observed in the solar wind and planetary
magnetospheres. We identify the key features of the velocity-space signatures
of electron Landau damping as a function of varying plasma \beta_i to provide a
critical framework for interpreting the results of field-particle correlation
analysis of in situ spacecraft observations of plasma turbulence.
|
2310.01242v2
|
2023-10-07
|
OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws
|
Controlling spurious oscillations is crucial for designing reliable numerical
schemes for hyperbolic conservation laws. This paper proposes a novel, robust,
and efficient oscillation-eliminating discontinuous Galerkin (OEDG) method on
general meshes, motivated by the damping technique in [Lu, Liu, and Shu, SIAM
J. Numer. Anal., 59:1299-1324, 2021]. The OEDG method incorporates an OE
procedure after each Runge-Kutta stage, devised by alternately evolving
conventional semidiscrete DG scheme and a damping equation. A novel damping
operator is carefully designed to possess scale-invariant and
evolution-invariant properties. We rigorously prove optimal error estimates of
the fully discrete OEDG method for linear scalar conservation laws. This might
be the first generic fully-discrete error estimates for nonlinear DG schemes
with automatic oscillation control mechanism. The OEDG method exhibits many
notable advantages. It effectively eliminates spurious oscillations for
challenging problems across various scales and wave speeds, without
problem-specific parameters. It obviates the need for characteristic
decomposition in hyperbolic systems. It retains key properties of conventional
DG method, such as conservation, optimal convergence rates, and
superconvergence. Moreover, it remains stable under normal CFL condition. The
OE procedure is non-intrusive, facilitating integration into existing DG codes
as an independent module. Its implementation is easy and efficient, involving
only simple multiplications of modal coefficients by scalars. The OEDG approach
provides new insights into the damping mechanism for oscillation control. It
reveals the role of damping operator as a modal filter and establishes close
relations between the damping and spectral viscosity techniques. Extensive
numerical results confirm the theoretical analysis and validate the
effectiveness and advantages of the OEDG method.
|
2310.04807v1
|
2023-12-07
|
Probing levitodynamics with multi-stochastic forces and the simple applications on the dark matter detection in optical levitation experiment
|
If the terrestrial environment is permeated by dark matter, the levitation
experiences damping forces and fluctuations attributed to dark matter. This
paper investigates levitodynamics with multiple stochastic forces, including
thermal drag, photon recoil, feedback, etc., assuming that all of these forces
adhere to the fluctuation-dissipation theorem. The ratio of total damping to
the stochastic damping coefficient distinguishes the levitodynamics from cases
involving only one single stochastic force. The heating and cooling processes
are formulated to determine the limits of temperature change. All sources of
stochastic forces are comprehensively examined, revealing that dark matter
collisions cannot be treated analogously to fluid dynamics. Additionally, a
meticulous analysis is presented, elucidating the intricate relationship
between the fundamental transfer cross-section and the macroscopic transfer
cross-section. While the dark damping coefficient is suppressed by the mass of
the levitated particle, scattering can be coherently enhanced based on the
scale of the component microscopic particle, the atomic form factor, and the
static structure factor. Hence, dark damping holds the potential to provide
valuable insights into the detection of the macroscopic strength of fundamental
particles. We propose experimental procedures for levitation and employ linear
estimation to extract the dark damping coefficient. Utilizing current
levitation results, we demonstrate that the fundamental transfer cross section
of dark matter can be of the order $\sigma^{\rm D}_{T}\lsim {\cal
O}(10^{-26})\rm cm^2$.
|
2312.04202v2
|
2024-01-23
|
Damped kink motions in a system of two solar coronal tubes with elliptic cross-sections
|
This study is motivated by observations of coordinated transverse
displacements in neighboring solar active region loops, addressing specifically
how the behavior of kink motions in straight two-tube equilibria is impacted by
tube interactions and tube cross-sectional shapes.We work with linear, ideal,
pressureless magnetohydrodynamics. Axially standing kink motions are examined
as an initial value problem for transversely structured equilibria involving
two identical, field-aligned, density-enhanced tubes with elliptic
cross-sections (elliptic tubes). Continuously nonuniform layers are implemented
around both tube boundaries. We numerically follow the system response to
external velocity drivers, largely focusing on the quasi-mode stage of internal
flows to derive the pertinent periods and damping times. The periods and
damping times we derive for two-circular-tube setups justify available modal
results found with the T-matrix approach. Regardless of cross-sectional shapes,
our nonuniform layers feature the development of small-scale shears and energy
accumulation around Alf\'ven resonances, indicative of resonant absorption and
phase-mixing. As with two-circular-tube systems, our configurational symmetries
make it still possible to classify lower-order kink motions by the polarization
and symmetric properties of the internal flows; hence such mode labels as $S_x$
and $A_x$. However, the periods and damping times for two-elliptic-tube setups
further depend on cross-sectional aspect ratios, with $A_x$ motions
occasionally damped less rapidly than $S_x$ motions. We find uncertainties up
to $\sim 20\%$ ($\sim 50\%$) for the axial Alfven time (the inhomogeneity
lengthscale) if the periods (damping times) computed for two-elliptic-tube
setups are seismologically inverted with canonical theories for isolated
circular tubes.
|
2401.12885v2
|
1995-02-08
|
The Chemical Evolution of Damped Lyman Alpha Galaxies
|
Measurements of element abundances in damped Lyman alpha systems are
providing new means to investigate the chemical evolution of galaxies,
particularly at early times. We review progress in this area, concentrating on
recent efforts to extend the range of existing surveys to both higher and lower
redshifts.
|
9502047v1
|
1996-01-19
|
The Chemical Enrichment History of Damped Lyman-alpha Galaxies
|
Studies of damped Lyman-alpha absorption systems in quasar spectra are
yielding very interesting results regarding the chemical evolution of these
galaxies. We present some preliminary results from such a program.
|
9601098v1
|
1997-01-30
|
Initial Chemical Enrichment in Galaxies
|
We present evidence that damped Lyman-alpha galaxies detected in spectra of
quasars may not have started forming stars until the redshift z~3. If damped
Lyman-alpha absorbers are the progenitors of disk galaxies, then the above
result may indicate that star formation in galactic disks first began at z~3.
|
9701241v1
|
1997-10-24
|
The N/Si Abundance Ratio in Fifteen Damped Lyman-alpha Galaxies: Implications for the Origin of Nitrogen
|
Galactic chemical evolution model calculations indicate that there should be
considerable scatter in the observed N/O ratios at a fixed metallicity (O/H)
for galaxies with very low metallicities due to the delayed release of primary
N from intermediate mass stars relative to that of O from short-lived massive
stars. Moreover, the scatter should increase progressively toward decreasing
metallicity. Such effects have not been convincingly demonstrated by
observations of H II regions in nearby metal-poor galaxies, raising doubts
about the time-delay model of primary N production. Pettini et al and Lipman et
al realized the utility of high-redshift damped Lyman-alpha galaxies for
gaining further insights into the origin of N and discussed abundances in three
damped Lyman-alpha galaxies. Since abundance measurements for O are generally
unavailable for damped Lyman-alpha galaxies, they used N/Si or N/S in place of
N/O under the reasonable assumption that the abundance ratios O/Si and O/S are
the same as solar in damped Lyman-alpha galaxies. We discuss observations of
heavy element abundances in 15 high-redshift (z>2) damped Lyman-alpha galaxies,
many of which have metallicities comparable to or lower than the lowest
metallicity galaxy known locally (I Zw 18). We find that the N/Si ratios in
damped Lyman-alpha galaxies exhibit a very large scatter (about 1 dex) at
[Si/H]~-2 and there is some indication that the scatter increases toward
decreasing metallicity. Considerations of various sources of uncertainties
suggest that they are not likely the main causes of the large scatter. These
results thus provide strong support for the time-delay model of primary N
production in intermediate mass stars if, indeed, O/Si=solar in damped
Lyman-alpha galaxies.
|
9710266v2
|
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