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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
|
2020-10-29
|
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
|
2020-12-07
|
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
|
2021-01-25
|
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
|
2021-03-01
|
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
|
2021-03-16
|
On an inverse problem of nonlinear imaging with fractional damping
|
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.
|
2103.08965v1
|
2021-03-17
|
Tunable exciton-optomechanical coupling in suspended monolayer MoSe2
|
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
|
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
|
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
|
2021-04-15
|
Flexural wave modulation and mitigation in airfoils using acoustic black holes
|
This study introduces a framework for the design and implementation of
acoustic black holes (ABHs) in airfoils. A generalized multi-parameter
damped-ABH generation function is mapped onto NACA series airfoils.
Representative geometries and a uniformly distributed baseline, all with the
same mass of structure and damping are fabricated using multi-material PolyJet
3D printing. Laser Doppler vibrometer measurements along the airfoil chord in
response to a broadband 0.1 - 12 kHz excitation show a decrease in trailing
edge vibrations by as much as 10 dB, a broadband 5 dB reduction across the
entire chord as well as substantial spatial and temporal modulation of flexural
waves by ABH-embedded foils. Finite element analysis (FEA) models are developed
and validated based on the measured data. Furthermore, a parametric FEA study
is performed on a set of comparable designs to elucidate the scope of
modulation achievable. These findings are applicable to trailing-edge noise
reduction, flow control, structural enhancement and energy harvesting for
airfoils.
|
2104.07374v1
|
2021-04-20
|
Entanglement robustness via spatial deformation of identical particle wave functions
|
We address the problem of entanglement protection against surrounding noise
by a procedure suitably exploiting spatial indistinguishability of identical
subsystems. To this purpose, we take two initially separated and entangled
identical qubits interacting with two independent noisy environments. Three
typical models of environments are considered: amplitude damping channel, phase
damping channel and depolarizing channel. After the interaction, we deform the
wave functions of the two qubits to make them spatially overlap before
performing spatially localized operations and classical communication (sLOCC)
and eventually computing the entanglement of the resulting state. This way, we
show that spatial indistinguishability of identical qubits can be utilized
within the sLOCC operational framework to partially recover the quantum
correlations spoiled by the environment. A general behavior emerges: the higher
the spatial indistinguishability achieved via deformation, the larger the
amount of recovered entanglement.
|
2104.09714v1
|
2021-04-22
|
Dissipation and fluctuations in elongated bosonic Josephson junctions
|
We investigate the dynamics of bosonic atoms in elongated Josephson
junctions. We find that these systems are characterized by an intrinsic
coupling between the Josephson mode of macroscopic quantum tunneling and the
sound modes. This coupling of Josephson and sound modes gives rise to a damped
and stochastic Langevin dynamics for the Josephson degree of freedom. From a
microscopic Lagrangian, we deduce and investigate the damping coefficient and
the stochastic noise, which includes thermal and quantum fluctuations. Finally,
we study the time evolution of relative-phase and population-imbalance
fluctuations of the Josephson mode and their oscillating thermalization to
equilibrium.
|
2104.11259v2
|
2021-04-24
|
The large-period limit for equations of discrete turbulence
|
We consider the damped/driven cubic NLS equation on the torus of a large
period $L$ with a small nonlinearity of size $\lambda$, a properly scaled
random forcing and dissipation. We examine its solutions under the subsequent
limit when first $\lambda\to 0$ and then $L\to \infty$. The first limit, called
the limit of discrete turbulence, is known to exist, and in this work we study
the second limit $L\to\infty$ for solutions to the equations of discrete
turbulence. Namely, we decompose the solutions to formal series in amplitude
and study the second order truncation of this series. We prove that the energy
spectrum of the truncated solutions becomes close to solutions of a
damped/driven nonlinear wave kinetic equation. Kinetic nonlinearity of the
latter is similar to that which usually appears in works on wave turbulence,
but is different from it (in particular, it is non-autonomous). Apart from
tools from analysis and stochastic analysis, our work uses two powerful results
from the number theory.
|
2104.11967v2
|
2021-05-13
|
Global Solutions of Three-dimensional Inviscid MHD Fluids with Velocity Damping in Horizontally Periodic Domains
|
The \emph{two-dimensional} (2D) existence result of global(-in-time)
solutions for the motion equations of incompressible, inviscid, non-resistive
magnetohydrodynamic (MHD) fluids with velocity damping had been established in
[Wu--Wu--Xu, SIAM J. Math. Anal. 47 (2013), 2630--2656]. This paper further
studies the existence of global solutions for the \emph{three-dimensional} (a
dimension of real world) initial-boundary value problem in a horizontally
periodic domain with finite height. Motivated by the multi-layers energy method
introduced in [Guo--Tice, Arch. Ration. Mech. Anal. 207 (2013), 459--531], we
develop a new type of two-layer energy structure to overcome the difficulty
arising from three-dimensional nonlinear terms in the MHD equations, and thus
prove the initial-boundary value problem admits a unique global solution.
Moreover the solution has the exponential decay-in-time around some rest state.
Our two-layer energy structure enjoys two features: (1) the lower-order energy
(functional) can not be controlled by the higher-order energy. (2) under the
\emph{a priori} smallness assumption of lower-order energy, we first close the
higher-order energy estimates, and then further close the lower-energy
estimates in turn.
|
2105.06080v1
|
2021-05-13
|
On Inhibition of Rayleigh--Taylor Instability by Horizontal Magnetic Field in an Inviscid MHD Fluid with Velocity Damping
|
It is still an open problem whether the inhibition phenomenon of
Rayleigh--Taylor (RT) instability by horizontal magnetic field can be
mathematically proved in a non-resistive magnetohydrodynamic (MHD) fluid in a
two-dimensional (2D) horizontal slab domain, since it had been roughly verified
by a 2D linearized motion equations in 2012 \cite{WYC}. In this paper, we find
that this inhibition phenomenon can be rigorously verified in the
inhomogeneous, incompressible, inviscid case with velocity damping. More
precisely, there exists a critical number $m_{\rm{C}}$ such that if the
strength $|m|$ of horizontal magnetic field is bigger than $m_{\rm{C}}$, then
the small perturbation solution around the magnetic RT equilibrium state is
exponentially stable in time. Our result is also the first mathematical one
based on the nonlinear motion equations for the proof of inhibition of flow
instabilities by a horizontal magnetic field in a horizontal slab domain. In
addition, we also provide a nonlinear instability result for the case $|m|\in
[0,m_{\rm{C}})$. Our instability result presents that horizontal magnetic field
can not inhibit the RT instability, if it's strength is to small.
|
2105.06472v1
|
2021-05-14
|
Quantum Langevin dynamics of a charged particle in a magnetic field : Response function, position-velocity and velocity autocorrelation functions
|
We use the Quantum Langevin equation as a starting point to study the
response function, the position-velocity correlation function and the velocity
autocorrelation function of a charged Quantum Brownian particle in the presence
of a magnetic field and linearly coupled to a heat bath via position
coordinate. We study two bath models -- the Ohmic bath model and the Drude bath
model -- and make a detailed comparison in various time-temperature regimes.
For both bath models there is a competition between the cyclotron frequency and
the viscous damping rate giving rise to a transition from an oscillatory to a
monotonic behaviour as the damping rate is increased. In the zero point
fluctuation dominated low temperature regime, non-trivial noise correlations
lead to some interesting features in this transition. We study the role of the
memory time scale which comes into play in the Drude model and study the effect
of this additional time scale. We discuss the experimental implications of our
analysis in the context of experiments in cold ions.
|
2105.07036v2
|
2021-05-16
|
Anatomy of inertial magnons in ferromagnets
|
We analyze dispersion relations of magnons in ferromagnetic nanostructures
with uniaxial anisotropy taking into account inertial terms, i.e. magnetic
nutation. Inertial effects are parametrized by damping-independent parameter
$\beta$, which allows for an unambiguous discrimination of inertial effects
from Gilbert damping parameter $\alpha$. The analysis of magnon dispersion
relation shows its two branches are modified by the inertial effect, albeit in
different ways. The upper nutation branch starts at $\omega=1/ \beta$, the
lower branch coincides with FMR in the long-wavelength limit and deviates from
the zero-inertia parabolic dependence $\simeq\omega_{FMR}+Dk^2$ of the exchange
magnon. Taking a realistic experimental geometry of magnetic thin films,
nanowires and nanodiscs, magnon eigenfrequencies, eigenvectors and $Q$-factors
are found to depend on the shape anisotropy. The possibility of phase-matched
magneto-elastic excitation of nutation magnons is discussed and the condition
was found to depend on $\beta$, exchange stiffness $D$ and the acoustic
velocity.
|
2105.07376v1
|
2021-05-18
|
Partially dissipative hyperbolic systems in the critical regularity setting : The multi-dimensional case
|
We are concerned with quasilinear symmetrizable partially dissipative
hyperbolic systems in the whole space $\mathbb{R}^d$ with $d\geq2$. Following
our recent work [10] dedicated to the one-dimensional case, we establish the
existence of global strong solutions and decay estimates in the critical
regularity setting whenever the system under consideration satisfies the
so-called (SK) (for Shizuta-Kawashima) condition. Our results in particular
apply to the compressible Euler system with damping in the velocity equation.
Compared to the papers by Kawashima and Xu [27, 28] devoted to similar issues,
our use of hybrid Besov norms with different regularity exponents in low and
high frequency enable us to pinpoint optimal smallness conditions for global
well-posedness and to get more accurate information on the qualitative
properties of the constructed solutions. A great part of our analysis relies on
the study of a Lyapunov functional in the spirit of that of Beauchard and
Zuazua in [2]. Exhibiting a damped mode with faster time decay than the whole
solution also plays a key role.
|
2105.08333v1
|
2021-05-24
|
Response Dynamics of Alkali Metal-Noble Gas Hybrid Trispin System
|
With numerical calculation of coupled Bloch equations, we have simulated the
spin dynamics of nuclear magnetic resonance gyroscope based on alkali
metal-noble gas hybrid trispin system. From the perspective of damping harmonic
oscillator, a thorough analysis of the response dynamics is demonstrated. The
simulation results shows a linear increasing response of gyroscope signal while
the noblge gas nuclear spin magnetization and alkali atomic spin lifetime
parameters are at the over damping condition. An upper limit of response is
imposed on the NMR gyroscope signal due to the inherent dynamics of the hybrid
trispin system. The results agrees with present available experimental results
and provide useful guidings for future experiments.
|
2105.11124v2
|
2021-05-26
|
Temperature Damping of Magneto-Intersubband Resistance Oscillations in Magnetically Entangled Subbands
|
Magneto-intersubband resistance oscillations (MISO) of highly mobile 2D
electrons in symmetric GaAs quantum wells with two populated subbands are
studied in magnetic fields tilted from the normal to the 2D electron layer at
different temperatures $T$. Decrease of MISO amplitude with temperature
increase is observed. At moderate tilts the temperature decrease of MISO
amplitude is consistent with decrease of Dingle factor due to reduction of
quantum electron lifetime at high temperatures. At large tilts new regime of
strong MISO suppression with the temperature is observed. Proposed model
relates this suppression to magnetic entanglement between subbands, leading to
beating in oscillating density of states. The model yields corresponding
temperature damping factor: $A_{MISO}(T)=X/\sinh(X)$, where $X=2\pi^2kT\delta
f$ and $\delta f$ is difference frequency of oscillations of density of states
in two subbands. This factor is in agreement with experiment. Fermi liquid
enhancement of MISO amplitude is observed.
|
2105.12263v1
|
2021-05-26
|
A statistical study of propagating MHD kink waves in the quiescent corona
|
The Coronal Multi-channel Polarimeter (CoMP) has opened up exciting
opportunities to probe transverse MHD waves in the Sun's corona. The archive of
CoMP data is utilised to generate a catalogue of quiescent coronal loops that
can be used for studying propagating kink waves. The catalogue contains 120
loops observed between 2012-2014. This catalogue is further used to undertake a
statistical study of propagating kink waves in the quiet regions of the solar
corona, investigating phase speeds, loop lengths, footpoint power ratio and
equilibrium parameter values. The statistical study enables us to establish the
presence of a relationship between the rate of damping and the length of the
coronal loop, with longer coronal loops displaying weaker wave damping. We
suggest the reason for this behaviour is related to a decreasing average
density contrast between the loop and ambient plasma as loop length increases.
The catalogue presented here will provide the community with the foundation for
the further study of propagating kink waves in the quiet solar corona.
|
2105.12451v1
|
2021-08-02
|
Interplay of periodic dynamics and noise: insights from a simple adaptive system
|
We study the dynamics of a simple adaptive system in the presence of noise
and periodic damping. The system is composed by two paths connecting a source
and a sink, the dynamics is governed by equations that usually describe food
search of the paradigmatic Physarum polycephalum. In this work we assume that
the two paths undergo damping whose relative strength is periodically modulated
in time and analyse the dynamics in the presence of stochastic forces
simulating Gaussian noise. We identify different responses depending on the
modulation frequency and on the noise amplitude. At frequencies smaller than
the mean dissipation rate, the system tends to switch to the path which
minimizes dissipation. Synchronous switching occurs at an optimal noise
amplitude which depends on the modulation frequency. This behaviour disappears
at larger frequencies, where the dynamics can be described by the time-averaged
equations. Here, we find metastable patterns that exhibit the features of
noise-induced resonances.
|
2108.01451v3
|
2021-08-06
|
Adjusting PageRank parameters and Comparing results
|
The effect of adjusting damping factor {\alpha} and tolerance {\tau} on
iterations needed for PageRank computation is studied here. Relative
performance of PageRank computation with L1, L2, and L{\infty} norms used as
convergence check, are also compared with six possible mean ratios. It is
observed that increasing the damping factor {\alpha} linearly increases the
iterations needed almost exponentially. On the other hand, decreasing the
tolerance {\tau} exponentially decreases the iterations needed almost
exponentially. On average, PageRank with L{\infty} norm as convergence check is
the fastest, quickly followed by L2 norm, and then L1 norm. For large graphs,
above certain tolerance {\tau} values, convergence can occur in a single
iteration. On the contrary, below certain tolerance {\tau} values, sensitivity
issues can begin to appear, causing computation to halt at maximum iteration
limit without convergence. The six mean ratios for relative performance
comparison are based on arithmetic, geometric, and harmonic mean, as well as
the order of ratio calculation. Among them GM-RATIO, geometric mean followed by
ratio calculation, is found to be most stable, followed by AM-RATIO.
|
2108.02997v1
|
2021-08-06
|
Magnon transport in $\mathrm{\mathbf{Y_3Fe_5O_{12}}}$/Pt nanostructures with reduced effective magnetization
|
For applications making use of magnonic spin currents damping effects, which
decrease the spin conductivity, have to be minimized. We here investigate the
magnon transport in an yttrium iron garnet thin film with strongly reduced
effective magnetization. We show that in a three-terminal device the effective
magnon conductivity can be increased by a factor of up to six by a current
applied to a modulator electrode, which generates damping compensation above a
threshold current. Moreover, we find a linear dependence of this threshold
current on the applied magnetic field. We can explain this behavior by the
reduced effective magnetization and the associated nearly circular
magnetization precession.
|
2108.03263v1
|
2021-08-12
|
On the critical exponent and sharp lifespan estimates for semilinear damped wave equations with data from Sobolev spaces of negative order
|
We study semilinear damped wave equations with power nonlinearity $|u|^p$ and
initial data belonging to Sobolev spaces of negative order $\dot{H}^{-\gamma}$.
In the present paper, we obtain a new critical exponent
$p=p_{\mathrm{crit}}(n,\gamma):=1+\frac{4}{n+2\gamma}$ for some
$\gamma\in(0,\frac{n}{2})$ and low dimensions in the framework of Soblev spaces
of negative order. Precisely, global (in time) existence of small data Sobolev
solutions of lower regularity is proved for $p>p_{\mathrm{crit}}(n,\gamma)$,
and blow-up of weak solutions in finite time even for small data if
$1<p<p_{\mathrm{crit}}(n,\gamma)$. Furthermore, in order to more accurately
describe the blow-up time, we investigate sharp upper bound and lower bound
estimates for the lifespan in the subcritical case.
|
2108.05667v1
|
2021-08-25
|
Numerical investigation of non-condensable gas effect on vapor bubble collapse
|
We numerically investigate the effect of non-condensable gas inside a vapor
bubble on bubble dynamics, collapse pressure and pressure impact of spherical
and aspherical bubble collapses. Free gas inside a vapor bubble has a damping
effect that can weaken the pressure wave and enhance the bubble rebound. To
estimate this effect numerically, we derive and validate a multi-component
model for vapor bubbles containing gas. For the cavitating liquid and the
non-condensable gas, we employ a homogeneous mixture model with a coupled
equation of state for all components. The cavitation model for the cavitating
liquid is a barotropic thermodynamic equilibrium model. Compressibility of all
phases is considered in order to capture the shock wave of the bubble collapse.
After validating the model with an analytical energy partitioning model,
simulations of collapsing wall-attached bubbles with different stand-off
distances are performed. The effect of the non-condensable gas on rebound and
damping of the emitted shock wave is well captured.
|
2108.11297v1
|
2021-08-23
|
PDM damped-driven oscillators: exact solvability, classical states crossings, and self-crossings
|
Within the standard Lagrangian and Hamiltonian setting, we consider a
position-dependent mass (PDM) classical particle performing a damped driven
oscillatory (DDO) motion under the influence of a conservative harmonic
oscillator force field $V\left( x\right) =\frac{1}{2}\omega ^{2}Q\left(
x\right) x^{2}$ and subjected to a Rayleigh dissipative force field
$\mathcal{R}\left( x,\dot{x}\right) =\frac{1}{2}b\,m\left( x\right)
\dot{x}^{2}$ in the presence of an external periodic (non-autonomous) force
$F\left( t\right) =F_{\circ }\,\cos \left( \Omega t\right) $. Where, the
correlation between the coordinate deformation $\sqrt{Q(x)}$ and the velocity
deformation $\sqrt{m(x)}$ is governed by a point canonical transformation
$q\left( x\right) =\int \sqrt{m\left( x\right) }dx=\sqrt{% Q\left( x\right)
}x$. Two illustrative examples are used: a non-singular PDM-DDO, and a
power-law PDM-DDO models. Classical-states $\{x(t),p(t)\}$ crossings are
analysed and reported. Yet, we observed/reported that as a classical state
$\{x_{i}(t),p_{i}(t)\}$ evolves in time it may cross itself at an earlier
and/or a latter time/s.
|
2108.13924v1
|
2021-09-06
|
A well-balanced oscillation-free discontinuous Galerkin method for shallow water equations
|
In this paper, we develop a well-balanced oscillation-free discontinuous
Galerkin (OFDG) method for solving the shallow water equations with a non-flat
bottom topography. One notable feature of the constructed scheme is the
well-balanced property, which preserves exactly the hydrostatic equilibrium
solutions up to machine error. Another feature is the non-oscillatory property,
which is very important in the numerical simulation when there exist some shock
discontinuities. To control the spurious oscillations, we construct an OFDG
method with an extra damping term to the existing well-balanced DG schemes
proposed in [Y. Xing and C.-W. Shu, CICP, 1(2006), 100-134.]. With a careful
construction of the damping term, the proposed method achieves both the
well-balanced property and non-oscillatory property simultaneously without
compromising any order of accuracy. We also present a detailed procedure for
the construction and a theoretical analysis for the preservation of the
well-balancedness property. Extensive numerical experiments including one- and
two-dimensional space demonstrate that the proposed methods possess the desired
properties without sacrificing any order of accuracy.
|
2109.02193v1
|
2021-09-16
|
Landau Modes are Eigenmodes of Stellar Systems in the Limit of Zero Collisions
|
We consider the spectrum of eigenmodes in a stellar system dominated by
gravitational forces in the limit of zero collisions. We show analytically and
numerically using the Lenard-Bernstein collision operator that the Landau
modes, which are not true eigenmodes in a strictly collisionless system (except
for the Jeans unstable mode), become part of the true eigenmode spectrum in the
limit of zero collisions. Under these conditions, the continuous spectrum of
true eigenmodes in the collisionless system, also known as the Case-van Kampen
modes, is eliminated. Furthermore, since the background distribution function
in a weakly collisional system can exhibit significant deviations from a
Maxwellian distribution function over long times, we show that the spectrum of
Landau modes can change drastically even in the presence of slight deviations
from a Maxwellian, primarily through the appearance of weakly damped modes that
may be otherwise heavily damped for a Maxwellian distribution. Our results
provide important insights for developing statistical theories to describe
thermal fluctuations in a stellar system, which are currently a subject of
great interest for N-body simulations as well as observations of gravitational
systems.
|
2109.07806v2
|
2021-09-16
|
Stabilization of physical systems via saturated controllers with only partial state measurements
|
This paper provides a constructive passivity-based control approach to solve
the set-point regulation problem for input-affine continuous nonlinear systems
while considering saturation in the inputs. As customarily in passivity-based
control, the methodology consists of two steps: energy shaping and damping
injection. In terms of applicability, the proposed controllers have two
advantages concerning other passivity-based control techniques: (i) the energy
shaping is carried out without solving partial differential equations, and (ii)
the damping injection is performed without measuring the passive output. The
proposed methodology is suitable to control a broad range of physical systems,
e.g., mechanical, electrical, and electro-mechanical systems. We illustrate the
applicability of the technique by designing controllers for systems in
different physical domains, where we validate the analytical results via
simulations and experiments.
|
2109.08111v2
|
2021-09-15
|
Universal relations between the quasinormal modes of neutron star and tidal deformability
|
Universal relations independently of the equation of state (EOS) for neutron
star matter are valuable, if they exist, for extracting the neutron star
properties, which generally depend on the EOS. In this study, we newly derive
the universal relations predicting the gravitational wave frequencies for the
fundamental ($f$), the 1st pressure ($p_1$), and the 1st spacetime ($w_1$)
modes and the damping rate for the $f$- and $w_1$-modes as a function of the
dimensionless tidal deformability. In particular, with the universal relations
for the $f$-modes one can predict the frequencies and damping rate with less
than $1\%$ accuracy for canonical neutron stars.
|
2109.08145v2
|
2021-09-27
|
Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations
|
We consider nonparametric invariant density and drift estimation for a class
of multidimensional degenerate resp. hypoelliptic diffusion processes,
so-called stochastic damping Hamiltonian systems or kinetic diffusions, under
anisotropic smoothness assumptions on the unknown functions. The analysis is
based on continuous observations of the process, and the estimators'
performance is measured in terms of the sup-norm loss. Regarding invariant
density estimation, we obtain highly nonclassical results for the rate of
convergence, which reflect the inhomogeneous variance structure of the process.
Concerning estimation of the drift vector, we suggest both non-adaptive and
fully data-driven procedures. All of the aforementioned results strongly rely
on tight uniform moment bounds for empirical processes associated to
deterministic and stochastic integrals of the investigated process, which are
also proven in this paper.
|
2109.13190v3
|
2021-10-04
|
Anomalous temperature dependence of phonon pumping by ferromagnetic resonance in Co/Pd multilayers with perpendicular anisotropy
|
We demonstrate the pumping of phonons by ferromagnetic resonance in a series
of [Co(0.8 nm)/Pd(1.5 nm)]$_n$ multilayers ($n =$ 6, 11, 15, and 20) with large
magnetostriction and perpendicular magnetic anisotropy. The effect is shown
using broadband ferromagnetic resonance over a range of temperatures (10 to 300
K), where a resonant damping enhancement is observed at frequencies
corresponding to standing wave phonons across the multilayer. The strength of
this effect is enhanced by approximately a factor of 4 at 10 K compared to room
temperature, which is anomalous in the sense that the temperature dependence of
the magnetostriction predicts an enhancement that is less than a factor of 2.
Lastly, we demonstrate that the damping enhancement is correlated with a shift
in the ferromagnetic resonance field as predicted quantitatively from linear
response theory.
|
2110.01714v1
|
2021-10-05
|
A BSDEs approach to pathwise uniqueness for stochastic evolution equations
|
We prove strong well-posedness for a class of stochastic evolution equations
in Hilbert spaces H when the drift term is Holder continuous. This class
includes examples of semilinear stochastic damped wave equations which describe
elastic systems with structural damping (for such equations even existence of
solutions in the linear case is a delicate issue) and semilinear stochastic 3D
heat equations. In the deterministic case, there are examples of non-uniqueness
in our framework. Strong (or pathwise) uniqueness is restored by means of a
suitable additive Wiener noise. The proof of uniqueness relies on the study of
related systems of infinite dimensional forward-backward SDEs (FBSDEs). This is
a different approach with respect to the well-known method based on the Ito
formula and the associated Kolmogorov equation (the so-called Zvonkin
transformation or Ito-Tanaka trick). We deal with approximating FBSDEs in which
the linear part generates a group of bounded linear operators in H; such
approximations depend on the type of SPDEs we are considering. We also prove
Lipschitz dependence of solutions from their initial conditions.
|
2110.01994v2
|
2021-10-07
|
Quantum speed limit for the maximum coherent state under squeezed environment
|
The quantum speed limit time for quantum system under squeezed environment is
studied. We consider two typical models, the damped Jaynes-Cummings model and
the dephasing model. For the damped Jaynes-Cummings model under squeezed
environment, we find that the quantum speed limit time becomes larger with the
squeezed parameter $r$ increasing and indicates symmetry about the phase
parameter value $\theta=\pi$. Meanwhile, the quantum speed limit time can also
be influenced by the coupling strength between the system and environment.
However, the quantum speed limit time for the dephasing model is determined by
the dephasing rate and the boundary of acceleration region that interacting
with vacuum reservoir can be broken when the squeezed environment parameters
are appropriately chosen.
|
2110.03132v1
|
2021-10-13
|
Effect of damped oscillations in the inflationary potential
|
We investigate the effect of damped oscillations on a nearly flat
inflationary potential and the features they produce in the power-spectrum and
bi-spectrum. We compare the model with the Planck data using Plik unbinned and
CamSpec clean likelihood and we are able to obtain noticeable improvement in
fit compared to the power-law $\Lambda$CDM model. We are able to identify three
plausible candidates each for the two likelihoods used. We find that the
best-fit to Plik and CamSpec likelihoods match closely to each other. The
improvement comes from various possible outliers at the intermediate to small
scales. We also compute the bi-spectrum for the best-fits. At all limits, the
amplitude of bi-spectrum, $f_{NL}$ is oscillatory in nature and its peak value
is determined by the amplitude and frequency of the oscillations in the
potential, as expected. We find that the bi-spectrum consistency relation
strictly holds at all scales in all the best-fit candidates.
|
2110.06837v2
|
2021-10-14
|
Thermalization in a Spin-Orbit coupled Bose gas by enhanced spin Coulomb drag
|
An important component of the structure of the atom, the effects of
spin-orbit coupling are present in many sub-fields of physics. Most of these
effects are present continuously. We present a detailed study of the dynamics
of changing the spin-orbit coupling in an ultra-cold Bose gas, coupling the
motion of the atoms to their spin. We find that the spin-orbit coupling greatly
increases the damping towards equilibrium. We interpret this damping as spin
drag, which is enhanced by spin-orbit coupling rate, scaled by a remarkable
factor of $8.9(6)$~s. We also find that spin-orbit coupling lowers the final
temperature of the Bose gas after thermalization.
|
2110.07094v3
|
2021-10-15
|
Superconducting dome in ferroelectric-type materials from soft mode instability
|
We present a minimal theory of superconductivity enhancement in
ferroelectric-type materials. Simple expressions for the optical mode
responsible for the soft mode transition are assumed. A key role is played by
the anharmonic phonon damping which is modulated by an external control
parameter (electron doping or mechanical strain) causing the appearance of the
soft mode. It is shown that the enhancement in the superconducting critical
temperature $T_{c}$ upon approaching the ferroelectric transition from either
side is due to the Stokes electron-phonon scattering processes promoted by
strong phonon damping effects.
|
2110.08114v2
|
2021-10-20
|
Dimensional control of tunneling two level systems in nanoelectromechanical resonators
|
Tunneling two level systems affect damping, noise and decoherence in a wide
range of devices, including nanoelectromechanical resonators, optomechanical
systems, and qubits. Theoretically this interaction is usually described within
the tunneling state model. The dimensions of such devices are often small
compared to the relevant phonon wavelengths at low temperatures, and extensions
of the theoretical description to reduced dimensions have been proposed, but
lack conclusive experimental verification. We have measured the intrinsic
damping and the frequency shift in magnetomotively driven aluminum
nanoelectromechanical resonators of various sizes at millikelvin temperatures.
We find good agreement of the experimental results with a model where the
tunneling two level systems couple to flexural phonons that are restricted to
one or two dimensions by geometry of the device. This model can thus be used as
an aid when optimizing the geometrical parameters of devices affected by
tunneling two level systems.
|
2110.10492v1
|
2021-10-27
|
Quantum oscillations in interaction-driven insulators
|
In recent years it has become understood that quantum oscillations of the
magnetization as a function of magnetic field, long recognized as phenomena
intrinsic to metals, can also manifest in insulating systems. Theory has shown
that in certain simple band insulators, quantum oscillations can appear with a
frequency set by the area traced by the minimum gap in momentum space, and are
suppressed for weak fields by an intrinsic "Dingle damping" factor reflecting
the size of the bandgap. Here we examine quantum oscillations of the
magnetization in excitonic and Kondo insulators, for which interactions play a
crucial role. In models of these systems, self-consistent parameters themselves
oscillate with changing magnetic field, generating additional contributions to
quantum oscillations. In the low-temperature, weak-field regime, we find that
the lowest harmonic of quantum oscillations of the magnetization are
unaffected, so that the zero-field bandgap can still be extracted by measuring
the Dingle damping factor of this harmonic. However, these contributions
dominate quantum oscillations at all higher harmonics, thereby providing a
route to measure this interaction effect.
|
2110.14643v2
|
2021-12-06
|
Decay properties and asymptotic behaviors for a wave equation with general strong damping
|
In this paper, we study the Cauchy problem for a wave equation with general
strong damping $-\mu(|D|)\Delta u_t$ motivated by [Tao, Anal. PDE (2009)] and
[Ebert-Girardi-Reissig, Math. Ann. (2020)]. By employing energy methods in the
Fourier space and WKB analysis, we derive decay estimates for solutions under a
large class of $\mu(|D|)$. In particularly, a threshold
$\lim\nolimits_{|\xi|\to\infty}\mu(|\xi|)=\infty$ is discovered for the
regularity-loss phenomenon, where $\mu(|\xi|)$ denotes the symbol of
$\mu(|D|)$. Furthermore, we investigate different asymptotic profiles of
solution with additionally $L^1$ initial data, where some refined estimates in
the sense of enhanced decay rate and reduced regularity are found. The derived
results almost cover the known results with sufficiently small loss.
|
2112.02795v1
|
2021-12-09
|
UV sensitivity of Casimir energy
|
We quantitatively estimate the effect of the UV physics on the Casimir energy
in a five-dimensional (5D) model on $S^1/Z_2$. If the cutoff scale of the 5D
theory is not far from the compactification scale, the UV physics may affect
the low energy result. We work in the cutoff regularization scheme by
introducing two independent cutoff scales for the spatial momentum in the
non-compact space and for the Kaluza-Klein masses. The effects of the UV
physics are incorporated as a damping effect of the contributions to the vacuum
energy around the cutoff scales. We numerically calculate the Casimir energy
and evaluate the deviation from the result obtained in the zeta-function
regularization, which does not include information on the UV physics. We find
that the result well agrees with the latter for the Gaussian-type damping,
while it can deviate for the kink-type one.
|
2112.04708v3
|
2021-12-11
|
Landau damping in hybrid plasmonics
|
Landau Damping (LD) mechanism of the Localized Surface Plasmon (LSP) decay is
studied for the hybrid nanoplasmonic (metal core/dielectric shell) structures.
It is shown that LD in hybrid structures is strongly affected by permittivity
and electron effective mass in the dielectric shell in accordance with previous
observations by Kreibig, and the strength of LD can be enhanced by an order of
magnitude for some combinations of permittivity and effective mass. The
physical reason for this effect is identified as electron spillover into the
dielectric where electric field is higher than in the metal and the presence of
quasi-discrete energy levels in the dielectric. The theory indicates that the
transition absorption at the interface metal-dielectric is a dominant
contribution to LD in such hybrid structures. Thus, by judicious selection of
dielectric material and its thickness one can engineer decay rates and hot
carrier production for important applications, such as photodetection and
photochemistry.
|
2112.06005v1
|
2021-12-12
|
Raman and infrared studies of CdSe/CdS core/shell nanoplatelets
|
The vibrational spectroscopy of semiconductor nanostructures can provide
important information on their structure. In this work, experimental Raman and
infrared spectra are compared with vibrational spectra of CdSe/CdS core/shell
nanoplatelets calculated from first principles using the density functional
theory. The calculations confirm the two-mode behavior of phonon spectra of
nanostructures. An analysis of the experimental spectra reveals the absence of
modes with a high amplitude of vibrations of surface atoms, which indicates
their strong damping. Taking into account the difference in the damping of
different modes and their calculated intensities, all bands in the spectra are
unambiguously identified. It is found that the frequencies of longitudinal
optical modes in heterostructures are close to the frequencies of LO phonons in
bulk strained constituents, whereas the frequencies of transverse modes can
differ significantly from those of the corresponding TO phonons. It is shown
that an anomalous thickness dependence of CdS TO mode is due to a noticeable
surface relaxation of the outer Cd layer in the nanostructure.
|
2112.06326v1
|
2021-12-20
|
Long-time behavior of solutions to the M1 model with boundray effect
|
In this paper, we are concerned with the asymptotic behavior of solutions of
M1 model on quadrant. From this model, combined with damped compressible Euler
equations, a more general system is introduced. We show that the solutions to
the initial boundary value problem of this system globally exist and tend
time-asymptotically to the corresponding nonlinear parabolic equation governed
by the related Darcy's law. Compared with previous results on compressible
Euler equations with damping obtained by Nishihara and Yang in [24], and
Marcati, Mei and Rubino in [16], the better convergence rates are obtained. The
approach adopted is based on the technical time-weighted energy estimates
together with the Green's function method.
|
2112.10392v1
|
2021-12-22
|
Quantum fisher information protection of N-qubit Greenberger-Horne-Zeilinger state from decoherence
|
In this paper we study the protection of N-qubit Greenberger-Horne- Zeilinger
(GHZ) state and generalized N-qubit GHZ states in amplitude damping channel by
means of quantum weak measurement and flip operations. We derive the explicit
formulas of the performances of the protection scheme: average fidelity,
average probability and the average quantum fisher information (QFI). Moreover,
the analytical results for maximizing the average fidelity and probability are
obtained. We show that our scheme can effectively protect the average QFI of
phase for GHZ states and generalized GHZ states. The proposed scheme has the
merit of protecting GHZ state and the QFI of phase against heavy amplitude
damping noise. Further we show that for some generalize GHZ state, the proposed
scheme can protect the state with probability one and fidelity more than 99%.
|
2112.11590v1
|
2021-12-23
|
Theory of Harmonic Hall Responses of Spin-Torque Driven Antiferromagnets
|
Harmonic analysis is a powerful tool to characterize and quantify
current-induced torques acting on magnetic materials, but so far it remains an
open question in studying antiferromagnets. Here we formulate a general theory
of harmonic Hall responses of collinear antiferromagnets driven by
current-induced torques including both field-like and damping-like components.
By scanning a magnetic field of variable strength in three orthogonal planes,
we are able to distinguish the contributions from field-like torque,
damping-like torque, and concomitant thermal effects by analyzing the second
harmonic signals in the Hall voltage. The analytical expressions of the first
and second harmonics as functions of the magnetic field direction and strength
are confirmed by numerical simulations with good agreement. We demonstrate our
predictions in two prototype antiferromagnets, $\alpha-$Fe$_{2}$O$_{3}$ and
NiO, providing direct and general guidance to current and future experiments.
|
2112.12772v2
|
2021-12-24
|
Total Energy Shaping with Neural Interconnection and Damping Assignment -- Passivity Based Control
|
In this work we exploit the universal approximation property of Neural
Networks (NNs) to design interconnection and damping assignment (IDA)
passivity-based control (PBC) schemes for fully-actuated mechanical systems in
the port-Hamiltonian (pH) framework. To that end, we transform the IDA-PBC
method into a supervised learning problem that solves the partial differential
matching equations, and fulfills equilibrium assignment and Lyapunov stability
conditions. A main consequence of this, is that the output of the learning
algorithm has a clear control-theoretic interpretation in terms of passivity
and Lyapunov stability. The proposed control design methodology is validated
for mechanical systems of one and two degrees-of-freedom via numerical
simulations.
|
2112.12999v2
|
2021-12-24
|
Critical comparison of collisionless fluid models: Nonlinear simulations of parallel firehose instability
|
Two different fluid models for collisionless plasmas are compared. One is
based on the classical Chew-Goldberger-Low (CGL) model that includes a finite
Larmor radius (FLR) correction and the Landau closure for the longitudinal
mode. Another one takes into account the effect of cyclotron resonance in
addition to Landau resonance, which is referred to as the cyclotron resonance
closure (CRC) model. While the linear property of the parallel firehose
instability is better described by the CGL model, the electromagnetic ion
cyclotron instability driven unstable by the cyclotron resonance is reproduced
only by the CRC model. Nonlinear simulation results for the parallel firehose
instability performed with the two models are also discussed. Although the
linear and quasilinear isotropization phases are consistent with theory in both
models, long-term behaviors may be substantially different. The final state
obtained by the CRC model may be reasonably understood in terms of the marginal
stability condition. In contrast, the lack of cyclotron damping in the CGL
model makes it rather difficult to predict the long-term behavior with a simple
physical argument. This suggests that incorporating the collisionless damping
both for longitudinal and transverse modes is crucial for a nonlinear fluid
simulation model of collisionless plasmas.
|
2112.13077v1
|
2022-01-04
|
Second order splitting dynamics with vanishing damping for additively structured monotone inclusions
|
In the framework of a real Hilbert space, we address the problem of finding
the zeros of the sum of a maximally monotone operator $A$ and a cocoercive
operator $B$. We study the asymptotic behaviour of the trajectories generated
by a second order equation with vanishing damping, attached to this problem,
and governed by a time-dependent forward-backward-type operator. This is a
splitting system, as it only requires forward evaluations of $B$ and backward
evaluations of $A$. A proper tuning of the system parameters ensures the weak
convergence of the trajectories to the set of zeros of $A + B$, as well as fast
convergence of the velocities towards zero. A particular case of our system
allows to derive fast convergence rates for the problem of minimizing the sum
of a proper, convex and lower semicontinuous function and a smooth and convex
function with Lipschitz continuous gradient. We illustrate the theoretical
outcomes by numerical experiments.
|
2201.01017v1
|
2022-01-15
|
Some Lq(R)-norm decay estimates for two Cauchy systems of type Rao-Nakra sandwich beam with a frictional damping or an infinite memory
|
In this paper, we consider two systems of type Rao-Nakra sandwich beam in the
whole line R with a frictional damping or an infinite memory acting on the
Euler-Bernoulli equation. When the speeds of propagation of the two wave
equations are equal, we show that the solutions do not converge to zero when
time goes to infinity. In the reverse situation, we prove some L2(R)-norm and
L1(R)-norm decay estimates of solutions and theirs higher order derivatives
with respect to the space variable. Thanks to interpolation inequalities and
Carlson inequality, these L2(R)-norm and L1(R)-norm decay estimates lead to
similar ones in the Lq(R)-norm, for any q>1. In our both L2(R)-norm and
L1(R)-norm decay estimates, we specify the decay rates in terms of the
regularity of the initial data and the nature of the control.
|
2201.05881v1
|
2022-01-24
|
Pseudospectral continuation for aeroelastic stability analysis
|
This technical note is concerned with aeroelastic flutter problems: the
analysis of aeroelastic systems undergoing airspeed-dependent dynamic
instability. Existing continuation methods for parametric stability analysis
are based on marching along an airspeed parameter until the flutter point is
found - an approach which may waste computational effort on low-airspeed system
behavior, before a flutter point is located and characterized. Here, we
describe a pseudospectral continuation approach which instead marches outwards
from the system's flutter points, from points of instability to points of
increasing damping, allowing efficient characterization of the subcritical and
supercritical behavior of the system. This approach ties together aeroelastic
stability analysis and abstract linear algebra, and provides efficient methods
for computing practical aeroelastic stability properties - for instance, flight
envelopes based on maximum modal damping, and the location of borderline-stable
zones.
|
2201.09816v1
|
2022-01-26
|
Enhanced weak force sensing through atom-based coherent noise cancellation in a hybrid cavity optomechanical system
|
We investigate weak force-sensing based on coherent quantum noise
cancellation in a nonlinear hybrid optomechanical system. The optomechanical
cavity contains a moveable mechanical mirror, a fixed semitransparent mirror,
an ensemble of ultracold atoms, and an optical parametric amplifier (OPA).
Using the coherent quantum noise cancellation (CQNC) process, one can eliminate
the back action noise at all frequencies. Also by tuning the OPA parameters,
one can suppress the quantum shot-noise at lower frequencies than the resonant
frequency. In the CQNC scheme, the damping rate of the mechanical oscillator
matches the damping rate of the atomic ensemble, which is experimentally
achievable even for a low-frequency mechanical oscillator with a high-quality
factor. Elimination of the back action noise and suppression of the shot noise
significantly enhance force sensing and thus overcome the standard quantum
limit of weak force sensing. This hybrid scheme can play an essential role in
the realization of quantum optomechanical sensors and quantum control.
|
2201.10805v1
|
2022-01-31
|
Indistinguishability-enhanced entanglement recovery by spatially localized operations and classical communication
|
We extend a procedure exploiting spatial indistinguishability of identical
particles to recover the spoiled entanglement between two qubits interacting
with Markovian noisy environments. Here, the spatially localized operations and
classical communication (sLOCC) operational framework is used to activate the
entanglement restoration from the indistinguishable constituents. We consider
the realistic scenario where noise acts for the whole duration of the process.
Three standard types of noises are considered: a phase damping, a depolarizing,
and an amplitude damping channel. Within this general scenario, we find the
entanglement to be restored in an amount proportional to the degree of spatial
indistinguishability. These results elevate sLOCC to a practical framework for
accessing and utilizing quantum state protection within a quantum network of
spatially indistinguishable subsystems.
|
2201.13365v1
|
2022-02-01
|
Uniform synchronization of an abstract linear second order evolution system
|
Although the mathematical study on the synchronization of wave equations at
finite horizon has been well developed, there was few results on the
synchronization of wave equations for long-time horizon. The aim of the paper
is to investigate the uniform synchronization at the infinite horizon for one
abstract linear second order evolution system in a Hilbert space.
First, using the classical compact perturbation theory on the uniform
stability of semigroups of contractions, we will establish a lower bound on the
number of damping, necessary for the uniform synchronization of the considered
system. Then, under the minimum number of damping, we clarify the algebraic
structure of the system as well as the necessity of the conditions of
compatibility on the coupling matrices. We then establish the uniform
synchronization by the compact perturbation method and then give the dynamics
of the asymptotic orbit. Various applications are given for the system of wave
equations with boundary feedback or (and) locally distributed feedback, and for
the system of Kirchhoff plate with distributed feedback. Some open questions
are raised at the end of the paper for future development.
The study is based on the synchronization theory and the compact perturbation
of semigroups.
|
2202.00771v1
|
2022-02-02
|
Electric field screening in pair discharges and generation of pulsar radio emission
|
Pulsar radio emission may be generated in pair discharges which fill the
pulsar magnetosphere with plasma as an accelerating electric field is screened
by freshly created pairs. In this Letter we develop a simplified analytic
theory for the screening of the electric field in these pair discharges and use
it to estimate total radio luminosity and spectrum. The discharge has three
stages. First, the electric field is screened for the first time and starts to
oscillate. Next, a nonlinear phase occurs. In this phase, the amplitude of the
electric field experiences strong damping because the field dramatically
changes the momenta of newly created pairs. This strong damping ceases, and the
system enters a final linear phase, when the electric field can no longer
dramatically change pair momenta. Applied to pulsars, this theory may explain
several aspects of radio emission, including the observed luminosity,
$L_{\rm{rad}} \sim 10^{28} \rm{erg} \, \rm{s}^{-1}$, and the observed spectrum,
$S_\omega \sim \omega^{-1.4 \pm 1.0} $.
|
2202.01303v2
|
2022-01-22
|
Dynamics of a Charged Thomas Oscillator in an External Magnetic Field
|
In this letter, we provide a detailed numerical examination of the dynamics
of a charged Thomas oscillator in an external magnetic field. We do so by
adopting and then modifying the cyclically symmetric Thomas oscillator to study
the dynamics of a charged particle in an external magnetic field. These
dynamical behaviours for weak and strong field strength parameters fall under
two categories; conservative and dissipative. The system shows a complex
quasi-periodic attractor whose topology depends on initial conditions for high
field strengths in the conservative regime. There is a transition from
adiabatic motion to chaos on decreasing the field strength parameter. In the
dissipative regime, the system is chaotic for weak field strength and weak
damping but shows a limit cycle for high field strengths. Such behaviour is due
to an additional negative feedback loop that comes into action at high field
strengths and forces the system dynamics to be stable in periodic oscillations.
For weak damping and weak field strength, the system dynamics mimic Brownian
motion via chaotic walks.
|
2202.02383v2
|
2022-02-15
|
Damped Online Newton Step for Portfolio Selection
|
We revisit the classic online portfolio selection problem, where at each
round a learner selects a distribution over a set of portfolios to allocate its
wealth. It is known that for this problem a logarithmic regret with respect to
Cover's loss is achievable using the Universal Portfolio Selection algorithm,
for example. However, all existing algorithms that achieve a logarithmic regret
for this problem have per-round time and space complexities that scale
polynomially with the total number of rounds, making them impractical. In this
paper, we build on the recent work by Haipeng et al. 2018 and present the first
practical online portfolio selection algorithm with a logarithmic regret and
whose per-round time and space complexities depend only logarithmically on the
horizon. Behind our approach are two key technical novelties of independent
interest. We first show that the Damped Online Newton steps can approximate
mirror descent iterates well, even when dealing with time-varying regularizers.
Second, we present a new meta-algorithm that achieves an adaptive logarithmic
regret (i.e. a logarithmic regret on any sub-interval) for mixable losses.
|
2202.07574v1
|
2022-02-22
|
Modal Estimation on a Warped Frequency Axis for Linear System Modeling
|
Linear systems such as room acoustics and string oscillations may be modeled
as the sum of mode responses, each characterized by a frequency, damping and
amplitude. Here, we consider finding the mode parameters from impulse response
measurements, and estimate the mode frequencies and decay rates as the
generalized eigenvalues of Hankel matrices of system response samples, similar
to ESPRIT. For greater resolution at low frequencies, such as desired in room
acoustics and musical instrument modeling, the estimation is done on a warped
frequency axis. The approach has the benefit of selecting the number of modes
to achieve a desired fidelity to the measured impulse response. An optimization
to further refine the frequency and damping parameters is presented. The method
is used to model coupled piano strings and room impulse responses, with its
performance comparing favorably to FZ-ARMA.
|
2202.11192v1
|
2022-02-28
|
Estimating the degree of non-Markovianity using variational quantum circuits
|
Several applications of quantum machine learning (QML) rely on a quantum
measurement followed by training algorithms using the measurement outcomes.
However, recently developed QML models, such as variational quantum circuits
(VQCs), can be implemented directly on the state of the quantum system (quantum
data). Here, we propose to use a qubit as a probe to estimate the degree of
non-Markovianity of the environment. Using VQCs, we find an optimal sequence of
qubit-environment interactions that yield accurate estimations of the degree of
non-Markovianity for the amplitude damping, phase damping, and the combination
of both models. We introduce a problem-based ansatz that optimizes upon the
probe qubit and the interaction time with the environment. This work
contributes to practical quantum applications of VQCs and delivers a feasible
experimental procedure to estimate the degree of non-Markovianity.
|
2202.13964v3
|
2022-03-08
|
Interplay between nonlinear spectral shift and nonlinear damping of spin waves in ultrathin YIG waveguides
|
We use the phase-resolved imaging to directly study the nonlinear
modification of the wavelength of spin waves propagating in 100-nm thick,
in-plane magnetized YIG waveguides. We show that, by using moderate microwave
powers, one can realize spin waves with large amplitudes corresponding to
precession angles in excess of 10 degrees and nonlinear wavelength variation of
up to 18 percent in this system. We also find that, at large precession angles,
the propagation of spin waves is strongly affected by the onset of nonlinear
damping, which results in a strong spatial dependence of the wavelength. This
effect leads to a spatially dependent controllability of the wavelength by the
microwave power. Furthermore, it leads to the saturation of nonlinear spectral
shift's effects several micrometers away from the excitation point. These
findings are important for the development of nonlinear, integrated spin-wave
signal processing devices and can be used to optimize their characteristics.
|
2203.04018v1
|
2022-03-08
|
The low energy excitation spectrum of magic-angle semimetals
|
We theoretically study the excitation spectrum of a two-dimensional Dirac
semimetal in the presence of an incommensurate potential. Such models have been
shown to possess magic-angle critical points in the single particle
wavefunctions, signalled by a momentum space delocalization of plane wave
eigenstates and flat bands due to a vanishing Dirac cone velocity. Using the
kernel polynomial method, we compute the single particle Green's function to
extract the nature of the single particle excitation energy, damping rate, and
quasiparticle residue. As a result, we are able to clearly demonstrate the
redistribution of spectral weight due to quasiperiodicity-induced downfolding
of the Brillouin zone creating minibands with effective mini Brillouin zones
that correspond to emergent superlattices. By computing the damping rate we
show that the vanishing of the velocity and generation of finite density of
states at the magic-angle transition coincides with the development of an
imaginary part in the self energy and a suppression of the quasiparticle
residue that vanishes in a power law like fashion. Observing these effects with
ultracold atoms using momentum resolved radiofrequency spectroscopy is
discussed.
|
2203.04318v1
|
2022-03-09
|
Nonequilibrium Hole Dynamics in Antiferromagnets: Damped Strings and Polarons
|
We develop a nonperturbative theory for hole dynamics in antiferromagnetic
spin lattices, as described by the $t$-$J$ model. This is achieved by
generalizing the selfconsistent Born approximation to nonequilibrium systems,
making it possible to calculate the full time-dependent many-body wave
function. Our approach reveals three distinct dynamical regimes, ultimately
leading to the formation of magnetic polarons. Following the initial ballistic
stage of the hole dynamics, coherent formation of string excitations gives rise
to characteristic oscillations in the hole density. Their damping eventually
leaves behind magnetic polarons that undergo ballistic motion with a greatly
reduced velocity. The developed theory provides a rigorous framework for
understanding nonequilibrium physics of defects in quantum magnets and
quantitatively explains recent observations from cold-atom quantum simulations
in the strong coupling regime.
|
2203.04789v2
|
2022-03-10
|
Dynamics of the collapse of a ferromagnetic skyrmion in a centrosymmetric lattice
|
Time dependence of the size and chirality of a ferromagnetic skyrmion in a
Heisenberg model with the magnetic field on a square lattice has been studied
analytically and numerically. The lattice and the magnetic field generate
strong time dependence of the skyrmion chirality. Due to nonlinearity, the
lattice alone also generates strong intrinsic damping that leads to the
skyrmion collapse via the emission of spin waves. In the absence of the
magnetic field the collapse is slow for a large skyrmion but it becomes
exponentially fast in the presence of the Landau-Lifshitz damping when the
field is turned on. Magnons emitted by a collapsing skyrmion must have a
discrete spectrum due to the quantization of the skyrmion magnetic moment.
|
2203.05342v1
|
2022-03-22
|
Viscous and centrifugal instabilities of massive stars
|
Massive stars exhibit a variety of instabilities, many of which are poorly
understood. We explore instabilities induced by centrifugal forces and angular
momentum transport in massive rotating stars. First, we derive and numerically
solve linearized oscillation equations for adiabatic radial modes in polytropic
stellar models. In the presence of differential rotation, we show that
centrifugal and Coriolis forces combined with viscous angular momentum
transport can excite stellar pulsation modes, under both low- or high-viscosity
conditions. In the low-viscosity limit, which is common in real stars, we
demonstrate how to compute mode growth/damping rates via a work integral.
Finally, we build realistic rotating $30\,M_\odot$ star models and show that
overstable (growing) radial modes are predicted to exist for most of the star's
life, in the absence of non-adiabatic effects. Peak growth rates are predicted
to occur while the star is crossing the Hertzsprung-Russell gap, though
non-adiabatic damping may dominate over viscous driving, depending on the
effective viscosity produced by convective and/or magnetic torques. Viscous
instability could be a new mechanism to drive massive star pulsations and is
possibly related to instabilities of luminous blue variable stars.
|
2203.11809v1
|
2022-03-27
|
Improvement on the blow-up for a weakly coupled wave equations with scale-invariant damping and mass and time derivative nonlinearity
|
An improvement of [18] on the blow-up region and the lifespan estimate of a
weakly coupled system of wave equations with damping and mass in the
scale-invariant case and with time-derivative nonlinearity is obtained in this
article. Indeed, thanks to a better understanding of the dynamics of the
solutions, we give here a better characterization of the blow-up region.
Furthermore, the techniques used in this article may be extended to other
systems and interestingly they simplify the proof of the blow-up result in [3]
which is concerned with the single wave equation in the same context as in the
present work.
|
2203.14403v1
|
2022-03-24
|
Walking droplets as a damped-driven system
|
We consider the dynamics of a droplet on a vibrating fluid bath. This
hydrodynamic quantum analog system is shown to elicit the canonical behavior of
damped-driven systems, including a period doubling route to chaos. By
approximating the system as a compositional map between the gain and loss
dynamics, the underlying nonlinear dynamics can be shown to be driven by energy
balances in the systems. The gain-loss iterative mapping is similar to a normal
form encoding for the pattern forming instabilities generated in such
spatially-extended system. Similar to mode-locked lasers and rotating
detonation engines, the underlying bifurcations persist for general forms of
the loss and gain, both of which admit explicit representations in our
approximation. Moreover, the resulting geometrical description of the
particle-wave interaction completely characterizes the instabilities observed
in experiments.
|
2203.14705v2
|
2022-04-07
|
Pseudo Numerical Ranges and Spectral Enclosures
|
We introduce the new concepts of pseu\-do numerical range for operator
functions and families of sesquilinear forms as well as the pseu\-do block
numerical range for $n \times n$ operator matrix functions. While these notions
are new even in the bounded case, we cover operator polynomials with unbounded
coefficients, unbounded holomorphic form families of type (a) and associated
operator families of type (B). Our main results include spectral inclusion
properties of pseudo numerical ranges and pseudo block numerical ranges. For
diagonally dominant and off-diagonally dominant operator matrices they allow us
to prove spectral enclosures in terms of the pseudo numerical ranges of Schur
complements that no longer require dominance order $0$ and not even $<1$. As an
application, we establish a new type of spectral bounds for linearly damped
wave equations with possibly unbounded and/or singular damping.
|
2204.03584v1
|
2022-04-13
|
Primordial Gravitational Waves Predictions for GW170817-compatible Einstein-Gauss-Bonnet Theory
|
In this work we shall calculate in detail the effect of an
GW170817-compatible Einstein-Gauss-Bonnet theory on the energy spectrum of the
primordial gravitational waves. The spectrum is affected by two
characteristics, the overall amplification/damping factor caused by the
GW170817-compatible Einstein-Gauss-Bonnet theory and by the tensor spectral
index and the tensor-to-scalar ratio. We shall present the formalism for
studying the inflationary dynamics and post-inflationary dynamics of
GW170817-compatible Einstein-Gauss-Bonnet theories for all redshifts starting
from the radiation era up to the dark energy era. We exemplify our formalism by
using two characteristic models, which produce viable inflationary and dark
energy eras. As we demonstrate, remarkably the overall damping/amplification
factor is of the order of unity, thus the GW170817-compatible
Einstein-Gauss-Bonnet models affect the primordial gravitational waves energy
spectrum only via their tensor spectral index and the tensor-to-scalar ratio.
Both models have a blue tilted tensor spectrum, and therefore the predicted
energy spectrum of the primordial gravity waves can be detectable by most of
the future gravitational waves experiments, for various reheating temperatures.
|
2204.06304v1
|
2022-04-14
|
Stability of Exponentially Damped Oscillations under Perturbations of the Mori-Chain
|
There is an abundance of evidence that some relaxation dynamics, e.g.,
exponential decays, are much more common in nature than others. Recently, there
have been attempts to trace this dominance back to a certain stability of the
prevalent dynamics versus generic Hamiltonian perturbations. In the paper at
hand, we tackle this stability issue from yet another angle, namely in the
framework of the recursion method. We investigate the behavior of various
relaxation dynamics with respect to alterations of the so-called Lanczos
coefficients. All considered scenarios are set up in order to comply with the
"universal operator growth hypothesis". Our numerical experiments suggest the
existence of stability in a larger class of relaxation dynamics consisting of
exponentially damped oscillations. Further, we propose a criterion to identify
"pathological" perturbations that lead to uncommon dynamics.
|
2204.06903v1
|
2022-04-24
|
Integrated Local Energy Decay for the Damped Wave Equation on Stationary Space-Times
|
We prove integrated local energy decay for the damped wave equation on
stationary, asymptotically flat space-times in (1 + 3) dimensions. Local energy
decay constitutes a powerful tool in the study of dispersive partial
differential equations on such geometric backgrounds. By utilizing the
geometric control condition to handle trapped trajectories, we are able to
recover high frequency estimates without any loss. We may then apply known
estimates from the work of Metcalfe, Sterbenz, and Tataru in the medium and low
frequency regimes in order to establish local energy decay. This generalizes
the integrated version of results established by Bouclet and Royer from the
setting of asymptotically Euclidean manifolds to the full Lorentzian case.
|
2204.11339v2
|
2022-04-26
|
Accelerated-gradient-based generalized Levenberg--Marquardt method with oracle complexity bound and local quadratic convergence
|
Minimizing the sum of a convex function and a composite function appears in
various fields. The generalized Levenberg--Marquardt (LM) method, also known as
the prox-linear method, has been developed for such optimization problems. The
method iteratively solves strongly convex subproblems with a damping term. This
study proposes a new generalized LM method for solving the problem with a
smooth composite function. The method enjoys three theoretical guarantees:
iteration complexity bound, oracle complexity bound, and local convergence
under a H\"olderian growth condition. The local convergence results include
local quadratic convergence under the quadratic growth condition; this is the
first to extend the classical result for least-squares problems to a general
smooth composite function. In addition, this is the first LM method with both
an oracle complexity bound and local quadratic convergence under standard
assumptions. These results are achieved by carefully controlling the damping
parameter and solving the subproblems by the accelerated proximal gradient
method equipped with a particular termination condition. Experimental results
show that the proposed method performs well in practice for several instances,
including classification with a neural network and nonnegative matrix
factorization.
|
2204.12016v3
|
2022-05-02
|
Thermoacoustic shocks in complex plasmas
|
The formation of thermoacoustic shocks is revealed in a fluid complex plasma.
The thermoacoustic wave mode can be damped (or anti-damped) when the
contribution from the thermoacoustic interaction is lower (or higher) than that
due to the particle collision and/or the kinematic viscosity. In the nonlinear
regime, the thermoacoustic wave, propagating with the acoustic speed, can
evolve into small amplitude shocks whose dynamics is governed by the
Bateman-Burgers equation with nonlocal nonlinearity. The latter can cause the
shock fronts to be stable (or unstable) depending on the collision frequency
remains below (or above) a critical value and the thermal feedback is positive.
The existence of different kinds of shocks and their characteristics are
analyzed with the system parameters that characterize the thermal feedback,
thermal diffusion, heat capacity per fluid particle, the particle collision and
the fluid viscosity. A good agreement between the analytical and numerical
results are also noticed.
|
2205.00896v1
|
2022-05-09
|
Mutual friction and diffusion of two-dimensional quantum vortices
|
We present a microscopic open quantum systems theory of thermally-damped
vortex motion in oblate atomic superfluids that includes previously neglected
energy-damping interactions between superfluid and thermal atoms. This
mechanism couples strongly to vortex core motion and causes dissipation of
vortex energy due to mutual friction, as well as Brownian motion of vortices
due to thermal fluctuations. We derive an analytic expression for the
dimensionless mutual friction coefficient that gives excellent quantitative
agreement with experimentally measured values, without any fitted parameters.
Our work closes an existing two orders of magnitude gap between dissipation
theory and experiments, previously bridged by fitted parameters, and provides a
microscopic origin for the mutual friction and diffusion of quantized vortices
in two-dimensional atomic superfluids.
|
2205.04065v2
|
2022-05-09
|
Nonlinear Landau damping for the Vlasov-Poisson system in $\R^3$: the Poisson equilibrium
|
We prove asymptotic stability of the Poisson homogeneous equilibrium among
solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$.
More precisely, we show that small, smooth, and localized perturbations of the
Poisson equilibrium lead to global solutions of the Vlasov-Poisson system,
which scatter to linear solutions at a polynomial rate as $t\to\infty$.
The Euclidean problem we consider here differs significantly from the
classical work on Landau damping in the periodic setting, in several ways. Most
importantly, the linearized problem cannot satisfy a "Penrose condition". As a
result, our system contains resonances (small divisors) and the electric field
is a superposition of an electrostatic component and a larger oscillatory
component, both with polynomially decaying rates.
|
2205.04540v2
|
2022-05-11
|
Domain wall damped harmonic oscillations induced by curvature gradients in elliptical magnetic nanowires
|
Understanding the domain wall (DW) dynamics in magnetic nanowires (NW) is
crucial for spintronic-based applications demanding the use of DWs as
information carriers. This work focuses on the dynamics of a DW displacing
along a bent NW with an elliptical shape under the action of spin-polarized
electric currents and external magnetic fields. Our results evidence that a
curvature gradient induces an exchange-driven effective tangential field
responsible for pinning a DW near the maximum curvature point in a NW. The DW
equilibrium position depends on the competition between the torques produced by
the external stimuli and the curvature-induced effective fields. When the
external stimuli are below a certain threshold, the DW follows a damped
harmonic oscillation around the equilibrium position. Above this threshold, DW
displaces along the NW under an oscillatory translational motion.
|
2205.05716v1
|
2022-05-12
|
Global existence and stability of subsonic time-periodic solution to the damped compressible Euler equations in a bounded domain
|
In this paper, we consider the one-dimensional isentropic compressible Euler
equations with source term $\beta(t,x)\rho|u|^{\alpha}u$ in a bounded domain,
which can be used to describe gas transmission in a nozzle.~The model is
imposed a subsonic time-periodic boundary condition.~Our main results reveal
that the time-periodic boundary can trigger an unique subsonic time-periodic
smooth solution and this unique periodic solution is stable under small
perturbations on initial and boundary data.~To get the existence of subsonic
time-periodic solution, we use the linear iterative skill and transfer the
boundary value problem into two initial value ones by using the hyperbolic
property of the system. Then the corresponding linearized system can be
decoupled.~The uniqueness is a direct by-product of the stability. There is no
small assumptions on the damping coefficient.
|
2205.05858v2
|
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