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2021-04-15 | Flexural wave modulation and mitigation in airfoils using acoustic black holes | This study introduces a framework for the design and implementation of
acoustic black holes (ABHs) in airfoils. A generalized multi-parameter
damped-ABH generation function is mapped onto NACA series airfoils.
Representative geometries and a uniformly distributed baseline, all with the
same mass of structure and damping are fabricated using multi-material PolyJet
3D printing. Laser Doppler vibrometer measurements along the airfoil chord in
response to a broadband 0.1 - 12 kHz excitation show a decrease in trailing
edge vibrations by as much as 10 dB, a broadband 5 dB reduction across the
entire chord as well as substantial spatial and temporal modulation of flexural
waves by ABH-embedded foils. Finite element analysis (FEA) models are developed
and validated based on the measured data. Furthermore, a parametric FEA study
is performed on a set of comparable designs to elucidate the scope of
modulation achievable. These findings are applicable to trailing-edge noise
reduction, flow control, structural enhancement and energy harvesting for
airfoils. | 2104.07374v1 |
2021-04-20 | Entanglement robustness via spatial deformation of identical particle wave functions | We address the problem of entanglement protection against surrounding noise
by a procedure suitably exploiting spatial indistinguishability of identical
subsystems. To this purpose, we take two initially separated and entangled
identical qubits interacting with two independent noisy environments. Three
typical models of environments are considered: amplitude damping channel, phase
damping channel and depolarizing channel. After the interaction, we deform the
wave functions of the two qubits to make them spatially overlap before
performing spatially localized operations and classical communication (sLOCC)
and eventually computing the entanglement of the resulting state. This way, we
show that spatial indistinguishability of identical qubits can be utilized
within the sLOCC operational framework to partially recover the quantum
correlations spoiled by the environment. A general behavior emerges: the higher
the spatial indistinguishability achieved via deformation, the larger the
amount of recovered entanglement. | 2104.09714v1 |
2021-04-22 | Dissipation and fluctuations in elongated bosonic Josephson junctions | We investigate the dynamics of bosonic atoms in elongated Josephson
junctions. We find that these systems are characterized by an intrinsic
coupling between the Josephson mode of macroscopic quantum tunneling and the
sound modes. This coupling of Josephson and sound modes gives rise to a damped
and stochastic Langevin dynamics for the Josephson degree of freedom. From a
microscopic Lagrangian, we deduce and investigate the damping coefficient and
the stochastic noise, which includes thermal and quantum fluctuations. Finally,
we study the time evolution of relative-phase and population-imbalance
fluctuations of the Josephson mode and their oscillating thermalization to
equilibrium. | 2104.11259v2 |
2021-04-24 | The large-period limit for equations of discrete turbulence | We consider the damped/driven cubic NLS equation on the torus of a large
period $L$ with a small nonlinearity of size $\lambda$, a properly scaled
random forcing and dissipation. We examine its solutions under the subsequent
limit when first $\lambda\to 0$ and then $L\to \infty$. The first limit, called
the limit of discrete turbulence, is known to exist, and in this work we study
the second limit $L\to\infty$ for solutions to the equations of discrete
turbulence. Namely, we decompose the solutions to formal series in amplitude
and study the second order truncation of this series. We prove that the energy
spectrum of the truncated solutions becomes close to solutions of a
damped/driven nonlinear wave kinetic equation. Kinetic nonlinearity of the
latter is similar to that which usually appears in works on wave turbulence,
but is different from it (in particular, it is non-autonomous). Apart from
tools from analysis and stochastic analysis, our work uses two powerful results
from the number theory. | 2104.11967v2 |
2021-05-13 | Global Solutions of Three-dimensional Inviscid MHD Fluids with Velocity Damping in Horizontally Periodic Domains | The \emph{two-dimensional} (2D) existence result of global(-in-time)
solutions for the motion equations of incompressible, inviscid, non-resistive
magnetohydrodynamic (MHD) fluids with velocity damping had been established in
[Wu--Wu--Xu, SIAM J. Math. Anal. 47 (2013), 2630--2656]. This paper further
studies the existence of global solutions for the \emph{three-dimensional} (a
dimension of real world) initial-boundary value problem in a horizontally
periodic domain with finite height. Motivated by the multi-layers energy method
introduced in [Guo--Tice, Arch. Ration. Mech. Anal. 207 (2013), 459--531], we
develop a new type of two-layer energy structure to overcome the difficulty
arising from three-dimensional nonlinear terms in the MHD equations, and thus
prove the initial-boundary value problem admits a unique global solution.
Moreover the solution has the exponential decay-in-time around some rest state.
Our two-layer energy structure enjoys two features: (1) the lower-order energy
(functional) can not be controlled by the higher-order energy. (2) under the
\emph{a priori} smallness assumption of lower-order energy, we first close the
higher-order energy estimates, and then further close the lower-energy
estimates in turn. | 2105.06080v1 |
2021-05-13 | On Inhibition of Rayleigh--Taylor Instability by Horizontal Magnetic Field in an Inviscid MHD Fluid with Velocity Damping | It is still an open problem whether the inhibition phenomenon of
Rayleigh--Taylor (RT) instability by horizontal magnetic field can be
mathematically proved in a non-resistive magnetohydrodynamic (MHD) fluid in a
two-dimensional (2D) horizontal slab domain, since it had been roughly verified
by a 2D linearized motion equations in 2012 \cite{WYC}. In this paper, we find
that this inhibition phenomenon can be rigorously verified in the
inhomogeneous, incompressible, inviscid case with velocity damping. More
precisely, there exists a critical number $m_{\rm{C}}$ such that if the
strength $|m|$ of horizontal magnetic field is bigger than $m_{\rm{C}}$, then
the small perturbation solution around the magnetic RT equilibrium state is
exponentially stable in time. Our result is also the first mathematical one
based on the nonlinear motion equations for the proof of inhibition of flow
instabilities by a horizontal magnetic field in a horizontal slab domain. In
addition, we also provide a nonlinear instability result for the case $|m|\in
[0,m_{\rm{C}})$. Our instability result presents that horizontal magnetic field
can not inhibit the RT instability, if it's strength is to small. | 2105.06472v1 |
2021-05-14 | Quantum Langevin dynamics of a charged particle in a magnetic field : Response function, position-velocity and velocity autocorrelation functions | We use the Quantum Langevin equation as a starting point to study the
response function, the position-velocity correlation function and the velocity
autocorrelation function of a charged Quantum Brownian particle in the presence
of a magnetic field and linearly coupled to a heat bath via position
coordinate. We study two bath models -- the Ohmic bath model and the Drude bath
model -- and make a detailed comparison in various time-temperature regimes.
For both bath models there is a competition between the cyclotron frequency and
the viscous damping rate giving rise to a transition from an oscillatory to a
monotonic behaviour as the damping rate is increased. In the zero point
fluctuation dominated low temperature regime, non-trivial noise correlations
lead to some interesting features in this transition. We study the role of the
memory time scale which comes into play in the Drude model and study the effect
of this additional time scale. We discuss the experimental implications of our
analysis in the context of experiments in cold ions. | 2105.07036v2 |
2021-05-18 | Partially dissipative hyperbolic systems in the critical regularity setting : The multi-dimensional case | We are concerned with quasilinear symmetrizable partially dissipative
hyperbolic systems in the whole space $\mathbb{R}^d$ with $d\geq2$. Following
our recent work [10] dedicated to the one-dimensional case, we establish the
existence of global strong solutions and decay estimates in the critical
regularity setting whenever the system under consideration satisfies the
so-called (SK) (for Shizuta-Kawashima) condition. Our results in particular
apply to the compressible Euler system with damping in the velocity equation.
Compared to the papers by Kawashima and Xu [27, 28] devoted to similar issues,
our use of hybrid Besov norms with different regularity exponents in low and
high frequency enable us to pinpoint optimal smallness conditions for global
well-posedness and to get more accurate information on the qualitative
properties of the constructed solutions. A great part of our analysis relies on
the study of a Lyapunov functional in the spirit of that of Beauchard and
Zuazua in [2]. Exhibiting a damped mode with faster time decay than the whole
solution also plays a key role. | 2105.08333v1 |
2021-05-24 | Response Dynamics of Alkali Metal-Noble Gas Hybrid Trispin System | With numerical calculation of coupled Bloch equations, we have simulated the
spin dynamics of nuclear magnetic resonance gyroscope based on alkali
metal-noble gas hybrid trispin system. From the perspective of damping harmonic
oscillator, a thorough analysis of the response dynamics is demonstrated. The
simulation results shows a linear increasing response of gyroscope signal while
the noblge gas nuclear spin magnetization and alkali atomic spin lifetime
parameters are at the over damping condition. An upper limit of response is
imposed on the NMR gyroscope signal due to the inherent dynamics of the hybrid
trispin system. The results agrees with present available experimental results
and provide useful guidings for future experiments. | 2105.11124v2 |
2021-05-26 | Temperature Damping of Magneto-Intersubband Resistance Oscillations in Magnetically Entangled Subbands | Magneto-intersubband resistance oscillations (MISO) of highly mobile 2D
electrons in symmetric GaAs quantum wells with two populated subbands are
studied in magnetic fields tilted from the normal to the 2D electron layer at
different temperatures $T$. Decrease of MISO amplitude with temperature
increase is observed. At moderate tilts the temperature decrease of MISO
amplitude is consistent with decrease of Dingle factor due to reduction of
quantum electron lifetime at high temperatures. At large tilts new regime of
strong MISO suppression with the temperature is observed. Proposed model
relates this suppression to magnetic entanglement between subbands, leading to
beating in oscillating density of states. The model yields corresponding
temperature damping factor: $A_{MISO}(T)=X/\sinh(X)$, where $X=2\pi^2kT\delta
f$ and $\delta f$ is difference frequency of oscillations of density of states
in two subbands. This factor is in agreement with experiment. Fermi liquid
enhancement of MISO amplitude is observed. | 2105.12263v1 |
2021-05-26 | A statistical study of propagating MHD kink waves in the quiescent corona | The Coronal Multi-channel Polarimeter (CoMP) has opened up exciting
opportunities to probe transverse MHD waves in the Sun's corona. The archive of
CoMP data is utilised to generate a catalogue of quiescent coronal loops that
can be used for studying propagating kink waves. The catalogue contains 120
loops observed between 2012-2014. This catalogue is further used to undertake a
statistical study of propagating kink waves in the quiet regions of the solar
corona, investigating phase speeds, loop lengths, footpoint power ratio and
equilibrium parameter values. The statistical study enables us to establish the
presence of a relationship between the rate of damping and the length of the
coronal loop, with longer coronal loops displaying weaker wave damping. We
suggest the reason for this behaviour is related to a decreasing average
density contrast between the loop and ambient plasma as loop length increases.
The catalogue presented here will provide the community with the foundation for
the further study of propagating kink waves in the quiet solar corona. | 2105.12451v1 |
2021-05-31 | Machine-Learning Non-Conservative Dynamics for New-Physics Detection | Energy conservation is a basic physics principle, the breakdown of which
often implies new physics. This paper presents a method for data-driven "new
physics" discovery. Specifically, given a trajectory governed by unknown
forces, our Neural New-Physics Detector (NNPhD) aims to detect new physics by
decomposing the force field into conservative and non-conservative components,
which are represented by a Lagrangian Neural Network (LNN) and a universal
approximator network (UAN), respectively, trained to minimize the force
recovery error plus a constant $\lambda$ times the magnitude of the predicted
non-conservative force. We show that a phase transition occurs at $\lambda$=1,
universally for arbitrary forces. We demonstrate that NNPhD successfully
discovers new physics in toy numerical experiments, rediscovering friction
(1493) from a damped double pendulum, Neptune from Uranus' orbit (1846) and
gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD
coupled with an integrator outperforms previous methods for predicting the
future of a damped double pendulum. | 2106.00026v2 |
2021-06-06 | Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation | We consider a singular limit problem from the damped wave equation with a
power type nonlinearity to the corresponding heat equation. We call our
singular limit problem non-delay limit. Our proofs are based on the argument
for non-relativistic limit from the nonlinear Klein-Gordon equation to the
nonlinear Schr\"{o}dinger equation by the second author, Nakanishi, and Ozawa
(2002), Nakanishi (2002), and Masmoudi and Nakanishi (2002). We can obtain
better results for the non-delay limit problem than that for the
non-relativistic limit problem due to the dissipation property. More precisely,
we get the better convergence rate of the $L^2$-norm and we also obtain the
global-in-time uniform convergence of the non-delay limit in the
$L^2$-supercritical case. | 2106.03030v1 |
2021-06-10 | Symmetrical emergence of extreme events at multiple regions in a damped and driven velocity-dependent mechanical system | In this work, we report the emergence of extreme events in a damped and
driven velocity-dependent mechanical system. We observe that the extreme events
emerge at multiple points. We further notice that the extreme events occur
symmetrically in both positive and negative values at all the points of
emergence. We statistically confirm the emergence of extreme events by plotting
the probability distribution function of peaks and interevent intervals. We
also determine the mechanism behind the emergence of extreme events at all the
points and classify these points into two categories depending on the region at
which the extreme events emerge. Finally, we plot the two parameter diagram in
order to have a complete overview of the system. | 2106.05510v2 |
2021-06-11 | On global existence for semilinear wave equations with spacedependent critical damping | The global existence for semilinear wave equations with space-dependent
critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in
an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are
in mind. Existence and non-existence of global-in-time solutions are discussed.
To obtain global existence, a weighted energy estimate for the linear problem
is crucial. The proof of such a weighted energy estimate contains an
alternative proof of energy estimates established by
Ikehata--Todorova--Yordanov [J.\ Math.\ Soc.\ Japan (2013), 183--236] but this
clarifies the precise independence of the location of the support of initial
data. The blowup phenomena is verified by using a test function method with
positive harmonic functions satisfying the Dirichlet boundary condition. | 2106.06107v1 |
2021-06-13 | Invariant measures for a stochastic nonlinear and damped 2D Schrödinger equation | We consider a stochastic nonlinear defocusing Schr\"{o}dinger equation with
zero-order linear damping, where the stochastic forcing term is given by a
combination of a linear multiplicative noise in the Stratonovich form and a
nonlinear noise in the It\^o form. We work at the same time on compact
Riemannian manifolds without boundary and on relatively compact smooth domains
with either the Dirichlet or the Neumann boundary conditions, always in
dimension 2. We construct a martingale solution using a modified
Faedo-Galerkin's method, following arXiv:1707.05610. Then by means of the
Strichartz estimates deduced from arXiv:math/0609455 but modified for our
stochastic setting we show the pathwise uniqueness of solutions. Finally, we
prove the existence of an invariant measure by means of a version of the
Krylov-Bogoliubov method, which involves the weak topology, as proposed by
Maslowski and Seidler. This is the first result of this type for stochastic NLS
on compact Riemannian manifolds without boundary and on relatively compact
smooth domains even for an additive noise. Some remarks on the uniqueness in a
particular case are provided as well. | 2106.07043v4 |
2021-06-13 | Blow-up and lifespan estimates for solutions to the weakly coupled system of nonlinear damped wave equations outside a ball | In this paper, we consider the initial-boundary value problems with several
fundamental boundary conditions (the Dirichlet/Neumann/Robin boundary
condition) for the multi-component system of semi-linear classical damped wave
equations outside a ball. By applying a test function approach with a judicious
choice of test functions, which approximates the harmonic functions being
subject to these boundary conditions on $\partial \Omega$, simultaneously we
have succeeded in proving the blow-up result in a finite time as well as in
catching the sharp upper bound of lifespan estimates for small solutions in two
and higher spatial dimensions. Moreover, such kind of these results will be
discussed in one-dimensional case at the end of this work. | 2106.07050v2 |
2021-06-14 | An Overview of Energy-Optimal Impedance Control of Cooperative Robot Manipulators | An impedance-based control scheme is introduced for cooperative manipulators
grasping a rigid load. The position and orientation of the load are to be
maintained close to a desired trajectory, trading off tracking accuracy by low
energy consumption and maintaining stability. To this end, the augmented
dynamics of the robots, their actuators and the load is formed, and an
impedance control is adopted. A virtual control strategy is used to decouple
torque control from actuator control. An optimization problem is then
formulated using energy balance equations. The optimization finds the damping
and stiffness gains of the impedance relation such that the energy consumption
is minimized. Furthermore, L2 stability techniques are used to allow for
time-varying damping and stiffness in the desired impedance. A numerical
example is provided to demonstrate the results. | 2106.07491v1 |
2021-06-17 | Adaptive Low-Rank Regularization with Damping Sequences to Restrict Lazy Weights in Deep Networks | Overfitting is one of the critical problems in deep neural networks. Many
regularization schemes try to prevent overfitting blindly. However, they
decrease the convergence speed of training algorithms. Adaptive regularization
schemes can solve overfitting more intelligently. They usually do not affect
the entire network weights. This paper detects a subset of the weighting layers
that cause overfitting. The overfitting recognizes by matrix and tensor
condition numbers. An adaptive regularization scheme entitled Adaptive Low-Rank
(ALR) is proposed that converges a subset of the weighting layers to their
Low-Rank Factorization (LRF). It happens by minimizing a new Tikhonov-based
loss function. ALR also encourages lazy weights to contribute to the
regularization when epochs grow up. It uses a damping sequence to increment
layer selection likelihood in the last generations. Thus before falling the
training accuracy, ALR reduces the lazy weights and regularizes the network
substantially. The experimental results show that ALR regularizes the deep
networks well with high training speed and low resource usage. | 2106.09677v1 |
2021-06-23 | Effect of different additional $L^{m}$ regularity on semi-linear damped $σ$-evolution models | The motivation of the present study is to discuss the global (in time)
existence of small data solutions to the following semi-linear structurally
damped $\sigma$-evolution models: \begin{equation*}
\partial_{tt}u+(-\Delta)^{\sigma}u+(-\Delta)^{\sigma/2}\partial_{t}u=\left|u\right|
^{p}, \ \sigma\geq 1, \ \ p>1, \end{equation*} where the Cauchy data $(u(0,x),
\partial_{t}u(0,x))$ will be chosen from energy space on the base of $L^{q}$
with different additional $L^{m}$ regularity, namely \begin{equation*}
u(0,x)\in H^{\sigma,q}(\mathbb{R}^{n})\cap L^{m_{1}}(\mathbb{R}^{n}) , \ \
\partial_{t}u(0,x)\in L^{q}(\mathbb{R}^{n})\cap L^{m_{2}}(\mathbb{R}^{n}), \ \
q\in(1,\infty),\ \ m_{1}, m_{2}\in [1,q). \end{equation*} Our new results will
show that the critical exponent which guarantees the global (in time) existence
is really affected by these different additional regularities and will take
\textit{two different values} under some restrictions on $m_{1}, m_{2}$, $q$,
$\sigma$ and the space dimension $n\geq1$. Moreover, in each case, we have no
loss of decay estimates of the unique solution with respect to the
corresponding linear models. | 2106.12286v1 |
2021-06-29 | Damping effect in innovation processes: case studies from Twitter | Understanding the innovation process, that is the underlying mechanisms
through which novelties emerge, diffuse and trigger further novelties is
undoubtedly of fundamental importance in many areas (biology, linguistics,
social science and others). The models introduced so far satisfy the Heaps'
law, regarding the rate at which novelties appear, and the Zipf's law, that
states a power law behavior for the frequency distribution of the elements.
However, there are empirical cases far from showing a pure power law behavior
and such a deviation is present for elements with high frequencies. We explain
this phenomenon by means of a suitable "damping" effect in the probability of a
repetition of an old element. While the proposed model is extremely general and
may be also employed in other contexts, it has been tested on some Twitter data
sets and demonstrated great performances with respect to Heaps' law and, above
all, with respect to the fitting of the frequency-rank plots for low and high
frequencies. | 2106.15528v1 |
2021-07-01 | Local available quantum correlations of X states: The symmetric and anti-symmetric cases | Local available quantum correlations (LAQC), as defined by Mundarain et al.,
are analyzed for 2-qubit X states with local Bloch vectors of equal magnitude.
Symmetric X-states are invariant under the exchange of subsystems, hence having
the same {local} Bloch vector. On the other hand, anti-symmetric X states have
{local} Bloch vectors with an equal magnitude but opposite direction
{(anti-parallel)}. In both cases, we obtain exact analytical expressions for
their LAQC quantifier. We present some examples and compare this quantum
correlation to concurrence and quantum discord. We have also included Markovian
decoherence, with Werner states under amplitude damping decoherence. As is the
case for depolarization and phase damping, no sudden death behavior occurs for
the LAQC of these states with this quantum channel. | 2107.00158v3 |
2021-07-06 | Dynamical System Parameter Identification using Deep Recurrent Cell Networks | In this paper, we investigate the parameter identification problem in
dynamical systems through a deep learning approach. Focusing mainly on
second-order, linear time-invariant dynamical systems, the topic of damping
factor identification is studied. By utilizing a six-layer deep neural network
with different recurrent cells, namely GRUs, LSTMs or BiLSTMs; and by feeding
input-output sequence pairs captured from a dynamical system simulator, we
search for an effective deep recurrent architecture in order to resolve damping
factor identification problem. Our study results show that, although previously
not utilized for this task in the literature, bidirectional gated recurrent
cells (BiLSTMs) provide better parameter identification results when compared
to unidirectional gated recurrent memory cells such as GRUs and LSTM. Thus,
indicating that an input-output sequence pair of finite length, collected from
a dynamical system and when observed anachronistically, may carry information
in both time directions for prediction of a dynamical systems parameter. | 2107.02427v1 |
2021-07-14 | Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering | The mechanism of the pseudogap observed in hole-doped cuprates remains one of
the central puzzles in condensed matter physics. We analyze this phenomenon via
a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures
the pivotal interplay between Mott localization and Fermi surface topology
beyond weak-coupling spin fluctuations, which would open a spectral gap near
hot spots. We show that strong coupling and particle-hole asymmetry trigger a
very different mechanism: a large imaginary part of the spin-fermion vertex
promotes damping of antinodal fermions and, at the same time, protects the
nodal Fermi arcs (antidamping). Our analysis naturally explains puzzling
features of the pseudogap observed in experiments, such as Fermi arcs being cut
off at the antiferromagnetic zone boundary and the subordinate role of hot
spots. | 2107.06529v2 |
2021-07-17 | Blow--up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources | The aim of this paper is to give global nonexistence and blow--up results for
the problem $$ \begin{cases} u_{tt}-\Delta u+P(x,u_t)=f(x,u) \qquad &\text{in
$(0,\infty)\times\Omega$,}\\ u=0 &\text{on $(0,\infty)\times \Gamma_0$,}\\
u_{tt}+\partial_\nu u-\Delta_\Gamma u+Q(x,u_t)=g(x,u)\qquad &\text{on
$(0,\infty)\times \Gamma_1$,}\\ u(0,x)=u_0(x),\quad u_t(0,x)=u_1(x) &
\text{in $\overline{\Omega}$,} \end{cases}$$ where $\Omega$ is a bounded open
$C^1$ subset of $\mathbb{R}^N$, $N\ge 2$, $\Gamma=\partial\Omega$,
$(\Gamma_0,\Gamma_1)$ is a partition of $\Gamma$, $\Gamma_1\not=\emptyset$
being relatively open in $\Gamma$, $\Delta_\Gamma$ denotes the
Laplace--Beltrami operator on $\Gamma$, $\nu$ is the outward normal to
$\Omega$, and the terms $P$ and $Q$ represent nonlinear damping terms, while
$f$ and $g$ are nonlinear source terms. These results complement the analysis
of the problem given by the author in two recent papers, dealing with local and
global existence, uniqueness and well--posedness. | 2107.08213v2 |
2021-07-22 | Collisional Growth Within the Solar System's Primordial Planetesimal Disk and the Timing of the Giant Planet Instability | The large scale structure of the Solar System has been shaped by a transient
dynamical instability that may have been triggered by the interaction of the
giants planets with a massive primordial disk of icy debris. In this work, we
investigate the conditions under which this primordial disk could have
coalesced into planets using analytic and numerical calculations. In
particular, we perform numerical simulations of the Solar System's early
dynamical evolution that account for the viscous stirring and collisional
damping within the disk. We demonstrate that if collisional damping would have
been sufficient to maintain a temperate velocity dispersion, Earth mass
trans-Neptunian planets could have emerged within a timescale of 10 Myr.
Therefore, our results favor a scenario wherein the dynamical instability of
the outer Solar System began immediately upon the dissipation of the gaseous
nebula to avoid the overproduction of Earth mass planets in the outer Solar
System. | 2107.10403v1 |
2021-07-29 | $n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability | We consider position-dependent mass (PDM) Lagrangians/Hamiltonians in their
standard textbook form, where the long-standing \emph{gain-loss balance}
between the kinetic and potential energies is kept intact to allow conservation
of total energy (i.e., $L=T-V$, $H=T+V$, and $dH/dt=dE/dt=0$). Under such
standard settings, we discuss and report on $n$-dimensional PDM damped harmonic
oscillators (DHO). We use some $n$-dimensional point canonical transformation
to facilitate the linearizability of their $n$-PDM dynamical equations into
some $n$-linear DHOs' dynamical equations for constant mass setting.
Consequently, the well know exact solutions for the linear DHOs are mapped,
with ease, onto the exact solutions for PDM DHOs. A set of one-dimensional and
a set of $n$-dimensional PDM-DHO illustrative examples are reported along with
their phase-space trajectories. | 2107.14617v1 |
2021-08-02 | Interplay of periodic dynamics and noise: insights from a simple adaptive system | We study the dynamics of a simple adaptive system in the presence of noise
and periodic damping. The system is composed by two paths connecting a source
and a sink, the dynamics is governed by equations that usually describe food
search of the paradigmatic Physarum polycephalum. In this work we assume that
the two paths undergo damping whose relative strength is periodically modulated
in time and analyse the dynamics in the presence of stochastic forces
simulating Gaussian noise. We identify different responses depending on the
modulation frequency and on the noise amplitude. At frequencies smaller than
the mean dissipation rate, the system tends to switch to the path which
minimizes dissipation. Synchronous switching occurs at an optimal noise
amplitude which depends on the modulation frequency. This behaviour disappears
at larger frequencies, where the dynamics can be described by the time-averaged
equations. Here, we find metastable patterns that exhibit the features of
noise-induced resonances. | 2108.01451v3 |
2021-08-06 | Adjusting PageRank parameters and Comparing results | The effect of adjusting damping factor {\alpha} and tolerance {\tau} on
iterations needed for PageRank computation is studied here. Relative
performance of PageRank computation with L1, L2, and L{\infty} norms used as
convergence check, are also compared with six possible mean ratios. It is
observed that increasing the damping factor {\alpha} linearly increases the
iterations needed almost exponentially. On the other hand, decreasing the
tolerance {\tau} exponentially decreases the iterations needed almost
exponentially. On average, PageRank with L{\infty} norm as convergence check is
the fastest, quickly followed by L2 norm, and then L1 norm. For large graphs,
above certain tolerance {\tau} values, convergence can occur in a single
iteration. On the contrary, below certain tolerance {\tau} values, sensitivity
issues can begin to appear, causing computation to halt at maximum iteration
limit without convergence. The six mean ratios for relative performance
comparison are based on arithmetic, geometric, and harmonic mean, as well as
the order of ratio calculation. Among them GM-RATIO, geometric mean followed by
ratio calculation, is found to be most stable, followed by AM-RATIO. | 2108.02997v1 |
2021-08-06 | Magnon transport in $\mathrm{\mathbf{Y_3Fe_5O_{12}}}$/Pt nanostructures with reduced effective magnetization | For applications making use of magnonic spin currents damping effects, which
decrease the spin conductivity, have to be minimized. We here investigate the
magnon transport in an yttrium iron garnet thin film with strongly reduced
effective magnetization. We show that in a three-terminal device the effective
magnon conductivity can be increased by a factor of up to six by a current
applied to a modulator electrode, which generates damping compensation above a
threshold current. Moreover, we find a linear dependence of this threshold
current on the applied magnetic field. We can explain this behavior by the
reduced effective magnetization and the associated nearly circular
magnetization precession. | 2108.03263v1 |
2021-08-12 | On the critical exponent and sharp lifespan estimates for semilinear damped wave equations with data from Sobolev spaces of negative order | We study semilinear damped wave equations with power nonlinearity $|u|^p$ and
initial data belonging to Sobolev spaces of negative order $\dot{H}^{-\gamma}$.
In the present paper, we obtain a new critical exponent
$p=p_{\mathrm{crit}}(n,\gamma):=1+\frac{4}{n+2\gamma}$ for some
$\gamma\in(0,\frac{n}{2})$ and low dimensions in the framework of Soblev spaces
of negative order. Precisely, global (in time) existence of small data Sobolev
solutions of lower regularity is proved for $p>p_{\mathrm{crit}}(n,\gamma)$,
and blow-up of weak solutions in finite time even for small data if
$1<p<p_{\mathrm{crit}}(n,\gamma)$. Furthermore, in order to more accurately
describe the blow-up time, we investigate sharp upper bound and lower bound
estimates for the lifespan in the subcritical case. | 2108.05667v1 |
2021-08-25 | Numerical investigation of non-condensable gas effect on vapor bubble collapse | We numerically investigate the effect of non-condensable gas inside a vapor
bubble on bubble dynamics, collapse pressure and pressure impact of spherical
and aspherical bubble collapses. Free gas inside a vapor bubble has a damping
effect that can weaken the pressure wave and enhance the bubble rebound. To
estimate this effect numerically, we derive and validate a multi-component
model for vapor bubbles containing gas. For the cavitating liquid and the
non-condensable gas, we employ a homogeneous mixture model with a coupled
equation of state for all components. The cavitation model for the cavitating
liquid is a barotropic thermodynamic equilibrium model. Compressibility of all
phases is considered in order to capture the shock wave of the bubble collapse.
After validating the model with an analytical energy partitioning model,
simulations of collapsing wall-attached bubbles with different stand-off
distances are performed. The effect of the non-condensable gas on rebound and
damping of the emitted shock wave is well captured. | 2108.11297v1 |
2021-08-23 | PDM damped-driven oscillators: exact solvability, classical states crossings, and self-crossings | Within the standard Lagrangian and Hamiltonian setting, we consider a
position-dependent mass (PDM) classical particle performing a damped driven
oscillatory (DDO) motion under the influence of a conservative harmonic
oscillator force field $V\left( x\right) =\frac{1}{2}\omega ^{2}Q\left(
x\right) x^{2}$ and subjected to a Rayleigh dissipative force field
$\mathcal{R}\left( x,\dot{x}\right) =\frac{1}{2}b\,m\left( x\right)
\dot{x}^{2}$ in the presence of an external periodic (non-autonomous) force
$F\left( t\right) =F_{\circ }\,\cos \left( \Omega t\right) $. Where, the
correlation between the coordinate deformation $\sqrt{Q(x)}$ and the velocity
deformation $\sqrt{m(x)}$ is governed by a point canonical transformation
$q\left( x\right) =\int \sqrt{m\left( x\right) }dx=\sqrt{% Q\left( x\right)
}x$. Two illustrative examples are used: a non-singular PDM-DDO, and a
power-law PDM-DDO models. Classical-states $\{x(t),p(t)\}$ crossings are
analysed and reported. Yet, we observed/reported that as a classical state
$\{x_{i}(t),p_{i}(t)\}$ evolves in time it may cross itself at an earlier
and/or a latter time/s. | 2108.13924v1 |
2021-09-06 | A well-balanced oscillation-free discontinuous Galerkin method for shallow water equations | In this paper, we develop a well-balanced oscillation-free discontinuous
Galerkin (OFDG) method for solving the shallow water equations with a non-flat
bottom topography. One notable feature of the constructed scheme is the
well-balanced property, which preserves exactly the hydrostatic equilibrium
solutions up to machine error. Another feature is the non-oscillatory property,
which is very important in the numerical simulation when there exist some shock
discontinuities. To control the spurious oscillations, we construct an OFDG
method with an extra damping term to the existing well-balanced DG schemes
proposed in [Y. Xing and C.-W. Shu, CICP, 1(2006), 100-134.]. With a careful
construction of the damping term, the proposed method achieves both the
well-balanced property and non-oscillatory property simultaneously without
compromising any order of accuracy. We also present a detailed procedure for
the construction and a theoretical analysis for the preservation of the
well-balancedness property. Extensive numerical experiments including one- and
two-dimensional space demonstrate that the proposed methods possess the desired
properties without sacrificing any order of accuracy. | 2109.02193v1 |
2021-09-16 | Landau Modes are Eigenmodes of Stellar Systems in the Limit of Zero Collisions | We consider the spectrum of eigenmodes in a stellar system dominated by
gravitational forces in the limit of zero collisions. We show analytically and
numerically using the Lenard-Bernstein collision operator that the Landau
modes, which are not true eigenmodes in a strictly collisionless system (except
for the Jeans unstable mode), become part of the true eigenmode spectrum in the
limit of zero collisions. Under these conditions, the continuous spectrum of
true eigenmodes in the collisionless system, also known as the Case-van Kampen
modes, is eliminated. Furthermore, since the background distribution function
in a weakly collisional system can exhibit significant deviations from a
Maxwellian distribution function over long times, we show that the spectrum of
Landau modes can change drastically even in the presence of slight deviations
from a Maxwellian, primarily through the appearance of weakly damped modes that
may be otherwise heavily damped for a Maxwellian distribution. Our results
provide important insights for developing statistical theories to describe
thermal fluctuations in a stellar system, which are currently a subject of
great interest for N-body simulations as well as observations of gravitational
systems. | 2109.07806v2 |
2021-09-16 | Stabilization of physical systems via saturated controllers with only partial state measurements | This paper provides a constructive passivity-based control approach to solve
the set-point regulation problem for input-affine continuous nonlinear systems
while considering saturation in the inputs. As customarily in passivity-based
control, the methodology consists of two steps: energy shaping and damping
injection. In terms of applicability, the proposed controllers have two
advantages concerning other passivity-based control techniques: (i) the energy
shaping is carried out without solving partial differential equations, and (ii)
the damping injection is performed without measuring the passive output. The
proposed methodology is suitable to control a broad range of physical systems,
e.g., mechanical, electrical, and electro-mechanical systems. We illustrate the
applicability of the technique by designing controllers for systems in
different physical domains, where we validate the analytical results via
simulations and experiments. | 2109.08111v2 |
2021-09-15 | Universal relations between the quasinormal modes of neutron star and tidal deformability | Universal relations independently of the equation of state (EOS) for neutron
star matter are valuable, if they exist, for extracting the neutron star
properties, which generally depend on the EOS. In this study, we newly derive
the universal relations predicting the gravitational wave frequencies for the
fundamental ($f$), the 1st pressure ($p_1$), and the 1st spacetime ($w_1$)
modes and the damping rate for the $f$- and $w_1$-modes as a function of the
dimensionless tidal deformability. In particular, with the universal relations
for the $f$-modes one can predict the frequencies and damping rate with less
than $1\%$ accuracy for canonical neutron stars. | 2109.08145v2 |
2021-09-27 | Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations | We consider nonparametric invariant density and drift estimation for a class
of multidimensional degenerate resp. hypoelliptic diffusion processes,
so-called stochastic damping Hamiltonian systems or kinetic diffusions, under
anisotropic smoothness assumptions on the unknown functions. The analysis is
based on continuous observations of the process, and the estimators'
performance is measured in terms of the sup-norm loss. Regarding invariant
density estimation, we obtain highly nonclassical results for the rate of
convergence, which reflect the inhomogeneous variance structure of the process.
Concerning estimation of the drift vector, we suggest both non-adaptive and
fully data-driven procedures. All of the aforementioned results strongly rely
on tight uniform moment bounds for empirical processes associated to
deterministic and stochastic integrals of the investigated process, which are
also proven in this paper. | 2109.13190v3 |
2021-10-04 | Anomalous temperature dependence of phonon pumping by ferromagnetic resonance in Co/Pd multilayers with perpendicular anisotropy | We demonstrate the pumping of phonons by ferromagnetic resonance in a series
of [Co(0.8 nm)/Pd(1.5 nm)]$_n$ multilayers ($n =$ 6, 11, 15, and 20) with large
magnetostriction and perpendicular magnetic anisotropy. The effect is shown
using broadband ferromagnetic resonance over a range of temperatures (10 to 300
K), where a resonant damping enhancement is observed at frequencies
corresponding to standing wave phonons across the multilayer. The strength of
this effect is enhanced by approximately a factor of 4 at 10 K compared to room
temperature, which is anomalous in the sense that the temperature dependence of
the magnetostriction predicts an enhancement that is less than a factor of 2.
Lastly, we demonstrate that the damping enhancement is correlated with a shift
in the ferromagnetic resonance field as predicted quantitatively from linear
response theory. | 2110.01714v1 |
2021-10-05 | A BSDEs approach to pathwise uniqueness for stochastic evolution equations | We prove strong well-posedness for a class of stochastic evolution equations
in Hilbert spaces H when the drift term is Holder continuous. This class
includes examples of semilinear stochastic damped wave equations which describe
elastic systems with structural damping (for such equations even existence of
solutions in the linear case is a delicate issue) and semilinear stochastic 3D
heat equations. In the deterministic case, there are examples of non-uniqueness
in our framework. Strong (or pathwise) uniqueness is restored by means of a
suitable additive Wiener noise. The proof of uniqueness relies on the study of
related systems of infinite dimensional forward-backward SDEs (FBSDEs). This is
a different approach with respect to the well-known method based on the Ito
formula and the associated Kolmogorov equation (the so-called Zvonkin
transformation or Ito-Tanaka trick). We deal with approximating FBSDEs in which
the linear part generates a group of bounded linear operators in H; such
approximations depend on the type of SPDEs we are considering. We also prove
Lipschitz dependence of solutions from their initial conditions. | 2110.01994v2 |
2021-10-07 | Quantum speed limit for the maximum coherent state under squeezed environment | The quantum speed limit time for quantum system under squeezed environment is
studied. We consider two typical models, the damped Jaynes-Cummings model and
the dephasing model. For the damped Jaynes-Cummings model under squeezed
environment, we find that the quantum speed limit time becomes larger with the
squeezed parameter $r$ increasing and indicates symmetry about the phase
parameter value $\theta=\pi$. Meanwhile, the quantum speed limit time can also
be influenced by the coupling strength between the system and environment.
However, the quantum speed limit time for the dephasing model is determined by
the dephasing rate and the boundary of acceleration region that interacting
with vacuum reservoir can be broken when the squeezed environment parameters
are appropriately chosen. | 2110.03132v1 |
2021-10-13 | Effect of damped oscillations in the inflationary potential | We investigate the effect of damped oscillations on a nearly flat
inflationary potential and the features they produce in the power-spectrum and
bi-spectrum. We compare the model with the Planck data using Plik unbinned and
CamSpec clean likelihood and we are able to obtain noticeable improvement in
fit compared to the power-law $\Lambda$CDM model. We are able to identify three
plausible candidates each for the two likelihoods used. We find that the
best-fit to Plik and CamSpec likelihoods match closely to each other. The
improvement comes from various possible outliers at the intermediate to small
scales. We also compute the bi-spectrum for the best-fits. At all limits, the
amplitude of bi-spectrum, $f_{NL}$ is oscillatory in nature and its peak value
is determined by the amplitude and frequency of the oscillations in the
potential, as expected. We find that the bi-spectrum consistency relation
strictly holds at all scales in all the best-fit candidates. | 2110.06837v2 |
2021-10-14 | Thermalization in a Spin-Orbit coupled Bose gas by enhanced spin Coulomb drag | An important component of the structure of the atom, the effects of
spin-orbit coupling are present in many sub-fields of physics. Most of these
effects are present continuously. We present a detailed study of the dynamics
of changing the spin-orbit coupling in an ultra-cold Bose gas, coupling the
motion of the atoms to their spin. We find that the spin-orbit coupling greatly
increases the damping towards equilibrium. We interpret this damping as spin
drag, which is enhanced by spin-orbit coupling rate, scaled by a remarkable
factor of $8.9(6)$~s. We also find that spin-orbit coupling lowers the final
temperature of the Bose gas after thermalization. | 2110.07094v3 |
2021-10-15 | Superconducting dome in ferroelectric-type materials from soft mode instability | We present a minimal theory of superconductivity enhancement in
ferroelectric-type materials. Simple expressions for the optical mode
responsible for the soft mode transition are assumed. A key role is played by
the anharmonic phonon damping which is modulated by an external control
parameter (electron doping or mechanical strain) causing the appearance of the
soft mode. It is shown that the enhancement in the superconducting critical
temperature $T_{c}$ upon approaching the ferroelectric transition from either
side is due to the Stokes electron-phonon scattering processes promoted by
strong phonon damping effects. | 2110.08114v2 |
2021-10-20 | Dimensional control of tunneling two level systems in nanoelectromechanical resonators | Tunneling two level systems affect damping, noise and decoherence in a wide
range of devices, including nanoelectromechanical resonators, optomechanical
systems, and qubits. Theoretically this interaction is usually described within
the tunneling state model. The dimensions of such devices are often small
compared to the relevant phonon wavelengths at low temperatures, and extensions
of the theoretical description to reduced dimensions have been proposed, but
lack conclusive experimental verification. We have measured the intrinsic
damping and the frequency shift in magnetomotively driven aluminum
nanoelectromechanical resonators of various sizes at millikelvin temperatures.
We find good agreement of the experimental results with a model where the
tunneling two level systems couple to flexural phonons that are restricted to
one or two dimensions by geometry of the device. This model can thus be used as
an aid when optimizing the geometrical parameters of devices affected by
tunneling two level systems. | 2110.10492v1 |
2021-10-27 | Quantum oscillations in interaction-driven insulators | In recent years it has become understood that quantum oscillations of the
magnetization as a function of magnetic field, long recognized as phenomena
intrinsic to metals, can also manifest in insulating systems. Theory has shown
that in certain simple band insulators, quantum oscillations can appear with a
frequency set by the area traced by the minimum gap in momentum space, and are
suppressed for weak fields by an intrinsic "Dingle damping" factor reflecting
the size of the bandgap. Here we examine quantum oscillations of the
magnetization in excitonic and Kondo insulators, for which interactions play a
crucial role. In models of these systems, self-consistent parameters themselves
oscillate with changing magnetic field, generating additional contributions to
quantum oscillations. In the low-temperature, weak-field regime, we find that
the lowest harmonic of quantum oscillations of the magnetization are
unaffected, so that the zero-field bandgap can still be extracted by measuring
the Dingle damping factor of this harmonic. However, these contributions
dominate quantum oscillations at all higher harmonics, thereby providing a
route to measure this interaction effect. | 2110.14643v2 |
2021-11-01 | Achieving increased Phasor POD performance by introducing a Control-Input Model | In this paper, an enhancement to the well known Phasor Power Oscillation
Damper is proposed, aiming to increase its performance. Fundamental to the
functioning of this controller is the estimation of a phasor representing
oscillatory behaviour at a particular frequency in a measured signal. The
phasor is transformed to time domain and applied as a setpoint signal to a
controllable device. The contribution in this paper specifically targets the
estimation algorithm of the controller: It is found that increased estimation
accuracy and thereby enhanced damping performance can be achieved by
introducing a prediction-correction scheme for the estimator, in the form of a
Kalman Filter. The prediction of the phasor at the next step is performed based
on the control signal that is applied at the current step. This enables more
precise damping of the targeted mode.
The presented results, which are obtained from simulations on a
Single-Machine Infinite Bus system and the IEEE 39-Bus system, indicate that
the proposed enhancement improves the performance of this type of controller. | 2111.00968v2 |
2021-11-02 | Escape kinetics of self-propelled particles from a circular cavity | We numerically investigate the mean exit time of an inertial active Brownian
particle from a circular cavity with single or multiple exit windows. Our
simulation results witness distinct escape mechanisms depending upon the
relative amplitudes of the thermal length and self-propulsion length compared
to the cavity and pore sizes. For exceedingly large self-propulsion lengths,
overdamped active particles diffuse on the cavity surface, and rotational
dynamics solely governs the exit process. On the other hand, the escape
kinetics of a very weakly damped active particle is largely dictated by
bouncing effects on the cavity walls irrespective of the amplitude of
self-propulsion persistence lengths. We show that the exit rate can be
maximized for an optimal self-propulsion persistence length, which depends on
the damping strength, self-propulsion velocity, and cavity size. However, the
optimal persistence length is insensitive to the opening windows' size, number,
and arrangement. Numerical results have been interpreted analytically based on
qualitative arguments. The present analysis aims to understand the transport
controlling mechanism of active matter in confined structures. | 2111.01324v1 |
2021-11-09 | Quantum Control of the Time-Dependent Interaction between a Three-Level $Ξ$-Type Atom and a Two-Mode Field with Damping Term | The purpose of this paper is to investigate some properties through a
three-level $\Xi$-type atom interacting with a two-mode field. We test this
system in the presence of the photon assisted atomic phase damping, detuning
parameter and Kerr nonlinearity. Also, the coupling parameter modulated to be
time-dependent. The problem solution of this model is given by using the
Schr\H{o}dinger equation when the atom and the field are initially prepared in
the excited state and coherent state, respectively. We used the results to
calculate some aspects such as atomic population inversion and concurrence. The
results show that the time-dependent coupling parameter and the detuning
parameter can be considered as a quantum control parameters of the atomic
population inversion and quantum entanglement in the considered model. | 2111.05449v1 |
2021-11-10 | On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy | Orthogonal/vector approximate message-passing (AMP) is a powerful
message-passing (MP) algorithm for signal reconstruction in compressed sensing.
This paper proves the convergence of Bayes-optimal orthogonal/vector AMP in the
large system limit. The proof strategy is based on a novel long-memory (LM) MP
approach: A first step is a construction of LM-MP that is guaranteed to
converge systematically. A second step is a large-system analysis of LM-MP via
an existing framework of state evolution. A third step is to prove the
convergence of state evolution recursions for Bayes-optimal LM-MP via a new
statistical interpretation of existing LM damping. The last is an exact
reduction of the state evolution recursions for Bayes-optimal LM-MP to those
for Bayes-optimal orthogonal/vector AMP. The convergence of the state evolution
recursions for Bayes-optimal LM-MP implies that for Bayes-optimal
orthogonal/vector AMP. Numerical simulations are presented to show the
verification of state evolution results for damped orthogonal/vector AMP and a
negative aspect of LM-MP in finite-sized systems. | 2111.05522v2 |
2021-11-15 | Spectral analysis of a viscoelastic tube conveying fluid with generalised boundary conditions | We study the spectral problem associated with the equation governing the
small transverse motions of a viscoelastic tube of finite length conveying an
ideal fluid. The boundary conditions considered are of general form, accounting
for a combination of elasticity and viscous damping acting on both the slopes
and the displacements of the ends of the tube. These include many standard
boundary conditions as special cases such as the clamped, free, hinged, and
guided conditions. We derive explicit asymptotic formulae for the eigenvalues
for the case of generalised boundary conditions and specialise these results to
the clamped case and the case in which damping acts on the slopes but not on
the displacements. In particular, the dependence of the eigenvalues on the
parameters of the problem is investigated and it is found that all eigenvalues
are located in certain sectorial sets in the complex plane. | 2111.07697v5 |
2021-11-18 | Confronting cosmic ray electron and positron excesses with hybrid triplet Higgs portal dark matter | We perform a detailed study of scalar dark matter with triplet Higgs
extensions of the Standard Model in order to explain the cosmic ray electron
and positron excesses reported by AMS-02 and DAMPE. A detailed analysis of
AMS-02 positron excess reveals that for different orderings (normal, inverted
and quasi-degenerate) of neutrino mass, the hybrid triplet Higgs portal
framework is more favored with respect to the single triplet Higgs portal for
TeV scale dark matter. We also show that the resonant peak and continuous
excess in DAMPE cosmic ray data can be well explained with the hybrid triplet
Higgs portal dark matter when a dark matter sub-halo nearby is taken into
account. | 2111.09559v3 |
2021-11-30 | Damping via the hyperfine interaction of a spin-rotation mode in a two-dimensional strongly magnetized electron plasma | We address damping of a Goldstone spin-rotation mode emerging in a quantum
Hall ferromagnet due to laser pulse excitation. Recent experimental data show
that the attenuation mechanism, dephasing of the observed Kerr precession, is
apparently related not only to spatial fluctuations of the electron Land\'e
factor in the quantum well, but to a hyperfine interaction with nuclei, because
local magnetization of GaAs nuclei should also experience spatial fluctuations.
The motion of the macroscopic spin-rotation state is studied microscopically by
solving a non-stationary Schr\"odinger equation. Comparison with the previously
studied channel of transverse spin relaxation (attenuation of Kerr oscilations)
shows that relaxation via nuclei involves a longer quadratic stage of
time-dependance of the transverse spin, and, accordingly, an elongated
transition to a linear stage, so that a linear time-dependance may not be
revealed. | 2111.15433v1 |
2021-11-30 | Heating of Magnetically Dominated Plasma by Alfvén-Wave Turbulence | Magnetic energy around astrophysical compact objects can strongly dominate
over plasma rest mass. Emission observed from these systems may be fed by
dissipation of Alfv\'en wave turbulence, which cascades to small damping
scales, energizing the plasma. We use 3D kinetic simulations to investigate
this process. When the cascade is excited naturally, by colliding large-scale
Alfv\'en waves, we observe quasithermal heating with no nonthermal particle
acceleration. We also find that the particles are energized along the magnetic
field lines and so are poor producers of synchrotron radiation. At low plasma
densities, our simulations show the transition to "charge-starved" cascades,
with a distinct damping mechanism. | 2111.15578v2 |
2021-12-06 | Decay properties and asymptotic behaviors for a wave equation with general strong damping | In this paper, we study the Cauchy problem for a wave equation with general
strong damping $-\mu(|D|)\Delta u_t$ motivated by [Tao, Anal. PDE (2009)] and
[Ebert-Girardi-Reissig, Math. Ann. (2020)]. By employing energy methods in the
Fourier space and WKB analysis, we derive decay estimates for solutions under a
large class of $\mu(|D|)$. In particularly, a threshold
$\lim\nolimits_{|\xi|\to\infty}\mu(|\xi|)=\infty$ is discovered for the
regularity-loss phenomenon, where $\mu(|\xi|)$ denotes the symbol of
$\mu(|D|)$. Furthermore, we investigate different asymptotic profiles of
solution with additionally $L^1$ initial data, where some refined estimates in
the sense of enhanced decay rate and reduced regularity are found. The derived
results almost cover the known results with sufficiently small loss. | 2112.02795v1 |
2021-12-09 | UV sensitivity of Casimir energy | We quantitatively estimate the effect of the UV physics on the Casimir energy
in a five-dimensional (5D) model on $S^1/Z_2$. If the cutoff scale of the 5D
theory is not far from the compactification scale, the UV physics may affect
the low energy result. We work in the cutoff regularization scheme by
introducing two independent cutoff scales for the spatial momentum in the
non-compact space and for the Kaluza-Klein masses. The effects of the UV
physics are incorporated as a damping effect of the contributions to the vacuum
energy around the cutoff scales. We numerically calculate the Casimir energy
and evaluate the deviation from the result obtained in the zeta-function
regularization, which does not include information on the UV physics. We find
that the result well agrees with the latter for the Gaussian-type damping,
while it can deviate for the kink-type one. | 2112.04708v3 |
2021-12-11 | Landau damping in hybrid plasmonics | Landau Damping (LD) mechanism of the Localized Surface Plasmon (LSP) decay is
studied for the hybrid nanoplasmonic (metal core/dielectric shell) structures.
It is shown that LD in hybrid structures is strongly affected by permittivity
and electron effective mass in the dielectric shell in accordance with previous
observations by Kreibig, and the strength of LD can be enhanced by an order of
magnitude for some combinations of permittivity and effective mass. The
physical reason for this effect is identified as electron spillover into the
dielectric where electric field is higher than in the metal and the presence of
quasi-discrete energy levels in the dielectric. The theory indicates that the
transition absorption at the interface metal-dielectric is a dominant
contribution to LD in such hybrid structures. Thus, by judicious selection of
dielectric material and its thickness one can engineer decay rates and hot
carrier production for important applications, such as photodetection and
photochemistry. | 2112.06005v1 |
2021-12-12 | Raman and infrared studies of CdSe/CdS core/shell nanoplatelets | The vibrational spectroscopy of semiconductor nanostructures can provide
important information on their structure. In this work, experimental Raman and
infrared spectra are compared with vibrational spectra of CdSe/CdS core/shell
nanoplatelets calculated from first principles using the density functional
theory. The calculations confirm the two-mode behavior of phonon spectra of
nanostructures. An analysis of the experimental spectra reveals the absence of
modes with a high amplitude of vibrations of surface atoms, which indicates
their strong damping. Taking into account the difference in the damping of
different modes and their calculated intensities, all bands in the spectra are
unambiguously identified. It is found that the frequencies of longitudinal
optical modes in heterostructures are close to the frequencies of LO phonons in
bulk strained constituents, whereas the frequencies of transverse modes can
differ significantly from those of the corresponding TO phonons. It is shown
that an anomalous thickness dependence of CdS TO mode is due to a noticeable
surface relaxation of the outer Cd layer in the nanostructure. | 2112.06326v1 |
2021-12-20 | Long-time behavior of solutions to the M1 model with boundray effect | In this paper, we are concerned with the asymptotic behavior of solutions of
M1 model on quadrant. From this model, combined with damped compressible Euler
equations, a more general system is introduced. We show that the solutions to
the initial boundary value problem of this system globally exist and tend
time-asymptotically to the corresponding nonlinear parabolic equation governed
by the related Darcy's law. Compared with previous results on compressible
Euler equations with damping obtained by Nishihara and Yang in [24], and
Marcati, Mei and Rubino in [16], the better convergence rates are obtained. The
approach adopted is based on the technical time-weighted energy estimates
together with the Green's function method. | 2112.10392v1 |
2021-12-22 | Quantum fisher information protection of N-qubit Greenberger-Horne-Zeilinger state from decoherence | In this paper we study the protection of N-qubit Greenberger-Horne- Zeilinger
(GHZ) state and generalized N-qubit GHZ states in amplitude damping channel by
means of quantum weak measurement and flip operations. We derive the explicit
formulas of the performances of the protection scheme: average fidelity,
average probability and the average quantum fisher information (QFI). Moreover,
the analytical results for maximizing the average fidelity and probability are
obtained. We show that our scheme can effectively protect the average QFI of
phase for GHZ states and generalized GHZ states. The proposed scheme has the
merit of protecting GHZ state and the QFI of phase against heavy amplitude
damping noise. Further we show that for some generalize GHZ state, the proposed
scheme can protect the state with probability one and fidelity more than 99%. | 2112.11590v1 |
2021-12-23 | Theory of Harmonic Hall Responses of Spin-Torque Driven Antiferromagnets | Harmonic analysis is a powerful tool to characterize and quantify
current-induced torques acting on magnetic materials, but so far it remains an
open question in studying antiferromagnets. Here we formulate a general theory
of harmonic Hall responses of collinear antiferromagnets driven by
current-induced torques including both field-like and damping-like components.
By scanning a magnetic field of variable strength in three orthogonal planes,
we are able to distinguish the contributions from field-like torque,
damping-like torque, and concomitant thermal effects by analyzing the second
harmonic signals in the Hall voltage. The analytical expressions of the first
and second harmonics as functions of the magnetic field direction and strength
are confirmed by numerical simulations with good agreement. We demonstrate our
predictions in two prototype antiferromagnets, $\alpha-$Fe$_{2}$O$_{3}$ and
NiO, providing direct and general guidance to current and future experiments. | 2112.12772v2 |
2021-12-24 | Total Energy Shaping with Neural Interconnection and Damping Assignment -- Passivity Based Control | In this work we exploit the universal approximation property of Neural
Networks (NNs) to design interconnection and damping assignment (IDA)
passivity-based control (PBC) schemes for fully-actuated mechanical systems in
the port-Hamiltonian (pH) framework. To that end, we transform the IDA-PBC
method into a supervised learning problem that solves the partial differential
matching equations, and fulfills equilibrium assignment and Lyapunov stability
conditions. A main consequence of this, is that the output of the learning
algorithm has a clear control-theoretic interpretation in terms of passivity
and Lyapunov stability. The proposed control design methodology is validated
for mechanical systems of one and two degrees-of-freedom via numerical
simulations. | 2112.12999v2 |
2021-12-24 | Critical comparison of collisionless fluid models: Nonlinear simulations of parallel firehose instability | Two different fluid models for collisionless plasmas are compared. One is
based on the classical Chew-Goldberger-Low (CGL) model that includes a finite
Larmor radius (FLR) correction and the Landau closure for the longitudinal
mode. Another one takes into account the effect of cyclotron resonance in
addition to Landau resonance, which is referred to as the cyclotron resonance
closure (CRC) model. While the linear property of the parallel firehose
instability is better described by the CGL model, the electromagnetic ion
cyclotron instability driven unstable by the cyclotron resonance is reproduced
only by the CRC model. Nonlinear simulation results for the parallel firehose
instability performed with the two models are also discussed. Although the
linear and quasilinear isotropization phases are consistent with theory in both
models, long-term behaviors may be substantially different. The final state
obtained by the CRC model may be reasonably understood in terms of the marginal
stability condition. In contrast, the lack of cyclotron damping in the CGL
model makes it rather difficult to predict the long-term behavior with a simple
physical argument. This suggests that incorporating the collisionless damping
both for longitudinal and transverse modes is crucial for a nonlinear fluid
simulation model of collisionless plasmas. | 2112.13077v1 |
2022-01-04 | Second order splitting dynamics with vanishing damping for additively structured monotone inclusions | In the framework of a real Hilbert space, we address the problem of finding
the zeros of the sum of a maximally monotone operator $A$ and a cocoercive
operator $B$. We study the asymptotic behaviour of the trajectories generated
by a second order equation with vanishing damping, attached to this problem,
and governed by a time-dependent forward-backward-type operator. This is a
splitting system, as it only requires forward evaluations of $B$ and backward
evaluations of $A$. A proper tuning of the system parameters ensures the weak
convergence of the trajectories to the set of zeros of $A + B$, as well as fast
convergence of the velocities towards zero. A particular case of our system
allows to derive fast convergence rates for the problem of minimizing the sum
of a proper, convex and lower semicontinuous function and a smooth and convex
function with Lipschitz continuous gradient. We illustrate the theoretical
outcomes by numerical experiments. | 2201.01017v1 |
2022-01-15 | Some Lq(R)-norm decay estimates for two Cauchy systems of type Rao-Nakra sandwich beam with a frictional damping or an infinite memory | In this paper, we consider two systems of type Rao-Nakra sandwich beam in the
whole line R with a frictional damping or an infinite memory acting on the
Euler-Bernoulli equation. When the speeds of propagation of the two wave
equations are equal, we show that the solutions do not converge to zero when
time goes to infinity. In the reverse situation, we prove some L2(R)-norm and
L1(R)-norm decay estimates of solutions and theirs higher order derivatives
with respect to the space variable. Thanks to interpolation inequalities and
Carlson inequality, these L2(R)-norm and L1(R)-norm decay estimates lead to
similar ones in the Lq(R)-norm, for any q>1. In our both L2(R)-norm and
L1(R)-norm decay estimates, we specify the decay rates in terms of the
regularity of the initial data and the nature of the control. | 2201.05881v1 |
2022-01-24 | Pseudospectral continuation for aeroelastic stability analysis | This technical note is concerned with aeroelastic flutter problems: the
analysis of aeroelastic systems undergoing airspeed-dependent dynamic
instability. Existing continuation methods for parametric stability analysis
are based on marching along an airspeed parameter until the flutter point is
found - an approach which may waste computational effort on low-airspeed system
behavior, before a flutter point is located and characterized. Here, we
describe a pseudospectral continuation approach which instead marches outwards
from the system's flutter points, from points of instability to points of
increasing damping, allowing efficient characterization of the subcritical and
supercritical behavior of the system. This approach ties together aeroelastic
stability analysis and abstract linear algebra, and provides efficient methods
for computing practical aeroelastic stability properties - for instance, flight
envelopes based on maximum modal damping, and the location of borderline-stable
zones. | 2201.09816v1 |
2022-01-26 | Enhanced weak force sensing through atom-based coherent noise cancellation in a hybrid cavity optomechanical system | We investigate weak force-sensing based on coherent quantum noise
cancellation in a nonlinear hybrid optomechanical system. The optomechanical
cavity contains a moveable mechanical mirror, a fixed semitransparent mirror,
an ensemble of ultracold atoms, and an optical parametric amplifier (OPA).
Using the coherent quantum noise cancellation (CQNC) process, one can eliminate
the back action noise at all frequencies. Also by tuning the OPA parameters,
one can suppress the quantum shot-noise at lower frequencies than the resonant
frequency. In the CQNC scheme, the damping rate of the mechanical oscillator
matches the damping rate of the atomic ensemble, which is experimentally
achievable even for a low-frequency mechanical oscillator with a high-quality
factor. Elimination of the back action noise and suppression of the shot noise
significantly enhance force sensing and thus overcome the standard quantum
limit of weak force sensing. This hybrid scheme can play an essential role in
the realization of quantum optomechanical sensors and quantum control. | 2201.10805v1 |
2022-01-31 | Indistinguishability-enhanced entanglement recovery by spatially localized operations and classical communication | We extend a procedure exploiting spatial indistinguishability of identical
particles to recover the spoiled entanglement between two qubits interacting
with Markovian noisy environments. Here, the spatially localized operations and
classical communication (sLOCC) operational framework is used to activate the
entanglement restoration from the indistinguishable constituents. We consider
the realistic scenario where noise acts for the whole duration of the process.
Three standard types of noises are considered: a phase damping, a depolarizing,
and an amplitude damping channel. Within this general scenario, we find the
entanglement to be restored in an amount proportional to the degree of spatial
indistinguishability. These results elevate sLOCC to a practical framework for
accessing and utilizing quantum state protection within a quantum network of
spatially indistinguishable subsystems. | 2201.13365v1 |
2022-02-01 | Uniform synchronization of an abstract linear second order evolution system | Although the mathematical study on the synchronization of wave equations at
finite horizon has been well developed, there was few results on the
synchronization of wave equations for long-time horizon. The aim of the paper
is to investigate the uniform synchronization at the infinite horizon for one
abstract linear second order evolution system in a Hilbert space.
First, using the classical compact perturbation theory on the uniform
stability of semigroups of contractions, we will establish a lower bound on the
number of damping, necessary for the uniform synchronization of the considered
system. Then, under the minimum number of damping, we clarify the algebraic
structure of the system as well as the necessity of the conditions of
compatibility on the coupling matrices. We then establish the uniform
synchronization by the compact perturbation method and then give the dynamics
of the asymptotic orbit. Various applications are given for the system of wave
equations with boundary feedback or (and) locally distributed feedback, and for
the system of Kirchhoff plate with distributed feedback. Some open questions
are raised at the end of the paper for future development.
The study is based on the synchronization theory and the compact perturbation
of semigroups. | 2202.00771v1 |
2022-02-02 | Electric field screening in pair discharges and generation of pulsar radio emission | Pulsar radio emission may be generated in pair discharges which fill the
pulsar magnetosphere with plasma as an accelerating electric field is screened
by freshly created pairs. In this Letter we develop a simplified analytic
theory for the screening of the electric field in these pair discharges and use
it to estimate total radio luminosity and spectrum. The discharge has three
stages. First, the electric field is screened for the first time and starts to
oscillate. Next, a nonlinear phase occurs. In this phase, the amplitude of the
electric field experiences strong damping because the field dramatically
changes the momenta of newly created pairs. This strong damping ceases, and the
system enters a final linear phase, when the electric field can no longer
dramatically change pair momenta. Applied to pulsars, this theory may explain
several aspects of radio emission, including the observed luminosity,
$L_{\rm{rad}} \sim 10^{28} \rm{erg} \, \rm{s}^{-1}$, and the observed spectrum,
$S_\omega \sim \omega^{-1.4 \pm 1.0} $. | 2202.01303v2 |
2022-01-22 | Dynamics of a Charged Thomas Oscillator in an External Magnetic Field | In this letter, we provide a detailed numerical examination of the dynamics
of a charged Thomas oscillator in an external magnetic field. We do so by
adopting and then modifying the cyclically symmetric Thomas oscillator to study
the dynamics of a charged particle in an external magnetic field. These
dynamical behaviours for weak and strong field strength parameters fall under
two categories; conservative and dissipative. The system shows a complex
quasi-periodic attractor whose topology depends on initial conditions for high
field strengths in the conservative regime. There is a transition from
adiabatic motion to chaos on decreasing the field strength parameter. In the
dissipative regime, the system is chaotic for weak field strength and weak
damping but shows a limit cycle for high field strengths. Such behaviour is due
to an additional negative feedback loop that comes into action at high field
strengths and forces the system dynamics to be stable in periodic oscillations.
For weak damping and weak field strength, the system dynamics mimic Brownian
motion via chaotic walks. | 2202.02383v2 |
2022-02-15 | Damped Online Newton Step for Portfolio Selection | We revisit the classic online portfolio selection problem, where at each
round a learner selects a distribution over a set of portfolios to allocate its
wealth. It is known that for this problem a logarithmic regret with respect to
Cover's loss is achievable using the Universal Portfolio Selection algorithm,
for example. However, all existing algorithms that achieve a logarithmic regret
for this problem have per-round time and space complexities that scale
polynomially with the total number of rounds, making them impractical. In this
paper, we build on the recent work by Haipeng et al. 2018 and present the first
practical online portfolio selection algorithm with a logarithmic regret and
whose per-round time and space complexities depend only logarithmically on the
horizon. Behind our approach are two key technical novelties of independent
interest. We first show that the Damped Online Newton steps can approximate
mirror descent iterates well, even when dealing with time-varying regularizers.
Second, we present a new meta-algorithm that achieves an adaptive logarithmic
regret (i.e. a logarithmic regret on any sub-interval) for mixable losses. | 2202.07574v1 |
2022-02-22 | Modal Estimation on a Warped Frequency Axis for Linear System Modeling | Linear systems such as room acoustics and string oscillations may be modeled
as the sum of mode responses, each characterized by a frequency, damping and
amplitude. Here, we consider finding the mode parameters from impulse response
measurements, and estimate the mode frequencies and decay rates as the
generalized eigenvalues of Hankel matrices of system response samples, similar
to ESPRIT. For greater resolution at low frequencies, such as desired in room
acoustics and musical instrument modeling, the estimation is done on a warped
frequency axis. The approach has the benefit of selecting the number of modes
to achieve a desired fidelity to the measured impulse response. An optimization
to further refine the frequency and damping parameters is presented. The method
is used to model coupled piano strings and room impulse responses, with its
performance comparing favorably to FZ-ARMA. | 2202.11192v1 |
2022-02-28 | Estimating the degree of non-Markovianity using variational quantum circuits | Several applications of quantum machine learning (QML) rely on a quantum
measurement followed by training algorithms using the measurement outcomes.
However, recently developed QML models, such as variational quantum circuits
(VQCs), can be implemented directly on the state of the quantum system (quantum
data). Here, we propose to use a qubit as a probe to estimate the degree of
non-Markovianity of the environment. Using VQCs, we find an optimal sequence of
qubit-environment interactions that yield accurate estimations of the degree of
non-Markovianity for the amplitude damping, phase damping, and the combination
of both models. We introduce a problem-based ansatz that optimizes upon the
probe qubit and the interaction time with the environment. This work
contributes to practical quantum applications of VQCs and delivers a feasible
experimental procedure to estimate the degree of non-Markovianity. | 2202.13964v3 |
2022-03-08 | Interplay between nonlinear spectral shift and nonlinear damping of spin waves in ultrathin YIG waveguides | We use the phase-resolved imaging to directly study the nonlinear
modification of the wavelength of spin waves propagating in 100-nm thick,
in-plane magnetized YIG waveguides. We show that, by using moderate microwave
powers, one can realize spin waves with large amplitudes corresponding to
precession angles in excess of 10 degrees and nonlinear wavelength variation of
up to 18 percent in this system. We also find that, at large precession angles,
the propagation of spin waves is strongly affected by the onset of nonlinear
damping, which results in a strong spatial dependence of the wavelength. This
effect leads to a spatially dependent controllability of the wavelength by the
microwave power. Furthermore, it leads to the saturation of nonlinear spectral
shift's effects several micrometers away from the excitation point. These
findings are important for the development of nonlinear, integrated spin-wave
signal processing devices and can be used to optimize their characteristics. | 2203.04018v1 |
2022-03-08 | The low energy excitation spectrum of magic-angle semimetals | We theoretically study the excitation spectrum of a two-dimensional Dirac
semimetal in the presence of an incommensurate potential. Such models have been
shown to possess magic-angle critical points in the single particle
wavefunctions, signalled by a momentum space delocalization of plane wave
eigenstates and flat bands due to a vanishing Dirac cone velocity. Using the
kernel polynomial method, we compute the single particle Green's function to
extract the nature of the single particle excitation energy, damping rate, and
quasiparticle residue. As a result, we are able to clearly demonstrate the
redistribution of spectral weight due to quasiperiodicity-induced downfolding
of the Brillouin zone creating minibands with effective mini Brillouin zones
that correspond to emergent superlattices. By computing the damping rate we
show that the vanishing of the velocity and generation of finite density of
states at the magic-angle transition coincides with the development of an
imaginary part in the self energy and a suppression of the quasiparticle
residue that vanishes in a power law like fashion. Observing these effects with
ultracold atoms using momentum resolved radiofrequency spectroscopy is
discussed. | 2203.04318v1 |
2022-03-09 | Nonequilibrium Hole Dynamics in Antiferromagnets: Damped Strings and Polarons | We develop a nonperturbative theory for hole dynamics in antiferromagnetic
spin lattices, as described by the $t$-$J$ model. This is achieved by
generalizing the selfconsistent Born approximation to nonequilibrium systems,
making it possible to calculate the full time-dependent many-body wave
function. Our approach reveals three distinct dynamical regimes, ultimately
leading to the formation of magnetic polarons. Following the initial ballistic
stage of the hole dynamics, coherent formation of string excitations gives rise
to characteristic oscillations in the hole density. Their damping eventually
leaves behind magnetic polarons that undergo ballistic motion with a greatly
reduced velocity. The developed theory provides a rigorous framework for
understanding nonequilibrium physics of defects in quantum magnets and
quantitatively explains recent observations from cold-atom quantum simulations
in the strong coupling regime. | 2203.04789v2 |
2022-03-10 | Dynamics of the collapse of a ferromagnetic skyrmion in a centrosymmetric lattice | Time dependence of the size and chirality of a ferromagnetic skyrmion in a
Heisenberg model with the magnetic field on a square lattice has been studied
analytically and numerically. The lattice and the magnetic field generate
strong time dependence of the skyrmion chirality. Due to nonlinearity, the
lattice alone also generates strong intrinsic damping that leads to the
skyrmion collapse via the emission of spin waves. In the absence of the
magnetic field the collapse is slow for a large skyrmion but it becomes
exponentially fast in the presence of the Landau-Lifshitz damping when the
field is turned on. Magnons emitted by a collapsing skyrmion must have a
discrete spectrum due to the quantization of the skyrmion magnetic moment. | 2203.05342v1 |
2022-03-22 | Viscous and centrifugal instabilities of massive stars | Massive stars exhibit a variety of instabilities, many of which are poorly
understood. We explore instabilities induced by centrifugal forces and angular
momentum transport in massive rotating stars. First, we derive and numerically
solve linearized oscillation equations for adiabatic radial modes in polytropic
stellar models. In the presence of differential rotation, we show that
centrifugal and Coriolis forces combined with viscous angular momentum
transport can excite stellar pulsation modes, under both low- or high-viscosity
conditions. In the low-viscosity limit, which is common in real stars, we
demonstrate how to compute mode growth/damping rates via a work integral.
Finally, we build realistic rotating $30\,M_\odot$ star models and show that
overstable (growing) radial modes are predicted to exist for most of the star's
life, in the absence of non-adiabatic effects. Peak growth rates are predicted
to occur while the star is crossing the Hertzsprung-Russell gap, though
non-adiabatic damping may dominate over viscous driving, depending on the
effective viscosity produced by convective and/or magnetic torques. Viscous
instability could be a new mechanism to drive massive star pulsations and is
possibly related to instabilities of luminous blue variable stars. | 2203.11809v1 |
2022-03-27 | Improvement on the blow-up for a weakly coupled wave equations with scale-invariant damping and mass and time derivative nonlinearity | An improvement of [18] on the blow-up region and the lifespan estimate of a
weakly coupled system of wave equations with damping and mass in the
scale-invariant case and with time-derivative nonlinearity is obtained in this
article. Indeed, thanks to a better understanding of the dynamics of the
solutions, we give here a better characterization of the blow-up region.
Furthermore, the techniques used in this article may be extended to other
systems and interestingly they simplify the proof of the blow-up result in [3]
which is concerned with the single wave equation in the same context as in the
present work. | 2203.14403v1 |
2022-03-24 | Walking droplets as a damped-driven system | We consider the dynamics of a droplet on a vibrating fluid bath. This
hydrodynamic quantum analog system is shown to elicit the canonical behavior of
damped-driven systems, including a period doubling route to chaos. By
approximating the system as a compositional map between the gain and loss
dynamics, the underlying nonlinear dynamics can be shown to be driven by energy
balances in the systems. The gain-loss iterative mapping is similar to a normal
form encoding for the pattern forming instabilities generated in such
spatially-extended system. Similar to mode-locked lasers and rotating
detonation engines, the underlying bifurcations persist for general forms of
the loss and gain, both of which admit explicit representations in our
approximation. Moreover, the resulting geometrical description of the
particle-wave interaction completely characterizes the instabilities observed
in experiments. | 2203.14705v2 |
2022-04-07 | Pseudo Numerical Ranges and Spectral Enclosures | We introduce the new concepts of pseu\-do numerical range for operator
functions and families of sesquilinear forms as well as the pseu\-do block
numerical range for $n \times n$ operator matrix functions. While these notions
are new even in the bounded case, we cover operator polynomials with unbounded
coefficients, unbounded holomorphic form families of type (a) and associated
operator families of type (B). Our main results include spectral inclusion
properties of pseudo numerical ranges and pseudo block numerical ranges. For
diagonally dominant and off-diagonally dominant operator matrices they allow us
to prove spectral enclosures in terms of the pseudo numerical ranges of Schur
complements that no longer require dominance order $0$ and not even $<1$. As an
application, we establish a new type of spectral bounds for linearly damped
wave equations with possibly unbounded and/or singular damping. | 2204.03584v1 |
2022-04-13 | Primordial Gravitational Waves Predictions for GW170817-compatible Einstein-Gauss-Bonnet Theory | In this work we shall calculate in detail the effect of an
GW170817-compatible Einstein-Gauss-Bonnet theory on the energy spectrum of the
primordial gravitational waves. The spectrum is affected by two
characteristics, the overall amplification/damping factor caused by the
GW170817-compatible Einstein-Gauss-Bonnet theory and by the tensor spectral
index and the tensor-to-scalar ratio. We shall present the formalism for
studying the inflationary dynamics and post-inflationary dynamics of
GW170817-compatible Einstein-Gauss-Bonnet theories for all redshifts starting
from the radiation era up to the dark energy era. We exemplify our formalism by
using two characteristic models, which produce viable inflationary and dark
energy eras. As we demonstrate, remarkably the overall damping/amplification
factor is of the order of unity, thus the GW170817-compatible
Einstein-Gauss-Bonnet models affect the primordial gravitational waves energy
spectrum only via their tensor spectral index and the tensor-to-scalar ratio.
Both models have a blue tilted tensor spectrum, and therefore the predicted
energy spectrum of the primordial gravity waves can be detectable by most of
the future gravitational waves experiments, for various reheating temperatures. | 2204.06304v1 |
2022-04-14 | Stability of Exponentially Damped Oscillations under Perturbations of the Mori-Chain | There is an abundance of evidence that some relaxation dynamics, e.g.,
exponential decays, are much more common in nature than others. Recently, there
have been attempts to trace this dominance back to a certain stability of the
prevalent dynamics versus generic Hamiltonian perturbations. In the paper at
hand, we tackle this stability issue from yet another angle, namely in the
framework of the recursion method. We investigate the behavior of various
relaxation dynamics with respect to alterations of the so-called Lanczos
coefficients. All considered scenarios are set up in order to comply with the
"universal operator growth hypothesis". Our numerical experiments suggest the
existence of stability in a larger class of relaxation dynamics consisting of
exponentially damped oscillations. Further, we propose a criterion to identify
"pathological" perturbations that lead to uncommon dynamics. | 2204.06903v1 |
2022-04-24 | Integrated Local Energy Decay for the Damped Wave Equation on Stationary Space-Times | We prove integrated local energy decay for the damped wave equation on
stationary, asymptotically flat space-times in (1 + 3) dimensions. Local energy
decay constitutes a powerful tool in the study of dispersive partial
differential equations on such geometric backgrounds. By utilizing the
geometric control condition to handle trapped trajectories, we are able to
recover high frequency estimates without any loss. We may then apply known
estimates from the work of Metcalfe, Sterbenz, and Tataru in the medium and low
frequency regimes in order to establish local energy decay. This generalizes
the integrated version of results established by Bouclet and Royer from the
setting of asymptotically Euclidean manifolds to the full Lorentzian case. | 2204.11339v2 |
2022-04-26 | Accelerated-gradient-based generalized Levenberg--Marquardt method with oracle complexity bound and local quadratic convergence | Minimizing the sum of a convex function and a composite function appears in
various fields. The generalized Levenberg--Marquardt (LM) method, also known as
the prox-linear method, has been developed for such optimization problems. The
method iteratively solves strongly convex subproblems with a damping term. This
study proposes a new generalized LM method for solving the problem with a
smooth composite function. The method enjoys three theoretical guarantees:
iteration complexity bound, oracle complexity bound, and local convergence
under a H\"olderian growth condition. The local convergence results include
local quadratic convergence under the quadratic growth condition; this is the
first to extend the classical result for least-squares problems to a general
smooth composite function. In addition, this is the first LM method with both
an oracle complexity bound and local quadratic convergence under standard
assumptions. These results are achieved by carefully controlling the damping
parameter and solving the subproblems by the accelerated proximal gradient
method equipped with a particular termination condition. Experimental results
show that the proposed method performs well in practice for several instances,
including classification with a neural network and nonnegative matrix
factorization. | 2204.12016v3 |
2022-05-02 | Thermoacoustic shocks in complex plasmas | The formation of thermoacoustic shocks is revealed in a fluid complex plasma.
The thermoacoustic wave mode can be damped (or anti-damped) when the
contribution from the thermoacoustic interaction is lower (or higher) than that
due to the particle collision and/or the kinematic viscosity. In the nonlinear
regime, the thermoacoustic wave, propagating with the acoustic speed, can
evolve into small amplitude shocks whose dynamics is governed by the
Bateman-Burgers equation with nonlocal nonlinearity. The latter can cause the
shock fronts to be stable (or unstable) depending on the collision frequency
remains below (or above) a critical value and the thermal feedback is positive.
The existence of different kinds of shocks and their characteristics are
analyzed with the system parameters that characterize the thermal feedback,
thermal diffusion, heat capacity per fluid particle, the particle collision and
the fluid viscosity. A good agreement between the analytical and numerical
results are also noticed. | 2205.00896v1 |
2022-05-09 | Mutual friction and diffusion of two-dimensional quantum vortices | We present a microscopic open quantum systems theory of thermally-damped
vortex motion in oblate atomic superfluids that includes previously neglected
energy-damping interactions between superfluid and thermal atoms. This
mechanism couples strongly to vortex core motion and causes dissipation of
vortex energy due to mutual friction, as well as Brownian motion of vortices
due to thermal fluctuations. We derive an analytic expression for the
dimensionless mutual friction coefficient that gives excellent quantitative
agreement with experimentally measured values, without any fitted parameters.
Our work closes an existing two orders of magnitude gap between dissipation
theory and experiments, previously bridged by fitted parameters, and provides a
microscopic origin for the mutual friction and diffusion of quantized vortices
in two-dimensional atomic superfluids. | 2205.04065v2 |
2022-05-09 | Nonlinear Landau damping for the Vlasov-Poisson system in $\R^3$: the Poisson equilibrium | We prove asymptotic stability of the Poisson homogeneous equilibrium among
solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$.
More precisely, we show that small, smooth, and localized perturbations of the
Poisson equilibrium lead to global solutions of the Vlasov-Poisson system,
which scatter to linear solutions at a polynomial rate as $t\to\infty$.
The Euclidean problem we consider here differs significantly from the
classical work on Landau damping in the periodic setting, in several ways. Most
importantly, the linearized problem cannot satisfy a "Penrose condition". As a
result, our system contains resonances (small divisors) and the electric field
is a superposition of an electrostatic component and a larger oscillatory
component, both with polynomially decaying rates. | 2205.04540v2 |
2022-05-11 | Domain wall damped harmonic oscillations induced by curvature gradients in elliptical magnetic nanowires | Understanding the domain wall (DW) dynamics in magnetic nanowires (NW) is
crucial for spintronic-based applications demanding the use of DWs as
information carriers. This work focuses on the dynamics of a DW displacing
along a bent NW with an elliptical shape under the action of spin-polarized
electric currents and external magnetic fields. Our results evidence that a
curvature gradient induces an exchange-driven effective tangential field
responsible for pinning a DW near the maximum curvature point in a NW. The DW
equilibrium position depends on the competition between the torques produced by
the external stimuli and the curvature-induced effective fields. When the
external stimuli are below a certain threshold, the DW follows a damped
harmonic oscillation around the equilibrium position. Above this threshold, DW
displaces along the NW under an oscillatory translational motion. | 2205.05716v1 |
2022-05-12 | Global existence and stability of subsonic time-periodic solution to the damped compressible Euler equations in a bounded domain | In this paper, we consider the one-dimensional isentropic compressible Euler
equations with source term $\beta(t,x)\rho|u|^{\alpha}u$ in a bounded domain,
which can be used to describe gas transmission in a nozzle.~The model is
imposed a subsonic time-periodic boundary condition.~Our main results reveal
that the time-periodic boundary can trigger an unique subsonic time-periodic
smooth solution and this unique periodic solution is stable under small
perturbations on initial and boundary data.~To get the existence of subsonic
time-periodic solution, we use the linear iterative skill and transfer the
boundary value problem into two initial value ones by using the hyperbolic
property of the system. Then the corresponding linearized system can be
decoupled.~The uniqueness is a direct by-product of the stability. There is no
small assumptions on the damping coefficient. | 2205.05858v2 |
2022-05-23 | Global existence, uniqueness and $L^{\infty}$-bound of weak solutions of fractional time-space Keller-Segel system | This paper studies the properties of weak solutions to a class of space-time
fractional parabolic-elliptic Keller-Segel equations with logistic source terms
in $\mathbb{R}^{n}$, $n\geq 2$. The global existence and $L^{\infty}$-bound of
weak solutions are established. We mainly divide the damping coefficient into
two cases: (i) $b>1-\frac{\alpha}{n}$, for any initial value and birth rate;
(ii) $0<b\leq 1-\frac{\alpha}{n}$, for small initial value and small birth
rate. The existence result is obtained by verifying the existence of a solution
to the constructed regularization equation and incorporate the generalized
compactness criterion of time fractional partial differential equation. At the
same time, we get the $L^{\infty}$-bound of weak solutions by establishing the
fractional differential inequality and using the Moser iterative method.
Furthermore, we prove the uniqueness of weak solutions by using the
hyper-contractive estimates when the damping coefficient is strong. Finally, we
also propose a blow-up criterion for weak solutions, that is, if a weak
solution blows up in finite time, then for all $h>q$, the $L^{h}$-norms of the
weak solution blow up at the same time. | 2205.11041v1 |
2022-05-23 | Schur complement dominant operator matrices | We propose a method for the spectral analysis of unbounded operator matrices
in a general setting which fully abstains from standard perturbative arguments.
Rather than requiring the matrix to act in a Hilbert space $\mathcal{H}$, we
extend its action to a suitable distributional triple $\mathcal{D} \subset
\mathcal{H} \subset \mathcal{D}_-$ and restrict it to its maximal domain in
$\mathcal{H}$. The crucial point in our approach is the choice of the spaces
$\mathcal{D}$ and $\mathcal{D}_-$ which are essentially determined by the Schur
complement of the matrix. We show spectral equivalence between the resulting
operator matrix in $\mathcal{H}$ and its Schur complement, which allows to pass
from a suitable representation of the Schur complement (e.g. by generalised
form methods) to a representation of the operator matrix. We thereby generalise
classical spectral equivalence results imposing standard dominance patterns.
The abstract results are applied to damped wave equations with possibly
unbounded and/or singular damping, to Dirac operators with Coulomb-type
potentials, as well as to generic second order matrix differential operators.
By means of our methods, previous regularity assumptions can be weakened
substantially. | 2205.11653v1 |
2022-05-24 | Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation | In this paper we extend analysis of the WaveHoltz iteration -- a time-domain
iterative method for the solution of the Helmholtz equation. We expand the
previous analysis of energy conserving problems and prove convergence of the
WaveHoltz iteration for problems with impedance boundary conditions in a single
spatial dimension. We then consider interior Dirichlet/Neumann problems with
damping in any spatial dimension, and show that for a sufficient level of
damping the WaveHoltz iteration converges in a number of iteration independent
of the frequency. Finally, we present a discrete analysis of the WaveHoltz
iteration for a family of higher order time-stepping schemes. We show that the
fixed-point of the discrete WaveHoltz iteration converges to the discrete
Helmholtz solution with the order of the time-stepper chosen. We present
numerical examples and demonstrate that it is possible to completely remove
time discretization error from the WaveHoltz solution through careful analysis
of the discrete iteration together with updated quadrature formulas. | 2205.12349v1 |
2022-05-31 | Phonon decay in 1D atomic Bose quasicondensates via Beliaev-Landau damping | In a 1D Bose gas, there is no non-trivial scattering channel involving three
Bogoliubov quasiparticles that conserves both energy and momentum.
Nevertheless, we show that such 3-wave mixing processes (Beliaev and Landau
damping) account for their decay via interactions with thermal fluctuations.
Within an appropriate time window where the Fermi Golden Rule is expected to
apply, the occupation number of the initially occupied mode decays
exponentially and the rate takes a simple analytic form. The result is shown to
compare favorably with simulations based on the Truncated Wigner Approximation.
It is also shown that the same processes slow down the exponential growth of
phonons induced by a parametric oscillation. | 2205.15826v2 |
2022-06-02 | Bistability in dissipatively coupled cavity magnonics | Dissipative coupling of resonators arising from their cooperative dampings to
a common reservoir induces intriguingly new physics such as energy level
attraction. In this study, we report the nonlinear properties in a
dissipatively coupled cavity magnonic system. A magnetic material YIG (yttrium
iron garnet) is placed at the magnetic field node of a Fabry-Perot-like
microwave cavity such that the magnons and cavity photons are dissipatively
coupled. Under high power excitation, a nonlinear effect is observed in the
transmission spectra, showing bistable behaviors. The observed bistabilities
are manifested as clockwise, counterclockwise, and butterfly-like hysteresis
loops with different frequency detuning. The experimental results are well
explained as a Duffing oscillator dissipatively coupled with a harmonic one and
the required trigger condition for bistability could be determined
quantitatively by the coupled oscillator model. Our results demonstrate that
the magnon damping has been suppressed by the dissipative interaction, which
thereby reduces the threshold for conventional magnon Kerr bistability. This
work sheds light upon potential applications in developing low power
nonlinearity devices, enhanced anharmonicity sensors and for exploring the
non-Hermitian physics of cavity magnonics in the nonlinear regime. | 2206.01231v1 |
2022-06-02 | Impact of Frequency Support by Wind Turbines on Small-Signal Stability of Power Systems | Rising wind energy integration, accompanied by a decreasing level of system
inertia, requires additional sources of ancillary services. Wind turbines based
on doubly fed induction generators (DFIG) can provide inertial and primary
frequency support, when equipped with specific controls. This paper
investigates the effect of frequency support provision by DFIGs on the
small-signal stability of power systems. To this end, a modified version of the
Kundur two-area test system is employed to analyze different scenarios. Wind
energy generation is either added to the existing system or displaces part of
the synchronous generation. Simulations show that primary frequency support
tends to improve the damping of electromechanical oscillations and deteriorate
it for converter control-based ones. On the other hand, inertial response may
be either beneficial, detrimental or negligible to damping, depending on the
tuning of control parameters. | 2206.01237v1 |
2022-06-03 | An Assessment Of Full-Wave Effects On Maxwellian Lower-Hybrid Wave Damping | Lower-hybrid current drive (LHCD) actuators are important components of
modern day fusion experiments as well as proposed fusion reactors. However,
simulations of LHCD often differ substantially from experimental results, and
from each other, especially in the inferred power deposition profile shape.
Here we investigate some possible causes of this discrepancy; "full-wave"
effects such as interference and diffraction, which are omitted from standard
raytracing simulations and the breakdown of the raytracing near reflections and
caustics. We compare raytracing simulations to state-of-the-art full-wave
simulations using matched hot-plasma dielectric tensors in realistic tokamak
scenarios for the first time. We show that differences between full-wave
simulations and raytracing in previous work were primarily due to numerical and
physical inconsistencies in the simulations, and we demonstrate that good
agreement between raytracing and converged full-wave simulations can be
obtained in reactor relevant-scenarios with large ray caustics and in
situations with weak damping. | 2206.01773v2 |
2022-06-06 | Fermi spin polaron and dissipative Fermi-polaron Rabi dynamics | We consider a spin impurity with multiple energy levels moving in a
non-interacting Fermi sea, and theoretically solve this Fermi spin polaron
problem at nonzero temperature by using a non-self-consistent many-body
$T$-matrix theory. We focus on the simplest case with spin half, where the two
energy states of the impurity are coupled by a Rabi flip term. At small Rabi
coupling, the impurity exhibits damped Rabi oscillations, where the decoherence
is caused by the interaction with the Fermi sea, as recently reported in Fermi
polaron experiments with ultracold atoms. We investigate the dependence of Rabi
oscillations on the Rabi coupling strength and examine the additional nonlinear
damping due to large Rabi coupling. At finite temperature and at nonzero
impurity concentration, the impurity can acquire a pronounced momentum
distribution. We show that the momentum/thermal average can sizably reduce the
visibility of Rabi oscillations. We compare our theoretical predictions to the
recent experimental data and find a good agreement without any adjustable
parameter. | 2206.02317v4 |
2022-06-09 | A deep learning method for the trajectory reconstruction of cosmic rays with the DAMPE mission | A deep learning method for the particle trajectory reconstruction with the
DAMPE experiment is presented. The developed algorithms constitute the first
fully machine-learned track reconstruction pipeline for space astroparticle
missions. Significant performance improvements over the standard
hand-engineered algorithms are demonstrated. Thanks to the better accuracy, the
developed algorithms facilitate the identification of the particle absolute
charge with the tracker in the entire energy range, opening a door to the
measurements of cosmic-ray proton and helium spectra at extreme energies,
towards the PeV scale, hardly achievable with the standard track reconstruction
methods. In addition, the developed approach demonstrates an unprecedented
accuracy in the particle direction reconstruction with the calorimeter at high
deposited energies, above several hundred GeV for hadronic showers and above a
few tens of GeV for electromagnetic showers. | 2206.04532v2 |
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