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2007-10-04 | Activation of additional energy dissipation processes in the magnetization dynamics of epitaxial chromium dioxide films | The precessional magnetization dynamics of a chromium dioxide$(100)$ film is
examined in an all-optical pump-probe setup. The frequency dependence on the
external field is used to extract the uniaxial in-plane anisotropy constant.
The damping shows a strong dependence on the frequency, but also on the laser
pump fluency, which is revealed as an important experiment parameter in this
work: above a certain threshold further channels of energy dissipation open and
the damping increases discontinuously. This behavior might stem from spin-wave
instabilities. | 0710.0986v2 |
2009-02-03 | Freezing of spin dynamics in underdoped cuprates | The Mori's memory function approach to spin dynamics in doped
antiferromagnetic insulator combined with the assumption of temperature
independent static spin correlations and constant collective mode damping leads
to w/T scaling in a broad range. The theory involving a nonuniversal scaling
parameter is used to analyze recent inelastic neutron scattering results for
underdoped cuprates. Adopting modified damping function also the emerging
central peak in low-doped cuprates at low temperatures can be explained within
the same framework. | 0902.0546v1 |
2011-04-06 | Relativistic magnetic reconnection at X-type neutral points | Relativistic effects in the oscillatory damping of magnetic disturbances near
two-dimensional X-points are investigated. By taking into account displacement
current, we study new features of extremely magnetized systems, in which the
Alfv\'en velocity is almost the speed of light. The frequencies of the
least-damped mode are calculated using linearized relativistic MHD equations
for wide ranges of the Lundquist number S and the magnetization parameter
$\sigma$. These timescales approach constant values in the large resistive
limit: the oscillation time becomes a few times the light crossing time,
irrespective of $\sigma$, and the decay time is proportional to $\sigma$ and
therefore is longer for a highly magnetized system. | 1104.1003v1 |
2011-11-08 | The entropy of large black holes in loop quantum gravity: A combinatorics/analysis approach | The issue of a possible damping of the entropy periodicity for large black
holes in Loop Quantum Gravity is highly debated. Using a combinatorics/analysis
approach, we give strong arguments in favor of this damping, at least for
prescriptions where the projection constraint is not fully implemented. This
means that black holes in loop gravity exhibit an asymptotic Bekenstein-Hawking
behavior, provided that a consistent choice of the Immirzi constant is made. | 1111.1975v1 |
2013-04-04 | Pais-Uhlenbeck Oscillator with a Benign Friction Force | It is shown that the Pais-Uhlenbeck oscillator with damping, considered by
Nesterenko, is a special case of a more general oscillator that has not only a
first order, but also a third order friction term. If the corresponding damping
constants, \alpha\ and \beta, are both positive and below certain critical
values, then the system is stable. In particular, if \alpha = - \beta, then we
have the unstable Nesterenko's oscillator | 1304.1325v2 |
2014-12-05 | Exponential dephasing of oscillators in the Kinetic Kuramoto Model | We study the kinetic Kuramoto model for coupled oscillators with coupling
constant below the synchronization threshold. We manage to prove that, for any
analytic initial datum, if the interaction is small enough, the order parameter
of the model vanishes exponentially fast, and the solution is asymptotically
described by a free flow. This behavior is similar to the phenomenon of Landau
damping in plasma physics. In the proof we use a combination of techniques from
Landau damping and from abstract Cauchy-Kowalewskaya theorem. | 1412.1923v1 |
2014-12-23 | Selftrapping triggered by losses in cavity QED | In a coupled cavity QED network model, we study the transition from a
localized super fluid like state to a delocalized Mott insulator like state,
triggered by losses. Without cavity losses, the transition never takes place.
Further, if one measures the quantum correlations between the polaritons via
the negativity, we find a critical cavity damping constant, above which the
negativity displays a single peak in the same time region where the transition
takes place. Additionally, we identify two regions in the parameter space,
where below the critical damping, oscillations of the initial localized state
are observed along with a multipeaked negativity, while above the critical
value, the oscillations die out and the transition is witnessed by a neat
single peaked negativity. | 1412.7495v1 |
2015-11-19 | Periodic damping gives polynomial energy decay | Let $u$ solve the damped Klein--Gordon equation $$ \big( \partial_t^2-\sum
\partial_{x_j}^2 +m \text{Id} +\gamma(x) \partial_t \big) u=0 $$ on
$\mathbb{R}^n$ with $m>0$ and $\gamma\geq 0$ bounded below on a $2 \pi
\mathbb{Z}^n$-invariant open set by a positive constant. We show that the
energy of the solution $u$ decays at a polynomial rate. This is proved via a
periodic observability estimate on $\mathbb{R}^n.$ | 1511.06144v5 |
2016-07-06 | Asymptotic profiles of solutions for structural damped wave equations | In this paper, we obtain several asymptotic profiles of solutions to the
Cauchy problem for structurally damped wave equations $\partial_{t}^{2} u -
\Delta u + \nu (-\Delta)^{\sigma} \partial_{t} u=0$, where $\nu >0$ and $0<
\sigma \le1$. Our result is the approximation formula of the solution by a
constant multiple of a special function as $t \to \infty$, which states that
the asymptotic profiles of the solutions are classified into $5$ patterns
depending on the values $\nu$ and $\sigma$. | 1607.01839v1 |
2018-01-19 | Robust integral action of port-Hamiltonian systems | Interconnection and damping assignment, passivity-based control (IDA-PBC) has
proven to be a successful control technique for the stabilisation of many
nonlinear systems. In this paper, we propose a method to robustify a system
which has been stabilised using IDA-PBC with respect to constant, matched
disturbances via the addition of integral action. The proposed controller
extends previous work on the topic by being robust against the damping of the
system, a quantity which may not be known in many applications. | 1801.06279v1 |
2018-04-10 | Motion of a superconducting loop in an inhomogeneous magnetic field: a didactic experiment | We present an experiment conductive to an understanding of both Faraday's law
and the properties of the superconducting state. It consists in the analysis of
the motion of a superconducting loop moving under the influence of gravity in
an inhomogeneous horizontal magnetic field. Gravity, conservation of magnetic
flux, and friction combine to give damped harmonic oscillations. The measured
frequency of oscillation and the damping constant as a function of the magnetic
field strength (the only free parameter) are in good agreement with the
theoretical model. | 1804.03553v1 |
2010-04-26 | Entanglement of a two-particle Gaussian state interacting with a heat bath | The effect of a thermal reservoir is investigated on a bipartite Gaussian
state. We derive a pre-Lindblad master equation in the non-rotating wave
approximation for the system. We then solve the master equation for a bipartite
harmonic oscillator Hamiltonian with entangled initial state. We show that for
strong damping the loss of entanglement is the same as for freely evolving
particles. However, if the damping is small, the entanglement is shown to
oscillate and eventually tend to a constant nonzero value. | 1004.4515v2 |
2019-09-11 | Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping | In this paper, we consider the 1D compressible Euler equation with the
damping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu
<1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, we prove that solutions
exist globally in time, if initial data are small $C^1$ perturbation near
constant states. In particular, we remove the conditions on the limit
$\lim_{|x| \rightarrow \infty} (u (0,x), v (0,x))$, assumed in previous
results. | 1909.05683v1 |
2021-04-12 | The pressureless damped Euler-Riesz equations | In this paper, we analyze the pressureless damped Euler-Riesz equations posed
in either $\mathbb{R}^d$ or $\mathbb{T}^d$. We construct the global-in-time
existence and uniqueness of classical solutions for the system around a
constant background state. We also establish large-time behaviors of classical
solutions showing the solutions towards the equilibrium as time goes to
infinity. For the whole space case, we first show the algebraic decay rate of
solutions under additional assumptions on the initial data compared to the
existence theory. We then refine the argument to have the exponential decay
rate of convergence even in the whole space. In the case of the periodic
domain, without any further regularity assumptions on the initial data, we
provide the exponential convergence of solutions. | 2104.05153v1 |
2021-05-20 | On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity | In this note, we derive a blow-up result for a semilinear generalized Tricomi
equation with damping and mass terms having time-dependent coefficients. We
consider these coefficients with critical decay rates. Due to this threshold
nature of the time-dependent coefficients (both for the damping and for the
mass), the multiplicative constants appearing in these lower-order terms
strongly influence the value of the critical exponent, determining a
competition between a Fujita-type exponent and a Strauss-type exponent. | 2105.09879v2 |
2016-06-08 | Energy Decay in a Wave Guide with Dissipation at Infinity | We prove local and global energy decay for the wave equation in a wave guide
with damping at infinity. More precisely, the absorption index is assumed to
converge slowly to a positive constant, and we obtain the diffusive phenomenon
typical for the contribution of low frequencies when the damping is effective
at infinity. On the other hand, the usual Geometric Control Condition is not
necessarily satisfied so we may have a loss of regularity for the contribution
of high frequencies. Since our results are new even in the Euclidean space, we
also state a similar result in this case. | 1606.02549v2 |
2020-10-18 | Classical limit of quantum mechanics for damped driven oscillatory systems: Quantum-classical correspondence | The investigation of quantum-classical correspondence may lead to gain a
deeper understanding of the classical limit of quantum theory. We develop a
quantum formalism on the basis of a linear-invariant theorem, which gives an
exact quantum-classical correspondence for damped oscillatory systems that are
perturbed by an arbitrary force. Within our formalism, the quantum trajectory
and expectation values of quantum observables are precisely coincide with their
classical counterparts in the case where we remove the global quantum constant
h from their quantum results. In particular, we illustrate the correspondence
of the quantum energy with the classical one in detail. | 2010.08971v1 |
2020-12-28 | An efficient method for approximating resonance curves of weakly-damped nonlinear mechanical systems | A method is presented for tracing the locus of a specific peak in the
frequency response under variation of a parameter. It is applicable to
periodic, steady-state vibrations of harmonically forced nonlinear mechanical
systems. It operates in the frequency domain and its central idea is to assume
a constant phase lag between forcing and response. The method is validated for
a two-degree-of-freedom oscillator with cubic spring and a bladed disk with
shroud contact. The method provides superior computational efficiency, but is
limited to weakly-damped systems. Finally, the capability to reveal isolated
solution branches is highlighted. | 2012.14458v1 |
2021-02-04 | Global existence results for semi-linear structurally damped wave equations with nonlinear convection | In this paper, we consider the Cauchy problem for semi-linear wave equations
with structural damping term $\nu (-\Delta)^2 u_t$, where $\nu >0$ is a
constant. As being mentioned in [8,10], the linear principal part brings both
the diffusion phenomenon and the regularity loss of solutions. This implies
that, for the nonlinear problems, the choice of solution spaces plays an
important role to obtain global solutions with sharp decay properties in time.
Our main purpose of this paper is to prove the global (in time) existence of
solutions for the small data and their decay properties for the supercritical
nonlinearities. | 2102.02445v2 |
2022-04-04 | Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions | In this paper, we investigate the exponential ergodicity in a
Wasserstein-type distance for a damping Hamiltonian dynamics with
state-dependent and non-local collisions, which indeed is a special case of
piecewise deterministic Markov processes while is very popular in numerous
modelling situations including stochastic algorithms. The approach adopted in
this work is based on a combination of the refined basic coupling and the
refined reflection coupling for non-local operators. In a certain sense, the
main result developed in the present paper is a continuation of the counterpart
in \cite{BW2022} on exponential ergodicity of stochastic Hamiltonian systems
with L\'evy noises and a complement of \cite{BA} upon exponential ergodicity
for Andersen dynamics with constant jump rate functions. | 2204.01372v1 |
2022-06-17 | On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers | This paper presents a stable finite element approximation for the acoustic
wave equation on second-order form, with perfectly matched layers (PML) at the
boundaries. Energy estimates are derived for varying PML damping for both the
discrete and the continuous case. Moreover, a priori error estimates are
derived for constant PML damping. Most of the analysis is performed in Laplace
space. Numerical experiments in physical space validate the theoretical
results. | 2206.08507v1 |
2022-12-27 | Stabilization of the Kawahara-Kadomtsev-Petviashvili equation with time-delayed feedback | Results of stabilization for the higher order of the Kadomtsev-Petviashvili
equation are presented in this manuscript. Precisely, we prove with two
different approaches that under the presence of a damping mechanism and an
internal delay term (anti-damping) the solutions of the
Kawahara-Kadomtsev-Petviashvili equation are locally and globally exponentially
stable. The main novelty is that we present the optimal constant, as well as
the minimal time, that ensures that the energy associated with this system goes
to zero exponentially. | 2212.13552v1 |
2014-10-20 | Frequency-dependent attenuation and elasticity in unconsolidated earth materials: effect of damping | We use the Discrete Element Method (DEM) to understand the underlying
attenuation mechanism in granular media, with special applicability to the
measurements of the so-called effective mass developed earlier. We consider
that the particles interact via Hertz-Mindlin elastic contact forces and that
the damping is describable as a force proportional to the velocity difference
of contacting grains. We determine the behavior of the complex-valued normal
mode frequencies using 1) DEM, 2) direct diagonalization of the relevant
matrix, and 3) a numerical search for the zeros of the relevant determinant.
All three methods are in strong agreement with each other. The real and the
imaginary parts of each normal mode frequency characterize the elastic and the
dissipative properties, respectively, of the granular medium. We demonstrate
that, as the interparticle damping, $\xi$, increases, the normal modes exhibit
nearly circular trajectories in the complex frequency plane and that for a
given value of $\xi$ they all lie on or near a circle of radius $R$ centered on
the point $-iR$ in the complex plane, where $R\propto 1/\xi$. We show that each
normal mode becomes critically damped at a value of the damping parameter $\xi
\approx 1/\omega_n^0$, where $\omega_n^0$ is the (real-valued) frequency when
there is no damping. The strong indication is that these conclusions carry over
to the properties of real granular media whose dissipation is dominated by the
relative motion of contacting grains. For example, compressional or shear waves
in unconsolidated dry sediments can be expected to become overdamped beyond a
critical frequency, depending upon the strength of the intergranular damping
constant. | 1410.5484v2 |
2004-04-15 | Is the slope of the intrinsic Baldwin effect constant? | We investigate the relationship between emission-line strength and continuum
luminosity in the best-studied nearby Seyfert 1 galaxy NGC5548. Our analysis of
13 years of ground-based optical monitoring data reveals significant
year-to-year variations in the observed H-beta emission-line response in this
source. More specifically, we confirm the result of Gilbert and Peterson (2003)
of a non-linear relationship between the continuum and H-beta emission-line
fluxes. Furthermore, we show that the slope of this relation is not constant,
but rather decreases as the continuum flux increases. Both effects are
consistent with photoionisation model predictions of a luminosity-dependent
response in this line. | 0404296v1 |
1993-04-01 | Wavelet transforms versus Fourier transforms | This note is a very basic introduction to wavelets. It starts with an
orthogonal basis of piecewise constant functions, constructed by dilation and
translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients
with respect to this basis. The mathematics is simple and the transform is fast
(faster than the Fast Fourier Transform, which we briefly explain), but
approximation by piecewise constants is poor. To improve this first wavelet, we
are led to dilation equations and their unusual solutions. Higher-order
wavelets are constructed, and it is surprisingly quick to compute with them ---
always indirectly and recursively. We comment informally on the contest between
these transforms in signal processing, especially for video and image
compression (including high-definition television). So far the Fourier
Transform --- or its 8 by 8 windowed version, the Discrete Cosine Transform ---
is often chosen. But wavelets are already competitive, and they are ahead for
fingerprints. We present a sample of this developing theory. | 9304214v1 |
2011-02-14 | Computing the Ball Size of Frequency Permutations under Chebyshev Distance | Let $S_n^\lambda$ be the set of all permutations over the multiset
$\{\overbrace{1,...,1}^{\lambda},...,\overbrace{m,...,m}^\lambda\}$ where
$n=m\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is a
subset of $S_n^\lambda$ in which every two elements have distance at least $d$.
FPAs have many applications related to error correcting codes. In coding
theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived
from the size of balls of certain radii. We propose two efficient algorithms
that compute the ball size of frequency permutations under Chebyshev distance.
Both methods extend previous known results. The first one runs in $O({2d\lambda
\choose d\lambda}^{2.376}\log n)$ time and $O({2d\lambda \choose
d\lambda}^{2})$ space. The second one runs in $O({2d\lambda \choose
d\lambda}{d\lambda+\lambda\choose \lambda}\frac{n}{\lambda})$ time and
$O({2d\lambda \choose d\lambda})$ space. For small constants $\lambda$ and $d$,
both are efficient in time and use constant storage space. | 1102.2799v2 |
2011-07-02 | Energy dissipation and switching delay in spin-transfer torque switching of nanomagnets with low-saturation magnetization in the presence of thermal fluctuations | A common ploy to reduce the switching current and energy dissipation in
spin-transfer-torque driven magnetization switching of shape-anisotropic
single-domain nanomagnets is to employ magnets with low saturation
magnetization $M_s$ and high shape-anisotropy. The high shape-anisotropy
compensates for low $M_s$ to keep the static switching error rate constant.
However, this ploy increases the switching delay, its variance in the presence
of thermal noise, and the dynamic switching error rate. Using the stochastic
Landau-Lifshitz-Gilbert equation with a random torque emulating thermal noise,
we show that pumping some excess spin-polarized current into the nanomagnet
during switching will keep the mean switching delay and its variance constant
as we reduce $M_s$, while still reducing the energy dissipation significantly. | 1107.0387v2 |
2015-08-11 | Analysis of a coupled spin drift-diffusion Maxwell-Landau-Lifshitz system | The existence of global weak solutions to a coupled spin drift-diffusion and
Maxwell-Landau-Lifshitz system is proved. The equations are considered in a
two-dimensional magnetic layer structure and are supplemented with
Dirichlet-Neumann boundary conditions. The spin drift-diffusion model for the
charge density and spin density vector is the diffusion limit of a spinorial
Boltzmann equation for a vanishing spin polarization constant. The
Maxwell-Landau-Lifshitz system consists of the time-dependent Maxwell equations
for the electric and magnetic fields and of the Landau-Lifshitz-Gilbert
equation for the local magnetization, involving the interaction between
magnetization and spin density vector. The existence proof is based on a
regularization procedure, $L^2$-type estimates, and Moser-type iterations which
yield the boundedness of the charge and spin densities. Furthermore, the free
energy is shown to be nonincreasing in time if the magnetization-spin
interaction constant in the Landau-Lifshitz equation is sufficiently small. | 1508.02660v1 |
2015-08-16 | The Computational Power of Beeps | In this paper, we study the quantity of computational resources (state
machine states and/or probabilistic transition precision) needed to solve
specific problems in a single hop network where nodes communicate using only
beeps. We begin by focusing on randomized leader election. We prove a lower
bound on the states required to solve this problem with a given error bound,
probability precision, and (when relevant) network size lower bound. We then
show the bound tight with a matching upper bound. Noting that our optimal upper
bound is slow, we describe two faster algorithms that trade some state
optimality to gain efficiency. We then turn our attention to more general
classes of problems by proving that once you have enough states to solve leader
election with a given error bound, you have (within constant factors) enough
states to simulate correctly, with this same error bound, a logspace TM with a
constant number of unary input tapes: allowing you to solve a large and
expressive set of problems. These results identify a key simplicity threshold
beyond which useful distributed computation is possible in the beeping model. | 1508.03859v1 |
2016-05-04 | Asymptotic behaviors of Landau-Lifshitz flows from $\Bbb R^2$ to Kähler manifolds | In this paper, we study the asymptotic behaviors of finite energy solutions
to the Landau-Lifshitz flows from $\Bbb R^2$ into K\"ahler manifolds. First, we
prove that the solution with initial data below the critical energy converges
to a constant map in the energy space as $t\to \infty$ for the compact
Riemannian surface targets. In particular, when the target is a two dimensional
sphere, we prove that the solution to the Landau-Lifshitz-Gilbert equation with
initial data having an energy below $4\pi$ converges to some constant map in
the energy space. Second, for general compact K\"ahler manifolds and initial
data of an arbitrary finite energy, we obtain a bubbling theorem analogous to
the Struwe's results on the heat flows. | 1605.01245v2 |
2018-07-30 | Graphs admitting only constant splines | We study {\em generalized graph splines,} introduced by Gilbert, Viel, and
the last author. For a large class of rings, we characterize the graphs that
only admit constant splines. To do this, we prove that if a graph has a
particular type of cutset (e.g., a bridge), then the space of splines naturally
decomposes as a certain direct sum of submodules. As an application, we use
these results to describe splines on a triangulation studied by Zhou and Lai,
but over a different ring than they used. | 1807.11515v2 |
2017-06-11 | Local List Recovery of High-rate Tensor Codes and Applications | In this work, we give the first construction of high-rate locally
list-recoverable codes. List-recovery has been an extremely useful building
block in coding theory, and our motivation is to use these codes as such a
building block. In particular, our construction gives the first
capacity-achieving locally list-decodable codes (over constant-sized alphabet);
the first capacity achieving globally list-decodable codes with nearly linear
time list decoding algorithm (once more, over constant-sized alphabet); and a
randomized construction of binary codes on the Gilbert-Varshamov bound that can
be uniquely decoded in near-linear-time, with higher rate than was previously
known.
Our techniques are actually quite simple, and are inspired by an approach of
Gopalan, Guruswami, and Raghavendra (Siam Journal on Computing, 2011) for
list-decoding tensor codes. We show that tensor powers of (globally)
list-recoverable codes are "approximately" locally list-recoverable, and that
the "approximately" modifier may be removed by pre-encoding the message with a
suitable locally decodable code. Instantiating this with known constructions of
high-rate globally list-recoverable codes and high-rate locally decodable codes
finishes the construction. | 1706.03383v1 |
2021-04-06 | Diffusion of a magnetic skyrmion in 2-dimensional space | Two-dimensional magnetic skyrmions are particle-like magnetic domains in
magnetic thin films. The kinetic property of the magnetic skyrmions at finite
temperature is well described by the Thiele equation, including a stochastic
field and a finite mass. In this paper, the validity of the constant-mass
approximation is examined by comparing the Fourier spectrum of Brownian motions
described by the Thiele equation and the Landau-Lifshitz-Gilbert equation.
Then, the 4-dimensional Fokker-Planck equation is derived from the Thiele
equation with a mass-term. Consequently, an expression of the diffusion flow
and diffusion constant in a tensor form is derived, extending Chandrasekhar's
method for Thiele dynamics. | 2104.02345v2 |
2019-02-13 | Dynamics of ferromagnetic domain walls under extreme fields | We report the existence of a new regime for domain wall motion in uniaxial
and near-uniaxial ferromagnetic nanowires, characterised by applied magnetic
fields sufficiently strong that one of the domains becomes unstable. There
appears a new stable solution of the Landau-Lifshitz-Gilbert equation,
describing a nonplanar domain wall moving with constant velocity and precessing
with constant frequency. Even in the presence of thermal noise, the new
solution can propagate for distances on the order of 500 times the field-free
domain wall width before fluctuations in the unstable domain become
appreciable. | 1902.04968v3 |
2018-10-29 | A Graceful Exit for the Cosmological Constant Damping Scenario | We present a broad and simple class of scalar-tensor scenarios that
successfully realize dynamical damping of the effective cosmological constant,
therefore providing a viable dynamical solution to the fine-tuning or "old"
cosmological constant problem. In contrast to early versions of this approach,
pioneered in the works of A. Dolgov in the 1980es, these do not suffer from
unacceptable variations of Newton's constant, as one aims at a small but
strictly positive (rather than zero) late-time curvature. In our approach, the
original fine-tuning issue is traded for a hierarchy of couplings, and we
further suggest a way to naturally generate this hierarchy based on fermion
condensation and softly broken field shift symmetry. | 1810.12336v2 |
2018-09-13 | Active Damping of a DC Network with a Constant Power Load: An Adaptive Passivity-based Control Approach | This paper proposes a nonlinear, adaptive controller to increase the
stability margin of a direct-current (DC) small-scale electrical network
containing a constant power load, whose value is unknown. Due to their negative
incremental impedance, constant power loads are known to reduce the effective
damping of a network, leading to voltage oscillations and even to network
collapse. To tackle this problem, we consider the incorporation of a controlled
DC-DC power converter between the feeder and the constant power load. The
design of the control law for the converter is based on the use of standard
Passivity-Based Control and Immersion and Invariance theories. The good
performance of the controller is evaluated with numerical simulations. | 1809.04920v1 |
2020-10-01 | Avoiding coherent errors with rotated concatenated stabilizer codes | Coherent errors, which arise from collective couplings, are a dominant form
of noise in many realistic quantum systems, and are more damaging than oft
considered stochastic errors. Here, we propose integrating stabilizer codes
with constant-excitation codes by code concatenation. Namely, by concatenating
an $[[n,k,d]]$ stabilizer outer code with dual-rail inner codes, we obtain a
$[[2n,k,d]]$ constant-excitation code immune from coherent phase errors and
also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer
code is fault-tolerant, the constant-excitation code has a positive
fault-tolerant threshold against stochastic errors. Setting the outer code as a
four-qubit amplitude damping code yields an eight-qubit constant-excitation
code that corrects a single amplitude damping error, and we analyze this code's
potential as a quantum memory. | 2010.00538v2 |
1995-05-17 | GRAVITATIONAL LENSING OF QUASARS BY THEIR DAMPED LYMAN-ALPHA ABSORBERS | Damped Lyman-alpha absorbers are believed to be associated with galactic
disks. We show that gravitational lensing can therefore affect the statistics
of these systems. First, the magnification bias due to lensing raises faint
QSOs above a given magnitude threshold and thereby enhances the probability for
observing damped absorption systems. Second, the bending of light rays from the
source effectively limits the minimum impact parameter of the line-of-sight
relative to the center of the absorber, thus providing an upper cut-off to the
observed neutral hydrogen (HI) column density. The combination of these effects
yields a pronounced peak in the observed abundance of absorbers with high
column densities (>2*10^{21} cm^{-2}) and low redshifts (z<1). The inferred
value of the cosmological density parameter of neutral hydrogen, Omega_{HI},
increases with increasing redshift and luminosity of the sources even if the
true HI density remains constant. This trend resembles the observed evolution
of Omega_{HI}(z). Damped Lyman-alpha absorbers with column densities >10^{21}
cm^{-2} and redshifts 0.5<z<1 are reliable flags for lensed QSOs with a close
pair of images separated by 0.3 arcsec. Detection of these gravitational
lensing signatures with the Hubble Space Telescope can be used to constrain the
depth of the absorber potential-wells and the cosmological constant. | 9505078v1 |
2000-06-01 | Crust-core coupling and r-mode damping in neutron stars: a toy model | R-modes in neutron stars with crusts are damped by viscous friction at the
crust-core boundary. The magnitude of this damping, evaluated by Bildsten and
Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the
maximum spin frequency for a neutron star spun up by accretion in a Low-Mass
X-ray binary (LMXB). In this paper we explore the mechanical coupling between
the core r-modes and the elastic crust, using a toy model of a constant density
neutron star with a constant shear modulus crust. We find that, at spin
frequencies in excess of ~50 Hz, the r-modes strongly penetrate the crust. This
reduces the relative motion (slippage) between the crust and the core compared
to the rigid crust limit. We therefore revise down, by as much as a factor of
10^2-10^3, the damping rate computed by BU, significantly reducing the maximal
possible spin frequency of neutron star with a solid crust. The dependence of
the crust-core slippage on the spin frequency is complicated, and is very
sensitive to the physical thickness of the crust. If the crust is sufficiently
thick, the curve of the critical spin frequency for the onset of the r-mode
instability becomes multi-valued for some temperatures; this is related to the
avoided crossings between the r-mode and the higher-order torsional modes in
the crust. The critical frequencies are comparable to the observed spins of
neutron stars in LMXBs and millisecond pulsars. | 0006028v1 |
2006-06-15 | Purity and decoherence in the theory of a damped harmonic oscillator | For the generalized master equations derived by Karrlein and Grabert for the
microscopic model of a damped harmonic oscillator, the conditions for purity of
states are written, in particular for different initial conditions and
different types of damping, including Ohmic, Drude and weak coupling cases,
Agarwal and Weidlich-Haake models. It is shown that the states which remain
pure are the squeezed states with constant in time variances. For pure states,
the generalized nonlinear Schr\" odinger-type equations corresponding to these
master equations are also obtained. Then the condition for purity of states of
a damped harmonic oscillator is considered in the framework of Lindblad theory
for open quantum systems. For a special choice of the environment coefficients,
the correlated coherent states with constant variances and covariance are shown
to be the only states which remain pure all the time during the evolution of
the considered system. In Karrlein-Grabert and Lindblad models, as well as in
the considered particular models, the expressions of the rate of entropy
production is written and it is shown that the states which preserve their
purity in time are also the states which minimize the entropy production and,
therefore, they are the most stable ones under evolution in the presence of the
environment and play an important role in the description of decoherence
phenomenon. | 0606134v1 |
2016-11-28 | First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO | Interferometric gravitational wave detectors operate with high optical power
in their arms in order to achieve high shot-noise limited strain sensitivity. A
significant limitation to increasing the optical power is the phenomenon of
three-mode parametric instabilities, in which the laser field in the arm
cavities is scattered into higher order optical modes by acoustic modes of the
cavity mirrors. The optical modes can further drive the acoustic modes via
radiation pressure, potentially producing an exponential buildup. One proposed
technique to stabilize parametric instability is active damping of acoustic
modes. We report here the first demonstration of damping a parametrically
unstable mode using active feedback forces on the cavity mirror. A 15,538 Hz
mode that grew exponentially with a time constant of 182 sec was damped using
electro-static actuation, with a resulting decay time constant of 23 sec. An
average control force of 0.03 nNrms was required to maintain the acoustic mode
at its minimum amplitude. | 1611.08997v1 |
2012-10-02 | Coherence and Stimulated Emission in the Tavis-Cummings Model: A Quantum Description of the Free Induction Signal and Radiation Damping in Magnetic Resonance | We numerically solve the Liouville equation for the Tavis Cummings model of
multiple spins coupled to a lossless single mode cavity, starting from an
initial condition with small numbers of fully polarized spins tipped by a
specified angle, and the cavity in its ground Fock state. Time evolution of the
magnetizations and cavity states, following small to medium nutation by a
classical field, yields a microscopic quantum mechanical picture of radiation
damping in magnetic resonance, and the formation of the free induction signal,
that is, the transfer of Zeeman energy, via spin coherence, to cavity
coherence. Although the motion of the Bloch vector is nonclassical, our quantum
description is related to the macroscopic picture of NMR reception, by showing
the close relationship between the usual radiation damping constant, and the
quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and
stimulated emission.) That is, each is the product, of a nutation rate per
oscillator current, and a current. Although the current in the damping constant
is explicitly limited by cavity losses, which do not enter the formula for the
Rabi frequency, we nonetheless show (in an appendix) how these losses can be
introduced into our problem by means of a master equation. Numerical solution
of the classical Bloch-Kirchhoff equations reinforces the conclusion that the
strength of the free induction | 1210.0868v2 |
2021-07-28 | Evolution of a Mode of Oscillation Within Turbulent Accretion Disks | We investigate the effects of subsonic turbulence on a normal mode of
oscillation [a possible origin of the high-frequency quasi-periodic
oscillations (HFQPOs) within some black hole accretion disks]. We consider
perturbations of a time-dependent background (steady state disk plus
turbulence), obtaining an oscillator equation with stochastic damping, (mildly)
nonlinear restoring, and stochastic driving forces. The (long-term) mean values
of our turbulent functions vanish. In particular, turbulence does not damp the
oscillation modes, so `turbulent viscosity' is not operative. However, the
frequency components of the turbulent driving force near that of the mode can
produce significant changes in the amplitude of the mode. Even with an
additional (phenomenological constant) source of damping, this leads to an
eventual `blowout' (onset of effects of nonlinearity) if the turbulence is
sufficiently strong or the damping constant is sufficiently small. The
infrequent large increases in the energy of the mode could be related to the
observed low duty cycles of the HFQPOs. The width of the peak in the power
spectral density (PSD) is proportional to the amount of nonlinearity. A
comparison with observed continuum PSDs indicates the conditions required for
visibility of the mode. | 2107.13546v1 |
2001-02-06 | Decay of cosmological constant as Bose condensate evaporation | We consider the process of decay of symmetric vacuum state as evaporation of
a Bose condensate of physical Higgs particles, defined over asymmetric vacuum
state. Energy density of their selfinteraction is identified with cosmological
constant $\Lambda$ in the Einstein equation. $\Lambda$ decay then provides
dynamical realization of spontaneous symmetry breaking. The effective mechanism
is found for damping of coherent oscillations of a scalar field, leading to
slow evaporation regime as the effective mechanism for $\Lambda$ decay
responsible for inflation without special fine-tuning of the microphysical
parameters. This mechanism is able to incorporate reheating, generation of
proper primordial fluctuations, and nonzero cosmological constant today. | 0102094v2 |
2003-07-12 | Time-variability of the fine-structure constant expected from the Oklo constraint and the QSO absorption lines | The data from the QSO absorption lines indicating a nonzero time-variability
of the fine-structure constant has been re-analyzed on the basis of a
"damped-oscillator" fit, as motivated by the same type of behavior of a scalar
field, dilaton, which mimics a cosmological constant to understand the
accelerating universe. We find nearly as good fit to the latest data as the
simple weighted mean. In this way, we offer a way to fit the more stringent
result from the Oklo phenomenon, as well. | 0307263v2 |
1996-01-30 | Role of a "Local" Cosmological Constant in Euclidean Quantum Gravity | In 4D non-perturbative Regge calculus a positive value of the effective
cosmological constant characterizes the collapsed phase of the system. If a
local term of the form $S'=\sum_{h \epsilon \{h_1,h_2,...\} } \lambda_h V_h$ is
added to the gravitational action, where $\{h_1,h_2,...\}$ is a subset of the
hinges and $\{\lambda_h\}$ are positive constants, one expects that the volumes
$V_{h_1}$, $V_{h_2}$, ... tend to collapse and that the excitations of the
lattice propagating through the hinges $\{h_1,h_2,...\}$ are damped. We study
the continuum analogue of this effect. The additional term $S'$ may represent
the coupling of the gravitational field to an external Bose condensate. | 9601160v1 |
1999-07-12 | General considerations of the cosmological constant and the stabilization of moduli in the brane-world picture | We argue that the brane-world picture with matter-fields confined to 4-d
domain walls and with gravitational interactions across the bulk disallows
adding an arbitrary constant to the low-energy, 4-d effective theory -- which
finesses the usual cosmological constant problem. The analysis also points to
difficulties in stabilizing moduli fields; as an alternative, we suggest
scenarios in which the moduli motion is heavily damped by various cosmological
mechanisms and varying ultra-slowly with time. | 9907080v1 |
2007-06-03 | A class of series acceleration formulae for Catalan's constant | In this note, we develop transformation formulae and expansions for the log
tangent integral, which are then used to derive series acceleration formulae
for certain values of Dirichlet L-functions, such as Catalan's constant. The
formulae are characterized by the presence of an infinite series whose general
term consists of a linear recurrence damped by the central binomial coefficient
and a certain quadratic polynomial. Typically, the series can be expressed in
closed form as a rational linear combination of Catalan's constant and pi times
the logarithm of an algebraic unit. | 0706.0356v1 |
2022-09-21 | Performance enhancement of a spin-wave-based reservoir computing system utilizing different physical conditions | The authors have numerically studied how to enhance reservoir computing
performance by thoroughly extracting their spin-wave device potential for
higher-dimensional information generation. The reservoir device has a 1-input
exciter and 120-output detectors on the top of a continuous magnetic garnet
film for spin-wave transmission. For various nonlinear and fading-memory
dynamic phenomena distributing in the film space, small in-plane magnetic
fields were used to prepare stripe domain structures and various damping
constants at the film sides and bottom were explored. The ferromagnetic
resonant frequency and relaxation time of spin precession clearly characterized
the change in spin dynamics with the magnetic field and damping constant. The
common input signal for reservoir computing was a 1 GHz cosine wave with random
6-valued amplitude modulation. A basic 120-dimensional reservoir output vector
was obtained from time-series signals at the 120 output detectors under each of
the three magnetic field conditions. Then, 240- and 360-dimensional reservoir
output vectors were also constructed by concatenating two and three basic ones,
respectively. In nonlinear autoregressive moving average (NARMA) prediction
tasks, the computational performance was enhanced as the dimension of the
reservoir output vector becomes higher and a significantly low prediction error
was achieved for the 10th-order NARMA using the 360-dimensional vector and
optimum damping constant. The results are clear evidence that the collection of
diverse output signals efficiently increases the dimensionality effective for
reservoir computing, i.e., reservoir-state richness. This paper demonstrates
that performance enhancement through various configuration settings is a
practical approach for on-chip reservoir computing devices with small numbers
of real output nodes. | 2209.10123v1 |
2008-12-31 | Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation | The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative
space-dependent noise is considered for a ferromagnet filling a bounded
three-dimensional domain. We show the existence of weak martingale solutions
taking values in a sphere $\mathbb S^2$. The regularity of weak solutions is
also discussed. Some of the regularity results are new even for the
deterministic Landau-Lifshitz-Gilbert equation. | 0901.0039v1 |
2023-09-08 | Branching points in the planar Gilbert--Steiner problem have degree 3 | Gilbert--Steiner problem is a generalization of the Steiner tree problem on a
specific optimal mass transportation.
We show that every branching point in a solution of the planar
Gilbert--Steiner problem has degree 3. | 2309.04202v2 |
2000-06-09 | Random values of the cosmological constant | One way that an anthropic selection mechanism may be manifest in a physical
theory involves multiple domains in the universe with different values of the
physical parameters. If this mechanism is to be relevant for understanding the
small observed value of the cosmological constant, it may involve a mechanism
by which some contributions to the cosmological constant can be fixed at a
continuous range of values in the different domains. I study the properties of
four possible mechanisms, including the possibility of the Hubble damping of a
scalar field with an extremely flat potential. Another interesting possibility
involves fixed random values of non-dynamical form fields, and a cosmological
mechanism is suggested. This case raises the possibility of anthropic selection
of other parameters in addition. Further requirements needed for a consistent
cosmology are discussed. | 0006088v2 |
2013-05-11 | Dividing Line between Quantum and Classical Trajectories: Bohmian Time Constant | This work proposes an answer to a challenge posed by Bell on the lack of
clarity in regards to the line between the quantum and classical regimes in a
measurement problem. To this end, a generalized logarithmic nonlinear
Schr\"odinger equation is proposed to describe the time evolution of a quantum
dissipative system under continuous measurement. Within the Bohmian mechanics
framework, a solution to this equation reveals a novel result: it displays a
time constant which should represent the dividing line between the quantum and
classical trajectories. It is shown that continuous measurements and damping
not only disturb the particle but compel the system to converge in time to a
Newtonian regime. While the width of the wave packet may reach a stationary
regime, its quantum trajectories converge exponentially in time to classical
trajectories. In particular, it is shown that damping tends to suppress further
quantum effects on a time scale shorter than the relaxation time of the system.
If the initial wave packet width is taken to be equal to 2.8 10^{-15} m (the
approximate size of an electron), the Bohmian time constant is found to have an
upper limit, i. e., ${\tau_{B\max}} = {10^{- 26}}s$. | 1305.2517v2 |
2014-08-20 | Building accurate initial models using gain functions for waveform inversion in the Laplace domain | We suggest an initial model building technique using time gain functions in
the Laplace domain. Applying the gain expressed as a power of time is
equivalent to taking the partial derivative of the Laplace-domain wavefield
with respect to a damping constant. We construct an objective function, which
minimizes the logarithmic differences between the gained field data and the
partial derivative of the modeled data with respect to the damping constant. We
calculate the modeled wavefield, the partial derivative wavefield, and the
gradient direction in the Laplace domain using the analytic Green's function
starting from a constant velocity model. This is an efficient method to
generate an accurate initial model for a following Laplace-domain inversion.
Numerical examples using two marine field datasets confirm that a starting
model updated once from a scratch using the gradient direction calculated with
the proposed method can be successfully used for a subsequent Laplace-domain
inversion. | 1408.5872v1 |
1995-10-16 | Star Formation and Chemical Evolution in Damped Lya Clouds | Using the redshift evolution of the neutral hydrogen density, as inferred
from observations of damped Ly$\alpha$ clouds, we calculate the evolution of
star formation rates and elemental abundances in the universe. For most
observables our calculations are in rough agreement with previous results based
on the instantaneous re-cycling approximation (IRA). However, for the key
metallicity tracer Zn, we find a better match to the observed abundance at high
redshift than that given by the constant-yield IRA model. We investigate
whether the redshift evolution of deuterium, depressions in the diffuse
extragalactic gamma-ray background, and measurement of the MeV neutrino
background may help determine if observational bias due to dust obscuration is
important. We also indicate how the importance of dust on the calculations can
be significantly reduced if correlations of the HI column density with
metallicity are present. The possibilities for measuring $q_o$ with
observations of elemental abundances in damped Ly$\alpha$ systems are
discussed. | 9510078v1 |
2003-03-27 | Oscillatory wave fronts in chains of coupled nonlinear oscillators | Wave front pinning and propagation in damped chains of coupled oscillators
are studied. There are two important thresholds for an applied constant stress
$F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate,
for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and
for $|F| > F_{cs}$ (static Peierls stress) there are only stable moving wave
fronts. For piecewise linear models, extending an exact method of Atkinson and
Cabrera's to chains with damped dynamics corroborates this description. For
smooth nonlinearities, an approximate analytical description is found by means
of the active point theory. Generically for small or zero damping, stable wave
front profiles are non-monotone and become wavy (oscillatory) in one of their
tails. | 0303576v1 |
2003-07-22 | Classical dynamics of a nano-mechanical resonator coupled to a single-electron transistor | We analyze the dynamics of a nano-mechanical resonator coupled to a
single-electron transistor (SET) in the regime where the resonator behaves
classically. A master equation is derived describing the dynamics of the
coupled system which is then used to obtain equations of motion for the average
charge state of the SET and the average position of the resonator. We show that
the action of the SET on the resonator is very similar to that of a thermal
bath, as it leads to a steady-state probability-distribution for the resonator
which can be described by mean values of the resonator position, a renormalized
frequency, an effective temperature and an intrinsic damping constant.
Including the effects of extrinsic damping and finite temperature, we find that
there remain experimentally accessible regimes where the intrinsic damping of
the resonator still dominates its behavior. We also obtain the average current
through the SET as a function of the coupling to the resonator. | 0307528v1 |
2006-05-16 | Collective mode damping and viscosity in a 1D unitary Fermi gas | We calculate the damping of the Bogoliubov-Anderson mode in a one-dimensional
two-component attractive Fermi gas for arbitrary coupling strength within a
quantum hydrodynamic approach. Using the Bethe-Ansatz solution of the 1D
BCS-BEC crossover problem, we derive analytic results for the viscosity
covering the full range from a Luther-Emery liquid of weakly bound pairs to a
Lieb-Liniger gas of strongly bound bosonic dimers. At the unitarity point, the
system is a Tonks-Girardeau gas with a universal constant $\alpha_{\zeta}=0.38$
in the viscosity $\zeta=\alpha_{\zeta}\hbar n$ for T=0. For the trapped case,
we calculate the Q-factor of the breathing mode and show that the damping
provides a sensitive measure of temperature in 1D Fermi gases. | 0605413v2 |
1996-03-14 | Dissipation and Topologically Massive Gauge Theories in Pseudoeuclidean Plane | In the pseudo-euclidean metrics Chern-Simons gauge theory in the infrared
region is found to be associated with dissipative dynamics. In the infrared
limit the Lagrangian of 2+1 dimensional pseudo-euclidean topologically massive
electrodynamics has indeed the same form of the Lagrangian of the damped
harmonic oscillator. On the hyperbolic plane a set of two damped harmonic
oscillators, each other time-reversed, is shown to be equivalent to a single
undamped harmonic oscillator. The equations for the damped oscillators are
proven to be the same as the ones for the Lorentz force acting on two particles
carrying opposite charge in a constant magnetic field and in the electric
harmonic potential. This provides an immediate link with Chern-Simons-like
dynamics of Bloch electrons in solids propagating along the lattice plane with
hyperbolic energy surface. The symplectic structure of the reduced theory is
finally discussed in the Dirac constrained canonical formalism. | 9603092v1 |
2002-02-12 | Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves | We study the nonlinear energy transfer around the peak of the spectrum of
surface gravity waves by taking into account nonhomogeneous effects. In the
narrow-banded approximation the kinetic equation resulting from a
nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at
the same time the random version of the Benjamin-Feir instability and the
Landau damping phenomenon. We analytically derive the values of the Phillips'
constant $\alpha$ and the enhancement factor $\gamma$ for which the
narrow-banded approximation of the JONSWAP spectrum is unstable. By performing
numerical simulations of the nonlinear Schr\"{o}dinger equation we check the
validity of the prediction of the related kinetic equation. We find that the
effect of Landau damping is to suppress the formation of coherent structures.
The problem of predicting freak waves is briefly discussed. | 0202026v1 |
2006-07-31 | Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions | We study the Landau-Zener Problem for a decaying two-level-system described
by a non-hermitean Hamiltonian, depending analytically on time. Use of a
super-adiabatic basis allows to calculate the non-adiabatic transition
probability P in the slow-sweep limit, without specifying the Hamiltonian
explicitly. It is found that P consists of a ``dynamical'' and a
``geometrical'' factors. The former is determined by the complex adiabatic
eigenvalues E_(t), only, whereas the latter solely requires the knowledge of
\alpha_(+-)(t), the ratio of the components of each of the adiabatic
eigenstates. Both factors can be split into a universal one, depending only on
the complex level crossing points, and a nonuniversal one, involving the full
time dependence of E_(+-)(t). This general result is applied to the
Akulin-Schleich model where the initial upper level is damped with damping
constant $\gamma$. For analytic power-law sweeps we find that Stueckelberg
oscillations of P exist for gamma smaller than a critical value gamma_c and
disappear for gamma > gamma_c. A physical interpretation of this behavior will
be presented by use of a damped harmonic oscillator. | 0607221v1 |
2007-06-01 | The geometrical quantity in damped wave equations on a square | The energy in a square membrane $\Omega$ subject to constant viscous damping
on a subset $\omega\subset \Omega$ decays exponentially in time as soon as
$\omega$ satisfies a geometrical condition known as the "Bardos-Lebeau-Rauch"
condition. The rate $\tau(\omega)$ of this decay satisfies $\tau(\omega)= 2
\min(-\mu(\omega), g(\omega))$ (see Lebeau [Math. Phys. Stud. 19 (1996)
73-109]). Here $\mu(\omega)$ denotes the spectral abscissa of the damped wave
equation operator and $g(\omega)$ is a number called the geometrical quantity
of $\omega$ and defined as follows. A ray in $\Omega$ is the trajectory
generated by the free motion of a mass-point in $\Omega$ subject to elastic
reflections on the boundary. These reflections obey the law of geometrical
optics. The geometrical quantity $g(\omega)$ is then defined as the upper limit
(large time asymptotics) of the average trajectory length. We give here an
algorithm to compute explicitly $g(\omega)$ when $\omega$ is a finite union of
squares. | 0706.0172v1 |
2009-10-14 | Constraint on the growth factor of the cosmic structure from the damping of the baryon acoustic oscillation signature | We determine a constraint on the growth factor by measuring the damping of
the baryon acoustic oscillations in the matter power spectrum using the Sloan
Digital Sky Survey luminous red galaxy sample. The damping of the BAO is
detected at the one sigma level. We obtain \sigma_8D_1(z=0.3) =
0.42^{+0.34}_{-0.28} at the 1\sigma statistical level, where \sigma_8 is the
root mean square overdensity in a sphere of radius 8h^{-1}Mpc and D_1(z) is the
growth factor at redshift z. The above result assumes that other parameters are
fixed and the cosmology is taken to be a spatially flat cold dark matter
universe with the cosmological constant. | 0910.2513v1 |
2011-02-04 | A symmetry trip from Caldirola to Bateman damped systems | For the Caldirola-Kanai system, describing a quantum damped harmonic
oscillator, a couple of constant-of-motion operators generating the Heisenberg
algebra can be found. The inclusion of the standard time evolution symmetry in
this algebra for damped systems, in a unitary manner, requires a non-trivial
extension of this basic algebra and hence the physical system itself.
Surprisingly, this extension leads directly to the so-called Bateman's dual
system, which now includes a new particle acting as an energy reservoir. The
group of symmetries of the dual system is presented, as well as a quantization
that implies, in particular, a first-order Schr\"odinger equation. The usual
second-order equation and the inclusion of the original Caldirola-Kanai model
in Bateman's system are also discussed. | 1102.0990v1 |
2011-03-08 | Steady states of the parametric rotator and pendulum | We discuss several steady-state rotation and oscillation modes of the planar
parametric rotator and pendulum with damping. We consider a general elliptic
trajectory of the suspension point for both rotator and pendulum, for the
latter at an arbitrary angle with gravity, with linear and circular
trajectories as particular cases. We treat the damped, non-linear equation of
motion of the parametric rotator and pendulum perturbatively for small
parametric excitation and damping, although our perturbative approach can be
extended to other regimes as well. Our treatment involves only ordinary
second-order differential equations with constant coefficients, and provides
numerically accurate perturbative solutions in terms of elementary functions.
Some of the steady-state rotation and oscillation modes studied here have not
been discussed in the previous literature. Other well-known ones, such as
parametric resonance and the inverted pendulum, are extended to elliptic
parametric excitation tilted with respect to gravity. The results presented
here should be accessible to advanced undergraduates, and of interest to
graduate students and specialists in the field of non-linear mechanics. | 1103.1413v1 |
2011-06-17 | Controlling Excitations Inversion of a Cooper Pair Box Interacting with a Nanomechanical Resonator | We investigate the action of time dependent detunings upon the excitation
inversion of a Cooper pair box interacting with a nanomechanical resonator. The
method employs the Jaynes-Cummings model with damping, assuming different decay
rates of the Cooper pair box and various fixed and t-dependent detunings. It is
shown that while the presence of damping plus constant detunings destroy the
collapse/revival effects, convenient choices of time dependent detunings allow
one to reconstruct such events in a perfect way. It is also shown that the mean
excitation of the nanomechanical resonator is more robust against damping of
the Cooper pair box for convenient values of t-dependent detunings. | 1106.3379v1 |
2011-07-24 | Traveling kinks in cubic nonlinear Ginzburg-Landau equations | Nonlinear cubic Euler-Lagrange equations of motion in the traveling variable
are usually derived from Ginzburg-Landau free energy functionals frequently
encountered in several fields of physics. Many authors considered in the past
damped versions of such equations with the damping term added by hand
simulating the friction due to the environment. It is known that even in this
damped case kink solutions can exist. By means of a factorization method, we
provide analytic formulas for several possible kink solutions of such equations
of motion in the undriven and constant field driven cases, including the
recently introduced Riccati parameter kinks which were not considered
previously in such a context. The latter parameter controls the delay of the
switching stage of the kinks | 1107.4773v4 |
2011-12-02 | An energy-based computational method in the analysis of the transmission of energy in a chain of coupled oscillators | In this paper we study the phenomenon of nonlinear supratransmission in a
semi-infinite discrete chain of coupled oscillators described by modified
sine-Gordon equations with constant external and internal damping, and subject
to harmonic external driving at the end. We develop a consistent and
conditionally stable finite-difference scheme in order to analyze the effect of
damping in the amount of energy injected in the chain of oscillators; numerical
bifurcation analyses to determine the dependence of the amplitude at which
supratransmission first occurs with respect to the frequency of the driving
oscillator are carried out in order to show the consequences of damping on
harmonic phonon quenching and the delay of appearance of critical amplitude. | 1112.0581v1 |
2014-08-25 | Spin-Scattering Rates in Metallic Thin Films Measured by Ferromagnetic Resonance Damping Enhanced by Spin-Pumping | We determined the spin-transport properties of Pd and Pt thin films by
measuring the increase in ferromagnetic resonance damping due to spin-pumping
in ferromagnetic (FM)-nonferromagnetic metal (NM) multilayers with varying NM
thicknesses. The increase in damping with NM thickness depends strongly on both
the spin- and charge-transport properties of the NM, as modeled by diffusion
equations that include both momentum- and spin-scattering parameters. We use
the analytical solution to the spin-diffusion equations to obtain
spin-diffusion lengths for Pt and Pd. By measuring the dependence of
conductivity on NM thickness, we correlate the charge- and spin-transport
parameters, and validate the applicability of various models for
momentum-scattering and spin-scattering rates in these systems: constant,
inverse-proportional (Dyakanov-Perel), and linear-proportional (Elliot-Yafet).
We confirm previous reports that the spin-scattering time can be shorter than
the momentum scattering time in Pt, and the Dyakanov-Perel-like model is the
best fit to the data. | 1408.5921v2 |
2015-04-09 | Periodic-coefficient damping estimates, and stability of large-amplitude roll waves in inclined thin film flow | A technical obstruction preventing the conclusion of nonlinear stability of
large-Froude number roll waves of the St. Venant equations for inclined thin
film flow is the "slope condition" of Johnson-Noble-Zumbrun, used to obtain
pointwise symmetrizability of the linearized equations and thereby
high-frequency resolvent bounds and a crucial H s nonlinear damping estimate.
Numerically, this condition is seen to hold for Froude numbers 2 \textless{} F
3.5, but to fail for 3.5 F. As hydraulic engineering applications typically
involve Froude number 3 F 5, this issue is indeed relevant to practical
considerations. Here, we show that the pointwise slope condition can be
replaced by an averaged version which holds always, thereby completing the
nonlinear theory in the large-F case. The analysis has potentially larger
interest as an extension to the periodic case of a type of weighted
"Kawashima-type" damping estimate introduced in the asymptotically-constant
coefficient case for the study of stability of large-amplitude viscous shock
waves. | 1504.02292v1 |
2015-05-08 | Existence and general stabilization of the Timoshenko system with a thermo-viscoelastic damping and a delay term in the internal feedback | In this paper, we consider a Timoshenko system with a thermo-viscoelastic
damping and a delay term in the internal feedback together with initial datum
and boundary conditions of Dirichlet type, where g is a positive non-increasing
relaxation function and {\mu}1, {\mu}2 are positive constants. Under an
hypothesis between the weight of the delay term in the feedback and the the
weight of the friction damping term, using the Faedo-Galerkin approximations
together with some energy estimates, we prove the global existence of the
solutions. Then, by introducing appropriate Lyapunov functionals, under the
imposed constrain on the weights of the two feedbacks and the coefficients, we
establish the general energy decay result from which the exponential and
polynomial types of decay are only special cases. | 1505.01899v1 |
2016-05-26 | Thickness and temperature dependence of the magnetodynamic damping of pulsed laser deposited $\text{La}_{0.7}\text{Sr}_{0.3}\text{MnO}_3$ on (111)-oriented SrTi$\text{O}_3$ | We have investigated the magnetodynamic properties of
$\text{La}_{0.7}\text{Sr}_{0.3}\text{MnO}_3$ (LSMO) films of thickness 10, 15
and 30 nm grown on (111)-oriented SrTi$\text{O}_3$ (STO) substrates by pulsed
laser deposition. Ferromagnetic resonance (FMR) experiments were performed in
the temperature range 100--300 K, and the magnetodynamic damping parameter
$\alpha$ was extracted as a function of both film thickness and temperature. We
found that the damping is lowest for the intermediate film thickness of 15 nm
with $\alpha \approx 2 \cdot 10^{-3}$, where $\alpha$ is relatively constant as
a function of temperature well below the Curie temperature of the respective
films. | 1605.08195v2 |
2017-08-30 | Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant | This paper is concerned with the asymptotic behavior of the solution to the
Euler equations with time-depending damping on quadrant $(x,t)\in
\mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v
-
\partial_x u=0, \qquad \partial_t u
+
\partial_x p(v)
=\displaystyle
-\frac{\alpha}{(1+t)^\lambda} u, \end{equation} with null-Dirichlet boundary
condition or null-Neumann boundary condition on $u$. We show that the
corresponding initial-boundary value problem admits a unique global smooth
solution which tends time-asymptotically to the nonlinear diffusion wave.
Compared with the previous work about Euler equations with constant coefficient
damping, studied by Nishihara and Yang (1999, J. Differential Equations, 156,
439-458), and Jiang and Zhu (2009, Discrete Contin. Dyn. Syst., 23, 887-918),
we obtain a general result when the initial perturbation belongs to the same
space. In addition, our main novelty lies in the facts that the cut-off points
of the convergence rates are different from our previous result about the
Cauchy problem. Our proof is based on the classical energy method and the
analyses of the nonlinear diffusion wave. | 1708.09127v1 |
2017-11-01 | Tunable magnetization relaxation of Fe_{2}Cr_{1-x}Co_{x}Si half-metallic Heusler alloys by band structure engineering | We report a systematic investigation on the magnetization relaxation
properties of iron-based half-metallic Heusler alloy
Fe$_{2}$Cr$_{1-x}$Co_${x}$Si (FCCS) thin films using broadband angular-resolved
ferromagnetic resonance. Band structure engineering through Co doping (x)
demonstrated by first-principles calculations is shown to tune the intrinsic
magnetic damping over an order of magnitude, namely 0.01-0.0008. Notably, the
intrinsic damping constants for samples with high Co concentration are among
the lowest reported for Heusler alloys and even comparable to magnetic
insulator yttrium iron garnet. Furthermore, a significant reduction of both
isotropic and anisotropic contributions of extrinsic damping of the FCCS alloys
was found in the FCCS films with x=0.5-0.75, which is of particular importance
for applications. These results demonstrate a practical recipe to tailor
functional magnetization for Heusler alloy-based spintronics at room
temperature | 1711.00406v1 |
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 |
2018-04-11 | 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 |
2018-12-21 | 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 |
2018-12-30 | 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 |
2017-03-28 | Singularity formation for the 1D compressible Euler equation with variable damping coefficient | In this paper, we consider some blow-up problems for the 1D Euler equation
with time and space dependent damping. We investigate sufficient conditions on
initial data and the rate of spatial or time-like decay of the coefficient of
damping for the occurrence of the finite time blow-up. In particular, our
sufficient conditions ensure that the derivative blow-up occurs in finite time
with the solution itself and the pressure bounded. Our method is based on
simple estimates with Riemann invariants. Furthermore, we give sharp lower and
upper estimates of the lifespan of solutions, when initial data are small
perturbations of constant states. | 1703.09821v3 |
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 |
2020-08-18 | Survey of 360$^{\circ}$ domain walls in magnetic heterostructures: topology, chirality and current-driven dynamics | Chirality and current-driven dynamics of topologically nontrivial
360$^{\circ}$ domain walls (360DWs) in magnetic heterostructures (MHs) are
systematically investigated. For MHs with normal substrates, the static 360DWs
are N\'{e}el-type with no chirality. While for those with heavy-metal
substrates, the interfacial Dzyaloshinskii-Moriya interaction (iDMI) therein
makes 360DWs prefer specific chirality. Under in-plane driving charge currents,
as the direct result of "full-circle" topology a certain 360DW does not undergo
the "Walker breakdown"-type process like a well-studied 180$^{\circ}$ domain
wall as the current density increases. Alternatively, it keeps a fixed
propagating mode (either steady-flow or precessional-flow, depending on the
effective damping constant of the MH) until it collapses or changes to other
types of solition when the current density becomes too high. Similarly, the
field-like spin-orbit torque (SOT) has no effects on the dynamics of 360DWs,
while the anti-damping SOT has. For both modes, modifications to the mobility
of 360DWs by iDMI and anti-damping SOT are provided. | 2008.08196v1 |
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 |
2021-11-26 | Transition from order to chaos in reduced quantum dynamics | We study a damped kicked top dynamics of a large number of qubits ($N
\rightarrow \infty$) and focus on an evolution of a reduced single-qubit
subsystem. Each subsystem is subjected to the amplitude damping channel
controlled by the damping constant $r\in [0,1]$, which plays the role of the
single control parameter. In the parameter range for which the classical
dynamics is chaotic, while varying $r$ we find the universal period-doubling
behavior characteristic to one-dimensional maps: period-two dynamics starts at
$r_1 \approx 0.3181$, while the next bifurcation occurs at $ r_2 \approx
0.5387$. In parallel with period-four oscillations observed for $r \leq r_3
\approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx
0.544$, responsible for a small-scale chaotic dynamics inside the attractor.
The doubling of the principal bifurcation tree continues until $r \leq
r_{\infty} \sim 0.578$, which marks the onset of the full scale chaos
interrupted by the windows of the oscillatory dynamics corresponding to the
Sharkovsky order. | 2111.13477v1 |
2022-01-12 | Local Well-Posedness of the Gravity-Capillary Water Waves System in the Presence of Geometry and Damping | We consider the gravity-capillary water waves problem in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features.
Namely, we consider a variable bottom, smooth obstacles in the flow and a
constant background current. We utilize a vortex sheet model introduced by
Ambrose, et. al. in arXiv:2108.01786. We show that the water waves problem is
locally-in-time well-posed in this geometric setting and study the lifespan of
solutions. We then add a damping term and derive evolution equations that
account for the damper. Ultimately, we show that the same well-posedness and
lifespan results apply to the damped system. We primarily utilize energy
methods. | 2201.04713v2 |
2023-05-09 | Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain | Lifespan estimates for semilinear damped wave equations of the form
$\partial_t^2u-\Delta u+\partial_tu=|u|^p$ in a two dimensional exterior domain
endowed with the Dirichlet boundary condition are dealt with. For the critical
case of the semilinear heat equation $\partial_tv-\Delta v=v^2$ with the
Dirichlet boundary condition and the initial condition $v(0)=\varepsilon f$,
the corresponding lifespan can be estimated from below and above by
$\exp(\exp(C\varepsilon^{-1}))$ with different constants $C$. This paper
clarifies that the same estimates hold even for the critical semilinear damped
wave equation in the exterior of the unit ball under the restriction of radial
symmetry. To achieve this result, a new technique to control $L^1$-type norm
and a new Gagliardo--Nirenberg type estimate with logarithmic weight are
introduced. | 2305.05124v1 |
2023-09-25 | Linearly implicit exponential integrators for damped Hamiltonian PDEs | Structure-preserving linearly implicit exponential integrators are
constructed for Hamiltonian partial differential equations with linear constant
damping. Linearly implicit integrators are derived by polarizing the polynomial
terms of the Hamiltonian function and portioning out the nonlinearly of
consecutive time steps. They require only a solution of one linear system at
each time step. Therefore they are computationally more advantageous than
implicit integrators. We also construct an exponential version of the
well-known one-step Kahan's method by polarizing the quadratic vector field.
These integrators are applied to one-dimensional damped Burger's,
Korteweg-de-Vries, and nonlinear Schr{\"o}dinger equations. Preservation of the
dissipation rate of linear and quadratic conformal invariants and the
Hamiltonian is illustrated by numerical experiments. | 2309.14184v2 |
2024-03-10 | Linear-in-temperature resistivity and Planckian dissipation arise in a stochastic quantization model of Cooper pairs | We suppose that a Cooper pair (CP) will experience a damping force exerted by
the condensed matter. A Langevin equation of a CP in two dimensional condensed
matter is established. Following a method similar to Nelson's stochastic
mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is
derived. If the CPs move with a constant velocity, then the corresponding
direct current (DC) electrical conductivity can be calculated. Therefore, a
Drude like formula of resistivity of CPs is derived. We suppose that the
damping coefficient of CPs in two dimensional cuprate superconductors is a
linear function of temperature. Then the resistivity and scattering rate of CPs
turn out to be also linear-in-temperature. The origin of linear-in-temperature
resistivity and Planckian dissipation in cuprate superconductors may be the
linear temperature dependence of the damping coefficient of CPs. | 2403.09710v1 |
2019-11-05 | Observation of Nanoscale Opto-Mechanical Molecular Damping; Origin of Spectroscopic Contrast in Photo Induced Force Microscopy | We experimentally investigated the contrast mechanism of infrared
photoinduced force microscopy (PiFM) for recording vibrational resonances.
Extensive experiments have demonstrated that spectroscopic contrast in PiFM is
mediated by opto-mechanical damping of the cantilever oscillation as the
optical wavelength is scanned through optical resonance. To our knowledge, this
is the first time opto-mechanical damping has been observed in the AFM. We
hypothesize that this damping force is a consequence of the dissipative
interaction between the sample and the vibrating tip; the modulated light
source in PiFM modulates the effective damping constant of the 2nd eigenmode of
the cantilever which in turn generate side-band signals producing the PiFM
signal at the 1st eigenmode. A series of experiments have eliminated other
mechanisms of contrast. By tracking the frequency shift of the PiFM signal at
the 1st cantilever eigenmode as the excitation wavenumber is tuned through a
mid-infrared absorption band, we showed that the near-field optical interaction
is attractive. By using a vibrating piezoelectric crystal to mimic sample
thermal expansion in a PiFM operating in mixing mode, we determined that the
minimum thermal expansion our system can detect is 30 pm limited by system
noise. We have confirmed that van der Waal mediated thermal-expansion forces
have negligible effect on PiFM signals by detecting the resonant response of a
4-methylbenzenethiol mono molecular layer deposited on template-stripped gold,
where thermal expansion was expected to be < 3 pm, i.e., 10 times lower than
our system noise level. Finally, the basic theory for dissipative tip-sample
interactions was introduced to model the photoinduced opto-mechanical damping.
Theoretical simulations are in excellent agreement with experiment. | 1911.05190v1 |
2024-03-28 | Constants of Motion for Conserved and Non-conserved Dynamics | This paper begins with a dynamical model that was obtained by applying a
machine learning technique (FJet) to time-series data; this dynamical model is
then analyzed with Lie symmetry techniques to obtain constants of motion. This
analysis is performed on both the conserved and non-conserved cases of the 1D
and 2D harmonic oscillators. For the 1D oscillator, constants are found in the
cases where the system is underdamped, overdamped, and critically damped. The
novel existence of such a constant for a non-conserved model is interpreted as
a manifestation of the conservation of energy of the {\em total} system (i.e.,
oscillator plus dissipative environment). For the 2D oscillator, constants are
found for the isotropic and anisotropic cases, including when the frequencies
are incommensurate; it is also generalized to arbitrary dimensions. In
addition, a constant is identified which generalizes angular momentum for all
ratios of the frequencies. The approach presented here can produce {\em
multiple} constants of motion from a {\em single}, generic data set. | 2403.19418v1 |
2003-06-30 | Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces | We study the boundedness problem for maximal operators in 3-dimensional
Euclidean space associated to hypersurfaces given as the graph of $c+f$, where
$f$ is a mixed homogeneous function which is smooth away from the origin and
$c$ is a constant. Our result generalizes a corresponding theorem on mixed
homogeneous polynomial functions by A. Iosevich and E. Sawyer. | 0306429v1 |
2005-07-26 | On simulations of the classical harmonic oscillator equation by difference equations | We show that any second order linear ordinary diffrential equation with
constant coefficients (including the damped and undumped harmonic oscillator
equation) admits an exact discretization, i.e., there exists a difference
equation whose solutions exactly coincide with solutions of the corresponding
differential equation evaluated at a discrete sequence of points (a lattice).
Such exact discretization is found for an arbitrary lattice spacing. | 0507182v1 |
2015-11-12 | Global weak solutions to 3D compressible Navier-Stokes-Poisson equations with density-dependent viscosity | Global-in-time weak solutions to the Compressible Navier-Stokes-Poisson
equations in a three-dimensional torus for large data are considered in this
paper. The system takes into account density-dependent viscosity and
non-monotone presseur. We prove the existence of global weak solutions to NSP
equations with damping term by using the Faedo-Galerkin method and the
compactness arguments on the condition that the adiabatic constant satisfies
$\gamma>\frac{4}{3}$. | 1511.03841v1 |
2017-09-24 | Exceptional points in two simple textbook examples | We propose to introduce the concept of exceptional points in intermediate
courses on mathematics and classical mechanics by means of simple textbook
examples. The first one is an ordinary second-order differential equation with
constant coefficients. The second one is the well known damped harmonic
oscillator. They enable one to connect the occurrence of linearly dependent
exponential solutions with a defective matrix that cannot be diagonalized but
can be transformed into a Jordan canonical form. | 1710.00067v1 |
2012-09-08 | Evidence for anisotropic polar nanoregions in relaxor PMN: A neutron study of the elastic constants and anomalous TA phonon damping | We use neutron scattering to characterize the acoustic phonons in the relaxor
PMN and demonstrate the presence of an anisotropic damping mechanism directly
related to short-range, polar correlations. For a large range of temperatures
above Tc ~ 210, K, where dynamic polar correlations exist, acoustic phonons
propagating along [1\bar{1}0] and polarized along [110] (TA2 phonons) are
overdamped and softened across most of the Brillouin zone. By contrast,
acoustic phonons propagating along [100] and polarized along [001] (TA1
phonons) are overdamped and softened for only a limited range of wavevectors.
The anisotropy and temperature dependence of the acoustic phonon energy
linewidth are directly correlated with the elastic diffuse scattering,
indicating that polar nanoregions are the cause of the anomalous behavior. The
damping and softening vanish for q -> 0, i.e. for long-wavelength acoustic
phonons, which supports the notion that the anomalous damping is a result of
the coupling between the relaxational component of the diffuse scattering and
the harmonic TA phonons. Therefore, these effects are not due to large changes
in the elastic constants with temperature because the elastic constants
correspond to the long-wavelength limit. We compare the elastic constants we
measure to those from Brillouin scattering and to values reported for pure PT.
We show that while the values of C44 are quite similar, those for C11 and C12
are significantly less in PMN and result in a softening of (C11-C12) over PT.
There is also an increased elastic anisotropy (2C44/(C11-C12)) versus that in
PT. These results suggest an instability to TA2 acoustic fluctuations in
relaxors. We discuss our results in the context of the debate over the
"waterfall" effect and show that they are inconsistent with TA-TO phonon
coupling or other models that invoke the presence of a second optic mode. | 1209.1736v1 |
2015-12-03 | Lieb-Thirring inequalities on the torus | We consider the Lieb-Thirring inequalities on the d-dimensional torus with
arbitrary periods. In the space of functions with zero average with respect to
the shortest coordinate we prove the Lieb-Thirring inequalities for the
$\gamma$-moments of the negative eigenvalues with constants independent of
ratio of the periods. Applications to the attractors of the damped
Navier-Stokes system are given. | 1512.01160v1 |
2021-07-21 | Convergence rates for the Heavy-Ball continuous dynamics for non-convex optimization, under Polyak-Łojasiewicz condition | We study convergence of the trajectories of the Heavy Ball dynamical system,
with constant damping coefficient, in the framework of convex and non-convex
smooth optimization. By using the Polyak-{\L}ojasiewicz condition, we derive
new linear convergence rates for the associated trajectory, in terms of
objective function values, without assuming uniqueness of the minimizer. | 2107.10123v2 |
2022-05-06 | Quaternion-based attitude stabilization via discrete-time IDA-PBC | In this paper, we propose a new sampled-data controller for stabilization of
the attitude dynamics at a desired constant configuration. The design is based
on discrete-time interconnection and damping assignment (IDA) passivity-based
control (PBC) and the recently proposed Hamiltonian representation of
discrete-time nonlinear dynamics. Approximate solutions are provided with
simulations illustrating performances. | 2205.03086v1 |
2024-04-03 | Comment on "Machine learning conservation laws from differential equations" | In lieu of abstract, first paragraph reads: Six months after the author
derived a constant of motion for a 1D damped harmonic oscillator [1], a similar
result appeared by Liu, Madhavan, and Tegmark [2, 3], without citing the
author. However, their derivation contained six serious errors, causing both
their method and result to be incorrect. In this Comment, those errors are
reviewed. | 2404.02896v1 |
1994-05-31 | The Behavior of a Spherical Hole in an Infinite Uniform Universe | In this paper, the behavior of a spherical hole in an otherwise infinite and
uniform universe is investigated. First, the Newtonian theory is developed. The
concept of negative gravity, an outward gravitational force acting away from
the center of the spherical hole, is presented, and the resulting expansion of
the hole is investigated. Then, the same result is derived using the techniques
of Einstein's theory of general relativity. The field equations are solved for
an infinite uniform universe and then for an infinite universe in which matter
is uniformly distributed except for a spherical hole. Negative pressure caused
by negative gravity is utilized. The physical significance of the cosmological
constant is explained, and a new physical concept, that of the gravitational
potential of a hole, is discussed. The relationship between the Newtonian
potential for a hole and the Schwarzschild solution of the field equations is
explored. Finally, the geodesic equations are considered. It is shown that
photons and particles are deflected away from the hole. An application of this
idea is pursued, in which a new cosmology based upon expanding holes in a
uniform universe is developed. The microwave background radiation and Hubble's
Law, among others, are explained. Finally, current astronomical data are used
to compute a remarkably accurate value of Hubble's constant, as well as
estimates of the average mass density of the universe and the cosmological
constant. | 9405075v1 |
2012-02-21 | Making Evildoers Pay: Resource-Competitive Broadcast in Sensor Networks | Consider a time-slotted, single-hop, wireless sensor network (WSN) consisting
of n correct devices and and t=f*n Byzantine devices where f>=0 is any
constant; that is, the Byzantine devices may outnumber the correct ones. There
exists a trusted sender Alice who wishes to deliver a message m over a single
channel to the correct devices. There also exists a malicious user Carol who
controls the t Byzantine devices and uses them to disrupt the communication
channel. For a constant k>=2, the correct and Byzantine devices each possess a
meager energy budget of O(n^{1/k}), Alice and Carol each possess a limited
budget of \tilde{O}(n^{1/k}), and sending or listening in a slot incurs unit
cost. This general setup captures the inherent challenges of guaranteeing
communication despite scarce resources and attacks on the network. Given this
Alice versus Carol scenario, we ask: Is communication of m feasible and, if so,
at what cost?
We develop a protocol which, for an arbitrarily small constant \epsilon>0,
ensures that at least (1-\epsilon)n correct devices receive m with high
probability. Furthermore, if Carol's devices expend T energy jamming the
channel, then Alice and the correct devices each spend only
\tilde{O}(T^{1/(k+1)}). In other words, delaying the transmission of m forces a
jammer to rapidly deplete its energy supply and, consequently, cease attacks on
the network. | 1202.4576v4 |
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