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2018-01-23
|
The effect of liquid on the vibrational intensity of a wineglass at steady state resonance
|
As a liquid is inserted into a wineglass, the natural frequency of the
wineglass decreases. This phenomenon, known as pitch lowering, is well
explained in past papers. However, previous literature have not yet mentioned
that pitch lowering also reduces the resonance intensity of a wineglass. Thus,
this present paper aims to extend the body of research on this topic by
describing the relationship between pitch lowering and its effect on resonation
intensity. To do so, we identify the vibrating wineglass wall as a damped
harmonic oscillator, derive a theoretical model, and find that the resonance
intensity of the wineglass is proportional to the square of its natural
frequency, under the assumption that damping stays constant. However, our
experiments showed the coefficient of damping to increase with respect to the
amount of liquid, which caused the data to deviate from its theoretical
predictions. We conclude by discussing the accuracy and limitation of our
proposed model.
|
1801.07514v5
|
2018-02-12
|
Chance-constrained optimal location of damping control actuators under wind power variability
|
This paper proposes a new probabilistic energy-based method to determine the
optimal installation location of electronically-interfaced resources (EIRs)
considering dynamic reinforcement under wind variability in systems with high
penetration of wind power. The oscillation energy and total action are used to
compare the dynamic performance for different EIR locations. A linear
approximation of the total action critically reduces the computational time
from hours to minutes. Simulating an IEEE-39 bus system with 30% of power
generation sourced from wind, a chance-constrained optimization is carried out
to decide the location of an energy storage system (ESS) adding damping to the
system oscillations. The results show that the proposed method, selecting the
bus location that guarantees the best dynamic performance with highest
probability, is superior to both traditional dominant mode analysis and
arbitrary benchmarks for damping ratios.
|
1802.04354v1
|
2018-02-21
|
On the vibron-polaron damping in quasi 1D macromolecular chains
|
The properties of the intramolecular vibrational excitation (vibron) in a
quasi 1D macromolecular structure are studied. It is supposed that due to the
vibron interaction with optical phonon modes, a vibron might form partially
dressed small polaron states. The properties of these states are investigated
in dependence on the basic system parameters and temperature of a thermal bath.
We also investigate the process of damping of the polaron amplitude as a
function of temperature and vibron-phonon coupling strength. Two different
regimes of the polaron damping are found and discussed.
|
1802.07424v1
|
2018-02-27
|
Impact of damping on superconducting gap oscillations induced by intense Terahertz pulses
|
We investigate the interplay between gap oscillations and damping in the
dynamics of superconductors taken out of equilibrium by strong optical pulses
with sub-gap Terahertz frequencies. A semi-phenomenological formalism is
developed to include the damping within the electronic subsystem that arises
from effects beyond BCS, such as interactions between Bogoliubov quasiparticles
and decay of the Higgs mode. Such processes are conveniently expressed as
$T_{1}$ and $T_{2}$ times in the standard pseudospin language for
superconductors. Comparing with data on NbN that we report here, we argue that
the superconducting dynamics in the picosecond time scale, after the pump is
turned off, is governed by the $T_{2}$ process.
|
1802.09711v2
|
2018-02-28
|
Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states
|
We study experimentally various physical limitations and technical
imperfections that lead to damping and finite contrast of optically-driven Rabi
oscillations between ground and Rydberg states of a single atom. Finite
contrast is due to preparation and detection errors and we show how to model
and measure them accurately. Part of these errors originates from the finite
lifetime of Rydberg states and we observe its $n^3$-scaling with the principal
quantum number $n$. To explain the damping of Rabi oscillations, we use simple
numerical models, taking into account independently measured experimental
imperfections, and show that the observed damping actually results from the
accumulation of several small effects, each at the level of a few percents. We
discuss prospects for improving the coherence of ground-Rydberg Rabi
oscillations in view of applications in quantum simulation and quantum
information processing with arrays of single Rydberg atoms.
|
1802.10424v1
|
2018-03-07
|
Connecting dissipation and noncommutativity: A Bateman system case study
|
Quantum effects on a pair of Bateman oscillators embedded in an ambient
noncommutative space (Moyal plane) is analyzed using both path integral and
canonical quantization schemes within the framework of Hilbert-Schmidt operator
formulation. We adopt a method which is distinct from the one which employs 't
Hooft's scheme of quantization, carried out earlier in the literature where the
ambient space was taken to be commutative. Our quantization shows that we end
up finally again with a Bateman system except that the damping factor undergoes
renormalization. The corresponding expression shows that the renormalized
damping factor can be non-zero even if "bare" one is zero to begin with.
Conversely, the noncommuatative parameter $\theta$, taken to be a free one now,
can be fine-tuned to get a vanishing renormalized damping factor. This
indicates a duality between dissipative commutative theory and non-dissipative
noncommutative theory.
|
1803.03334v1
|
2018-03-18
|
A machine learning method to separate cosmic ray electrons from protons from 10 to 100 GeV using DAMPE data
|
DArk Matter Particle Explorer (DAMPE) is a general purpose high energy cosmic
ray and gamma ray observatory, aiming to detect high energy electrons and
gammas in the energy range 5 GeV to 10 TeV and hundreds of TeV for nuclei. This
paper provides a method using machine learning to identify electrons and
separate them from gammas,protons,helium and heavy nuclei with the DAMPE data
from 2016 January 1 to 2017 June 30, in energy range from 10 to 100 GeV.
|
1803.06628v2
|
2018-03-20
|
Estimating Participation Factors and Mode Shapes for Electromechanical Oscillations in Ambient Conditions
|
In this paper, a new technique is applied to conduct mode identification
using ambient measurement data. The proposed hybrid measurement- and
model-based method can accurately estimate the system state matrix in ambient
conditions, the eigenvalues and eigenvectors of which readily provide all the
modal knowledge including frequencies, damping ratios, mode shapes, and more
importantly, participation factors. Numerical simulations show that the
proposed technique is able to provide accurate estimation of modal knowledge
for all modes. In addition, the discrepancy between the participation factor
and the mode shape is shown through a numerical example, demonstrating that
using the mode shape may not effectively pinpoint the best location for damping
control. Therefore, the proposed technique capable of estimating participation
factors may greatly facilitate designing damping controls.
|
1803.07264v1
|
2018-03-21
|
Globally Stable Output Feedback Synchronization of Teleoperation with Time-Varying Delays
|
This paper presents a globally stable teleoperation control strategy for
systems with time-varying delays that eliminates the need for velocity
measurements through novel augmented Immersion and Invariance velocity
observers. The new observers simplify a recent constructive Immersion and
Invariance velocity observer to achieve globally convergent velocity estimation
with only $n+2$ states, where $n$ is the number of degrees of freedom of the
master and slave robots. They introduce dynamic scaling factors to accelerate
the speed of convergence of the velocity estimates and, thus, to limit the
energy generated by the velocity estimation errors and to guarantee sufficient
estimate-based damping injection to dissipate the energy generated by the
time-varying delays. The paper shows that Proportional plus damping control
with the simplified and augmented Immersion and Invariance-based velocity
observers can synchronize the free master and slave motions in the presence of
time-varying delays without using velocity measurements. Numerical results
illustrate the estimation performance of the new observers and the stability of
a simulated two degrees-of-freedom nonlinear teleoperation system with
time-varying delays under the proposed output feedback Proportional plus
damping control.
|
1803.08159v1
|
2018-03-29
|
Stochastic conformal multi-symplectic method for damped stochastic nonlinear Schrodinger equation
|
In this paper, we propose a stochastic conformal multi-symplectic method for
a class of damped stochastic Hamiltonian partial differential equations in
order to inherit the intrinsic properties, and apply the numerical method to
solve a kind of damped stochastic nonlinear Schrodinger equation with
multiplicative noise. It is shown that the stochastic conformal
multi-symplectic method preserves the discrete stochastic conformal
multi-symplectic conservation law, the discrete charge exponential dissipation
law almost surely, and we also deduce the recurrence relation of the discrete
global energy. Numerical experiments are preformed to verify the good
performance of the proposed stochastic conformal multi-symplectic method,
compared with a Crank-Nicolson type method. Finally, we present the mean square
convergence result of the proposed numerical method in temporal direction
numerically.
|
1803.10885v1
|
2018-04-01
|
Bounded Connectivity-Preserving Coordination of Networked Euler-Lagrange Systems
|
This paper derives sufficient conditions for bounded distributed
connectivity-preserving coordination of Euler-Lagrange systems with only
position measurements and with system uncertainties, respectively. The paper
proposes two strategies that suitably scale conventional gradient-based
controls to account for the actuation bounds and to reserve sufficient
actuation for damping injection. For output feedback control of networked
systems with only position measurements, the paper incorporates a first-order
filter to estimate velocities and to inject damping for stability. For networks
of uncertain systems, the paper augments conventional linear filter-based
adaptive compensation with damping injection to maintain the local connectivity
of the network. Analyses based on monotonically decreasing Lyapunov-like
functions and Barbalat's lemma lead to sufficient conditions for bounded local
connectivity-preserving coordination of Euler-Lagrange networks under the two
strategies. The sufficient conditions clarify the interrelationships among the
bounded actuations, initial system velocities and initial inter-system
distances. Simulation results validate these conditions.
|
1804.00333v1
|
2018-04-09
|
Damping and clustering into crowded environment of catalytic chemical oscillators
|
A system formed by a crowded environment of catalytic obstacles and complex
oscillatory chemical reactions is inquired. The obstacles are static spheres of
equal radius, which are placed in a random way. The chemical reactions are
carried out in a fluid following a multiparticle collision scheme where the
mass, energy and local momentum are conserved. Firstly, it is explored how the
presence of catalytic obstacles changes the oscillatory dynamics from a limit
cycle to a fix point reached after a damping. The damping is characterized by
the decay constant, which grows linearly with volume fraction for low values of
the mesoscale collision time and the catalytic reaction constant. Additionally,
it is shown that, although the distribution of obstacles is random, there are
regions in the system where the catalytic chemical reactions are favored. This
entails that in average the radius of gyrations of catalytic chemical reaction
does not match with the radius of gyration of obstacles, that is, clusters of
reactions emerge on the catalytic obstacles, even when the diffusion is
significant.
|
1804.03174v1
|
2018-04-11
|
A global existence result for a semilinear wave equation with scale-invariant damping and mass in even space dimension
|
In the present article a semilinear wave equation with scale-invariant
damping and mass is considered. The global (in time) existence of radial
symmetric solutions in even spatial dimension $n$ is proved using weighted
$L^\infty-L^\infty$ estimates, under the assumption that the multiplicative
constants, which appear in the coefficients of damping and of mass terms,
fulfill an interplay condition which yields somehow a "wave-like" model. In
particular, combining this existence result with a recently proved blow-up
result, a suitable shift of Strauss exponent is proved to be the critical
exponent for the considered model. Moreover, the still open part of a
conjecture done by D'Abbicco - Lucente - Reissig is proved to be true in the
massless case.
|
1804.03978v1
|
2018-04-17
|
Modelling linewidths of Kepler red giants in NGC 6819
|
We present a comparison between theoretical, frequency-dependent, damping
rates and linewidths of radial-mode oscillations in red-giant stars located in
the open cluster NGC 6819. The calculations adopt a time-dependent non-local
convection model, with the turbulent pressure profile being calibrated to
results of 3D hydrodynamical simulations of stellar atmospheres. The linewidths
are obtained from extensive peakbagging of Kepler lightcurves. These
observational results are of unprecedented quality owing to the long continuous
observations by Kepler. The uniqueness of the Kepler mission also means that,
for asteroseismic properties, this is the best data that will be available for
a long time to come. We therefore take great care in modelling nine RGB stars
in NGC 6819 using information from 3D simulations to obtain realistic
temperature stratifications and calibrated turbulent pressure profiles. Our
modelled damping rates reproduce well the Kepler observations, including the
characteristic depression in the linewidths around the frequency of maximum
oscillation power. Furthermore, we thoroughly test the sensitivity of the
calculated damping rates to changes in the parameters of the nonlocal
convection model.
|
1804.06255v1
|
2018-04-24
|
$\text{Co}_{25}\text{Fe}_{75}$ Thin Films with Ultralow Total Damping
|
We measure the dynamic properties of $\text{Co}_{25}\text{Fe}_{75}$ thin
films grown by dc magnetron sputtering. Using ferromagnetic resonance
spectroscopy, we demonstrate an ultralow total damping parameter in the
out-of-plane configuration of < 0.0013, whereas for the in-plane configuration
we find a minimum total damping of < 0.0020. In both cases, we observe low
inhomogeneous linewidth broadening in macroscopic films. We observe a minimum
full-width half-maximum linewidth of 1 mT at 10 GHz resonance frequency for a
12 nm thick film. We characterize the morphology and structure of these films
as a function of seed layer combinations and find large variation of the
qualitative behavior of the in-plane linewidth vs. resonance frequency.
Finally, we use wavevector-dependent Brillouin light scattering spectroscopy to
characterize the spin-wave dispersion at wave vectors up to 23 $\mu
\text{m}^{-1}$.
|
1804.08786v1
|
2018-05-15
|
Simple Nonlinear Models with Rigorous Extreme Events and Heavy Tails
|
Extreme events and the heavy tail distributions driven by them are ubiquitous
in various scientific, engineering and financial research. They are typically
associated with stochastic instability caused by hidden unresolved processes.
Previous studies have shown that such instability can be modeled by a
stochastic damping in conditional Gaussian models. However, these results are
mostly obtained through numerical experiments, while a rigorous understanding
of the underlying mechanism is sorely lacking. This paper contributes to this
issue by establishing a theoretical framework, in which the tail density of
conditional Gaussian models can be rigorously determined. In rough words, we
show that if the stochastic damping takes negative values, the tail is
polynomial; if the stochastic damping is nonnegative but takes value zero, the
tail is between exponential and Gaussian. The proof is established by
constructing a novel, product-type Lyapunov function, where a Feynman-Kac
formula is applied. The same framework also leads to a non-asymptotic large
deviation bound for long-time averaging processes.
|
1805.05615v3
|
2018-06-18
|
Theoretical interpretations of DAMPE first results: a critical review
|
The DAMPE experiment recently published its first results on the lepton ($e^+
+ e^-$) cosmic-ray (CRs) flux. These results are of importance since they
account for the first direct detection of the lepton break around the energy of
1 TeV and confirm the discoveries of ground-based Cherenkov detectors.
Meanwhile they reveal a new high-energy feature in the spectrum which triggered
a lot of excitement on the theory side, when interpreted as the typical
signature of leptophilic dark-matter annihilation. In this proceeding I mainly
focus on the theoretical understanding of the lepton break. Then I quickly
review the status of the more speculative line-like DAMPE excess, whose
astrophysical (pulsar) or exotic (dark matter) explanation is strongly
constrained by multi-messenger astronomy.
|
1806.06534v1
|
2018-06-22
|
Optimal Design of Virtual Inertia and Damping Coefficients for Virtual Synchronous Machines
|
Increased penetration of inverter-connected renewable energy sources (RES) in
the power system has resulted in a decrease in available rotational inertia
which serves as an immediate response to frequency deviation due to
disturbances. The concept of virtual inertia has been proposed to combat this
decrease by enabling the inverters to produce active power in response to a
frequency deviation like a synchronous generator. In this paper, we present an
algorithm to optimally design the inertia and damping coefficient required for
an inverter-based virtual synchronous machine (VSM) to participate efficiently
in the inertia response portion of primary frequency control. We design the
objective function to explicitly trade-off between competing objectives such as
the damping rate the the frequency nadir. Specifically, we formulate the design
problem as a constrained and regularized H2 norm minimization problem, and
develop an efficient gradient algorithm for this non-convex problem. This
proposed algorithm is applied to a test case to demonstrate its performance
against existing methods.
|
1806.08488v1
|
2018-07-17
|
Bipartite and Tripartite Entanglement for Three Damped Driven Qubits
|
We investigate bipartite and tripartite entanglement in an open quantum
system, specifically three qubits, all of which are damped, and one of which is
driven. We adapt a systematic approach in calculating the entanglement of
various bipartite splits usinga generalized concurrence as an indicator of
entanglement. Our calculations are based on a direct detection scheme that is a
particular unravelling of the density matrix. This system has a collective
dipole-dipole energy shift that couples the atoms and the dissipation is via
partially collective spontaneous emission described by the Lehmberg-Agarwal
master equation.Our results are unravelling dependent, but apply to
applications of entanglement based on direct detection. We also calculate the
three-way tangle or residual entanglement for this system. We present
calculations for a variety of driving and damping rates, and examine what decay
rate is adequate for the system to be reduced to two qubits with a readout
port. We also consider a specific model of three atoms located at particular
positions in free space.
|
1807.06178v1
|
2018-07-17
|
Boundary-to-Displacement Asymptotic Gains for Wave Systems With Kelvin-Voigt Damping
|
We provide estimates for the asymptotic gains of the displacement of a
vibrating string with endpoint forcing, modeled by the wave equation with
Kelvin-Voigt and viscous damping and a boundary disturbance. Two asymptotic
gains are studied: the gain in the L2 spatial norm and the gain in the spatial
sup norm. It is shown that the asymptotic gain property holds in the L2 norm of
the displacement without any assumption for the damping coefficients. The
derivation of the upper bounds for the asymptotic gains is performed by either
employing an eigenfunction expansion methodology or by means of a small-gain
argument, whereas a novel frequency analysis methodology is employed for the
derivation of the lower bounds for the asymptotic gains. The graphical
illustration of the upper and lower bounds for the gains shows that that the
asymptotic gain in the L2 norm is estimated much more accurately than the
asymptotic gain in the sup norm.
|
1807.06549v1
|
2018-07-24
|
Stabilization of an unstable wave equation using an infinite dimensional dynamic controller
|
This paper deals with the stabilization of an anti-stable string equation
with Dirichlet actuation where the instability appears because of the
uncontrolled boundary condition. Then, infinitely many unstable poles are
generated and an infinite dimensional control law is therefore proposed to
exponentially stabilize the system. The idea behind the choice of the
controller is to extend the domain of the PDE so that the anti-damping term is
compensated by a damping at the other boundary condition. Additionally, notice
that the system can then be exponentially stabilized with a chosen decay-rate
and is robust to uncertainties on the wave speed and the anti-damped
coefficient of the wave equation, with the only use of a point-wise boundary
measurement. The efficiency of this new control strategy is then compared to
the backstepping approach.
|
1807.08999v2
|
2018-07-24
|
Interplay between intermittency and dissipation in collisionless plasma turbulence
|
We study the damping of collisionless Alfv\'enic turbulence by two
mechanisms: stochastic heating (whose efficiency depends on the local
turbulence amplitude $\delta z_\lambda$) and linear Landau damping (whose
efficiency is independent of $\delta z_\lambda$), describing in detail how they
affect and are affected by intermittency. The overall efficiency of linear
Landau damping is not affected by intermittency in critically balanced
turbulence, while stochastic heating is much more efficient in the presence of
intermittent turbulence. Moreover, stochastic heating leads to a drop in the
scale-dependent kurtosis over a narrow range of scales around the ion
gyroscale.
|
1807.09301v2
|
2018-07-31
|
Input-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary Disturbances
|
This note establishes the Exponential Input-to-State Stability (EISS)
property for a clamped-free damped string with respect to distributed and
boundary disturbances. While efficient methods for establishing ISS properties
for distributed parameter systems with respect to distributed disturbances have
been developed during the last decades, establishing ISS properties with
respect to boundary disturbances remains challenging. One of the well-known
methods for well-posedness analysis of systems with boundary inputs is the use
of a lifting operator for transferring the boundary disturbance to a
distributed one. However, the resulting distributed disturbance involves time
derivatives of the boundary perturbation. Thus, the subsequent ISS estimate
depends on its amplitude, and may not be expressed in the strict form of ISS
properties. To solve this problem, we show for a clamped-free damped string
equation that the projection of the original system trajectories in an adequate
Riesz basis can be used to establish the desired EISS property.
|
1807.11696v2
|
2018-07-31
|
Spin absorption at ferromagnetic-metal/platinum-oxide interface
|
We investigate the absorption of a spin current at a
ferromagnetic-metal/Pt-oxide interface by measuring current-induced
ferromagnetic resonance. The spin absorption was characterized by the magnetic
damping of the heterostructure. We show that the magnetic damping of a
Ni$_{81}$Fe$_{19}$ film is clearly enhanced by attaching Pt-oxide on the
Ni$_{81}$Fe$_{19}$ film. The damping enhancement is disappeared by inserting an
ultrathin Cu layer between the Ni$_{81}$Fe$_{19}$ and Pt-oxide layers. These
results demonstrate an essential role of the direct contact between the
Ni$_{81}$Fe$_{19}$ and Pt-oxide to induce sizable interface spin-orbit
coupling. Furthermore, the spin-absorption parameter of the
Ni$_{81}$Fe$_{19}$/Pt-oxide interface is comparable to that of intensively
studied heterostructures with strong spin-orbit coupling, such as an oxide
interface, topological insulators, metallic junctions with Rashba spin-orbit
coupling. This result illustrates strong spin-orbit coupling at the
ferromagnetic-metal/Pt-oxide interface, providing an important piece of
information for quantitative understanding the spin absorption and spin-charge
conversion at the ferromagnetic-metal/metallic-oxide interface.
|
1807.11806v1
|
2018-08-16
|
Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques
|
In this article, we provide a general strategy based on Lyapunov functionals
to analyse global asymptotic stability of linear infinite-dimensional systems
subject to nonlinear dampings under the assumption that the origin of the
system is globally asymp-totically stable with a linear damping. To do so, we
first characterize, in terms of Lyapunov functionals, several types of
asymptotic stability for linear infinite-dimensional systems, namely the
exponential and the polynomial stability. Then, we derive a Lyapunov functional
for the nonlinear system, which is the sum of a Lyapunov functional coming from
the linear system and another term with compensates the nonlinearity. Our
results are then applied to the linearized Korteweg-de Vries equation and some
wave equations.
|
1808.05370v1
|
2018-08-30
|
The influence of the coefficients of a system of coupled wave equations with fractional damping on its stabilization
|
In this work, we consider a system of two wave equations coupled by
velocities in one-dimensional space, with one boundary fractional damping.
First, we show that the system is strongly asymptotically stable if and only if
the coupling parameter b of the two equations is outside a discrete set of
exceptional real values. Next, we show that our system is not uniformly stable.
Hence, we look for a polynomial decay rate for smooth initial data. Using
frequency domain approach combining with multiplier method, we prove that the
energy decay rate is greatly influenced by the nature of the coupling parameter
b, the arithmetic property of the ratio of the wave propagation speeds a, the
order of the fractional damping. Indeed, under the equal speed propagation
condition, we establish an optimal polynomial energy decay rate. Furthermore,
when the wave propagate with different speeds, under some arithmetic conditions
on the ratio of the wave propagation speeds, we prove that the energy of our
system decays polynomially to zero.
|
1808.10285v4
|
2018-09-05
|
On the forced Euler and Navier-Stokes equations: Linear damping and modified scattering
|
We study the asymptotic behavior of the forced linear Euler and nonlinear
Navier-Stokes equations close to Couette flow in a periodic channel. As our
main result we show that for smooth time-periodic forcing linear inviscid
damping persists, i.e. the velocity field (weakly) asymptotically converges.
However, stability and scattering to the transport problem fail in $H^{s},
s>-1$. We further show that this behavior is consistent with the nonlinear
Euler equations and that a similar result also holds for the nonlinear
Navier-Stokes equations. Hence, these results provide an indication that
nonlinear inviscid damping may still hold in Sobolev regularity in the above
sense despite the Gevrey regularity instability results of [Deng-Masmoudi
2018].
|
1809.01729v1
|
2018-09-12
|
Theory of bifurcation amplifiers utilizing the nonlinear dynamical response of an optically damped mechanical oscillator
|
We consider a standard optomechanical system where a mechanical oscillator is
coupled to a cavity mode through the radiation pressure interaction. The
oscillator is coherently driven at its resonance frequency, whereas the cavity
mode is driven below its resonance, providing optical damping of the mechanical
oscillations. We study the nonlinear coherent response of the mechanical
oscillator in this setup. For large mechanical amplitudes, we find that the
system can display dynamical multistability if the optomechanical cooperativity
exceeds a critical value. This analysis relates standard optomechanical damping
to the dynamical attractors known from the theory of optomechanical
self-sustained oscillations. We also investigate the effect of thermal and
quantum noise and estimate the noise-induced switching rate between the stable
states of the system. We then consider applications of this system and
primarily focus on how it can be used as bifurcation amplifiers for the
detection of small mechanical or optical signals. Finally, we show that in a
related but more complicated setup featuring resonant optomechanical
interactions, the same effects can be realized with a relaxed requirement on
the size of the mechanical oscillations.
|
1809.04592v2
|
2018-09-13
|
Second order asymptotical regularization methods for inverse problems in partial differential equations
|
We develop Second Order Asymptotical Regularization (SOAR) methods for
solving inverse source problems in elliptic partial differential equations with
both Dirichlet and Neumann boundary data. We show the convergence results of
SOAR with the fixed damping parameter, as well as with a dynamic damping
parameter, which is a continuous analog of Nesterov's acceleration method.
Moreover, by using Morozov's discrepancy principle together with a newly
developed total energy discrepancy principle, we prove that the approximate
solution of SOAR weakly converges to an exact source function as the
measurement noise goes to zero. A damped symplectic scheme, combined with the
finite element method, is developed for the numerical implementation of SOAR,
which yields a novel iterative regularization scheme for solving inverse source
problems. Several numerical examples are given to show the accuracy and the
acceleration effect of SOAR. A comparison with the state-of-the-art methods is
also provided.
|
1809.04971v2
|
2018-09-24
|
Oscillation Damping Control of Pendulum-like Manipulation Platform using Moving Masses
|
This paper presents an approach to damp out the oscillatory motion of the
pendulum-like hanging platform on which a robotic manipulator is mounted. To
this end, moving masses were installed on top of the platform. In this paper,
asymptotic stability of the platform (which implies oscillation damping) is
achieved by designing reference acceleration of the moving masses properly. A
main feature of this work is that we can achieve asymptotic stability of not
only the platform, but also the moving masses, which may be challenging due to
the under-actuation nature. The proposed scheme is validated by the simulation
studies.
|
1809.08819v1
|
2018-07-16
|
A unified N-SECE strategy for highly coupled piezoelectric energy scavengers
|
This paper proposes a novel vibration energy harvesting strategy based on an
extension of the Synchronous Electric Charge Extraction (SECE) approach,
enabling both the maximization of the harvested power and a consequent
bandwidth enlargement in the case of highly coupled/lightly damped
piezoelectric energy harvesters. The proposed strategy relies on the tuning of
the frequency of the energy extraction events, which is either N times greater
than the vibration frequency (Multiple SECE case, N > 1) or 1/N times smaller
(Regenerative SECE, N < 1). We first prove analytically than increasing or
decreasing N both lead to a damping reduction. While N has no impact on the
system's resonance frequency in the Regenerative case (N < 1), we show that
this resonant frequency becomes a function of N in the Multiple SECE case (N >
1). Experimental results on a highly coupled/lowly damped piezoelectric
harvester (k^2= 0.44, Q_m = 20) demonstrates the potential of this strategy,
leading to 257% harvested power improvement compared to SECE (N = 1). and the
possibility to tune the resonant frequency on a range as large as 35% of the
short-circuit resonant frequency of the harvester.
|
1809.09685v1
|
2018-10-09
|
The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension
|
The critical constant of time-decaying damping in the scale-invariant case is
recently conjectured. It also has been expected that the lifespan estimate is
the same as for the associated semilinear heat equations if the constant is in
the \heat-like" domain. In this paper, we point out that this is not true if
the total integral of the sum of initial position and speed vanishes. In such a
case, we have a new type of the lifespan estimates which is closely related to
the non-damped case in shifted space dimensions.
|
1810.03780v2
|
2018-10-24
|
Justification of the Lugiato-Lefever model from a damped driven $φ^4$ equation
|
The Lugiato-Lefever equation is a damped and driven version of the well-known
nonlinear Schr\"odinger equation. It is a mathematical model describing complex
phenomena in dissipative and nonlinear optical cavities. Within the last two
decades, the equation has gained a wide attention as it becomes the basic model
describing optical frequency combs. Recent works derive the Lugiato-Lefever
equation from a class of damped driven $\phi^4$ equations closed to resonance.
In this paper, we provide a justification of the envelope approximation. From
the analysis point of view, the result is novel and non-trivial as the drive
yields a perturbation term that is not square integrable. The main approach
proposed in this work is to decompose the solutions into a combination of the
background and the integrable component. This paper is the first part of a
two-manuscript series.
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1810.10630v1
|
2018-11-06
|
Decay properties and asymptotic profiles for elastic waves with Kelvin-Voigt damping in 2D
|
In this paper we consider elastic waves with Kelvin-Voigt damping in 2D. For
the linear problem, applying pointwise estimates of the partial Fourier
transform of solutions in the Fourier space and asymptotic expansions of
eigenvalues and their eigenprojections, we obtain sharp energy decay estimates
with additional $L^m$ regularity and $L^p-L^q$ estimates on the conjugate line.
Furthermore, we derive asymptotic profiles of solutions under different
assumptions of initial data. For the semilinear problem, we use the derived
$L^2-L^2$ estimates with additional $L^m$ regularity to prove global (in time)
existence of small data solutions to the weakly coupled system. Finally, to
deal with elastic waves with Kelvin-Voigt damping in 3D, we apply the Helmholtz
decomposition.
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1811.02223v3
|
2018-12-06
|
Damping and Anti-Damping Phenomena in Metallic Antiferromagnets: An ab-initio Study
|
We report on a first principles study of anti-ferromagnetic resonance (AFMR)
phenomena in metallic systems [MnX (X=Ir,Pt,Pd,Rh) and FeRh] under an external
electric field. We demonstrate that the AFMR linewidth can be separated into a
relativistic component originating from the angular momentum transfer between
the collinear AFM subsystem and the crystal through the spin orbit coupling
(SOC), and an exchange component that originates from the spin exchange between
the two sublattices. The calculations reveal that the latter component becomes
significant in the low temperature regime. Furthermore, we present results for
the current-induced intersublattice torque which can be separated into the
Field-Like (FL) and Damping-Like (DL) components, affecting the intersublattice
exchange coupling and AFMR linewidth, respectively.
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1812.02844v2
|
2018-12-12
|
Extreme wave events for a nonlinear Schrödinger equation with linear damping and Gaussian driving
|
We perform a numerical study of the initial-boundary value problem, with
vanishing boundary conditions, of a driven nonlinear Schr\"odinger equation
(NLS) with linear damping and a Gaussian driver. We identify Peregrine-like
rogue waveforms, excited by two different types of vanishing initial data
decaying at an algebraic or exponential rate. The observed extreme events
emerge on top of a decaying support. Depending on the spatial/temporal scales
of the driver, the transient dynamics -- prior to the eventual decay of the
solutions -- may resemble the one in the semiclassical limit of the integrable
NLS, or may, e.g., lead to large-amplitude breather-like patterns. The effects
of the damping strength and driving amplitude, in suppressing or enhancing
respectively the relevant features, as well as of the phase of the driver in
the construction of a diverse array of spatiotemporal patterns, are numerically
analyzed.
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1812.05439v3
|
2018-12-13
|
Stability of elastic transmission systems with a local Kelvin-Voigt damping
|
In this paper, we consider the longitudinal and transversal vibrations of the
transmission Euler-Bernoulli beam with Kelvin-Voigt damping distributed locally
on any subinterval of the region occupied by the beam and only in one side of
the transmission point. We prove that the semigroup associated with the
equation for the transversal motion of the beam is exponentially stable,
although the semigroup associated with the equation for the longitudinal motion
of the beam is polynomially stable. Due to the locally distributed and
unbounded nature of the damping, we use a frequency domain method and combine a
contradiction argument with the multiplier technique to carry out a special
analysis for the resolvent.
|
1812.05923v1
|
2018-12-13
|
Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin-Voigt damping
|
We consider a beam and a wave equations coupled on an elastic beam through
transmission conditions. The damping which is locally distributed acts through
one of the two equations only; its effect is transmitted to the other equation
through the coupling. First we consider the case where the dissipation acts
through the beam equation. Using a recent result of Borichev and Tomilov on
polynomial decay characterization of bounded semigroups we provide a precise
decay estimates showing that the energy of this coupled system decays
polynomially as the time variable goes to infinity. Second, we discuss the case
where the damping acts through the wave equation. Proceeding as in the first
case, we prove that this system is also polynomially stable and we provide
precise polynomial decay estimates for its energy. Finally, we show the lack of
uniform exponential decay of solutions for both models.
|
1812.05924v1
|
2018-12-20
|
Sound attenuation in stable glasses
|
Understanding the difference between universal low-temperature properties of
amorphous and crystalline solids requires an explanation of the stronger
damping of long-wavelength phonons in amorphous solids. A longstanding sound
attenuation scenario, resulting from a combination of experiments, theories,
and simulations, leads to a quartic scaling of sound attenuation with the
wavevector, which is commonly attributed to Rayleigh scattering of the sound.
Modern computer simulations offer conflicting conclusions regarding the
validity of this picture. We simulate glasses with an unprecedentedly broad
range of stabilities to perform the first microscopic analysis of sound damping
in model glass formers across a range of experimentally relevant preparation
protocols. We present a convincing evidence that quartic scaling is recovered
for small wavevectors irrespective of the glass's stability. With increasing
stability, the wavevector where the quartic scaling begins increases by
approximately a factor of three and the sound attenuation decreases by over an
order of magnitude. Our results uncover an intimate connection between glass
stability and sound damping.
|
1812.08736v2
|
2018-12-21
|
Reply to the Comment on "Negative Landau damping in bilayer graphene"
|
Here we address the concerns of Svintsov and Ryzhii [arXiv:1812.03764] on our
article on negative Landau damping in graphene [Phys. Rev. Lett. 119, 133901
(2017)]. We prove that due to the differences between the kinetic and canonical
momenta, the conductivity of drift-current biased graphene is ruled by a
Galilean transformation when the electron-electron interactions predominate and
force the electron gas to move with constant velocity, similar to a moving
medium. Furthermore, it is shown that the nonlocal effects in graphene neither
preclude a negative Landau damping nor the emergence of instabilities in
graphene platforms.
|
1812.09103v3
|
2018-12-27
|
Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case
|
In this paper we consider the blow-up for solutions to a weakly coupled
system of semilinear damped wave equations of derivative type in the scattering
case. After introducing suitable functionals proposed by Lai-Takamura for the
corresponding single semilinear equation, we employ Kato's lemma to derive the
blow-up result in the subcritical case. On the other hand, in the critical case
an iteration procedure based on the slicing method is employed. Let us point
out that we find as critical curve in the p-q plane for the pair of exponents
(p, q) in the nonlinear terms the same one as for the weakly coupled system of
semilinear not-damped wave equations with the same kind of nonlinearities.
|
1812.10653v1
|
2018-12-30
|
Smooth, Time-invariant Regulation of Nonholonomic Systems via Energy Pumping-and-Damping
|
In this paper we propose an energy pumping-and-damping technique to regulate
nonholonomic systems described by kinematic models. The controller design
follows the widely popular interconnection and damping assignment
passivity-based methodology, with the free matrices partially structured. Two
asymptotic regulation objectives are considered: drive to zero the state or
drive the systems total energy to a desired constant value. In both cases, the
control laws are smooth, time-invariant, state-feedbacks. For the nonholonomic
integrator we give an almost global solution for both problems, with the
objectives ensured for all system initial conditions starting outside a set
that has zero Lebesgue measure and is nowhere dense. For the general case of
higher-order nonholonomic systems in chained form, a local stability result is
given. Simulation results comparing the performance of the proposed controller
with other existing designs are also provided.
|
1812.11538v2
|
2019-01-05
|
Simulations of wobble damping in viscoelastic rotators
|
Using a damped mass-spring model, we simulate wobble of spinning homogeneous
viscoelastic ellipsoids undergoing non-principal axis rotation. Energy damping
rates are measured for oblate and prolate bodies with different spin rates,
spin states, viscoelastic relaxation timescales, axis ratios, and strengths.
Analytical models using a quality factor by Breiter et al. (2012) and for the
Maxwell rheology by Frouard & Efroimsky (2018) match our numerical measurements
of the energy dissipation rate after we modify their predictions for the
numerically simulated Kelvin-Voigt rheology. Simulations of nearly spherical
but wobbling bodies with hard and soft cores show that the energy dissipation
rate is more sensitive to the material properties in the core than near the
surface. The sensitivity to viscoelastic model implies that inferred statistics
of tumbling lifetimes in asteroids might be interpreted in terms of differences
in their material properties.
|
1901.01439v3
|
2019-01-16
|
Laboratory investigations of the bending rheology of floating saline ice, and physical mechanisms of wave damping, in the HSVA ice tank
|
An experiment on the propagation of flexural-gravity waves was performed in
the HSVA ice tank. Physical characteristics of the water-ice system were
measured in different locations in the tank during the tests, with a number of
sensors deployed in the water, on the ice and in the air. Water velocity was
measured with an acoustic doppler velocimeter (ADV) and an acoustic doppler
current profiler (ADCP); wave amplitudes were measured with ultrasonic sensors
and the optical system Qualisys; in-plane deformations of the ice and the
temperature of the ice and water were measured by fiber optic sensors, and
acoustic emissions were recorded with compressional crystal sensors. All
together 61 tests were performed, with ice thicknesses of 3 cm and 5 cm. The
experimental setup and selected results of the tests are discussed in this
paper. We show that cyclic motion of the ice along the tank, imitating ice
drift, causes an increase in wave damping. We also show that the formation of
non-through cracks in the ice, caused by the action of waves, increases wave
damping.
|
1901.05333v1
|
2019-01-24
|
Generalized framework for testing gravity with gravitational-wave propagation. III. Future prospect
|
The properties of gravitational-wave (GW) propagation are modified in
alternative theories of gravity and are crucial observables to test gravity at
cosmological distance. The propagation speed has already been measured from
GW170817 so precisely and pinned down to the speed of light, while other
properties of GW propagation have not constrained tightly yet. In this paper,
we investigate the measurement precisions of the amplitude damping rate
(equivalently, the time variation of the gravitational coupling for GWs) and
graviton mass in the generalized framework of GW propagation with the future
detectors such as Voyager, Cosmic Explorer, and Einstein Telescope. As a
result, we show that the future GW observation can reach 1% error for the
amplitude damping. We also study the time variation of the gravitational
couplings in Horndeski theory by performing Monte Carlo-based numerical
simulations. From the simulation results, we find that the current accelerating
Universe prefers the models with less damping of GWs and that the equivalence
principle can be tested at the level of 1% by the future GW observation.
|
1901.08249v2
|
2019-01-31
|
Perturbed Markov Chains and Information Networks
|
The paper is devoted to studies of perturbed Markov chains commonly used for
description of information networks. In such models, the matrix of transition
probabilities for the corresponding Markov chain is usually regularised by
adding a special damping matrix multiplied by a small damping (perturbation)
parameter $\varepsilon$. We give effective upper bounds for the rate of
approximation for stationary distributions of unperturbed Markov chains by
stationary distributions of perturbed Markov chains with regularised matrices
of transition probabilities, asymptotic expansions for approximating stationary
distributions with respect to damping parameter, as well as explicit upper
bounds for the rate of convergence in ergodic theorems for $n$-step transition
probabilities in triangular array mode, where perturbation parameter
$\varepsilon \to 0$ and $n \to \infty$, simultaneously. The results of
numerical experiments are also presented
|
1901.11483v3
|
2019-02-14
|
Dynamic Interconnection and Damping Injection for Input-to-State Stable Bilateral Teleoperation
|
In bilateral teleoperation, the human who operates the master and the
environment which interacts with the slave are part of the force feedback loop.
Yet, both have time-varying and unpredictable dynamics and are challenging to
model. A conventional strategy for sidestepping the demand for their models in
the stability analysis is to assume passive user and environment, and to
control the master-communications-slave system to be passive as well. This
paper circumvents the need to model the user and environment in a novel way: it
regards their forces as external excitations for a semi-autonomous force
feedback loop, which it outfits with a dynamic interconnection and damping
injection controller that renders bilateral teleoperation with time-varying
delays exponentially input-to-state stable. The controller uses the position
and velocity measurements of the local robot and the delayed position
transmitted from the other robot to robustly synchronize the master and slave
under the user and environment perturbations. Lyapunov-Krasovskii stability
analysis shows that the proposed strategy (i) can confine the position error
between the master and slave to an invariant set, and (ii) can drive it
exponentially to a globally attractive set. Thus, the dynamic interconnection
and damping injection approach has practical relevance for telemanipulation
tasks with given precision requirements.
|
1902.05500v1
|
2019-02-15
|
Evidence for Electron Landau Damping in Space Plasma Turbulence
|
How turbulent energy is dissipated in weakly collisional space and
astrophysical plasmas is a major open question. Here, we present the
application of a field-particle correlation technique to directly measure the
transfer of energy between the turbulent electromagnetic field and electrons in
the Earth's magnetosheath, the region of solar wind downstream of the Earth's
bow shock. The measurement of the secular energy transfer from the parallel
electric field as a function of electron velocity shows a signature consistent
with Landau damping. This signature is coherent over time, close to the
predicted resonant velocity, similar to that seen in kinetic Alfv\'en
turbulence simulations, and disappears under phase randomisation. This suggests
that electron Landau damping could play a significant role in turbulent plasma
heating, and that the technique is a valuable tool for determining the particle
energisation processes operating in space and astrophysical plasmas.
|
1902.05785v1
|
2019-02-22
|
Thermal induced monochromatic microwave generation in magnon-polariton
|
We propose thermal induced generation of monochromatic microwave radiation in
magnon-polariton. Mechanism of thermal to microwave energy transformation is
based on intrinsic energy loss compensation of coupled magnon and microwave
cavity oscillators by thermal induced "negative damping". A singularity at an
exceptional point is achieved when at the critical value of "negative damping"
the damping of the system is fully compensated. At the exceptional point, the
input energy is equally distributed between the magnon and photon subsystems of
the magnon-polariton. The efficiency of transformation of thermal energy into
useful microwave radiation is estimated to be as large as 17 percent due to
magnon-photon coupling mediated direct conversation of spin current into
microwave photons.
|
1902.08383v1
|
2019-03-04
|
Nonlinear inviscid damping for zero mean perturbation of the 2D Euler Couette flow
|
In this note we revisit the proof of Bedrossian and Masmoudi
[arXiv:1306.5028] about the inviscid damping of planar shear flows in the 2D
Euler equations under the assumption of zero mean perturbation. We prove that a
small perturbation to the 2D Euler Couette flow in $\mathbb{T}\times
\mathbb{R}$ strongly converge to zero, under the additional assumption that the
average in $x$ is always zero. In general the mean is not a conserved quantity
for the nonlinear dynamics, for this reason this is a particular case.
Nevertheless our assumption allow the presence of echoes in the problem, which
we control by an approximation of the weight built in [arXiv:1306.5028]. The
aim of this note is to present the mathematical techniques used in
[arXiv:1306.5028] and can be useful as a first approach to the nonlinear
inviscid damping.
|
1903.01543v1
|
2019-03-10
|
Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection
|
In this paper we show that a slight modification to the widely popular
interconnection and damping assignment passivity-based control
method---originally proposed for stabilization of equilibria of nonlinear
systems---allows us to provide a solution to the more challenging orbital
stabilization problem. Two different, though related, ways how this procedure
can be applied are proposed. First, the assignment of an energy function that
has a minimum in a closed curve, i.e., with the shape of a Mexican sombrero.
Second, the use of a damping matrix that changes "sign" according to the
position of the state trajectory relative to the desired orbit, that is,
pumping or dissipating energy. The proposed methodologies are illustrated with
the example of the induction motor and prove that it yields the industry
standard field oriented control.
|
1903.04070v3
|
2019-03-11
|
Impact of thermal effects on the evolution of eccentricity and inclination of low-mass planets
|
Using linear perturbation theory, we evaluate the time-dependent force
exerted on an eccentric and inclined low-mass planet embedded in a gaseous
protoplanetary disc with finite thermal diffusivity $\chi$. We assume the
eccentricity and inclination to be small compared to the size of the thermal
lobes $\lambda\sim(\chi/\Omega)^{1/2}$, itself generally much smaller than the
scalelength of pressure $H$. When the planet is non-luminous, we find that its
eccentricity and inclination are vigorously damped by the disc, over a
timescale shorter by a factor $H/\lambda$ than the damping timescale in
adiabatic discs. On the contrary, when the luminosity-to-mass ratio of the
planet exceeds a threshold that depends on the disc's properties, its
eccentricity and inclination undergo an exponential growth. In the limit of a
large luminosity, the growth rate of the eccentricity is 2.5~times larger than
that of the inclination, in agreement with previous numerical work. Depending
on their luminosity, planetary embryos therefore exhibit much more diverse
behaviours than the mild damping of eccentricity and inclination considered
hitherto.
|
1903.04470v2
|
2019-03-14
|
The Strichartz estimates for the damped wave equation and the behavior of solutions for the energy critical nonlinear equation
|
For the linear damped wave equation (DW), the $L^p$-$L^q$ type estimates have
been well studied. Recently, Watanabe showed the Strichartz estimates for DW
when $d=2,3$. In the present paper, we give Strichartz estimates for DW in
higher dimensions. Moreover, by applying the estimates, we give the local
well-posedness of the energy critical nonlinear damped wave equation (NLDW)
$\partial_t^2 u - \Delta u +\partial_t u = |u|^{\frac{4}{d-2}}u$, $(t,x) \in
[0,T) \times \mathbb{R}^d$, where $3 \leq d \leq 5$. Especially, we show the
small data global existence for NLDW. In addition, we investigate the behavior
of the solutions to NLDW. Namely, we give a decay result for solutions with
finite Strichartz norm and a blow-up result for solutions with negative Nehari
functional.
|
1903.05887v1
|
2019-04-17
|
Decays for Kelvin-Voigt damped wave equations I : the black box perturbative method
|
We show in this article how perturbative approaches~from our work with Hitrik
(see also the work by Anantharaman-Macia) and the {\em black box} strategy
from~ our work with Zworski allow to obtain decay rates for Kelvin-Voigt damped
wave equations from quite standard resolvent estimates : Carleman estimates or
geometric control estimates for Helmoltz equationCarleman or other resolvent
estimates for the Helmoltz equation. Though in this context of Kelvin Voigt
damping, such approach is unlikely to allow for the optimal results when
additional geometric assumptions are considered (see \cite{BuCh, Bu19}), it
turns out that using this method, we can obtain the usual logarithmic decay
which is optimal in general cases. We also present some applications of this
approach giving decay rates in some particular geometries (tori).
|
1904.08318v2
|
2019-04-17
|
Non-Hermitian skin effect and chiral damping in open quantum systems
|
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian
skin effect, namely that the eigenstates are exponentially localized at the
boundary of the system. For open quantum systems, a short-time evolution can
often be well described by the effective non-Hermitian Hamiltonians, while
long-time dynamics calls for the Lindblad master equations, in which the
Liouvillian superoperators generate time evolution. In this Letter, we find
that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and
uncover its unexpected physical consequences. It is shown that the
non-Hermitian skin effect dramatically shapes the long-time dynamics, such that
the damping in a class of open quantum systems is algebraic under periodic
boundary condition but exponential under open boundary condition. Moreover, the
non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a
sharp wavefront. These phenomena are beyond the effective non-Hermitian
Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged
open quantum dynamics.
|
1904.08432v2
|
2019-04-19
|
Plasmon-Emitter Interactions at the Nanoscale
|
Plasmon-emitter interactions are of paramount importance in modern
nanoplasmonics and are generally maximal at short emitter-surface separations.
However, when the separation falls below 10-20 nm, the classical theory
progressively deteriorates due to its neglect of quantum mechanical effects
such as nonlocality, electronic spill-out, and Landau damping. Here, we show
how this neglect can be remedied by presenting a unified theoretical treatment
of mesoscopic electrodynamics grounded on the framework of Feibelman
$d$-parameters. Crucially, our technique naturally incorporates nonclassical
resonance shifts and surface-enabled Landau damping - a nonlocal damping effect
- which have a dramatic impact on the amplitude and spectral distribution of
plasmon-emitter interactions. We consider a broad array of plasmon-emitter
interactions ranging from dipolar and multipolar spontaneous emission
enhancement, to plasmon-assisted energy transfer and enhancement of two-photon
transitions. The formalism presented here gives a complete account of both
plasmons and plasmon-emitter interactions at the nanoscale, constituting a
simple yet rigorous and general platform to incorporate nonclassical effects in
plasmon-empowered nanophotonic phenomena.
|
1904.09279v1
|
2019-04-23
|
Ultrafast depinning of domain wall in notched antiferromagnetic nanostructures
|
The pinning and depinning of antiferromagnetic (AFM) domain wall is certainly
the core issue of AFM spintronics. In this work, we study theoretically the
N\'eel-type domain wall pinning and depinning at a notch in an
antiferromagnetic (AFM) nano-ribbon. The depinning field depending on the notch
dimension and intrinsic physical parameters are deduced and also numerically
calculated. Contrary to conventional conception, it is revealed that the
depinning field is remarkably dependent of the damping constant and the
time-dependent oscillation of the domain wall position in the weakly damping
regime benefits to the wall depinning, resulting in a gradual increase of the
depinning field up to a saturation value with increasing damping constant. A
one-dimensional model accounting of the internal dynamics of domain wall is
used to explain perfectly the simulated results. It is demonstrated that the
depinning mechanism of an AFM domain wall differs from ferromagnetic domain
wall by exhibiting a depinning speed typically three orders of magnitude faster
than the latter, suggesting the ultrafast dynamics of an AFM system.
|
1904.10197v2
|
2019-05-08
|
Discrete Energy behavior of a damped Timoshenko system
|
In this article, we consider a one-dimensional Timoshenko system subject to
different types of dissipation (linear and nonlinear dampings). Based on a
combination between the finite element and the finite difference methods, we
design a discretization scheme for the different Timoshenko systems under
consideration. We first come up with a numerical scheme to the free-undamped
Timoshenko system. Then, we adapt this numerical scheme to the corresponding
linear and nonlinear damped systems. Interestingly, this scheme reaches to
reproduce the most important properties of the discrete energy. Namely, we show
for the discrete energy the positivity, the energy conservation property and
the different decay rate profiles. We numerically reproduce the known
analytical results established on the decay rate of the energy associated with
each type of dissipation.
|
1905.03050v1
|
2019-05-08
|
Attractors for semilinear wave equations with localized damping and external forces
|
This paper is concerned with long-time dynamics of semilinear wave equations
defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and
locally distributed damping. The existence of regular finite-dimensional global
attractors established by Chueshov, Lasiecka and Toundykov (2008) reflects a
good deal of the current state of the art on this matter. Our contribution is
threefold. First, we prove uniform boundedness of attractors with respect to a
forcing parameter. Then, we study the continuity of attractors with respect to
the parameter in a residual dense set. Finally, we show the existence of
generalized exponential attractors. These aspects were not previously
considered for wave equations with localized damping.
|
1905.03285v1
|
2019-05-16
|
Global attractors and their upper semicontinuity for a structural damped wave equation with supercritical nonlinearity on $\mathbb{R}^{N}$
|
The paper investigates the existence of global attractors and their upper
semicontinuity for a structural damped wave equation on $\mathbb{R}^{N}:
u_{tt}-\Delta u+(-\Delta)^\alpha u_{t}+u_{t}+u+g(u)=f(x)$, where $\alpha\in
(1/2, 1)$ is called a dissipative index. We propose a new method based on the
harmonic analysis technique and the commutator estimate to exploit the
dissipative effect of the structural damping $(-\Delta)^\alpha u_{t}$ and to
overcome the essential difficulty: "both the unbounded domain $\mathbb{R}^N$
and the supercritical nonlinearity cause that the Sobolev embedding loses its
compactness"; Meanwhile we show that there exists a supercritical index
$p_\alpha\equiv\frac{N+4\alpha}{N-4\alpha}$ depending on $\alpha$ such that
when the growth exponent $p$ of the nonlinearity $g(u)$ is up to the
supercritical range: $1\leqslant p<p_\alpha$: (i) the IVP of the equation is
well-posed and its solution is of additionally global smoothness when $t>0$;
(ii) the related solution semigroup possesses a global attractor
$\mathcal{A}_\alpha$ in natural energy space for each $\alpha\in (1/2, 1)$;
(iii) the family of global attractors $\{\mathcal{A}_\alpha\}_{\alpha\in (1/2,
1) }$ is upper semicontinuous at each point $\alpha_0\in (1/2, 1)$.
|
1905.06778v1
|
2019-05-20
|
Quantum parameter-estimation of frequency and damping of a harmonic-oscillator
|
We determine the quantum Cram\'er-Rao bound for the precision with which the
oscillator frequency and damping constant of a damped quantum harmonic
oscillator in an arbitrary Gaussian state can be estimated. This goes beyond
standard quantum parameter estimation of a single mode Gaussian state for which
typically a mode of fixed frequency is assumed. We present a scheme through
which the frequency estimation can nevertheless be based on the known results
for single-mode quantum parameter estimation with Gaussian states. Based on
these results, we investigate the optimal measurement time. For measuring the
oscillator frequency, our results unify previously known partial results and
constitute an explicit solution for a general single-mode Gaussian state.
Furthermore, we show that with existing carbon nanotube resonators (see J.
Chaste et al.~Nature Nanotechnology 7, 301 (2012)) it should be possible to
achieve a mass sensitivity of the order of an electron mass $\text{Hz}^{-1/2}$.
|
1905.08288v1
|
2019-05-24
|
Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results
|
There are numerous examples of natural and artificial processes that
represent stochastic sequences of events followed by an absolute refractory
period during which the occurrence of a subsequent event is impossible. In the
simplest case of a generalized Bernoulli scheme for uniform random events
followed by the absolute refractory period, the event probability as a function
of time can exhibit damped transient oscillations. Using stochastically-spiking
point neuron as a model example, we present an exact and compact analytical
description for the oscillations without invoking the standard renewal theory.
The resulting formulas stand out for their relative simplicity, allowing one to
analytically obtain the amplitude damping of the 2nd and 3rd peaks of the event
probability.
|
1905.10172v3
|
2019-06-10
|
Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosity
|
We study the compressible quantum Navier-Stokes (QNS) equations with
degenerate viscosity in the three dimensional periodic domains. On the one
hand, we consider QNS with additional damping terms. Motivated by the recent
works [Li-Xin, arXiv:1504.06826] and [Antonelli-Spirito, Arch. Ration. Mech.
Anal., 203(2012), 499--527], we construct a suitable approximate system which
has smooth solutions satisfying the energy inequality and the BD entropy
estimate. Using this system, we obtain the global existence of weak solutions
to the compressible QNS equations with damping terms for large initial data.
Moreover, we obtain some new a priori estimates, which can avoid using the
assumption that the gradient of the velocity is a well-defined function, which
is indeed used directly in [Vasseur-Yu, SIAM J. Math. Anal., 48 (2016),
1489--1511; Invent. Math., 206 (2016), 935--974]. On the other hand, in the
absence of damping terms, we also prove the global existence of weak solutions
to the compressible QNS equations without the lower bound assumption on the
dispersive coefficient, which improves the previous result due to
[Antonelli-Spirito, Arch. Ration. Mech. Anal., 203(2012), 499--527].
|
1906.03971v1
|
2019-06-11
|
Study of semi-linear $σ$-evolution equations with frictional and visco-elastic damping
|
In this article, we study semi-linear $\sigma$-evolution equations with
double damping including frictional and visco-elastic damping for any
$\sigma\ge 1$. We are interested in investigating not only higher order
asymptotic expansions of solutions but also diffusion phenomenon in the
$L^p-L^q$ framework, with $1\le p\le q\le \infty$, to the corresponding linear
equations. By assuming additional $L^{m}$ regularity on the initial data, with
$m\in [1,2)$, we prove the global (in time) existence of small data energy
solutions and indicate the large time behavior of the global obtained solutions
as well to semi-linear equations. Moreover, we also determine the so-called
critical exponent when $\sigma$ is integers.
|
1906.04471v1
|
2019-07-08
|
Damping of density oscillations in neutrino-transparent nuclear matter
|
We calculate the bulk-viscous dissipation time for adiabatic density
oscillations in nuclear matter at densities of 1-7 times nuclear saturation
density and at temperatures ranging from 1 MeV, where corrections to previous
low-temperature calculations become important, up to 10 MeV, where the
assumption of neutrino transparency is no longer valid. Under these conditions,
which are expected to occur in neutron star mergers, damping of density
oscillations arises from beta equilibration via weak interactions. We find that
for 1 kHz oscillations the shortest dissipation times are in the 5 to 20 ms
range, depending on the equation of state, which means that bulk viscous
damping could affect the dynamics of a neutron star merger. For higher
frequencies the dissipation time can be even shorter.
|
1907.03795v2
|
2019-07-12
|
Decoherence of collective motion in warm nuclei
|
Collective states in cold nuclei are represented by a wave function that
assigns coherent phases to the participating nucleons. The degree of coherence
decreases with excitation energy above the yrast line because of coupling to
the increasingly dense background of quasiparticle excitations. The
consequences of decoherence are discussed, starting with the well studied case
of rotational damping. In addition to superdeformed bands, a highly excited
oblate band is presented as a new example of screening from rotational damping.
Suppression of pair correlation leads to incoherent thermal M1 radiation, which
appears as an exponential spike (LEMAR) at zero energy in the $\gamma$ strength
function of spherical nuclei. In deformed nuclei a Scissors Resonance appears
and LEMAR changes to damped magnetic rotation, which is interpreted as partial
restoration of coherence.
|
1907.05569v1
|
2019-07-24
|
First-order optimization algorithms via inertial systems with Hessian driven damping
|
In a Hilbert space setting, for convex optimization, we analyze the
convergence rate of a class of first-order algorithms involving inertial
features. They can be interpreted as discrete time versions of inertial
dynamics involving both viscous and Hessian-driven dampings. The geometrical
damping driven by the Hessian intervenes in the dynamics in the form $\nabla^2
f (x(t)) \dot{x} (t)$. By treating this term as the time derivative of $ \nabla
f (x (t)) $, this gives, in discretized form, first-order algorithms in time
and space. In addition to the convergence properties attached to Nesterov-type
accelerated gradient methods, the algorithms thus obtained are new and show a
rapid convergence towards zero of the gradients. On the basis of a
regularization technique using the Moreau envelope, we extend these methods to
non-smooth convex functions with extended real values. The introduction of time
scale factors makes it possible to further accelerate these algorithms. We also
report numerical results on structured problems to support our theoretical
findings.
|
1907.10536v2
|
2019-07-26
|
L^p-asymptotic stability analysis of a 1D wave equation with a nonlinear damping
|
This paper is concerned with the asymptotic stability analysis of a one
dimensional wave equation with Dirichlet boundary conditions subject to a
nonlinear distributed damping with an L p functional framework, p $\in$ [2,
$\infty$]. Some well-posedness results are provided together with exponential
decay to zero of trajectories, with an estimation of the decay rate. The
well-posedness results are proved by considering an appropriate functional of
the energy in the desired functional spaces introduced by Haraux in [11].
Asymptotic behavior analysis is based on an attractivity result on a trajectory
of an infinite-dimensional linear time-varying system with a special structure,
which relies on the introduction of a suitable Lyapunov functional. Note that
some of the results of this paper apply for a large class of nonmonotone
dampings.
|
1907.11712v1
|
2019-08-13
|
A Gevrey class semigroup, exponential decay and Lack of analyticity for a system formed by a Kirchhoff-Love plate equation and the equation of a membrane-like electric network with indirect fractional damping
|
The emphasis in this paper is on the Coupled System of a Kirchhoff-Love Plate
Equation with the Equation of a Membrane-like Electrical Network, where the
coupling is of higher order given by the Laplacian of the displacement velocity
$\gamma\Delta u_t$ and the Laplacian of the electric potential field
$\gamma\Delta v_t $, here only one of the equations is conservative and the
other has dissipative properties. The dissipative mechanism is given by an
intermediate damping $(-\Delta)^\theta v_t$ between the electrical damping
potential for $\theta=0$ and the Laplacian of the electric potential for
$\theta=1$. We show that $S(t)=e^{\mathbb{B}t}$ is not analytic for
$\theta\in[0, 1)$ and analytic for $\theta=1$, however $S(t)=e^{\mathbb{B}t}$
decays exponentially for $0\leq \theta\leq 1$ and $S(t)$ is of Gevrey class $s>
\frac{2+\theta}{\theta}$ when the parameter $\theta$ lies in the interval
$(0,1)$.
|
1908.04826v3
|
2019-08-20
|
Partial Optomechanical Refrigeration via Multimode Cold-Damping Feedback
|
We provide a fully analytical treatment for the partial refrigeration of the
thermal motion of a quantum mechanical resonator under the action of feedback.
As opposed to standard cavity optomechanics where the aim is to isolate and
cool a single mechanical mode, the aim here is to extract the thermal energy
from many vibrational modes within a large frequency bandwidth. We consider a
standard cold-damping technique where homodyne read-out of the cavity output
field is fed into a feedback loop that provides a cooling action directly
applied on the mechanical resonator. Analytical and numerical results predict
that low final occupancies are achievable independently of the number of modes
addressed by the feedback as long as the cooling rate is smaller than the
intermode frequency separation. For resonators exhibiting a few nearly
degenerate pairs of modes cooling is less efficient and a weak dependence on
the number of modes is obtained. These scalings hint towards the design of
frequency resolved mechanical resonators where efficient refrigeration is
possible via simultaneous cold-damping feedback.
|
1908.07348v2
|
2019-08-19
|
Time Delay in the Swing Equation: A Variety of Bifurcations
|
The present paper addresses the swing equation with additional delayed
damping as an example for pendulum-like systems. In this context, it is proved
that recurring sub- and supercritical Hopf bifurcations occur if time delay is
increased. To this end, a general formula for the first Lyapunov coefficient in
second order systems with additional delayed damping and delay-free
nonlinearity is given. In so far the paper extends results about stability
switching of equilibria in linear time delay systems from Cooke and Grossman.
In addition to the analytical results, periodic solutions are numerically dealt
with. The numerical results demonstrate how a variety of qualitative behaviors
is generated in the simple swing equation by only introducing time delay in a
damping term.
|
1908.07996v3
|
2019-08-26
|
Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
|
We describe completely 2-solitary waves related to the ground state of the
nonlinear damped Klein-Gordon equation \begin{equation*}
\partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \end{equation*} on
$\bf R^N$, for $1\leq N\leq 5$ and energy subcritical exponents $p>2$. The
description is twofold.
First, we prove that 2-solitary waves with same sign do not exist. Second, we
construct and classify the full family of 2-solitary waves in the case of
opposite signs. Close to the sum of two remote solitary waves, it turns out
that only the components of the initial data in the unstable direction of each
ground state are relevant in the large time asymptotic behavior of the
solution. In particular, we show that $2$-solitary waves have a universal
behavior: the distance between the solitary waves is asymptotic to $\log t$ as
$t\to \infty$. This behavior is due to damping of the initial data combined
with strong interactions between the solitary waves.
|
1908.09527v1
|
2019-08-30
|
Magnetization reversal, damping properties and magnetic anisotropy of L10-ordered FeNi thin films
|
L10 ordered magnetic alloys such as FePt, FePd, CoPt and FeNi are well known
for their large magnetocrystalline anisotropy. Among these, L10-FeNi alloy is
economically viable material for magnetic recording media because it does not
contain rare earth and noble elements. In this work, L10-FeNi films with three
different strengths of anisotropy were fabricated by varying the deposition
process in molecular beam epitaxy system. We have investigated the
magnetization reversal along with domain imaging via magneto optic Kerr effect
based microscope. It is found that in all three samples, the magnetization
reversal is happening via domain wall motion. Further ferromagnetic resonance
(FMR) spectroscopy was performed to evaluate the damping constant and magnetic
anisotropy. It was observed that the FeNi sample with moderate strength of
anisotropy exhibits low value of damping constant ~ 4.9X10^-3. In addition to
this, it was found that the films possess a mixture of cubic and uniaxial
anisotropies.
|
1908.11761v1
|
2019-09-24
|
DAMPE Excess from Leptophilic Vector Dark Matter: Model Independent Approach
|
We study all extensions of the Standard Model (SM) with a vector dark matter
(VDM) candidate which can explain the peak structure observed by recent DAMPE
experiment in electron-positron cosmic ray spectrum. In this regard, we
consider all leptophilic renormalizable VDM-SM interactions through scalar,
spinor, and vector mediators. We show that only two out of six possible models
could produce DAMPE signal by annihilation of VDM with the mass about 1.5 TeV
in a nearby subhalo whilst simultaneously satisfying constraints from DM relic
density, direct/indirect detection, and the collider bounds. These two models
are the ones with scalar/pseudoscalar mediator $ \phi $ with $ M_{\phi} \in
[1500,3000] $ GeV.
|
1909.10729v2
|
2019-09-24
|
Evaluating the Impacts of Transmission Expansion on Sub-Synchronous Resonance Risk
|
While transmission expansions are planned to have positive impact on
reliability of power grids, they could increase the risk and severity of some
of the detrimental incidents in power grid mainly by virtue of changing system
configuration, consequently electrical distance. This paper aims to evaluate
and quantify the impact of transmission expansion projects on Sub-Synchronous
Resonance (SSR) risk through a two-step approach utilizing outage count index
and Sub-synchronous damping index. A graph-theory based SSR screening tool is
introduced to quantify the outage count associated with all grid contingencies
which results in radial connection between renewable generation resources and
nearby series compensated lines. Moreover, a frequency-scan based damping
analysis is performed to assess the impact of transmission expansion on the
system damping in sub-synchronous frequency range. The proposed approach has
been utilized to evaluate the impact of recently-built transmission expansion
project on SSR risk in a portion of Electric Reliability Council of Texas
(ERCOT) grid.
|
1909.11024v1
|
2019-10-02
|
Data-Driven Identification of Rayleigh-Damped Second-Order Systems
|
In this paper, we present a data-driven approach to identify second-order
systems, having internal Rayleigh damping. This means that the damping matrix
is given as a linear combination of the mass and stiffness matrices. These
systems typically appear when performing various engineering studies, e.g.,
vibrational and structural analysis. In an experimental setup, the frequency
response of a system can be measured via various approaches, for instance, by
measuring the vibrations using an accelerometer. As a consequence, given
frequency samples, the identification of the underlying system relies on
rational approximation. To that aim, we propose an identification of the
corresponding second-order system, extending the Loewner framework for this
class of systems. The efficiency of the proposed method is demonstrated by
means of various numerical benchmarks.
|
1910.00838v1
|
2019-10-06
|
Deterministic and random attractors for a wave equation with sign changing damping
|
The paper gives a detailed study of long-time dynamics generated by weakly
damped wave equations in bounded 3D domains where the damping exponent depends
explicitly on time and may change sign. It is shown that in the case when the
non-linearity is superlinear, the considered equation remains dissipative if
the weighted mean value of the dissipation rate remains positive and that the
conditions of this type are not sufficient in the linear case. Two principally
different cases are considered. In the case when this mean is uniform (which
corresponds to deterministic dissipation rates), it is shown that the
considered system possesses smooth uniform attractors as well as non-autonomous
exponential attractors. In the case where the mean is not uniform (which
corresponds to the random dissipation rate, for instance, when this dissipation
rate is generated by the Bernoulli process), the tempered random attractor is
constructed. In contrast to the usual situation, this random attractor is
expected to have infinite Hausdorff and fractal dimension. The simplified model
example which demonstrates infinite-dimensionality of the random attractor is
also presented.
|
1910.02430v1
|
2019-10-23
|
On the exponential stability of a stratified flow to the 2D IDEAL MHD equations with damping
|
We study the stability of a type of stratified flows of the two dimensional
inviscid incompressible MHD equations with velocity damping. The exponential
stability for the perturbation near certain stratified flow is investigated in
a strip-type area R*[0,1]. Although the magnetic filed potential is governed by
a transport equation, by using the algebraic structure of the incompressible
condition, it turns out that the linearized MHD equations around the given
stratified flow retain a non-local damping mechanism. After carefully analyzing
the non-linear structure and introducing some suitable weighted energy norms,
we get the exponential stability by combining the exponential decay in time in
the lower order energy with that in the high order energy.
|
1910.10598v1
|
2019-10-24
|
Wigner instability analysis of the damped Hirota equation
|
We address the modulation instability of the Hirota equation in the presence
of stochastic spatial incoherence and linear time-dependent
amplification/attenuation processes via the Wigner function approach. We show
that the modulation instability remains baseband type, though the damping
mechanisms substantially reduce the unstable spectrum independent of the
higher-order contributions (e.g. the higher-order nonlinear interaction and the
third-order dispersion). Additionally, we find out that the unstable structure
due to the Kerr interaction exhibits a significant resilience to the
third-order-dispersion stabilizing effects in comparison with the higher-order
nonlinearity, as well as a moderate Lorentzian spectrum damping may assist the
rising of instability. Finally, we also discuss the relevance of our results in
the context of current experiments exploring extreme wave events driven by the
modulation instability (e.g. the generation of the so-called rogue waves).
|
1910.11045v2
|
2019-11-01
|
The spherical multipole resonance probe: kinetic damping in its spectrum
|
The multipole resonance probe is one of the recently developed measurement
devices to measure plasma parameter like electron density and temperature based
on the concept of active plasma resonance spectroscopy. The dynamical
interaction between the probe and the plasma in electrostatic, kinetic
description can be modeled in an abstract notation based on functional analytic
methods. These methods provide the opportunity to derive a general solution,
which is given as the response function of the probe-plasma system. It is
defined by the matrix elements of the resolvent of an appropriate dynamical
operator. Based on the general solution a residual damping for vanishing
pressure can be predicted and can only be explained by kinetic effects. Within
this manuscript an explicit response function of the multipole resonance probe
is derived. Therefore, the resolvent is determined by its algebraic
representation based on an expansion in orthogonal basis functions. This allows
to compute an approximated response function and its corresponding spectra,
which show additional damping due to kinetic effects.
|
1911.00514v1
|
2019-11-04
|
Current-driven skyrmion motion in granular films
|
Current-driven skyrmion motion in random granular films is investigated with
interesting findings. For a given current, there exists a critical disorder
strength below which its transverse motion could either be boosted below a
critical damping or be hindered above the critical damping, resulting in
current and disorder dependences of skyrmion Hall angle. The boosting comes
mainly from the random force that is opposite to the driving force (current).
The critical damping depends on the current density and disorder strength.
However, the longitudinal motion of a skyrmion is always hindered by the
disorder. Above the critical disorder strength, skyrmions are pinned. The
disorder-induced random force on a skyrmion can be classified as static and
kinetic ones, similar to the friction force in the Newtonian mechanics. In the
pinning phase, the static (pinning) random force is transverse to the current
density. The kinetic random force is opposite to the skyrmion velocity when
skyrmions are in motion. Furthermore, we provide strong evidences that the
Thiele equation can perfectly describe skyrmion dynamics in granular films.
These findings provide insight to skyrmion motion and should be important for
skyrmiontronics.
|
1911.01245v1
|
2019-11-05
|
Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schrödinger equation: justification and numerical comparisons
|
We consider a discrete nonlinear Klein-Gordon equations with damping and
external drive. Using a small amplitude ansatz, one usually approximates the
equation using a damped, driven discrete nonlinear Schr\"odinger equation.
Here, we show for the first time the justification of this approximation by
finding the error bound using energy estimate. Additionally, we prove the local
and global existence of the Schr\"odinger equation. Numerical simulations are
performed that describe the analytical results. Comparisons between discrete
breathers of the Klein-Gordon equation and discrete solitons of the discrete
nonlinear Schr\"odinger equation are presented.
|
1911.01631v1
|
2019-11-14
|
Stability of coupled solitary wave in biomembranes and nerves
|
In this work, we consider the electromechanical density pulse as a coupled
solitary waves represented by a longitudinal compression wave and an
out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We
analyzed using, the variational approach, the characteristics of the coupled
solitary waves in the presence of damping within the framework of coupled
nonlinear Burger-Korteweg-de Vries-Benjamin-Bona-Mahony (BKdV-BBM) equation. It
is shown that, the inertia parameter increases the stability of coupled
solitary waves while the damping parameter decreases it. Moreover, the presence
of damping term induces a discontinuity of stable regions in the inertia-speed
parameter space, appearing in he form of an island of points. Bell shape and
solitary-shock like wave profiles were obtained by varying the propagation
speed and their linear stability spectrum computed. It is shown that bell shape
solitary wave exhibit bound state eigenvalue spectrum, therefore stable. On the
other hand, the solitary-shock like wave profiles exhibit unbound state
eigenvalue spectrum and are therefore generally unstable.
|
1911.05993v1
|
2019-11-19
|
On the theory of the nonlinear Landau damping
|
An exact solution of the collisionless time-dependent Vlasov equation is
found for the first time. By means of this solution the behavior of the
Langmuir waves in the nonlinear stage is considered. The analysis is restricted
by the consideration of the first nonlinear approximation keeping the second
power of the electric strength. It is shown that in general the waves with
finite amplitudes are not subject to damping. Only in the linear approximation,
when the wave amplitude is very small, are the waves experiencing damping. It
is shown that with the definite resonance conditions imposed, the waves become
unstable.
|
1911.08294v2
|
2019-11-16
|
Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons
|
We consider a damped, parametrically driven discrete nonlinear Klein-Gordon
equation, that models coupled pendula and micromechanical arrays, among others.
To study the equation, one usually uses a small-amplitude wave ansatz, that
reduces the equation into a discrete nonlinear Schr\"odinger equation with
damping and parametric drive. Here, we justify the approximation by looking for
the error bound with the method of energy estimates. Furthermore, we prove the
local and global existence of {solutions to the discrete nonlinear}
Schr\"odinger equation. To illustrate the main results, we consider numerical
simulations showing the dynamics of errors made by the discrete nonlinear
equation. We consider two types of initial conditions, with one of them being a
discrete soliton of the nonlinear Schr\"odinger equation, that is expectedly
approximate discrete breathers of the nonlinear Klein-Gordon equation.
|
1911.08514v1
|
2019-11-26
|
On the Complexity of Minimum-Cost Networked Estimation of Self-Damped Dynamical Systems
|
In this paper, we consider the optimal design of networked estimators to
minimize the communication/measurement cost under the networked observability
constraint. This problem is known as the minimum-cost networked estimation
problem, which is generally claimed to be NP-hard. The main contribution of
this work is to provide a polynomial-order solution for this problem under the
constraint that the underlying dynamical system is self-damped. Using
structural analysis, we subdivide the main problem into two NP-hard subproblems
known as (i) optimal sensor selection, and (ii) minimum-cost communication
network. For self-damped dynamical systems, we provide a polynomial-order
solution for subproblem (i). Further, we show that the subproblem (ii) is of
polynomial-order complexity if the links in the communication network are
bidirectional. We provide an illustrative example to explain the methodologies.
|
1911.11381v1
|
2019-12-30
|
A Link Between Relativistic Rest Energy and Fractionary Momentum Operators of Order 1/2
|
The solution of a causal fractionary wave equation in an infinite potential
well was obtained. First, the so-called "free particle" case was solved, giving
as normalizable solutions a superposition of damped oscillations similar to a
wave packet. From this results, the infinite potential well case was then
solved. The damping coefficient of the equation obtained was matched with the
exponent appearing in the Yucawa potential or "screened" Coulomb potential.
When this matching was forced, the particle aquires an offset energy of E =
mc^2/2 which then can be increased by each energy level. The expontential
damping of the wave solutions in the box was found to be closely related with
the radius of the proton when the particle has a mass equal to the mass of the
proton. Lastly the fractionary wave equation was expressed in spherical
coordinates and remains to be solved through analytical or numerical methods.
|
1912.12770v4
|
2020-01-06
|
A continuous contact force model for impact analysis in multibody dynamics
|
A new continuous contact force model for contacting problems with regular or
irregular contacting surfaces and energy dissipations in multibody systems is
presented and discussed in this work. The model is developed according to Hertz
law and a hysteresis damping force is introduced for modeling the energy
dissipation during the contact process. As it is almost impossible to obtain an
analytical solution based on the system dynamic equation, an approximate
dynamic equation for the collision system is proposed, achieving a good
approximation of the system dynamic equation. An approximate function between
deformation velocity and deformation is founded on the approximate dynamic
equation, then it is utilized to calculate the energy loss due to the damping
force. The model is established through modifying the original formula of the
hysteresis damping parameter derived by combining the energy balance and the
law of conservation of linear momentum. Numerical results of five different
continuous contact models reveal the capability of our new model as well as the
effect of the geometry of the contacting surfaces on the dynamic system
response.
|
2001.01344v1
|
2020-01-06
|
Boresight Alignment of DArk Matter Particle Explorer
|
The DArk Matter Particle Explorer (DAMPE) can measure $\gamma$-rays in the
energy range from a few GeV to about 10 TeV. The direction of each $\gamma$-ray
is reconstructed with respect to the reference system of the DAMPE payload. In
this paper, we adopt a maximum likelihood method and use the $\gamma$-ray data
centered around several bright point-like sources to measure and correct the
angular deviation from the real celestial coordinate system, the so called
``boresight alignment'' of the DAMPE payload. As a check, we also estimate the
boresight alignment for some sets of simulation data with artificial
orientation and obtain consistent results. The time-dependent boresight
alignment analysis does not show evidence for significant variation of the
parameters.
|
2001.01804v1
|
2020-01-09
|
Nonlinear inviscid damping near monotonic shear flows
|
We prove nonlinear asymptotic stability of a large class of monotonic shear
flows among solutions of the 2D Euler equations in the channel
$\mathbb{T}\times[0,1]$. More precisely, we consider shear flows $(b(y),0)$
given by a function $b$ which is Gevrey smooth, strictly increasing, and linear
outside a compact subset of the interval $(0,1)$ (to avoid boundary
contributions which are incompatible with inviscid damping). We also assume
that the associated linearized operator satisfies a suitable spectral
condition, which is needed to prove linear inviscid damping.
Under these assumptions, we show that if $u$ is a solution which is a small
and Gevrey smooth perturbation of such a shear flow $(b(y),0)$ at time $t=0$,
then the velocity field $u$ converges strongly to a nearby shear flow as the
time goes to infinity. This is the first nonlinear asymptotic stability result
for Euler equations around general steady solutions for which the linearized
flow cannot be explicitly solved.
|
2001.03087v1
|
2020-02-03
|
Semi-active $\mathcal{H}_{\infty}$ damping optimization by adaptive interpolation
|
In this work we consider the problem of semi-active damping optimization of
mechanical systems with fixed damper positions. Our goal is to compute a
damping that is locally optimal with respect to the $\mathcal{H}_\infty$-norm
of the transfer function from the exogenous inputs to the performance outputs.
We make use of a new greedy method for computing the $\mathcal{H}_\infty$-norm
of a transfer function based on rational interpolation. In this paper, this
approach is adapted to parameter-dependent transfer functions. The
interpolation leads to parametric reduced-order models that can be optimized
more efficiently. At the optimizers we then take new interpolation points to
refine the reduced-order model and to obtain updated optimizers. In our
numerical examples we show that this approach normally converges fast and thus
can highly accelerate the optimization procedure. Another contribution of this
work are heuristics for choosing initial interpolation points.
|
2002.00617v1
|
2020-03-25
|
A Novel Wide-Area Control Strategy for Damping of Critical Frequency Oscillations via Modulation of Active Power Injections
|
This paper proposes a novel wide-area control strategy for modulating the
active power injections to damp the critical frequency oscillations in power
systems, this includes the inter-area oscillations and the transient frequency
swing. The proposed method pursues an efficient utilization of the limited
power reserve of existing distributed energy resources (DERs) to mitigate these
oscillations. This is accomplished by decoupling the damping control actions at
different sites using the oscillation signals of the concerned mode as the
power commands. A theoretical basis for this decoupled modulating control is
provided. Technically, the desired sole modal oscillation signals are filtered
out by linearly combining the system-wide frequencies, which is determined by
the linear quadratic regulator based sparsity-promoting (LQRSP) technique. With
the proposed strategy, the modulation of each active power injection can be
effectively engineered considering the response limit and steady-state output
capability of the supporting device. The method is validated based on a
two-area test system and is further demonstrated based on the New England
39-bus test system.
|
2003.11397v1
|
2020-03-25
|
Sharp ultimate velocity bounds for the general solution of some linear second order evolution equation with damping and bounded forcing
|
We consider a class of linear second order differential equations with
damping and external force. We investigate the link between a uniform bound on
the forcing term and the corresponding ultimate bound on the velocity of
solutions, and we study the dependence of that bound on the damping and on the
"elastic force".
We prove three results. First of all, in a rather general setting we show
that different notions of bound are actually equivalent. Then we compute the
optimal constants in the scalar case. Finally, we extend the results of the
scalar case to abstract dissipative wave-type equations in Hilbert spaces. In
that setting we obtain rather sharp estimates that are quite different from the
scalar case, in both finite and infinite dimensional frameworks.
The abstract theory applies, in particular, to dissipative wave, plate and
beam equations.
|
2003.11579v1
|
2020-03-28
|
Energy correction based on fluorescence attenuation of DAMPE
|
The major scientific goals of DArk Matter Particle Explorer (DAMPE) are to
study cosmic-ray electrons (including positrons) and gamma rays from 5 GeV to
10 TeV and nuclei from Z = 1 to 26 up to 100 TeV. The deposited energy measured
by the Bismuth Germanate Oxide (BGO) calorimeter of DAMPE is affected by
fluorescence attenuation in BGO crystals that are 600 mm long. In this work, an
in-orbit attenuation calibration method is reported, and energy correction of
the sensitive detector unit of the BGO calorimeter is also presented.
|
2003.12717v1
|
2020-04-02
|
A finite element model for seismic response analysis of free-standing rocking columns with vertical dampers
|
This paper investigates finite-element modeling of a vertically damped
free-standing rocking column. The paper first derives the nonlinear equation of
motion for the coupled system and then compares the analytical solution with
finite-element model. Finite-element model is being produced using open source
framework named OpenSees. The rocking surface is modeled using zero-length
fiber cross-section element and the dampers are modeled with two node link
elements. In order to simulate energy dissipation during the rocking motion
Hilber-Hughes-Taylor numerical dissipative time step integration is being
adopted. The paper also compares two types of hysteretic and viscous damping
devices and it shows that the viscous damping behavior is favorable when it is
used along with a rocking block. The results of analytical model of a rigid
block with viscous dampers in MATLAB is then compared with OpenSees model and
the paper concludes that the finite-element model compares satisfactory with
the analytical model.
|
2004.01060v1
|
2020-04-02
|
Simulating the effect of weak measurements by a phase damping channel and determining different measures of bipartite correlations in nuclear magnetic resonance
|
Quantum discord is a measure based on local projective measurements which
captures quantum correlations that may not be fully captured by entanglement. A
change in the measurement process, achieved by replacing rank-one projectors
with a weak positive operator-valued measure (POVM), allows one to define weak
variants of quantum discord. In this work, we experimentally simulate the
effect of a weak POVM on a nuclear magnetic resonance quantum information
processor. The two-qubit system under investigation is part of a three-qubit
system, where one of the qubits is used as an ancillary to implement the phase
damping channel. The strength of the weak POVM is controlled by varying the
strength of the phase damping channel. We experimentally observed two weak
variants of quantum discord namely, super quantum discord and weak quantum
discord, in two-qubit Werner and Bell-diagonal states. The resultant dynamics
of the states is investigated as a function of the measurement strength.
|
2004.01237v2
|
2020-04-24
|
A rigorous derivation and energetics of a wave equation with fractional damping
|
We consider a linear system that consists of a linear wave equation on a
horizontal hypersurface and a parabolic equation in the half space below. The
model describes longitudinal elastic waves in organic monolayers at the
water-air interface, which is an experimental setup that is relevant for
understanding wave propagation in biological membranes. We study the scaling
regime where the relevant horizontal length scale is much larger than the
vertical length scale and provide a rigorous limit leading to a
fractionally-damped wave equation for the membrane. We provide the associated
existence results via linear semigroup theory and show convergence of the
solutions in the scaling limit. Moreover, based on the energy-dissipation
structure for the full model, we derive a natural energy and a natural
dissipation function for the fractionally-damped wave equation with a time
derivative of order 3/2
|
2004.11830v1
|
2020-04-25
|
Pulse-assisted magnetization switching in magnetic nanowires at picosecond and nanosecond timescales with low energy
|
Detailed understanding of spin dynamics in magnetic nanomaterials is
necessary for developing ultrafast, low-energy and high-density spintronic
logic and memory. Here, we develop micromagnetic models and analytical
solutions to elucidate the effect of increasing damping and uniaxial anisotropy
on magnetic field pulse-assisted switching time, energy and field requirements
of nanowires with perpendicular magnetic anisotropy and yttrium iron
garnet-like spin transport properties. A nanowire is initially magnetized using
an external magnetic field pulse (write) and self-relaxation. Next, magnetic
moments exhibit deterministic switching upon receiving 2.5 ns-long external
magnetic pulses in both vertical polarities. Favorable damping
({\alpha}~0.1-0.5) and anisotropy energies (10^4-10^5 J m^-3) allow for as low
as picosecond magnetization switching times. Magnetization reversal with fields
below coercivity was observed using spin precession instabilities. A
competition or a nanomagnetic trilemma arises among the switching rate, energy
cost and external field required. Developing magnetic nanowires with optimized
damping and effective anisotropy could reduce the switching energy barrier down
to 3163kBT at room temperature. Thus, pulse-assisted picosecond and low energy
switching in nanomagnets could enable ultrafast nanomagnetic logic and cellular
automata.
|
2004.12243v1
|
2020-05-01
|
Stability of Forced-Damped Response in Mechanical Systems from a Melnikov Analysis
|
Frequency responses of multi-degree-of-freedom mechanical systems with weak
forcing and damping can be studied as perturbations from their conservative
limit. Specifically, recent results show how bifurcations near resonances can
be predicted analytically from conservative families of periodic orbits
(nonlinear normal modes). However, the stability of forced-damped motions is
generally determined a posteriori via numerical simulations. In this paper, we
present analytic results on the stability of periodic orbits that perturb from
conservative nonlinear normal modes. In contrast with prior approaches to the
same problem, our method can tackle strongly nonlinear oscillations, high-order
resonances and arbitrary types of non-conservative forces affecting the system,
as we show with specific examples.
|
2005.00444v2
|
2020-05-04
|
Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with $L^r$-data
|
In the present paper, we consider the linear wave equation with the
scale-invariant damping and mass. It is known that the global behavior of the
solution depends on the size of the coefficients in front of the damping and
mass at initial time $t=0$. Indeed, the solution satisfies the similar decay
estimate to that of the corresponding heat equation if it is large and to that
of the modified wave equation if it is small. In our previous paper, we obtain
the scattering result and its asymptotic order for the data in the energy space
$H^1\times L^2$ when the coefficients are in the wave regime. In fact, the
threshold of the coefficients relies on the spatial decay of the initial data.
Namely, it varies depending on $r$ when the initial data is in $L^r$ ($1\leq r
< 2$). In the present paper, we will show the scattering result and the
asymptotic order in the wave regime for $L^r$-data, which is wider than the
wave regime for the data in the energy space. Moreover, we give an improvement
of the asymptotic order obtained in our previous paper for the data in the
energy space.
|
2005.01335v2
|
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