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2020-11-02 | On the stability of Bresse and Timoshenko systems with hyperbolic heat conduction | We investigate the stability of three thermoelastic beam systems with
hyperbolic heat conduction. First, we study the Bresse-Gurtin-Pipkin system,
providing a necessary and sufficient condition for the exponential stability
and the optimal polynomial decay rate when the condition is violated. Second,
we obtain analogous results for the Bresse-Maxwell-Cattaneo system, completing
an analysis recently initiated in the literature. Finally, we consider the
Timoshenko-Gurtin-Pipkin system and we find the optimal polynomial decay rate
when the known exponential stability condition does not hold. As a byproduct,
we fully recover the stability characterization of the
Timoshenko-Maxwell-Cattaneo system. The classical "equal wave speeds"
conditions are also recovered through singular limit procedures. Our conditions
are compatible with some physical constraints on the coefficients as the
positivity of the Poisson's ratio of the material. The analysis faces several
challenges connected with the thermal damping, whose resolution rests on
recently developed mathematical tools such as quantitative Riemann-Lebesgue
lemmas. | 2011.00994v2 |
2020-11-21 | A Trace-restricted Kronecker-Factored Approximation to Natural Gradient | Second-order optimization methods have the ability to accelerate convergence
by modifying the gradient through the curvature matrix. There have been many
attempts to use second-order optimization methods for training deep neural
networks. Inspired by diagonal approximations and factored approximations such
as Kronecker-Factored Approximate Curvature (KFAC), we propose a new
approximation to the Fisher information matrix (FIM) called Trace-restricted
Kronecker-factored Approximate Curvature (TKFAC) in this work, which can hold
the certain trace relationship between the exact and the approximate FIM. In
TKFAC, we decompose each block of the approximate FIM as a Kronecker product of
two smaller matrices and scaled by a coefficient related to trace. We
theoretically analyze TKFAC's approximation error and give an upper bound of
it. We also propose a new damping technique for TKFAC on convolutional neural
networks to maintain the superiority of second-order optimization methods
during training. Experiments show that our method has better performance
compared with several state-of-the-art algorithms on some deep network
architectures. | 2011.10741v1 |
2020-12-12 | Stabilized explicit Adams-type methods | In this work we present explicit Adams-type multistep methods with extended
stability interval, which are analogous to the stabilized Chebyshev
Runge--Kutta methods. It is proved that for any $k\geq 1$ there exists an
explicit $k$-step Adams-type method of order one with stability interval of
length $2k$. The first order methods have remarkably simple expressions for
their coefficients and error constant. A damped modification of these methods
is derived. In general case to construct a $k$-step method of order $p$ it is
necessary to solve a constrained optimization problem in which the objective
function and $p$ constraints are second degree polynomials in $k$ variables. We
calculate higher-order methods up to order six numerically and perform some
numerical experiments to confirm the accuracy and stability of the methods. | 2012.06767v1 |
2020-12-18 | Intermodal Brillouin scattering in solid-core photonic crystal fibers | We investigate intermodal forward Brillouin scattering in a solid-core PCF,
demonstrating efficient power conversion between the HE11 and HE21 modes, with
a maximum gain coefficient of 21.4/W/km. By exploring mechanical modes of
different symmetries, we observe both polarization-dependent and
polarization-independent intermodal Brillouin interaction. Finally, we discuss
the role of squeeze film air damping and leakage mechanisms, ultimately
critical to the engineering of PCF structures with enhanced interaction between
high order optical modes through flexural mechanical modes. | 2012.10007v1 |
2021-04-25 | Multiphoton resonance in a driven Kerr oscillator in presence of high-order nonlinearities | We considered the multiphoton resonance in the periodically driven quantum
oscillator with Kerr nonlinearity in the presence of weak high-order
nonlinearities. Multiphoton resonance leads to the emergence of peaks and dips
in the dependence of the stationary occupations of the stable states on
detuning. We demonstrated that due to high-order nonlinearities, these peaks
and dips acquire additional fine structure and split into several closely
spaced ones. Quasiclassically, multiphoton resonance is treated as tunneling
between the regions of the oscillator phase portrait, and the fine structure of
the multiphoton resonance is a consequence of a special quasienergy dependence
of the tunneling rate between different regions of the classical phase
portrait. For different values of damping and high-order nonlinearity
coefficients, we identified the domain of quasienergies where tunneling
strongly influences the system kinetics. The corresponding tunneling term in
the Fokker-Planck equation in quasienergy space was derived directly from the
quantum master equation. | 2104.12140v2 |
2021-04-27 | Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation | We consider the Cauchy problem for the Burgers hierarchy with general time
dependent coefficients. The closed form for the Green's function of the
corresponding linear equation of arbitrary order $N$ is shown to be a sum of
generalised hypergeometric functions. For suitably damped initial conditions we
plot the time dependence of the Cauchy problem over a range of $N$ values. For
$N=1$, we introduce a spatial forcing term. Using connections between the
associated second order linear Schr\"{o}dinger and Fokker-Planck equations, we
give closed form expressions for the corresponding Green's functions of the
sinked Bessel process with constant drift. We then apply the Green's function
to give time dependent profiles for the corresponding forced Burgers Cauchy
problem. | 2104.12976v1 |
2021-05-27 | Polarization-dependent excitons and plasmon activity in nodal-line semimetal ZrSiS | The optical properties of bulk ZrSiS nodal-line semimetal are theoretically
studied within a many-body formalism. The G0W0 bands are similar to those
calculated within the density functional theory, except near the {\Gamma}
point; in particular, no significant differences are found around the Fermi
energy. On the other hand, the solution of the Bethe-Salpeter equation reveals
a significant excitonic activity, mostly as dark excitons which appear in a
wide energy range. Bright excitons, on the contrary, are less numerous, but
their location and intensity depend greatly on the polarization of the incident
electric field, as the absorption coefficient itself does. The binding energy
of these excitons correlate well with their spatial distribution functions. In
any case, a good agreement with available experimental data for
absorption-reflection is achieved. Finally, the possible activation of plasma
oscillations at low energies is discarded, because these are damped by
producing electron-hole pairs, more importantly for q along the {\Gamma}-M
path. | 2105.13285v1 |
2021-07-07 | Growth of Aggregates with Liquid-Like Ice-Shells in Protoplanetary Discs | During the first stages of planet formation, the collision growth of dust
aggregates in protoplanetary discs (PPDs) is interrupted at the bouncing
barrier. Dust aggregates coated by different species of ice turn out to be
helpful to shift the bouncing barrier towards larger sizes due to their
enhanced sticking properties in some cases. A rarely noticed fact is that
H$_2$O- and H$_2$O-CH$_3$OH-NH$_3$-ice behave liquid-like when UV-irradiated
within a PPD-similar environment. Dust aggregates coated by these ice species
might be damped in collisions due to the liquid-like ice-shell which would
effectively results in an increase of the sticking velocity. In this work,
collisions of dust aggregates covered by the liquid-like
H$_2$O-CH$_3$OH-NH$_3$-ice-shell are considered numerically. The coefficient of
restitution and the sticking velocity are calculated for different thicknesses
of the ice-shell. The simulation predicts that an ice-shell-thickness of few
microns would be sufficient to allow the growth of cm-sized clusters in the
PPD. | 2107.03188v1 |
2021-07-08 | A Comparison of Data-Driven Techniques for Power Grid Parameter Estimation | Power grid parameter estimation involves the estimation of unknown
parameters, such as inertia and damping coefficients, using observed dynamics.
In this work, we present a comparison of data-driven algorithms for the power
grid parameter estimation problem. First, we propose a new algorithm to solve
the parameter estimation problem based on the Sparse Identification of
Nonlinear Dynamics (SINDy) approach, which uses linear regression to infer the
parameters that best describe the observed data. We then compare its
performance against two benchmark algorithms, namely, the unscented Kalman
filter (UKF) approach and the physics-informed neural networks (PINN) approach.
We perform extensive simulations on IEEE bus systems to examine the performance
of the aforementioned algorithms. Our results show that the SINDy algorithm
outperforms the PINN and UKF algorithms in being able to accurately estimate
the power grid parameters over a wide range of system parameters (including
high and low inertia systems). Moreover, it is extremely efficient
computationally and so takes significantly less time than the PINN algorithm,
thus making it suitable for real-time parameter estimation. | 2107.03762v1 |
2021-08-09 | Learning Langevin dynamics with QCD phase transition | In this proceeding, the deep Convolutional Neural Networks (CNNs) are
deployed to recognize the order of QCD phase transition and predict the
dynamical parameters in Langevin processes. To overcome the intrinsic
randomness existed in a stochastic process, we treat the final spectra as
image-type inputs which preserve sufficient spatiotemporal correlations. As a
practical example, we demonstrate this paradigm for the scalar condensation in
QCD matter near the critical point, in which the order parameter of chiral
phase transition can be characterized in a $1+1$-dimensional Langevin equation
for $\sigma$ field. The well-trained CNNs accurately classify the first-order
phase transition and crossover from $\sigma$ field configurations with
fluctuations, in which the noise does not impair the performance of the
recognition. In reconstructing the dynamics, we demonstrate it is robust to
extract the damping coefficients $\eta$ from the intricate field
configurations. | 2108.03987v1 |
2021-08-21 | Consistent SPH simulations of the anisotropic dispersion of a contaminant plume | Solute transport through heterogeneous porous media is governed by fuid
advection, molecular diffusion and anisotropic dispersion. The dispersion is
assumed to obey Fick's law and the dispersion coefficient is defined as a
second rank tensor. However, this problem has revealed to be a very difficult
one because independently of the numerical methods employed, the solutions are
seen to exhibit artificial oscillations and negative concentrations when the
dispersivity becomes anisotropic. Here we report consistent SPH simulations of
the anisotropic dispersion of a Gaussian contaminant plume in porous media
using the open source code DualSPHysics. Consistency of the SPH method is
restored by increasing the spatial resolution along with the number of
neighbours within the compact support of the interpolating kernel. The solution
shows that as the number of neighbours is increased with resolution, full
convergence of the numerical solutions is guaranteed regardless of the
dispersivity. However, despite the restored consistency, negative
concentrations, albeit at a lower level, are still present. This suggests that
a compromise between the number of neighbours and the size of the smoothing
length must be guaranteed such that sufficient implicit numerical diffusion
remains to damp out unphysical oscillations. | 2108.09488v1 |
2021-11-01 | Retesting the no-hair theorem with GW150914 | For a distorted black hole (BH), its ringdown waveform is a superposition of
quasi-normal modes (QNMs). In general relativity (GR), the lower order QNM
frequencies and damping rates can be well approximated by a polynomial of BH's
dimensionless spin and overall scaled by BH's mass. That is to say, we can test
the no-hair theorem of BH in GR model-independently by allowing not only an
overall fractional deviation (as M. Isi {\it et al.} did) but also a set of
fractional deviation for every coefficient. In the paper, we will apply the
latter method to retest the no-hair theorem with GW150914 and probe hairs'
behaviors if hairs exist. Eventually, we find the data favors GR. | 2111.00953v2 |
2021-11-17 | Global stability dynamics of the timelike extremal hypersurfaces in Minkowski space | This paper aims to study the relationship between the timelike extremal
hypersurfaces and the classical minimal surfaces. This target also gives the
long time dynamics of timelike extremal hypersurfaces in Minkowski spacetime
$\mathbb{R}^{1+M}$ with the dimension $2\leq M\leq7$. In this dimension, the
stationary solution of timelike extremal hypersurface equation is the solution
of classical minimal surface equation, which only admits the hyperplane
solution by Bernstein theorem. We prove that this hyperplane solution as the
stationary solution of timelike extremal hypersurface equation is asymptotic
stablely by finding the hidden dissipative structure of linearized equation.
Here we overcome that the vector field method (based on the energy estimate and
bootstrap argument) is lose effectiveness due to the lack of time-decay of
solution for the linear perturbation equation. Meanwhile, a global well-posed
result of linear damped wave with variable time-space coefficients is
established. Hence, our result construct a unique global timelike non-small
solution near the hyperplane. | 2111.08877v3 |
2021-11-17 | A Generalized Proportionate-Type Normalized Subband Adaptive Filter | We show that a new design criterion, i.e., the least squares on subband
errors regularized by a weighted norm, can be used to generalize the
proportionate-type normalized subband adaptive filtering (PtNSAF) framework.
The new criterion directly penalizes subband errors and includes a sparsity
penalty term which is minimized using the damped regularized Newton's method.
The impact of the proposed generalized PtNSAF (GPtNSAF) is studied for the
system identification problem via computer simulations. Specifically, we study
the effects of using different numbers of subbands and various sparsity penalty
terms for quasi-sparse, sparse, and dispersive systems. The results show that
the benefit of increasing the number of subbands is larger than promoting
sparsity of the estimated filter coefficients when the target system is
quasi-sparse or dispersive. On the other hand, for sparse target systems,
promoting sparsity becomes more important. More importantly, the two aspects
provide complementary and additive benefits to the GPtNSAF for speeding up
convergence. | 2111.08952v1 |
2021-12-07 | Complexity for Open Quantum System | We study the complexity for an open quantum system. Our system is a harmonic
oscillator coupled to a one-dimensional massless scalar field, which acts as
the bath. Specifically, we consider the reduced density matrix by tracing out
the bath degrees of freedom for both regular and inverted oscillator and
computed the complexity of purification (COP) and complexity by using the
operator-state mapping. We found that when the oscillator is regular the COP
saturates quickly for both underdamped and overdamped oscillators.
Interestingly, when the oscillator is underdamped, we discover a kink like
behaviour for the saturation value of COP with varying damping coefficient. For
the inverted oscillator, we found a linear growth of COP with time for all
values of bath-system interaction. However, when the interaction is increased
the slope of the linear growth decreases, implying that the unstable nature of
the system can be regulated by the bath. | 2112.03955v1 |
2021-12-14 | Strong coupling in a Au plasmonic antenna-SiO$_{2}$ layer system: a hybrid mode analysis | A detailed analysis of the optical response of a system accommodating several
coupled modes is needed for the complete understanding of the strong coupling
effect. In this paper, we report on the analysis of scattering cross section
spectra of Au antennas on a SiO$_{2}$ layer on a Si substrate in the IR region.
A classical model of coupled oscillators is used for determining the resonant
energies, damping rates and coupling strengths of four phonon polariton modes
in the SiO$_{2}$ layer coupled to a localized surface plasmon mode in a Au
antenna. The calculated Hopfield mixing coefficients then show the contribution
of the individual uncoupled modes to the hybrid modes of the coupled system. | 2112.07767v1 |
2021-12-22 | Dynamic structure factor of the magnetized one-component plasma: crossover from weak to strong coupling | Plasmas in strong magnetic fields have been mainly studied in two distinct
limiting cases--that of weak and strong nonideality with very different
physical properties. While the former is well described by the familiar theory
of Braginskii, the latter regime is closer to the behavior of a Coulomb liquid.
Here we study in detail the transition between both regimes. We focus on the
evolution of the dynamic structure factor of the magnetized one-component
plasma from weak to strong coupling, which is studied with first-principle
molecular dynamics simulations. The simulations show the vanishing of Bernstein
modes and the emergence of higher harmonics of the upper hybrid mode across the
magnetic field, a redistribution of spectral power between the two main
collective modes under oblique angles, and a suppression of plasmon damping
along the magnetic field. Comparison with results from various models,
including the random phase approximation, a Mermin-type dielectric function,
and the Quasi-Localized Charge Approximation show that none of the theories is
capable of reproducing the crossover that occurs when the coupling parameter is
on the order of unity. The findings are relevant to the scattering spectra,
stopping power, and transport coefficients of correlated magnetized plasmas. | 2112.11981v1 |
2021-12-29 | Stabilization results for delayed fifth order KdV-type equation in a bounded domain | Studied here is the Kawahara equation, a fifth order Korteweg-de Vries type
equation, with time-delayed internal feedback. Under suitable assumptions on
the time delay coefficients we prove that solutions of this system are
exponentially stable. First, considering a damping and delayed system, with
some restriction of the spatial length of the domain, we prove that the
Kawahara system is exponentially stable for $T> T_{\min}$. After that,
introducing a more general delayed system, and by introducing suitable
energies, we show using Lyapunov approach, that the energy of the Kawahara
equation goes to zero exponentially, considering the initial data small and a
restriction in the spatial length of the domain. To remove these hypotheses, we
use the compactness-uniqueness argument which reduces our problem to prove an
observability inequality, showing a semi-global stabilization result. | 2112.14854v1 |
2022-01-25 | Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately | Understanding natural symmetries is key to making sense of our complex and
ever-changing world. Recent work has shown that neural networks can learn such
symmetries directly from data using Hamiltonian Neural Networks (HNNs). But
HNNs struggle when trained on datasets where energy is not conserved. In this
paper, we ask whether it is possible to identify and decompose conservative and
dissipative dynamics simultaneously. We propose Dissipative Hamiltonian Neural
Networks (D-HNNs), which parameterize both a Hamiltonian and a Rayleigh
dissipation function. Taken together, they represent an implicit Helmholtz
decomposition which can separate dissipative effects such as friction from
symmetries such as conservation of energy. We train our model to decompose a
damped mass-spring system into its friction and inertial terms and then show
that this decomposition can be used to predict dynamics for unseen friction
coefficients. Then we apply our model to real world data including a large,
noisy ocean current dataset where decomposing the velocity field yields useful
scientific insights. | 2201.10085v2 |
2022-02-08 | Spin waves in spin hydrodynamics | The propagation properties of spin degrees of freedom are analyzed in the
framework of relativistic hydrodynamics with spin based on the de Groot--van
Leeuwen--van Weert definitions of the energy-momentum and spin tensors. We
derive the analytical expression for the spin wave velocity for arbitrary
statistics and show that it goes to half the speed of light in the
ultra-relativistic limit. We find that only the transverse degrees of freedom
propagate, analogously to electromagnetic waves. Finally, we consider the
effect of dissipative corrections and calculate the damping coefficients for
the case of Maxwell-J\"uttner statistics. | 2202.03952v2 |
2022-03-14 | Eliashberg theory of the Jahn-Teller-Hubbard model | We study a multiorbital Hubbard model coupled to local Jahn-Teller phonons to
investigate the superconducting state realized in fullerides. A weak-coupling
approach is employed in combination with a local self-energy approximation. In
addition to the normal and anomalous self-energies of the electrons, we
consider the phonon self-energy, which allows a self-consistent treatment of
the energetics. The frequency dependence of the self-energies and their
characteristic coefficients, such as renormalization factors and dampings, are
investigated in detail using numerical calculations. It is clarified that the
anisotropic phonons play an important role in the stabilization of the
superconducting state. By comparing the full results to those without phonon
self-energies, we show that the superconductivity is stabilized by the
softening of the phonon frequency. The effects of electronic fluctuations are
also considered, which leads to the coupling to orbitons, an analog of plasmons
in the electron gas. This additional contribution further stabilizes the
superconducting state. | 2203.06946v1 |
2022-04-20 | A theoretical framework for the Hamiltonian of angular momentum optomechanical system | Photon carries linear momentum and angular momentum simultaneously. Within
the light-matter interaction process, exchange of linear momentum results in
optical forces, whereas exchange of angular momentum leads to optical torques.
Use of optical forces (light pressure or damping) have been long and wide in
quantum optomechanics, however, those of optical torque and optical angular
momentum are not. Here we propose a theoretical framework based on optical
angular momentum and optical torques to derive the Hamiltonians of cavity
orbital and spin angular momentum optomechanical systems, respectively.
Moreover, based on the method, we successfully obtain the Hamiltonian of the
complex angular momentum optomechanical systems consisting of micro-cavity and
several torsional oscillators, whose reflection coefficients are non-unit. Our
results indicate the general applicability of our theoretical framework for the
Hamiltonian of angular momentum optomechanical systems and extend the research
scope of quantum optomechanics. | 2204.09446v2 |
2022-05-17 | Acoustic gravitational interaction revised | In this paper, we deduce the expression of the gravito-acoustic force between
two oscillating bubbles using the hypothesis that this type of force is a force
of scattering-absorption of the energy of excitatory waves. The expression of
the gravito-acoustic force at resonance highlights the dependence of this force
on the product of the virtual masses of the two bubbles and on an acoustic
gravitational constant. The acoustic gravitational constant depends on the
absorption damping coefficient. We may say also that the expression of the
acoustic gravitational constant is analogous to the expression of the
gravitational constant in the electromagnetic world, that one obtained in the
Einstein-Sciama model and the Dirac-Eddington large numbers hypothesis. The
results obtained for this type of phenomenon in the acoustic world support the
similarity between the acoustic world and the electromagnetic world. | 2206.00435v1 |
2022-06-03 | Kinetic chemotaxis tumbling kernel determined from macroscopic quantities | Chemotaxis is the physical phenomenon that bacteria adjust their motions
according to chemical stimulus. A classical model for this phenomenon is a
kinetic equation that describes the velocity jump process whose
tumbling/transition kernel uniquely determines the effect of chemical stimulus
on bacteria. The model has been shown to be an accurate model that matches with
bacteria motion qualitatively. For a quantitative modeling, biophysicists and
practitioners are also highly interested in determining the explicit value of
the tumbling kernel. Due to the experimental limitations, measurements are
typically macroscopic in nature. Do macroscopic quantities contain enough
information to recover microscopic behavior? In this paper, we give a positive
answer. We show that when given a special design of initial data, the
population density, one specific macroscopic quantity as a function of time,
contains sufficient information to recover the tumbling kernel and its
associated damping coefficient. Moreover, we can read off the chemotaxis
tumbling kernel using the values of population density directly from this
specific experimental design. This theoretical result using kinetic theory
sheds light on how practitioners may conduct experiments in laboratories. | 2206.01629v2 |
2022-06-28 | Origin of the spontaneous oscillations in a simplified coagulation-fragmentation system driven by a source | We consider a system of aggregated clusters of particles, subjected to
coagulation and fragmentation processes with mass dependent rates. Each monomer
particle can aggregate with larger clusters, and each cluster can fragment into
individual monomers with a rate directly proportional to the aggregation rate.
The dynamics of the cluster densities is governed by a set of Smoluchowski
equations, and we consider the addition of a source of monomers at constant
rate. The whole dynamics can be reduced to solving a unique non-linear
differential equation which displays self-oscillations in a specific range of
parameters, and for a number of distinct clusters in the system large enough.
This collective phenomenon is due to the presence of a fluctuating damping
coefficient and is closely related to the Li\'enard self-oscillation mechanism
observed in a more general class of physical systems such as the van der Pol
oscillator. | 2206.13884v1 |
2022-07-25 | Modelling and well-posedness of evolutionary differential variational-hemivariational inequalities | In this paper, we study the well-posedness of a class of evolutionary
variational-hemivariational inequalities coupled with a nonlinear ordinary
differential equation in Banach spaces. The proof is based on an iterative
approximation scheme showing that the problem has a unique mild solution. In
addition, we established continuity of the flow map with respect to the initial
data. Under the general framework, we consider two new applications for
modelling of frictional contact with viscoelastic materials, where the friction
coefficient $\mu$ depends on an external state variable $\alpha$ and the slip
rate $|\dot{u}_\tau|$. In the first application, we consider Coulomb friction
with normal compliance, and in the second, normal damped response. In both
cases, we present a new first-order approximation of the Dieterich
rate-and-state friction law. | 2207.12284v2 |
2022-08-05 | Giant oscillations of diffusion in ac-driven periodic systems | We revisit the problem of diffusion in a driven system consisting of an
inertial Brownian particle moving in a symmetric periodic potential and
subjected to a symmetric time-periodic force. We reveal parameter domains in
which diffusion is normal in the long time limit and exhibits intriguing giant
damped quasiperiodic oscillations as a function of the external driving
amplitude. As the mechanism behind this effect we identify the corresponding
oscillations of difference in the number of locked and running trajectories
which carries the leading contribution to the diffusion coefficient. Our
findings can be verified experimentally in a multitude of physical systems
including colloidal particles, Josephson junction or cold atoms dwelling in
optical lattices, to name only a few. | 2208.03223v2 |
2022-08-24 | Out-of-equilibrium optomechanical resonance self-excitation | The fundamental sensitivity limit of atomic force microscopy is strongly
correlated to the thermal noise of the cantilever oscillation. A method to
suppress this unwanted noise is to reduce the bandwidth of the measurement, but
this approach is limited by the speed of the measurement and the width of the
cantilever resonance, commonly defined through the quality factor Q. However,
it has been shown that optomechanical resonances in interferometers might
affect the cantilever oscillations resulting in an effective quality factor
Q$_{eff}$ . When the laser power is sufficiently increased the cantilever
oscillations might even reach the regime of self-oscillation. In this
self-oscillation state, the noise of the system is partially determined by the
interaction with the laser light far from equilibrium. Here, we show and
discuss how tuning of the laser power leads to nonlinear optomechanical effects
that can dramatically increase the effective quality factor of the cantilever
leading to out-of-equilibrium noise. We model the effects using a fourth order
nonlinearity of the damping coefficient. | 2208.11390v1 |
2022-09-19 | Stationary states of an active Brownian particle in a harmonic trap | We study the stationary states of an over-damped active Brownian particle
(ABP) in a harmonic trap in two dimensions, via mathematical calculations and
numerical simulations. In addition to translational diffusion, the ABP
self-propels with a certain velocity, whose magnitude is constant, but its
direction is subject to Brownian rotation. In the limit where translational
diffusion is negligible, the stationary distribution of the particle's position
shows a transition between two different shapes, one with maximum and the other
with minimum density at the centre, as the trap stiffness is increased. We show
that this non-intuitive behaviour is captured by the relevant Fokker-Planck
equation, which, under minimal assumptions, predicts a continuous ``phase
transition" between the two different shapes. As the translational diffusion
coefficient is increased, both these distributions converge into the
equilibrium, Boltzmann form. Our simulations support the analytical
predictions, and also show that the probability distribution of the orientation
angle of the self-propulsion velocity undergoes a transition from unimodal to
bimodal forms in this limit. We also extend our simulations to a three
dimensional trap, and find similar behaviour. | 2209.09184v2 |
2022-10-07 | Optimal Energy Shaping Control for a Backdrivable Hip Exoskeleton | Task-dependent controllers widely used in exoskeletons track predefined
trajectories, which overly constrain the volitional motion of individuals with
remnant voluntary mobility. Energy shaping, on the other hand, provides
task-invariant assistance by altering the human body's dynamic characteristics
in the closed loop. While human-exoskeleton systems are often modeled using
Euler-Lagrange equations, in our previous work we modeled the system as a
port-controlled-Hamiltonian system, and a task-invariant controller was
designed for a knee-ankle exoskeleton using interconnection-damping assignment
passivity-based control. In this paper, we extend this framework to design a
controller for a backdrivable hip exoskeleton to assist multiple tasks. A set
of basis functions that contains information of kinematics is selected and
corresponding coefficients are optimized, which allows the controller to
provide torque that fits normative human torque for different activities of
daily life. Human-subject experiments with two able-bodied subjects
demonstrated the controller's capability to reduce muscle effort across
different tasks. | 2210.03777v2 |
2022-10-18 | Nanoscale friction controlled by top layer thickness in [LaMnO$_{3}$]$_{m}$/[SrMnO$_{3}$]$_{n}$ superlattices | We conducted lateral force microscopy measurements on seven
[LaMnO$_{3}$]$_{m}$/[SrMnO$_{3}$]$_{n}$ superlattices with varied layer
thicknesses. We observe that the friction forces and the friction coefficients
initially increase with increasing LaMnO3 top layer thickness, followed by
saturation when the top layer thickness exceeds a few nanometers. These
observations clearly demonstrate that sliding friction is affected by
sub-surface material properties to a depth of several nanometers and is not
just determined by dynamics in the contact interface. We argue that the
sub-surface dissipated energy is governed by damping in the elastically
strained volume below the AFM tip, an effect which we estimate via
thermoelasticity. The absence of a correlation between friction and the thermal
resistivity of our superlattices shows furthermore that high-frequency phonons
and heat conduction do not play a role in determining friction. Our
observations thus demonstrate that friction can be tailored by sub-surface
material properties. | 2210.09677v1 |
2022-12-15 | Resonant and off-resonant magnetoacoustic waves in epitaxial Fe$_3$Si/GaAs hybrid structures | Surface acoustic waves (SAWs) provide an efficient dynamical coupling between
strain and magnetization in micro/nano-metric devices. Using a hybrid device
composed of a piezoelectric, GaAs, and a ferromagnetic Heusler alloy thin film,
Fe$_3$Si, we are able to quantify the amplitude of magnetoacoustic waves
generated with SAWs via magnetic imaging in an X-ray photoelectron microscope.
The cubic anisotropy of the sample together with a low damping coefficient
allows for the observation of resonant and non-resonant magnetoelastic
coupling. Additionally, via micromagnetic simulation, we verify the
experimental behavior and quantify the magnetoelastic shear strain component in
Fe$_3$Si that appears to be very large ($b_2=14\times 10^6$ J/m$^3$), much
larger than the one found in Nickel. | 2212.07994v1 |
2022-12-22 | State-and-rate friction in contact-line dynamics | In order to probe the dynamics of contact-line motion, we study the
macroscopic properties of sessile drops deposited on and then aspirated from
carefully prepared horizontal surfaces. By measuring the contact angle and drop
width simultaneously during droplet removal, we determine the changes in the
shape of the drop as it depins and recedes. Our data indicate that there is a
force which opposes the motion of the contact line that depends both on the
amount of time that the drop has been in contact with the surface and on the
withdrawal rate. For water on silanized glass, we capture the experimentally
observed behavior with an overdamped dynamical model of contact-line motion in
which the phenomenological drag coefficient and the assumed equilibrium contact
angle are the only inputs. For other liquid/substrate pairs, the observed
contact-line motion suggests that a maximum static friction force is important
in addition to damping. The dependence on time of contact and withdrawal rate,
reminiscent of rate-and-state friction between solid surfaces, is qualitatively
consistent across three substrate-liquid pairs. | 2212.11759v1 |
2023-02-07 | SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics | We introduce adversarial learning methods for data-driven generative modeling
of the dynamics of $n^{th}$-order stochastic systems. Our approach builds on
Generative Adversarial Networks (GANs) with generative model classes based on
stable $m$-step stochastic numerical integrators. We introduce different
formulations and training methods for learning models of stochastic dynamics
based on observation of trajectory samples. We develop approaches using
discriminators based on Maximum Mean Discrepancy (MMD), training protocols
using conditional and marginal distributions, and methods for learning dynamic
responses over different time-scales. We show how our approaches can be used
for modeling physical systems to learn force-laws, damping coefficients, and
noise-related parameters. The adversarial learning approaches provide methods
for obtaining stable generative models for dynamic tasks including long-time
prediction and developing simulations for stochastic systems. | 2302.03663v1 |
2023-02-26 | Topology optimization method with nonlinear diffusion | This paper is concerned with topology optimization based on a level set
method using (doubly) nonlinear diffusion equations. Topology optimization
using the level set method is called level set-based topology optimization,
which is possible to determine optimal configurations that minimize objective
functionals by updating level set functions. In this paper, as an update
equation for level set functions, (doubly) nonlinear diffusion equations with
reaction terms are derived, and then the singularity and degeneracy of the
diffusion coefficient are applied to obtain fast convergence of configurations
and damping oscillation on boundary structures. In particular, the reaction
terms in the proposed method do not depend on the topological derivatives, and
therefore, sensitivity analysis to determine a descent direction for objective
functionals is relaxed. Furthermore, a numerical algorithm for the proposed
method is constructed and applied to typical minimization problems to show
numerical validity. This paper is a justification and generalization of the
method using reaction-diffusion equations developed by one of the authors in
Yamada et al. (2010). | 2302.13310v1 |
2023-02-27 | Natural Gradient Hybrid Variational Inference with Application to Deep Mixed Models | Stochastic models with global parameters $\bm{\theta}$ and latent variables
$\bm{z}$ are common, and variational inference (VI) is popular for their
estimation. This paper uses a variational approximation (VA) that comprises a
Gaussian with factor covariance matrix for the marginal of $\bm{\theta}$, and
the exact conditional posterior of $\bm{z}|\bm{\theta}$. Stochastic
optimization for learning the VA only requires generation of $\bm{z}$ from its
conditional posterior, while $\bm{\theta}$ is updated using the natural
gradient, producing a hybrid VI method. We show that this is a well-defined
natural gradient optimization algorithm for the joint posterior of
$(\bm{z},\bm{\theta})$. Fast to compute expressions for the Tikhonov damped
Fisher information matrix required to compute a stable natural gradient update
are derived. We use the approach to estimate probabilistic Bayesian neural
networks with random output layer coefficients to allow for heterogeneity.
Simulations show that using the natural gradient is more efficient than using
the ordinary gradient, and that the approach is faster and more accurate than
two leading benchmark natural gradient VI methods. In a financial application
we show that accounting for industry level heterogeneity using the deep model
improves the accuracy of probabilistic prediction of asset pricing models. | 2302.13536v1 |
2023-05-03 | An identification method for oscillators with response-dependent inertia | This paper is concerned with identifying the instantaneous modal parameters
of forced oscillatory systems with response-dependent generalized inertia
(mass, inductance, or equivalent) based on their measured dynamics. An
identification method is proposed, which is a variation of the "FORCEVIB"
method. The method utilizes analytic signal representation and the properties
of the Hilbert transform to obtain an analytic relationship between a system's
natural frequency and damping coefficient to its response and excitation
signals. The proposed method is validated by comparing the identification
results to the asymptotic solution of a simple system with response-dependent
inertia and is then demonstrated, numerically and experimentally, for other
more complicated nonlinear systems. | 2305.02135v2 |
2023-05-06 | Asymptotic stability of Couette flow in a strong uniform magnetic field for the Euler-MHD system | In this paper, we prove the asymptotic stability of Couette flow in a strong
uniform magnetic field for the Euler-MHD system, when the perturbations are in
Gevrey-$\frac{1}{s}$, $(\frac12<s\leq 1)$ and of size smaller than the
resistivity coefficient $\mu$. More precisely, we prove (1) the
$\mu^{-\frac13}$-amplification of the perturbed vorticity, namely, the size of
the vorticity grows from
$\|\omega_{\mathrm{in}}\|_{\mathcal{G}^{\lambda_{0}}}\lesssim \mu$ to
$\|\omega_{\infty}\|_{\mathcal{G}^{\lambda'}}\lesssim \mu^{\frac23}$; (2) the
polynomial decay of the perturbed current density, namely,
$\left\|j_{\neq}\right\|_{L^2}\lesssim \frac{c_0 }{\langle t\rangle^2
}\min\left\{\mu^{-\frac13},\langle t \rangle\right\}$; (3) and the damping for
the perturbed velocity and magnetic field, namely, \[
\left\|(u^1_{\neq},b^1_{\neq})\right\|_{L^2}\lesssim \frac{c_0\mu }{\langle
t\rangle }\min\left\{\mu^{-\frac13},\langle t \rangle\right\}, \quad
\left\|(u^2,b^2)\right\|_{L^2}\lesssim \frac{c_0\mu }{\langle t\rangle^2
}\min\left\{\mu^{-\frac13},\langle t \rangle\right\}. \] We also confirm that
the strong uniform magnetic field stabilizes the Euler-MHD system near Couette
flow. | 2305.04052v1 |
2023-05-06 | Robust optimization of control parameters for WEC arrays using stochastic methods | This work presents a new computational optimization framework for the robust
control of parks of Wave Energy Converters (WEC) in irregular waves. The power
of WEC parks is maximized with respect to the individual control damping and
stiffness coefficients of each device. The results are robust with respect to
the incident wave direction, which is treated as a random variable.
Hydrodynamic properties are computed using the linear potential model, and the
dynamics of the system is computed in the frequency domain. A slamming
constraint is enforced to ensure that the results are physically realistic. We
show that the stochastic optimization problem is well posed. Two optimization
approaches for dealing with stochasticity are then considered: stochastic
approximation and sample average approximation. The outcomes of the above
mentioned methods in terms of accuracy and computational time are presented.
The results of the optimization for complex and realistic array configurations
of possible engineering interest are then discussed. Results of extensive
numerical experiments demonstrate the efficiency of the proposed computational
framework. | 2305.04130v2 |
2023-05-17 | Composite operators of stochastic model A | By means of the field-theoretic renormalization group, we study the damping
of the viscosity coefficient near the superfluid phase transition. We utilize
the fact that in the infrared region, the complex model used to describe the
phase transition belongs to the same universality class as the well-known
stochastic model A. This allows us a determination of the critical behavior of
viscosity using composite operators for model A. Our analysis is based on the
$\varepsilon$-expansion near the upper critical dimension $d_c = 4$ of model A.
The critical exponent of viscosity is then calculated from the critical
dimensions of composite operators of massless two-component model A. In
particular, we present results for critical dimensions of a selected class of
composite operators with the canonical dimension $8$ to the leading order. | 2305.10094v1 |
2023-05-30 | Gravitational traces of bumblebee gravity in metric-affine formalism | This work explores various manifestations of bumblebee gravity within the
metric-affine formalism. We investigate the impact of the Lorentz violation
parameter, denoted as $X$, on the modification of the Hawking temperature. Our
calculations reveal that as $X$ increases, the values of the Hawking
temperature attenuate. To examine the behavior of massless scalar
perturbations, specifically the quasinormal modes, we employ the WKB method.
The transmission and reflection coefficients are determined through our
calculations. The outcomes indicate that a stronger Lorentz-violating parameter
results in slower damping oscillations of gravitational waves. To comprehend
the influence of the quasinormal spectrum on time-dependent scattering
phenomena, we present a detailed analysis of scalar perturbations in the
time-domain solution. Additionally, we conduct an investigation on shadows,
revealing that larger values of $X$ correspond to larger shadow radii.
Furthermore, we constrain the magnitude of the shadow radii using the EHT
horizon-scale image of $Sgr A^*$. Finally, we calculate both the time delay and
the deflection angle. | 2305.18871v2 |
2023-06-22 | Global dynamics of a predator-prey model with alarm-taxis | This paper concerns with the global dynamics of classical solutions to an
important alarm-taxis ecosystem, which demonstrates the behaviors of prey that
attract secondary predator when threatened by primary predator. And the
secondary predator pursues the signal generated by the interaction of the prey
and primary predator. However, it seems that the necessary gradient estimates
for global existence cannot be obtained in critical case due to strong coupled
structure. Thereby, we develop a new approach to estimate the gradient of prey
and primary predator which takes advantage of slightly higher damping power.
Then the boundedness of classical solutions in two dimension with Neumann
boundary conditions can be established by energy estimates and semigroup
theory. Moreover, by constructing Lyapunov functional, it is proved that the
coexistence homogeneous steady states is asymptotically stability and the
convergence rate is exponential under certain assumptions on the system
coefficients. | 2306.12828v1 |
2023-07-13 | Current status and desired accuracy of the isotopic production cross-sections relevant to astrophysics of cosmic rays II. Fluorine to Silicon (and updated LiBeB) | High-precision cosmic-ray data from ongoing and recent past experiments
(Voyager, ACE-CRIS, PAMELA, ATIC, CREAM, NUCLEON, AMS-02, CALET, DAMPE) are
being released in the tens of MeV/n to multi-TeV/n energy range. Astrophysical
and dark matter interpretations of these data are limited by the precision of
nuclear production cross-sections. In Paper I, PRC 98, 034611 (2018), we set up
a procedure to rank nuclear reactions whose desired measurements will enable us
to fully exploit currently available data on CR Li to N ($Z=3-7$) species. Here
we extend these rankings to O up to Si nuclei ($Z=8-14$), also updating our
results on the LiBeB species. We also highlight how comprehensive new high
precision nuclear data, that could e.g. be obtained at the SPS at CERN, would
be a game-changer for the determination of key astrophysical quantities
(diffusion coefficient, halo size of the Galaxy) and indirect searches for dark
matter signatures. | 2307.06798v1 |
2023-08-18 | Numerical analysis of the Maxwell-Cattaneo-Vernotte nonlinear model | In the literature, one can find numerous modifications of Fourier's law from
which the first one is called Maxwell-Cattaneo-Vernotte heat equation. Although
this model has been known for decades and successfully used to model
low-temperature damped heat wave propagation, its nonlinear properties are
rarely investigated. In this paper, we aim to present the functional
relationship between the transport coefficients and the consequences of their
temperature dependence. Furthermore, we introduce a particular implicit
numerical scheme in order to solve such nonlinear heat equations reliably. We
investigate the scheme's stability, dissipation, and dispersion attributes as
well. We demonstrate the effect of temperature-dependent thermal conductivity
on two different initial-boundary value problems, including time-dependent
boundaries and heterogeneous initial conditions. | 2308.09494v1 |
2023-08-20 | On the Approximation of Operator-Valued Riccati Equations in Hilbert Spaces | In this work, we present an abstract theory for the approximation of
operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated
here, under the assumption of compactness in the coefficient operators, that
the error of the approximate solution to the operator-valued Riccati equation
is bounded above by the approximation error of the governing semigroup. One
significant outcome of this result is the correct prediction of optimal
convergence for finite element approximations of the operator-valued Riccati
equations for when the governing semigroup involves parabolic, as well as
hyperbolic processes. We derive the abstract theory for the time-dependent and
time-independent operator-valued Riccati equations in the first part of this
work. In the second part, we prove optimal convergence rates for the finite
element approximation of the functional gain associated with model
one-dimensional weakly damped wave and thermal LQR control systems. These
theoretical claims are then corroborated with computational evidence. | 2308.10130v4 |
2023-09-14 | Where are the Pevatrons that Form the Knee in the Spectrum of the Cosmic Ray Nucleon Component around 4 PeV? | The paper discusses an approach that made it possible to estimate the
distance to the nearest pevatrons, which form a knee in the spectrum of the
cosmic ray nucleon component of about $4$ PeV. It is based on the spectra of
nucleons and electrons obtained by the authors in the framework of the
superdiffusion model of nonclassical cosmic rays diffusion, which have a knee,
on the assumption that nucleons and electrons are accelerated by the same type
sources and their propagation in an inhomogeneous turbulent galactic medium is
characterized by the same diffusion coefficient, and also on the knee in the
spectrum of the electronic component in the region of $0.9$ TeV, established in
the DAMPE experiment.
It is shown that pevatrons, which form a knee in the spectrum of the cosmic
ray nucleon component of about $4$ PeV, are located at distances of the order
of $0.75$ kpc from the Earth. | 2309.07421v1 |
2023-09-25 | Magnetism on the thermal dynamics of 2D antiferromagnetic membranes | We developed a theoretical scheme of incorporating the magnetoelastic
contribution into the thermal elastic dynamics for the thin membranes of 2D
antiferromagnetic material with restricted geometry. We extended the elastic
Gr\"uneisen relation into an effective version which includes the magnetic
counterpart to the volume change of internal energy. Based on the specific heat
and thermal conductivity from the elastic and magnetic origins we predicted the
dependency of observables, such as effective Gr\"uneisen parameter, thermal
expansion coefficient, and the damping factor, with respect to a wide range of
temperature across the phase transition. Our model of analysis as been
validated by applying to the case of FePS3 flake resonator and the theoretical
predictions fits well with the reported experiment data. | 2309.13991v2 |
2023-09-27 | Stochastic Differential Equation for a System Coupled to a Thermostatic Bath via an Arbitrary Interaction Hamiltonian | The conventional Langevin equation offers a mathematically convenient
framework for investigating open stochastic systems interacting with their
environment or a bath. However, it is not suitable for a wide variety of
systems whose dynamics rely on the nature of the environmental interaction, as
the equation does not incorporate any specific information regarding that
interaction. Here, we present a universal formulation of the stochastic
differential equation (SDE) for an open system coupled to a thermostatic bath
via an arbitrary interaction Hamiltonian. This SDE encodes the interaction
information to a fictitious potential (mean force) and a position-dependent
damping coefficient. Surprisingly, we find that the conventional Langevin
equation can be recovered in the presence of arbitrary strong interactions
given two conditions: translational invariance of the potential and disjoint
separability of the bath particles. Our results provide a universal framework
for studying open stochastic systems with an arbitrary interaction Hamiltonian
and yield deeper insight into why various experiments fit the conventional
Langevin description regardless of the strength or type of interaction. | 2309.15359v1 |
2023-09-28 | A Lagrangian theory for galaxy shape statistics | We formulate the Lagrangian perturbation theory of galaxy intrinsic
alignments and compute the resulting auto and cross power spectra of galaxy
shapes, densities and matter to 1-loop order. Our model represents a consistent
effective-theory description of galaxy shape including the resummation of
long-wavelength displacements which damp baryon acoustic oscillations, and
includes one linear, three quadratic and two cubic dimensionless bias
coefficients at this order, along with counterterms and stochastic
contributions whose structure we derive. We compare this Lagrangian model
against the three-dimensional helicity spectra of halo shapes measured in
N-body simulations by Akitsu et al (2023) and find excellent agreement on
perturbative scales while testing a number of more restrictive bias
parametrizations. The calculations presented are immediately relevant to
analyses of both cosmic shear surveys and spectroscopic shape measurements, and
we make a fast FFTLog-based code spinosaurus publicly available with this
publication. | 2309.16761v2 |
2023-10-09 | Anomaly and Brownian fluid particle in Navier-Stokes turbulence | We investigate the Navier-Stokes turbulence driven by a stochastic random
Gaussian force. Using a field-theoretic approach, we uncover an anomaly that
brings hidden structure to the theory. The anomaly is generated by a
non-self-adjoint operator of the Jacobian and it follows the symmetries of the
stochastic Navier-Stokes equation. We calculate the anomaly and demonstrate
that by forcing the anomaly to vanish, the velocity field is constrained and a
monopole-type object with a constant charge is formed. When the viscosity is
zero, the anomaly can be interpreted as the Brownian damping coefficient of a
random fluid particle. We provide the Brownian particle equation and its
solution in the presence of a pump and viscosity. Our results suggest that the
anomaly is an inherent feature of stochastic turbulence and must be taken into
account in all stochastic turbulence calculations. This constitutes an
additional law for the original set of stochastic Navier-Stokes equations. | 2310.06007v3 |
2023-10-23 | Forget metamaterial: It does not improve sound absorption performance as it claims | The term `sub-wavelength' is commonly used to describe innovative
sound-absorbing structures usually labeled as `metamaterials'. Such structures,
however, inherently do not bring groundbreaking advancements. This study
addresses the limitations imposed by the thickness criterion of Yang et al. by
introducing the concept of equivalent mass-spring-damping parameters within the
resonator framework. This innovative approach introduces an index of
`half-absorption bandwidth' to effectively overcome the thickness restriction.
Four practical cases are then presented to correct prevalent misleading
conceptions about low-frequency, broadband absorption as claimed. The
phenomenon of mass disappearing in the expression of sound absorption
coefficient supports the conclusion that volume is the only determinant factor
in sound absorption performance. Any attempts to improve sound absorption
solely through geometry and structural designs would inevitably sacrifice the
half-absorption bandwidth. Additionally, the concept of negative stiffness or
bulk modulus is merely a mathematical convention without any real improvement
in absorption performance. Overall, this research focuses on the physical
mechanism of sound-absorbing structures by correcting traditional
misunderstandings, and offers a comprehensive framework for assessing and
enhancing sound absorption. | 2310.14638v1 |
2023-10-30 | Optimal control theory for maximum power of Brownian heat engines | The pursuit of achieving the maximum power in microscopic thermal engines has
gained increasing attention in recent studies of stochastic thermodynamics. We
employ the optimal control theory to study the performance of Brownian heat
engines and determine the optimal heat-engine cycles in generic damped
situation, which were previously known only in the overdamped and the
underdamped limits. These optimal cycles include two isothermal processes, two
adiabatic processes, and an extra isochoric relaxation process at the upper
stiffness constraint. Our results not only interpolate the optimal cycles
between the overdamped and the underdamped limits, but also determine the
appropriate friction coefficient of the Brownian heat engine to achieve the
maximum power. These findings offer valuable insights for the development of
high-performance Brownian heat engines in experimental setups. | 2310.19622v1 |
2023-11-15 | On the interaction between compressible inviscid flow and an elastic plate | We address a free boundary model for the compressible Euler equations where
the free boundary, which is elastic, evolves according to a weakly damped
fourth order hyperbolic equation forced by the fluid pressure. This system
captures the interaction of an inviscid fluid with an elastic plate. We
establish a priori estimates on local-in-time solutions in low regularity
Sobolev spaces, namely with velocity and density initial data v0,R0 in H3. The
main new device is a variable coefficients space tangential-time differential
operator of order 1 with non-homogeneous boundary conditions, which captures
the hyperbolic nature of the compressible Euler equations as well as the
coupling with the structural dynamics. | 2311.08731v1 |
2023-11-28 | Data-Driven Constraints on Cosmic-Ray Diffusion: Probing Self-Generated Turbulence in the Milky Way | We employ a data-driven approach to investigate the rigidity and spatial
dependence of the diffusion of cosmic rays in the turbulent magnetic field of
the Milky Way. Our analysis combines data sets from the experiments Voyager,
AMS-02, CALET, and DAMPE for a range of cosmic ray nuclei from protons to
oxygen. Our findings favor models with a smooth behavior in the diffusion
coefficient, indicating a good qualitative agreement with the predictions of
self-generated magnetic turbulence models. Instead, the current cosmic-ray data
do not exhibit a clear preference for or against inhomogeneous diffusion, which
is also a prediction of these models. Future progress might be possible by
combining cosmic-ray data with gamma rays or radio observations, enabling a
more comprehensive exploration. | 2311.17150v1 |
2023-12-13 | Efficient solution of sequences of parametrized Lyapunov equations with applications | Sequences of parametrized Lyapunov equations can be encountered in many
application settings. Moreover, solutions of such equations are often
intermediate steps of an overall procedure whose main goal is the computation
of quantities of the form $f(X)$ where $X$ denotes the solution of a Lyapunov
equation. We are interested in addressing problems where the parameter
dependency of the coefficient matrix is encoded as a low-rank modification to a
\emph{seed}, fixed matrix. We propose two novel numerical procedures that fully
exploit such a common structure. The first one builds upon recycling Krylov
techniques, and it is well-suited for small dimensional problems as it makes
use of dense numerical linear algebra tools. The second algorithm can instead
address large-scale problems by relying on state-of-the-art projection
techniques based on the extended Krylov subspace. We test the new algorithms on
several problems arising in the study of damped vibrational systems and the
analyses of output synchronization problems for multi-agent systems. Our
results show that the algorithms we propose are superior to state-of-the-art
techniques as they are able to remarkably speed up the computation of accurate
solutions. | 2312.08201v1 |
2023-12-24 | Resonance effects for linear wave equations with scale invariant oscillating damping | We consider an abstract linear wave equation with a time-dependent
dissipation that decays at infinity with the so-called scale invariant rate,
which represents the critical case. We do not assume that the coefficient of
the dissipation term is smooth, and we investigate the effect of its
oscillations on the decay rate of solutions.
We prove a decay estimate that holds true regardless of the oscillations.
Then we show that oscillations that are too fast have no effect on the decay
rate, while oscillations that are in resonance with one of the frequencies of
the elastic part can alter the decay rate.
In the proof we first reduce ourselves to estimating the decay of solutions
to a family of ordinary differential equations, then by using polar coordinates
we obtain explicit formulae for the energy decay of these solutions, so that in
the end the problem is reduced to the analysis of the asymptotic behavior of
suitable oscillating integrals. | 2312.15531v2 |
2024-01-26 | Maximum plasmon thermal conductivity of a thin metal film | Due to their extremely long propagation lengths compared to the wavelengths,
surface plasmon polaritons (SPPs) have been considered as a key in enhancing
thermal conductivity in thin metal films. This study explores the conditions at
which the plasmon thermal conductivity is maximized, considering the
thickness-dependent metal permittivity. We derived the analytical solutions for
the plasmon thermal conductivity in both the thin-film and thick-film limits to
analyze the effect of the permittivities of metals and substrates. From the
analytical solutions of plasmon thermal conductivity, we deduced that the
plasmon thermal conductivity is proportional to the electron thermal
conductivity based on the Wiedemann-Franz law. Additionally, we analyzed the
conditions where the enhancement ratio of the thermal conductivity via SPPs is
maximized. Metals with high plasma frequency and low damping coefficient are
desirable for achieving the maximum plasmon thermal conductivity as well as the
maximum enhancement ratio of thermal conductivity among metals. Significantly,
10-cm-long and 14-nm-thick Al film demonstrates most superior in-plane heat
transfer via SPPs, showing a 53.5\% enhancement in thermal conductivity
compared to its electron thermal counterpart on a lossless glass substrate. | 2401.14677v1 |
2024-02-19 | Subspace methods for the simulation of molecular response properties on a quantum computer | We explore Davidson methods for obtaining excitation energies and other
linear response properties within quantum self-consistent linear response
(q-sc-LR) theory. Davidson-type methods allow for obtaining only a few selected
excitation energies without explicitly constructing the electronic Hessian
since they only require the ability to perform Hessian-vector multiplications.
We apply the Davidson method to calculate the excitation energies of hydrogen
chains (up to H$_{10}$) and analyze aspects of statistical noise for computing
excitation energies on quantum simulators. Additionally, we apply Davidson
methods for computing linear response properties such as static
polarizabilities for H$_2$, LiH, H$_2$O, OH$^-$, and NH$_3$, and show that
unitary coupled cluster outperforms classical projected coupled cluster for
molecular systems with strong correlation. Finally, we formulate the Davidson
method for damped (complex) linear response, with application to the nitrogen
K-edge X-ray absorption of ammonia, and the $C_6$ coefficients of H$_2$, LiH,
H$_2$O, OH$^-$, and NH$_3$. | 2402.12186v1 |
2024-03-06 | Non-homogeneous anisotropic bulk viscosity for acoustic wave attenuation in weakly compressible methods | A major limitation of the weakly compressible approaches to simulate
incompressible flows is the appearance of artificial acoustic waves that
introduce a large mass conservation error and lead to spurious oscillations in
the force coefficients. In this work, we propose a non-homogeneous anisotropic
bulk viscosity term to effectively damp the acoustic waves. By implementing
this term in a computational framework based on the recently proposed general
pressure equation, we demonstrate that the non-homogeneous and anisotropic
nature of the term makes it significantly more effective than the isotropic
homogeneous version widely used in the literature. Moreover, it is
computationally more efficient than the pressure (or mass) diffusion term,
which is an alternative mechanism used to suppress acoustic waves. We simulate
a range of benchmark problems to comprehensively investigate the performance of
the bulk viscosity on the effective suppression of acoustic waves, mass
conservation error, order of convergence of the solver, and computational
efficiency. The proposed form of the bulk viscosity enables fairly accurate
modelling of the initial transients of unsteady simulations, which is highly
challenging for weakly compressible approaches, and to the best of our
knowledge, existing approaches can't provide an accurate prediction of such
transients. | 2403.03475v1 |
2024-03-07 | Experimental amplification and squeezing of a motional state of an optically levitated nanoparticle | A contactless control of fluctuations of phase space variables of a
nanoobject belongs among the key methods needed for ultra-precise
nanotechnology and the upcoming quantum technology of macroscopic systems. Here
we utilize the experimental platform of a single levitating nanoparticle (NP)
to demonstrate essential protocols providing linear amplification of the
mechanical phase space variables together with squeezing of phase space
probability distribution. The protocol combines a controlled fast switching
between the parabolic trapping potential and either weak parabolic or inverted
parabolic amplifying potential leading to amplification of mean value and
variance (fluctuations) along an arbitrary phase space variable and squeezing
along the complementary one. The protocol is completed with cold damping scheme
to control the initial fluctuations of the NP phase space variables. We reached
the amplification gain $|G|>2$, the squeezing coefficient above 4 dB, and the
second-order energy correlation function approaching 3 which corresponds to a
maximum for a stochastic non-equilibrium classical state. These experimental
results will already allow pre-amplification and manipulation of nanomechanical
NP motion for all quantum protocols if the NP cooling towards the ground state
is applied. | 2403.04302v1 |
2024-03-14 | Dynamical Friction and Black Holes in Ultralight Dark Matter Solitons | We numerically simulate the motion of a black hole as it plunges radially
through an ultralight dark matter soliton. We investigate the timescale in
which dynamical friction reduces the kinetic energy of the black hole to a
minimum, and consider the sensitivity of this timescale to changes in the ULDM
particle mass, the total soliton mass, and the mass of the black hole. We
contrast our numerical results with a semi-analytic treatment of dynamical
friction, and find that the latter is poorly suited to this scenario. In
particular, we find that the back-reaction of the soliton to the presence of
the black hole is significant, resulting in oscillations in the coefficient of
dynamical friction which cannot be described in the simple semi-analytical
framework. Furthermore, we observe a late-time reheating effect, in which a
significant amount of kinetic energy is transferred back to the black hole
after an initial damping phase. This complicates the discussion of ULDM
dynamical friction on the scales relevant to the final parsec problem. | 2403.09038v1 |
2024-03-21 | Partially explicit splitting scheme with explicit-implicit-null method for nonlinear multiscale flow problems | In this work, we present an efficient approach to solve nonlinear
high-contrast multiscale diffusion problems. We incorporate the
explicit-implicit-null (EIN) method to separate the nonlinear term into a
linear term and a damping term, and then utilise the implicit and explicit time
marching scheme for the two parts respectively. Due to the multiscale property
of the linear part, we further introduce a temporal partially explicit
splitting scheme and construct suitable multiscale subspaces to speed up the
computation. The approximated solution is splitted into these subspaces
associated with different physics. The temporal splitting scheme employs
implicit discretization in the subspace with small dimension that representing
the high-contrast property and uses explicit discretization for the other
subspace. We exploit the stability of the proposed scheme and give the
condition for the choice of the linear diffusion coefficient. The convergence
of the proposed method is provided. Several numerical tests are performed to
show the efficiency and accuracy of the proposed approach. | 2403.14220v1 |
2024-03-13 | The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q | For any positive integer $q\geq 2$ and any real number $\delta\in(0,1)$, let
$\alpha_q(n,\delta n)$ denote the maximum size of a subset of $\mathbb{Z}_q^n$
with minimum Hamming distance at least $\delta n$, where
$\mathbb{Z}_q=\{0,1,\dotsc,q-1\}$ and $n\in\mathbb{N}$. The asymptotic rate
function is defined by $ R_q(\delta) =
\limsup_{n\rightarrow\infty}\frac{1}{n}\log_q\alpha_q(n,\delta n).$ The famous
$q$-ary asymptotic Gilbert-Varshamov bound, obtained in the 1950s, states that
\[ R_q(\delta) \geq 1 -
\delta\log_q(q-1)-\delta\log_q\frac{1}{\delta}-(1-\delta)\log_q\frac{1}{1-\delta}
\stackrel{\mathrm{def}}{=}R_\mathrm{GV}(\delta,q) \] for all positive integers
$q\geq 2$ and $0<\delta<1-q^{-1}$. In the case that $q$ is an even power of a
prime with $q\geq 49$, the $q$-ary Gilbert-Varshamov bound was firstly improved
by using algebraic geometry codes in the works of Tsfasman, Vladut, and Zink
and of Ihara in the 1980s. These algebraic geometry codes have been modified to
improve the $q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at a
specific tangent point $\delta=\delta_0\in (0,1)$ of the curve
$R_\mathrm{GV}(\delta,q)$ for each given integer $q\geq 46$. However, the
$q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at $\delta=1/2$,
i.e., $R_\mathrm{GV}(1/2,q)$, remains the largest known lower bound of
$R_q(1/2)$ for infinitely many positive integers $q$ which is a generic prime
and which is a generic non-prime-power integer. In this paper, by using codes
from geometry of numbers introduced by Lenstra in the 1980s, we prove that the
$q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ with $\delta\in(0,1)$
can be improved for all but finitely many positive integers $q$. It is shown
that the growth defined by $\eta(\delta)=
\liminf_{q\rightarrow\infty}\frac{1}{\log q}\log[1-\delta-R_q(\delta)]^{-1}$
for every $\delta\in(0,1)$ has actually a nontrivial lower bound. | 2403.08727v2 |
2002-06-27 | Initial-amplitude dependence in weakly damped oscillators | A pedagogically instructive experimental procedure is suggested for
distinguishing between different damping terms in a weakly damped oscillator,
which highclights the connection between non-linear damping and
initial-amplitude dependence. The most common damping terms such as contact
friction, air resistance, viscous drag, and electromagnetic damping have
velocity dependences of the form constant, v, or v^2. The corresponding energy
dependences of the form \sqrt{E}, E, or E\sqrt{E} in the energy loss equation
give rise to characteristic dependence of the amplitude decay slope on the
initial amplitude. | 0206086v1 |
2006-05-22 | The entanglement of damped noon-state and its performance in phase measurement | The state evolution of the initial optical \textit{noon} state is
investigated. The residue entanglement of the state is calculated after it is
damped by amplitude and phase damping. The relative entropy of entanglement of
the damped state is exactly obtained. The performance of direct application of
the damped \textit{noon} state is compared with that of firstly distilling the
docoherence damped state then applying it in measurement. | 0605184v1 |
2007-10-04 | Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel | We consider error correction procedures designed specifically for the
amplitude damping channel. We analyze amplitude damping errors in the
stabilizer formalism. This analysis allows a generalization of the [4,1]
`approximate' amplitude damping code of quant-ph/9704002. We present this
generalization as a class of [2(M+1),M] codes and present quantum circuits for
encoding and recovery operations. We also present a [7,3] amplitude damping
code based on the classical Hamming code. All of these are stabilizer codes
whose encoding and recovery operations can be completely described with
Clifford group operations. Finally, we describe optimization options in which
recovery operations may be further adapted according to the damping probability
gamma. | 0710.1052v1 |
2010-03-24 | Dynamical shift condition for unequal mass black hole binaries | Certain numerical frameworks used for the evolution of binary black holes
make use of a gamma driver, which includes a damping factor. Such simulations
typically use a constant value for damping. However, it has been found that
very specific values of the damping factor are needed for the calculation of
unequal mass binaries. We examine carefully the role this damping plays, and
provide two explicit, non-constant forms for the damping to be used with
mass-ratios further from one. Our analysis of the resultant waveforms compares
well against the constant damping case. | 1003.4681v1 |
2011-11-30 | Local phase damping of single qubits sets an upper bound on the phase damping rate of entangled states | I derive an inequality in which the phase damping rates of single qubits set
an upper bound for the phase damping rate of entangled states of many qubits.
The derivation is based on two assumptions: first, that the phase damping can
be described by a dissipator in Lindblad form and, second, that the phase
damping preserves the population of qubit states in a given basis. | 1111.7152v2 |
2012-05-11 | Quantum dynamics of the damped harmonic oscillator | The quantum theory of the damped harmonic oscillator has been a subject of
continual investigation since the 1930s. The obstacle to quantization created
by the dissipation of energy is usually dealt with by including a discrete set
of additional harmonic oscillators as a reservoir. But a discrete reservoir
cannot directly yield dynamics such as Ohmic damping (proportional to velocity)
of the oscillator of interest. By using a continuum of oscillators as a
reservoir, we canonically quantize the harmonic oscillator with Ohmic damping
and also with general damping behaviour. The dynamics of a damped oscillator is
determined by an arbitrary effective susceptibility that obeys Kramers-Kronig
relations. This approach offers an alternative description of nano-mechanical
oscillators and opto-mechanical systems. | 1205.2545v1 |
2014-02-28 | Escape rate for the power-law distribution in low-to-intermediate damping | Escape rate in the low-to-intermediate damping connecting the low damping
with the intermediate damping is established for the power-law distribution on
the basis of flux over population theory. We extend the escape rate in the low
damping to the low-to-intermediate damping, and get an expression for the
power-law distribution. Then we apply the escape rate for the power-law
distribution to the experimental study of the excited-state isomerization, and
show a good agreement with the experimental value. The extra current and the
improvement of the absorbing boundary condition are discussed. | 1402.7194v2 |
2015-03-21 | On damping created by heterogeneous yielding in the numerical analysis of nonlinear reinforced concrete frame elements | In the dynamic analysis of structural engineering systems, it is common
practice to introduce damping models to reproduce experimentally observed
features. These models, for instance Rayleigh damping, account for the damping
sources in the system altogether and often lack physical basis. We report on an
alternative path for reproducing damping coming from material nonlinear
response through the consideration of the heterogeneous character of material
mechanical properties. The parameterization of that heterogeneity is performed
through a stochastic model. It is shown that such a variability creates the
patterns in the concrete cyclic response that are classically regarded as
source of damping. | 1503.07122v1 |
2016-01-20 | Introduction to Landau Damping | The mechanism of Landau damping is observed in various systems from plasma
oscillations to accelerators. Despite its widespread use, some confusion has
been created, partly because of the different mechanisms producing the damping
but also due to the mathematical subtleties treating the effects. In this
article the origin of Landau damping is demonstrated for the damping of plasma
oscillations. In the second part it is applied to the damping of coherent
oscillations in particle accelerators. The physical origin, the mathematical
treatment leading to the concept of stability diagrams and the applications are
discussed. | 1601.05227v1 |
2018-07-25 | Regularity and asymptotic behaviour for a damped plate-membrane transmission problem | We consider a transmission problem where a structurally damped plate equation
is coupled with a damped or undamped wave equation by transmission conditions.
We show that exponential stability holds in the damped-damped situation and
polynomial stability (but no exponential stability) holds in the
damped-undamped case. Additionally, we show that the solutions first defined by
the weak formulation, in fact have higher Sobolev space regularity. | 1807.09730v1 |
2002-11-03 | Damping of coupled phonon--plasmon modes | The effect of free carriers on dispersion and damping of coupled
phonon-plasmon modes is considered in the long-wave approximation. The electron
and phonon scattering rate as well as Landau damping are taken into account. | 0211040v1 |
2002-02-01 | On "the authentic damping mechanism" of the phonon damping model | Some general features of the phonon damping model are presented. It is
concluded that the fits performed within this model have no physical content. | 0202006v1 |
2018-01-28 | Observations of excitation and damping of transversal oscillation in coronal loops by AIA/SDO | The excitation and damping of transversal coronal loop oscillations and
quantitative relation between damping time, damping quality (damping time per
period), oscillation amplitude, dissipation mechanism and the wake phenomena
are investigated. The observed time series data with the \textit{Atmospheric
Imaging Assembly} (AIA) telescope on NASA's \textit{Solar Dynamics Observatory}
(SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12
seconds cadence in the 171 $ \rm{{\AA}}$ pass band is analyzed for evidence of
transversal oscillations along the coronal loops by Lomb-Scargle periodgram. In
this analysis signatures of transversal coronal loop oscillations that are
damped rapidly were found with dominant oscillation periods in the range of
$\rm{P=12.25-15.80}$ minutes. Also, damping times and damping qualities of
transversal coronal loop oscillations at dominant oscillation periods are
estimated in the range of $ \rm{\tau_d=11.76-21.46}$ minutes and $
\rm{\tau_d/P=0.86-1.49}$, respectively. The observational results of this
analysis show that damping qualities decrease slowly with increasing the
amplitude of oscillation, but periods of oscillations are not sensitive
function of amplitude of oscillations. The order of magnitude of the damping
qualities and damping times are in good agreement with previous findings and
the theoretical prediction for damping of kink mode oscillations by dissipation
mechanism. Furthermore, oscillation of loop segments attenuate with time
roughly as $t^{-\alpha}$ that magnitude values of $\alpha$ for 30 different
segments change from 0.51 to 0.75. | 1801.09217v1 |
1999-11-16 | Probing supernovae ejecta by Halpha damping wings | It is predicted that H$\alpha$ emission line at the early nebular epoch of
type II-P supernovae may display robust observational effects of damping wings.
This is illustrated by Monte-Carlo simulations. The strength of damping wing
effects may be used to constrain parameters of the line-emitting zone. An
anomalous redshift, width and red wing of H$\alpha$ revealed by SN 1997D on day
150 are explained in terms of damping wing effects. | 9911300v1 |
2009-01-23 | Rheological Interpretation of Rayleigh Damping | Damping is defined through various terms such as energy loss per cycle (for
cyclic tests), logarithmic decrement (for vibration tests), complex modulus,
rise-time or spectrum ratio (for wave propagation analysis), etc. For numerical
modeling purposes, another type of damping is frequently used : it is called
Rayleigh damping. It is a very convenient way of accounting for damping in
numerical models, although the physical or rheological meaning of this approach
is not clear. A rheological model is proposed to be related to classical
Rayleigh damping : it is a generalized Maxwell model with three parameters. For
moderate damping (<25%), this model perfectly coincide with Rayleigh damping
approach since internal friction has the same expression in both cases and
dispersive phenomena are negligible. This is illustrated by finite element
(Rayleigh damping) and analytical (generalized Maxwell model) results in a
simple one-dimensional case. | 0901.3717v1 |
2009-05-20 | Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation | We determine the general form of the asymptotics for Dirichlet eigenvalues of
the one-dimensional linear damped wave operator. As a consequence, we obtain
that given a spectrum corresponding to a constant damping term this determines
the damping term in a unique fashion. We also derive a trace formula for this
problem. | 0905.3242v1 |
2015-05-06 | Remarks on the asymptotic behavior of the solution of an abstract damped wave equation | We study an abstract damped wave equation. We prove that the solution of the
damped wave equation becomes closer to the solution of a heat type equation as
time tend to infinity. As an application of our approach, we also study the
asymptotic behavior of the damped wave equation in Euclidean space under the
geometric control condition. | 1505.01794v2 |
2017-01-18 | Two types of spurious damping forces potentially modeled in numerical seismic nonlinear response history analysis | The purpose of this paper is to provide practitioners with further insight
into spurious damping forces that can be generated in nonlinear seismic
response history analyses (RHA). The term 'spurious' is used to refer to
damping forces that are not present in an elastic system and appear as
nonlinearities develop: such damping forces are not necessarily intended and
appear as a result of modifications in the structural properties as it yields
or damages due to the seismic action. In this paper, two types of spurious
damping forces are characterized. Each type has often been treated separately
in the literature, but each has been qualified as 'spurious', somehow blurring
their differences. Consequently, in an effort to clarify the consequences of
choosing a particular viscous damping model for nonlinear RHA, this paper shows
that damping models that avoid spurious damping forces of one type do not
necessarily avoid damping forces of the other type. | 1701.05092v1 |
2017-02-02 | Exponential stability for a coupled system of damped-undamped plate equations | We consider the transmission problem for a coupled system of undamped and
structurally damped plate equations in two sufficiently smooth and bounded
subdomains. It is shown that, independently of the size of the damped part, the
damping is strong enough to produce uniform exponential decay of the energy of
the coupled system. | 1702.00637v1 |
2017-09-11 | Comparison of damping mechanisms for transverse waves in solar coronal loops | We present a method to assess the plausibility of alternative mechanisms to
explain the damping of magnetohydrodynamic (MHD) transverse waves in solar
coronal loops. The considered mechanisms are resonant absorption of kink waves
in the Alfv\'en continuum, phase-mixing of Alfv\'en waves, and wave leakage.
Our methods make use of Bayesian inference and model comparison techniques. We
first infer the values for the physical parameters that control the wave
damping, under the assumption of a particular mechanism, for typically observed
damping time-scales. Then, the computation of marginal likelihoods and Bayes
factors enable us to quantify the relative plausibility between the alternative
mechanisms. We find that, in general, the evidence is not large enough to
support a single particular damping mechanism as the most plausible one.
Resonant absorption and wave leakage offer the most probable explanations in
strong damping regimes, while phase mixing is the best candidate for
weak/moderate damping. When applied to a selection of 89 observed transverse
loop oscillations, with their corresponding measurements of damping times
scales and taking into account data uncertainties, we find that only in a few
cases positive evidence for a given damping mechanism is available. | 1709.03347v1 |
2019-03-25 | Distributed Inter-Area Oscillation Damping Control for Power Systems by Using Wind Generators and Load Aggregators | This paper investigates the potential of wind turbine generators (WTGs) and
load aggregators (LAs) to provide supplementary damping control services for
low frequency inter-area oscillations (LFOs) through the additional distributed
damping control units (DCUs) proposed in their controllers. In order to provide
a scalable methodology for the increasing number of WTGs and LAs, a novel
distributed control framework is proposed to coordinate damping controllers.
Firstly, a distributed algorithm is designed to reconstruct the system Jacobian
matrix for each damping bus (buses with damping controllers). Thus, the
critical LFO can be identified locally at each damping bus by applying
eigen-analysis to the obtained system Jacobian matrix. Then, if the damping
ratio of the critical LFO is less than a preset threshold, the control
parameters of DCUs will be tuned in a distributed and coordinated manner to
improve the damping ratio and minimize the total control cost at the same time.
The proposed control framework is tested in a modified IEEE 39-bus test system.
The simulation results with and without the proposed control framework are
compared to demonstrate the effectiveness of the proposed framework. | 1903.10135v1 |
2020-12-05 | On Periodical Damping Ratio of a Controlled Dynamical System with Parametric Resonances | This report provides an interpretation on the periodically varying damping
ratio of a dynamical system with direct control of oscillation or vibration
damping. The principal parametric resonance of the system and a new type of
parametric resonance, named "zero-th order" parametric resonance, are
investigated by using the method of multiple scales to find approximate,
analytical solutions of the system, which provide an interpretation on such
damping variations. | 2012.02932v1 |
2021-06-22 | Sharp decay rate for the damped wave equation with convex-shaped damping | We revisit the damped wave equation on two-dimensional torus where the damped
region does not satisfy the geometric control condition. We show that if the
damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the
boundary of the damped region is strictly convex, the wave is stable at rate
$t^{-1+\frac{2}{2\beta+7}}$, which is better than the known optimal decay rate
$t^{-1+\frac{1}{\beta+3}}$ for strip-shaped dampings of the same H\"older
regularity. Moreover, we show by example that the decay rate is optimal. This
illustrates the fact that the energy decay rate depends not only on the order
of vanishing of the damping, but also on the shape of the damped region. The
main ingredient of the proof is the averaging method (normal form reduction)
developed by Hitrick and Sj\"ostrand (\cite{Hi1}\cite{Sj}). | 2106.11782v3 |
2021-08-09 | Effect of stepwise adjustment of Damping factor upon PageRank | The effect of adjusting damping factor {\alpha}, from a small initial value
{\alpha}0 to the final desired {\alpha}f value, upon then iterations needed for
PageRank computation is observed. Adjustment of the damping factor is done in
one or more steps. Results show no improvement in performance over a fixed
damping factor based PageRank. | 2108.04150v1 |
2021-08-17 | Asymptotic behaviour of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity | In this paper we prove the existence of the global attractor for the wave
equation with nonlocal weak damping, nonlocal anti-damping and critical
nonlinearity. | 2108.07395v2 |
1997-11-20 | Symmetric matrices and quantum codes | This paper has been withdrawn since a Gilbert-Varshamov bound for general
quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett.
77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with
orthogonal geometry, or equivalently, with symmetric matrices as in this paper,
has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p.
405. I would like to thank Robert Calderbank for pointing out these references
to me. | 9711026v2 |
1994-06-09 | Black Holes from Blue Spectra | Blue primordial power spectra with a spectral index $n>1$ can lead to a
significant production of primordial black holes in the very early Universe.
The evaporation of these objects leads to a number of observational
consequences and a model independent upper limit of $n \approx 1.4$. In some
cases this limit is strengthened to $n=1.3$. Such limits may be employed to
define the boundary to the region of parameter space consistent with
generalized inflationary predictions. [To appear in Proceedings of the CASE
WESTERN CMB WORKSHOP, April 22-24 1994. Figures available on request from
J.H.Gilbert@qmw.ac.uk] | 9406028v1 |
1995-06-14 | Inversions in astronomy and the SOLA method | This paper was presented at the Institute for Mathematics and its
Applications workshop "Inverse problems in wave propagation" and will appear in
the series IMA volumes (Springer). A brief overview of applications of
inversions within astronomy is presented and also an inventory of techniques
commonly in use. Most of this paper is focussed on the method of Subtractive
Optimally Localized Averages (SOLA) which is an adaptation of the Backus and
Gilbert method. This method was originally developed for use in helioseismology
where the Backus and Gilbert method is computationally too slow. Since then it
has also been applied to the problem of reverberation mapping of active
galactic nuclei and the differences between this inverse problem and the ones
of helioseismology are also discussed. | 9506084v1 |
1997-11-11 | No Need for MACHOS in the Halo | A simple interpretation of the more than dozen microlensing events seen in
the direction of the LMC is a halo population of MACHOs which accounts for
about half of the mass of the Galaxy. Such an interpretation is not without its
problems, and we show that current microlensing data can, with some advantage,
be explained by dark components of the disk and spheroid, whose total mass is
only about 10% of the mass of the Galaxy. | 9711110v1 |
2006-02-11 | Likelihood Functions for Galaxy Cluster Surveys | Galaxy cluster surveys offer great promise for measuring cosmological
parameters, but survey analysis methods have not been widely studied. Using
methods developed decades ago for galaxy clustering studies, it is shown that
nearly exact likelihood functions can be written down for galaxy cluster
surveys. The sparse sampling of the density field by galaxy clusters allows
simplifications that are not possible for galaxy surveys. An application to
counts in cells is explicitly tested using cluster catalogs from numerical
simulations and it is found that the calculated probability distributions are
very accurate at masses above several times 10^{14}h^{-1} solar masses at z=0
and lower masses at higher redshift. | 0602251v3 |
2000-03-25 | Thermokinetic approach of the generalized Landau-Lifshitz-Gilbert equation with spin polarized current | In order to describe the recently observed effect of current induced
magnetization reversal in magnetic nanostructures, the thermokinetic theory is
applied to a metallic ferromagnet in contact with a reservoir of spin polarized
conduction electrons. The spin flip relaxation of the conduction electrons is
described thermodynamically as a chemical reaction. The diffusion equation of
the chemical potential (or the giant magnetoresistance) and the usual
Landau-Lifshitz-Gilbert (LLG) equation are derived from the entropy variation.
The expression of the conservation laws of the magnetic moments, including spin
dependent scattering processes, leads then to the generalized LLG equation with
spin polarized current. The equation is applied to the measurements obtained on
single magnetic Ni nanowires. | 0003409v1 |
2004-05-26 | Nonequilibrium Extension of the Landau-Lifshitz-Gilbert Equation for Magnetic Systems | Using the invariant operator method for an effective Hamiltonian including
the radiation-spin interaction, we describe the quantum theory for
magnetization dynamics when the spin system evolves nonadiabatically and out of
equilibrium, $d \hat{\rho}/dt \neq 0$. It is shown that the vector parameter of
the invariant operator and the magnetization defined with respect to the
density operator, both satisfying the quantum Liouville equation, still obey
the Landau-Lifshitz-Gilbert equation. | 0405599v1 |
2006-10-16 | Properties of Codes with the Rank Metric | In this paper, we study properties of rank metric codes in general and
maximum rank distance (MRD) codes in particular. For codes with the rank
metric, we first establish Gilbert and sphere-packing bounds, and then obtain
the asymptotic forms of these two bounds and the Singleton bound. Based on the
asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is
exceeded by MRD codes and sphere-packing bound cannot be attained. We also
establish bounds on the rank covering radius of maximal codes, and show that
all MRD codes are maximal codes and all the MRD codes known so far achieve the
maximum rank covering radius. | 0610099v2 |
1994-08-26 | On the Dirichlet problem for harmonic maps with prescribed singularities | Let $\M$ be a classical Riemannian globally symmetric space of rank one and
non-compact type. We prove the existence and uniqueness of solutions to the
Dirichlet problem for harmonic maps into $\M$ with prescribed singularities
along a closed submanifold of the domain. This generalizes our previous work
where such maps into the hyperbolic plane were constructed. This problem, in
the case where $\M$ is the complex-hyperbolic plane, has applications to
equilibrium configurations of co-axially rotating charged black holes in
General Relativity. | 9408005v1 |
1997-08-15 | One-Loop Minimization Conditions in the Minimal Supersymmetric Standard Model | We study, in the Minimal Supersymmetric Standard Model, the electroweak
symmetry breaking conditions obtained from the one-loop effective potential.
Novel model-independent lower and upper bounds on $\tan \beta$, involving the
other free parameters of the model, are inferred and determined analytically.
We discuss briefly some of the related issues and give an outlook for further
applications. | 9708368v1 |
2004-05-31 | On a Penrose Inequality with Charge | We construct a time-symmetric asymptotically flat initial data set to the
Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) <
0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost
horizon and Q is the total charge. This yields a counter-example to a natural
extension of the Penrose Inequality to charged black holes. | 0405602v3 |
2004-07-26 | Automorphisms of free groups have asymptotically periodic dynamics | We show that every automorphism $\alpha$ of a free group $F_k$ of finite rank
$k$ has {\it asymptotically periodic} dynamics on $F_k$ and its boundary
$\partial F_k$: there exists a positive power $\alpha^q$ such that every
element of the compactum $F_k \cup \partial F_k$ converges to a fixed point
under iteration of $\alpha^q$. | 0407437v2 |
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