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2019-05-08
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Attractors for semilinear wave equations with localized damping and external forces
|
This paper is concerned with long-time dynamics of semilinear wave equations
defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and
locally distributed damping. The existence of regular finite-dimensional global
attractors established by Chueshov, Lasiecka and Toundykov (2008) reflects a
good deal of the current state of the art on this matter. Our contribution is
threefold. First, we prove uniform boundedness of attractors with respect to a
forcing parameter. Then, we study the continuity of attractors with respect to
the parameter in a residual dense set. Finally, we show the existence of
generalized exponential attractors. These aspects were not previously
considered for wave equations with localized damping.
|
1905.03285v1
|
2019-05-16
|
Global attractors and their upper semicontinuity for a structural damped wave equation with supercritical nonlinearity on $\mathbb{R}^{N}$
|
The paper investigates the existence of global attractors and their upper
semicontinuity for a structural damped wave equation on $\mathbb{R}^{N}:
u_{tt}-\Delta u+(-\Delta)^\alpha u_{t}+u_{t}+u+g(u)=f(x)$, where $\alpha\in
(1/2, 1)$ is called a dissipative index. We propose a new method based on the
harmonic analysis technique and the commutator estimate to exploit the
dissipative effect of the structural damping $(-\Delta)^\alpha u_{t}$ and to
overcome the essential difficulty: "both the unbounded domain $\mathbb{R}^N$
and the supercritical nonlinearity cause that the Sobolev embedding loses its
compactness"; Meanwhile we show that there exists a supercritical index
$p_\alpha\equiv\frac{N+4\alpha}{N-4\alpha}$ depending on $\alpha$ such that
when the growth exponent $p$ of the nonlinearity $g(u)$ is up to the
supercritical range: $1\leqslant p<p_\alpha$: (i) the IVP of the equation is
well-posed and its solution is of additionally global smoothness when $t>0$;
(ii) the related solution semigroup possesses a global attractor
$\mathcal{A}_\alpha$ in natural energy space for each $\alpha\in (1/2, 1)$;
(iii) the family of global attractors $\{\mathcal{A}_\alpha\}_{\alpha\in (1/2,
1) }$ is upper semicontinuous at each point $\alpha_0\in (1/2, 1)$.
|
1905.06778v1
|
2019-05-24
|
Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results
|
There are numerous examples of natural and artificial processes that
represent stochastic sequences of events followed by an absolute refractory
period during which the occurrence of a subsequent event is impossible. In the
simplest case of a generalized Bernoulli scheme for uniform random events
followed by the absolute refractory period, the event probability as a function
of time can exhibit damped transient oscillations. Using stochastically-spiking
point neuron as a model example, we present an exact and compact analytical
description for the oscillations without invoking the standard renewal theory.
The resulting formulas stand out for their relative simplicity, allowing one to
analytically obtain the amplitude damping of the 2nd and 3rd peaks of the event
probability.
|
1905.10172v3
|
2019-06-10
|
Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosity
|
We study the compressible quantum Navier-Stokes (QNS) equations with
degenerate viscosity in the three dimensional periodic domains. On the one
hand, we consider QNS with additional damping terms. Motivated by the recent
works [Li-Xin, arXiv:1504.06826] and [Antonelli-Spirito, Arch. Ration. Mech.
Anal., 203(2012), 499--527], we construct a suitable approximate system which
has smooth solutions satisfying the energy inequality and the BD entropy
estimate. Using this system, we obtain the global existence of weak solutions
to the compressible QNS equations with damping terms for large initial data.
Moreover, we obtain some new a priori estimates, which can avoid using the
assumption that the gradient of the velocity is a well-defined function, which
is indeed used directly in [Vasseur-Yu, SIAM J. Math. Anal., 48 (2016),
1489--1511; Invent. Math., 206 (2016), 935--974]. On the other hand, in the
absence of damping terms, we also prove the global existence of weak solutions
to the compressible QNS equations without the lower bound assumption on the
dispersive coefficient, which improves the previous result due to
[Antonelli-Spirito, Arch. Ration. Mech. Anal., 203(2012), 499--527].
|
1906.03971v1
|
2019-06-11
|
Study of semi-linear $σ$-evolution equations with frictional and visco-elastic damping
|
In this article, we study semi-linear $\sigma$-evolution equations with
double damping including frictional and visco-elastic damping for any
$\sigma\ge 1$. We are interested in investigating not only higher order
asymptotic expansions of solutions but also diffusion phenomenon in the
$L^p-L^q$ framework, with $1\le p\le q\le \infty$, to the corresponding linear
equations. By assuming additional $L^{m}$ regularity on the initial data, with
$m\in [1,2)$, we prove the global (in time) existence of small data energy
solutions and indicate the large time behavior of the global obtained solutions
as well to semi-linear equations. Moreover, we also determine the so-called
critical exponent when $\sigma$ is integers.
|
1906.04471v1
|
2019-07-08
|
Damping of density oscillations in neutrino-transparent nuclear matter
|
We calculate the bulk-viscous dissipation time for adiabatic density
oscillations in nuclear matter at densities of 1-7 times nuclear saturation
density and at temperatures ranging from 1 MeV, where corrections to previous
low-temperature calculations become important, up to 10 MeV, where the
assumption of neutrino transparency is no longer valid. Under these conditions,
which are expected to occur in neutron star mergers, damping of density
oscillations arises from beta equilibration via weak interactions. We find that
for 1 kHz oscillations the shortest dissipation times are in the 5 to 20 ms
range, depending on the equation of state, which means that bulk viscous
damping could affect the dynamics of a neutron star merger. For higher
frequencies the dissipation time can be even shorter.
|
1907.03795v2
|
2019-07-12
|
Decoherence of collective motion in warm nuclei
|
Collective states in cold nuclei are represented by a wave function that
assigns coherent phases to the participating nucleons. The degree of coherence
decreases with excitation energy above the yrast line because of coupling to
the increasingly dense background of quasiparticle excitations. The
consequences of decoherence are discussed, starting with the well studied case
of rotational damping. In addition to superdeformed bands, a highly excited
oblate band is presented as a new example of screening from rotational damping.
Suppression of pair correlation leads to incoherent thermal M1 radiation, which
appears as an exponential spike (LEMAR) at zero energy in the $\gamma$ strength
function of spherical nuclei. In deformed nuclei a Scissors Resonance appears
and LEMAR changes to damped magnetic rotation, which is interpreted as partial
restoration of coherence.
|
1907.05569v1
|
2019-07-24
|
First-order optimization algorithms via inertial systems with Hessian driven damping
|
In a Hilbert space setting, for convex optimization, we analyze the
convergence rate of a class of first-order algorithms involving inertial
features. They can be interpreted as discrete time versions of inertial
dynamics involving both viscous and Hessian-driven dampings. The geometrical
damping driven by the Hessian intervenes in the dynamics in the form $\nabla^2
f (x(t)) \dot{x} (t)$. By treating this term as the time derivative of $ \nabla
f (x (t)) $, this gives, in discretized form, first-order algorithms in time
and space. In addition to the convergence properties attached to Nesterov-type
accelerated gradient methods, the algorithms thus obtained are new and show a
rapid convergence towards zero of the gradients. On the basis of a
regularization technique using the Moreau envelope, we extend these methods to
non-smooth convex functions with extended real values. The introduction of time
scale factors makes it possible to further accelerate these algorithms. We also
report numerical results on structured problems to support our theoretical
findings.
|
1907.10536v2
|
2019-07-26
|
L^p-asymptotic stability analysis of a 1D wave equation with a nonlinear damping
|
This paper is concerned with the asymptotic stability analysis of a one
dimensional wave equation with Dirichlet boundary conditions subject to a
nonlinear distributed damping with an L p functional framework, p $\in$ [2,
$\infty$]. Some well-posedness results are provided together with exponential
decay to zero of trajectories, with an estimation of the decay rate. The
well-posedness results are proved by considering an appropriate functional of
the energy in the desired functional spaces introduced by Haraux in [11].
Asymptotic behavior analysis is based on an attractivity result on a trajectory
of an infinite-dimensional linear time-varying system with a special structure,
which relies on the introduction of a suitable Lyapunov functional. Note that
some of the results of this paper apply for a large class of nonmonotone
dampings.
|
1907.11712v1
|
2019-07-27
|
Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation
|
In this paper, we present two improved Gauss-Seidel projection methods with
unconditional stability. The first method updates the gyromagnetic term and the
damping term simultaneously and follows by a projection step. The second method
introduces two sets of approximate solutions, where we update the gyromagnetic
term and the damping term simultaneously for one set of approximate solutions
and apply the projection step to the other set of approximate solutions in an
alternating manner. Compared to the original Gauss-Seidel projection method
which has to solve heat equations $7$ times at each time step, the improved
methods solve heat equations $5$ times and $3$ times, respectively. First-order
accuracy in time and second-order accuracy in space are verified by examples in
both 1D and 3D. In addition, unconditional stability with respect to both the
grid size and the damping parameter is confirmed numerically. Application of
both methods to a realistic material is also presented with hysteresis loops
and magnetization profiles. Compared with the original method, the recorded
running times suggest that savings of both methods are about $2/7$ and $4/7$
for the same accuracy requirement, respectively.
|
1907.11853v1
|
2019-08-13
|
A Gevrey class semigroup, exponential decay and Lack of analyticity for a system formed by a Kirchhoff-Love plate equation and the equation of a membrane-like electric network with indirect fractional damping
|
The emphasis in this paper is on the Coupled System of a Kirchhoff-Love Plate
Equation with the Equation of a Membrane-like Electrical Network, where the
coupling is of higher order given by the Laplacian of the displacement velocity
$\gamma\Delta u_t$ and the Laplacian of the electric potential field
$\gamma\Delta v_t $, here only one of the equations is conservative and the
other has dissipative properties. The dissipative mechanism is given by an
intermediate damping $(-\Delta)^\theta v_t$ between the electrical damping
potential for $\theta=0$ and the Laplacian of the electric potential for
$\theta=1$. We show that $S(t)=e^{\mathbb{B}t}$ is not analytic for
$\theta\in[0, 1)$ and analytic for $\theta=1$, however $S(t)=e^{\mathbb{B}t}$
decays exponentially for $0\leq \theta\leq 1$ and $S(t)$ is of Gevrey class $s>
\frac{2+\theta}{\theta}$ when the parameter $\theta$ lies in the interval
$(0,1)$.
|
1908.04826v3
|
2019-08-20
|
Partial Optomechanical Refrigeration via Multimode Cold-Damping Feedback
|
We provide a fully analytical treatment for the partial refrigeration of the
thermal motion of a quantum mechanical resonator under the action of feedback.
As opposed to standard cavity optomechanics where the aim is to isolate and
cool a single mechanical mode, the aim here is to extract the thermal energy
from many vibrational modes within a large frequency bandwidth. We consider a
standard cold-damping technique where homodyne read-out of the cavity output
field is fed into a feedback loop that provides a cooling action directly
applied on the mechanical resonator. Analytical and numerical results predict
that low final occupancies are achievable independently of the number of modes
addressed by the feedback as long as the cooling rate is smaller than the
intermode frequency separation. For resonators exhibiting a few nearly
degenerate pairs of modes cooling is less efficient and a weak dependence on
the number of modes is obtained. These scalings hint towards the design of
frequency resolved mechanical resonators where efficient refrigeration is
possible via simultaneous cold-damping feedback.
|
1908.07348v2
|
2019-08-19
|
Time Delay in the Swing Equation: A Variety of Bifurcations
|
The present paper addresses the swing equation with additional delayed
damping as an example for pendulum-like systems. In this context, it is proved
that recurring sub- and supercritical Hopf bifurcations occur if time delay is
increased. To this end, a general formula for the first Lyapunov coefficient in
second order systems with additional delayed damping and delay-free
nonlinearity is given. In so far the paper extends results about stability
switching of equilibria in linear time delay systems from Cooke and Grossman.
In addition to the analytical results, periodic solutions are numerically dealt
with. The numerical results demonstrate how a variety of qualitative behaviors
is generated in the simple swing equation by only introducing time delay in a
damping term.
|
1908.07996v3
|
2019-08-26
|
Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
|
We describe completely 2-solitary waves related to the ground state of the
nonlinear damped Klein-Gordon equation \begin{equation*}
\partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \end{equation*} on
$\bf R^N$, for $1\leq N\leq 5$ and energy subcritical exponents $p>2$. The
description is twofold.
First, we prove that 2-solitary waves with same sign do not exist. Second, we
construct and classify the full family of 2-solitary waves in the case of
opposite signs. Close to the sum of two remote solitary waves, it turns out
that only the components of the initial data in the unstable direction of each
ground state are relevant in the large time asymptotic behavior of the
solution. In particular, we show that $2$-solitary waves have a universal
behavior: the distance between the solitary waves is asymptotic to $\log t$ as
$t\to \infty$. This behavior is due to damping of the initial data combined
with strong interactions between the solitary waves.
|
1908.09527v1
|
2019-09-24
|
DAMPE Excess from Leptophilic Vector Dark Matter: Model Independent Approach
|
We study all extensions of the Standard Model (SM) with a vector dark matter
(VDM) candidate which can explain the peak structure observed by recent DAMPE
experiment in electron-positron cosmic ray spectrum. In this regard, we
consider all leptophilic renormalizable VDM-SM interactions through scalar,
spinor, and vector mediators. We show that only two out of six possible models
could produce DAMPE signal by annihilation of VDM with the mass about 1.5 TeV
in a nearby subhalo whilst simultaneously satisfying constraints from DM relic
density, direct/indirect detection, and the collider bounds. These two models
are the ones with scalar/pseudoscalar mediator $ \phi $ with $ M_{\phi} \in
[1500,3000] $ GeV.
|
1909.10729v2
|
2019-09-24
|
Evaluating the Impacts of Transmission Expansion on Sub-Synchronous Resonance Risk
|
While transmission expansions are planned to have positive impact on
reliability of power grids, they could increase the risk and severity of some
of the detrimental incidents in power grid mainly by virtue of changing system
configuration, consequently electrical distance. This paper aims to evaluate
and quantify the impact of transmission expansion projects on Sub-Synchronous
Resonance (SSR) risk through a two-step approach utilizing outage count index
and Sub-synchronous damping index. A graph-theory based SSR screening tool is
introduced to quantify the outage count associated with all grid contingencies
which results in radial connection between renewable generation resources and
nearby series compensated lines. Moreover, a frequency-scan based damping
analysis is performed to assess the impact of transmission expansion on the
system damping in sub-synchronous frequency range. The proposed approach has
been utilized to evaluate the impact of recently-built transmission expansion
project on SSR risk in a portion of Electric Reliability Council of Texas
(ERCOT) grid.
|
1909.11024v1
|
2019-10-02
|
Data-Driven Identification of Rayleigh-Damped Second-Order Systems
|
In this paper, we present a data-driven approach to identify second-order
systems, having internal Rayleigh damping. This means that the damping matrix
is given as a linear combination of the mass and stiffness matrices. These
systems typically appear when performing various engineering studies, e.g.,
vibrational and structural analysis. In an experimental setup, the frequency
response of a system can be measured via various approaches, for instance, by
measuring the vibrations using an accelerometer. As a consequence, given
frequency samples, the identification of the underlying system relies on
rational approximation. To that aim, we propose an identification of the
corresponding second-order system, extending the Loewner framework for this
class of systems. The efficiency of the proposed method is demonstrated by
means of various numerical benchmarks.
|
1910.00838v1
|
2019-10-06
|
Deterministic and random attractors for a wave equation with sign changing damping
|
The paper gives a detailed study of long-time dynamics generated by weakly
damped wave equations in bounded 3D domains where the damping exponent depends
explicitly on time and may change sign. It is shown that in the case when the
non-linearity is superlinear, the considered equation remains dissipative if
the weighted mean value of the dissipation rate remains positive and that the
conditions of this type are not sufficient in the linear case. Two principally
different cases are considered. In the case when this mean is uniform (which
corresponds to deterministic dissipation rates), it is shown that the
considered system possesses smooth uniform attractors as well as non-autonomous
exponential attractors. In the case where the mean is not uniform (which
corresponds to the random dissipation rate, for instance, when this dissipation
rate is generated by the Bernoulli process), the tempered random attractor is
constructed. In contrast to the usual situation, this random attractor is
expected to have infinite Hausdorff and fractal dimension. The simplified model
example which demonstrates infinite-dimensionality of the random attractor is
also presented.
|
1910.02430v1
|
2019-10-23
|
On the exponential stability of a stratified flow to the 2D IDEAL MHD equations with damping
|
We study the stability of a type of stratified flows of the two dimensional
inviscid incompressible MHD equations with velocity damping. The exponential
stability for the perturbation near certain stratified flow is investigated in
a strip-type area R*[0,1]. Although the magnetic filed potential is governed by
a transport equation, by using the algebraic structure of the incompressible
condition, it turns out that the linearized MHD equations around the given
stratified flow retain a non-local damping mechanism. After carefully analyzing
the non-linear structure and introducing some suitable weighted energy norms,
we get the exponential stability by combining the exponential decay in time in
the lower order energy with that in the high order energy.
|
1910.10598v1
|
2019-10-24
|
Wigner instability analysis of the damped Hirota equation
|
We address the modulation instability of the Hirota equation in the presence
of stochastic spatial incoherence and linear time-dependent
amplification/attenuation processes via the Wigner function approach. We show
that the modulation instability remains baseband type, though the damping
mechanisms substantially reduce the unstable spectrum independent of the
higher-order contributions (e.g. the higher-order nonlinear interaction and the
third-order dispersion). Additionally, we find out that the unstable structure
due to the Kerr interaction exhibits a significant resilience to the
third-order-dispersion stabilizing effects in comparison with the higher-order
nonlinearity, as well as a moderate Lorentzian spectrum damping may assist the
rising of instability. Finally, we also discuss the relevance of our results in
the context of current experiments exploring extreme wave events driven by the
modulation instability (e.g. the generation of the so-called rogue waves).
|
1910.11045v2
|
2019-11-01
|
The spherical multipole resonance probe: kinetic damping in its spectrum
|
The multipole resonance probe is one of the recently developed measurement
devices to measure plasma parameter like electron density and temperature based
on the concept of active plasma resonance spectroscopy. The dynamical
interaction between the probe and the plasma in electrostatic, kinetic
description can be modeled in an abstract notation based on functional analytic
methods. These methods provide the opportunity to derive a general solution,
which is given as the response function of the probe-plasma system. It is
defined by the matrix elements of the resolvent of an appropriate dynamical
operator. Based on the general solution a residual damping for vanishing
pressure can be predicted and can only be explained by kinetic effects. Within
this manuscript an explicit response function of the multipole resonance probe
is derived. Therefore, the resolvent is determined by its algebraic
representation based on an expansion in orthogonal basis functions. This allows
to compute an approximated response function and its corresponding spectra,
which show additional damping due to kinetic effects.
|
1911.00514v1
|
2019-11-04
|
Current-driven skyrmion motion in granular films
|
Current-driven skyrmion motion in random granular films is investigated with
interesting findings. For a given current, there exists a critical disorder
strength below which its transverse motion could either be boosted below a
critical damping or be hindered above the critical damping, resulting in
current and disorder dependences of skyrmion Hall angle. The boosting comes
mainly from the random force that is opposite to the driving force (current).
The critical damping depends on the current density and disorder strength.
However, the longitudinal motion of a skyrmion is always hindered by the
disorder. Above the critical disorder strength, skyrmions are pinned. The
disorder-induced random force on a skyrmion can be classified as static and
kinetic ones, similar to the friction force in the Newtonian mechanics. In the
pinning phase, the static (pinning) random force is transverse to the current
density. The kinetic random force is opposite to the skyrmion velocity when
skyrmions are in motion. Furthermore, we provide strong evidences that the
Thiele equation can perfectly describe skyrmion dynamics in granular films.
These findings provide insight to skyrmion motion and should be important for
skyrmiontronics.
|
1911.01245v1
|
2019-11-05
|
Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schrödinger equation: justification and numerical comparisons
|
We consider a discrete nonlinear Klein-Gordon equations with damping and
external drive. Using a small amplitude ansatz, one usually approximates the
equation using a damped, driven discrete nonlinear Schr\"odinger equation.
Here, we show for the first time the justification of this approximation by
finding the error bound using energy estimate. Additionally, we prove the local
and global existence of the Schr\"odinger equation. Numerical simulations are
performed that describe the analytical results. Comparisons between discrete
breathers of the Klein-Gordon equation and discrete solitons of the discrete
nonlinear Schr\"odinger equation are presented.
|
1911.01631v1
|
2019-11-14
|
Stability of coupled solitary wave in biomembranes and nerves
|
In this work, we consider the electromechanical density pulse as a coupled
solitary waves represented by a longitudinal compression wave and an
out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We
analyzed using, the variational approach, the characteristics of the coupled
solitary waves in the presence of damping within the framework of coupled
nonlinear Burger-Korteweg-de Vries-Benjamin-Bona-Mahony (BKdV-BBM) equation. It
is shown that, the inertia parameter increases the stability of coupled
solitary waves while the damping parameter decreases it. Moreover, the presence
of damping term induces a discontinuity of stable regions in the inertia-speed
parameter space, appearing in he form of an island of points. Bell shape and
solitary-shock like wave profiles were obtained by varying the propagation
speed and their linear stability spectrum computed. It is shown that bell shape
solitary wave exhibit bound state eigenvalue spectrum, therefore stable. On the
other hand, the solitary-shock like wave profiles exhibit unbound state
eigenvalue spectrum and are therefore generally unstable.
|
1911.05993v1
|
2019-11-19
|
On the theory of the nonlinear Landau damping
|
An exact solution of the collisionless time-dependent Vlasov equation is
found for the first time. By means of this solution the behavior of the
Langmuir waves in the nonlinear stage is considered. The analysis is restricted
by the consideration of the first nonlinear approximation keeping the second
power of the electric strength. It is shown that in general the waves with
finite amplitudes are not subject to damping. Only in the linear approximation,
when the wave amplitude is very small, are the waves experiencing damping. It
is shown that with the definite resonance conditions imposed, the waves become
unstable.
|
1911.08294v2
|
2019-11-16
|
Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons
|
We consider a damped, parametrically driven discrete nonlinear Klein-Gordon
equation, that models coupled pendula and micromechanical arrays, among others.
To study the equation, one usually uses a small-amplitude wave ansatz, that
reduces the equation into a discrete nonlinear Schr\"odinger equation with
damping and parametric drive. Here, we justify the approximation by looking for
the error bound with the method of energy estimates. Furthermore, we prove the
local and global existence of {solutions to the discrete nonlinear}
Schr\"odinger equation. To illustrate the main results, we consider numerical
simulations showing the dynamics of errors made by the discrete nonlinear
equation. We consider two types of initial conditions, with one of them being a
discrete soliton of the nonlinear Schr\"odinger equation, that is expectedly
approximate discrete breathers of the nonlinear Klein-Gordon equation.
|
1911.08514v1
|
2019-11-26
|
On the Complexity of Minimum-Cost Networked Estimation of Self-Damped Dynamical Systems
|
In this paper, we consider the optimal design of networked estimators to
minimize the communication/measurement cost under the networked observability
constraint. This problem is known as the minimum-cost networked estimation
problem, which is generally claimed to be NP-hard. The main contribution of
this work is to provide a polynomial-order solution for this problem under the
constraint that the underlying dynamical system is self-damped. Using
structural analysis, we subdivide the main problem into two NP-hard subproblems
known as (i) optimal sensor selection, and (ii) minimum-cost communication
network. For self-damped dynamical systems, we provide a polynomial-order
solution for subproblem (i). Further, we show that the subproblem (ii) is of
polynomial-order complexity if the links in the communication network are
bidirectional. We provide an illustrative example to explain the methodologies.
|
1911.11381v1
|
2019-12-30
|
A Link Between Relativistic Rest Energy and Fractionary Momentum Operators of Order 1/2
|
The solution of a causal fractionary wave equation in an infinite potential
well was obtained. First, the so-called "free particle" case was solved, giving
as normalizable solutions a superposition of damped oscillations similar to a
wave packet. From this results, the infinite potential well case was then
solved. The damping coefficient of the equation obtained was matched with the
exponent appearing in the Yucawa potential or "screened" Coulomb potential.
When this matching was forced, the particle aquires an offset energy of E =
mc^2/2 which then can be increased by each energy level. The expontential
damping of the wave solutions in the box was found to be closely related with
the radius of the proton when the particle has a mass equal to the mass of the
proton. Lastly the fractionary wave equation was expressed in spherical
coordinates and remains to be solved through analytical or numerical methods.
|
1912.12770v4
|
2020-01-06
|
A continuous contact force model for impact analysis in multibody dynamics
|
A new continuous contact force model for contacting problems with regular or
irregular contacting surfaces and energy dissipations in multibody systems is
presented and discussed in this work. The model is developed according to Hertz
law and a hysteresis damping force is introduced for modeling the energy
dissipation during the contact process. As it is almost impossible to obtain an
analytical solution based on the system dynamic equation, an approximate
dynamic equation for the collision system is proposed, achieving a good
approximation of the system dynamic equation. An approximate function between
deformation velocity and deformation is founded on the approximate dynamic
equation, then it is utilized to calculate the energy loss due to the damping
force. The model is established through modifying the original formula of the
hysteresis damping parameter derived by combining the energy balance and the
law of conservation of linear momentum. Numerical results of five different
continuous contact models reveal the capability of our new model as well as the
effect of the geometry of the contacting surfaces on the dynamic system
response.
|
2001.01344v1
|
2020-01-06
|
Boresight Alignment of DArk Matter Particle Explorer
|
The DArk Matter Particle Explorer (DAMPE) can measure $\gamma$-rays in the
energy range from a few GeV to about 10 TeV. The direction of each $\gamma$-ray
is reconstructed with respect to the reference system of the DAMPE payload. In
this paper, we adopt a maximum likelihood method and use the $\gamma$-ray data
centered around several bright point-like sources to measure and correct the
angular deviation from the real celestial coordinate system, the so called
``boresight alignment'' of the DAMPE payload. As a check, we also estimate the
boresight alignment for some sets of simulation data with artificial
orientation and obtain consistent results. The time-dependent boresight
alignment analysis does not show evidence for significant variation of the
parameters.
|
2001.01804v1
|
2020-01-09
|
Nonlinear inviscid damping near monotonic shear flows
|
We prove nonlinear asymptotic stability of a large class of monotonic shear
flows among solutions of the 2D Euler equations in the channel
$\mathbb{T}\times[0,1]$. More precisely, we consider shear flows $(b(y),0)$
given by a function $b$ which is Gevrey smooth, strictly increasing, and linear
outside a compact subset of the interval $(0,1)$ (to avoid boundary
contributions which are incompatible with inviscid damping). We also assume
that the associated linearized operator satisfies a suitable spectral
condition, which is needed to prove linear inviscid damping.
Under these assumptions, we show that if $u$ is a solution which is a small
and Gevrey smooth perturbation of such a shear flow $(b(y),0)$ at time $t=0$,
then the velocity field $u$ converges strongly to a nearby shear flow as the
time goes to infinity. This is the first nonlinear asymptotic stability result
for Euler equations around general steady solutions for which the linearized
flow cannot be explicitly solved.
|
2001.03087v1
|
2020-02-03
|
Semi-active $\mathcal{H}_{\infty}$ damping optimization by adaptive interpolation
|
In this work we consider the problem of semi-active damping optimization of
mechanical systems with fixed damper positions. Our goal is to compute a
damping that is locally optimal with respect to the $\mathcal{H}_\infty$-norm
of the transfer function from the exogenous inputs to the performance outputs.
We make use of a new greedy method for computing the $\mathcal{H}_\infty$-norm
of a transfer function based on rational interpolation. In this paper, this
approach is adapted to parameter-dependent transfer functions. The
interpolation leads to parametric reduced-order models that can be optimized
more efficiently. At the optimizers we then take new interpolation points to
refine the reduced-order model and to obtain updated optimizers. In our
numerical examples we show that this approach normally converges fast and thus
can highly accelerate the optimization procedure. Another contribution of this
work are heuristics for choosing initial interpolation points.
|
2002.00617v1
|
2020-03-25
|
A Novel Wide-Area Control Strategy for Damping of Critical Frequency Oscillations via Modulation of Active Power Injections
|
This paper proposes a novel wide-area control strategy for modulating the
active power injections to damp the critical frequency oscillations in power
systems, this includes the inter-area oscillations and the transient frequency
swing. The proposed method pursues an efficient utilization of the limited
power reserve of existing distributed energy resources (DERs) to mitigate these
oscillations. This is accomplished by decoupling the damping control actions at
different sites using the oscillation signals of the concerned mode as the
power commands. A theoretical basis for this decoupled modulating control is
provided. Technically, the desired sole modal oscillation signals are filtered
out by linearly combining the system-wide frequencies, which is determined by
the linear quadratic regulator based sparsity-promoting (LQRSP) technique. With
the proposed strategy, the modulation of each active power injection can be
effectively engineered considering the response limit and steady-state output
capability of the supporting device. The method is validated based on a
two-area test system and is further demonstrated based on the New England
39-bus test system.
|
2003.11397v1
|
2020-03-28
|
Energy correction based on fluorescence attenuation of DAMPE
|
The major scientific goals of DArk Matter Particle Explorer (DAMPE) are to
study cosmic-ray electrons (including positrons) and gamma rays from 5 GeV to
10 TeV and nuclei from Z = 1 to 26 up to 100 TeV. The deposited energy measured
by the Bismuth Germanate Oxide (BGO) calorimeter of DAMPE is affected by
fluorescence attenuation in BGO crystals that are 600 mm long. In this work, an
in-orbit attenuation calibration method is reported, and energy correction of
the sensitive detector unit of the BGO calorimeter is also presented.
|
2003.12717v1
|
2020-04-02
|
A finite element model for seismic response analysis of free-standing rocking columns with vertical dampers
|
This paper investigates finite-element modeling of a vertically damped
free-standing rocking column. The paper first derives the nonlinear equation of
motion for the coupled system and then compares the analytical solution with
finite-element model. Finite-element model is being produced using open source
framework named OpenSees. The rocking surface is modeled using zero-length
fiber cross-section element and the dampers are modeled with two node link
elements. In order to simulate energy dissipation during the rocking motion
Hilber-Hughes-Taylor numerical dissipative time step integration is being
adopted. The paper also compares two types of hysteretic and viscous damping
devices and it shows that the viscous damping behavior is favorable when it is
used along with a rocking block. The results of analytical model of a rigid
block with viscous dampers in MATLAB is then compared with OpenSees model and
the paper concludes that the finite-element model compares satisfactory with
the analytical model.
|
2004.01060v1
|
2020-04-02
|
Simulating the effect of weak measurements by a phase damping channel and determining different measures of bipartite correlations in nuclear magnetic resonance
|
Quantum discord is a measure based on local projective measurements which
captures quantum correlations that may not be fully captured by entanglement. A
change in the measurement process, achieved by replacing rank-one projectors
with a weak positive operator-valued measure (POVM), allows one to define weak
variants of quantum discord. In this work, we experimentally simulate the
effect of a weak POVM on a nuclear magnetic resonance quantum information
processor. The two-qubit system under investigation is part of a three-qubit
system, where one of the qubits is used as an ancillary to implement the phase
damping channel. The strength of the weak POVM is controlled by varying the
strength of the phase damping channel. We experimentally observed two weak
variants of quantum discord namely, super quantum discord and weak quantum
discord, in two-qubit Werner and Bell-diagonal states. The resultant dynamics
of the states is investigated as a function of the measurement strength.
|
2004.01237v2
|
2020-04-24
|
A rigorous derivation and energetics of a wave equation with fractional damping
|
We consider a linear system that consists of a linear wave equation on a
horizontal hypersurface and a parabolic equation in the half space below. The
model describes longitudinal elastic waves in organic monolayers at the
water-air interface, which is an experimental setup that is relevant for
understanding wave propagation in biological membranes. We study the scaling
regime where the relevant horizontal length scale is much larger than the
vertical length scale and provide a rigorous limit leading to a
fractionally-damped wave equation for the membrane. We provide the associated
existence results via linear semigroup theory and show convergence of the
solutions in the scaling limit. Moreover, based on the energy-dissipation
structure for the full model, we derive a natural energy and a natural
dissipation function for the fractionally-damped wave equation with a time
derivative of order 3/2
|
2004.11830v1
|
2020-04-25
|
Pulse-assisted magnetization switching in magnetic nanowires at picosecond and nanosecond timescales with low energy
|
Detailed understanding of spin dynamics in magnetic nanomaterials is
necessary for developing ultrafast, low-energy and high-density spintronic
logic and memory. Here, we develop micromagnetic models and analytical
solutions to elucidate the effect of increasing damping and uniaxial anisotropy
on magnetic field pulse-assisted switching time, energy and field requirements
of nanowires with perpendicular magnetic anisotropy and yttrium iron
garnet-like spin transport properties. A nanowire is initially magnetized using
an external magnetic field pulse (write) and self-relaxation. Next, magnetic
moments exhibit deterministic switching upon receiving 2.5 ns-long external
magnetic pulses in both vertical polarities. Favorable damping
({\alpha}~0.1-0.5) and anisotropy energies (10^4-10^5 J m^-3) allow for as low
as picosecond magnetization switching times. Magnetization reversal with fields
below coercivity was observed using spin precession instabilities. A
competition or a nanomagnetic trilemma arises among the switching rate, energy
cost and external field required. Developing magnetic nanowires with optimized
damping and effective anisotropy could reduce the switching energy barrier down
to 3163kBT at room temperature. Thus, pulse-assisted picosecond and low energy
switching in nanomagnets could enable ultrafast nanomagnetic logic and cellular
automata.
|
2004.12243v1
|
2020-05-01
|
Stability of Forced-Damped Response in Mechanical Systems from a Melnikov Analysis
|
Frequency responses of multi-degree-of-freedom mechanical systems with weak
forcing and damping can be studied as perturbations from their conservative
limit. Specifically, recent results show how bifurcations near resonances can
be predicted analytically from conservative families of periodic orbits
(nonlinear normal modes). However, the stability of forced-damped motions is
generally determined a posteriori via numerical simulations. In this paper, we
present analytic results on the stability of periodic orbits that perturb from
conservative nonlinear normal modes. In contrast with prior approaches to the
same problem, our method can tackle strongly nonlinear oscillations, high-order
resonances and arbitrary types of non-conservative forces affecting the system,
as we show with specific examples.
|
2005.00444v2
|
2020-05-04
|
Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with $L^r$-data
|
In the present paper, we consider the linear wave equation with the
scale-invariant damping and mass. It is known that the global behavior of the
solution depends on the size of the coefficients in front of the damping and
mass at initial time $t=0$. Indeed, the solution satisfies the similar decay
estimate to that of the corresponding heat equation if it is large and to that
of the modified wave equation if it is small. In our previous paper, we obtain
the scattering result and its asymptotic order for the data in the energy space
$H^1\times L^2$ when the coefficients are in the wave regime. In fact, the
threshold of the coefficients relies on the spatial decay of the initial data.
Namely, it varies depending on $r$ when the initial data is in $L^r$ ($1\leq r
< 2$). In the present paper, we will show the scattering result and the
asymptotic order in the wave regime for $L^r$-data, which is wider than the
wave regime for the data in the energy space. Moreover, we give an improvement
of the asymptotic order obtained in our previous paper for the data in the
energy space.
|
2005.01335v2
|
2020-05-13
|
Periodically Forced Nonlinear Oscillators With Hysteretic Damping
|
We perform a detailed study of the dynamics of a nonlinear, one-dimensional
oscillator driven by a periodic force under hysteretic damping, whose linear
version was originally proposed and analyzed by Bishop in [1]. We first add a
small quadratic stiffness term in the constitutive equation and construct the
periodic solution of the problem by a systematic perturbation method,
neglecting transient terms as $t\rightarrow \infty$. We then repeat the
analysis replacing the quadratic by a cubic term, which does not allow the
solutions to escape to infinity. In both cases, we examine the dependence of
the amplitude of the periodic solution on the different parameters of the model
and discuss the differences with the linear model. We point out certain
undesirable features of the solutions, which have also been alluded to in the
literature for the linear Bishop's model, but persist in the nonlinear case as
well. Finally, we discuss an alternative hysteretic damping oscillator model
first proposed by Reid [2], which appears to be free from these difficulties
and exhibits remarkably rich dynamical properties when extended in the
nonlinear regime.
|
2005.06187v1
|
2020-05-13
|
Magnetic circular dichroism spectra from resonant and damped coupled cluster response theory
|
A computational expression for the Faraday A term of magnetic circular
dichroism (MCD) is derived within coupled cluster response theory and
alternative computational expressions for the B term are discussed. Moreover,
an approach to compute the (temperature-independent) MCD ellipticity in the
context of coupled cluster damped response is presented, and its equivalence
with the stick-spectrum approach in the limit of infinite lifetimes is
demonstrated. The damped response approach has advantages for molecular systems
or spectral ranges with a high density of states. Illustrative results are
reported at the coupled cluster singles and doubles level and compared to
time-dependent density functional theory results.
|
2005.06190v1
|
2020-05-21
|
Convective Excitation and Damping of Solar-like Oscillations
|
The last decade has seen a rapid development in asteroseismology thanks to
the CoRoT and Kepler missions. With more detailed asteroseismic observations
available, it is becoming possible to infer exactly how oscillations are driven
and dissipated in solar-type stars. We have carried out three-dimensional (3D)
stellar atmosphere simulations together with one-dimensional (1D) stellar
structural models of key benchmark turn-off and subgiant stars to study this
problem from a theoretical perspective. Mode excitation and damping rates are
extracted from 3D and 1D stellar models based on analytical expressions. Mode
velocity amplitudes are determined by the balance between stochastic excitation
and linear damping, which then allows the estimation of the frequency of
maximum oscillation power, $\nu_{\max}$, for the first time based on ab initio
and parameter-free modelling. We have made detailed comparisons between our
numerical results and observational data and achieved very encouraging
agreement for all of our target stars. This opens the exciting prospect of
using such realistic 3D hydrodynamical stellar models to predict solar-like
oscillations across the HR-diagram, thereby enabling accurate estimates of
stellar properties such as mass, radius and age.
|
2005.10519v1
|
2020-05-21
|
Non-Markovian memory in a measurement-based quantum computer
|
We study the exact open system dynamics of single qubit gates during a
measurement-based quantum computation considering non-Markovian environments.
We obtain analytical solutions for the average gate fidelities and analyze it
for amplitude damping and dephasing channels. We show that the average fidelity
is identical for the X-gate and Z-gate and that neither fast application of the
projective measurements necessarily implies high gate fidelity, nor slow
application necessarily implies low gate fidelity. Indeed, for highly
non-Markovian environments, it is of utmost importance to know the best time to
perform the measurements, since a huge variation in the gate fidelity may occur
given this scenario. Furthermore, we show that while for the amplitude damping
the knowledge of the dissipative map is sufficient to determine the best
measurement times, i.e. the best times in which measures are taken, the same is
not necessarily true for the phase damping. To the later, the time of the set
of measures becomes crucial since a phase error in one qubit can fix the phase
error that takes place in another.
|
2005.10883v1
|
2020-05-22
|
Improving Dynamic Performance of Low-Inertia Systems through Eigensensitivity Optimization
|
An increasing penetration of renewable generation has led to reduced levels
of rotational inertia and damping in the system. The consequences are higher
vulnerability to disturbances and deterioration of the dynamic response of the
system. To overcome these challenges, novel converter control schemes that
provide virtual inertia and damping have been introduced, which raises the
question of optimal distribution of such devices throughout the network. This
paper presents a framework for performance-based allocation of virtual inertia
and damping to the converter-interfaced generators in a low-inertia system.
This is achieved through an iterative, eigensensitivity-based optimization
algorithm that determines the optimal controller gains. Two conceptually
different problem formulations are presented and validated on a 3-area, 12-bus
test system.
|
2005.11032v1
|
2020-05-24
|
Theory of Solutions for An Inextensible Cantilever
|
Recent equations of motion for the large deflections of a cantilevered
elastic beam are analyzed. In the traditional theory of beam (and plate) large
deflections, nonlinear restoring forces are due to the effect of stretching on
bending; for an inextensible cantilever, the enforcement of arc-length
preservation leads to quasilinear stiffness effects and inertial effects that
are both nonlinear and nonlocal. For this model, smooth solutions are
constructed via a spectral Galerkin approach. Additional compactness is needed
to pass to the limit, and this is obtained through a complex procession of
higher energy estimates. Uniqueness is obtained through a non-trivial
decomposition of the nonlinearity. The confounding effects of nonlinear inertia
are overcome via the addition of structural (Kelvin-Voigt) damping to the
equations of motion. Local well-posedness of smooth solutions is shown first in
the absence of nonlinear inertial effects, and then shown with these inertial
effects present, taking into account structural damping. With damping in force,
global-in-time, strong well-posedness result is obtained by achieving
exponential decay for small data.
|
2005.11836v2
|
2020-05-25
|
Nonlinear losses in magnon transport due to four-magnon scattering
|
We report on the impact of nonlinear four-magnon scattering on magnon
transport in microstructured Co25Fe75 waveguides with low magnetic damping. We
determine the magnon propagation length with microfocused Brillouin light
scattering over a broad range of excitation powers and detect a decrease of the
attenuation length at high powers. This is consistent with the onset of
nonlinear four-magnon scattering. Hence, it is critical to stay in the linear
regime, when deriving damping parameters from the magnon propagation length.
Otherwise, the intrinsic nonlinearity of magnetization dynamics may lead to a
misinterpretation of magnon propagation lengths and, thus, to incorrect values
of the magnetic damping of the system.
|
2005.12113v2
|
2020-06-02
|
Rigid body dynamics of diamagnetically levitating graphite resonators
|
Diamagnetic levitation is a promising technique for realizing resonant
sensors and energy harvesters, since it offers thermal and mechanical isolation
from the environment at zero power. To advance the application of
diamagnetically levitating resonators, it is important to characterize their
dynamics in the presence of both magnetic and gravitational fields. Here we
experimentally actuate and measure rigid body modes of a diamagnetically
levitating graphite plate. We numerically calculate the magnetic field and
determine the influence of magnetic force on the resonance frequencies of the
levitating plate. By analyzing damping mechanisms, we conclude that eddy
current damping dominates dissipation in mm-sized plates. We use finite element
simulations to model eddy current damping and find close agreement with
experimental results. We also study the size-dependent Q-factors (Qs) of
diamagnetically levitating plates and show that Qs above 100 million are
theoretically attainable by reducing the size of the diamagnetic resonator down
to microscale, making these systems of interest for next generation low-noise
resonant sensors and oscillators.
|
2006.01733v3
|
2020-06-11
|
Signatures of Spatial Curvature on Growth of Structures
|
We write down Boltzmann equation for massive particles in a spatially curved
FRW universe and solve the approximate line-of-sight solution for evolution of
matter density, including the effects of spatial curvature to the first order
of approximation. It is shown that memory of early time gravitational potential
is affected by presence of spatial curvature. Then we revisit Boltzmann
equation for photons in the general FRW background. Using it, we show that how
the frequency of oscillations and damping factor (known as Silk damping)
changed in presence of spatial curvature. At last, using this modified damping
factor in hydrodynamic regime of cosmological perturbations, we find our
analytic solution which shows the effects of spatial curvature on growing mode
of matter density.
|
2006.06347v2
|
2020-06-29
|
HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. II. Magnetohydrodynamic simulations
|
Trapped inertial oscillations (r-modes) provide a promising explanation for
high-frequency quasi-periodic oscillations (HFQPOs) observed in the emission
from black hole X-ray binary systems. An eccentricity (or warp) can excite
r-modes to large amplitudes, but concurrently the oscillations are likely
damped by magnetohydrodynamic (MHD) turbulence driven by the magnetorotational
instability (MRI). We force eccentricity in global, unstratified, zero-net flux
MHD simulations of relativistic accretion discs, and find that a sufficiently
strong disc distortion generates trapped inertial waves despite this damping.
In our simulations, eccentricities above ~ 0.03 in the inner disc excite
trapped waves. In addition to the competition between r-mode damping and
driving, we observe that larger amplitude eccentric structures modify and in
some cases suppress MRI turbulence. Given the variety of distortions (warps as
well as eccentricities) capable of amplifying r-modes, the robustness of
trapped inertial wave excitation in the face of MRI turbulence in our
simulations provides support for a discoseismic explanation for HFQPOs.
|
2006.16266v2
|
2020-07-01
|
An integrable family of torqued, damped, rigid rotors
|
Expositions of the Euler equations for the rotation of a rigid body often
invoke the idea of a specially damped system whose energy dissipates while its
angular momentum magnitude is conserved in the body frame. An attempt to
explicitly construct such a damping function leads to a more general, but still
integrable, system of cubic equations whose trajectories are confined to nested
sets of quadric surfaces in angular momentum space. For some choices of
parameters, the lines of fixed points along both the largest and smallest
moment of inertia axes can be simultaneously attracting. Limiting cases are
those that conserve either the energy or the magnitude of the angular momentum.
Parallels with rod mechanics, micromagnetics, and particles with effective mass
are briefly discussed.
|
2007.00707v1
|
2020-07-10
|
Approximate Time-Optimal Trajectories for Damped Double Integrator in 2D Obstacle Environments under Bounded Inputs
|
This article provides extensions to existing path-velocity decomposition
based time optimal trajectory planning algorithm \cite{kant1986toward} to
scenarios in which agents move in 2D obstacle environment under double
integrator dynamics with drag term (damped double integrator). Particularly, we
extend the idea of a tangent graph \cite{liu1992path} to $\calC^1$-Tangent
graph to find continuously differentiable ($\calC^1$) shortest path between any
two points. $\calC^1$-Tangent graph has a continuously differentiable
($\calC^1$) path between any two nodes. We also provide analytical expressions
for a near time-optimal velocity profile for an agent moving on these shortest
paths under the damped double integrator with bounded acceleration.
|
2007.05155v2
|
2020-08-11
|
Ab initio results for the plasmon dispersion and damping of the warm dense electron gas
|
Warm dense matter (WDM) is an exotic state on the border between condensed
matter and dense plasmas. Important occurrences of WDM include dense
astrophysical objects, matter in the core of our Earth, as well as matter
produced in strong compression experiments. As of late, x-ray Thomson
scattering has become an advanced tool to diagnose WDM. The interpretation of
the data requires model input for the dynamic structure factor $S(q,\omega)$
and the plasmon dispersion $\omega(q)$. Recently the first \textit{ab initio}
results for $S(q,\omega)$ of the homogeneous warm dense electron gas were
obtained from path integral Monte Carlo simulations, [Dornheim \textit{et al.},
Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. Here, we analyse the effects of
correlations and finite temperature on the dynamic dielectric function and the
plasmon dispersion. Our results for the plasmon dispersion and damping differ
significantly from the random phase approximation and from earlier models of
the correlated electron gas. Moreover, we show when commonly used weak damping
approximations break down and how the method of complex zeros of the dielectric
function can solve this problem for WDM conditions.
|
2008.04605v1
|
2020-08-18
|
Singularity formation for compressible Euler equations with time-dependent damping
|
In this paper, we consider the compressible Euler equations with
time-dependent damping \frac{\a}{(1+t)^\lambda}u in one space dimension. By
constructing 'decoupled' Riccati type equations for smooth solutions, we
provide some sufficient conditions under which the classical solutions must
break down in finite time. As a byproduct, we show that the derivatives blow
up, somewhat like the formation of shock wave, if the derivatives of initial
data are appropriately large at a point even when the damping coefficient goes
to infinity with a algebraic growth rate. We study the case \lambda\neq1 and
\lambda=1 respectively, moreover, our results have no restrictions on the size
of solutions and the positivity/monotonicity of the initial Riemann invariants.
In addition, for 1<\gamma<3 we provide time-dependent lower bounds on density
for arbitrary classical solutions, without any additional assumptions on the
initial data.
|
2008.07756v1
|
2020-08-20
|
Combining $T_1$ and $T_2$ estimation with randomized benchmarking and bounding the diamond distance
|
The characterization of errors in a quantum system is a fundamental step for
two important goals. First, learning about specific sources of error is
essential for optimizing experimental design and error correction methods.
Second, verifying that the error is below some threshold value is required to
meet the criteria of threshold theorems. We consider the case where errors are
dominated by the generalized damping channel (encompassing the common intrinsic
processes of amplitude damping and dephasing) but may also contain additional
unknown error sources. We demonstrate the robustness of standard $T_1$ and
$T_2$ estimation methods and provide expressions for the expected error in
these estimates under the additional error sources. We then derive expressions
that allow a comparison of the actual and expected results of fine-grained
randomized benchmarking experiments based on the damping parameters. Given the
results of this comparison, we provide bounds that allow robust estimation of
the thresholds for fault-tolerance.
|
2008.09197v1
|
2020-08-25
|
The atomic damping basis and the collective decay of interacting two-level atoms
|
We find analytical solutions to the evolution of interacting two-level atoms
when the master equation is symmetric under the permutation of atomic labels.
The master equation includes atomic independent dissipation. The method to
obtain the solutions is: First, we use the system symmetries to describe the
evolution in an operator space whose dimension grows polynomially with the
number of atoms. Second, we expand the solutions in a basis composed of
eigenvectors of the dissipative part of the master equation that models the
independent dissipation of the atoms. This atomic damping basis is an atomic
analog to the damping basis used for bosonic fields. The solutions show that
the system decays as a sum of sub- and super-radiant exponential terms.
|
2008.11056v1
|
2020-09-11
|
Accuracy of relativistic Cowling approximation in protoneutron star asteroseismology
|
The relativistic Cowling approximation, where the metric perturbations are
neglected during the fluid oscillations, is often adopted for considering the
gravitational waves from the protoneutron stars (PNSs) provided via
core-collapse supernova explosions. In this study, we evaluate how the Cowling
approximation works well by comparing the frequencies with the Cowling
approximation to those without the approximation. Then, we find that the
behavior of the frequencies with the approximation is qualitatively the same
way as that without the approximation, where the frequencies with the
approximation can totally be determined within $\sim 20\%$ accuracy. In
particular, the fundamental mode with the Cowling approximation is
overestimated. In addition, we also discuss the damping time of various
eigenmodes in gravitational waves from the PNSs, where the damping time for the
PNSs before the avoided crossing between the $f$- and $g_1$-modes, is quite
different from that for cold neutron stars, but it is more or less similar to
that for cold neutron stars in the later phase. The damping time is long enough
compared to the typical time interval of short-Fourier transformation that
often used in the analysis, and that ideally guarantees the validity of the
transformation.
|
2009.05206v1
|
2020-09-17
|
Resonant absorption: transformation of compressive motions into vortical motions
|
This paper investigates the changes in spatial properties when
magnetohydrodynamic (MHD) waves undergo resonant damping in the Alfv\'en
continuum. The analysis is carried out for a 1D cylindrical pressure-less
plasma with a straight magnetic field. The effect of the damping on the spatial
wave variables is determined by using complex frequencies that arise as a
result of the resonant damping. Compression and vorticity are used to
characterise the spatial evolution of the MHD wave. The most striking result is
the huge spatial variation in the vorticity component parallel to the magnetic
field. Parallel vorticity vanishes in the uniform part of the equilibrium.
However, when the MHD wave moves into the non-uniform part, parallel vorticity
explodes to values that are orders of magnitude higher than those attained by
the transverse components in planes normal to the straight magnetic field. In
the non-uniform part of the equilibrium plasma, the MHD wave is controlled by
parallel vorticity and resembles an Alfv\'en wave, with the unfamiliar property
that it has pressure variations even in the linear regime.
|
2009.08152v1
|
2020-09-19
|
Random vibrations of stress-driven nonlocal beams with external damping
|
Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with
external damping are investigated by stress-driven nonlocal mechanics. Damping
effects are simulated considering viscous interactions between beam and
surrounding environment. Loadings are modeled by accounting for their random
nature. Such a dynamic problem is characterized by a stochastic partial
differential equation in space and time governing time-evolution of the
relevant displacement field. Differential eigenanalyses are performed to
evaluate modal time coordinates and mode shapes, providing a complete
stochastic description of response solutions. Closed-form expressions of power
spectral density, correlation function, stationary and non-stationary variances
of displacement fields are analytically detected. Size-dependent dynamic
behaviour is assessed in terms of stiffness, variance and power spectral
density of displacements. The outcomes can be useful for design and
optimization of structural components of modern small-scale devices, such as
Micro- and Nano-Electro-Mechanical-Systems (MEMS and NEMS).
|
2009.09184v1
|
2020-09-20
|
Correction Method for the Readout Saturation of the DAMPE Calorimeter
|
The DArk Matter Particle Explorer (DAMPE) is a space-borne high energy
cosmic-ray and $\gamma$-ray detector which operates smoothly since the launch
on December 17, 2015. The bismuth germanium oxide (BGO) calorimeter is one of
the key sub-detectors of DAMPE used for energy measurement and electron proton
identification. For events with total energy deposit higher than decades of
TeV, the readouts of PMTs coupled on the BGO crystals would become saturated,
which results in an underestimation of the energy measurement. Based on
detailed simulations, we develop a correction method for the saturation effect
according to the shower development topologies and energies measured by
neighbouring BGO crystals. The verification with simulated and on-orbit events
shows that this method can well reconstruct the energy deposit in the saturated
BGO crystal.
|
2009.09438v1
|
2020-09-21
|
Complete complementarity relations in system-environment decoherent dynamics
|
We investigate the system-environment information flow from the point of view
ofcomplete complementarity relations. We consider some commonly used noisy
quantum channels:Amplitude damping, phase damping, bit flip, bit-phase flip,
phase flip, depolarizing, and correlatedamplitude damping. By starting with an
entangled bipartite pure quantum state, with the linearentropy being the
quantifier of entanglement, we study how entanglement is redistributed and
turnedinto general correlations between the degrees of freedom of the whole
system. For instance, it ispossible to express the entanglement entropy in
terms of the multipartite quantum coherence or interms of the correlated
quantum coherence of the different partitions of the system. In addition,we
notice that for the depolarizing and bit-phase flip channels the wave and
particle aspects candecrease or increase together. Besides, by considering the
environment as part of a pure quantumsystem, the linear entropy is shown to be
not just a measure of mixedness of a particular subsystem,but a correlation
measure of the subsystem with rest of the world.
|
2009.09769v3
|
2020-09-15
|
Delay-induced resonance suppresses damping-induced unpredictability
|
Combined effects of the damping and forcing in the underdamped time-delayed
Duffing oscillator are considered in this paper. We analyze the generation of a
certain damping-induced unpredictability, due to the gradual suppression of
interwell oscillations. We find the minimal amount of the forcing amplitude and
the right forcing frequency to revert the effect of the dissipation, so that
the interwell oscillations can be restored, for different time delay values.
This is achieved by using the delay-induced resonance, in which the time delay
replaces one of the two periodic forcings present in the vibrational resonance.
A discussion in terms of the time delay of the critical values of the forcing
for which the delay-induced resonance can tame the dissipation effect is
finally carried out.
|
2009.11760v1
|
2020-10-01
|
Modeling coupled spin and lattice dynamics
|
A unified model of molecular and atomistic spin dynamics is presented
enabling simulations both in microcanonical and canonical ensembles without the
necessity of additional phenomenological spin damping. Transfer of energy and
angular momentum between the lattice and the spin systems is achieved by a
coupling term based upon the spin-orbit interaction. The characteristic spectra
of the spin and phonon systems are analyzed for different coupling strength and
temperatures. The spin spectral density shows magnon modes together with the
uncorrelated noise induced by the coupling to the lattice. The effective
damping parameter is investigated showing an increase with both coupling
strength and temperature. The model paves the way to understanding magnetic
relaxation processes beyond the phenomenological approach of the Gilbert
damping and the dynamics of the energy transfer between lattice and spins.
|
2010.00642v1
|
2020-10-06
|
A dissiptive logarithmic type evolution equation: asymptotic profile and optimal estimates
|
We introduce a new model of the logarithmic type of wave-like equation with a
nonlocal logarithmic damping mechanism, which is rather weakly effective as
compared with frequently studied fractional damping cases. We consider the
Cauchy problem for this new model in the whole space, and study the asymptotic
profile and optimal decay and/or blowup rates of solutions as time goes to
infinity in L^{2}-sense. The operator L considered in this paper was used to
dissipate the solutions of the wave equation in the paper studied by
Charao-Ikehata in 2020, and in the low frequency parameters the principal part
of the equation and the damping term is rather weakly effective than those of
well-studied power type operators.
|
2010.02485v1
|
2020-10-12
|
Line-drag damping of Alfvén waves in radiatively driven winds of magnetic massive stars
|
Line-driven stellar winds from massive (OB) stars are subject to a strong
line-deshadowing instability. Recently, spectropolarimetric surveys have
collected ample evidence that a subset of Galactic massive stars hosts strong
surface magnetic fields. We investigate here the propagation and stability of
magneto-radiative waves in such a magnetised, line-driven wind. Our analytic,
linear stability analysis includes line-scattering from the stellar radiation,
and accounts for both radial and non-radial perturbations. We establish a
bridging law for arbitrary perturbation wavelength after which we analyse
separately the long- and short-wavelength limits. While long-wavelength
radiative and magnetic waves are found to be completely decoupled, a key result
is that short-wavelength, radially propagating Alfv\'en waves couple to the
scattered radiation field and are strongly damped due to the line-drag effect.
This damping of magnetic waves in a scattering-line-driven flow could have
important effects on regulating the non-linear wind dynamics, and so might also
have strong influence on observational diagnostics of the wind structure and
clumping of magnetic line-driven winds.
|
2010.05650v1
|
2020-10-20
|
Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes
|
The paper studies the long time behavior of a system that describes the
motion of a piece of elastic membrane driven by surface tension and inner air
pressure. The system is a degenerate quasilinear hyperbolic one that involves
the mean curvature, and also includes a damping term that models the
dissipative nature of genuine physical systems. With the presence of damping, a
small perturbation of the sphere converges exponentially in time to the sphere,
and without the damping the evolution that is $\varepsilon$-close to the sphere
has life span longer than $\varepsilon^{-1/6}$. Both results are proved using a
new Nash-Moser-H\"{o}rmander type theorem proved by Baldi and Haus.
|
2010.10663v6
|
2020-10-09
|
Rapid parameter determination of discrete damped sinusoidal oscillations
|
We present different computational approaches for the rapid extraction of the
signal parameters of discretely sampled damped sinusoidal signals. We compare
time- and frequency-domain-based computational approaches in terms of their
accuracy and precision and computational time required in estimating the
frequencies of such signals, and observe a general trade-off between precision
and speed. Our motivation is precise and rapid analysis of damped sinusoidal
signals as these become relevant in view of the recent experimental
developments in cavity-enhanced polarimetry and ellipsometry, where the
relevant time scales and frequencies are typically within the $\sim1-10\,\mu$s
and $\sim1-100$MHz ranges, respectively. In such experimental efforts,
single-shot analysis with high accuracy and precision becomes important when
developing experiments that study dynamical effects and/or when developing
portable instrumentations. Our results suggest that online, running-fashion,
microsecond-resolved analysis of polarimetric/ellipsometric measurements with
fractional uncertainties at the $10^{-6}$ levels, is possible, and using a
proof-of-principle experimental demonstration we show that using a
frequency-based analysis approach we can monitor and analyze signals at kHz
rates and accurately detect signal changes at microsecond time-scales.
|
2010.11690v1
|
2020-10-22
|
Effective shear and bulk viscosities for anisotropic flow
|
We evaluate the viscous damping of anisotropic flow in heavy-ion collisions
for arbitrary temperature-dependent shear and bulk viscosities. We show that
the damping is solely determined by effective shear and bulk viscosities, which
are weighted averages over the temperature. We determine the relevant weights
for nucleus-nucleus collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and 200 GeV,
corresponding to the maximum LHC and RHIC energies, by running ideal and
viscous hydrodynamic simulations. The effective shear viscosity is driven by
temperatures below $210$ MeV at RHIC, and below $280$ MeV at the LHC, with the
largest contributions coming from the lowest temperatures, just above
freeze-out. The effective bulk viscosity is driven by somewhat higher
temperatures, corresponding to earlier stages of the collision. We show that at
a fixed collision energy, the effective viscosity is independent of centrality
and system size, to the same extent as the mean transverse momentum of outgoing
hadrons. The variation of viscous damping is determined by Reynolds number
scaling.
|
2010.11919v2
|
2020-10-23
|
Is PSR J0855$-$4644 responsible for the 1.4 TeV electron spectral bump hinted by DAMPE?
|
DAMPE observation on the cosmic ray electron spectrum hints a narrow excess
at $\sim$ 1.4 TeV. Although the excess can be ascribed to dark matter
particles, pulsars and pulsar wind nebulae are believed to be a more natural
astrophysical origin: electrons injected from nearby pulsars at their early
ages can form a bump-like feature in the spectrum due to radiative energy
losses. In this paper, with a survey of nearby pulsars, we find 4 pulsars that
may have notable contributions to $\sim$ 1.4 TeV cosmic ray electrons. Among
them, PSR J0855$-$4644 has a spin down luminosity more than 50 times higher
than others and presumably dominates the electron fluxes from them. X-ray
observations on the inner compact part (which may represent a tunnel for the
transport of electrons from the pulsar) of PWN G267.0$-$01.0 are then used to
constrain the spectral index of high energy electrons injected by the pulsar.
We show that high-energy electrons released by PSR J0855$-$4644 could indeed
reproduce the 1.4 TeV spectral feature hinted by the DAMPE with reasonable
parameters.
|
2010.12170v1
|
2020-11-02
|
Effect of retardation on the frequency and linewidth of plasma resonances in a two-dimensional disk of electron gas
|
We theoretically analyze dominant plasma modes in a two-dimensional disk of
electron gas by calculating the absorption of an incident electromagnetic wave.
The problem is solved in a self-consistent approximation, taking into account
electromagnetic retardation effects. We use the Drude model to describe the
conductivity of the system. The absorption spectrum exhibits a series of peaks
corresponding to the excitation of plasma waves. The position and linewidth of
the peaks designating, respectively, the frequency and damping rate of the
plasma modes. We estimate the influence of retardation effects on the frequency
and linewidth of the fundamental (dipole) and axisymmetric (quadrupole) plasma
modes both numerically and analytically. We find the net damping rate of the
modes to be dependent on not only the sum of the radiative and collisional
decays but also their intermixture, even for small retardation. We show that
the net damping rate can be noticeably less than that determined by collisions
alone.
|
2011.00877v1
|
2020-11-05
|
Low-Complexity Models for Acoustic Scene Classification Based on Receptive Field Regularization and Frequency Damping
|
Deep Neural Networks are known to be very demanding in terms of computing and
memory requirements. Due to the ever increasing use of embedded systems and
mobile devices with a limited resource budget, designing low-complexity models
without sacrificing too much of their predictive performance gained great
importance. In this work, we investigate and compare several well-known methods
to reduce the number of parameters in neural networks. We further put these
into the context of a recent study on the effect of the Receptive Field (RF) on
a model's performance, and empirically show that we can achieve high-performing
low-complexity models by applying specific restrictions on the RFs, in
combination with parameter reduction methods. Additionally, we propose a
filter-damping technique for regularizing the RF of models, without altering
their architecture and changing their parameter counts. We will show that
incorporating this technique improves the performance in various low-complexity
settings such as pruning and decomposed convolution. Using our proposed filter
damping, we achieved the 1st rank at the DCASE-2020 Challenge in the task of
Low-Complexity Acoustic Scene Classification.
|
2011.02955v1
|
2020-11-14
|
Learning a Reduced Basis of Dynamical Systems using an Autoencoder
|
Machine learning models have emerged as powerful tools in physics and
engineering. Although flexible, a fundamental challenge remains on how to
connect new machine learning models with known physics. In this work, we
present an autoencoder with latent space penalization, which discovers finite
dimensional manifolds underlying the partial differential equations of physics.
We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV),
and damped KdV equations. We show that the resulting optimal latent space of
the K-S equation is consistent with the dimension of the inertial manifold. The
results for the KdV equation imply that there is no reduced latent space, which
is consistent with the truly infinite dimensional dynamics of the KdV equation.
In the case of the damped KdV equation, we find that the number of active
dimensions decreases with increasing damping coefficient. We then uncover a
nonlinear basis representing the manifold of the latent space for the K-S
equation.
|
2011.07346v1
|
2020-11-23
|
Sharp lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case
|
The open question, which seems to be also the final part, in terms of
studying the Cauchy problem for the weakly coupled system of damped wave
equations or reaction-diffusion equations, is so far known as the sharp
lifespan estimates in the critical case. In this paper, we mainly investigate
lifespan estimates for solutions to the weakly coupled system of semilinear
damped wave equations in the critical case. By using a suitable test function
method associated with nonlinear differential inequalities, we catch upper
bound estimates for the lifespan. Moreover, we establish polynomial-logarithmic
type time-weighted Sobolev spaces to obtain lower bound estimates for the
lifespan in low spatial dimensions. Then, together with the derived lifespan
estimates, new and sharp results on estimates for the lifespan in the critical
case are claimed. Finally, we give an application of our results to the
semilinear reaction-diffusion system in the critical case.
|
2011.11366v2
|
2020-12-10
|
Stochastic Damped L-BFGS with Controlled Norm of the Hessian Approximation
|
We propose a new stochastic variance-reduced damped L-BFGS algorithm, where
we leverage estimates of bounds on the largest and smallest eigenvalues of the
Hessian approximation to balance its quality and conditioning. Our algorithm,
VARCHEN, draws from previous work that proposed a novel stochastic damped
L-BFGS algorithm called SdLBFGS. We establish almost sure convergence to a
stationary point and a complexity bound. We empirically demonstrate that
VARCHEN is more robust than SdLBFGS-VR and SVRG on a modified DavidNet problem
-- a highly nonconvex and ill-conditioned problem that arises in the context of
deep learning, and their performance is comparable on a logistic regression
problem and a nonconvex support-vector machine problem.
|
2012.05783v1
|
2020-12-29
|
Twist-induced Near-field Thermal Switch Using Nonreciprocal Surface Magnon-Polaritons
|
We explore that two ferromagnetic insulator slabs host a strong twist-induced
near-field radiative heat transfer in the presence of twisted magnetic fields.
Using the formalism of fluctuational electrodynamics, we find the existence of
large twist-induced thermal switch ratio in large damping condition and
nonmonotonic twist manipulation for heat transfer in small damping condition,
associated with the different twist-induced effects of nonreciprocal elliptic
surface magnon-polaritons, hyperbolic surface magnon-polaritons, and
twist-non-resonant surface magnon-polaritons. Moreover, the near-field
radiative heat transfer can be significantly enhanced by the twist-non-resonant
surface magnon-polaritons in the ultra-small damping condition. Such
twist-induced effect is applicable for other kinds of anisotropic slabs with
timereversal symmetry breaking. Our findings provide a way to twisted and
magnetic control in nanoscale thermal management and improve it with
twistronics concepts.
|
2012.14733v1
|
2021-01-04
|
The damped harmonic oscillator at the classical limit of the Snyder-de Sitter space
|
Valtancoli in his paper entitled [P. Valtancoli, Canonical transformations,
and minimal length J. Math. Phys. 56, 122107 (2015)] has shown how the
deformation of the canonical transformations can be made compatible with the
deformed Poisson brackets. Based on this work and through an appropriate
canonical transformation, we solve the problem of one dimensional (1D) damped
harmonic oscillator at the classical limit of the Snyder-de Sitter (SdS) space.
We show that the equations of the motion can be described by trigonometric
functions with frequency and period depending on the deformed and the damped
parameters. We eventually discuss the influences of these parameters on the
motion of the system.
|
2101.01223v2
|
2021-01-11
|
Damped (linear) response theory within the resolution-of-identity coupled cluster singles and approximate doubles (RI-CC2) method
|
An implementation of a complex solver for the solution of the response
equations required to compute the complex response functions of damped response
theory is presented for the resolution-of-identity (RI) coupled-cluster singles
and approximate doubles CC2 method. The implementation uses a partitioned
formulation that avoids the storage of double excitation amplitudes to make it
applicable to large molecules. The solver is the keystone element for the
development of the damped coupled-cluster response formalism for linear and
nonlinear effects in resonant frequency regions at the RI-CC2 level of theory.
Illustrative results are reported for the one-photon absorption cross section
of C60, the electronic circular dichroism of $n$-helicenes ($n$ = 5, 6, 7), and
the $C_6$ dispersion coefficients of a set of selected organic molecules and
fullerenes.
|
2101.03756v1
|
2021-01-26
|
Generalized Damped Newton Algorithms in Nonsmooth Optimization via Second-Order Subdifferentials
|
The paper proposes and develops new globally convergent algorithms of the
generalized damped Newton type for solving important classes of nonsmooth
optimization problems. These algorithms are based on the theory and
calculations of second-order subdifferentials of nonsmooth functions with
employing the machinery of second-order variational analysis and generalized
differentiation. First we develop a globally superlinearly convergent damped
Newton-type algorithm for the class of continuously differentiable functions
with Lipschitzian gradients, which are nonsmooth of second order. Then we
design such a globally convergent algorithm to solve a structured class of
nonsmooth quadratic composite problems with extended-real-valued cost
functions, which typically arise in machine learning and statistics. Finally,
we present the results of numerical experiments and compare the performance of
our main algorithm applied to an important class of Lasso problems with those
achieved by other first-order and second-order optimization algorithms.
|
2101.10555v3
|
2021-01-26
|
Damped and Driven Breathers and Metastability
|
In this article we prove the existence of a new family of periodic solutions
for discrete, nonlinear Schrodinger equations subject to spatially localized
driving and damping. They provide an alternate description of the metastable
behavior in such lattice systems which agrees with previous predictions for the
evolution of metastable states while providing more accurate approximations to
these states. We analyze the stability of these breathers, finding a very small
positive eigenvalue whose eigenvector lies almost tangent to the surface of the
cylinder formed by the family of breathers. This causes solutions to slide
along the cylinder without leaving its neighborhood for very long times.
|
2101.10999v2
|
2021-02-05
|
A simple artificial damping method for total Lagrangian smoothed particle hydrodynamics
|
In this paper, we present a simple artificial damping method to enhance the
robustness of total Lagrangian smoothed particle hydrodynamics (TL-SPH).
Specifically, an artificial damping stress based on the Kelvin-Voigt type
damper with a scaling factor imitating a von Neumann-Richtmyer type artificial
viscosity is introduced in the constitutive equation to alleviate the spurious
oscillation in the vicinity of the sharp spatial gradients. After validating
the robustness and accuracy of the present method with a set of benchmark tests
with very challenging cases, we demonstrate its potentials in the field of
bio-mechanics by simulating the deformation of complex stent structures.
|
2102.04898v1
|
2021-02-18
|
Probing black hole microstructure with the kinetic turnover of phase transition
|
By treating black hole as the macroscopic stable state on the free energy
landscape, we propose that the stochastic dynamics of the black hole phase
transition can be effectively described by the Langevin equation or
equivalently by the Fokker-Planck equation in phase space. We demonstrate the
turnover of the kinetics for the charged anti-de Sitter black hole phase
transition, which shows that the mean first passage time is linear with the
friction in the high damping regime and inversely proportional to the friction
in the low damping regime. The fluctuations in the kinetics are shown to be
large/small in the high/low damping regime and the switching behavior from the
small fluctuations to the large fluctuations takes place at the kinetic
turnover point. Because the friction is a reflection of the microscopic degrees
of freedom acting on the order parameter of the black hole, the turnover and
the corresponding fluctuations of the phase transition kinetics can be used to
probe the black hole microstructure.
|
2102.09439v1
|
2021-02-25
|
Energy Decay of some boundary coupled systems involving wave$\backslash$ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping
|
In this paper, we investigate the energy decay of hyperbolic systems of
wave-wave, wave-Euler- Bernoulli beam and beam-beam types. The two equations
are coupled through boundary connection with only one localized non-smooth
fractional Kelvin-Voigt damping. First, we reformulate each system into an
augmented model and using a general criteria of Arendt-Batty, we prove that our
models are strongly stable. Next, by using frequency domain approach, combined
with multiplier technique and some interpolation inequalities, we establish
different types of polynomial energy decay rate which depends on the order of
the fractional derivative and the type of the damped equation in the system.
|
2102.12732v2
|
2021-03-01
|
Fluid-plate interaction under periodic forcing
|
The motion of a thin elastic plate interacting with a viscous fluid is
investigated. A periodic force acting on the plate is considered, which in a
setting without damping could lead to a resonant response. The interaction with
the viscous fluid provides a damping mechanism due to the energy dissipation in
the fluid. Moreover, an internal damping mechanism in the plate is introduced.
In this setting, we show that the periodic forcing leads to a time-periodic
(non-resonant) solution. We employ the Navier-Stokes and the Kirchhoff-Love
plate equation in a periodic cell structure to model the motion of the viscous
fluid and the elastic plate, respectively. Maximal Lp regularity for the
linearized system is established in a framework of time-periodic function
spaces. Existence of a solution to the fully nonlinear system is subsequently
shown with a fixed-point argument.
|
2103.00795v1
|
2021-03-25
|
Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations
|
We investigate the long-time properties of the two-dimensional inviscid
Boussinesq equations near a stably stratified Couette flow, for an initial
Gevrey perturbation of size $\varepsilon$. Under the classical Miles-Howard
stability condition on the Richardson number, we prove that the system
experiences a shear-buoyancy instability: the density variation and velocity
undergo an $O(t^{-1/2})$ inviscid damping while the vorticity and density
gradient grow as $O(t^{1/2})$. The result holds at least until the natural,
nonlinear timescale $t \approx \varepsilon^{-2}$. Notice that the density
behaves very differently from a passive scalar, as can be seen from the
inviscid damping and slower gradient growth. The proof relies on several
ingredients: (A) a suitable symmetrization that makes the linear terms amenable
to energy methods and takes into account the classical Miles-Howard spectral
stability condition; (B) a variation of the Fourier time-dependent energy
method introduced for the inviscid, homogeneous Couette flow problem developed
on a toy model adapted to the Boussinesq equations, i.e. tracking the potential
nonlinear echo chains in the symmetrized variables despite the vorticity
growth.
|
2103.13713v1
|
2021-03-31
|
Research of Damped Newton Stochastic Gradient Descent Method for Neural Network Training
|
First-order methods like stochastic gradient descent(SGD) are recently the
popular optimization method to train deep neural networks (DNNs), but
second-order methods are scarcely used because of the overpriced computing cost
in getting the high-order information. In this paper, we propose the Damped
Newton Stochastic Gradient Descent(DN-SGD) method and Stochastic Gradient
Descent Damped Newton(SGD-DN) method to train DNNs for regression problems with
Mean Square Error(MSE) and classification problems with Cross-Entropy
Loss(CEL), which is inspired by a proved fact that the hessian matrix of last
layer of DNNs is always semi-definite. Different from other second-order
methods to estimate the hessian matrix of all parameters, our methods just
accurately compute a small part of the parameters, which greatly reduces the
computational cost and makes convergence of the learning process much faster
and more accurate than SGD. Several numerical experiments on real datesets are
performed to verify the effectiveness of our methods for regression and
classification problems.
|
2103.16764v1
|
2021-04-08
|
Landau Damping in the Transverse Modulational Dynamics of Co-Propagating Light and Matter Beams
|
The optomechanical coupling and transverse stability of a co-propagating
monochromatic electromagnetic wave and mono-energetic beam of two-level atoms
is investigated in the collisionless regime. The coupled dynamics are studied
through a Landau stability analysis of the coupled gas- kinetic and paraxial
wave equations, including the effect of the electronic nonlinearity. The
resulting dispersion relation captures the interaction of kinetic and
saturation effects and shows that for blue detuning the combined nonlinear
interaction is unstable below a critical wavenumber which reduces to the result
of Bespalov and Talanov in the limit of a negligible kinetic nonlinearity. For
red detuning we find that under a saturation parameter threshold exists whereby
the system stabilizes unconditionally. With negligible saturation, an
optomechanical form of Landau damping stabilizes all wavenumbers above a
critical wavenumber determined by the combined strength of the kinetic and
refractive optomechanical feedback. The damping is mediated primarily by atoms
traveling along the primary diagonals of the Talbot carpet.
|
2104.04100v1
|
2021-04-15
|
Simulating cosmological supercooling with a cold atom system II
|
We perform an analysis of the supercooled state in an analogue of an early
universe phase transition based on a one dimensional, two-component Bose gas
with time-dependent interactions. We demonstrate that the system behaves in the
same way as a thermal, relativistic Bose gas undergoing a first order phase
transition. We propose a way to prepare the state of the system in the
metastable phase as an analogue to supercooling in the early universe. While we
show that parametric resonances in the system can be suppressed by thermal
damping, we find that the theoretically estimated thermal damping in our model
is too weak to suppress the resonances for realistic experimental parameters.
However, we propose that experiments to investigate the effective damping rate
in experiments would be worthwhile.
|
2104.07428v1
|
2021-04-22
|
Impact of Fe$_{80}$B$_{20}$ insertion on the properties of dual-MgO perpendicular magnetic tunnel junctions
|
We explore the impact of Fe80B20 inserted at both
Co$_{20}$Fe$_{80}$B$_{20}$/MgO interfaces of dual-MgO free layers (FLs) in
bottom-pinned magnetic tunnel junctions (MTJs). MTJ stacks are annealed for 30
min at 350 $^\circ$C and 400 $^\circ$C in a vacuum after film deposition.
Current-in-plane tunneling measurements are carried out to characterize
magnetotransport properties of the MTJs. Conventional magnetometry measurements
and ferromagnetic resonance are conducted to estimate the saturation
magnetization, the effective perpendicular anisotropy field and the Gilbert
damping of dual-MgO FLs as a function of the Fe$_{80}$B$_{20}$ thickness and
annealing temperatures. With ultrathin Fe$_{80}$B$_{20}$ (0.2 - 0.4 nm)
inserted, perpendicular magnetic anisotropy (PMA) of FLs increases with similar
tunnel magneto-resistance (TMR) and low damping values. As Fe$_{80}$B$_{20}$
layer thickness further increases (0.6 - 1.2 nm), both TMR and PMA degrade, and
damping increases dramatically. This study demonstrates a novel approach to
tune properties of MTJ stacks with dual-MgO FLs up to 400 $^\circ$C annealing,
which enables MTJ stacks for various applications.
|
2104.10918v1
|
2021-04-29
|
Nano-patterning of surfaces by ion sputtering: Numerical study of the anisotropic damped Kuramoto-Sivashinsky equation
|
Nonlinear models for pattern evolution by ion beam sputtering on a material
surface present an ongoing opportunity for new numerical simulations. A
numerical analysis of the evolution of preexisting patterns is proposed to
investigate surface dynamics, based on a 2D anisotropic damped
Kuramoto-Sivashinsky equation, with periodic boundary conditions. A
finite-difference semi-implicit time splitting scheme is employed on the
discretization of the governing equation. Simulations were conducted with
realistic coefficients related to physical parameters (anisotropies, beam
orientation, diffusion). The stability of the numerical scheme is analyzed with
time step and grid spacing tests for the pattern evolution, and the Method of
Manufactured Solutions has been used to verify the proposed scheme. Ripples and
hexagonal patterns were obtained from a monomodal initial condition for certain
values of the damping coefficient, while spatiotemporal chaos appeared for
lower values. The anisotropy effects on pattern formation were studied, varying
the angle of incidence of the ion beam with respect to the irradiated surface.
Analytical discussions are based on linear and weakly nonlinear analysis.
|
2104.14104v1
|
2021-05-04
|
Linear response theory and damped modes of stellar clusters
|
Because all stars contribute to its gravitational potential, stellar clusters
amplify perturbations collectively. In the limit of small fluctuations, this is
described through linear response theory, via the so-called response matrix.
While the evaluation of this matrix is somewhat straightforward for unstable
modes (i.e. with a positive growth rate), it requires a careful analytic
continuation for damped modes (i.e. with a negative growth rate). We present a
generic method to perform such a calculation in spherically symmetric stellar
clusters. When applied to an isotropic isochrone cluster, we recover the
presence of a low-frequency weakly damped $\ell = 1$ mode. We finally use a set
of direct $N$-body simulations to test explicitly this prediction through the
statistics of the correlated random walk undergone by a cluster's density
centre.
|
2105.01371v1
|
2021-05-10
|
Passivity-based control of mechanical systems with linear damping identification
|
We propose a control approach for a class of nonlinear mechanical systems to
stabilize the system under study while ensuring that the oscillations of the
transient response are reduced. The approach is twofold: (i) we apply our
technique for linear viscous damping identification of the system to improve
the accuracy of the selected control technique, and (ii) we implement a
passivity-based controller to stabilize and reduce the oscillations by
selecting the control parameters properly in accordance with the identified
damping. Moreover, we provide an analysis for a particular passivity-based
control approach that has been shown successfully for reducing such
oscillations. Also, we validate the methodology by implementing it
experimentally in a planar manipulator.
|
2105.04324v4
|
2021-05-26
|
Decay dynamics of Localised Surface Plasmons: damping of coherences and populations of the oscillatory plasmon modes
|
Properties of plasmonic materials are associated with surface plasmons - the
electromagnetic excitations coupled to coherent electron charge density
oscillations on a metal/dielectric interface. Although decay of such
oscillations cannot be avoided, there are prospects for controlling plasmon
damping dynamics. In spherical metal nanoparticles (MNPs) the basic properties
of Localized Surface Plasmons (LSPs) can be controlled with their radius. The
present paper handles the link between the size-dependent description of LSP
properties derived from the dispersion relation based on Maxwell's equations
and the quantum picture in which MNPs are treated as "quasi-particles". Such
picture, based on the reduced density-matrix of quantum open systems ruled by
the master equation in the Lindblad form, enables to distinguish between
damping processes of populations and coherences of multipolar plasmon
oscillatory states and to establish the intrinsic relations between the rates
of these processes, independently of the size of MNP. The impact of the
radiative and the nonradiative energy dissipation channels is discussed.
|
2105.12463v1
|
2021-06-05
|
The electron acoustic waves in plasmas with two kappa-distributed electrons at the same temperatures and immobile ions
|
The linear electron acoustic waves propagating in plasmas with two
kappa-distributed electrons and stationary ions are investigated. The
temperatures of the two electrons are assumed to be the same, but the kappa
indices are not. It shows that if one kappa index is small enough and the other
one is large enough, a weak damping regime of the electron acoustic waves
exists. The dispersions and damping rates are numerically studied. The
parameter spaces for the weakly damped electron acoustic waves are analyzed.
Moreover, the electron acoustic waves in the present model are compared with
those in other models, especially the plasmas with two-temperature electrons.
At last, we perform Vlasov-Poisson simulations to verify the theory.
|
2106.02910v2
|
2021-06-18
|
Global existence and asymptotic behavior for semilinear damped wave equations on measure spaces
|
This paper is concerned with the semilinear damped wave equation on a measure
space with a self-adjoint operator, instead of the standard Laplace operator.
Under a certain decay estimate on the corresponding heat semigroup, we
establish the linear estimates which generalize the so-called Matsumura
estimates, and prove the small data global existence of solutions to the damped
wave equation based on the linear estimates. Our approach is based on a direct
spectral analysis analogous to the Fourier analysis. The self-adjoint operators
treated in this paper include some important examples such as the Laplace
operators on Euclidean spaces, the Dirichlet Laplacian on an arbitrary open
set, the Robin Laplacian on an exterior domain, the Schr\"odinger operator, the
elliptic operator, the Laplacian on Sierpinski gasket, and the fractional
Laplacian.
|
2106.10322v3
|
2021-06-21
|
On the small time asymptotics of stochastic Ladyzhenskaya-Smagorinsky equations with damping perturbed by multiplicative noise
|
The Ladyzhenskaya-Smagorinsky equations model turbulence phenomena, and are
given by $$\frac{\partial \boldsymbol{u}}{\partial t}-\mu
\mathrm{div}\left(\left(1+|\nabla\boldsymbol{u}|^2\right)^{\frac{p-2}{2}}\nabla\boldsymbol{u}\right)+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\nabla
p=\boldsymbol{f}, \ \nabla\cdot\boldsymbol{u}=0,$$ for $p\geq 2,$ in a bounded
domain $\mathcal{O}\subset\mathbb{R}^d$ ($2\leq d\leq 4$). In this work, we
consider the stochastic Ladyzhenskaya-Smagorinsky equations with the damping
$\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-2}\boldsymbol{u},$ for $r\geq 2$
($\alpha,\beta\geq 0$), subjected to multiplicative Gaussian noise. We show the
local monotoincity ($p\geq \frac{d}{2}+1,\ r\geq 2$) as well as global
monotonicity ($p\geq 2,\ r\geq 4$) properties of the linear and nonlinear
operators, which along with an application of stochastic version of
Minty-Browder technique imply the existence of a unique pathwise strong
solution. Then, we discuss the small time asymptotics by studying the effect of
small, highly nonlinear, unbounded drifts (small time large deviation
principle) for the stochastic Ladyzhenskaya-Smagorinsky equations with damping.
|
2106.10861v1
|
2021-06-23
|
Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping
|
In this work, we approach the minimization of a continuously differentiable
convex function under linear equality constraints by a second-order dynamical
system with asymptotically vanishing damping term. The system is formulated in
terms of the augmented Lagrangian associated to the minimization problem. We
show fast convergence of the primal-dual gap, the feasibility measure, and the
objective function value along the generated trajectories. In case the
objective function has Lipschitz continuous gradient, we show that the
primal-dual trajectory asymptotically weakly converges to a primal-dual optimal
solution of the underlying minimization problem. To the best of our knowledge,
this is the first result which guarantees the convergence of the trajectory
generated by a primal-dual dynamical system with asymptotic vanishing damping.
Moreover, we will rediscover in case of the unconstrained minimization of a
convex differentiable function with Lipschitz continuous gradient all
convergence statements obtained in the literature for Nesterov's accelerated
gradient method.
|
2106.12294v1
|
2021-06-24
|
Landau damping of electron-acoustic waves due to multi-plasmon resonances
|
The linear and nonlinear theories of electron-acoustic waves (EAWs) are
studied in a partially degenerate quantum plasma with two-temperature electrons
and stationary ions. The initial equilibrium of electrons is assumed to be
given by the Fermi-Dirac distribution at finite temperature. By employing the
multi-scale asymptotic expansion technique to the one-dimensional Wigner-Moyal
and Poisson equations, it is shown that the effects of multi-plasmon resonances
lead to a modified complex Korteweg-de Vries (KdV) equation with a new nonlocal
nonlinearity. Besides giving rise to a nonlocal nonlinear term, the
wave-particle resonance also modifies the local nonlinear coupling coefficient
of the KdV equation. The latter is shown to conserve the number of particles,
however, the wave energy decays with time. A careful analysis shows that the
two-plasmon resonance is the dominant mechanism for nonlinear Landau damping of
EAWs. An approximate soliton solution of the KdV equation is also obtained, and
it is shown that the nonlinear Landau damping causes the wave amplitude to
decay slowly with time compared to the classical theory.
|
2106.12754v2
|
2021-06-28
|
Stability of a Magnetically Levitated Nanomagnet in Vacuum: Effects of Gas and Magnetization Damping
|
In the absence of dissipation a non-rotating magnetic nanoparticle can be
stably levitated in a static magnetic field as a consequence of the spin origin
of its magnetization. Here we study the effects of dissipation on the stability
of the system, considering the interaction with the background gas and the
intrinsic Gilbert damping of magnetization dynamics. At large applied magnetic
fields we identify magnetization switching induced by Gilbert damping as the
key limiting factor for stable levitation. At low applied magnetic fields and
for small particle dimensions magnetization switching is prevented due to the
strong coupling of rotation and magnetization dynamics, and the stability is
mainly limited by the gas-induced dissipation. In the latter case, high vacuum
should be sufficient to extend stable levitation over experimentally relevant
timescales. Our results demonstrate the possibility to experimentally observe
the phenomenon of quantum spin stabilized magnetic levitation.
|
2106.14858v3
|
2021-07-01
|
On behavior of solutions to a Petrovsky equation with damping and variable-exponent source
|
This paper deals with the following Petrovsky equation with damping and
nonlinear source \[u_{tt}+\Delta^2 u-M(\|\nabla u\|_2^2)\Delta u-\Delta
u_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-boundary value conditions,
where $M(s)=a+ bs^\gamma$ is a positive $C^1$ function with parameters
$a>0,~b>0,~\gamma\geq 1$, and $m(x),~p(x)$ are given measurable functions. The
upper bound of the blow-up time is derived for low initial energy using the
differential inequality technique. For $m(x)\equiv2$, in particular, the upper
bound of the blow-up time is obtained by the combination of Levine's concavity
method and some differential inequalities under high initial energy. In
addition, by making full use of the strong damping, the lower bound of the
blow-up time is discussed. Moreover, the global existence of solutions and an
energy decay estimate are presented by establishing some energy estimates and
by exploiting a key integral inequality.
|
2107.00273v2
|
2021-07-21
|
A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemes
|
There has been an increasing interest in developing efficient immersed
boundary method (IBM) based on Cartesian grids, recently in the context of
high-order methods. IBM based on volume penalization is a robust and easy to
implement method to avoid body-fitted meshes and has been recently adapted to
high order discretisations (Kou et al., 2021). This work proposes an
improvement over the classic penalty formulation for flux reconstruction high
order solvers. We include a selective frequency damping (SFD) approach
(Aakervik et al., 2006) acting only inside solid body defined through the
immersed boundary masking, to damp spurious oscillations. An encapsulated
formulation for the SFD method is implemented, which can be used as a wrapper
around an existing time-stepping code. The numerical properties have been
studied through eigensolution analysis based on the advection equation. These
studies not only show the advantages of using the SFD method as an alternative
of the traditional volume penalization, but also show the favorable properties
of combining both approaches. This new approach is then applied to the
Navier-Stokes equation to simulate steady flow past an airfoil and unsteady
flow past a circular cylinder. The advantages of the SFD method in providing
improved accuracy are reported.
|
2107.10177v1
|
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