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2020-03-13
|
Photon and Phonon Spectral-Functions for Continuum Quantum Optomechanics
|
We study many-particle phenomena of propagating multi-mode photons and
phonons interacting through Brillouin scattering-type Hamiltonian in nanoscale
waveguides. We derive photon and phonon retarded Green's functions and extract
their spectral functions in applying the factorization approximation of the
mean-field theory. The real part of the self-energy provides renormalization
energy shifts for the photons and the phonons. Besides the conventional leaks,
the imaginary part gives effective photon and phonon damping rates induced due
to many-particle phenomena. The results extend the simple spectral functions of
quantum optomechanics into continuum quantum optomechanics. We present the
influence of thermal phonons on the photon effective damping rates, and
consider cases of specific photon fields to be excited within the waveguide and
which are of importance for phonon cooling scenarios.
|
2003.06355v1
|
2020-03-13
|
Surface waves in a collisional quark-gluon plasma
|
Surface waves propagating in the semi-bounded collisional hot QCD medium
(quark-gluon plasma) are considered. To investigate the effect of collisions as
damping and non-ideality factor, the longitudinal and transverse dielectric
functions of the quark-gluon plasma are used within the Bhatnagar-Gross-Krook
(BGK) approach. The results were obtained both analytically and numerically in
the long wavelength limit. First of all, collisions lead to smaller values of
surface wave frequency and their stronger damping. Secondly, the results show
that non-ideality leads to the appearance of a new branch of surface waves
compared to the collisionless case. The relevance of the surface excitations
(waves) for the QGP realized in experiments is discussed.
|
2003.06373v2
|
2020-03-18
|
Finite time extinction for the strongly damped nonlinear Schr{ö}dinger equation in bounded domains
|
We prove the \textit{finite time extinction property} $(u(t)\equiv 0$ on
$\Omega$ for any $t\ge T_\star,$ for some $T_\star>0)$ for solutions of the
nonlinear Schr\"{o}dinger problem ${\rm i} u_t+\Delta u+a|u|^{-(1-m)}u=f(t,x),$
on a bounded domain $\Omega$ of $\mathbb{R}^N,$ $N\le 3,$ $a\in\mathbb{C}$ with
$\Im(a)>0$ (the damping case) and under the crucial assumptions $0<m<1$ and the
dominating condition $2\sqrt m\,\Im(a)\ge(1-m)|\Re(a)|.$ We use an energy
method as well as several a priori estimates to prove the main conclusion. The
presence of the non-Lipschitz nonlinear term in the equation introduces a lack
of regularity of the solution requiring a study of the existence and uniqueness
of solutions satisfying the equation in some different senses according to the
regularity assumed on the data.
|
2003.08105v2
|
2020-03-19
|
Challenge for describing the cluster states starting with realistic interaction
|
We aim to describe the cluster states of nuclear systems starting with a
realistic interaction, which is a challenge of modern nuclear theories. Here,
the short-range correlation of realistic interaction is treated by employing
the damping factor, and the resultant interaction can be applied to the cluster
structure of light nuclei. We start with a realistic interaction (G3RS) and
transform it in this way, and the $\alpha$-$\alpha$ energy curve is compared
with the results of phenomenological interactions. The attractive effect
between two $\alpha$'s is found to be not enough even with a damping factor for
the short-range repulsion, and the necessity of a finite-range three-body term
is discussed. With this three-body term, the resonance energy of the ground
state and the scattering phase shift of two $\alpha$'s can be reproduced. Also,
the binding energy of $^{16}$O from the four $\alpha$ threshold is reasonably
reproduced. The linear-chain structure of three and four $\alpha$ clusters in
$^{12}$C and $^{16}$O are calculated with this interaction and compared with
the results of the conventional approaches including the density functional
theories.
|
2003.08546v1
|
2020-03-20
|
Large Deflections of A Structurally Damped Panel in A Subsonic Flow
|
The large deflections of panels in subsonic flow are considered.
Specifically, a fully clamped von Karman plate accounting for both rotational
inertia in plate filaments and structural damping of square root type is
considered. The panel is taken to be embedded in the boundary of a linear,
subsonic potential flow on the positive halfspace in $\mathbb R^3$. Solutions
are constructed via a semigroup approach despite the lack of natural
dissipativity associated to the generator of the linear dynamics. The
flow-plate dynamics are then reduced---via an explicit Neumann-to-Dirichlet
(downwash-to-pressure) solver for the flow---to a memory-type dynamical system
for the plate. For the non-conservative plate dynamics, a global attractor is
explicitly constructed via Lyapunov and quasi-stability methods. Finally, it is
shown that via the compactness of the attractor and finiteness of the
dissipation integral, that all trajectories converge strongly to the set of
stationary states.
|
2003.09232v1
|
2020-03-24
|
Pulsed RF Schemes for Tearing Mode Stabilization
|
The RF stabilization of tearing modes with current condensation has the
potential to increase stabilization efficiency and loosen power localization
requirements. Such benefits stem from the cooperative feedback between the RF
deposition and resulting island temperature perturbation governed by diffusion.
A self consistent treatment of the damping of an rf ray as it traverses the
island shows that low damping scenarios can require unfavorably high powers to
overcome initial power leakage and effectively capitalize on the nonlinear
effect. In this work it is demonstrated that for such regimes,modulated
stabilization schemes can achieve significant improvements in heating and
current drive contributions to stabilization for the same average power as a
continuous wave scheme. The impact of modulation frequency and duty cycle on
the performance is explored, the results of which suggest modulation strategies
in which the pulsing periods are kept on the order of a diffusive time.
|
2003.10896v1
|
2020-03-24
|
Detecting Multiple DLAs per Spectrum in SDSS DR12 with Gaussian Processes
|
We present a revised version of our automated technique using Gaussian
processes (GPs) to detect Damped Lyman-$\alpha$ absorbers (DLAs) along quasar
(QSO) sightlines. The main improvement is to allow our Gaussian process
pipeline to detect multiple DLAs along a single sightline. Our DLA detections
are regularised by an improved model for the absorption from the Lyman-$\alpha$
forest which improves performance at high redshift. We also introduce a model
for unresolved sub-DLAs which reduces mis-classifications of absorbers without
detectable damping wings. We compare our results to those of two different
large-scale DLA catalogues and provide a catalogue of the processed results of
our Gaussian process pipeline using 158 825 Lyman-$\alpha$ spectra from SDSS
data release 12. We present updated estimates for the statistical properties of
DLAs, including the column density distribution function (CDDF), line density
($dN/dX$), and neutral hydrogen density ($\Omega_{\textrm{DLA}}$).
|
2003.11036v2
|
2020-03-28
|
Quantum speed limit based on the bound of Bures angle
|
In this paper, we investigate the unified bound of quantum speed limit time
in open systems based on the modified Bures angle. This bound is applied to the
damped Jaynes-Cummings model and the dephasing model, and the analytical
quantum speed limit time is obtained for both models. As an example, the
maximum coherent qubit state with white noise is chosen as the initial states
for the damped Jaynes-Cummings model. It is found that the quantum speed limit
time in both the non-Markovian and the Markovian regimes can be decreased by
the white noise compared with the pure state. In addition, for the dephasing
model, we find that the quantum speed limit time is not only related to the
coherence of initial state and non-Markovianity, but also dependent on the
population of initial excited state.
|
2003.12758v1
|
2020-03-31
|
First-principles study of ultrafast dynamics of Dirac plasmon in graphene
|
Exploring low-loss two-dimensional plasmon modes is considered central for
achieving light manipulation at the nanoscale and applications in plasmonic
science and technology. In this context, pump-probe spectroscopy is a powerful
tool for investigating these collective modes and the corresponding energy
transfer processes. Here, I present a first-principles study on non-equilibrium
Dirac plasmon in graphene, wherein damping channels under ultrafast conditions
are still not fully explored. The laser-induced blueshift of plasmon energy is
explained in terms of thermal increase of the electron-hole pair concentration
in the intraband channel. Interestingly, while damping pathways of the
equilibrium graphene plasmon are entirely ruled by scatterings with acoustic
phonons, the photoinduced plasmon predominantly transfers its energy to the
strongly coupled hot optical phonons, which explains the
experimentally-observed tenfold increase of the plasmon linewidth. The present
study paves the way for an in-depth theoretical comprehension of plasmon
temporal dynamics in novel two-dimensional systems and heterostructures.
|
2003.14074v2
|
2020-03-31
|
Parametric analysis of COVID-19 expansion in European countries in the period of February to June 2020
|
The data on number of registered cases of COVID-19 disease in twenty European
countries is analyzed by the least-squares fitting procedure with generic
analytic functions. Three regimes of the expansion of the disease are
identified and quantified -- early exponential expansion, damped exponential,
and linear expansion. Differences among countries in the early expansion period
are quantified. The velocity of the expansion in the exponential regime lies
within one standard deviation from the average value for 11 countries. The
number of infected individuals at the initial time is excessively high for
Italy, 7 standard deviations from the average value.
Method for predicting the expansion based on extrapolation in the parametric
space is presented. One-week predictions based on extrapolations have average
precision of 18% and 29% during the later period of the damped exponential
expansion for the case of Italy and Czechia, respectively. The method based on
extrapolations in the parametric space may provide an elementary method to
quantify the impact of restrictive measures on the spreading of the disease.
|
2003.14283v2
|
2020-04-14
|
Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients
|
We investigate the stabilization of a locally coupled wave equations with
only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty
in this paper is that both the damping and the coupling coefficients are non
smooth. First, using a general criteria of Arendt-Batty, combined with an
uniqueness result, we prove that our system is strongly stable. Next, using a
spectrum approach, we prove the non-exponential (uniform) stability of the
system. Finally, using a frequency domain approach, combined with a piecewise
multiplier technique and the construction of a new multiplier satisfying some
ordinary differential equations, we show that the energy of smooth solutions of
the system decays polynomially of type t^{-1}.
|
2004.06758v1
|
2020-04-16
|
Ergodicity effects on transport-diffusion equations with localized damping
|
The main objective of this paper is to study the time decay of
transport-diffusion equation with inhomogeneous localized damping in the
multi-dimensional torus. The drift is governed by an autonomous Lipschitz
vector field and the diffusion by the standard heat equation with small
viscosity parameter $\nu$. In the first part we deal with the inviscid case and
show some results on the time decay of the energy using in a crucial way the
ergodicity and the unique ergodicity of the flow generated by the drift. In the
second part we analyze the same problem with small viscosity and provide quite
similar results on the exponential decay uniformly with respect to the
viscosity in some logarithmic time scaling of the \mbox{type $t\in
[0,C_0\ln(1/\nu)]$}.
|
2004.07712v1
|
2020-04-17
|
Majorization-Minimization-Based Levenberg--Marquardt Method for Constrained Nonlinear Least Squares
|
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares
problems with convex constraints is described. Various versions of the LM
method have been proposed, their main differences being in the choice of a
damping parameter. In this paper, we propose a new rule for updating the
parameter so as to achieve both global and local convergence even under the
presence of a convex constraint set. The key to our results is a new
perspective of the LM method from majorization-minimization methods.
Specifically, we show that if the damping parameter is set in a specific way,
the objective function of the standard subproblem in LM methods becomes an
upper bound on the original objective function under certain standard
assumptions.
Our method solves a sequence of the subproblems approximately using an
(accelerated) projected gradient method. It finds an $\epsilon$-stationary
point after $O(\epsilon^{-2})$ computation and achieves local quadratic
convergence for zero-residual problems under a local error bound condition.
Numerical results on compressed sensing and matrix factorization show that our
method converges faster in many cases than existing methods.
|
2004.08259v3
|
2020-04-23
|
Many-body Decay of the Gapped Lowest Excitation of a Bose-Einstein Condensate
|
We study the decay mechanism of the gapped lowest-lying excitation of a
quasi-pure box-trapped atomic Bose-Einstein condensate. Owing to the absence of
lower-energy modes, or direct coupling to an external bath, this excitation is
protected against one-body (linear) decay and the damping mechanism is
exclusively nonlinear. We develop a universal theoretical model that explains
this fundamental nonlinear damping as a process whereby two quanta of the
gapped lowest excitation mode couple to a higher-energy mode, which
subsequently decays into a continuum. We find quantitative agreement between
our experiments and the predictions of this model. Finally, by strongly driving
the system below its (lowest) resonant frequency we observe third-harmonic
generation, a hallmark of nonlinear behavior.
|
2004.11363v1
|
2020-05-05
|
Hydrodynamic memory can boost enormously driven nonlinear diffusion and transport
|
Hydrodynamic memory force or Basset force is known since the 19th-century.
Its influence on Brownian motion remains, however, mostly unexplored. Here, we
investigate its role in nonlinear transport and diffusion within a paradigmatic
model of tilted washboard potential. In this model, a giant enhancement of
driven diffusion over its potential-free limit presents a well-established
paradoxical phenomenon. In the overdamped limit, it occurs at a critical tilt
of vanishing potential barriers. However, for weak damping, it takes place
surprisingly at another critical tilt, where the potential barriers are clearly
expressed. Recently we showed that Basset force could make such a diffusion
enhancement enormously large. In this paper, we discover that even for
moderately strong damping, where the overdamped theory works very well when the
memory effects are negligible, substantial hydrodynamic memory unexpectedly
makes a strong impact. First, the diffusion boost occurs at non-vanishing
potential barriers and can be orders of magnitude larger. Second, transient
anomalous diffusion regimes emerge over many time decades and potential
periods. Third, particles' mobility can also be dramatically enhanced, and a
long transient super-transport regime emerges.
|
2005.01984v2
|
2020-05-05
|
Diffraction losses of a Fabry-Perot cavity with nonidentical non-spherical mirrors
|
Optical cavities with both optimized resonant conditions and high quality
factors are important metrological tools. In particular, they are used for
laser gravitational wave (GW) detectors. It is necessary to suppress the
parametric instability by damping the resonant conditions of harmful higher
order optical modes (HOOM) in order to have high cavity powers in GW detectors.
This can be achieved effectively by using non spherical mirrors in symmetric
Fabry-Perot (FP) cavities by increasing roundtrip losses of HOOMs. Fabry-Perot
cavities in most of the GW detectors have non-identical mirrors to optimize
clipping losses and reduce thermal noise by reducing the beam size on one side
of the cavity facing to the beam splitter and recycling cavities. We here
present a general method to design non spherical non-identical mirrors in
non-symmetric FP cavities to damp HOOMs. The proposed design allows to the
suppress the loss of the arm power caused by point absorbers on test masses.
|
2005.02033v1
|
2020-05-11
|
Sound Absorption in Partially Ionized Hydrogen Plasma and Heating Mechanism of Solar Chromosphere
|
The temperature dependence of rates of electron impact ionization and two
electrons recombination are calculated using Wannier cross section of electron
impact ionization of neutral hydrogen atom. Entropy production and power
dissipation are derived for the case when the ionization degree deviates from
its equilibrium value. This is the special case of the obtained general formula
for entropy production accompanying chemical reactions. Damping rate of the
sound waves is calculated and the conditions when ionization processes dominate
are considered. A quasi-classical approximation for the heating mechanism of
solar chromosphere is proposed. Several analogous phenomena for damping rates
in liquids and crystals are shortly discussed, for example, deaf sound of a
glass of beer or English salt solution. An explicit expression for the second
or bulk (or volume) viscosity of hydrogen plasma is calculated from firsts
principles. For the first time some second viscosity is calculated from first
principles.
|
2005.05056v4
|
2020-05-12
|
Calculating RF current condensation with self-consistent ray-tracing
|
By exploiting the nonlinear amplification of the power deposition of RF
waves, current condensation promises new pathways to the stabilisation of
magnetic islands. We present a numerical analysis of current condensation,
coupling a geometrical optics treatment of wave propagation and damping to a
thermal diffusion equation solver in the island. Taking into account the island
geometry and relativistic damping, previous analytical theory can be made more
precise and specific scenarios can be realistically predicted. With this more
precise description, bifurcations and associated hysteresis effects could be
obtained in an ITER-like scenario at realistic parameter values. Moreover, it
is shown that dynamically varying the RF wave launching angles can lead to
hysteresis and help to avoid the nonlinear shadowing effect.
|
2005.05997v1
|
2020-05-13
|
Sustaining a temperature difference
|
We derive an expression for the minimal rate of entropy that sustains two
reservoirs at different temperatures $T_0$ and $T_\ell$. The law displays an
intuitive $\ell^{-1}$ dependency on the relative distance and a characterisic
$\log^2 (T_\ell/T_0)$ dependency on the boundary temperatures. First we give a
back-of-envelope argument based on the Fourier Law (FL) of conduction, showing
that the least-dissipation profile is exponential. Then we revisit a model of a
chain of oscillators, each coupled to a heat reservoir. In the limit of large
damping we reobtain the exponential and squared-log behaviors, providing a
self-consistent derivation of the FL. For small damping "equipartition
frustration" leads to a well-known balistic behaviour, whose incompatibility
with the FL posed a long-time challenge.
|
2005.06289v2
|
2020-05-13
|
Numerical simulations of unsteady viscous incompressible flows using general pressure equation
|
In fluid dynamics, an important problem is linked to the knowledge of the
fluid pressure. Recently, another approach to study incompressible fluid flow
was suggested. It consists in using a general pressure equation (GPE) derived
from compressible Navier-Stokes equation. In this paper, GPE is considered and
compared with the Chorin's artificial compressibility method (ACM) and the
Entropically damped artificial compressibility (EDAC) method. The three methods
are discretized in a staggered grid system with second order centered schemes
in space and a third order Runge-Kutta scheme in time. Three test cases are
realized: two-dimensional Taylor-Green vortex flow, the traveling wave and the
doubly periodic shear layers. It is demonstrated that GPE is accurate and
efficient to capture the correct behavior for unsteady incompressible flows.
The numerical results obtained by GPE are in excellent agreement with those
obtained by ACM, EDAC and a classical finite volume method with a Poisson
equation. Furthermore, GPE convergence is better than ACM convergence. The
proposed general pressure equation (GPE) allows to solve general, time-accurate
, incompressible Navier-Stokes flows. Finally, the parametric study realized in
terms of Mach and Prandtl numbers shows that the velocity divergence can be
limited by an arbitrary maximum and that acoustic waves can be damped.
|
2005.06448v1
|
2020-05-15
|
Response of the BGO Calorimeter to Cosmic Ray Nuclei in the DAMPE Experiment on Orbit
|
This paper is about a study on the response of the BGO calorimeter of DAMPE
experiment. Four elements in Cosmic Ray nuclei are used as sources for this
analysis. A feature resulting from the geomagnetic cutoff exhibits in the
energy spectrum, both in simulated and reconstructed data, and is compared
between them.
|
2005.07621v1
|
2020-05-18
|
Linear inviscid damping for shear flows near Couette in the 2D stably stratified regime
|
We investigate the linear stability of shears near the Couette flow for a
class of 2D incompressible stably stratified fluids. Our main result consists
of nearly optimal decay rates for perturbations of stationary states whose
velocities are monotone shear flows $(U(y),0)$ and have an exponential density
profile. In the case of the Couette flow $U(y)=y$, we recover the rates
predicted by Hartman in 1975, by adopting an explicit point-wise approach in
frequency space. As a by-product, this implies optimal decay rates as well as
Lyapunov instability in $L^2$ for the vorticity. For the previously unexplored
case of more general shear flows close to Couette, the inviscid damping results
follow by a weighted energy estimate. Each outcome concerning the stably
stratified regime applies to the Boussinesq equations as well. Remarkably, our
results hold under the celebrated Miles-Howard criterion for stratified fluids.
|
2005.09058v2
|
2020-05-19
|
High-redshift Damped Ly-alpha Absorbing Galaxy Model Reproducing the N(HI)-Z Distribution
|
We investigate how damped Lyman-$\alpha$ absorbers (DLAs) at z ~ 2-3,
detected in large optical spectroscopic surveys of quasars, trace the
population of star-forming galaxies. Building on previous results, we construct
a model based on observed and physically motivated scaling relations in order
to reproduce the bivariate distributions of metallicity, Z, and HI column
density, N(HI). Furthermore, the observed impact parameters for galaxies
associated to DLAs are in agreement with the model predictions. The model
strongly favours a metallicity gradient, which scales with the luminosity of
the host galaxy, with a value of $\gamma$* = -0.019 $\pm$ 0.008 dex kpc$^{-1}$
for L* galaxies that gets steeper for fainter galaxies. We find that DLAs trace
galaxies over a wide range of galaxy luminosities, however, the bulk of the DLA
cross-section arises in galaxies with L ~ 0.1 L* at z ~ 2.5 broadly consistent
with numerical simulations.
|
2005.09660v1
|
2020-05-20
|
Dynamical phase transitions in dissipative quantum dynamics with quantum optical realization
|
We study dynamical phase transitions (DPT) in the driven and damped Dicke
model, realizable for example by a driven atomic ensemble collectively coupled
to a damped cavity mode. These DPTs are characterized by non-analyticities of
certain observables, primarily the overlap of time evolved and initial state.
Even though the dynamics is dissipative, this phenomenon occurs for a wide
range of parameters and no fine-tuning is required. Focusing on the state of
the 'atoms' in the limit of a bad cavity, we are able to asymptotically
evaluate an exact path integral representation of the relevant overlaps. The
DPTs then arise by minimization of a certain action function, which is related
to the large deviation theory of a classical stochastic process. From a more
general viewpoint, in the considered system, non-analyticities emerge
generically in a Fock space representation of the state. Finally, we present a
scheme which allows a measurement of the DPT in a cavity-QED setup.
|
2005.10013v2
|
2020-05-21
|
The critical exponent for nonlinear damped $σ$-evolution equations
|
In this paper, we derive suitable optimal $L^p-L^q$ decay estimates, $1\leq
p\leq q\leq \infty$, for the solutions to the $\sigma$-evolution equation,
$\sigma>1$, with structural damping and power nonlinearity $|u|^{1+\alpha}$ or
$|u_t|^{1+\alpha}$, \[ u_{tt}+(-\Delta)^\sigma u +(-\Delta)^\theta
u_t=\begin{cases} |u|^{1+\alpha}, \\ |u_t|^{1+\alpha}, \end{cases}\] where
$t\geq0$ and $x\in\mathbb{R}^n$. Using these estimates, we can solve the
problem of finding the critical exponents for the two nonlinear problems above
in the so-called non-effective case, $\theta\in(\sigma/2,\sigma]$. This latter
is more difficult than the effective case $\theta\in[0,\sigma/2)$, since the
asymptotic profile of the solution involves a diffusive component and an
oscillating one. The novel idea in this paper consists in treating separately
the two components to neglect the loss of decay rate created by the interplay
of the two components. We deal with the oscillating component, by localizing
the low frequencies, where oscillations appear, in the extended phase space.
This strategy allows us to recover a quasi-scaling property which replaces the
lack of homogeneity of the equation.
|
2005.10946v1
|
2020-05-22
|
Particle pairs and trains in inertial microfluidics
|
Staggered and linear multi-particle trains constitute characteristic
structures in inertial microfluidics. Using lattice-Boltzmann simulations, we
investigate their properties and stability, when flowing through microfluidic
channels. We confirm the stability of cross-streamline pairs by showing how
they contract or expand to their equilibrium axial distance. In contrast,
same-streamline pairs quickly expand to a characteristic separation but even at
long times slowly drift apart. We reproduce the distribution of particle
distances with its characteristic peak as measured in experiments.
Staggered multi-particle trains initialized with an axial particle spacing
larger than the equilibrium distance contract non-uniformly due to collective
drag reduction. Linear particle trains, similar to pairs, rapidly expand
towards a value about twice the equilibrium distance of staggered trains and
then very slowly drift apart non-uniformly. Again, we reproduce the statistics
of particle distances and the characteristic peak observed in experiments.
Finally, we thoroughly analyze the damped displacement pulse traveling as a
microfluidic phonon through a staggered train and show how a defect strongly
damps its propagation.
|
2005.12701v2
|
2020-05-20
|
Dynamic Peach-Koehler self-force, inertia, and radiation damping of a regularized dislocation
|
The elastodynamic Peach-Koehler force is computed for a fully-regularized
straight dislocation with isotropic core in continuum isotropic elastic
elasticity, in compact forms involving partial mass or impulsion functions
relative to shear and compressional waves. The force accounts for both dynamic
radiation damping and inertia. The expressions are valid indifferently for
subsonic or supersonic velocities. Results are compared with the case of a
flat-core dislocation of the Peierls-Eshelby type, for a motion of jump from
rest to constant velocity. In the steady-state limit, the Lagrangian function
relevant to expressing the force in the flat-core case must be replaced by a
related but different function for the regularized dislocation. However, by
suitably defining the regularizing dislocation width, the steady-state limits
of the force for the fully-regularized and flat-core dislocations can be
matched exactly.
|
2005.12704v2
|
2020-05-27
|
Experimental diagnostics of entanglement swapping by a collective entanglement test
|
The paper reports on experimental diagnostics of entanglement swapping
protocol by means of collective entanglement witness. Our approach is suitable
to detect disturbances occurring in the preparation of quantum states, quantum
communication channel and imperfect Bell-state projection. More specifically we
demonstrate that our method can distinguish disturbances such as
depolarization, phase-damping, amplitude-damping and imperfect Bell-state
measurement by observing four probabilities and estimating collective
entanglement witness. Since entanglement swapping is a key procedure for
quantum repeaters, quantum relays, device-independent quantum communications or
entanglement assisted error correction, this can aid in faster and practical
resolution of quality-of-transmission related problems as our approach requires
less measurements then other means of diagnostics.
|
2005.13292v2
|
2020-05-27
|
Magnon antibunching in a nanomagnet
|
We investigate the correlations of magnons inside a nanomagnet and identify a
regime of parameters where the magnons become antibunched, i.e., where there is
a large probability for occupation of the single-magnon state. This antibunched
state is very different from magnons at thermal equilibrium and
microwave-driven coherent magnons. We further obtain the steady state
analytically and describe the magnon dynamics numerically, and ascertain the
stability of such antibunched magnons over a large window of magnetic
anisotropy, damping and temperature. This means that the antibunched magnon
state is feasible in a wide class of low-damping magnetic nanoparticles. To
detect this quantum effect, we propose to transfer the quantum information of
magnons to photons by magnon-photon coupling and then measure the correlations
of photons to retrieve the magnon correlations. Our findings may provide a
promising platform to study quantum-classical transitions and for designing a
single magnon source.
|
2005.13637v1
|
2020-05-31
|
Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation
|
The article is devoted to the mathematical analysis of a fluid-structure
interaction system where the fluid is compressible and heat conducting and
where the structure is deformable and located on a part of the boundary of the
fluid domain. The fluid motion is modeled by the compressible
Navier-Stokes-Fourier system and the structure displacement is described by a
structurally damped plate equation. Our main results are the existence of
strong solutions in an $L^p-L^q$ setting for small time or for small data.
Through a change of variables and a fixed point argument, the proof of the main
results is mainly based on the maximal regularity property of the corresponding
linear systems. For small time existence, this property is obtained by
decoupling the linear system into several standard linear systems whereas for
global existence and for small data, the maximal regularity property is proved
by showing that the corresponding linear coupled {\em fluid-structure} operator
is $\mathcal{R}-$sectorial.
|
2006.00488v1
|
2020-06-03
|
Giant voltage control of spin Hall nano-oscillator damping
|
Spin Hall nano-oscillators (SHNOs) are emerging spintronic devices for
microwave signal generation and oscillator based neuromorphic computing
combining nano-scale footprint, fast and ultra-wide microwave frequency
tunability, CMOS compatibility, and strong non-linear properties providing
robust large-scale mutual synchronization in chains and two-dimensional arrays.
While SHNOs can be tuned via magnetic fields and the drive current, neither
approach is conducive for individual SHNO control in large arrays. Here, we
demonstrate electrically gated W/CoFeB/MgO nano-constrictions in which the
voltage-dependent perpendicular magnetic anisotropy, tunes the frequency and,
thanks to nano-constriction geometry, drastically modifies the spin-wave
localization in the constriction region resulting in a giant 42 % variation of
the effective damping over four volts. As a consequence, the SHNO threshold
current can be strongly tuned. Our demonstration adds key functionality to
nano-constriction SHNOs and paves the way for energy-efficient control of
individual oscillators in SHNO chains and arrays for neuromorphic computing.
|
2006.02151v1
|
2020-06-08
|
Rogue wave, interaction solutions to the KMM system
|
In this paper, the consistent tanh expansion (CTE) method and the truncated
Painlev$\acute{\rm e}$ analysis are applied to the Kraenkel-Manna-Merle (KMM)
system, which describes propagation of short wave in ferromagnets. Two series
of analytic solutions of the original KMM system (free of damping effect) are
obtained via the CTE method. The interaction solutions contain an arbitrary
function, which provides a wide variety of choices to acquire new propagation
structures. Particularly, the breather soliton, periodic oscillation soliton
and multipole instanton are obtained. Furthermore, we obtain some exact
solutions of the damped-KMM equation at the first time. On the other hand, a
coupled equation containing quadri-linear form and tri-linear form for the
original KMM system is obtained by the truncated Painlev$\acute{\rm e}$
analysis, and the rogue wave solution and interaction solutions between rogue
wave and multi-soliton for the KMM system are discussed.
|
2006.04312v1
|
2020-06-10
|
Interpolation between Residual and Non-Residual Networks
|
Although ordinary differential equations (ODEs) provide insights for
designing network architectures, its relationship with the non-residual
convolutional neural networks (CNNs) is still unclear. In this paper, we
present a novel ODE model by adding a damping term. It can be shown that the
proposed model can recover both a ResNet and a CNN by adjusting an
interpolation coefficient. Therefore, the damped ODE model provides a unified
framework for the interpretation of residual and non-residual networks. The
Lyapunov analysis reveals better stability of the proposed model, and thus
yields robustness improvement of the learned networks. Experiments on a number
of image classification benchmarks show that the proposed model substantially
improves the accuracy of ResNet and ResNeXt over the perturbed inputs from both
stochastic noise and adversarial attack methods. Moreover, the loss landscape
analysis demonstrates the improved robustness of our method along the attack
direction.
|
2006.05749v4
|
2020-06-15
|
Multimode cold-damping optomechanics with delayed feedback
|
We investigate the role of time delay in cold-damping optomechanics with
multiple mechanical resonances. For instantaneous electronic response, it was
recently shown in \textit{Phys. Rev. Lett. \textbf{123}, 203605 (2019)}, that a
single feedback loop is sufficient to simultaneously remove thermal noise from
many mechanical modes. While the intrinsic delayed response of the electronics
can induce single mode and mutual heating between adjacent modes, we propose to
counteract such detrimental effects by introducing an additional time delay to
the feedback loop. For lossy cavities and broadband feedback, we derive
analytical results for the final occupancies of the mechanical modes within the
formalism of quantum Langevin equations. For modes that are frequency
degenerate collective effects dominate, mimicking behavior similar to Dicke
super- and subradiance. These analytical results, corroborated with numerical
simulations of both transient and steady state dynamics, allow to find suitable
conditions and strategies for efficient single or multimode feedback
optomechanics.
|
2006.08430v2
|
2020-06-12
|
Analytic solution of the SEIR epidemic model via asymptotic approximant
|
An analytic solution is obtained to the SEIR Epidemic Model. The solution is
created by constructing a single second-order nonlinear differential equation
in $\ln S$ and analytically continuing its divergent power series solution such
that it matches the correct long-time exponential damping of the epidemic
model. This is achieved through an asymptotic approximant (Barlow et. al, 2017,
Q. Jl Mech. Appl. Math, 70 (1), 21-48) in the form of a modified symmetric
Pad\'e approximant that incorporates this damping. The utility of the
analytical form is demonstrated through its application to the COVID-19
pandemic.
|
2006.09818v2
|
2020-06-20
|
On The Energy Transfer To High Frequencies In The Damped/Driven Nonlinear Schrödinger Equation (Extended Version)
|
We consider a damped/driven nonlinear Schr\"odinger equation in an $n$-cube
$K^{n}\subset\mathbb{R}^n$, $n$ is arbitrary, under Dirichlet boundary
conditions \[ u_t-\nu\Delta u+i|u|^2u=\sqrt{\nu}\eta(t,x),\quad x\in
K^{n},\quad u|_{\partial K^{n}}=0, \quad \nu>0, \] where $\eta(t,x)$ is a
random force that is white in time and smooth in space. It is known that the
Sobolev norms of solutions satisfy $ \| u(t)\|_m^2 \le C\nu^{-m}, $ uniformly
in $t\ge0$ and $\nu>0$. In this work we prove that for small $\nu>0$ and any
initial data, with large probability the Sobolev norms $\|u(t,\cdot)\|_m$ of
the solutions with $m>2$ become large at least to the order of
$\nu^{-\kappa_{n,m}}$ with $\kappa_{n,m}>0$, on time intervals of order
$\mathcal{O}(\frac{1}{\nu})$.
|
2006.11518v2
|
2020-06-23
|
The Contour Method: a new approach to finding modes of non-adiabatic stellar pulsations
|
The contour method is a new approach to calculating the non-adiabatic
pulsation frequencies of stars. These frequencies can be found by solving for
the complex roots of a characteristic equation constructed from the linear
non-adiabatic stellar pulsation equations. A complex-root solver requires an
initial trial frequency for each non adiabatic root. A standard method for
obtaining initial trial frequencies is to use a star's adiabatic pulsation
frequencies, but this method can fail to converge to non-adiabatic roots,
especially as the growth and/or damping rate of the pulsations becomes large.
The contour method provides an alternative way for obtaining initial trial
frequencies that robustly converges to non-adiabatic roots, even for stellar
models with extremely non-adiabatic pulsations and thus large growth/damping
rates. We describe the contour method implemented in the GYRE stellar pulsation
code and use it to calculate the non-adiabatic pulsation frequencies of
$10\,\rm{M_{\odot}}$ and $20\,\rm{M_{\odot}}$ $\beta$ Cephei star models, and
of a $0.9\,\rm{M_{\odot}}$ extreme helium star model.
|
2006.13223v2
|
2020-06-24
|
The Complex Permeability of Split-Ring Resonator Arrays Measured at Microwave Frequencies
|
We have measured the relative permeability of split-ring resonator (SRR)
arrays used in metamaterials designed to have $\mu^\prime< 0$ over a narrow
range of microwave frequencies. The SRR arrays were loaded into the bore of a
loop-gap resonator (LGR) and reflection coefficient measurements were used to
determine both the real and imaginary parts of the array's effective
permeability. Data were collected as a function of array size and SRR spacing.
The results were compared to those obtained from continuous extended split-ring
resonators (ESRRs). The arrays of planar SRRs exhibited enhanced damping and a
narrower range of frequencies with $\mu^\prime<0$ when compared to the ESRRs.
The observed differences in damping, however, were diminished considerably when
the array size was expanded from a one-dimensional array of $N$ SRRs to a
$2\times 2\times N$ array. Our method can also be used to experimentally
determine the effective permeability of other metamaterial designs.
|
2006.13861v1
|
2020-06-25
|
Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids
|
We characterize the $L^2$ decay rate of solutions to the 3D
magneto-micropolar system in terms of the decay character of the initial datum.
Due to a linear damping term, the micro-rotational field has a faster decay
rate. We also address the asymptotic behaviour of solutions by comparing them
to solutions to the linear part. As a result of the linear damping, the
difference between the micro-rotational field and its linear part also decays
faster. As part of the proofs of these results, we prove estimates for the
derivatives of solutions which might be of independent interest.
|
2006.14427v2
|
2020-06-27
|
Measurement-Based Estimation of System State Matrix for AC Power Systems with Integrated VSCs
|
In this paper, a wide-area measurement system (WAMS)-based method is proposed
to estimate the system state matrix for AC system with integrated voltage
source converters (VSCs) and identify the electromechanical modes. The proposed
method is purely model-free, requiring no knowledge of accurate network
topology and system parameters. Numerical studies in the IEEE 68-bus system
with integrated VSCs show that the proposed measurementbased method can
accurately identify the electromechanical modes and estimate the damping
ratios, the mode shapes, and the participation factors. The work may serve as a
basis for developing WAMS-based damping control using VSCs in the future.
|
2006.15244v1
|
2020-06-29
|
Collective excitations in spin-polarized bilayer graphene
|
We calculate the plasmon frequency and damping rate of plasma oscillations in
a spin-polarized BLG system. Using the long wavelength approximation for
dynamical dielectric function, we obtain an analytical expression for plasmon
frequency showing that the degree of spin polarization P has negligible effect
on the long wavelength plasmon frequency. Numerical calculations demonstrate
that the degree of spin polarization affects slightly (strongly) plasmon
frequency at small (large) wave-vectors and the maximum value of damping rate
increases with increasing P. We also study the effects of carrier density and
substrate dielectric constant on plasmon properties for different value of spin
polarization. The numerically calculated critical wave-vector, at which the
plasmon dispersion curve hits the edge of electron-hole continuum, decreases
with P and can be used to determine experimentally the degree of spin
polarization.
|
2006.16042v2
|
2020-06-29
|
Quadratic optomechanical cooling of a cavity-levitated nanosphere
|
We report on cooling the center-of-mass motion of a nanoparticle due to a
purely quadratic coupling between its motion and the optical field of a high
finesse cavity. The resulting interaction gives rise to a Van der Pol nonlinear
damping, which is analogous to conventional parametric feedback where the
cavity provides passive feedback without measurement. We show experimentally
that like feedback cooling the resulting energy distribution is strongly
nonthermal and can be controlled by the nonlinear damping of the cavity. As
quadratic coupling has a prominent role in proposed protocols to generate
deeply nonclassical states, our work represents a first step for producing such
states in a levitated system.
|
2006.16103v1
|
2020-07-01
|
Entanglement of quantum oscillators coupled to different heat baths
|
We study the non-equilibrium dynamics of two coupled oscillators interacting
with their own heat baths of quantum scalar fields at different temperature
$T_1$ and $T_2$ with bilinear couplings between them. We particularly focus on
the entanglement or inseparability property of their quantum states. The
critical temperatures of two respective oscillators, $T_{1c}$ and $T_{2c}$,
higher than which the entanglement disappears, can be determined. It is found
that when two damping parameters are largely different, say $\gamma_1 \ll
\gamma_2$, the critical temperature $T_{1c}$ with respect to the frequency
$\Omega_+$, the higher frequency among two normal modes frequencies, can be
very large, $T_{1c} \gg \Omega_+$, while $T_{2c} \propto \Omega_+$ with the
possibility of hot entanglement. The entanglement of two oscillators with the
temperature-dependent damping parameters $\gamma_{1;2,T}$ from heat baths is
also discussed.
|
2007.00288v2
|
2020-07-01
|
Stabilization of the critical and subcritical semilinear inhomogeneous and anisotropic elastic wave equation
|
{\bf Abstract} \,\,We prove exponential decay of the critical and subcritical
semilinear inhomogeneous and anisotropic elastic wave equation with locally
distributed damping on bounded domain. One novelty compared to previous
results, is to give a checkable condition of the inhomogeneous and anisotropic
medias. Another novelty is to establish a framework to study the stability of
the damped semilinear inhomogeneous and anisotropic elastic wave equation,
which is hard to apply Carleman estimates to deal with. We develop the Morawetz
estimates and the compactness-uniqueness arguments for the semiliear elastic
wave equation to prove the unique continuation, observability inequality and
stabilization result.
It is pointing that our proof is different from the classical method (See
Dehman et al.\cite{ZYY11}, Joly et al.\cite{ZYY16} and Zuazua \cite{ZYY43}),
which succeeds for the subcritical semilinear wave equation and fails for the
critical semilinear wave equation.
|
2007.00813v1
|
2020-07-06
|
Collective excitations and universal broadening of cyclotron absorption in Dirac semimetals in a quantizing magnetic field
|
The spectrum of electromagnetic collective excitations in Dirac semimetals
placed in a quantizing magnetic field is considered. We have found the Landau
damping regions using the energy and momentum conservation law for allowed
transitions between one-particle states of electron excitations. Analysis of
dispersion equations for longitudinal and transverse waves near the window
boundaries in the Landau damping regions reveals different types of collective
excitations. We also indicate the features of universal broadening of cyclotron
absorption for a magnetic field variation in systems with linear dispersion of
the electron spectrum. The use of the obtained spectrum also allows us to
predict a number of oscillation and resonance effects in the field of
magneto-optical phenomena.
|
2007.02979v1
|
2020-07-06
|
Fast convex optimization via a third-order in time evolution equation: TOGES-V an improved version of TOGES
|
In a Hilbert space setting H, for convex optimization, we analyze the fast
convergence properties as t tends to infinity of the trajectories generated by
a third-order in time evolution system. The function f to minimize is supposed
to be convex, continuously differentiable, with a nonempty set of minimizers.
It enters into the dynamic through its gradient. Based on this new dynamical
system, we improve the results obtained by [Attouch, Chbani, Riahi: Fast convex
optimization via a third-order in time evolution equation, Optimization 2020].
As a main result, when the damping parameter $\alpha$ satisfies $\alpha > 3$,
we show that the convergence of the values at the order 1/t3 as t goes to
infinity, as well as the convergence of the trajectories. We complement these
results by introducing into the dynamic an Hessian driven damping term, which
reduces the oscillations. In the case of a strongly convex function f, we show
an autonomous evolution system of the third order in time with an exponential
rate of convergence. All these results have natural extensions to the case of a
convex lower semicontinuous function with extended real values. Just replace f
with its Moreau envelope.
|
2007.03062v1
|
2020-08-13
|
Using Machine Learning to Find Ghostly Damped Ly$α$ Systems in SDSS DR14
|
We report the discovery of 59 new ghostly absorbers from the Sloan Digital
Sky Survey (SDSS) Data Release 14 (DR14). These absorbers, with $z_{\rm
abs}$$\sim$$z_{\rm QSO}$, reveal no Ly$\alpha$ absorption, and they are mainly
identified through the detection of strong metal absorption lines in the
spectra. The number of previously known such systems is 30. The new systems are
found with the aid of machine learning algorithms. The spectra of 41 (out of
total of 89) absorbers also cover the Ly$\beta$ spectral region. By fitting the
damping wings of the Ly$\beta$ absorption in the stacked spectrum of 21 (out of
41) absorbers with relatively stronger Ly$\beta$ absorption, we measured an HI
column density of log$N$(HI)=21.50. This column density is 0.5dex higher than
that of the previous work. We also found that the metal absorption lines in the
stacked spectrum of the 21 ghostly absorbers with stronger Ly$\beta$ absorption
have similar properties as those in the stacked spectrum of the remaining
systems. These circumstantial evidence strongly suggest that the majority of
our ghostly absorbers are indeed DLAs.
|
2008.05910v1
|
2020-08-14
|
Testing Dissipative Collapse Models with a Levitated Micromagnet
|
We present experimental tests of dissipative extensions of spontaneous wave
function collapse models based on a levitated micromagnet with ultralow
dissipation. The spherical micromagnet, with radius $R=27$ $\mu$m, is levitated
by Meissner effect in a lead trap at $4.2$ K and its motion is detected by a
SQUID. We perform accurate ringdown measurements on the vertical translational
mode with frequency $57$ Hz, and infer the residual damping at vanishing
pressure $\gamma/2\pi<9$ $\mu$Hz. From this upper limit we derive improved
bounds on the dissipative versions of the CSL (continuous spontaneous
localization) and the DP (Di\'{o}si-Penrose) models with proper choices of the
reference mass. In particular, dissipative models give rise to an intrinsic
damping of an isolated system with the effect parameterized by a temperature
constant; the dissipative CSL model with temperatures below 1 nK is ruled out,
while the dissipative DP model is excluded for temperatures below $10^{-13}$ K.
Furthermore, we present the first bounds on dissipative effects in a more
recent model, which relates the wave function collapse to fluctuations of a
generalized complex-valued spacetime metric.
|
2008.06245v2
|
2020-08-15
|
$L^1$-convergence to generalized Barenblatt solution for compressible Euler equations with time-dependent damping
|
The large time behavior of entropy solution to the compressible Euler
equations for polytropic gas (the pressure $p(\rho)=\kappa\rho^{\gamma},
\gamma>1$) with time dependent damping like $-\frac{1}{(1+t)^\lambda}\rho u$
($0<\lambda<1$) is investigated. By introducing an elaborate iterative method
and using the intensive entropy analysis, it is proved that the $L^\infty$
entropy solution of compressible Euler equations with finite initial mass
converges strongly in the natural $L^1$ topology to a fundamental solution of
porous media equation (PME) with time-dependent diffusion, called by
generalized Barenblatt solution. It is interesting that the $L^1$ decay rate is
getting faster and faster as $\lambda$ increases in $(0,
\frac{\gamma}{\gamma+2}]$, while is getting slower and slower in $[
\frac{\gamma}{\gamma+2}, 1)$.
|
2008.06704v1
|
2020-08-21
|
Structure preserving algorithms for simulation of linearly damped acoustic systems
|
Energy methods for constructing time-stepping algorithms are of increased
interest in application to nonlinear problems, since numerical stability can be
inferred from the conservation of the system energy. Alternatively, symplectic
integrators may be constructed that preserve the symplectic form of the system.
This methodology has been established for Hamiltonian systems, with numerous
applications in engineering problems. In this paper an extension of such
methods to non-conservative acoustic systems is presented. Discrete
conservation laws, equivalent to that of energy-conserving schemes, are derived
for systems with linear damping, incorporating the action of external forces.
Furthermore the evolution of the symplectic structure is analysed in the
continuous and the discrete case. Existing methods are examined and novel
methods are designed using a lumped oscillator as an elemental model. The
proposed methodology is extended to the case of distributed systems and
exemplified through a case study of a vibrating string bouncing against a rigid
obstacle.
|
2008.09479v1
|
2020-08-24
|
The move from Fujita to Kato type exponent for a class of semilinear evolution equations with time-dependent damping
|
In this paper, we derive suitable optimal $L^p-L^q$ decay estimates, $1\leq
p\leq 2\leq q\leq \infty$, for the solutions to the $\sigma$-evolution
equation, $\sigma>1$, with scale-invariant time-dependent damping and power
nonlinearity~$|u|^p$, \[ u_{tt}+(-\Delta)^\sigma u + \frac{\mu}{1+t} u_t=
|u|^{p}, \] where $\mu>0$, $p>1$. The critical exponent $p=p_c$ for the global
(in time) existence of small data solutions to the Cauchy problem is related to
the long time behavior of solutions, which changes accordingly $\mu \in (0, 1)$
or $\mu>1$. Under the assumption of small initial data in $L^1\cap L^2$, we
find the critical exponent \[ p_c=1+ \max
\left\{\frac{2\sigma}{[n-\sigma+\sigma\mu]_+}, \frac{2\sigma}{n} \right\}
=\begin{cases} 1+ \frac{2\sigma}{[n-\sigma+\sigma\mu]_+}, \quad \mu \in (0,
1)\\ 1+ \frac{2\sigma}{n}, \quad \mu>1. \end{cases} \]
For $\mu>1$ it is well known as Fujita type exponent, whereas for $\mu \in
(0, 1)$ one can read it as a shift of Kato exponent.
|
2008.10374v1
|
2020-09-01
|
On the decay in $W^{1,\infty}$ for the 1D semilinear damped wave equation on a bounded domain
|
In this paper we study a semilinear wave equation with nonlinear,
time-dependent damping in one space dimension. For this problem, we prove a
well-posedness result in $W^{1,\infty}$ in the space-time domain $(0,1)\times
[0,+\infty)$. Then we address the problem of the time-asymptotic stability of
the zero solution and show that, under appropriate conditions, the solution
decays to zero at an exponential rate in the space $W^{1,\infty}$. The proofs
are based on the analysis of the corresponding semilinear system for the first
order derivatives, for which we show a contractive property of the invariant
domain.
|
2009.00731v2
|
2020-09-08
|
Nanomechanical damping via electron-assisted relaxation of two-level systems
|
We report on measurements of dissipation and frequency noise at millikelvin
temperatures of nanomechanical devices covered with aluminum. A clear excess
damping is observed after switching the metallic layer from superconducting to
the normal state with a magnetic field. Beyond the standard model of internal
tunneling systems coupled to the phonon bath, here we consider the relaxation
to the conduction electrons together with the nature of the mechanical
dispersion laws for stressed/unstressed devices. With these key ingredients, a
model describing the relaxation of two-level systems inside the structure due
to interactions with electrons and phonons with well separated timescales
captures the data. In addition, we measure an excess 1/f-type frequency noise
in the normal state, which further emphasizes the impact of conduction
electrons.
|
2009.03804v3
|
2020-09-10
|
Inclination damping on Callisto
|
Callisto is thought to possess a subsurface ocean, which will dissipate
energy due to obliquity tides. This dissipation should have damped any
primordial inclination within 1 Gyr - and yet Callisto retains a present-day
inclination. We argue that Callisto's inclination and eccentricity were both
excited in the relatively recent past (~0.3 Gyr). This excitation occurred as
Callisto migrated outwards according to the "resonance-locking" model and
passed through a 2:1 mean-motion resonance with Ganymede. Ganymede's orbital
elements were likewise excited by the same event. To explain the present-day
orbital elements we deduce a solid-body tidal k2/Q~0.05 for Callisto and a
significantly lower value for Ganymede.
|
2009.05002v1
|
2020-09-25
|
Sound in a system of chiral one-dimensional fermions
|
We consider a system of one-dimensional fermions moving in one direction,
such as electrons at the edge of a quantum Hall system. At sufficiently long
time scales the system is brought to equilibrium by weak interactions between
the particles, which conserve their total number, energy, and momentum. Time
evolution of the system near equilibrium is described by hydrodynamics based on
the three conservation laws. We find that the system supports three sound
modes. In the low temperature limit one mode is a pure oscillation of particle
density, analogous to the ordinary sound. The other two modes involve
oscillations of both particle and entropy densities. In the presence of
disorder, the first sound mode is strongly damped at frequencies below the
momentum relaxation rate, whereas the other two modes remain weakly damped.
|
2009.12364v1
|
2020-09-30
|
Dynamical properties of a driven dissipative dimerized $S = 1/2$ chain
|
We consider the dynamical properties of a gapped quantum spin system coupled
to the electric field of a laser, which drives the resonant excitation of
specific phonon modes that modulate the magnetic interactions. We deduce the
quantum master equations governing the time-evolution of both the lattice and
spin sectors, by developing a Lindblad formalism with bath operators providing
an explicit description of their respective phonon-mediated damping terms. We
investigate the nonequilibrium steady states (NESS) of the spin system
established by a continuous driving, delineating parameter regimes in driving
frequency, damping, and spin-phonon coupling for the establishment of
physically meaningful NESS and their related non-trivial properties. Focusing
on the regime of generic weak spin-phonon coupling, we characterize the NESS by
their frequency and wave-vector content, explore their transient and relaxation
behavior, and discuss the energy flow, the system temperature, and the critical
role of the type of bath adopted. Our study lays a foundation for the
quantitative modelling of experiments currently being designed to control
coherent many-body spin states in quantum magnetic materials.
|
2009.14805v2
|
2020-10-01
|
Avoiding coherent errors with rotated concatenated stabilizer codes
|
Coherent errors, which arise from collective couplings, are a dominant form
of noise in many realistic quantum systems, and are more damaging than oft
considered stochastic errors. Here, we propose integrating stabilizer codes
with constant-excitation codes by code concatenation. Namely, by concatenating
an $[[n,k,d]]$ stabilizer outer code with dual-rail inner codes, we obtain a
$[[2n,k,d]]$ constant-excitation code immune from coherent phase errors and
also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer
code is fault-tolerant, the constant-excitation code has a positive
fault-tolerant threshold against stochastic errors. Setting the outer code as a
four-qubit amplitude damping code yields an eight-qubit constant-excitation
code that corrects a single amplitude damping error, and we analyze this code's
potential as a quantum memory.
|
2010.00538v2
|
2020-10-02
|
Parametric instability in a free evolving warped protoplanetary disc
|
Warped accretion discs of low viscosity are prone to hydrodynamic instability
due to parametric resonance of inertial waves as confirmed by local
simulations. Global simulations of warped discs, using either smoothed particle
hydrodynamics (SPH) or grid-based codes, are ubiquitous but no such instability
has been seen. Here we utilize a hybrid Godunov-type Lagrangian method to study
parametric instability in global simulations of warped Keplerian discs at
unprecedentedly high resolution (up to 120 million particles). In the global
simulations, the propagation of the warp is well described by the linear
bending-wave equations before the instability sets in. The ensuing turbulence,
captured for the first time in a global simulation, damps relative orbital
inclinations and leads to a decrease in the angular momentum deficit. As a
result, the warp undergoes significant damping within one bending-wave crossing
time. Observed protoplanetary disc warps are likely maintained by companions or
aftermath of disc breaking.
|
2010.00862v2
|
2020-10-15
|
Dephasing in strongly disordered interacting quantum wires
|
Many-body localization is a fascinating theoretical concept describing the
intricate interplay of quantum interference, i.e. localization, with many-body
interaction induced dephasing. Numerous computational tests and also several
experiments have been put forward to support the basic concept. Typically,
averages of time-dependent global observables have been considered, such as the
charge imbalance. We here investigate within the disordered spin-less Hubbard
($t-V$) model how dephasing manifests in time dependent variances of
observables. We find that after quenching a N\'eel state the local charge
density exhibits strong temporal fluctuations with a damping that is sensitive
to disorder $W$: variances decay in a power law manner, $t^{-\zeta}$, with an
exponent $\zeta(W)$ strongly varying with $W$. A heuristic argument suggests
the form, $\zeta\approx\alpha(W)\xi_\text{sp}$, where $\xi_\text{sp}(W)$
denotes the noninteracting localization length and $\alpha(W)$ characterizes
the multifractal structure of the dynamically active volume fraction of the
many-body Hilbert space. In order to elucidate correlations underlying the
damping mechanism, exact computations are compared with results from the
time-dependent Hartree-Fock approximation. Implications for experimentally
relevant observables, such as the imbalance, will be discussed.
|
2010.07919v1
|
2020-10-19
|
Modified EP MIMO Detection Algorithm with Deep Learning Parameters Selection
|
Expectation Propagation (EP)-based Multiple-Input Multiple-Output (MIMO)
detector is regarded as a state-of-the-art MIMO detector because of its
exceptional performance. However, we find that the EP MIMO detector cannot
guarantee to achieve the optimal performance due to the empirical parameter
selection, including initial variance and damping factors. According to the
influence of the moment matching and parameter selection for the performance of
the EP MIMO detector, we propose a modified EP MIMO detector (MEPD). In order
to obtain the optimal initial variance and damping factors, we adopt a deep
learning scheme, in which we unfold the iterative processing of MEPD to
establish MEPNet for parameters training. The simulation results show that MEPD
with off-line trained parameters outperforms the original one in various MIMO
scenarios. Besides, the proposed MEPD with deep learning parameters selection
is more robust than EPD in practical scenarios.
|
2010.09183v2
|
2020-10-23
|
A damped point-vortex model for polar-core spin vortices in a ferromagnetic spin-1 Bose-Einstein condensate
|
Ferromagnetic spin-1 Bose-Einstein condensates in the broken-axisymmetric
phase support polar-core spin vortices (PCVs), which are intimately linked to
the nonequilibrium dynamics of the system. For a purely transversely magnetized
system, the Turner point-vortex model predicts that PCVs behave like massive
charged particles interacting via a two-dimensional Coulomb potential. We test
the accuracy of the Turner model for two oppositely charged PCVs, via
comparisons with numerical simulations. While the bare Turner model shows
discrepancies with our numerical results, we find that a simple rescaling of
the PCV mass gives much better agreement. This can be explained via a
phenomenological damping arising from coupling to modes extrinsic to the
point-vortex phase space. We also identify the excitations produced following
PCV annihilation, which help elucidate recent phase ordering results. We extend
the Turner model to cases where the system is magnetized both transversally and
axially, identifying a crossover to scalar vortex dynamics for increasing
external Zeeman field.
|
2010.12154v1
|
2020-10-26
|
Viscous damping of chiral dynamos in the early universe
|
Chiral dynamo converting asymmetry between right and left-handed leptons in
the early universe into helical magnetic field has been proposed as a possible
cosmological magnetogenesis scenario. We show that this mechanism is strongly
affected by viscous damping of primordial plasma motions excited by the dynamo.
This effect modifies the expected range of strength and correlation length of
the chiral dynamo field which could have survived till present epoch in the
voids of the Large Scale Structure. We show the range of parameters of chiral
dynamo field that may have survived in the voids is still consistent with
existing lower bounds on intergalactic magnetic field from gamma-ray
observations, but only if the right-left lepton asymmetry at the temperature
T~80 TeV is very high, close to the maximal possible value.
|
2010.13571v1
|
2020-10-28
|
Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets
|
We construct quasimodes for some non-selfadjoint semiclassical operators at
the boundary of the pseudo-spectrum using propagation of Hagedorn wave-packets.
Assuming that the imaginary part of the principal symbol of the operator is
non-negative and vanishes on certain points of the phase-space satisfying a
subelliptic finite-type condition, we construct quasimodes that concentrate on
these non-damped points. More generally, we apply this technique to construct
quasimodes for non-selfadjoint semiclassical perturbations of the harmonic
oscillator that concentrate on non-damped periodic orbits or invariant tori
satisfying a weak-geometric-control condition
|
2010.14967v5
|
2020-10-28
|
Spin-valley collective modes of the electron liquid in graphene
|
We develop the theory of collective modes supported by a Fermi liquid of
electrons in pristine graphene. Under reasonable assumptions regarding the
electron-electron interaction, all the modes but the plasmon are over-damped.
In addition to the $SU(2)$ symmetric spin mode, these include also the valley
imbalance modes obeying a $U(1)$ symmetry, and a $U(2)$ symmetric valley spin
imbalance mode. We derive the interactions and diffusion constants
characterizing the over-damped modes. The corresponding relaxation rates set
fundamental constraints on graphene valley- and spintronics applications.
|
2010.15154v2
|
2020-10-29
|
Collisionless sound of bosonic superfluids in lower dimensions
|
The superfluidity of low-temperature bosons is well established in the
collisional regime. In the collisionless regime, however, the presence of
superfluidity is not yet fully clarified, in particular in lower spatial
dimensions. Here we compare the Vlasov-Landau equation, which does not take
into account the superfluid nature of the bosonic system, with the
Andreev-Khalatnikov equations, which instead explicitly contain a superfluid
velocity. We show that recent experimental data of the sound mode in a
two-dimensional collisionless Bose gas of $^{87}$Rb atoms are in good agreement
with both theories but the sound damping is better reproduced by the Andreev
-Khalatnikov equations below the Berezinskii-Kosterlitz-Thouless critical
temperature $T_c$ while above $T_c$ the Vlasov-Landau results are closer to the
experimental ones. For one dimensional bosonic fluids, where experimental data
are not yet available, we find larger differences between the sound velocities
predicted by the two transport theories and, also in this case, the existence
of a superfluid velocity reduces the sound damping.
|
2010.15724v3
|
2020-11-02
|
Constraining the Halo Mass of Damped Ly$α$ Absorption Systems (DLAs) at $z=2-3.5$ using the Quasar-CMB Lensing Cross-correlation
|
We study the cross correlation of damped Ly$\alpha$ systems (DLAs) and their
background quasars, using the most updated DLA catalog and the Planck 2018 CMB
lensing convergence field. Our measurement suggests that the DLA bias $b_{\rm
DLA}$ is smaller than $3.1$, corresponding to $\log(M/M_\odot h^{-1})\leq 12.3$
at a confidence of $90\%$. These constraints are broadly consistent with Alonso
et al. (2018) and previous measurements by cross-correlation between DLAs and
the Ly$\alpha$ forest (e.g. Font-Ribera et al. 2012; Perez-Rafols et al. 2018).
Further, our results demonstrate the potential of obtaining a more precise
measurement of the halo mass of high-redshift sources using next generation CMB
experiments with a higher angular resolution. The python-based codes and data
products of our analysis are available at
https://github.com/LittleLin1999/CMB-lensingxDLA.
|
2011.01234v1
|
2020-11-07
|
Bresse-Timoshenko type systems with thermodiffusion effects: Well-possedness, stability and numerical results
|
Bresse-Timoshenko beam model with thermal, mass diffusion and theormoelastic
effects is studied. We state and prove the well-posedness of problem. The
global existence and uniqueness of the solution is proved by using the
classical Faedo-Galerkin approximations along with two a priori estimates. We
prove an exponential stability estimate for problem under an unusual
assumption, and by using a multiplier technique in two different cases, with
frictional damping in the angular rotation and with frictional damping in the
vertical displacement. In numerical parts, we first obtained a numerical scheme
for problem by $P_1$-finite element method for space discretization and
implicit Euler scheme for time discretization. Then, we showed that the
discrete energy decays, later a priori error estimates are established. Finally
, some numerical simulations are presented.
|
2011.03680v2
|
2020-11-09
|
Impedance Optimization for Uncertain Contact Interactions Through Risk Sensitive Optimal Control
|
This paper addresses the problem of computing optimal impedance schedules for
legged locomotion tasks involving complex contact interactions. We formulate
the problem of impedance regulation as a trade-off between disturbance
rejection and measurement uncertainty. We extend a stochastic optimal control
algorithm known as Risk Sensitive Control to take into account measurement
uncertainty and propose a formal way to include such uncertainty for unknown
contact locations. The approach can efficiently generate optimal state and
control trajectories along with local feedback control gains, i.e. impedance
schedules. Extensive simulations demonstrate the capabilities of the approach
in generating meaningful stiffness and damping modulation patterns before and
after contact interaction. For example, contact forces are reduced during early
contacts, damping increases to anticipate a high impact event and tracking is
automatically traded-off for increased stability. In particular, we show a
significant improvement in performance during jumping and trotting tasks with a
simulated quadruped robot.
|
2011.04684v2
|
2020-11-12
|
A priori bounds for rough differential equations with a non-linear damping term
|
We consider a rough differential equation with a non-linear damping drift
term: \begin{align*} dY(t) = - |Y|^{m-1} Y(t) dt + \sigma(Y(t)) dX(t),
\end{align*} where $X$ is a branched rough path of arbitrary regularity $\alpha
>0$, $m>1$ and where $\sigma$ is smooth and satisfies an $m$ and
$\alpha$-dependent growth property. We show a strong a priori bound for $Y$,
which includes the "coming down from infinity" property, i.e. the bound on
$Y(t)$ for a fixed $t>0$ holds uniformly over all choices of initial datum
$Y(0)$. The method of proof builds on recent work by Chandra, Moinat and Weber
on a priori bounds for the $\phi^4$ SPDE in arbitrary subcritical dimension. A
key new ingredient is an extension of the algebraic framework which permits to
derive an estimate on higher order conditions of a coherent controlled rough
path in terms of the regularity condition at lowest level.
|
2011.06645v4
|
2020-11-14
|
Oscillating charge currents of one-dimensional Hubbard model in an electric field
|
The time evolution properties of charge current for the one-dimensional
Hubbard model in an electric field have been studied in a rigorous manner. We
find that there is a complete and orthonormal set of time-evolution states for
which the charge current can only keep zero or oscillate constantly, differing
from the possible picture of damped or over-damped Bloch oscillations due to
strong correlations. It is also found that, associated with these states, there
is a set of constant phase factors, which are uniquely determined and are very
useful on discussing the long-time evolution behaviors of the system.
|
2011.07220v2
|
2020-12-07
|
Damped Neutrino Oscillations in a Conformal Coupling Model
|
Flavor transitions of Neutrinos with a nonstandard interaction are studied. A
scalar field is conformally coupled to matter and neutrinos. This interaction
alters the neutrino effective mass and its wavefunction leading to a damping
factor, causing deficits in the probability densities and affecting the
oscillation phase. As the matter density determines the scalar field's
behavior, we also have an indirect matter density effect on the flavor
conversion. We explain our results in the context of screening models and study
the deficit in the total flux of electron-neutrinos produced in the Sun through
the decay process and confront our results with observational data.
|
2012.03633v3
|
2020-12-10
|
Wakefield decay in a radially bounded plasma due to formation of electron halo
|
There is a new effect that can limit the lifetime of a weakly nonlinear
wakefield in a radially bounded plasma. If the drive beam is narrow, some of
the plasma electrons fall out of the collective motion and leave the plasma
radially, forming a negatively charged halo around it. These electrons
repeatedly return to the plasma under the action of the charge separation
field, interact with the plasma wave and cause its damping. The lowest-energy
halo electrons take the energy from the wave more efficiently, because their
trajectories are bent by the plasma wave towards the regions of the strongest
acceleration. For correct accounting of the wave damping in simulations, it is
necessary and sufficient to take the simulation window twice as wide as the
plasma.
|
2012.05676v1
|
2020-12-17
|
Magnetic equivalent of electric superradiance: radiative damping in yttrium-iron-garnet films
|
A dense system of independent oscillators, connected only by their
interaction with the same cavity excitation mode, will radiate coherently,
which effect is termed superradiance. In several cases, especially if the
density of oscillators is high, the superradiance may dominate the intrinsic
relaxation processes. This limit can be achieved, e.g., with cyclotron
resonance in two-dimensional electron gases. In those experiments, the
cyclotron resonance is coupled to the electric field of light, while the
oscillator density can be easily controlled by varying the gate voltage.
However, in the case of magnetic oscillators, to achieve the dominance of
superradiance is more tricky, as material parameters limit the oscillator
density, and the magnetic coupling to the light wave is rather small. Here we
present quasi-optical magnetic resonance experiments on thin films of yttrium
iron garnet. Due to the simplicity of experimental geometry, the intrinsic
damping and the superradiance can be easily separated in the transmission
spectra. We show that with increasing film thickness, the losses due to
coherent radiation prevail the system's internal broadening.
|
2012.09440v1
|
2020-12-21
|
Dissipation-driven strange metal behavior
|
Anomalous metallic properties are often observed in the proximity of quantum
critical points (QCPs), with violation of the Fermi Liquid paradigm. We propose
a scenario where, due to the presence of a nearby QCP, dynamical fluctuations
of the order parameter with finite correlation length mediate a nearly
isotropic scattering among the quasiparticles over the entire Fermi surface.
This scattering produces an anomalous metallic behavior, which is extended to
the lowest temperatures by an increase of the damping of the fluctuations. We
phenomenologically identify one single parameter ruling this increasing damping
when the temperature decreases, accounting for both the linear-in-temperature
resistivity and the seemingly divergent specific heat observed, e.g., in
high-temperature superconducting cuprates and some heavy-fermion metals.
|
2012.11697v1
|
2020-12-22
|
Damped perturbations of systems with centre-saddle bifurcation
|
An autonomous system of ordinary differential equations in the plane with a
centre-saddle bifurcation is considered. The influence of time damped
perturbations with power-law asymptotics is investigated. The particular
solutions tending at infinity to the fixed points of the limiting system are
considered. The stability of these solutions is analyzed when the bifurcation
parameter of the unperturbed system takes critical and non-critical values.
Conditions that ensure the persistence of the bifurcation in the perturbed
system are described. When the bifurcation is broken, a pair of solutions
tending to a degenerate fixed point of the limiting system appears in the
critical case. It is shown that, depending on the structure and the parameters
of the perturbations, one of these solutions can be stable, metastable or
unstable, while the other solution is always unstable.
|
2012.12116v1
|
2020-12-22
|
Mechanical parametric feedback-cooling for pendulum-based gravity experiments
|
Gravitational forces that oscillate at audio-band frequencies are measured
with masses suspended as pendulums that have resonance frequencies even lower.
If the pendulum is excited by thermal energy or by seismic motion of the
environment, the measurement sensitivity is reduced. Conventionally, this
problem is mitigated by seismic isolation and linear damping, potentially
combined with cryogenic cooling. Here, we propose mechanical parametric cooling
of the pendulum motion during the gravitational field measurement. We report a
proof of principle demonstration in the seismic noise dominated regime and
achieve a damping factor of the pendulum motion of 5.7. We find a model system
for which mechanical parametric feedback cooling reaches the quantum mechanical
regime near the ground state. More feasible applications we anticipate in
gravitational-wave detectors.
|
2012.12158v2
|
2020-12-23
|
The fate of nonlinear perturbations near the QCD critical point
|
The impact of the QCD critical point on the propagation of nonlinear waves
has been studied. The effects have been investigated within the scope of
second-order causal dissipative hydrodynamics by incorporating the critical
point into the equation of state, and the scaling behaviour of transport
coefficients and of thermodynamic response functions. Near the critical point,
the nonlinear waves are found to be significantly damped which may result in
the disappearance of the Mach cone effects of the away side jet. Such damping
may lead to enhancement in the fluctuations of elliptic and higher flow
coefficients. Therefore, the disappearance of Mach cone effects and the
enhancement of fluctuations in flow harmonics in the event-by-event analysis
may be considered as signals of the critical endpoint.
|
2012.12668v3
|
2020-12-28
|
A weakly nonlinear wave equation for damped acoustic waves with thermodynamic non-equilibrium effects
|
The problem of propagating nonlinear acoustic waves is considered; the
solution to which, both with and without damping, having been obtained to-date
starting from the Navier-Stokes-Duhem equations together with the continuity
and thermal conduction equation. The novel approach reported here adopts
instead, a discontinuous Lagrangian approach, i.e. from Hamilton's principle
together with a discontinuous Lagrangian for the case of a general viscous
flow. It is shown that ensemble averaging of the equation of motion resulting
from the Euler-Lagrange equations, under the assumption of irrotational flow,
leads to a weakly nonlinear wave equation for the velocity potential: in effect
a generalisation of Kuznetsov's well known equation with an additional term due
to thermodynamic non-equilibrium effects.
|
2012.14399v2
|
2020-12-28
|
Reliability optimization of friction-damped systems using nonlinear modes
|
A novel probabilistic approach for the design of mechanical structures with
friction interfaces is proposed. The objective function is defined as the
probability that a specified performance measure of the forced vibration
response is achieved subject to parameter uncertainties. The practicability of
the approach regarding the extensive amount of required design evaluations is
strictly related to the computational efficiency of the nonlinear dynamic
analysis. Therefore, it is proposed to employ a recently developed parametric
reduced order model (ROM) based on nonlinear modes of vibration, which can
facilitate a decrease of the computational burden by several orders of
magnitude. The approach was applied to a rotationally periodic assembly of a
bladed disk with underplatform friction dampers. The robustness of the optimum
damper design was significantly improved compared to the deterministic
approach, taking into account uncertainties in the friction coefficient, the
excitation level and the linear damping. Moreover, a scale invariance for
piecewise linear contact constraints is proven, which can be very useful for
the reduction of the numerical effort for the analysis of such systems.
|
2012.14466v1
|
2021-01-04
|
Fast flavor oscillations in dense neutrino media with collisions
|
We investigate the impact of the nonzero neutrino splitting and elastic
neutrino-nucleon collisions on fast neutrino oscillations. Our calculations
confirm that a small neutrino mass splitting and the neutrino mass hierarchy
have very little effect on fast oscillation waves. We also demonstrate
explicitly that fast oscillations remain largely unaffected for the
time/distance scales that are much smaller than the neutrino mean free path but
are damped on larger scales. This damping originates from both the direct
modification of the dispersion relation of the oscillation waves in the
neutrino medium and the flattening of the neutrino angular distributions over
time. Our work suggests that fast neutrino oscillation waves produced near the
neutrino sphere can propagate essentially unimpeded which may have
ramifications in various aspects of the supernova physics.
|
2101.01278v2
|
2021-01-15
|
Efficient Spin-Orbit Torque Generation in Semiconducting WTe2 with Hopping Transport
|
Spin-orbit torques (SOTs) from transition metal dichalcogenides systems
(TMDs) in conjunction with ferromagnetic materials are recently attractive in
spintronics for their versatile features. However, most of the previously
studied crystalline TMDs are prepared by mechanical exfoliation, which limits
their potentials for industrial applications. Here we show that amorphous WTe2
heterostructures deposited by magnetron sputtering possess a sizable
damping-like SOT efficiency {\xi}_DL^WTe2 ~ 0.20 and low damping constant
{\alpha} = 0.009/pm0.001. Only an extremely low critical switching current
density J_c ~ 7.05\times10^9 A/m^2 is required to achieve SOT-driven
magnetization switching. The SOT efficiency is further proved to depend on the
W and Te relative compositions in the co-sputtered W_100-xTe_x samples, from
which a sign change of {\xi}_DL^WTe2 is observed. Besides, the electronic
transport in amorphous WTe2 is found to be semiconducting and is governed by a
hopping mechanism. With the above advantages and rich tunability, amorphous and
semiconducting WTe2 serves as a unique SOT source for future spintronics
applications.
|
2101.06047v1
|
2021-01-25
|
A modified Kačanov iteration scheme with application to quasilinear diffusion models
|
The classical Ka\v{c}anov scheme for the solution of nonlinear variational
problems can be interpreted as a fixed point iteration method that updates a
given approximation by solving a linear problem in each step. Based on this
observation, we introduce a modified Ka\v{c}anov method, which allows for
(adaptive) damping, and, thereby, to derive a new convergence analysis under
more general assumptions and for a wider range of applications. For instance,
in the specific context of quasilinear diffusion models, our new approach does
no longer require a standard monotonicity condition on the nonlinear diffusion
coefficient to hold. Moreover, we propose two different adaptive strategies for
the practical selection of the damping parameters involved.
|
2101.10137v3
|
2021-01-29
|
One-parameter robust global frequency estimator for slowly varying amplitude and noisy oscillations
|
Robust online estimation of oscillation frequency belongs to classical
problems of system identification and adaptive control. The given harmonic
signal can be noisy and with varying amplitude at the same time, as in the case
of damped vibrations. A novel robust frequency-estimation algorithm is proposed
here, motivated by the existing globally convergent frequency estimator. The
advantage of the proposed estimator is in requiring one design parameter only
and being robust against measurement noise and initial conditions. The proven
global convergence also allows for slowly varying amplitudes, which is useful
for applications with damped oscillations or additionally shaped harmonic
signals. The proposed analysis is simple and relies on an averaging theory of
the periodic signals. Our results show an exponential convergence rate, which
depends, analytically, on the sought frequency, adaptation gain and oscillation
amplitude. Numerical and experimental examples demonstrate the robustness and
efficiency of the proposed estimator for signals with slowly varying amplitude
and noise.
|
2101.12497v3
|
2021-01-29
|
Quarter and Full Car Models Optimisation of Passive and Active Suspension System Using Genetic Algorithm
|
This study evaluates a suspension design of a passenger car to obtain maximum
rider's comfort when the vehicle is subjected to different road profile or road
surface condition. The challenge will be on finding a balance between the
rider's comfort and vehicle handling to optimize design parameters. The study
uses a simple passive suspension system and an active suspension model
integrated with a pneumatic actuator controlled by proportional integral
derivative (PID) controller in both quarter car and full car models having a
different degree of freedoms (DOF) and increasing degrees of complexities. The
quarter car considered as a 2-DOF model, while the full car model is a 7-DOF
model. The design process set to optimise the spring stiffnesses, damping
coefficients and actuator PID controller gains. For optimisation, the research
featured genetic algorithm optimisation technique to obtain a balanced response
of the vehicle as evaluated from the displacement, velocity and acceleration of
sprung and unsprung masses along with different human comfort and vehicle
performance criteria. The results revealed that the active suspension system
with optimised spring stiffness, damping coefficients and PID gains
demonstrated the superior riding comfort and road holding compared to a passive
suspension system.
|
2101.12629v1
|
2021-02-01
|
Performance and limits of feedback cooling methods for levitated oscillators: a direct comparison
|
Cooling the centre-of-mass motion is an important tool for levitated
optomechanical systems, but it is often not clear which method can practically
reach lower temperatures for a particular experiment. We directly compare the
parametric and velocity feedback damping methods, which are used extensively
for cooling the motion of single trapped particles in a range of traps. By
performing experiments on the same particle, and with the same detection
system, we demonstrate that velocity damping cools the oscillator to lower
temperatures and is more resilient to imperfect experimental conditions. We
show that these results are consistent with analytical limits as well as
numerical simulations that include experimental noise.
|
2102.01060v3
|
2021-02-16
|
A homogenized damping model for the propagation of elastic wave in a porous solid
|
This paper develops an averaging technique based on the combination of the
eigenfunction expansion method and the collaboration method to investigate the
multiple scattering effect of the SH wave propagation in a porous medium. The
semi-analytical averaging technique is conducted using Monto Carlo method to
understand the macroscopic dispersion and attenuation phenomena of the stress
wave propagation in a porous solid caused by the multiple scattering effects.
The averaging technique is verified by finite element analysis. Finally, a
simple homogenized elastic model with damping is proposed to describe the
macroscopic dispersion and attenuation effects of SH waves in porous media.
|
2102.08334v1
|
2021-02-11
|
Semi-linear Poisson-mediated Flocking in a Cucker-Smale Model
|
We propose a family of compactly supported parametric interaction functions
in the general Cucker-Smale flocking dynamics such that the mean-field
macroscopic system of mass and momentum balance equations with non-local
damping terms can be converted from a system of partial integro-differential
equations to an augmented system of partial differential equations in a compact
set. We treat the interaction functions as Green's functions for an operator
corresponding to a semi-linear Poisson equation and compute the density and
momentum in a translating reference frame, i.e. one that is taken in reference
to the flock's centroid. This allows us to consider the dynamics in a fixed,
flock-centered compact set without loss of generality. We approach the
computation of the non-local damping using the standard finite difference
treatment of the chosen differential operator, resulting in a tridiagonal
system which can be solved quickly.
|
2102.08772v1
|
2021-02-22
|
Robust formation of nanoscale magnetic skyrmions in easy-plane thin film multilayers with low damping
|
We experimentally demonstrate the formation of room-temperature skyrmions
with radii of about 25\,nm in easy-plane anisotropy multilayers with
interfacial Dzyaloshinskii-Moriya interaction (DMI). We detect the formation of
individual magnetic skyrmions by magnetic force microscopy and find that the
skyrmions are stable in out-of-plane fields up to about 200 mT. We determine
the interlayer exchange coupling as well as the strength of the interfacial
DMI. Additionally, we investigate the dynamic microwave spin excitations by
broadband magnetic resonance spectroscopy. From the uniform Kittel mode we
determine the magnetic anisotropy and low damping $\alpha_{\mathrm{G}} < 0.04$.
We also find clear magnetic resonance signatures in the non-uniform (skyrmion)
state. Our findings demonstrate that skyrmions in easy-plane multilayers are
promising for spin-dynamical applications.
|
2102.11117v1
|
2021-02-22
|
Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation
|
We consider the nonlinear damped Klein-Gordon equation \[
\partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \quad \text{on} \ \
[0,\infty)\times \mathbb{R}^N \] with $\alpha>0$, $2 \le N\le 5$ and energy
subcritical exponents $p>2$. We study the behavior of solutions for which it is
supposed that only one nonlinear object appears asymptotically for large times,
at least for a sequence of times.
We first prove that the nonlinear object is necessarily a bound state. Next,
we show that when the nonlinear object is a non-degenerate state or a
degenerate excited state satisfying a simplicity condition, the convergence
holds for all positive times, with an exponential or algebraic rate
respectively. Last, we provide an example where the solution converges exactly
at the rate $t^{-1}$ to the excited state.
|
2102.11178v1
|
2021-02-23
|
The tipping effect of delayed interventions on the evolution of COVID-19 incidence
|
We combine infectious disease transmission and the non-pharmaceutical
intervention (NPI) response to disease incidence into one closed model
consisting of two coupled delay differential equations for the incidence rate
and the time-dependent reproduction number. The model contains three free
parameters, the initial reproduction number, the intervention strength, and the
response delay relative to the time of infection. The NPI response is modeled
by assuming that the rate of change of the reproduction number is proportional
to the negative deviation of the incidence rate from an intervention threshold.
This delay dynamical system exhibits damped oscillations in one part of the
parameter space, and growing oscillations in another, and these are separated
by a surface where the solution is a strictly periodic nonlinear oscillation.
For parameters relevant for the COVID-19 pandemic, the tipping transition from
damped to growing oscillations occurs for response delays of the order of one
week, and suggests that effective control and mitigation of successive epidemic
waves cannot be achieved unless NPIs are implemented in a precautionary manner,
rather than merely as a response to the present incidence rate.
|
2102.11750v1
|
2021-03-01
|
Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping
|
We study dynamics of a ring of three unidirectionally coupled double-well
Duffing oscillators for three different values of the damping coefficient:
fixed dumping, proportional to time, and inversely proportional to time. The
dynamics in all cases is analyzed through time series, Fourier and Hilbert
transforms, Poincar\'e sections, as well as bifurcation diagrams and Lyapunov
exponents with respect to the coupling strength. In the first case, we observe
a well-known route from a stable steady state to hyperchaos through Hopf
bifurcation and a series of torus bifurcations, as the coupling strength is
increased. In the second case, the system is highly dissipative and converges
into one of stable equilibria. Finally, in the third case, transient toroidal
hyperchaos takes place.
|
2103.01297v1
|
2021-03-06
|
Deep learning stochastic processes with QCD phase transition
|
It is non-trivial to recognize phase transitions and track dynamics inside a
stochastic process because of its intrinsic stochasticity. In this paper, we
employ the deep learning method to classify the phase orders and predict the
damping coefficient of fluctuating systems under Langevin's description. As a
concrete set-up, 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. In a supervised learning manner, the Convolutional Neural
Networks(CNNs) accurately classify the first-order phase transition and
crossover based on $\sigma$ field configurations with fluctuations. Noise in
the stochastic process does not significantly hinder the performance of the
well-trained neural network for phase order recognition. For mixed dynamics
with diverse dynamical parameters, we further devise and train the machine to
predict the damping coefficients $\eta$ in a broad range. The results show that
it is robust to extract the dynamics from the bumpy field configurations.
|
2103.04090v1
|
2021-03-12
|
Longitudinal Modes of Bunched Beams with Weak Space Charge
|
Longitudinal collective modes of a bunched beam with a repulsive inductive
impedance (the space charge below transition or the chamber inductance above
it) are analytically described by means of reduction of the linearized Vlasov
equation to a parameter-less integral equation. For any multipolarity, the
discrete part of the spectrum is found to consist of infinite number of modes
with real tunes, which limit point is the incoherent zero-amplitude frequency.
In other words, notwithstanding the RF bucket nonlinearity and potential well
distortion, the Landau damping is lost. Hence, even a tiny coupled-bunch
interaction makes the beam unstable; such growth rates for all the modes are
analytically obtained for arbitrary multipolarity. In practice, however, the
finite threshold of this loss of Landau damping is set either by the
high-frequency impedance roll-off or intrabeam scattering. Above the threshold,
growth of the leading collective mode should result in persistent nonlinear
oscillations.
|
2103.07523v4
|
2021-03-13
|
Microscopic Calculation of Spin Torques in Textured Antiferromagnets
|
A microscopic calculation is presented for the spin-transfer torques (STT)
and damping torques in metallic antiferromagnets (AF). It is found that the
sign of the STT is opposite to that in ferromagnets because of the AF transport
character, and the current-to-STT conversion factor is enhanced near the AF gap
edge. The dissipative torque parameter $\beta_n$ and the damping parameter
$\alpha_n$ for the N\'eel vector arise from spin relaxation of electrons.
Physical consequences are demonstrated for the AF domain wall motion using
collective coordinates, and some similarities to the ferromagnetic case are
pointed out such as intrinsic pinning and the specialty of $\alpha_n =
\beta_n$. A recent experiment on a ferrimagnetic GdFeCo near its
angular-momentum compensation temperature is discussed.
|
2103.07634v1
|
2021-03-13
|
Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
|
Discrete dissipative coupled systems exhibit complex behavior such as chaos,
spatiotemporal intermittence, chimera among others. We construct and
investigate chimera states, in the form of confined stationary and dynamical
states in a chain of parametrically driven sites with onsite damping and cubic
nonlinearity. The system is modeled by the respective discrete parametrically
driven damped nonlinear Schrodinger equation. Chimeras feature quasi-periodic
or chaotic dynamic in the filled area, quantified by time dependence of the
total norm (along with its power spectrum), and by the largest Lyapunov
exponent. Systematic numerical simulations, in combination with some analytical
results, reveal regions in the parameter space populated by stable localized
states of different types. A phase transition from the stationary disorder
states to spatially confined dynamical chaotic one is identified. Essential
parameters of the system are the strength and detuning of the forcing, as well
as the lattice's coupling constant.
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2103.07748v1
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2021-03-16
|
On an inverse problem of nonlinear imaging with fractional damping
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This paper considers the attenuated Westervelt equation in pressure
formulation. The attenuation is by various models proposed in the literature
and characterised by the inclusion of non-local operators that give power law
damping as opposed to the exponential of classical models. The goal is the
inverse problem of recovering a spatially dependent coefficient in the
equation, the parameter of nonlinearity $\kappa(x)$, in what becomes a
nonlinear hyperbolic equation with nonlocal terms. The overposed measured data
is a time trace taken on a subset of the domain or its boundary. We shall show
injectivity of the linearised map from $\kappa$ to the overposed data used to
recover it and from this basis develop and analyse Newton-type schemes for its
effective recovery.
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2103.08965v1
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2021-03-17
|
Tunable exciton-optomechanical coupling in suspended monolayer MoSe2
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The strong excitonic effect in monolayer transition metal dichalcogenide
(TMD) semiconductors has enabled many fascinating light-matter interaction
phenomena. Examples include strongly coupled exciton-polaritons and nearly
perfect atomic monolayer mirrors. The strong light-matter interaction also
opens the door for dynamical control of mechanical motion through the exciton
resonance of monolayer TMDs. Here we report the observation of
exciton-optomechanical coupling in a suspended monolayer MoSe2 mechanical
resonator. By moderate optical pumping near the MoSe2 exciton resonance, we
have observed optical damping and anti-damping of mechanical vibrations as well
as the optical spring effect. The exciton-optomechanical coupling strength is
also gate-tunable. Our observations can be understood in a model based on
photothermal backaction and gate-induced mirror symmetry breaking in the device
structure. The observation of gate-tunable exciton-optomechanical coupling in a
monolayer semiconductor may find applications in nanoelectromechanical systems
(NEMS) and in exciton-optomechanics.
|
2103.09897v2
|
2021-03-18
|
Perturbation theory for solitons of the Fokas--Lenells equation : Inverse scattering transform approach
|
We present perturbation theory based on the inverse scattering transform
method for solitons described by an equation with the inverse linear dispersion
law $\omega\sim 1/k$, where $\omega$ is the frequency and $k$ is the wave
number, and cubic nonlinearity. This equation, first suggested by Davydova and
Lashkin for describing dynamics of nonlinear short-wavelength ion-cyclotron
waves in plasmas and later known as the Fokas--Lenells equation, arises from
the first negative flow of the Kaup--Newell hierarchy. Local and nonlocal
integrals of motion, in particular the energy and momentum of nonlinear
ion-cyclotron waves, are explicitly expressed in terms of the discrete
(solitonic) and continuous (radiative) scattering data. Evolution equations for
the scattering data in the presence of a perturbation are presented. Spectral
distributions in the wave number domain of the energy emitted by the soliton in
the presence of a perturbation are calculated analytically for two cases: (i)
linear damping that corresponds to Landau damping of plasma waves, and (ii)
multiplicative noise which corresponds to thermodynamic fluctuations of the
external magnetic field (thermal noise) and/or the presence of a weak plasma
turbulence.
|
2103.10090v1
|
2021-04-07
|
Indirect stability of a multidimensional coupled wave equations with one locally boundary fractional damping
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In this work, we consider a system of multidimensional wave equations coupled
by velocities with one localized fractional boundary damping. First, using a
general criteria of Arendt- Batty, by assuming that the boundary control region
satisfy some geometric conditions, under the equality speed propagation and the
coupling parameter of the two equations is small enough, we show the strong
stability of our system in the absence of the compactness of the resolvent. Our
system is not uniformly stable in general since it is the case of the interval.
Hence, we look for a polynomial decay rate for smooth initial data for our
system by applying a frequency domain approach combining with a multiplier
method. Indeed, by assuming that the boundary control region satisfy some
geometric conditions and the waves propagate with equal speed and the coupling
parameter term is small enough, we establish a polynomial energy decay rate for
smooth solutions, which depends on the order of the fractional derivative.
|
2104.03389v1
|
2021-04-10
|
Free and forced vibrations of damped locally-resonant sandwich beams
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This paper addresses the dynamics of locally-resonant sandwich beams, where
multi-degree-of-freedom viscously-damped resonators are periodically
distributed within the core matrix. Using an equivalent single-layer Timoshenko
beam model coupled with mass-spring-dashpot subsystems representing the
resonators, two solution methods are presented. The first is a direct
integration method providing the exact frequency response under arbitrary
loads. The second is a complex modal analysis approach obtaining exact modal
impulse and frequency response functions, upon deriving appropriate
orthogonality conditions for the complex modes. The challenging issue of
calculating all eigenvalues, without missing anyone, is solved applying a
recently-introduced contour-integral algorithm to a characteristic equation
built as determinant of an exact frequency-response matrix, whose size is $4
\times 4$ regardless of the number of resonators. Numerical applications prove
exactness and robustness of the proposed solutions.
|
2104.04870v1
|
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