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2020-01-09
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Photon correlation measurements of stochastic limit cycles emerging from high-$Q$ nonlinear silicon photonic crystal microcavities
|
We performed measurements of photon correlation [$g^{(2)}(\tau)$] in driven
nonlinear high-$Q$ silicon (Si) photonic crystal (PhC) microcavities. The
measured $g^{(2)}(\tau)$ exhibits a damped oscillatory behavior when input pump
power exceeds a critical value. From comparison between experiments and
simulations, we attribute the measured oscillation of $g^{(2)}(\tau)$ to
self-pulsing (a limit cycle) emerging from an interplay between photon,
carrier, and thermal dynamics. Namely, the oscillation frequency of
$g^{(2)}(\tau)$ corresponds to the oscillation period of the limit cycle, while
its finite coherence (damping) time originates from the stochastic nature of
the limit cycle. From the standpoint of phase reduction theory, we interpret
the measured coherence time of $g^{(2)}(\tau)$ as the coherence (diffusion)
time of a generalized phase of the limit cycle. Furthermore, we show that an
increase in laser input power enhances the coherence time of $g^{(2)}(\tau)$ up
to the order of microseconds, which could be a demonstration of the
stabilization of a stochastic limit cycle through pumping.
|
2001.02838v2
|
2020-01-12
|
Linear programming bounds for quantum amplitude damping codes
|
Given that approximate quantum error-correcting (AQEC) codes have a
potentially better performance than perfect quantum error correction codes, it
is pertinent to quantify their performance. While quantum weight enumerators
establish some of the best upper bounds on the minimum distance of quantum
error-correcting codes, these bounds do not directly apply to AQEC codes.
Herein, we introduce quantum weight enumerators for amplitude damping (AD)
errors and work within the framework of approximate quantum error correction.
In particular, we introduce an auxiliary exact weight enumerator that is
intrinsic to a code space and moreover, we establish a linear relationship
between the quantum weight enumerators for AD errors and this auxiliary exact
weight enumerator. This allows us to establish a linear program that is
infeasible only when AQEC AD codes with corresponding parameters do not exist.
To illustrate our linear program, we numerically rule out the existence of
three-qubit AD codes that are capable of correcting an arbitrary AD error.
|
2001.03976v1
|
2020-01-22
|
Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data
|
In the present paper, we study the Cauchy problem for the wave equation with
a time-dependent scale invariant damping, i.e.$\frac{2}{1+t}\partial_t v$ and a
cubic convolution $(|x|^{-\gamma}*v^2)v$ with $\gamma\in (0,n)$, where
$v=v(x,t)$ is an unknown function on $\mathbb{R}^n\times[0,T)$. Our aim of the
present paper is to prove a small data blow-up result and show an upper
estimate of lifespan of the problem for slowly decaying positive initial data
$(v(x,0),\partial_t v(x,0))$ such as $\partial_t v(x,0)=O(|x|^{-(1+\nu)})$ as
$|x|\rightarrow\infty$. Here $\nu$ belongs to the scaling supercritical case
$\nu<\frac{n-\gamma}{2}$. Our main new contribution is to estimate the
convolution term in high spatial dimensions, i.e. $n\ge 4$. This paper is the
first blow-up result to treat wave equations with the cubic convolution in high
spatial dimensions ($n\ge 4$).
|
2001.07985v1
|
2020-01-22
|
Testing a Quantum Error-Correcting Code on Various Platforms
|
Quantum error correction plays an important role in fault-tolerant quantum
information processing. It is usually difficult to experimentally realize
quantum error correction, as it requires multiple qubits and quantum gates with
high fidelity. Here we propose a simple quantum error-correcting code for the
detected amplitude damping channel. The code requires only two qubits. We
implement the encoding, the channel, and the recovery on an optical platform,
the IBM Q System, and a nuclear magnetic resonance system. For all of these
systems, the error correction advantage appears when the damping rate exceeds
some threshold. We compare the features of these quantum information processing
systems used and demonstrate the advantage of quantum error correction on
current quantum computing platforms.
|
2001.07998v1
|
2020-01-22
|
Dynamic state reconstruction of quantum systems subject to pure decoherence
|
The article introduces efficient quantum state tomography schemes for qutrits
and entangled qubits subject to pure decoherence. We implement the dynamic
state reconstruction method for open systems sent through phase-damping
channels which was proposed in: Open Syst. Inf. Dyn. 23, 1650019 (2016). In the
current article we prove that two distinct observables measured at four
different time instants suffice to reconstruct the initial density matrix of a
qutrit with evolution given by a phase-damping channel. Furthermore, we
generalize the approach in order to determine the optimal criteria for quantum
tomography of entangled qubits. Finally, we prove two universal theorems
concerning the minimal number of distinct observables required for quantum
tomography of qudits. We believe that dynamic state reconstruction schemes
bring significant advancement and novelty to quantum tomography since they
allow to reduce the number of distinct measurements required to solve the
problem, which is important from the experimental point of view.
|
2001.08167v1
|
2020-01-28
|
Rate of Estimation for the Stationary Distribution of Stochastic Damping Hamiltonian Systems with Continuous Observations
|
We study the problem of the non-parametric estimation for the density $\pi$
of the stationary distribution of a stochastic two-dimensional damping
Hamiltonian system $(Z_t)_{t\in[0,T]}=(X_t,Y_t)_{t \in [0,T]}$. From the
continuous observation of the sampling path on $[0,T]$, we study the rate of
estimation for $\pi(x_0,y_0)$ as $T \to \infty$. We show that kernel based
estimators can achieve the rate $T^{-v}$ for some explicit exponent $v \in
(0,1/2)$. One finding is that the rate of estimation depends on the smoothness
of $\pi$ and is completely different with the rate appearing in the standard
i.i.d.\ setting or in the case of two-dimensional non degenerate diffusion
processes. Especially, this rate depends also on $y_0$. Moreover, we obtain a
minimax lower bound on the $L^2$-risk for pointwise estimation, with the same
rate $T^{-v}$, up to $\log(T)$ terms.
|
2001.10423v1
|
2020-01-28
|
Image polaritons in boron nitride for extreme polariton confinement with low losses
|
Polaritons in two-dimensional materials provide extreme light confinement
that is difficult to achieve with metal plasmonics. However, such tight
confinement inevitably increases optical losses through various damping
channels. Here we demonstrate that hyperbolic phonon polaritons in hexagonal
boron nitride can overcome this fundamental trade-off. Among two observed
polariton modes, featuring a symmetric and antisymmetric charge distribution,
the latter exhibits lower optical losses and tighter polariton confinement.
Far-field excitation and detection of this high-momenta mode becomes possible
with our resonator design that can boost the coupling efficiency via virtual
polariton modes with image charges that we dub image polaritons. Using these
image polaritons, we experimentally observe a record-high effective index of up
to 132 and quality factors as high as 501. Further, our phenomenological theory
suggests an important role of hyperbolic surface scattering in the damping
process of hyperbolic phonon polaritons.
|
2001.10583v2
|
2020-02-06
|
Fractional derivative order determination from harmonic oscillator damping factor
|
This article analysis differential equations which represents damped and
fractional oscillators. First, it is shown that prior to using physical
quantities in fractional calculus, it is imperative that they are turned
dimensionless. Afterwards, approximated expressions that relate the two
equations parameters for the case that the fractional order is close to an
integer number are presented. Following, a numerical regression is made using
power series expansion, and, also from fractional calculus, the fact that both
equations cannot be equivalent is concluded. In the end, from the numerical
regression data, the analytical approximated expressions that relate the two
equations' parameters are refined.
|
2002.02479v1
|
2020-02-11
|
A numerical damped oscillator approach to constrained Schrödinger equations
|
This article explains and illustrates the use of a set of coupled dynamical
equations, second order in a fictitious time, which converges to solutions of
stationary Schr\"{o}dinger equations with additional constraints. We include
three qualitative different numerical examples: the radial Schr\"{o}dinger
equation for the hydrogen atom; the two-dimensional harmonic oscillator with
degenerate excited states; and finally a non-linear Schr\"{o}dinger equation
for rotating states. The presented method is intuitive, with analogies in
classical mechanics for damped oscillators, and easy to implement, either in
own coding, or with software for dynamical systems. Hence, we find it suitable
to introduce it in a continuation course in quantum mechanics or generally in
applied mathematics courses which contain computational parts.
|
2002.04400v2
|
2020-02-12
|
Fast computation of optimal damping parameters for linear vibrational systems
|
We formulate the quadratic eigenvalue problem underlying the mathematical
model of a linear vibrational system as an eigenvalue problem of a
diagonal-plus-low-rank matrix $A$. The eigenvector matrix of $A$ has a
Cauchy-like structure. Optimal viscosities are those for which $trace(X)$ is
minimal, where $X$ is the solution of the Lyapunov equation $AX+XA^{*}=GG^{*}$.
Here $G$ is a low-rank matrix which depends on the eigenfrequencies that need
to be damped. After initial eigenvalue decomposition of linearized problem
which requires $O(n^3)$ operations, our algorithm computes optimal viscosities
for each choice of external dampers in $O(n^2)$ operations, provided that the
number of dampers is small. Hence, the subsequent optimization is order of
magnitude faster than in the standard approach which solves Lyapunov equation
in each step, thus requiring $O(n^3)$ operations. Our algorithm is based on
$O(n^2)$ eigensolver for complex symmetric diagonal-plus-rank-one matrices and
fast $O(n^2)$ multiplication of linked Cauchy-like matrices.
|
2002.04917v2
|
2020-02-13
|
Low-loss two-dimensional plasmon modes in antimonene
|
The effects of spin-orbit (SOC) and electron-phonon coupling on the
collective excitation of doped monolayer Sb$_2$ are investigated using density
functional and many-body perturbation theories. The spin-orbit coupling is
exclusively important for the monolayer Sb$_2$ and it leads to the
reconstruction of the electronic band structure. In particular, plasmon modes
of monolayer Sb$_2$ are quite sensitive to the SOC and are characterized by
very low damping rates owing to small electron-phonon scatterings. Our results
show plasmons in antimonene are significantly less damped compared to monolayer
graphene when plasmon energies are $\hbar \omega> 0.2$ eV due to smaller
plasmon-phonon coupling in the former material.
|
2002.05302v1
|
2020-02-13
|
Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian
|
An approach to quantization of the damped harmonic oscillator (DHO) is
developed on the basis of a modified Bateman Lagrangian (MBL); thereby some
quantum mechanical aspects of the DHO are clarified. We treat the energy
operator for the DHO, in addition to the Hamiltonian operator that is
determined from the MBL and corresponds to the total energy of the system. It
is demonstrated that the energy eigenvalues of the DHO exponentially decrease
with time and that transitions between the energy eigenstates occur in
accordance with the Schr\"{o}dinger equation. Also, it is pointed out that a
new critical parameter discriminates different behaviours of transition
probabilities.
|
2002.05435v1
|
2020-02-17
|
Charge Transfer Through Redox Molecular Junctions in Non-Equilibrated Solvents
|
Molecular conduction operating in dielectric solvent environments are often
described using kinetic rates based on Marcus theory of electron transfer at a
molecule-metal electrode interface. However, the successive nature of charge
transfer in such system implies that the solvent does not necessarily reach
equilibrium in such process. Here we generalize the theory to account for
solvent nonequilibrium and consider a molecular junction consisting of an
electronic donor-acceptor system coupled to two metallic electrodes and placed
in a polarizable solvent. We determine the nonequilbrium distribution of the
solvent by solving diffusion equations in the strong- and weak-friction limits
and calculate the charge current and its fluctuating behavior. In extreme
limits: the absence of the solvent or fast solvent relaxation, the charge
transfer statistics is Poissonian, while it becomes correlated by the dynamic
solvent in between these limits. A Kramers-like turnover of the nonequilibrium
current as a function of the solvent damping is found. Finally, we propose a
way to tune the solvent-induced damping using geometrical control of the
solvent dielectric response in nanostructured solvent channels.
|
2002.06932v1
|
2020-02-19
|
Diagnostics of plasma ionisation using torsional Alfén waves
|
Using the recently observed torsional Alfv\'en waves in solar prominences, we
determine the ionisation state of the plasma by taking into account that
Alfv\'en waves propagate in a partially ionised prominence plasma. We derive
the evolutionary equation of waves and compare the analytical solutions to
observations to determine the number density of neutrals. Using a single fluid
plasma approximation, where the wave damping is provided by the Cowling
resistivity, we study the temporal evolution of waves. By comparing the
solution of equations with observational data (period, amplitude, propagation
speed), we determined the value of the Cowling resistivity that led us to draw
a conclusion on the amount of neutrals in the partially ionised plasma, a
quantity that cannot be measured directly or indirectly. Our results show that
damped torsional Alfv\'en waves are an ideal diagnostic tool for the ionisation
state of the plasma. Using a simple model, we find that at the observational
temperature of torsional Alfv\'en waves, the number of neutrals is of the order
of $5\times 10^{10}$ cm$^{-3}$.
|
2002.08441v1
|
2020-02-27
|
Ultrafast magnetization dynamics in half-metallic Co$_2$FeAl Heusler alloy
|
We report on optically induced, ultrafast magnetization dynamics in the
Heusler alloy $\mathrm{Co_{2}FeAl}$, probed by time-resolved magneto-optical
Kerr effect. Experimental results are compared to results from electronic
structure theory and atomistic spin-dynamics simulations. Experimentally, we
find that the demagnetization time ($\tau_{M}$) in films of
$\mathrm{Co_{2}FeAl}$ is almost independent of varying structural order, and
that it is similar to that in elemental 3d ferromagnets. In contrast, the
slower process of magnetization recovery, specified by $\tau_{R}$, is found to
occur on picosecond time scales, and is demonstrated to correlate strongly with
the Gilbert damping parameter ($\alpha$). Our results show that
$\mathrm{Co_{2}FeAl}$ is unique, in that it is the first material that clearly
demonstrates the importance of the damping parameter in the remagnetization
process. Based on these results we argue that for $\mathrm{Co_{2}FeAl}$ the
remagnetization process is dominated by magnon dynamics, something which might
have general applicability.
|
2002.12255v1
|
2020-04-14
|
Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients
|
We investigate the stabilization of a locally coupled wave equations with
only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty
in this paper is that both the damping and the coupling coefficients are non
smooth. First, using a general criteria of Arendt-Batty, combined with an
uniqueness result, we prove that our system is strongly stable. Next, using a
spectrum approach, we prove the non-exponential (uniform) stability of the
system. Finally, using a frequency domain approach, combined with a piecewise
multiplier technique and the construction of a new multiplier satisfying some
ordinary differential equations, we show that the energy of smooth solutions of
the system decays polynomially of type t^{-1}.
|
2004.06758v1
|
2020-04-16
|
Ergodicity effects on transport-diffusion equations with localized damping
|
The main objective of this paper is to study the time decay of
transport-diffusion equation with inhomogeneous localized damping in the
multi-dimensional torus. The drift is governed by an autonomous Lipschitz
vector field and the diffusion by the standard heat equation with small
viscosity parameter $\nu$. In the first part we deal with the inviscid case and
show some results on the time decay of the energy using in a crucial way the
ergodicity and the unique ergodicity of the flow generated by the drift. In the
second part we analyze the same problem with small viscosity and provide quite
similar results on the exponential decay uniformly with respect to the
viscosity in some logarithmic time scaling of the \mbox{type $t\in
[0,C_0\ln(1/\nu)]$}.
|
2004.07712v1
|
2020-04-17
|
Majorization-Minimization-Based Levenberg--Marquardt Method for Constrained Nonlinear Least Squares
|
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares
problems with convex constraints is described. Various versions of the LM
method have been proposed, their main differences being in the choice of a
damping parameter. In this paper, we propose a new rule for updating the
parameter so as to achieve both global and local convergence even under the
presence of a convex constraint set. The key to our results is a new
perspective of the LM method from majorization-minimization methods.
Specifically, we show that if the damping parameter is set in a specific way,
the objective function of the standard subproblem in LM methods becomes an
upper bound on the original objective function under certain standard
assumptions.
Our method solves a sequence of the subproblems approximately using an
(accelerated) projected gradient method. It finds an $\epsilon$-stationary
point after $O(\epsilon^{-2})$ computation and achieves local quadratic
convergence for zero-residual problems under a local error bound condition.
Numerical results on compressed sensing and matrix factorization show that our
method converges faster in many cases than existing methods.
|
2004.08259v3
|
2020-04-23
|
Many-body Decay of the Gapped Lowest Excitation of a Bose-Einstein Condensate
|
We study the decay mechanism of the gapped lowest-lying excitation of a
quasi-pure box-trapped atomic Bose-Einstein condensate. Owing to the absence of
lower-energy modes, or direct coupling to an external bath, this excitation is
protected against one-body (linear) decay and the damping mechanism is
exclusively nonlinear. We develop a universal theoretical model that explains
this fundamental nonlinear damping as a process whereby two quanta of the
gapped lowest excitation mode couple to a higher-energy mode, which
subsequently decays into a continuum. We find quantitative agreement between
our experiments and the predictions of this model. Finally, by strongly driving
the system below its (lowest) resonant frequency we observe third-harmonic
generation, a hallmark of nonlinear behavior.
|
2004.11363v1
|
2020-05-05
|
Hydrodynamic memory can boost enormously driven nonlinear diffusion and transport
|
Hydrodynamic memory force or Basset force is known since the 19th-century.
Its influence on Brownian motion remains, however, mostly unexplored. Here, we
investigate its role in nonlinear transport and diffusion within a paradigmatic
model of tilted washboard potential. In this model, a giant enhancement of
driven diffusion over its potential-free limit presents a well-established
paradoxical phenomenon. In the overdamped limit, it occurs at a critical tilt
of vanishing potential barriers. However, for weak damping, it takes place
surprisingly at another critical tilt, where the potential barriers are clearly
expressed. Recently we showed that Basset force could make such a diffusion
enhancement enormously large. In this paper, we discover that even for
moderately strong damping, where the overdamped theory works very well when the
memory effects are negligible, substantial hydrodynamic memory unexpectedly
makes a strong impact. First, the diffusion boost occurs at non-vanishing
potential barriers and can be orders of magnitude larger. Second, transient
anomalous diffusion regimes emerge over many time decades and potential
periods. Third, particles' mobility can also be dramatically enhanced, and a
long transient super-transport regime emerges.
|
2005.01984v2
|
2020-05-05
|
Diffraction losses of a Fabry-Perot cavity with nonidentical non-spherical mirrors
|
Optical cavities with both optimized resonant conditions and high quality
factors are important metrological tools. In particular, they are used for
laser gravitational wave (GW) detectors. It is necessary to suppress the
parametric instability by damping the resonant conditions of harmful higher
order optical modes (HOOM) in order to have high cavity powers in GW detectors.
This can be achieved effectively by using non spherical mirrors in symmetric
Fabry-Perot (FP) cavities by increasing roundtrip losses of HOOMs. Fabry-Perot
cavities in most of the GW detectors have non-identical mirrors to optimize
clipping losses and reduce thermal noise by reducing the beam size on one side
of the cavity facing to the beam splitter and recycling cavities. We here
present a general method to design non spherical non-identical mirrors in
non-symmetric FP cavities to damp HOOMs. The proposed design allows to the
suppress the loss of the arm power caused by point absorbers on test masses.
|
2005.02033v1
|
2020-05-11
|
Sound Absorption in Partially Ionized Hydrogen Plasma and Heating Mechanism of Solar Chromosphere
|
The temperature dependence of rates of electron impact ionization and two
electrons recombination are calculated using Wannier cross section of electron
impact ionization of neutral hydrogen atom. Entropy production and power
dissipation are derived for the case when the ionization degree deviates from
its equilibrium value. This is the special case of the obtained general formula
for entropy production accompanying chemical reactions. Damping rate of the
sound waves is calculated and the conditions when ionization processes dominate
are considered. A quasi-classical approximation for the heating mechanism of
solar chromosphere is proposed. Several analogous phenomena for damping rates
in liquids and crystals are shortly discussed, for example, deaf sound of a
glass of beer or English salt solution. An explicit expression for the second
or bulk (or volume) viscosity of hydrogen plasma is calculated from firsts
principles. For the first time some second viscosity is calculated from first
principles.
|
2005.05056v4
|
2020-05-12
|
Calculating RF current condensation with self-consistent ray-tracing
|
By exploiting the nonlinear amplification of the power deposition of RF
waves, current condensation promises new pathways to the stabilisation of
magnetic islands. We present a numerical analysis of current condensation,
coupling a geometrical optics treatment of wave propagation and damping to a
thermal diffusion equation solver in the island. Taking into account the island
geometry and relativistic damping, previous analytical theory can be made more
precise and specific scenarios can be realistically predicted. With this more
precise description, bifurcations and associated hysteresis effects could be
obtained in an ITER-like scenario at realistic parameter values. Moreover, it
is shown that dynamically varying the RF wave launching angles can lead to
hysteresis and help to avoid the nonlinear shadowing effect.
|
2005.05997v1
|
2020-05-13
|
Sustaining a temperature difference
|
We derive an expression for the minimal rate of entropy that sustains two
reservoirs at different temperatures $T_0$ and $T_\ell$. The law displays an
intuitive $\ell^{-1}$ dependency on the relative distance and a characterisic
$\log^2 (T_\ell/T_0)$ dependency on the boundary temperatures. First we give a
back-of-envelope argument based on the Fourier Law (FL) of conduction, showing
that the least-dissipation profile is exponential. Then we revisit a model of a
chain of oscillators, each coupled to a heat reservoir. In the limit of large
damping we reobtain the exponential and squared-log behaviors, providing a
self-consistent derivation of the FL. For small damping "equipartition
frustration" leads to a well-known balistic behaviour, whose incompatibility
with the FL posed a long-time challenge.
|
2005.06289v2
|
2020-05-13
|
Numerical simulations of unsteady viscous incompressible flows using general pressure equation
|
In fluid dynamics, an important problem is linked to the knowledge of the
fluid pressure. Recently, another approach to study incompressible fluid flow
was suggested. It consists in using a general pressure equation (GPE) derived
from compressible Navier-Stokes equation. In this paper, GPE is considered and
compared with the Chorin's artificial compressibility method (ACM) and the
Entropically damped artificial compressibility (EDAC) method. The three methods
are discretized in a staggered grid system with second order centered schemes
in space and a third order Runge-Kutta scheme in time. Three test cases are
realized: two-dimensional Taylor-Green vortex flow, the traveling wave and the
doubly periodic shear layers. It is demonstrated that GPE is accurate and
efficient to capture the correct behavior for unsteady incompressible flows.
The numerical results obtained by GPE are in excellent agreement with those
obtained by ACM, EDAC and a classical finite volume method with a Poisson
equation. Furthermore, GPE convergence is better than ACM convergence. The
proposed general pressure equation (GPE) allows to solve general, time-accurate
, incompressible Navier-Stokes flows. Finally, the parametric study realized in
terms of Mach and Prandtl numbers shows that the velocity divergence can be
limited by an arbitrary maximum and that acoustic waves can be damped.
|
2005.06448v1
|
2020-05-15
|
Response of the BGO Calorimeter to Cosmic Ray Nuclei in the DAMPE Experiment on Orbit
|
This paper is about a study on the response of the BGO calorimeter of DAMPE
experiment. Four elements in Cosmic Ray nuclei are used as sources for this
analysis. A feature resulting from the geomagnetic cutoff exhibits in the
energy spectrum, both in simulated and reconstructed data, and is compared
between them.
|
2005.07621v1
|
2020-05-18
|
Linear inviscid damping for shear flows near Couette in the 2D stably stratified regime
|
We investigate the linear stability of shears near the Couette flow for a
class of 2D incompressible stably stratified fluids. Our main result consists
of nearly optimal decay rates for perturbations of stationary states whose
velocities are monotone shear flows $(U(y),0)$ and have an exponential density
profile. In the case of the Couette flow $U(y)=y$, we recover the rates
predicted by Hartman in 1975, by adopting an explicit point-wise approach in
frequency space. As a by-product, this implies optimal decay rates as well as
Lyapunov instability in $L^2$ for the vorticity. For the previously unexplored
case of more general shear flows close to Couette, the inviscid damping results
follow by a weighted energy estimate. Each outcome concerning the stably
stratified regime applies to the Boussinesq equations as well. Remarkably, our
results hold under the celebrated Miles-Howard criterion for stratified fluids.
|
2005.09058v2
|
2020-05-19
|
High-redshift Damped Ly-alpha Absorbing Galaxy Model Reproducing the N(HI)-Z Distribution
|
We investigate how damped Lyman-$\alpha$ absorbers (DLAs) at z ~ 2-3,
detected in large optical spectroscopic surveys of quasars, trace the
population of star-forming galaxies. Building on previous results, we construct
a model based on observed and physically motivated scaling relations in order
to reproduce the bivariate distributions of metallicity, Z, and HI column
density, N(HI). Furthermore, the observed impact parameters for galaxies
associated to DLAs are in agreement with the model predictions. The model
strongly favours a metallicity gradient, which scales with the luminosity of
the host galaxy, with a value of $\gamma$* = -0.019 $\pm$ 0.008 dex kpc$^{-1}$
for L* galaxies that gets steeper for fainter galaxies. We find that DLAs trace
galaxies over a wide range of galaxy luminosities, however, the bulk of the DLA
cross-section arises in galaxies with L ~ 0.1 L* at z ~ 2.5 broadly consistent
with numerical simulations.
|
2005.09660v1
|
2020-05-20
|
Dynamical phase transitions in dissipative quantum dynamics with quantum optical realization
|
We study dynamical phase transitions (DPT) in the driven and damped Dicke
model, realizable for example by a driven atomic ensemble collectively coupled
to a damped cavity mode. These DPTs are characterized by non-analyticities of
certain observables, primarily the overlap of time evolved and initial state.
Even though the dynamics is dissipative, this phenomenon occurs for a wide
range of parameters and no fine-tuning is required. Focusing on the state of
the 'atoms' in the limit of a bad cavity, we are able to asymptotically
evaluate an exact path integral representation of the relevant overlaps. The
DPTs then arise by minimization of a certain action function, which is related
to the large deviation theory of a classical stochastic process. From a more
general viewpoint, in the considered system, non-analyticities emerge
generically in a Fock space representation of the state. Finally, we present a
scheme which allows a measurement of the DPT in a cavity-QED setup.
|
2005.10013v2
|
2020-05-21
|
The critical exponent for nonlinear damped $σ$-evolution equations
|
In this paper, we derive suitable optimal $L^p-L^q$ decay estimates, $1\leq
p\leq q\leq \infty$, for the solutions to the $\sigma$-evolution equation,
$\sigma>1$, with structural damping and power nonlinearity $|u|^{1+\alpha}$ or
$|u_t|^{1+\alpha}$, \[ u_{tt}+(-\Delta)^\sigma u +(-\Delta)^\theta
u_t=\begin{cases} |u|^{1+\alpha}, \\ |u_t|^{1+\alpha}, \end{cases}\] where
$t\geq0$ and $x\in\mathbb{R}^n$. Using these estimates, we can solve the
problem of finding the critical exponents for the two nonlinear problems above
in the so-called non-effective case, $\theta\in(\sigma/2,\sigma]$. This latter
is more difficult than the effective case $\theta\in[0,\sigma/2)$, since the
asymptotic profile of the solution involves a diffusive component and an
oscillating one. The novel idea in this paper consists in treating separately
the two components to neglect the loss of decay rate created by the interplay
of the two components. We deal with the oscillating component, by localizing
the low frequencies, where oscillations appear, in the extended phase space.
This strategy allows us to recover a quasi-scaling property which replaces the
lack of homogeneity of the equation.
|
2005.10946v1
|
2020-05-22
|
Particle pairs and trains in inertial microfluidics
|
Staggered and linear multi-particle trains constitute characteristic
structures in inertial microfluidics. Using lattice-Boltzmann simulations, we
investigate their properties and stability, when flowing through microfluidic
channels. We confirm the stability of cross-streamline pairs by showing how
they contract or expand to their equilibrium axial distance. In contrast,
same-streamline pairs quickly expand to a characteristic separation but even at
long times slowly drift apart. We reproduce the distribution of particle
distances with its characteristic peak as measured in experiments.
Staggered multi-particle trains initialized with an axial particle spacing
larger than the equilibrium distance contract non-uniformly due to collective
drag reduction. Linear particle trains, similar to pairs, rapidly expand
towards a value about twice the equilibrium distance of staggered trains and
then very slowly drift apart non-uniformly. Again, we reproduce the statistics
of particle distances and the characteristic peak observed in experiments.
Finally, we thoroughly analyze the damped displacement pulse traveling as a
microfluidic phonon through a staggered train and show how a defect strongly
damps its propagation.
|
2005.12701v2
|
2020-05-27
|
Experimental diagnostics of entanglement swapping by a collective entanglement test
|
The paper reports on experimental diagnostics of entanglement swapping
protocol by means of collective entanglement witness. Our approach is suitable
to detect disturbances occurring in the preparation of quantum states, quantum
communication channel and imperfect Bell-state projection. More specifically we
demonstrate that our method can distinguish disturbances such as
depolarization, phase-damping, amplitude-damping and imperfect Bell-state
measurement by observing four probabilities and estimating collective
entanglement witness. Since entanglement swapping is a key procedure for
quantum repeaters, quantum relays, device-independent quantum communications or
entanglement assisted error correction, this can aid in faster and practical
resolution of quality-of-transmission related problems as our approach requires
less measurements then other means of diagnostics.
|
2005.13292v2
|
2020-05-27
|
Magnon antibunching in a nanomagnet
|
We investigate the correlations of magnons inside a nanomagnet and identify a
regime of parameters where the magnons become antibunched, i.e., where there is
a large probability for occupation of the single-magnon state. This antibunched
state is very different from magnons at thermal equilibrium and
microwave-driven coherent magnons. We further obtain the steady state
analytically and describe the magnon dynamics numerically, and ascertain the
stability of such antibunched magnons over a large window of magnetic
anisotropy, damping and temperature. This means that the antibunched magnon
state is feasible in a wide class of low-damping magnetic nanoparticles. To
detect this quantum effect, we propose to transfer the quantum information of
magnons to photons by magnon-photon coupling and then measure the correlations
of photons to retrieve the magnon correlations. Our findings may provide a
promising platform to study quantum-classical transitions and for designing a
single magnon source.
|
2005.13637v1
|
2020-05-31
|
Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation
|
The article is devoted to the mathematical analysis of a fluid-structure
interaction system where the fluid is compressible and heat conducting and
where the structure is deformable and located on a part of the boundary of the
fluid domain. The fluid motion is modeled by the compressible
Navier-Stokes-Fourier system and the structure displacement is described by a
structurally damped plate equation. Our main results are the existence of
strong solutions in an $L^p-L^q$ setting for small time or for small data.
Through a change of variables and a fixed point argument, the proof of the main
results is mainly based on the maximal regularity property of the corresponding
linear systems. For small time existence, this property is obtained by
decoupling the linear system into several standard linear systems whereas for
global existence and for small data, the maximal regularity property is proved
by showing that the corresponding linear coupled {\em fluid-structure} operator
is $\mathcal{R}-$sectorial.
|
2006.00488v1
|
2020-06-03
|
Giant voltage control of spin Hall nano-oscillator damping
|
Spin Hall nano-oscillators (SHNOs) are emerging spintronic devices for
microwave signal generation and oscillator based neuromorphic computing
combining nano-scale footprint, fast and ultra-wide microwave frequency
tunability, CMOS compatibility, and strong non-linear properties providing
robust large-scale mutual synchronization in chains and two-dimensional arrays.
While SHNOs can be tuned via magnetic fields and the drive current, neither
approach is conducive for individual SHNO control in large arrays. Here, we
demonstrate electrically gated W/CoFeB/MgO nano-constrictions in which the
voltage-dependent perpendicular magnetic anisotropy, tunes the frequency and,
thanks to nano-constriction geometry, drastically modifies the spin-wave
localization in the constriction region resulting in a giant 42 % variation of
the effective damping over four volts. As a consequence, the SHNO threshold
current can be strongly tuned. Our demonstration adds key functionality to
nano-constriction SHNOs and paves the way for energy-efficient control of
individual oscillators in SHNO chains and arrays for neuromorphic computing.
|
2006.02151v1
|
2020-06-05
|
Controlling the nonlinear relaxation of quantized propagating magnons in nanodevices
|
Relaxation of linear magnetization dynamics is well described by the viscous
Gilbert damping processes. However, for strong excitations, nonlinear damping
processes such as the decay via magnon-magnon interactions emerge and trigger
additional relaxation channels. Here, we use space- and time-resolved
microfocused Brillouin light scattering spectroscopy and micromagnetic
simulations to investigate the nonlinear relaxation of strongly driven
propagating spin waves in yttrium iron garnet nanoconduits. We show that the
nonlinear magnon relaxation in this highly quantized system possesses
intermodal features, i.e., magnons scatter to higher-order quantized modes
through a cascade of scattering events. We further show how to control such
intermodal dissipation processes by quantization of the magnon band in
single-mode devices, where this phenomenon approaches its fundamental limit.
Our study extends the knowledge about nonlinear propagating spin waves in
nanostructures which is essential for the construction of advanced spin-wave
elements as well as the realization of Bose-Einstein condensates in scaled
systems.
|
2006.03400v2
|
2020-06-08
|
Rogue wave, interaction solutions to the KMM system
|
In this paper, the consistent tanh expansion (CTE) method and the truncated
Painlev$\acute{\rm e}$ analysis are applied to the Kraenkel-Manna-Merle (KMM)
system, which describes propagation of short wave in ferromagnets. Two series
of analytic solutions of the original KMM system (free of damping effect) are
obtained via the CTE method. The interaction solutions contain an arbitrary
function, which provides a wide variety of choices to acquire new propagation
structures. Particularly, the breather soliton, periodic oscillation soliton
and multipole instanton are obtained. Furthermore, we obtain some exact
solutions of the damped-KMM equation at the first time. On the other hand, a
coupled equation containing quadri-linear form and tri-linear form for the
original KMM system is obtained by the truncated Painlev$\acute{\rm e}$
analysis, and the rogue wave solution and interaction solutions between rogue
wave and multi-soliton for the KMM system are discussed.
|
2006.04312v1
|
2020-06-10
|
Interpolation between Residual and Non-Residual Networks
|
Although ordinary differential equations (ODEs) provide insights for
designing network architectures, its relationship with the non-residual
convolutional neural networks (CNNs) is still unclear. In this paper, we
present a novel ODE model by adding a damping term. It can be shown that the
proposed model can recover both a ResNet and a CNN by adjusting an
interpolation coefficient. Therefore, the damped ODE model provides a unified
framework for the interpretation of residual and non-residual networks. The
Lyapunov analysis reveals better stability of the proposed model, and thus
yields robustness improvement of the learned networks. Experiments on a number
of image classification benchmarks show that the proposed model substantially
improves the accuracy of ResNet and ResNeXt over the perturbed inputs from both
stochastic noise and adversarial attack methods. Moreover, the loss landscape
analysis demonstrates the improved robustness of our method along the attack
direction.
|
2006.05749v4
|
2020-06-15
|
Multimode cold-damping optomechanics with delayed feedback
|
We investigate the role of time delay in cold-damping optomechanics with
multiple mechanical resonances. For instantaneous electronic response, it was
recently shown in \textit{Phys. Rev. Lett. \textbf{123}, 203605 (2019)}, that a
single feedback loop is sufficient to simultaneously remove thermal noise from
many mechanical modes. While the intrinsic delayed response of the electronics
can induce single mode and mutual heating between adjacent modes, we propose to
counteract such detrimental effects by introducing an additional time delay to
the feedback loop. For lossy cavities and broadband feedback, we derive
analytical results for the final occupancies of the mechanical modes within the
formalism of quantum Langevin equations. For modes that are frequency
degenerate collective effects dominate, mimicking behavior similar to Dicke
super- and subradiance. These analytical results, corroborated with numerical
simulations of both transient and steady state dynamics, allow to find suitable
conditions and strategies for efficient single or multimode feedback
optomechanics.
|
2006.08430v2
|
2020-06-12
|
Analytic solution of the SEIR epidemic model via asymptotic approximant
|
An analytic solution is obtained to the SEIR Epidemic Model. The solution is
created by constructing a single second-order nonlinear differential equation
in $\ln S$ and analytically continuing its divergent power series solution such
that it matches the correct long-time exponential damping of the epidemic
model. This is achieved through an asymptotic approximant (Barlow et. al, 2017,
Q. Jl Mech. Appl. Math, 70 (1), 21-48) in the form of a modified symmetric
Pad\'e approximant that incorporates this damping. The utility of the
analytical form is demonstrated through its application to the COVID-19
pandemic.
|
2006.09818v2
|
2020-06-20
|
On The Energy Transfer To High Frequencies In The Damped/Driven Nonlinear Schrödinger Equation (Extended Version)
|
We consider a damped/driven nonlinear Schr\"odinger equation in an $n$-cube
$K^{n}\subset\mathbb{R}^n$, $n$ is arbitrary, under Dirichlet boundary
conditions \[ u_t-\nu\Delta u+i|u|^2u=\sqrt{\nu}\eta(t,x),\quad x\in
K^{n},\quad u|_{\partial K^{n}}=0, \quad \nu>0, \] where $\eta(t,x)$ is a
random force that is white in time and smooth in space. It is known that the
Sobolev norms of solutions satisfy $ \| u(t)\|_m^2 \le C\nu^{-m}, $ uniformly
in $t\ge0$ and $\nu>0$. In this work we prove that for small $\nu>0$ and any
initial data, with large probability the Sobolev norms $\|u(t,\cdot)\|_m$ of
the solutions with $m>2$ become large at least to the order of
$\nu^{-\kappa_{n,m}}$ with $\kappa_{n,m}>0$, on time intervals of order
$\mathcal{O}(\frac{1}{\nu})$.
|
2006.11518v2
|
2020-06-23
|
The Contour Method: a new approach to finding modes of non-adiabatic stellar pulsations
|
The contour method is a new approach to calculating the non-adiabatic
pulsation frequencies of stars. These frequencies can be found by solving for
the complex roots of a characteristic equation constructed from the linear
non-adiabatic stellar pulsation equations. A complex-root solver requires an
initial trial frequency for each non adiabatic root. A standard method for
obtaining initial trial frequencies is to use a star's adiabatic pulsation
frequencies, but this method can fail to converge to non-adiabatic roots,
especially as the growth and/or damping rate of the pulsations becomes large.
The contour method provides an alternative way for obtaining initial trial
frequencies that robustly converges to non-adiabatic roots, even for stellar
models with extremely non-adiabatic pulsations and thus large growth/damping
rates. We describe the contour method implemented in the GYRE stellar pulsation
code and use it to calculate the non-adiabatic pulsation frequencies of
$10\,\rm{M_{\odot}}$ and $20\,\rm{M_{\odot}}$ $\beta$ Cephei star models, and
of a $0.9\,\rm{M_{\odot}}$ extreme helium star model.
|
2006.13223v2
|
2020-06-24
|
The Complex Permeability of Split-Ring Resonator Arrays Measured at Microwave Frequencies
|
We have measured the relative permeability of split-ring resonator (SRR)
arrays used in metamaterials designed to have $\mu^\prime< 0$ over a narrow
range of microwave frequencies. The SRR arrays were loaded into the bore of a
loop-gap resonator (LGR) and reflection coefficient measurements were used to
determine both the real and imaginary parts of the array's effective
permeability. Data were collected as a function of array size and SRR spacing.
The results were compared to those obtained from continuous extended split-ring
resonators (ESRRs). The arrays of planar SRRs exhibited enhanced damping and a
narrower range of frequencies with $\mu^\prime<0$ when compared to the ESRRs.
The observed differences in damping, however, were diminished considerably when
the array size was expanded from a one-dimensional array of $N$ SRRs to a
$2\times 2\times N$ array. Our method can also be used to experimentally
determine the effective permeability of other metamaterial designs.
|
2006.13861v1
|
2020-06-25
|
Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids
|
We characterize the $L^2$ decay rate of solutions to the 3D
magneto-micropolar system in terms of the decay character of the initial datum.
Due to a linear damping term, the micro-rotational field has a faster decay
rate. We also address the asymptotic behaviour of solutions by comparing them
to solutions to the linear part. As a result of the linear damping, the
difference between the micro-rotational field and its linear part also decays
faster. As part of the proofs of these results, we prove estimates for the
derivatives of solutions which might be of independent interest.
|
2006.14427v2
|
2020-06-27
|
Measurement-Based Estimation of System State Matrix for AC Power Systems with Integrated VSCs
|
In this paper, a wide-area measurement system (WAMS)-based method is proposed
to estimate the system state matrix for AC system with integrated voltage
source converters (VSCs) and identify the electromechanical modes. The proposed
method is purely model-free, requiring no knowledge of accurate network
topology and system parameters. Numerical studies in the IEEE 68-bus system
with integrated VSCs show that the proposed measurementbased method can
accurately identify the electromechanical modes and estimate the damping
ratios, the mode shapes, and the participation factors. The work may serve as a
basis for developing WAMS-based damping control using VSCs in the future.
|
2006.15244v1
|
2020-06-29
|
Quadratic optomechanical cooling of a cavity-levitated nanosphere
|
We report on cooling the center-of-mass motion of a nanoparticle due to a
purely quadratic coupling between its motion and the optical field of a high
finesse cavity. The resulting interaction gives rise to a Van der Pol nonlinear
damping, which is analogous to conventional parametric feedback where the
cavity provides passive feedback without measurement. We show experimentally
that like feedback cooling the resulting energy distribution is strongly
nonthermal and can be controlled by the nonlinear damping of the cavity. As
quadratic coupling has a prominent role in proposed protocols to generate
deeply nonclassical states, our work represents a first step for producing such
states in a levitated system.
|
2006.16103v1
|
2020-07-01
|
Entanglement of quantum oscillators coupled to different heat baths
|
We study the non-equilibrium dynamics of two coupled oscillators interacting
with their own heat baths of quantum scalar fields at different temperature
$T_1$ and $T_2$ with bilinear couplings between them. We particularly focus on
the entanglement or inseparability property of their quantum states. The
critical temperatures of two respective oscillators, $T_{1c}$ and $T_{2c}$,
higher than which the entanglement disappears, can be determined. It is found
that when two damping parameters are largely different, say $\gamma_1 \ll
\gamma_2$, the critical temperature $T_{1c}$ with respect to the frequency
$\Omega_+$, the higher frequency among two normal modes frequencies, can be
very large, $T_{1c} \gg \Omega_+$, while $T_{2c} \propto \Omega_+$ with the
possibility of hot entanglement. The entanglement of two oscillators with the
temperature-dependent damping parameters $\gamma_{1;2,T}$ from heat baths is
also discussed.
|
2007.00288v2
|
2020-07-01
|
Stabilization of the critical and subcritical semilinear inhomogeneous and anisotropic elastic wave equation
|
{\bf Abstract} \,\,We prove exponential decay of the critical and subcritical
semilinear inhomogeneous and anisotropic elastic wave equation with locally
distributed damping on bounded domain. One novelty compared to previous
results, is to give a checkable condition of the inhomogeneous and anisotropic
medias. Another novelty is to establish a framework to study the stability of
the damped semilinear inhomogeneous and anisotropic elastic wave equation,
which is hard to apply Carleman estimates to deal with. We develop the Morawetz
estimates and the compactness-uniqueness arguments for the semiliear elastic
wave equation to prove the unique continuation, observability inequality and
stabilization result.
It is pointing that our proof is different from the classical method (See
Dehman et al.\cite{ZYY11}, Joly et al.\cite{ZYY16} and Zuazua \cite{ZYY43}),
which succeeds for the subcritical semilinear wave equation and fails for the
critical semilinear wave equation.
|
2007.00813v1
|
2020-07-06
|
Collective excitations and universal broadening of cyclotron absorption in Dirac semimetals in a quantizing magnetic field
|
The spectrum of electromagnetic collective excitations in Dirac semimetals
placed in a quantizing magnetic field is considered. We have found the Landau
damping regions using the energy and momentum conservation law for allowed
transitions between one-particle states of electron excitations. Analysis of
dispersion equations for longitudinal and transverse waves near the window
boundaries in the Landau damping regions reveals different types of collective
excitations. We also indicate the features of universal broadening of cyclotron
absorption for a magnetic field variation in systems with linear dispersion of
the electron spectrum. The use of the obtained spectrum also allows us to
predict a number of oscillation and resonance effects in the field of
magneto-optical phenomena.
|
2007.02979v1
|
2020-07-06
|
Fast convex optimization via a third-order in time evolution equation: TOGES-V an improved version of TOGES
|
In a Hilbert space setting H, for convex optimization, we analyze the fast
convergence properties as t tends to infinity of the trajectories generated by
a third-order in time evolution system. The function f to minimize is supposed
to be convex, continuously differentiable, with a nonempty set of minimizers.
It enters into the dynamic through its gradient. Based on this new dynamical
system, we improve the results obtained by [Attouch, Chbani, Riahi: Fast convex
optimization via a third-order in time evolution equation, Optimization 2020].
As a main result, when the damping parameter $\alpha$ satisfies $\alpha > 3$,
we show that the convergence of the values at the order 1/t3 as t goes to
infinity, as well as the convergence of the trajectories. We complement these
results by introducing into the dynamic an Hessian driven damping term, which
reduces the oscillations. In the case of a strongly convex function f, we show
an autonomous evolution system of the third order in time with an exponential
rate of convergence. All these results have natural extensions to the case of a
convex lower semicontinuous function with extended real values. Just replace f
with its Moreau envelope.
|
2007.03062v1
|
2021-02-01
|
Performance and limits of feedback cooling methods for levitated oscillators: a direct comparison
|
Cooling the centre-of-mass motion is an important tool for levitated
optomechanical systems, but it is often not clear which method can practically
reach lower temperatures for a particular experiment. We directly compare the
parametric and velocity feedback damping methods, which are used extensively
for cooling the motion of single trapped particles in a range of traps. By
performing experiments on the same particle, and with the same detection
system, we demonstrate that velocity damping cools the oscillator to lower
temperatures and is more resilient to imperfect experimental conditions. We
show that these results are consistent with analytical limits as well as
numerical simulations that include experimental noise.
|
2102.01060v3
|
2021-02-16
|
A homogenized damping model for the propagation of elastic wave in a porous solid
|
This paper develops an averaging technique based on the combination of the
eigenfunction expansion method and the collaboration method to investigate the
multiple scattering effect of the SH wave propagation in a porous medium. The
semi-analytical averaging technique is conducted using Monto Carlo method to
understand the macroscopic dispersion and attenuation phenomena of the stress
wave propagation in a porous solid caused by the multiple scattering effects.
The averaging technique is verified by finite element analysis. Finally, a
simple homogenized elastic model with damping is proposed to describe the
macroscopic dispersion and attenuation effects of SH waves in porous media.
|
2102.08334v1
|
2021-02-11
|
Semi-linear Poisson-mediated Flocking in a Cucker-Smale Model
|
We propose a family of compactly supported parametric interaction functions
in the general Cucker-Smale flocking dynamics such that the mean-field
macroscopic system of mass and momentum balance equations with non-local
damping terms can be converted from a system of partial integro-differential
equations to an augmented system of partial differential equations in a compact
set. We treat the interaction functions as Green's functions for an operator
corresponding to a semi-linear Poisson equation and compute the density and
momentum in a translating reference frame, i.e. one that is taken in reference
to the flock's centroid. This allows us to consider the dynamics in a fixed,
flock-centered compact set without loss of generality. We approach the
computation of the non-local damping using the standard finite difference
treatment of the chosen differential operator, resulting in a tridiagonal
system which can be solved quickly.
|
2102.08772v1
|
2021-02-22
|
Robust formation of nanoscale magnetic skyrmions in easy-plane thin film multilayers with low damping
|
We experimentally demonstrate the formation of room-temperature skyrmions
with radii of about 25\,nm in easy-plane anisotropy multilayers with
interfacial Dzyaloshinskii-Moriya interaction (DMI). We detect the formation of
individual magnetic skyrmions by magnetic force microscopy and find that the
skyrmions are stable in out-of-plane fields up to about 200 mT. We determine
the interlayer exchange coupling as well as the strength of the interfacial
DMI. Additionally, we investigate the dynamic microwave spin excitations by
broadband magnetic resonance spectroscopy. From the uniform Kittel mode we
determine the magnetic anisotropy and low damping $\alpha_{\mathrm{G}} < 0.04$.
We also find clear magnetic resonance signatures in the non-uniform (skyrmion)
state. Our findings demonstrate that skyrmions in easy-plane multilayers are
promising for spin-dynamical applications.
|
2102.11117v1
|
2021-02-22
|
Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation
|
We consider the nonlinear damped Klein-Gordon equation \[
\partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \quad \text{on} \ \
[0,\infty)\times \mathbb{R}^N \] with $\alpha>0$, $2 \le N\le 5$ and energy
subcritical exponents $p>2$. We study the behavior of solutions for which it is
supposed that only one nonlinear object appears asymptotically for large times,
at least for a sequence of times.
We first prove that the nonlinear object is necessarily a bound state. Next,
we show that when the nonlinear object is a non-degenerate state or a
degenerate excited state satisfying a simplicity condition, the convergence
holds for all positive times, with an exponential or algebraic rate
respectively. Last, we provide an example where the solution converges exactly
at the rate $t^{-1}$ to the excited state.
|
2102.11178v1
|
2021-02-23
|
The tipping effect of delayed interventions on the evolution of COVID-19 incidence
|
We combine infectious disease transmission and the non-pharmaceutical
intervention (NPI) response to disease incidence into one closed model
consisting of two coupled delay differential equations for the incidence rate
and the time-dependent reproduction number. The model contains three free
parameters, the initial reproduction number, the intervention strength, and the
response delay relative to the time of infection. The NPI response is modeled
by assuming that the rate of change of the reproduction number is proportional
to the negative deviation of the incidence rate from an intervention threshold.
This delay dynamical system exhibits damped oscillations in one part of the
parameter space, and growing oscillations in another, and these are separated
by a surface where the solution is a strictly periodic nonlinear oscillation.
For parameters relevant for the COVID-19 pandemic, the tipping transition from
damped to growing oscillations occurs for response delays of the order of one
week, and suggests that effective control and mitigation of successive epidemic
waves cannot be achieved unless NPIs are implemented in a precautionary manner,
rather than merely as a response to the present incidence rate.
|
2102.11750v1
|
2021-06-06
|
Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
|
We consider a singular limit problem from the damped wave equation with a
power type nonlinearity to the corresponding heat equation. We call our
singular limit problem non-delay limit. Our proofs are based on the argument
for non-relativistic limit from the nonlinear Klein-Gordon equation to the
nonlinear Schr\"{o}dinger equation by the second author, Nakanishi, and Ozawa
(2002), Nakanishi (2002), and Masmoudi and Nakanishi (2002). We can obtain
better results for the non-delay limit problem than that for the
non-relativistic limit problem due to the dissipation property. More precisely,
we get the better convergence rate of the $L^2$-norm and we also obtain the
global-in-time uniform convergence of the non-delay limit in the
$L^2$-supercritical case.
|
2106.03030v1
|
2021-06-10
|
Symmetrical emergence of extreme events at multiple regions in a damped and driven velocity-dependent mechanical system
|
In this work, we report the emergence of extreme events in a damped and
driven velocity-dependent mechanical system. We observe that the extreme events
emerge at multiple points. We further notice that the extreme events occur
symmetrically in both positive and negative values at all the points of
emergence. We statistically confirm the emergence of extreme events by plotting
the probability distribution function of peaks and interevent intervals. We
also determine the mechanism behind the emergence of extreme events at all the
points and classify these points into two categories depending on the region at
which the extreme events emerge. Finally, we plot the two parameter diagram in
order to have a complete overview of the system.
|
2106.05510v2
|
2021-06-11
|
On global existence for semilinear wave equations with spacedependent critical damping
|
The global existence for semilinear wave equations with space-dependent
critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in
an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are
in mind. Existence and non-existence of global-in-time solutions are discussed.
To obtain global existence, a weighted energy estimate for the linear problem
is crucial. The proof of such a weighted energy estimate contains an
alternative proof of energy estimates established by
Ikehata--Todorova--Yordanov [J.\ Math.\ Soc.\ Japan (2013), 183--236] but this
clarifies the precise independence of the location of the support of initial
data. The blowup phenomena is verified by using a test function method with
positive harmonic functions satisfying the Dirichlet boundary condition.
|
2106.06107v1
|
2021-06-13
|
Invariant measures for a stochastic nonlinear and damped 2D Schrödinger equation
|
We consider a stochastic nonlinear defocusing Schr\"{o}dinger equation with
zero-order linear damping, where the stochastic forcing term is given by a
combination of a linear multiplicative noise in the Stratonovich form and a
nonlinear noise in the It\^o form. We work at the same time on compact
Riemannian manifolds without boundary and on relatively compact smooth domains
with either the Dirichlet or the Neumann boundary conditions, always in
dimension 2. We construct a martingale solution using a modified
Faedo-Galerkin's method, following arXiv:1707.05610. Then by means of the
Strichartz estimates deduced from arXiv:math/0609455 but modified for our
stochastic setting we show the pathwise uniqueness of solutions. Finally, we
prove the existence of an invariant measure by means of a version of the
Krylov-Bogoliubov method, which involves the weak topology, as proposed by
Maslowski and Seidler. This is the first result of this type for stochastic NLS
on compact Riemannian manifolds without boundary and on relatively compact
smooth domains even for an additive noise. Some remarks on the uniqueness in a
particular case are provided as well.
|
2106.07043v4
|
2021-06-13
|
Blow-up and lifespan estimates for solutions to the weakly coupled system of nonlinear damped wave equations outside a ball
|
In this paper, we consider the initial-boundary value problems with several
fundamental boundary conditions (the Dirichlet/Neumann/Robin boundary
condition) for the multi-component system of semi-linear classical damped wave
equations outside a ball. By applying a test function approach with a judicious
choice of test functions, which approximates the harmonic functions being
subject to these boundary conditions on $\partial \Omega$, simultaneously we
have succeeded in proving the blow-up result in a finite time as well as in
catching the sharp upper bound of lifespan estimates for small solutions in two
and higher spatial dimensions. Moreover, such kind of these results will be
discussed in one-dimensional case at the end of this work.
|
2106.07050v2
|
2021-06-14
|
An Overview of Energy-Optimal Impedance Control of Cooperative Robot Manipulators
|
An impedance-based control scheme is introduced for cooperative manipulators
grasping a rigid load. The position and orientation of the load are to be
maintained close to a desired trajectory, trading off tracking accuracy by low
energy consumption and maintaining stability. To this end, the augmented
dynamics of the robots, their actuators and the load is formed, and an
impedance control is adopted. A virtual control strategy is used to decouple
torque control from actuator control. An optimization problem is then
formulated using energy balance equations. The optimization finds the damping
and stiffness gains of the impedance relation such that the energy consumption
is minimized. Furthermore, L2 stability techniques are used to allow for
time-varying damping and stiffness in the desired impedance. A numerical
example is provided to demonstrate the results.
|
2106.07491v1
|
2021-06-17
|
Adaptive Low-Rank Regularization with Damping Sequences to Restrict Lazy Weights in Deep Networks
|
Overfitting is one of the critical problems in deep neural networks. Many
regularization schemes try to prevent overfitting blindly. However, they
decrease the convergence speed of training algorithms. Adaptive regularization
schemes can solve overfitting more intelligently. They usually do not affect
the entire network weights. This paper detects a subset of the weighting layers
that cause overfitting. The overfitting recognizes by matrix and tensor
condition numbers. An adaptive regularization scheme entitled Adaptive Low-Rank
(ALR) is proposed that converges a subset of the weighting layers to their
Low-Rank Factorization (LRF). It happens by minimizing a new Tikhonov-based
loss function. ALR also encourages lazy weights to contribute to the
regularization when epochs grow up. It uses a damping sequence to increment
layer selection likelihood in the last generations. Thus before falling the
training accuracy, ALR reduces the lazy weights and regularizes the network
substantially. The experimental results show that ALR regularizes the deep
networks well with high training speed and low resource usage.
|
2106.09677v1
|
2021-06-23
|
Effect of different additional $L^{m}$ regularity on semi-linear damped $σ$-evolution models
|
The motivation of the present study is to discuss the global (in time)
existence of small data solutions to the following semi-linear structurally
damped $\sigma$-evolution models: \begin{equation*}
\partial_{tt}u+(-\Delta)^{\sigma}u+(-\Delta)^{\sigma/2}\partial_{t}u=\left|u\right|
^{p}, \ \sigma\geq 1, \ \ p>1, \end{equation*} where the Cauchy data $(u(0,x),
\partial_{t}u(0,x))$ will be chosen from energy space on the base of $L^{q}$
with different additional $L^{m}$ regularity, namely \begin{equation*}
u(0,x)\in H^{\sigma,q}(\mathbb{R}^{n})\cap L^{m_{1}}(\mathbb{R}^{n}) , \ \
\partial_{t}u(0,x)\in L^{q}(\mathbb{R}^{n})\cap L^{m_{2}}(\mathbb{R}^{n}), \ \
q\in(1,\infty),\ \ m_{1}, m_{2}\in [1,q). \end{equation*} Our new results will
show that the critical exponent which guarantees the global (in time) existence
is really affected by these different additional regularities and will take
\textit{two different values} under some restrictions on $m_{1}, m_{2}$, $q$,
$\sigma$ and the space dimension $n\geq1$. Moreover, in each case, we have no
loss of decay estimates of the unique solution with respect to the
corresponding linear models.
|
2106.12286v1
|
2021-06-29
|
Damping effect in innovation processes: case studies from Twitter
|
Understanding the innovation process, that is the underlying mechanisms
through which novelties emerge, diffuse and trigger further novelties is
undoubtedly of fundamental importance in many areas (biology, linguistics,
social science and others). The models introduced so far satisfy the Heaps'
law, regarding the rate at which novelties appear, and the Zipf's law, that
states a power law behavior for the frequency distribution of the elements.
However, there are empirical cases far from showing a pure power law behavior
and such a deviation is present for elements with high frequencies. We explain
this phenomenon by means of a suitable "damping" effect in the probability of a
repetition of an old element. While the proposed model is extremely general and
may be also employed in other contexts, it has been tested on some Twitter data
sets and demonstrated great performances with respect to Heaps' law and, above
all, with respect to the fitting of the frequency-rank plots for low and high
frequencies.
|
2106.15528v1
|
2021-07-01
|
Local available quantum correlations of X states: The symmetric and anti-symmetric cases
|
Local available quantum correlations (LAQC), as defined by Mundarain et al.,
are analyzed for 2-qubit X states with local Bloch vectors of equal magnitude.
Symmetric X-states are invariant under the exchange of subsystems, hence having
the same {local} Bloch vector. On the other hand, anti-symmetric X states have
{local} Bloch vectors with an equal magnitude but opposite direction
{(anti-parallel)}. In both cases, we obtain exact analytical expressions for
their LAQC quantifier. We present some examples and compare this quantum
correlation to concurrence and quantum discord. We have also included Markovian
decoherence, with Werner states under amplitude damping decoherence. As is the
case for depolarization and phase damping, no sudden death behavior occurs for
the LAQC of these states with this quantum channel.
|
2107.00158v3
|
2021-07-06
|
Dynamical System Parameter Identification using Deep Recurrent Cell Networks
|
In this paper, we investigate the parameter identification problem in
dynamical systems through a deep learning approach. Focusing mainly on
second-order, linear time-invariant dynamical systems, the topic of damping
factor identification is studied. By utilizing a six-layer deep neural network
with different recurrent cells, namely GRUs, LSTMs or BiLSTMs; and by feeding
input-output sequence pairs captured from a dynamical system simulator, we
search for an effective deep recurrent architecture in order to resolve damping
factor identification problem. Our study results show that, although previously
not utilized for this task in the literature, bidirectional gated recurrent
cells (BiLSTMs) provide better parameter identification results when compared
to unidirectional gated recurrent memory cells such as GRUs and LSTM. Thus,
indicating that an input-output sequence pair of finite length, collected from
a dynamical system and when observed anachronistically, may carry information
in both time directions for prediction of a dynamical systems parameter.
|
2107.02427v1
|
2021-07-14
|
Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering
|
The mechanism of the pseudogap observed in hole-doped cuprates remains one of
the central puzzles in condensed matter physics. We analyze this phenomenon via
a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures
the pivotal interplay between Mott localization and Fermi surface topology
beyond weak-coupling spin fluctuations, which would open a spectral gap near
hot spots. We show that strong coupling and particle-hole asymmetry trigger a
very different mechanism: a large imaginary part of the spin-fermion vertex
promotes damping of antinodal fermions and, at the same time, protects the
nodal Fermi arcs (antidamping). Our analysis naturally explains puzzling
features of the pseudogap observed in experiments, such as Fermi arcs being cut
off at the antiferromagnetic zone boundary and the subordinate role of hot
spots.
|
2107.06529v2
|
2021-07-17
|
Blow--up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources
|
The aim of this paper is to give global nonexistence and blow--up results for
the problem $$ \begin{cases} u_{tt}-\Delta u+P(x,u_t)=f(x,u) \qquad &\text{in
$(0,\infty)\times\Omega$,}\\ u=0 &\text{on $(0,\infty)\times \Gamma_0$,}\\
u_{tt}+\partial_\nu u-\Delta_\Gamma u+Q(x,u_t)=g(x,u)\qquad &\text{on
$(0,\infty)\times \Gamma_1$,}\\ u(0,x)=u_0(x),\quad u_t(0,x)=u_1(x) &
\text{in $\overline{\Omega}$,} \end{cases}$$ where $\Omega$ is a bounded open
$C^1$ subset of $\mathbb{R}^N$, $N\ge 2$, $\Gamma=\partial\Omega$,
$(\Gamma_0,\Gamma_1)$ is a partition of $\Gamma$, $\Gamma_1\not=\emptyset$
being relatively open in $\Gamma$, $\Delta_\Gamma$ denotes the
Laplace--Beltrami operator on $\Gamma$, $\nu$ is the outward normal to
$\Omega$, and the terms $P$ and $Q$ represent nonlinear damping terms, while
$f$ and $g$ are nonlinear source terms. These results complement the analysis
of the problem given by the author in two recent papers, dealing with local and
global existence, uniqueness and well--posedness.
|
2107.08213v2
|
2021-07-22
|
Collisional Growth Within the Solar System's Primordial Planetesimal Disk and the Timing of the Giant Planet Instability
|
The large scale structure of the Solar System has been shaped by a transient
dynamical instability that may have been triggered by the interaction of the
giants planets with a massive primordial disk of icy debris. In this work, we
investigate the conditions under which this primordial disk could have
coalesced into planets using analytic and numerical calculations. In
particular, we perform numerical simulations of the Solar System's early
dynamical evolution that account for the viscous stirring and collisional
damping within the disk. We demonstrate that if collisional damping would have
been sufficient to maintain a temperate velocity dispersion, Earth mass
trans-Neptunian planets could have emerged within a timescale of 10 Myr.
Therefore, our results favor a scenario wherein the dynamical instability of
the outer Solar System began immediately upon the dissipation of the gaseous
nebula to avoid the overproduction of Earth mass planets in the outer Solar
System.
|
2107.10403v1
|
2021-11-01
|
Achieving increased Phasor POD performance by introducing a Control-Input Model
|
In this paper, an enhancement to the well known Phasor Power Oscillation
Damper is proposed, aiming to increase its performance. Fundamental to the
functioning of this controller is the estimation of a phasor representing
oscillatory behaviour at a particular frequency in a measured signal. The
phasor is transformed to time domain and applied as a setpoint signal to a
controllable device. The contribution in this paper specifically targets the
estimation algorithm of the controller: It is found that increased estimation
accuracy and thereby enhanced damping performance can be achieved by
introducing a prediction-correction scheme for the estimator, in the form of a
Kalman Filter. The prediction of the phasor at the next step is performed based
on the control signal that is applied at the current step. This enables more
precise damping of the targeted mode.
The presented results, which are obtained from simulations on a
Single-Machine Infinite Bus system and the IEEE 39-Bus system, indicate that
the proposed enhancement improves the performance of this type of controller.
|
2111.00968v2
|
2021-11-02
|
Escape kinetics of self-propelled particles from a circular cavity
|
We numerically investigate the mean exit time of an inertial active Brownian
particle from a circular cavity with single or multiple exit windows. Our
simulation results witness distinct escape mechanisms depending upon the
relative amplitudes of the thermal length and self-propulsion length compared
to the cavity and pore sizes. For exceedingly large self-propulsion lengths,
overdamped active particles diffuse on the cavity surface, and rotational
dynamics solely governs the exit process. On the other hand, the escape
kinetics of a very weakly damped active particle is largely dictated by
bouncing effects on the cavity walls irrespective of the amplitude of
self-propulsion persistence lengths. We show that the exit rate can be
maximized for an optimal self-propulsion persistence length, which depends on
the damping strength, self-propulsion velocity, and cavity size. However, the
optimal persistence length is insensitive to the opening windows' size, number,
and arrangement. Numerical results have been interpreted analytically based on
qualitative arguments. The present analysis aims to understand the transport
controlling mechanism of active matter in confined structures.
|
2111.01324v1
|
2021-11-05
|
Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions
|
Interfaces between materials with differently ordered phases present unique
opportunities for exotic physical properties, especially the interplay between
ferromagnetism and superconductivity in the ferromagnet/superconductor
heterostructures. The investigation of zero- and pi-junctions has been of
particular interest for both fundamental physical science and emerging
technologies. Here, we report the experimental observation of giant oscillatory
Gilbert damping in the superconducting Nb/NiFe/Nb junctions with respect to the
NiFe thickness. This observation suggests an unconventional spin pumping and
relaxation via zero-energy Andreev bound states that exist only in the
Nb/NiFe/Nb pi-junctions, but not in the Nb/NiFe/Nb zero-junctions. Our findings
could be important for further exploring the exotic physical properties of
ferromagnet/superconductor heterostructures, and potential applications of
ferromagnet pi-junctions in quantum computing, such as half-quantum flux
qubits.
|
2111.03233v1
|
2021-11-09
|
Quantum Control of the Time-Dependent Interaction between a Three-Level $Ξ$-Type Atom and a Two-Mode Field with Damping Term
|
The purpose of this paper is to investigate some properties through a
three-level $\Xi$-type atom interacting with a two-mode field. We test this
system in the presence of the photon assisted atomic phase damping, detuning
parameter and Kerr nonlinearity. Also, the coupling parameter modulated to be
time-dependent. The problem solution of this model is given by using the
Schr\H{o}dinger equation when the atom and the field are initially prepared in
the excited state and coherent state, respectively. We used the results to
calculate some aspects such as atomic population inversion and concurrence. The
results show that the time-dependent coupling parameter and the detuning
parameter can be considered as a quantum control parameters of the atomic
population inversion and quantum entanglement in the considered model.
|
2111.05449v1
|
2021-11-10
|
On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy
|
Orthogonal/vector approximate message-passing (AMP) is a powerful
message-passing (MP) algorithm for signal reconstruction in compressed sensing.
This paper proves the convergence of Bayes-optimal orthogonal/vector AMP in the
large system limit. The proof strategy is based on a novel long-memory (LM) MP
approach: A first step is a construction of LM-MP that is guaranteed to
converge systematically. A second step is a large-system analysis of LM-MP via
an existing framework of state evolution. A third step is to prove the
convergence of state evolution recursions for Bayes-optimal LM-MP via a new
statistical interpretation of existing LM damping. The last is an exact
reduction of the state evolution recursions for Bayes-optimal LM-MP to those
for Bayes-optimal orthogonal/vector AMP. The convergence of the state evolution
recursions for Bayes-optimal LM-MP implies that for Bayes-optimal
orthogonal/vector AMP. Numerical simulations are presented to show the
verification of state evolution results for damped orthogonal/vector AMP and a
negative aspect of LM-MP in finite-sized systems.
|
2111.05522v2
|
2021-11-15
|
Spectral analysis of a viscoelastic tube conveying fluid with generalised boundary conditions
|
We study the spectral problem associated with the equation governing the
small transverse motions of a viscoelastic tube of finite length conveying an
ideal fluid. The boundary conditions considered are of general form, accounting
for a combination of elasticity and viscous damping acting on both the slopes
and the displacements of the ends of the tube. These include many standard
boundary conditions as special cases such as the clamped, free, hinged, and
guided conditions. We derive explicit asymptotic formulae for the eigenvalues
for the case of generalised boundary conditions and specialise these results to
the clamped case and the case in which damping acts on the slopes but not on
the displacements. In particular, the dependence of the eigenvalues on the
parameters of the problem is investigated and it is found that all eigenvalues
are located in certain sectorial sets in the complex plane.
|
2111.07697v5
|
2021-11-18
|
Confronting cosmic ray electron and positron excesses with hybrid triplet Higgs portal dark matter
|
We perform a detailed study of scalar dark matter with triplet Higgs
extensions of the Standard Model in order to explain the cosmic ray electron
and positron excesses reported by AMS-02 and DAMPE. A detailed analysis of
AMS-02 positron excess reveals that for different orderings (normal, inverted
and quasi-degenerate) of neutrino mass, the hybrid triplet Higgs portal
framework is more favored with respect to the single triplet Higgs portal for
TeV scale dark matter. We also show that the resonant peak and continuous
excess in DAMPE cosmic ray data can be well explained with the hybrid triplet
Higgs portal dark matter when a dark matter sub-halo nearby is taken into
account.
|
2111.09559v3
|
2021-11-30
|
Damping via the hyperfine interaction of a spin-rotation mode in a two-dimensional strongly magnetized electron plasma
|
We address damping of a Goldstone spin-rotation mode emerging in a quantum
Hall ferromagnet due to laser pulse excitation. Recent experimental data show
that the attenuation mechanism, dephasing of the observed Kerr precession, is
apparently related not only to spatial fluctuations of the electron Land\'e
factor in the quantum well, but to a hyperfine interaction with nuclei, because
local magnetization of GaAs nuclei should also experience spatial fluctuations.
The motion of the macroscopic spin-rotation state is studied microscopically by
solving a non-stationary Schr\"odinger equation. Comparison with the previously
studied channel of transverse spin relaxation (attenuation of Kerr oscilations)
shows that relaxation via nuclei involves a longer quadratic stage of
time-dependance of the transverse spin, and, accordingly, an elongated
transition to a linear stage, so that a linear time-dependance may not be
revealed.
|
2111.15433v1
|
2021-11-30
|
Heating of Magnetically Dominated Plasma by Alfvén-Wave Turbulence
|
Magnetic energy around astrophysical compact objects can strongly dominate
over plasma rest mass. Emission observed from these systems may be fed by
dissipation of Alfv\'en wave turbulence, which cascades to small damping
scales, energizing the plasma. We use 3D kinetic simulations to investigate
this process. When the cascade is excited naturally, by colliding large-scale
Alfv\'en waves, we observe quasithermal heating with no nonthermal particle
acceleration. We also find that the particles are energized along the magnetic
field lines and so are poor producers of synchrotron radiation. At low plasma
densities, our simulations show the transition to "charge-starved" cascades,
with a distinct damping mechanism.
|
2111.15578v2
|
2022-07-07
|
Control of Oscillatory Temperature Field in a Building via Damping Assignment to Nonlinear Koopman Mode
|
This paper addresses a control problem on air-conditioning systems in
buildings that is regarded as a control practice of nonlinear
distributed-parameter systems. Specifically, we consider the design of a
controller for suppressing an oscillatory response of in-room temperature
field. The main idea in this paper is to apply the emergent theory of Koopman
operator and Koopman mode decomposition for nonlinear systems, and to formulate
a technique of damping assignment to a nonlinear Koopman mode in a fully
data-driven manner. Its effectiveness is examined by numerical simulations
guided by measurement of a practical room space.
|
2207.03219v1
|
2022-07-07
|
New perspectives on transient stability between grid-following and grid-forming VSCs
|
The grid-following and grid-forming controls in voltage-source converters are
considered as different operation modes and the synchronization mechanism of
them are studied separately. In this article, the intrinsic relationships
between gridfollowing and grid-forming controlled converters are established as
follows: 1) the proportional gain of PLL is in inverse proportion to damping;
2) the integral gain of PLL is similar to integral droop; 3) PLL has no
practical inertia but acts like grid-forming control in zero inertia cases.
Further, a general stability-enhanced method combining damping and inertia is
proposed, and the modified energy function is obtained to estimate the region
of attraction for the system. Finally, these findings are corroborated by
simulation tests with an intuitive conclusion.
|
2207.03273v1
|
2022-07-11
|
Rapid Stabilization of Timoshenko Beam by PDE Backstepping
|
In this paper, we present a rapid boundary stabilization of a Timoshenko beam
with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE
backstepping. We introduce a transformation to map the Timoshenko beam states
into a (2+2) x (2+2) hyperbolic PIDE-ODE system. Then backstepping is applied
to obtain a control law guaranteeing closed-loop stability of the origin in the
H^1 sense. Arbitrarily rapid stabilization can be achieved by adjusting control
parameters. Finally, a numerical simulation shows that the proposed controller
can rapidly stabilize the Timoshenko beam. This result extends a previous work
which considered a slender Timoshenko beam with Kelvin-Voigt damping, allowing
destabilizing boundary conditions at the uncontrolled boundary and attaining an
arbitrarily rapid convergence rate.
|
2207.04746v1
|
2022-07-20
|
MsSpec-DFM (Dielectric function module): Towards a multiple scattering approach to plasmon description
|
We present here the MsSpec Dielectric Function module (MsSpec-DFM), which
generates dielectric functions in an electron gas or a liquid, either isolated
or embedded into an environment. In addition to standard models such as the
plasmon pole and the RPA, this module also provides more involved methods
incorporating local field corrections (in order to account for correlations),
Boltzmann-Vlasov hydrodynamical methods, the relaxation-damped Mermin and the
diffusion-damped Hu-O'Connell methods, as well as moment-based methods using
either a Nevanlinna function or a memory function. Ultimately, through the use
of form factors, the MsSpec-DFM module will be able to address a wide range of
materials such as metals, semiconductors, including inversion layers,
hetero-structures, superconductors, quantum wells, quantum wires, quantum dots,
Dirac materials such as graphene, and liquids.
|
2207.09924v1
|
2022-07-25
|
Extreme bursting events via pulse-shaped explosion in mixed Rayleigh-Lienard nonlinear oscillator
|
We study the dynamics of a parametrically and externally driven
Rayleigh-Lienard hybrid model and report the emergence of extreme bursting
events due to a novel pulse-shaped explosion mechanism. The system exhibits
complex periodic and chaotic bursting patterns amid small oscillations as a
function of excitation frequencies. In particular, the advent of rare and
recurrent chaotic bursts that emerged for certain parameter regions is
characterized as extreme events. We have identified that the appearance of a
sharp pulse-like transition that occurred in the equilibrium points of the
system is the underlying mechanism for the development of bursting events.
Further, the controlling aspect of extreme events is attempted by incorporating
a linear damping term, and we show that for sufficiently strong damping
strength, the extreme events are eliminated from the system, and only periodic
bursting is feasible.
|
2207.11916v1
|
2022-07-26
|
The Global Existence of Martingale Solutions to Stochastic Compressible Navier-Stokes Equations with Density-dependent Viscosity
|
The global existence of martingale solutions to the compressible
Navier-Stokes equations driven by stochastic external forces, with
density-dependent viscosity and vacuum, is established in this paper. This work
can be regarded as a stochastic version of the deterministic Navier-Stokes
equations \cite{Vasseur-Yu2016} (Vasseur-Yu, Invent. Math., 206:935--974,
2016.), in which the global existence of weak solutions was established for
adiabatic exponent $\gamma > 1$. For the stochastic case, the regularity of
density and velocity is even worse for passing the limit in nonlinear terms. We
design a regularized system to approximate the original system. To make up for
the lack of regularity of velocity, we need to add an artificial Rayleigh
damping term besides the artificial viscosity and damping forces in
\cite{Vasseur-Yu-q2016,Vasseur-Yu2016}. Moreover, we have to send the
artificial terms to $0$ in a different order.
|
2207.12835v5
|
2017-04-03
|
Sensing Coherent Phonons with Two-photon Interference
|
Detecting coherent phonons pose different challenges compared to coherent
photons due to the much stronger interaction between phonons and matter. This
is especially true for high frequency heat carrying phonons, which are
intrinsic lattice vibrations experiencing many decoherence events with the
environment, and are thus generally assumed to be incoherent. Two photon
interference techniques, especially coherent population trapping (CPT) and
electromagnetically induced transparency (EIT), have led to extremely sensitive
detection, spectroscopy and metrology. Here, we propose the use of two photon
interference in a three level system to sense coherent phonons. Unlike prior
works which have treated phonon coupling as damping, we account for coherent
phonon coupling using a full quantum-mechanical treatment. We observe strong
asymmetry in absorption spectrum in CPT and negative dispersion in EIT
susceptibility in the presence of coherent phonon coupling which cannot be
accounted for if only pure phonon damping is considered. Our proposal has
application in sensing heat carrying coherent phonons effects and understanding
coherent bosonic multi-pathway interference effects in three coupled oscillator
systems.
|
1704.00446v1
|
2017-04-03
|
Simulating spin-boson models with trapped ions
|
We propose a method to simulate the dynamics of spin-boson models with small
crystals of trapped ions where the electronic degree of freedom of one ion is
used to encode the spin while the collective vibrational degrees of freedom are
employed to form an effective harmonic environment. The key idea of our
approach is that a single damped mode can be used to provide a harmonic
environment with Lorentzian spectral density. More complex spectral functions
can be tailored by combining several individually damped modes. We propose to
work with mixed-species crystals such that one species serves to encode the
spin while the other species is used to cool the vibrational degrees of freedom
to engineer the environment. The strength of the dissipation on the spin can be
controlled by tuning the coupling between spin and vibrational degrees of
freedom. In this way the dynamics of spin-boson models with macroscopic and
non-Markovian environments can be simulated using only a few ions. We
illustrate the approach by simulating an experiment with realistic parameters
and show by computing quantitative measures that the dynamics is genuinely
non-Markovian.
|
1704.00629v1
|
2017-04-07
|
Coherent-induced state ordering with fixed mixedness
|
In this paper, we study coherence-induced state ordering with Tsallis
relative entropy of coherence, relative entropy of coherence and $l_{1}$ norm
of coherence. Firstly, we show that these measures give the same ordering for
single-qubit states with a fixed mixedness or a fixed length along the
direction $\sigma_{z}$. Secondly, we consider some special cases of high
dimensional states, we show that these measures generate the same ordering for
the set of high dimensional pure states if any two states of the set satisfy
majorization relation. Moreover, these three measures generate the same
ordering for all $X$ states with a fixed mixedness. Finally, we discuss
dynamics of coherence-induced state ordering under Markovian channels. We find
phase damping channel don't change the coherence-induced state ordering for
some single-qubit states with fixed mixedness, instead amplitude damping
channel change the coherence-induced ordering even though for single-qubit
states with fixed mixedness.
|
1704.02244v1
|
2017-04-13
|
A possible connection between the spin temperature of damped Lyman-alpha absorption systems and star formation history
|
We present a comprehensive analysis of the spin temperature/covering factor
degeneracy, T/f, in damped Lyman-alpha absorption systems. By normalising the
upper limits and including these via a survival analysis, there is, as
previously claimed, an apparent increase in T/f with redshift at z > 1.
However, when we account for the geometry effects of an expanding Universe,
neglected by the previous studies, this increase in T/f at z > 1 is preceded by
a decrease at z < 1. Using high resolution radio images of the background
continuum sources, we can transform the T/f degeneracy to T/d^2, where d is the
projected linear size of the absorber. Again, there is no overall increase with
redshift, although a dip at z ~ 2 persists. Furthermore, we find d^2/T to
follow a similar variation with redshift as the star formation rate. This
suggests that, although the total hydrogen column density shows little relation
to the SFR, the fraction of the cold neutral medium may. Therefore, further
efforts to link the neutral gas with the star formation history should also
consider the cool component of the gas.
|
1704.04294v2
|
2017-04-17
|
Magnetic field line random walk in two-dimensional dynamical turbulence
|
The field line random walk (FLRW) of magnetic turbulence is one of the
important topics in plasma physics and astrophysics. In this article by using
the field line tracing method mean square displacements (MSD) of FLRW is
calculated in all possible length scales for pure two-dimensional turbulence
with damping dynamical model. We demonstrate that in order to describe FLRW
with damping dynamical model a new dimensionless quantity $R$ is needed to be
introduced. In different length scales dimensionless MSD shows different
relationship with the dimensionless quantity $R$. Although temporal effect
impacts MSD of FLRW and even changes regimes of FLRW, it dose not affect the
relationship between the dimensionless MSD and dimensionless quantity $R$ in
all possible length scales.
|
1704.05059v3
|
2017-04-19
|
Quantum simulation of quantum channels in nuclear magnetic resonance
|
We propose and experimentally demonstrate an efficient framework for the
quantum simulation of quantum channels in NMR. Our approach relies on the
suitable decomposition of non-unitary operators in a linear combination of $d$
unitary ones, which can be then experimentally implemented with the assistance
of a number of ancillary qubits that grows logarithmically in $d$. As a
proof-of-principle demonstration, we realize the quantum simulation of three
quantum channels for a single-qubit: phase damping (PD), amplitude damping
(AD), and depolarizing (DEP) channels. For these paradigmatic cases, we measure
key features, such as the fidelity of the initial state and the associated von
Neuman entropy for a qubit evolving through these channels. Our experiments are
carried out using nuclear spins in a liquid sample and NMR control techniques.
|
1704.05593v2
|
2017-04-24
|
Beating the Classical Limits of Information Transmission using a Quantum Decoder
|
Encoding schemes and error-correcting codes are widely used in information
technology to improve the reliability of data transmission over real-world
communication channels. Quantum information protocols can further enhance the
performance in data transmission by encoding a message in quantum states,
however, most proposals to date have focused on the regime of a large number of
uses of the noisy channel, which is unfeasible with current quantum technology.
We experimentally demonstrate quantum enhanced communication over an amplitude
damping noisy channel with only two uses of the channel per bit and a single
entangling gate at the decoder. By simulating the channel using a photonic
interferometric setup, we experimentally increase the reliability of
transmitting a data bit by greater than 20% for a certain damping range over
classically sending the message twice. We show how our methodology can be
extended to larger systems by simulating the transmission of a single bit with
up to eight uses of the channel and a two-bit message with three uses of the
channel, predicting a quantum enhancement in all cases.
|
1704.07036v2
|
2017-04-24
|
Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas
|
In this paper, a reduced model of quasilinear diffusion by a small Larmor
radius approximation is derived to couple the Maxwell's equations and the
Fokker-Planck equation self-consistently for ion cyclotron range of frequency
waves in a tokamak. The reduced model ensures the important properties of the
full model by Kennel-Engelmann diffusion, such as diffusion directions, wave
polarizations, and H-theorem. The kinetic energy change (W-dot) is used to
derive the reduced model diffusion coefficients for the fundamental damping and
the second harmonic damping to the lowest order of the finite Larmor radius
expansion. The quasilinear diffusion coefficients are implemented in a coupled
code (TORIC-CQL3D) with the equivalent reduced model of dielectric tensor. We
also present the simulations of the ITER minority heating scenario, in which
the reduced model is verified within the allowable errors from the full model
results.
|
1704.07283v1
|
2017-04-27
|
Chirality-induced Antisymmetry in Magnetic Domain-Wall Speed
|
In chiral magnetic materials, numerous intriguing phenomena such as built in
chiral magnetic domain walls (DWs) and skyrmions are generated by the
Dzyaloshinskii Moriya interaction (DMI). The DMI also results in asymmetric DW
speed under in plane magnetic field, which provides a useful scheme to measure
the DMI strengths. However, recent findings of additional asymmetries such as
chiral damping have disenabled unambiguous DMI determination and the underlying
mechanism of overall asymmetries becomes under debate. By extracting the
DMI-induced symmetric contribution, here we experimentally investigated the
nature of the additional asymmetry. The results revealed that the additional
asymmetry has a truly antisymmetric nature with the typical behavior governed
by the DW chirality. In addition, the antisymmetric contribution changes the DW
speed more than 100 times, which cannot be solely explained by the chiral
damping scenario. By calibrating such antisymmetric contributions, experimental
inaccuracies can be largely removed, enabling again the DMI measurement scheme.
|
1704.08751v1
|
2017-05-04
|
Phase-space mixing in dynamically unstable, integrable few-mode quantum systems
|
Quenches in isolated quantum systems are currently a subject of intense
study. Here, we consider quantum few-mode systems that are integrable in their
classical mean-field limit and become dynamically unstable after a quench of a
system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a
double-well potential and an antiferromagnetic spinor BEC constrained to a
single spatial mode. We study the time dynamics after the quench within the
truncated Wigner approximation (TWA) and find that system relaxes to a steady
state due to phase-space mixing. Using the action-angle formalism and a
pendulum as an illustration, we derive general analytical expressions for the
time evolution of expectation values of observables and their long-time limits.
We find that the deviation of the long-time expectation value from its
classical value scales as $1/O(\ln N )$, where $N$ is the number of atoms in
the condensate. Furthermore, the relaxation of an observable to its steady
state value is a damped oscillation and the damping is Gaussian in time. We
confirm our results with numerical TWA simulations.
|
1705.01702v1
|
2017-05-11
|
Quantum Correlations and Bell Inequality Violation under Decoherence
|
Quantum Correlations are studied extensively in quantum information domain.
Entanglement Measures and Quantum Discord are good examples of these actively
studied correlations. Detection of violation in Bell inequalities is also a
widely active area in quantum information theory world. In this work, we
revisit the problem of analyzing the behavior of quantum correlations and
violation of Bell inequalities in noisy channels. We extend the problem defined
in [1] by observing the changes in negativity measure, quantum discord and a
modified version of Horodecki measure for violation of Bell inequalities under
amplitude damping, phase damping and depolarizing channels. We report different
interesting results for each of these correlations and measures. All these
correlations and measures decrease under decoherence channels, but some changes
are very dramatical comparing to others. We investigate also separability
conditions of example studied states.
|
1705.03882v2
|
2017-05-18
|
Local and global existence of solutions to a strongly damped wave equation of the $p$-Laplacian type
|
This article focuses on a quasilinear wave equation of $p$-Laplacian type: $$
u_{tt} - \Delta_p u - \Delta u_t=0$$ in a bounded domain
$\Omega\subset\mathbb{R}^3$ with a sufficiently smooth boundary
$\Gamma=\partial\Omega$ subject to a generalized Robin boundary condition
featuring boundary damping and a nonlinear source term. The operator
$\Delta_p$, $2 < p < 3$, denotes the classical $p$-Laplacian. The nonlinear
boundary term $f (u)$ is a source feedback that is allowed to have a
supercritical exponent, in the sense that the associated Nemytskii operator is
not locally Lipschitz from $W^{1,p}(\Omega)$ into $L^2(\Gamma)$. Under suitable
assumptions on the parameters we provide a rigorous proof of existence of a
local weak solution which can be extended globally in time provided the source
term satisfies an appropriate growth condition.
|
1705.06696v2
|
2017-05-23
|
Unifying description of the damping regimes of a stochastic particle in a periodic potential
|
We analyze the classical problem of the stochastic dynamics of a particle
confined in a periodic potential, through the so called Il'in and Khasminskii
model, with a novel semi-analytical approach. Our approach gives access to the
transient and the asymptotic dynamics in all damping regimes, which are
difficult to investigate in the usual Brownian model. We show that the
crossover from the overdamped to the underdamped regime is associated with the
loss of a typical time scale and of a typical length scale, as signaled by the
divergence of the probability distribution of a certain dynamical event. In the
underdamped regime, normal diffusion coexists with a non Gaussian displacement
probability distribution for a long transient, as recently observed in a
variety of different systems. We rationalize the microscopic physical processes
leading to the non-Gaussian behavior, as well as the timescale to recover the
Gaussian statistics. The theoretical results are supported by numerical
calculations and are compared to those obtained for the Brownian model.
|
1705.08083v2
|
2017-05-27
|
Experimental Observation of Electron-Acoustic Wave Propagation in Laboratory Plasma
|
In the field of fundamental plasma waves, direct observation of
electron-acoustic wave (EAW) propagation in laboratory plasmas remains a
challenging problem, mainly because of heavy damping. In the MaPLE device, the
wave is observed and seen to propagate with phase velocity $\sim1.8$ times the
electron thermal velocity. A small amount of cold, drifting electrons, with
moderate bulk to cold temperature ratio ($\approx 2 - 3$), is present in the
device. It plays a crucial role in reducing the damping. Our calculation
reveals that the drift relaxes the stringent condition on the temperature ratio
for wave destabilization. Growth rate becomes positive above a certain drift
velocity even if the temperature ratio is moderate. The observed phase velocity
agrees well with the theoretical estimate. Experimental realization of the mode
may open up a new avenue in EAW research.
|
1705.09806v1
|
2017-06-08
|
Superconductivity around nematic quantum critical point in two-dimensional metals
|
We study the properties of $s$-wave superconductivity induced around a
nematic quantum critical point in two-dimensional metals. The strong Landau
damping and the Cooper pairing between incoherent fermions have dramatic mutual
influence on each other, and hence should be treated on an equal footing. This
problem is addressed by analyzing the self-consistent Dyson-Schwinger equations
for the superconducting gap and Landau damping rate. We solve the equations at
zero temperature without making any linearization, and show that the
superconducting gap is maximized at the quantum critical point and decreases
rapidly as the system departs from this point. The interplay between nematic
fluctuation and an additional pairing interaction, caused by phonon or other
boson mode, is also investigated. The total superconducting gap generated by
such interplay can be several times larger than the direct sum of the gaps
separately induced by these two pairing interactions. This provides a promising
way to achieve remarkable enhancement of superconductivity.
|
1706.02583v2
|
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