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2021-04-15
|
Explaining Neptune's Eccentricity
|
Early migration damped Neptune's eccentricity. Here, we assume that the
damped value was much smaller than the value observed today, and show that the
closest flyby of $\sim 0.1 \; \mathrm{M_{\odot}}$ star over $\sim 4.5
\mathrm{\; Gyr}$ in the field, at a distance of $\sim 10^3 \mathrm{\; AU}$
would explain the value of Neptune's eccentricity observed today.
|
2104.07672v3
|
2021-04-17
|
Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds
|
In this work, we investigate the problem of finite time blow up as well as
the upper bound estimates of lifespan for solutions to small-amplitude
semilinear wave equations with time dependent damping and potential, and mixed
nonlinearities $c_1 |u_t|^p+c_2 |u|^q$, posed on asymptotically Euclidean
manifolds, which is related to both the Strauss conjecture and the Glassey
conjecture.
|
2104.08497v2
|
2021-06-02
|
Convergent dynamics of optimal nonlinear damping control
|
Following Demidovich's concept and definition of convergent systems, we
analyze the optimal nonlinear damping control, recently proposed [1] for the
second-order systems. Targeting the problem of output regulation,
correspondingly tracking of $\mathcal{C}^1$-trajectories, it is shown that all
solutions of the control system are globally uniformly asymptotically stable.
The existence of the unique limit solution in the origin of the control error
and its time derivative coordinates are shown in the sense of Demidovich's
convergent dynamics. Explanative numerical examples are also provided along
with analysis.
|
2106.00962v1
|
2021-06-26
|
Role of Dissipation on the Stability of a Parametrically Driven Quantum Harmonic Oscillator
|
We study the dissipative dynamics of a single quantum harmonic oscillator
subjected to a parametric driving with in an effective Hamiltonian approach.
Using Liouville von Neumann approach, we show that the time evolution of a
parametrically driven dissipative quantum oscillator has a strong connection
with the classical damped Mathieu equation. Based on the numerical analysis of
the Monodromy matrix, we demonstrate that the dynamical instability generated
by the parametric driving are reduced by the effect of dissipation. Further, we
obtain a closed relationship between the localization of the Wigner function
and the stability of the damped Mathieu equation.
|
2106.14018v1
|
2021-07-11
|
Space-time arithmetic quasi-periodic homogenization for damped wave equations
|
This paper is concerned with space-time homogenization problems for damped
wave equations with spatially periodic oscillating elliptic coefficients and
temporally (arithmetic) quasi-periodic oscillating viscosity coefficients. Main
results consist of a homogenization theorem, qualitative properties of
homogenized matrices which appear in homogenized equations and a corrector
result for gradients of solutions. In particular, homogenized equations and
cell problems will turn out to deeply depend on the quasi-periodicity as well
as the log ratio of spatial and temporal periods of the coefficients. Even
types of equations will change depending on the log ratio and
quasi-periodicity. Proofs of the main results are based on a (very weak)
space-time two-scale convergence theory.
|
2107.04966v1
|
2021-07-29
|
Global existence for damped $σ$-evolution equations with nonlocal nonlinearity
|
In this research, we would like to study the global (in time) existence of
small data solutions to the following damped $\sigma$-evolution equations with
nonlocal (in space) nonlinearity: \begin{equation*}
\partial_{t}^{2}u+(-\Delta)^{\sigma}u+\partial_{t}u+(-\Delta)^{\sigma}\partial_{t}u=I_{\alpha}(|u|^{p}),
\ \ t>0, \ \ x\in \mathbb{R}^{n}, \end{equation*} where $\sigma\geq1$, $p>1$
and $I_{\alpha}$ is the Riesz potential of power nonlinearity $|u|^{p}$ for any
$\alpha\in (0,n)$. More precisely, by using the $(L^{m}\cap L^{2})-L^{2}$ and
$L^{2}-L^{2}$ linear estimates, where $m\in[1,2]$, we show the new influence of
the parameter $\alpha$ on the admissible ranges of the exponent $p$.
|
2107.13924v1
|
2021-08-17
|
Estimate of the attractive velocity of attractors for some dynamical systems
|
In this paper, we first prove an abstract theorem on the existence of
polynomial attractors and the concrete estimate of their attractive velocity
for infinite-dimensional dynamical systems, then apply this theorem to a class
of wave equations with nonlocal weak damping and anti-damping in case that the
nonlinear term~$f$~is of subcritical growth.
|
2108.07410v4
|
2021-08-27
|
Distributed Mirror Descent Algorithm with Bregman Damping for Nonsmooth Constrained Optimization
|
To solve distributed optimization efficiently with various constraints and
nonsmooth functions, we propose a distributed mirror descent algorithm with
embedded Bregman damping, as a generalization of conventional distributed
projection-based algorithms. In fact, our continuous-time algorithm well
inherits good capabilities of mirror descent approaches to rapidly compute
explicit solutions to the problems with some specific constraint structures.
Moreover, we rigorously prove the convergence of our algorithm, along with the
boundedness of the trajectory and the accuracy of the solution.
|
2108.12136v1
|
2021-08-27
|
Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation
|
We study the non relativistic and ultra relativistic limits in the
two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time
white noise on the torus. In order to take the limits, it is crucial to clarify
the parameter dependence in the estimates of solution. In this paper we present
two methods to confirm this parameter dependence. One is the classical, simple
energy method. Another is the method via Strichartz estimates.
|
2108.12183v4
|
2021-09-08
|
The isothermal limit for the compressible Euler equations with damping
|
We consider the isothermal Euler system with damping. We rigorously show the
convergence of Barenblatt solutions towards a limit Gaussian profile in the
isothermal limit $\gamma$ $\rightarrow$ 1, and we explicitly compute the
propagation and the behavior of Gaussian initial data. We then show the weak L
1 convergence of the density as well as the asymptotic behavior of its first
and second moments. Contents 1. Introduction 1 2. Assumptions and main results
3 3. The limit $\gamma$ $\rightarrow$ 1 of Barenblatt's solutions 6 4. Gaussian
solutions 9 5. Evolution of certain quantities 10 6. Convergence 15 7.
Conclusion 17 References 17
|
2109.03590v1
|
2021-11-01
|
Strong solution of modified 3D-Navier-stockes equations
|
In this paper we study the incompressible Navier-Stokes equations with
logarithme damping {\alpha} log(e + |u|2)|u|2u, where we used new methods, new
tools and Fourier analysis
|
2111.00859v2
|
2021-11-02
|
Blow-up of solutions to semilinear wave equations with a time-dependent strong damping
|
The paper investigates a class of a semilinear wave equation with
time-dependent damping term ($-\frac{1}{{(1+t)}^{\beta}}\Delta u_t$) and a
nonlinearity $|u|^p$. We will show the influence of the the parameter $\beta$
in the blow-up results under some hypothesis on the initial data and the
exponent $p$ by using the test function method. We also study the local
existence in time of mild solution in the energy space $H^1(\mathbb{R}^n)\times
L^2(\mathbb{R}^n)$.
|
2111.01433v1
|
2021-11-02
|
Around plane waves solutions of the Schr{ö}dinger-Langevin equation
|
We consider the logarithmic Schr{\"o}dinger equations with damping, also
called Schr{\"o}dinger-Langevin equation. On a periodic domain, this equation
possesses plane wave solutions that are explicit. We prove that these solutions
are asymptotically stable in Sobolev regularity. In the case without damping,
we prove that for almost all value of the nonlinear parameter, these solutions
are stable in high Sobolev regularity for arbitrary long times when the
solution is close to a plane wave. We also show and discuss numerical
experiments illustrating our results.
|
2111.01487v1
|
2021-11-11
|
Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping
|
We consider the Euler-Bernoulli beam equation with a local Kelvin-Voigt
dissipation type in the interval $(-1,1)$. The coefficient damping is only
effective in $(0,1)$ and is degenerating near the $0$ point with a speed at
least equal to $x^{\alpha}$ where $\alpha\in(0,5)$. We prove that the semigroup
corresponding to the system is polynomially stable and the decay rate depends
on the degeneracy speed $\alpha$.
|
2111.06431v1
|
2021-11-12
|
GCGE: A Package for Solving Large Scale Eigenvalue Problems by Parallel Block Damping Inverse Power Method
|
We propose an eigensolver and the corresponding package, GCGE, for solving
large scale eigenvalue problems. This method is the combination of damping
idea, subspace projection method and inverse power method with dynamic shifts.
To reduce the dimensions of projection subspaces, a moving mechanism is
developed when the number of desired eigenpairs is large. The numerical
methods, implementing techniques and the structure of the package are
presented. Plenty of numerical results are provided to demonstrate the
efficiency, stability and scalability of the concerned eigensolver and the
package GCGE for computing many eigenpairs of large symmetric matrices arising
from applications.
|
2111.06552v1
|
2021-11-25
|
Continuity and topological structural stability for nonautonomous random attractors
|
In this work, we study continuity and topological structural stability of
attractors for nonautonomous random differential equations obtained by small
bounded random perturbations of autonomous semilinear problems. First, we study
existence and permanence of unstable sets of hyperbolic solutions. Then, we use
this to establish lower semicontinuity of nonautonomous random attractors and
to show that the gradient structure persists under nonautonomous random
perturbations. Finally, we apply the abstract results in a stochastic
differential equation and in a damped wave equation with a perturbation on the
damping.
|
2111.13006v1
|
2021-11-30
|
Determining damping terms in fractional wave equations
|
This paper deals with the inverse problem of recovering an arbitrary number
of fractional damping terms in a wave equation. We develop several approaches
on uniqueness and reconstruction, some of them relying on Tauberian theorems on
the relation between the asymptotics of solutions in time and Laplace domain.
Also the possibility of additionally recovering space dependent coefficients or
initial data is discussed. The resulting methods for reconstructing
coefficients and fractional orders in these terms are tested numerically.
Additionally, we provide an analysis of the forward problem, a multiterm
fractional wave equation.
|
2112.00080v2
|
2021-12-20
|
Dense Coding Capacity in Correlated Noisy Channels with Weak Measurement
|
Capacity of dense coding via correlated noisy channel is greater than that in
uncorrelated noisy channel. It is shown that weak measurement and reversal
measurement can make further effort to improve quantum dense coding capacity in
correlated amplitude damping channel, but this effort is very small in
correlated phase damping channel and correlated depolarizing channel.
|
2112.10346v1
|
2021-12-22
|
Low-frequency squeezing spectrum of a laser drivenpolar quantum emitter
|
It was shown by a study of the incoherent part of the low-frequency resonance
fluorescence spectrum of the polar quantum emitter driven by semiclassical
external laser field and damped by non-squeezed vacuum reservoir that the
emitted fluorescence field is squeezed to some degree nevertheless. As was also
found, a higher degree of squeezing could, in principle, be achieved by damping
the emitter by squeezed vacuum reservoir.
|
2112.11809v1
|
2022-01-13
|
Cavity optomechanics in a fiber cavity: the role of stimulated Brillouin scattering
|
We study the role of stimulated Brillouin scattering in a fiber cavity by
numerical simulations and a simple theoretical model and find good agreement
between experiment, simulation and theory. We also investigate an
optomechanical system based on a fiber cavity in the presence on the nonlinear
Brillouin scattering. Using simulation and theory, we show that this hybrid
optomechanical system increases optomechanical damping for low mechanical
resonance frequencies in the unresolved sideband regime. Furthermore, optimal
damping occurs for blue detuning in stark contrast to standard optomechanics.
We investigate whether this hybrid optomechanical system is capable cooling a
mechanical oscillator to the quantum ground state.
|
2201.04987v1
|
2022-01-20
|
Vacuum and singularity formation for compressible Euler equations with time-dependent damping
|
In this paper, vacuum and singularity formation are considered for
compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$,
by constructing some new control functions ingeniously, we obtain the lower
bounds estimates on density for arbitrary classical solutions. Basing on these
lower estimates, we succeed in proving the singular formation theorem for all
$\lambda$, which was open in [1] for some cases.Moreover, the singularity
formation of the compressible Euler equations when $\gamma=3$ is investigated,
too.
|
2201.07957v1
|
2022-01-22
|
Absorption of charged particles in Perfectly-Matched-Layers by optimal damping of the deposited current
|
Perfectly-Matched Layers (PML) are widely used in Particle-In-Cell
simulations, in order to absorb electromagnetic waves that propagate out of the
simulation domain. However, when charged particles cross the interface between
the simulation domain and the PMLs, a number of numerical artifacts can arise.
In order to mitigate these artifacts, we introduce a new PML algorithm whereby
the current deposited by the macroparticles in the PML is damped by an
analytically-derived, optimal coefficient. The benefits of this new algorithm
is illustrated in practical simulations.
|
2201.09084v2
|
2022-03-19
|
The Equilibrium Temperature of Planets on Eccentric Orbits: Time Scales and Averages
|
From estimates of the near-surface heat capacity of planets it is shown that
the thermal time scale is larger than the orbital period in the presence of a
global ocean that is well-mixed to a depth of 100 m, or of an atmosphere with a
pressure of several tens of bars. As a consequence, the temperature
fluctuations of such planets on eccentric orbits are damped. The average
temperature should be calculated by taking the temporal mean of the irradiation
over an orbit, which increases with $1/\sqrt{1-e^2}$. This conclusion is
independent of the orbital distance and valid for Sun-like stars; the damping
is even stronger for low-mass main sequence hosts.
|
2203.11723v1
|
2022-03-31
|
Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings
|
This paper is concerned with the long-time dynamical behavior of a
piezoelectric system with magnetic effect, which has nonlinear damping terms
and external forces with a parameter. At first, we use the nonlinear semigroup
theory to prove the well-posedness of solutions. Then, we investigate the
properties of global attractors and the existence of exponential attractors.
Finally, the upper semicontinuity of global attractors has been investigated.
|
2203.16736v1
|
2022-04-08
|
Effect of Tamm surface states on hot electron generation and Landau damping in nanostructures metal-semiconductor
|
The hot electron generation in plasmonic nanoparticles is the key to
efficient plasmonic photocatalysis. In the paper, we study theoretically for
the first time the effect of Tamm states (TSs) at the interface
metal-semiconductor on hot electron generation and Landau damping (LD) in metal
nanoparticles. TSs can lead to resonant hot electron generation and to the LD
rate enhanced by several times. The resonant hot electron generation is
reinforced by the transition absorption due to the jump of the permittivity at
the metal-semiconductor interface.
|
2204.04021v1
|
2022-04-11
|
Certified Reduced Basis Method for the Damped Wave Equations on Networks
|
In this paper we present a reduced basis method which yields
structure-preservation and a tight a posteriori error bound for the simulation
of the damped wave equations on networks. The error bound is based on the
exponential decay of the energy inside the system and therefore allows for
sharp bounds without the need of regularization parameters. The fast
convergence of the reduced solution to the truth solution as well as the
tightness of the error bound are verified numerically using an academic network
as example.
|
2204.05010v1
|
2022-04-27
|
Spectrum of the wave equation with Dirac damping on a non-compact star graph
|
We consider the wave equation on non-compact star graphs, subject to a
distributional damping defined through a Robin-type vertex condition with
complex coupling. It is shown that the non-self-adjoint generator of the
evolution problem admits an abrupt change in its spectral properties for a
special coupling related to the number of graph edges. As an application, we
show that the evolution problem is highly unstable for the critical couplings.
The relationship with the Dirac equation in non-relativistic quantum mechanics
is also mentioned.
|
2204.12747v1
|
2022-04-27
|
Dependence on the thermodynamic state of self-diffusion of pseudo hard-spheres
|
Self-diffusion, $D$, in a system of particles that interact with a pseudo
hard sphere potential is analyzed. Coupling with a solvent is represented by a
Langevin thermostat, characterized by the damping time $t_d$. The hypotheses
that $D=D_0 \varphi$ is proposed, where $D_0$ is the small concentration
diffusivity and $\varphi$ is a thermodynamic function that represents the
effects of interactions as concentration is increased. Molecular dynamics
simulations show that different values of the noise intensity modify $D_0$ but
do not modify $\varphi$. This result is consistent with the assumption that
$\varphi$ is a thermodynamic function, since the thermodynamic state is not
modified by the presence of damping and noise.
|
2204.12969v1
|
2022-04-29
|
Plasmon damping rates in Coulomb-coupled two-dimensional layers in a heterostructure
|
The Coulomb excitations of charge density oscillation are calculated for a
double-layer heterostructure. Specifically, we consider two-dimensional (2D)
layers of silicene and graphene on a substrate. From the obtained surface
response function, we calculated the plasmon dispersion relations which
demonstrate the way in which the Coulomb coupling renormalizes the plasmon
frequencies. Additionally, we present a novel result for the damping rates of
the plasmons in this Coulomb coupled heterostructure and compare these results
as the separation between layers is varied.
|
2205.00053v1
|
2022-05-08
|
A regularity criterion for a 3D tropical climate model with damping
|
In this paper we deal with the 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, and we establish a regularity criterion
for this system thanks to which the local smooth solution $(u, v, \theta)$ can
actually be extended globally in time.
|
2205.03841v3
|
2022-06-04
|
Radiation backreaction in axion electrodynamics
|
Energy-momentum conservation of classical axion-electrodynamics is carefully
analyzed in the Hamiltonian formulation of the theory. The term responsible for
the energy transfer between the electromagnetic and the axion sectors is
identified. As a special application the axion-to-light Primakoff-process in
the background of a static magnetic field is worked out and the radiative
self-damping of the axion oscillations is characterized quantitatively. The
damping time turns out comparable to the age of the Universe in the preferred
axion mass range.
|
2206.02052v1
|
2022-06-07
|
Strong attractors for weakly damped quintic wave equation in bounded domains
|
In this paper, we study the longtime dynamics for the weakly damped wave
equation with quintic non-linearity in a bounded smooth domain of
$\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded
domains, we establish the existence of a strong global attractor in the phase
space $H^2(\Omega)\cap H^1_0(\Omega)\times H^1_0(\Omega)$. Moreover, the finite
fractal dimension of the attractor is also shown with the help of the
quasi-stable estimation.
|
2206.03158v1
|
2022-06-07
|
Long-time dynamics of the wave equation with nonlocal weak damping and sup-cubic nonlinearity in 3-D domains
|
In this paper, we study the long-time dynamics for the wave equation with
nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of
$\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded
domains, we first prove the global well-posedness of the Shatah-Struwe
solutions. Then we establish the existence of the global attractor for the
Shatah-Struwe solution semigroup by the method of contractive function.
Finally, we verify the existence of a polynomial attractor for this semigroup.
|
2206.03163v1
|
2022-06-10
|
Spin Pumping into Anisotropic Dirac Electrons
|
We study spin pumping into an anisotropic Dirac electron system induced by
microwave irradiation to an adjacent ferromagnetic insulator theoretically. We
formulate the Gilbert damping enhancement due to the spin current flowing into
the Dirac electron system using second-order perturbation with respect to the
interfacial exchange coupling. As an illustration, we consider the anisotropic
Dirac system realized in bismuth to show that the Gilbert damping varies
according to the magnetization direction in the ferromagnetic insulator. Our
results indicate that this setup can provide helpful information on the
anisotropy of the Dirac electron system.
|
2206.04899v1
|
2022-06-20
|
Harmonic Oscillators of Mathematical Biology: Many Faces of a Predator-Prey Model
|
We show that a number of models in virus dynamics, epidemiology and plant
biology can be presented as ``damped" versions of the Lotka-Volterra
predator-prey model, by analogy to the damped harmonic oscillator. The analogy
deepens with the use of Lyapunov functions, which allow us to characterize
their dynamics and even make some estimates.
|
2206.09561v1
|
2022-06-21
|
Phase-covariant mixtures of non-unital qubit maps
|
We analyze convex combinations of non-unital qubit maps that are
phase-covariant. In particular, we consider the behavior of maps that combine
amplitude damping, inverse amplitude damping, and pure dephasing. We show that
mixing non-unital channels can result in restoring the unitality, whereas
mixing commutative maps can lead to non-commutativity. For the convex
combinations of Markovian semigroups, we prove that classical uncertainties
cannot break quantum Markovianity. Moreover, contrary to the Pauli channel
case, the semigroup can be recovered only by mixing two other semigroups.
|
2206.10742v1
|
2022-07-01
|
Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings
|
In this paper, we investigate the stabilization of a one-dimensional Lorenz
piezoelectric (Stretching system) with partial viscous dampings. First, by
using Lorenz gauge conditions, we reformulate our system to achieve the
existence and uniqueness of the solution. Next, by using General criteria of
Arendt-Batty, we prove the strong stability in different cases. Finally, we
prove that it is sufficient to control the stretching of the center-line of the
beam in x-direction to achieve the exponential stability. Numerical results are
also presented to validate our theoretical result.
|
2207.00488v1
|
2022-07-06
|
Quantum Decomposition Algorithm For Master Equations of Stochastic Processes: The Damped Spin Case
|
We introduce a quantum decomposition algorithm (QDA) that decomposes the
problem $\frac{\partial \rho}{\partial t}=\mathcal{L}\rho=\lambda \rho$ into a
summation of eigenvalues times phase-space variables. One interesting feature
of QDA stems from its ability to simulate damped spin systems by means of pure
quantum harmonic oscillators adjusted with the eigenvalues of the original
eigenvalue problem. We test the proposed algorithm in the case of undriven
qubit with spontaneous emission and dephasing.
|
2207.02755v3
|
2022-07-25
|
Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport
|
In this paper we describe a fast algorithm for generating periodic RVEs of
polycrystalline materials. In particular, we use the damped Newton method from
semi-discrete optimal transport theory to generate 3D periodic Laguerre
tessellations (or power diagrams) with cells of given volumes. Complex,
polydisperse RVEs with up to 100,000 grains of prescribed volumes can be
created in a few minutes on a standard laptop. The damped Newton method relies
on the Hessian of the objective function, which we derive by extending recent
results in semi-discrete optimal transport theory to the periodic setting.
|
2207.12036v1
|
2022-07-27
|
Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain
|
In this paper, we consider the one-dimensional isentropic compressible Euler
equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can
be used to describe the process of compressible flows through a porous
medium.~And the model is imposed a dissipative subsonic time-periodic boundary
condition.~Our main results reveal that the time-periodic boundary can trigger
a unique subsonic time-periodic smooth solution which is stable under small
perturbations on initial data. Moreover, the time-periodic solution possesses
higher regularity and stability provided a higher regular boundary condition.
|
2207.13433v1
|
2022-09-10
|
Landau damping on the torus for the Vlasov-Poisson system with massless electrons
|
This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$
for the Vlasov-Poisson system with massless electrons (VPME). We consider
solutions with analytic or Gevrey ($\gamma > 1/3$) initial data, close to a
homogeneous equilibrium satisfying a Penrose stability condition. We show that
for such solutions, the corresponding density and force field decay
exponentially fast as time goes to infinity. This work extends the results for
Vlasov-Poisson on the torus to the case of ions and, more generally, to
arbitrary analytic nonlinear couplings.
|
2209.04676v2
|
2022-09-25
|
Polynomial mixing of a stochastic wave equation with dissipative damping
|
We study the long time statistics of a class of semi--linear wave equations
modeling the motions of a particle suspended in continuous media while being
subjected to random perturbations via an additive Gaussian noise. By comparison
with the nonlinear reaction settings, of which the solutions are known to
possess geometric ergodicity, we find that, under the impact of nonlinear
dissipative damping, the mixing rate is at least polynomial of any order. This
relies on a combination of Lyapunov conditions, the contracting property of the
Markov transition semigroup as well as the notion of $d$--small sets.
|
2209.12151v2
|
2022-09-30
|
A Lyapunov approach for the exponential stability of a damped Timoshenko beam
|
In this technical note, we consider the stability properties of a viscously
damped Timoshenko beam equation with spatially varying parameters. With the
help of the port-Hamiltonian framework, we first prove the existence of
solutions and show, by an appropriate Lyapunov function, that the system is
exponentially stable and has an explicit decay rate. The explicit exponential
bound is computed for an illustrative example of which we provide some
numerical simulations.
|
2209.15281v1
|
2022-11-01
|
Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping
|
This paper is devoted to initial-boundary value problem of an extensible beam
equation with degenerate nonlocal energy damping in
$\Omega\subset\mathbb{R}^n$: $u_{tt}-\kappa\Delta u+\Delta^2u-\gamma(\Vert
\Delta u\Vert^2+\Vert u_t\Vert^2)^q\Delta u_t+f(u)=0$. We prove the global
existence and uniqueness of weak solutions, which gives a positive answer to an
open question in [24]. Moreover, we establish the existence of a strong
attractor for the corresponding weak solution semigroup, where the ``strong"
means that the compactness and attractiveness of the attractor are in the
topology of a stronger space $\mathcal{H}_{\frac{1}{q}}$.
|
2211.00287v3
|
2022-12-01
|
The viscous damping of three dimensional spherical gas bubble inside unbounded compressible liquid
|
The present paper considers a homogeneous bubble inside an unbounded
polytropic compressible liquid with viscosity. The system is governed by the
Navier-Stokes equation with free boundary which is determined by the kinematic
and dynamic boundary conditions on the bubble-liquid interface. The global
existence of solution is proved, and the $\dot{H}^1$ asymptotic stability of
the spherical equilibrium in terms of viscous damping together with a explicit
decay rate is given in bare energy methods.
|
2212.00299v1
|
2023-02-17
|
Control of magnon-photon coupling by spin torque
|
We demonstrate the influence of damping and field-like torques in the
magnon-photon coupling process by classically integrating the generalized
Landau-Lifshitz-Gilbert equation with RLC equation in which a phase correlation
between dynamic magnetization and microwave current through combined Amp\`ere
and Faraday effects are considered. We show that the gap between two hybridized
modes can be controlled in samples with damping parameter in the order of
$10^{-3}$ by changing the direction of the dc current density $J$ if a certain
threshold is reached. Our results suggest that an experimental realization of
the proposed magnon-photon coupling control mechanism is feasible in yttrium
iron garnet/Pt hybrid structures.
|
2302.08910v1
|
2023-02-23
|
Hopf-Like Bifurcation in a Wave Equation at a Removable Singularity
|
It is shown that a one-dimensional damped wave equation with an odd time
derivative nonlinearity exhibits small amplitude bifurcating time periodic
solutions, when the bifurcation parameter is the linear damping coefficient is
positive and accumulates to zero. The upshot is that the singularity of the
linearized operator at criticality which stems from the well known small
divisor problem for the wave operator, is entirely removed without the need to
exclude parameters via Diophantine conditions, nor the use of accelerated
convergence schemes. Only the contraction mapping principle is used.
|
2302.12092v2
|
2023-03-02
|
Spin Pumping into Carbon Nanotubes
|
We theoretically study spin pumping from a ferromagnetic insulator (FI) into
a carbon nanotube (CNT). By employing the bosonization method, we formulate the
Gilbert damping induced by the FI/CNT junction, which can be measured by
ferromagnetic resonance. We show that the increase in the Gilbert damping has a
temperature dependence characteristic of a Luttinger liquid and is highly
sensitive to the Luttinger parameter of the spin sector for a clean interface.
We also discuss the experimental relevance of our findings based on numerical
estimates, using realistic parameters.
|
2303.01343v2
|
2023-03-11
|
Control estimates for 0th order pseudodifferential operators
|
We introduce the control conditions for 0th order pseudodifferential
operators $\mathbf{P}$ whose real parts satisfy the Morse--Smale dynamical
condition. We obtain microlocal control estimates under the control conditions.
As a result, we show that there are no singular profiles in the solution to the
evolution equation $(i\partial_t-\mathbf{P})u=f$ when $\mathbf{P}$ has a
damping term that satisfies the control condition and $f\in C^{\infty}$. This
is motivated by the study of a microlocal model for the damped internal waves.
|
2303.06443v2
|
2023-03-24
|
Exponential decay estimates for semilinear wave-type equations with time-dependent time delay
|
In this paper, we analyze a semilinear damped second order evolution equation
with time-dependent time delay and time-dependent delay feedback coefficient.
The nonlinear term satisfies a local Lipschitz continuity assumption. Under
appropriate conditions, we prove well-posedness and exponential stability of
our model for small initial data. Our arguments combine a Lyapunov functional
approach with some continuity arguments. Moreover, as an application of our
abstract results, the damped wave equation with a source term and delay
feedback is analyzed.
|
2303.14208v1
|
2023-03-25
|
Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory
|
This paper is concerned with the existence and regularity of global attractor
$\mathcal A$ for a Kirchhoff wave equation with strong damping and memory in
the weighted time-dependent spaces $\mathcal H$ and $\mathcal H^{1}$,
respectively. In order to obtain the existence of $\mathcal A$, we mainly use
the energy method in the priori estimations, and then verify the asymptotic
compactness of the semigroup by the method of contraction function. Finally, by
decomposing the weak solutions into two parts and some elaborate calculations,
we prove the regularity of $\mathcal A$.
|
2303.14387v1
|
2023-03-27
|
Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions
|
This paper concerns the linear Landau damping for the two species
Vlasov-Poisson system for ions and electrons near Penrose stable equilibria.
The result is an extension of the result on the one species Vlasov-Poisson
equation by Mouhout and Villani. Different from their work we do not describe
the ions as a background species but as a species which is also described by a
separate Vlasov equation. We show an exponential decay of the electric energy
for the linearised system near Penrose stable equilibria.
|
2303.14981v2
|
2023-03-28
|
Role of intersublattice exchange interaction on ultrafast longitudinal and transverse magnetization dynamics in Permalloy
|
We report about element specific measurements of ultrafast demagnetization
and magnetization precession damping in Permalloy (Py) thin films.
Magnetization dynamics induced by optical pump at $1.5$eV is probed
simultaneously at the $M_{2,3}$ edges of Ni and Fe with High order Harmonics
for moderate demagnetization rates (less than $50$%). The role of the
intersublattice exchange interaction on both longitudinal and transverse
dynamics is analyzed with a Landau Lifshitz Bloch description of
ferromagnetically coupled Fe and Ni sublattices. It is shown that the
intersublattice exchange interaction governs the dissipation during
demagnetization as well as precession damping of the magnetization vector.
|
2303.15837v1
|
2023-03-31
|
Polynomial Mixing for a Weakly Damped Stochastic Nonlinear Schrödinger Equation
|
This paper is devoted to proving the polynomial mixing for a weakly damped
stochastic nonlinear Schr\"{o}dinger equation with additive noise on a 1D
bounded domain. The noise is white in time and smooth in space. We consider
both focusing and defocusing nonlinearities, respectively, with exponents of
the nonlinearity $\sigma\in[0,2)$ and $\sigma\in[0,\infty)$ and prove the
polynomial mixing which implies the uniqueness of the invariant measure by
using a coupling method.
|
2303.18082v1
|
2023-05-07
|
Nonexistence of global weak solutions to semilinear wave equations involving time-dependent structural damping terms
|
We consider a semilinear wave equation involving a time-dependent structural
damping term of the form
$\displaystyle\frac{1}{{(1+t)}^{\beta}}(-\Delta)^{\sigma/2} u_t$. Our results
show the influence of the parameters $\beta,\sigma$ on the nonexistence of
global weak solutions under assumptions on the given system data.
|
2305.04278v1
|
2023-05-15
|
Blow-up phenomena for a class of extensible beam equations
|
In this paper, we investigate the initial boundary value problem of the
following nonlinear extensible beam equation with nonlinear damping term $$u_{t
t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta
u_t+\left|u_t\right|^{r-1} u_t=|u|^{p-1} u$$ which was considered by Yang et
al. (Advanced Nonlinear Studies 2022; 22:436-468). We consider the problem with
the nonlinear damping and establish the finite time blow-up of the solution for
the initial data at arbitrary high energy level, including the estimate lower
and upper bounds of the blowup time. The result provides some affirmative
answer to the open problems given in (Advanced Nonlinear Studies 2022;
22:436-468).
|
2305.08398v1
|
2023-06-08
|
Vanishing of long time average p-enstrophy dissipation rate in the inviscid limit of the 2D damped Navier-Stokes equations
|
In 2007, Constantin and Ramos proved a result on the vanishing long time
average enstrophy dissipation rate in the inviscid limit of the 2D damped
Navier-Stokes equations. In this work, we prove a generalization of this for
the p-enstrophy, sequences of distributions of initial data and sequences of
strongly converging right-hand sides. We simplify their approach by working
with invariant measures on the global attractors which can be characterized via
bounded complete solution trajectories. Then, working on the level of
trajectories allows us to directly employ some recent results on strong
convergence of the vorticity in the inviscid limit.
|
2306.05081v1
|
2023-06-13
|
Stability of asymptotically Hamiltonian systems with damped oscillatory and stochastic perturbations
|
A class of asymptotically autonomous systems on the plane with oscillatory
coefficients is considered. It is assumed that the limiting system is
Hamiltonian with a stable equilibrium. The effect of damped multiplicative
stochastic perturbations of white noise type on the stability of the system is
discussed. It is shown that different long-term asymptotic regimes for
solutions are admissible in the system and the stochastic stability of the
equilibrium depends on the realized regime. In particular, we show that stable
phase locking is possible in the system due to decaying stochastic
perturbations. The proposed analysis is based on a combination of the averaging
technique and the construction of stochastic Lyapunov functions.
|
2306.07694v1
|
2023-06-16
|
Algorithm MGB to solve highly nonlinear elliptic PDEs in $\tilde{O}(n)$ FLOPS
|
We introduce Algorithm MGB (Multi Grid Barrier) for solving highly nonlinear
convex Euler-Lagrange equations. This class of problems includes many highly
nonlinear partial differential equations, such as $p$-Laplacians. We prove
that, if certain regularity hypotheses are satisfied, then our algorithm
converges in $\tilde{O}(1)$ damped Newton iterations, or $\tilde{O}(n)$ FLOPS,
where the tilde indicates that we neglect some polylogarithmic terms. This the
first algorithm whose running time is proven optimal in the big-$\tilde{O}$
sense. Previous algorithms for the $p$-Laplacian required $\tilde{O}(\sqrt{n})$
damped Newton iterations or more.
|
2306.10183v1
|
2023-06-28
|
Global solutions and blow-up for the wave equation with variable coefficients: II. boundary supercritical source
|
In this paper, we consider the wave equation with variable coefficients and
boundary damping and supercritical source terms. The goal of this work is
devoted to prove the local and global existence, and classify decay rate of
energy depending on the growth near zero on the damping term. Moreover, we
prove the blow-up of the weak solution with positive initial energy as well as
nonpositive initial energy.
|
2306.15897v4
|
2023-07-24
|
On the stability of a double porous elastic system with visco-porous dampings
|
In this paper we consider a one dimensional elastic system with double
porosity structure and with frictional damping in both porous equations. We
introduce two stability numbers $\chi_{0}$ and $\chi_{1}$ and prove that the
solution of the system decays exponentially provided that $\chi_{0}=0$ and
$\chi_{1}\neq0.$ Otherwise, we prove the lack of exponential decay. Our results
improve the results of \cite{Bazarra} and \cite{Nemsi}.
|
2307.12690v1
|
2023-07-29
|
An inverse problem for the fractionally damped wave equation
|
We consider an inverse problem for a Westervelt type nonlinear wave equation
with fractional damping. This equation arises in nonlinear acoustic imaging,
and we show the forward problem is locally well-posed. We prove that the smooth
coefficient of the nonlinearity can be uniquely determined, based on the
knowledge of the source-to-solution map and a priori knowledge of the
coefficient in an arbitrarily small subset of the domain. Our approach relies
on a second order linearization as well as the unique continuation property of
the spectral fractional Laplacian.
|
2307.16065v1
|
2023-08-02
|
Blow-up and lifespan estimate for the generalized tricomi equation with the scale-invariant damping and time derivative nonlinearity on exterior domain
|
The article is devoted to investigating the initial boundary value problem
for the damped wave equation in the scale-invariant case with time-dependent
speed of propagation on the exterior domain. By presenting suitable multipliers
and applying the test-function technique, we study the blow-up and the lifespan
of the solutions to the problem with derivative-type nonlinearity
$ \d u_{tt}-t^{2m}\Delta u+\frac{\mu}{t}u_t=|u_t|^p, \quad \mbox{in}\
\Omega^{c}\times[1,\infty),$ that we associate with appropriate small initial
data.
|
2308.01272v2
|
2023-08-03
|
Gravitational Wave Heating
|
It was shown in previous work that when a gravitational wave (GW) passes
through a viscous shell of matter the magnitude of the GW will be damped and
there are astrohysical circumstances in which the damping is almost complete.
The energy transfer from the GWs to the fluid will increase its temperature. We
construct a model for this process and obtain an expression for the temperature
distribution inside the shell in terms of spherical harmonics. Further, it is
shown that this effect is astrophysically significant: a model problem is
constructed for which the temperature increase is of order $10^6{}^\circ$K.
|
2308.01615v2
|
2023-08-08
|
Stabilization of piezoelectric beam with Coleman-Gurtin or Gurtin-Pipkin thermal law and under Lorenz gauge condition
|
In this paper, we present the analysis of stability for a piezoelectric beam
subject to a thermal law (Coleman-Gurtin or Gurtin-Pipkin thermal law) adding
some viscous damping mechanism to the electric field in $x-$direction and
$z-$direction, and we discuss several cases. Then, there is no need to control
the electrical field components in $x$-direction and $z-$ direction to
establish an exponential decay of solutions when the beam is subjected to a
Coleman-Gurtin law, otherwise a polynomial stability is established with
Gurtin-Pipkin thermal law in case when the electrical field components are
damped.
|
2308.04231v2
|
2023-08-11
|
Well-posedness and global attractor for wave equation with nonlinear damping and super-cubic nonlinearity
|
In the paper, we study the semilinear wave equation involving the nonlinear
damping $g(u_t) $ and nonlinearity $f(u)$. Under the wider ranges of exponents
of $g$ and $f$, the well-posedness of the weak solution is achieved by
establishing a priori space-time estimates. Then, the existence of the global
attractor in the naturally phase space $H^1_0(\Omega)\times L^2(\Omega)$ is
obtained. Moreover, we prove that the global attrator is regular, that is, the
global attractor is a bounded subset of $(H^2(\Omega)\cap H^1_0(\Omega))\times
H^1_0(\Omega)$.
|
2308.06208v1
|
2023-08-16
|
Stability for degenerate wave equations with drift under simultaneous degenerate damping
|
In this paper we study the stability of two different problems. The first one
is a one-dimensional degenerate wave equation with degenerate damping,
incorporating a drift term and a leading operator in non-divergence form. In
the second problem we consider a system that couples degenerate and
non-degenerate wave equations, connected through transmission, and subject to a
single dissipation law at the boundary of the non-degenerate equation. In both
scenarios, we derive exponential stability results.
|
2308.08645v3
|
2023-09-02
|
Existence and nonexistence of global solutions for time-dependent damped NLS equations
|
We investigate the Cauchy problem for the nonlinear Schr\"odinger equation
with a time-dependent linear damping term. Under non standard assumptions on
the loss dissipation, we prove the blow-up in the inter-critical regime, and
the global existence in the energy subcritical case. Our results generalize and
improve the ones in [9, 11, 21].
|
2309.00849v1
|
2023-09-04
|
On the small-mass limit for stationary solutions of stochastic wave equations with state dependent friction
|
We investigate the convergence, in the small mass limit, of the stationary
solutions of a class of stochastic damped wave equations, where the friction
coefficient depends on the state and the noisy perturbation if of
multiplicative type. We show that the Smoluchowski-Kramers approximation that
has been previously shown to be true in any fixed time interval, is still valid
in the long time regime. Namely we prove that the first marginals of any
sequence of stationary solutions for the damped wave equation converge to the
unique invariant measure of the limiting stochastic quasilinear parabolic
equation. The convergence is proved with respect to the Wasserstein distance
associated with the $H^{-1}$ norm.
|
2309.01549v1
|
2023-09-09
|
Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping
|
In this paper we study the fractal dimension of global attractors for a class
of wave equations with (single-point) degenerate nonlocal damping. Both the
equation and its linearization degenerate into linear wave equations at the
degenerate point and the usual approaches to bound the dimension of the
entirety of attractors do not work directly. Instead, we develop a new process
concerning the dimension near the degenerate point individually and show the
finite dimensionality of the attractor.
|
2309.04712v2
|
2023-09-19
|
The Raman gap and collisional absorption
|
One of the long-standing puzzles observed in many laser-plasma experiments is
the gap in the Raman backscattering spectrum. This gap is characterized by the
absence of backscattered light between some critical wavelength and twice the
incident laser wavelength. The latter is associated with the absolute Raman
instability from the quarter-critical density surface. Supported by
particle-in-cell (PIC) simulations, it is suggested that the gap can result
from the collisional damping of the backscattered light. A linear analysis of
the competition between the Raman growth rate and the damping rate in a
non-homogenous plasma predicts the gap's existence and width as a function of
the system's parameters. The theory is compared with the PIC simulations and
past experiments.
|
2309.10366v1
|
2023-09-21
|
Inverse problems for a quasilinear strongly damped wave equation arising in nonlinear acoustics
|
We consider inverse problems for a Westervelt equation with a strong damping
and a time-dependent potential $q$. We first prove that all boundary
measurements, including the initial data, final data, and the lateral boundary
measurements, uniquely determine $q$ and the nonlinear coefficient $\beta$. The
proof is based on complex geometric optics construction and the approach
proposed by Isakov. Further, by considering fundamental solutions supported in
a half-space constructed by H\"ormander, we prove that with vanishing initial
conditions the Dirichlet-to-Neumann map determines $q$ and $\beta$.
|
2309.11775v1
|
2023-09-28
|
On inverse problems for a strongly damped wave equation on compact manifolds
|
We consider a strongly damped wave equation on compact manifolds, both with
and without boundaries, and formulate the corresponding inverse problems. For
closed manifolds, we prove that the metric can be uniquely determined, up to an
isometry, from the knowledge of the source-to-solution map. Similarly, for
manifolds with boundaries, we prove that the metric can be uniquely determined,
up to an isometry, from partial knowledge of the Dirichlet-to-Neumann map. The
key point is to retrieve the spectral information of the Laplace-Beltrami
operator, from the Laplace transform of the measurements. Further we show that
the metric can be determined up to an isometry, using a single measurement in
both scenarios.
|
2309.16182v1
|
2023-10-10
|
Emerging Spin-Orbit Torques in Low Dimensional Dirac Materials
|
We report a theoretical description of novel spin-orbit torque components
emerging in two-dimensional Dirac materials with broken inversion symmetry. In
contrast to usual metallic interfaces where field-like and damping-like torque
components are competing, we find that an intrinsic damping-like torque which
derives from all Fermi-sea electrons can be simultaneously enhanced along with
the field-like component. Additionally, hitherto overlooked torque components
unique to Dirac materials, emerge from the coupling between spin and pseudospin
degrees of freedom. These torques are found to be resilient to disorder and
could enhance the magnetic switching performance of nearby magnets.
|
2310.06447v1
|
2023-10-26
|
Efficient Numerical Algorithm for Large-Scale Damped Natural Gradient Descent
|
We propose a new algorithm for efficiently solving the damped Fisher matrix
in large-scale scenarios where the number of parameters significantly exceeds
the number of available samples. This problem is fundamental for natural
gradient descent and stochastic reconfiguration. Our algorithm is based on
Cholesky decomposition and is generally applicable. Benchmark results show that
the algorithm is significantly faster than existing methods.
|
2310.17556v1
|
2023-11-09
|
Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings
|
We study the global well-posedness and asymptotic behavior for a semilinear
damped wave equation with Neumann boundary conditions, modelling a
one-dimensional linearly elastic body interacting with a rigid substrate
through an adhesive material. The key feature of of the problem is that the
interplay between the nonlinear force and the boundary conditions allows for a
continuous set of equilibrium points. We prove an exponential rate of
convergence for the solution towards a (uniquely determined) equilibrium point.
|
2311.05295v1
|
2023-11-29
|
On the exponential stability of uniformly damped wave equations
|
We study damped wave propagation problems phrased as abstract evolution
equations in Hilbert spaces. Under some general assumptions, including a
natural compatibility condition for initial values, we establish exponential
decay estimates for all mild solutions using the language and tools of Hilbert
complexes. This framework turns out strong enough to conduct our analysis but
also general enough to include a number of interesting examples. Some of these
are briefly discussed. By a slight modification of the main arguments, we also
obtain corresponding decay results for numerical approximations obtained by
compatible discretization strategies.
|
2311.18084v1
|
2023-12-01
|
Semilinear wave inequalities with double damping and potential terms on Riemannian Manifolds
|
We study a semilinear wave inequality with double damping on a complete
noncompact Riemannian manifold. The considered problem involves a potential
function $V$ depending on the space variable in front of the power nonlinearity
and an inhomogeneous term $W$ depending on both time and space variables.
Namely, we establish sufficient conditions for the nonexistence of weak
solutions in both cases: $W\equiv 0$ and $W\not\equiv 0$. The obtained
conditions depend on the parameters of the problem as well as the geometry of
the manifold. Some special cases of manifolds, and of $V$ and $W$ are discussed
in detail.
|
2312.00617v1
|
2023-12-29
|
On damping a control system of arbitrary order with global aftereffect on a tree
|
We study a problem of damping a control system described by
functional-differential equations of natural order $n$ and neutral type with
non-smooth complex coefficients on an arbitrary tree with global delay. The
latter means that the delay propagates through internal vertices of the tree.
Minimization of the energy functional of the system leads to a variational
problem. We establish its equivalence to a certain self-adjoint boundary value
problem on the tree for equations of order $2n$ with nonlocal quasi-derivatives
and multidirectional shifts of the argument, as well as Kirchhoff-type
conditions emerging at the internal vertices. The unique solvability of both
problems is proved.
|
2312.17592v1
|
2024-01-11
|
Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system
|
We investigate the impact of weak collisions on Landau damping in the
Vlasov-Poisson-Fokker-Planck system on a torus, specifically focusing on its
proximity to a Maxwellian distribution. In the case where the Gevrey index
satisfies $\frac{1}{s}<3$, we establish the global stability and enhanced
dissipation of small initial data, which remain unaffected by the small
diffusion coefficient $\nu$. For Gevrey index $\frac{1}{s}\ge3$, we prove the
global stability and enhanced dissipation of initial data, whose size is on the
order of $O(\nu^a)$ for any $a>\frac{1-3s}{3-3s}$. Our analysis provides
insights into the effects of phase mixing, enhanced dissipation, and plasma
echoes.
|
2401.05601v3
|
2024-01-23
|
Revisit on global existence of solutions for semilinear damped wave equations in $\mathbb{R}^N$ with noncompactly supported initial data
|
In this note, we study the Cauchy problem of the semilinear damped wave
equation and our aim is the small data global existence for noncompactly
supported initial data. For this problem, Ikehata and Tanizawa [5] introduced
the energy method with the exponential-type weight function $e^{|x|^2/(1+t)}$,
which is the so-called Ikehata--Todorova--Yordanov type weight. In this note,
we suggest another weight function of the form $(1+|x|^2/(1+t))^{\lambda}$,
which allows us to treat polynomially decaying initial data and give a simpler
proof than the previous studies treating such initial data.
|
2401.12530v1
|
2024-01-24
|
Eigenmode analysis of the damped Jaynes-Cummings model
|
The generating functions for density matrix elements of the Jaynes-Cummings
model with cavity damping are analysed in terms of their eigenmodes, which are
characterised by a specific temporal behaviour. These eigenmodes are shown to
be proportional to particular generalised hypergeometric functions. The
relative weights of these eigenmodes in the generating functions are determined
by the initial conditions of the model. These weights are found by deriving
orthogonality relations involving adjoint modes. In an example it is shown how
the time-dependent density matrix elements and the related factorial moments
can be extracted from the eigenmode decompositions of the generating functions.
|
2401.13348v1
|
2024-02-15
|
A comprehensive modelling and experimental approach for damped oscillations in U-tubes via Easy JavaScript Simulations
|
In recent years, science simulations have become popular among educators due
to their educational usefulness, availability, and potential for increasing the
students' knowledge on scientific topics. In this paper, we introduce the
implementation of a user-friendly simulation based on Easy Java/JavaScript
Simulations (EJS) to study the problem of damped oscillations in U-tubes.
Furthermore, we illustrate various advantages associated with the capabilities
of EJS in terms of design and usability in order to encourage teachers to use
it as an educational supplement to physics laboratories.
|
2402.09866v1
|
2024-02-21
|
Hybrid Multi-Directional Quantum Communication Protocol
|
The way a new type of state called a hybrid state, which contains more than
one degree of freedom, is used in many practical applications of quantum
communication tasks with lesser amount of resources. Similarly, our aim is here
to perform multi-quantum communication tasks in a protocol to approach quantum
information in multipurpose and multi-directional. We propose a hybrid
multi-directional six-party scheme of implementing quantum teleportation and
joint remote state preparation under the supervision of a controller via a
multi-qubit entangled state as a quantum channel with 100% success probability.
Moreover, we analytically derive the average fidelities of this hybrid scheme
under the amplitude-damping and the phase-damping noise.
|
2402.14043v1
|
2024-03-19
|
Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions
|
We derive a posteriori error estimates for the the scalar wave equation
discretized in space by continuous finite elements and in time by the explicit
leapfrog scheme. Our analysis combines the idea of invoking extra
time-regularity for the right-hand side, as previously introduced in the space
semi-discrete setting, with a novel, piecewise quartic, globally
twice-differentiable time-reconstruction of the fully discrete solution. Our
main results show that the proposed estimator is reliable and efficient in a
damped energy norm. These properties are illustrated in a series of numerical
examples.
|
2403.12954v1
|
2009-02-10
|
A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants
|
A recurrence relation for the Li/Keiper constants in terms of the Stieltjes
constants is derived in this paper. In addition, we also report a formula for
the Stieltjes constants in terms of the higher derivatives of the Riemann zeta
function. A formula for the Stieltjes constants in terms of the (exponential)
complete Bell polynomials containing the eta constants as the arguments is also
derived.
|
0902.1691v1
|
2020-04-04
|
Generalized Von Neumann-Jordan Constant for Morrey Spaces and Small Morrey Spaces
|
In this paper we calculate some geometric constants for Morrey spaces and
small Morrey spaces, namely generalized Von Neumann-Jordan constant, modified
Von Neumann-Jordan constants, and Zb\'{a}ganu constant. All these constants
measure the uniformly nonsquareness of the spaces. We obtain that their values
are the same as the value of Von Neumann-Jordan constant for Morrey spaces and
small Morrey spaces.
|
2004.01895v1
|
1995-02-09
|
A linear thermohaline oscillator driven by stochastic atmospheric forcing
|
The interdecadal variability of a stochastically forced four-box model of the
oceanic meridional thermohaline circulation (THC) is described and compared to
the THC variability in the coupled ocean-atmosphere GCM of Delworth, Manabe,
and Stouffer (1993). The box model is placed in a linearly stable thermally
dominant mean state under mixed boundary conditions. A linear stability
analysis of this state reveals one damped oscillatory THC mode in addition to
purely damped modes. The variability of the model under a moderate amount of
stochastic forcing, meant to emulate the random variability of the atmosphere
affecting the coupled model's interdecadal THC variability, is studied. A
linear interpretation, in which the damped oscillatory mode is of primary
importance, is sufficient for understanding the mechanism accounting for the
stochastically forced variability. Direct comparison of the variability in the
box model and coupled GCM reveals common qualitative aspects. Such a comparison
supports, although does not verify, the hypothesis that the coupled model's THC
variability can be interpreted as the result of atmospheric weather exciting a
linear damped oscillatory THC mode.
|
9502002v2
|
1993-09-30
|
The metal systems in Q0000--2619 at high resolution
|
We have obtained high, 11 and 14 \kms, and medium, 40 and 53 \kms, resolution
spectra of the $z_{em} = 4.11$ quasar Q0000--2619 covering the range 4400 \AA\
to 9265 \AA . We identify nine metal absorption systems, of which four were
previously known. A fifth previously suggested system at $z_{abs} \approx
3.409$ (Turnshek et al~ 1991) is ruled out by our data. Two of the eight
systems for which the \lya~ line is in the observable range have a damped \lya~
line. Six of the nine systems show evidence for complex sub--component
structure. At our resolution and S/N we identify a total of 21 sub--components
in the nine systems. Five of the nine systems (11 of the 21 components) fall
within the $\pm 5000$ \kms~ range of the emission redshift, and are hence
classified as \zae~ absorbers. For the two damped systems we find metal
abundances of $\leq 1$% and $\leq 8$% of solar values at redshifts of 3.0541
and 3.3901 respectively. These upper limits are consistent with what would be
expected from previous determinations at lower redshifts, and our data are
hence compatible with earlier conclusions that no evidence is yet found for
chemical evolution of intervening damped and Lyman limit absorbers. For the
\zae~ systems we found indications of metallicities comparable to, and even in
excess of solar values. These much higher values compared to the damped
systems, are in favour of the intrinsic hypothesis for these systems.
|
9309053v1
|
1994-12-27
|
The z=0.8596 Damped Lyman Alpha Absorbing Galaxy Toward PKS 0454+039
|
We present {\it Hubble Space Telescope} and ground--based data on the
$z_{abs}=0.8596$ metal line absorption system along the line of sight to PKS
0454+0356. The system is a moderate redshift damped Lyman alpha system, with
${\rm N(HI)}=(5.7\pm0.3)\times10^{20}$~cm$^{-2}$ as measured from the {\it
Faint Object Spectrograph} spectrum. We also present ground--based images which
we use to identify the galaxy which most probably gives rise to the damped
system; the most likely candidate is relatively underluminous by QSO absorber
standards ($M_B \sim -19.0$ for $q_0=0.5$ and $H_0=50$ \kms Mpc$^{-1}$), and
lies $\sim 8.5h^{-1}$ kpc in projection from the QSO sightline. Ground--based
measurements of Zn~II, Cr~II, and Fe~II absorption lines from this system allow
us to infer abundances of [Zn/H]=$-1.1$, [Cr/H]=$-1.2$, and [Fe/H]=$-1.2$,
indicating overall metallicity similar to damped systems at $z >2$, and that
the depletion of Cr and Fe onto dust grains may be even {\it less} important
than in many of the high redshift systems of comparable metallicity. Limits
previously placed on the 21-cm optical depth in the $z=0.8596$ system, together
with our new N(H~I) measurement, suggest a very high spin temperature for the
H~I, $T_S >> 580$ K.
|
9412093v2
|
1996-08-22
|
APM z>4 QSO Survey: Distribution and Evolution of High Column Density HI Absorbers
|
Eleven candidate damped Lya absorption systems were identified in 27 spectra
of the quasars from the APM z>4 survey covering the redshift range
2.8<z(abs)<4.4 (8 with z(abs)>3.5). High resolution echelle spectra (0.8A FWHM)
have been obtained for three quasars, including 2 of the highest redshift
objects in the survey. Two damped systems have confirmed HI column densities of
N(HI) >= 10^20.3 atoms cm^-2, with a third falling just below this threshold.
We have discovered the highest redshift damped Lya absorber known at z=4.383 in
QSO BR1202-0725. The APM QSOs provide a substantial increase in the redshift
path available for damped surveys for z>3. We combine this high redshift sample
with other quasar samples covering the redshift range 0.008 < z < 4.7 to study
the redshift evolution and the column density distribution function for
absorbers with log N(HI)>=17.2. In the HI column density distribution
f(N)=kN^-beta we find evidence for breaks in the power law, flattening for
17.2< log N(HI)<21 and steepening for log N(HI)>21.2. The column density
distribution function for the data with log N(HI)>=20.3 is better fit with the
form f(N)=(f*/N*)(N/N*)^-beta exp(-N/N*). Significant redshift evolution in the
number density per unit redshift is evident in the higher column density
systems with an apparent decline in N(z) for z>3.5.
|
9608146v1
|
1997-05-16
|
Testing Cosmological Models Against the Abundance of Damped Lyman-Alpha Absorbers
|
We calculate the number of damped Lyman-alpha absorbers expected in various
popular cosmological models as a function of redshift and compare our
predictions with observed abundances. The Press-Schechter formalism is used to
obtain the distribution of halos with circular velocity in different
cosmologies, and we calibrate the relation between circular velocity and
absorption cross-section using detailed gas dynamical simulations of a
``standard'' cold dark matter (CDM) model. Because of this calibration, our
approach makes more realistic assumptions about the absorption properties of
collapsed objects than previous, analytic calculations of the damped
Lyman-alpha abundance. CDM models with Omega_0=1, H_0=50, baryon density
Omega_b=0.05, and scale-invariant primeval fluctuations reproduce the observed
incidence and redshift evolution of damped Lyman-alpha absorption to within
observational uncertainty, for both COBE normalization (sigma_8=1.2) and a
lower normalization (sigma_8=0.7) that better matches the observed cluster
abundance at z=0. A tilted (n=0.8, sigma_8=0.7) CDM model tends to underproduce
absorption, especially at z=4. With COBE normalization, a CDM model with
Omega_0=0.4, Omega_{Lambda}=0.6 gives an acceptable fit to the observed
absorption; an open CDM model is marginally acceptable if Omega_0 is at least
0.4 and strongly inconsistent with the z=4 data if Omega_0=0.3. Mixed dark
matter models tend not to produce sufficient absorption, being roughly
comparable to tilted CDM models if Omega_{nu} = 0.2 and failing drastically if
Omega_{nu} = 0.3.
|
9705118v1
|
1997-05-28
|
Zinc and Chromium Abundances in a Third Damped Lyman alpha System at Intermediate Redshift
|
We have determined the metallicity of the $z_{abs} = 1.0093$ damped Lyman
alpha system in the bright QSO EX 0302-223; this is only the third such
measurement at redshifts $z \simlt 1$. Unlike the previous two cases, we find
that the abundance of Zn is only a factor of $\sim 2$ lower than in the
Galactic interstellar medium today and is entirely compatible with the typical
metallicity of stars in the Milky Way disk at a look-back time of 9.5 Gyrs.
Although the galaxy responsible for producing the absorption system has yet to
be positively identified, our observations show that galaxies on a chemical
evolution path similar to that of the Milky Way do contribute to the damped
Lyman alpha population at intermediate redshifts. Cr is 2.5 times less abundant
than Zn, presumably because of depletion onto dust; however, the degree of
depletion is less severe than in diffuse interstellar clouds in the disk of our
Galaxy and in the Magellanic Clouds. Evidently, the interstellar environment in
damped Lyman alpha galaxies is less conducive to the formation and survival of
dust grains (and molecular hydrogen), but the physical processes at the root of
this effect have yet to be clarified.
|
9705222v1
|
1998-11-18
|
The Closest Damped Lyman Alpha System
|
A difficulty of studying damped Lyman alpha systems is that they are distant,
so one knows little about the interstellar medium of the galaxy. Here we report
upon a damped Lyman alpha system in the nearby galaxy NGC 4203, which is so
close (v_helio = 1117 km/s) and bright (B_o = 11.62) that its HI disk has been
mapped. The absorption lines are detected against Ton 1480, which lies only
1.9' (12 h_50 kpc) from the center of NGC 4203. Observations were obtained with
the Faint Object Spectrograph on HST (G270H grating) over the 2222-3277
Angstrom region with 200 km/s resolution. Low ionization lines of Fe, Mn, and
Mg were detected, leading to metallicities of -2.29, < -0.68, and > -2.4, which
are typical of other damped Lyman alpha systems, but well below the stellar
metallicity of this type of galaxy. Most notably, the velocity of the lines is
1160 +- 10 km/s, which is identical to the HI rotational velocity of 1170 km/s
at that location in NGC 4203, supporting the view that these absorption line
systems can be associated with the rotating disks of galaxies. In addition, the
line widths of the Mg lines give an upper limit to the velocity dispersion of
167 km/s, to the 99% confidence level.
|
9811274v1
|
1999-07-29
|
Ionized Gas in Damped Lyman-alpha Systems and Its Effects on Elemental Abundance Studies
|
Recent high-resolution observations of metal absorption lines in
high-redshift damped Ly-alpha systems have shown that Al III, a tracer of
moderately-ionized gas, very often has a velocity structure indistinguishable
from that of low-ionization gas. Regions of ionized and neutral hydrogen in
these systems are likely cospatial. The higher-ionization Si IV and C IV
absorption shows a much weaker or non-existent correlation with the low
ionization material, implying that the regions traced by Al III are
photoionized by a soft (stellar) spectrum, by a hard (power law) spectrum with
a very low ionization parameter, or a combination of both. We discuss the
ionization of the damped Ly-alpha systems and use photoionization equilibrium
models to make quantitative estimates of its effects on abundance studies in
these systems. We show that ionization effects may be large enough to account
for the observed dispersion in absolute metal abundances in damped Ly-alpha
systems, causing systematically higher abundances in lower column density
systems. The observed Si^+/Fe^+ and Zn^+/Cr^+ ratios may systematically
overestimate the intrinsic Si/Fe and Zn/Cr ratios, respectively, if ionized gas
is present in these systems, thereby mimicking the effects of alpha-element
enrichment or dust depletion.
|
9907428v1
|
1999-11-09
|
Detection of Warm and Cold Phases of the Neutral ISM in a Damped Ly-alpha Absorber
|
We present a detailed study of the HI 21cm absorption system at z=0.0912
towards the radio quasar B0738+313. The uncommonly narrow main absorption line
and weak secondary line are resolved for the first time. In addition we find it
necessary to add a third, broader shallow component to obtain a good fit to the
spectrum. Although the harmonic mean spin temperature calculated by comparison
of the 21cm lines to the damped Ly-alpha line is T_s = 775 K, the thermal
kinetic temperatures of the two narrow components, calculated from their
widths, are much lower: T_k \leq 297 and \leq 103 K respectively. This is the
first case of a redshifted absorption system for which T_k is measured to be
less than T_s. We discuss this result in the context of a two phase gas model,
in which the damped Ly-alpha gas is sensitive to a significant neutral column
density of warm phase gas as well as the cold phase gas of the narrow 21cm
lines. The third component is interpreted as representing the warm phase gas
with with T_k \leq 5050 K. The combined column density of the three 21cm
components is approximately equal to that derived from fits to the damped
Ly-alpha line.
|
9911142v1
|
2001-03-23
|
First Investigation of the Clustering Environment of Damped Lyman Alpha Absorbers at z=4
|
We report the first observations of the clustering environment of damped
Lyman alpha absorption systems at z=4. Color selection and photometric
redshifts were used to select 44 candidate Lyman-break galaxies brighter than
I_AB=25.5 from deep BRI images of the 35 sq. arcmin field containing the quasar
BR 0951-04. Multislit spectroscopy of 35 candidate galaxies was performed and 8
of these candidates have been confirmed as z>3.5 Lyman-break galaxies. With
only BRI photometry, the photometric redshifts are quite accurate for the
spectroscopically confirmed galaxies but have a high rate of misclassification
due to color degeneracies between Lyman-break galaxies and low-redshift
ellipticals. Both of the z>3.5 galaxies found within 15'' of the quasar
line-of-sight appear to be causing absorption systems in the quasar spectrum.
We use a battery of statistical tests to look for clustering in the redshift
histogram of the z>3.5 galaxies but do not find measurable clustering of these
Lyman-break galaxies with the damped Lyman alpha absorbers. With a larger
sample of galaxies, our method should determine the cross-correlation between
these objects, which probes the bias and hence the mass of the damped Lyman
alpha absorbers.
|
0103387v2
|
2002-11-11
|
Damped Lyman alpha systems and galaxy formation models - II. High ions and Lyman limit systems
|
We investigate a model for the high-ionization state gas associated with
observed damped Lyman-alpha systems, based on a semi-analytic model of galaxy
formation set within the paradigm of hierarchical structure formation. In our
model, the hot gas in halos and sub-halos gives rise to CIV absorption, while
the low-ionization state gas is associated with the cold gas in galaxies. The
model matches the distribution of CIV column densities and leads naturally to
kinematic properties that are in good agreement with the data.
We examine the contribution of both hot and cold gas to sub-damped systems
and suggest that the properties of these systems can be used as an important
test of the model. We expect that sub-DLA systems will generally be composed of
a single gas disk and thus predict that they should have markedly different
kinematics than the damped systems.
Finally, we find that hot halo gas produces less than one third of Lyman
limit systems at redshift three. We model the contribution of mini-halos (halos
with virial velocities < 35 km/s) to Lyman limit systems and find that they may
contain as much gas as is observed in these systems. However, if we adopt
realistic models of the gas density distribution we find that these systems are
not a significant source of Lyman limit absorption. Instead we suggest that
uncollapsed gas outside of virialized halos is responsible for most of the
Lyman limit systems at high redshift.
|
0211231v1
|
2003-05-16
|
The Age-Metallicity Relation of the Universe in Neutral Gas: The First 100 Damped Lya Systems
|
We present accurate metallicity measurements for 121 damped Lya systems at
0.5<z<5 including ~50 new measurements from our recently published Echellette
Spectrograph and Imager surveys. This dataset is analysed to determine the
age-metallicity relation of neutral gas in the universe. Contrary to previous
datasets this sample shows statistically significant evolution in the mean
metallicity. The best linear fit rate to metallicity vs. redshift is -0.26 +/-
0.07 dex corresponding to approximately a factor of 2 every Gyr at z=3. The DLA
continue to maintain a floor in metallicity of ~1/700 solar independent of
observational effects. This metallicity threshold limits the prevalence of
primordial gas in high redshift galaxies and stresses the correspondence
between damped systems and star formation (i.e. galaxy formation). This floor
is significantly offset from the metallicity of the Lya forest and therefore we
consider it to be more related to active star formation within these galaxies
than scenarios of enrichment in the very early universe. Finally, we comment on
an apparent 'missing metals problem': the mean metallicity of the damped
systems is ~10x lower than the value expected from their observed star
formation history. This problem is evident in current theoretical treatments of
chemical evolution and galaxy formation; it may indicate a serious flaw in our
understanding of the interplay between star formation and metal production.
|
0305314v1
|
2003-09-24
|
WIMP matter power spectra and small scale power generation
|
Dark Matter (DM) is generally assumed to be massive, cold and collisionless
from the structure formation point of view. A more correct statement however is
that DM indeed experiences collisional damping, but on a scale which is
supposed to be too small to be relevant for structure formation. The aim of
this paper is to present a Cold (although ``collisional'') Dark Matter particle
whose matter power spectrum is damped and see whether it is distinguishable
from standard candidates. To achieve this purpose, we calculate the collisional
damping and free-streaming scales of neutralinos and non conventional
candidates (say light particles heavier than ~1 MeV but lighter than O(10)
GeV). The latter can be considered as Cold Dark Matter (CDM) particles in the
sense that they become non relativistic before their thermal decoupling epoch.
Unlike neutralinos, however, their linear matter power spectrum can be damped
on scales of ~ 10^3 Msol due to their interactions. Since these scales are of
cosmological interest for structure formation, we perform a series of numerical
simulations to obtain the corresponding non linear matter power spectra
P(k)_{nl} at the present epoch. We show that because of small scale
regeneration, they all resemble each other at low redshifts, i.e. become very
similar to a typical CDM matter power spectrum on all but the smallest scales.
Therefore, even if lensing measurements at redshift below unity were to yield a
P(k)_{nl} consistent with CDM models, this would not constitute a sufficiently
robust evidence in favour of the neutralino to rule out alternative DM
candidates.
|
0309652v1
|
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