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2017-09-13
|
Effects of pressure on suspended micromechanical membrane arrays
|
The effects of pressure on micromechanical air-filled cavities made by a pair
of suspended, parallel silicon nitride membranes are investigated in the free
molecular and quasi-molecular regimes. Variations of the fundamental drummode
mechanical resonant frequencies and damping with air pressure are determined by
means of optical interferometry. A kinetic damping linear friction force and a
positive resonant frequency shift due to the compression of the fluid between
the membranes are observed to be proportional with pressure in the range
0.01-10 mbars. For resonators with near-degenerate modes hybridization of the
modes due to this squeeze film effect is also observed and well accounted for
by a simple spring-coupled oscillator model.
|
1710.00043v2
|
2017-10-11
|
Parametric Decay Instability and Dissipation of Low-frequency Alfvén Waves in Low-beta Turbulent Plasmas
|
Evolution of the parametric decay instability (PDI) of a circularly polarized
Aflv\'en wave in a turbulent low-beta plasma background is investigated using
3D hybrid simulations. It is shown that the turbulence reduces the growth rate
of PDI as compared to the linear theory predictions, but PDI can still exist.
Interestingly, the damping rate of ion acoustic mode (as the product of PDI) is
also reduced as compared to the linear Vlasov predictions. Nonetheless,
significant heating of ions in the direction parallel to the background
magnetic field is observed due to resonant Landau damping of the ion acoustic
waves. In low-beta turbulent plasmas, PDI can provide an important channel for
energy dissipation of low-frequency Alfv\'en waves at a scale much larger than
the ion kinetic scales, different from the traditional turbulence dissipation
models.
|
1710.04149v3
|
2017-10-14
|
Doubly Damped Stochastic Parallel Translations and Hessian Formulas
|
We study the Hessian of the solutions of time-independent Schr\"odinger
equations, aiming to obtain as large a class as possible of complete Riemannian
manifolds for which the estimate $C(\frac 1 t +\frac {d^2}{t^2})$ holds. For
this purpose we introduce the doubly damped stochastic parallel transport
equation, study them and make exponential estimates on them, deduce a second
order Feynman-Kac formula and obtain the desired estimates. Our aim here is to
explain the intuition, the basic techniques, and the formulas which might be
useful in other studies.
|
1710.05169v1
|
2017-10-20
|
Magnetic field amplification in supernova remnants
|
Based on the new findings on the turbulent dynamo in \citet{XL16}, we examine
the magnetic field amplification in the context of supernova remnants. Due to
the strong ion-neutral collisional damping in the weakly-ionized interstellar
medium, the dynamo in the preshock turbulence remains in the damping kinematic
regime, which leads to {\it a linear-in-time growth of the magnetic field
strength}. The resultant magnetic field structure enables effective diffusion
upstream and shock acceleration of cosmic rays to energies above the "knee".
Differently, the nonlinear dynamo in the postshock turbulence leads to {\it a
linear-in-time growth of the magnetic energy} due to the turbulent magnetic
diffusion. Given a weak initial field strength in the postshock region, the
magnetic field saturates at a significant distance from the shock front as a
result of the inefficiency of the nonlinear dynamo. This result is in a good
agreement with existing numerical simulations and well explains the X-ray spots
detected far behind the shock front.
|
1710.07717v1
|
2017-10-26
|
Coarse-graining in the derivation of Markovian master equations and its significance in quantum thermodynamics
|
The coarse-graining approach to deriving the quantum Markovian master
equation is revisited, with close attention given to the underlying
approximations. It is further argued that the time interval over which the
coarse-graining is performed is a free parameter that can be given a physical
measurement-based interpretation. In the case of the damping of composite
systems to reservoirs of different temperatures, currently of much interest in
the study of quantum thermal machines with regard to the validity of `local'
and `global' forms of these equations, the coupling of the subsystems leads to
a further timescale with respect to which the coarse-graining time interval can
be chosen. Different choices lead to different master equations that correspond
to the local and global forms. These can be then understood as having different
physical interpretations based on the role of the coarse-graining, as well as
different limitations in application.
|
1710.09939v2
|
2017-10-27
|
The Marangoni effect on small-amplitude capillary waves in viscous fluids
|
We derive a general integrodifferential equation for the transient behaviour
of small-amplitude capillary waves on the planar surface of a viscous fluid in
the presence of the Marangoni effect. The equation is solved for an insoluble
surfactant solution in concentration below the critical micelle concentration
(cmc) undergoing convective-diffusive surface transport. The special case of a
diffusion-driven surfactant is considered near the the critical damping
wavelength. The Marangoni effect is shown to contribute to the overall damping
mechanism and a first-order term correction to the critical wavelength with
respect to the surfactant concentration difference and the Schmidt number is
proposed.
|
1710.10137v1
|
2017-11-03
|
Remark on upper bound for lifespan of solutions to semilinear evolution equations in a two-dimensional exterior domain
|
In this paper we consider the initial-boundary value problem for the heat,
damped wave, complex-Ginzburg-Landau and Schr"odinger equations with the power
type nonlinearity $|u|^p$ with $p in (1,2]$ in a two-dimensional exterior
domain. Remark that $2=1+2/N$ is well-known as the Fujita exponent. If $p>2$,
then there exists a small global-in-time solution of the damped wave equation
for some initial data small enough (see Ikehata'05), and if $p<2$, then
global-in-time solutions cannot exist for any positive initial data (see
Ogawa-Takeda'09 and Lai-Yin'17). The result is that for given initial data
$(f,tau g)in H^1_0(Omega)times L^2(Omega)$ satisfying $(f+tau g)log |x|in
L^1(Omega)$ with some requirement, the solution blows up at finite time, and
moreover, the upper bound for lifespan of solutions to the problem is given as
the following {it double exponential type} when $p=2$: [ lifespan(u) leq
exp[exp(Cep^{-1})] . ] The crucial idea is to use test functions which
approximates the harmonic function $log |x|$ satisfying Dirichlet boundary
condition and the technique for derivation of lifespan estimate in
Ikeda-Sobajima(arXiv:1710.06780).
|
1711.00994v1
|
2017-11-03
|
A flowing pair of particles in inertial microfluidics
|
A flowing pair of particles in inertial microfluidics gives important
insights into understanding and controlling the collective dynamics of
particles like cells or droplets in microfluidic devices. They are applied in
medical cell analysis and engineering. We study the dynamics of a pair of solid
particles flowing through a rectangular microchannel using lattice Boltzmann
simulations. We determine the inertial lift force profiles as a function of the
two particle positions, their axial distance, and the Reynolds number.
Generally, the profiles strongly differ between particles leading and lagging
in flow and the lift forces are enhanced due to the presence of a second
particle. At small axial distances, they are determined by viscous forces,
while inertial forces dominate at large separations. Depending on the initial
conditions, the two-particle lift forces in combination with the Poiseuille
flow give rise to three types of unbound particle trajectories, called
moving-apart, passing, and swapping, and one type of bound trajectories, where
the particles perform damped oscillations. The damping rate scales with
Reynolds number squared, since inertial forces are responsible for driving the
particles to their steady-state positions.
|
1711.01148v2
|
2017-11-07
|
Application of the coupled classical oscillators model to the Fano resonance build-up in a plasmonic nanosystem
|
We study the excitation dynamics of Fano resonance within the classical model
framework of two linear coupled oscillators. An exact solution for the model
with a damped harmonic force is obtained. The details of growth a Fano profile
under the harmonic excitation is shown. For incident ultra-wideband pulse, the
reaction of a system becomes universal and coincides with the time-dependent
response function. The results of numerical calculations clarify two
alternative ways for experimental measurement of the complete characteristics
of a system: direct observation of the system response to a monochromatic force
by frequency scanning or recording of time-dependent response to the
delta-pulse. As a specific example, time-dependent excitation in a system
consisting of a quantum dot and a metal nanoparticle is calculated. Then it is
shown the applicability of the extended model of damped oscillators with
radiative correction to describe the build-up a plasmon Fano resonance in a
scattering of a femtosecond laser pulse by nanoantenna.
|
1711.02498v2
|
2017-11-11
|
Quantum Thermodynamics for Driven Dissipative Bosonic Systems
|
We investigate two prototypical dissipative bosonic systems under slow
driving and arbitrary system-bath coupling strength, recovering their dynamic
evolution as well as the heat and work rates, and we verify that thermodynamic
laws are respected. Specifically, we look at the damped harmonic oscillator and
the damped two-level system. For the former, we study independently the slow
time- dependent perturbation in the oscillator frequency and in the coupling
strength. For the latter, we concentrate on the slow modulation of the energy
gap between the two levels. Importantly, we are able to find the entropy
production rates for each case without explicitly defining nonequilibrium
extensions for the entropy functional. This analysis also permits the
definition of phenomenological friction coefficients in terms of structural
properties of the system-bath composite.
|
1711.04077v1
|
2017-11-29
|
Constraints on box-shaped cosmic ray electron feature from dark matter annihilation with the AMS-02 and DAMPE data
|
Precise measurements of spectra of cosmic ray electrons and positrons can
effectively probe the nature of dark matter (DM) particles. In a class of
models where DM particles initially annihilate into a pair of intermediate
particles which then decay into standard model particles, box-shaped spectra
can be generated. Such a kind of spectra are distinct from astrophysical
backgrounds, and can probably be regarded as characteristic features of the DM
annihilation. In this work, we search for such a feature in the total electron
plus positron spectrum measured by AMS-02 and DAMPE. No significant evidence
for such a DM annihilation component has been found. The 95\% confidence level
upper limits of the velocity-weighted annihilation cross section are derived,
which range from $\sim 10^{-26}~{\rm cm^3~s^{-1}}$ for DM mass of 50 GeV to
$\sim 10^{-23}~{\rm cm^3~s^{-1}}$ for DM mass of 10 TeV.
|
1711.11052v2
|
2017-11-30
|
TeV dark matter and the DAMPE electron excess
|
The recent high energy electron and positron flux observed by the DAMPE
experiment indicates possible excess events near 1.4 TeV. Such an excess may be
evidence of dark matter annihilations or decays in a dark matter subhalo that
is located close to the solar system. We give here an analysis of this excess
from annihilations of Dirac fermion dark matter which is charged under a new
$U(1)_X$ gauge symmetry. The interactions between dark matter and the standard
model particles are mediated the $U(1)_X$ gauge boson. We show that dark matter
annihilations from a local subhalo can explain the excess with the canonical
thermal annihilation cross section. We further discuss the constraints from the
relic density, from the dark matter direct detection, from the dark matter
indirect detection, from the cosmic microwave background, and from the particle
colliders.
|
1711.11579v1
|
2017-12-04
|
Quasi-degenerate dark matter for DAMPE excess and $3.5\,\textrm{keV}$ line
|
We propose a quasi-degenerate dark matter scenario to simultaneously explain
the $1.4\,\textrm{TeV}$ peak in the high-energy cosmic-ray electron-positron
spectrum reported by the DAMPE collaboration very recently and the
$3.5\,\textrm{keV}$ X-ray line observed in galaxies clusters and from the
Galactic centre and confirmed by the Chandra and NuSTAR satellites. We consider
a dark $SU(2)'\times U(1)'$ gauge symmetry under which the dark matter is a
Dirac fermion doublet composed of two $SU(2)'$ doublets with non-trivial
$U(1)'$ charges. At one-loop level the two dark fermion components can have a
mass split as a result of the dark gauge symmetry breaking. Through the
exchange of a mediator scalar doublet the two quasi-degenerate dark fermions
can mostly annihilate into the electron-positron pairs at tree level for
explaining the $1.4\,\textrm{TeV}$ positron anomaly, meanwhile, the heavy dark
fermion can very slowly decay into the light dark fermion with a photon at
one-loop level for explaining the $3.5\,\textrm{keV}$ X-ray line. Our dark
fermions can be also verified in the direct detection experiments.
|
1712.00922v1
|
2017-12-06
|
Collective modes of an imbalanced unitary Fermi gas
|
We study theoretically the collective mode spectrum of a strongly imbalanced
two-component unitary Fermi gas in a cigar-shaped trap, where the minority
species forms a gas of polarons. We describe the collective breathing mode of
the gas in terms of the Fermi liquid kinetic equation taking collisions into
account using the method of moments. Our results for the frequency and damping
of the longitudinal in-phase breathing mode are in good quantitative agreement
with an experiment by Nascimb\`ene et al. [Phys. Rev. Lett. 103, 170402 (2009)]
and interpolate between a hydrodynamic and a collisionless regime as the
polarization is increased. A separate out-of phase breathing mode, which for a
collisionless gas is sensitive to the effective mass of the polaron, however,
is strongly damped at finite temperature, whereas the experiment observes a
well-defined oscillation.
|
1712.02181v1
|
2017-12-07
|
Bias of Damped Lyman-$α$ systems from their cross-correlation with CMB lensing
|
We cross-correlate the positions of damped Lyman-$\alpha$ systems (DLAs) and
their parent quasar catalog with a convergence map derived from the Planck
cosmic microwave background (CMB) temperature data. We make consistent
measurements of the lensing signal of both samples in both Fourier and
configuration space. By interpreting the excess signal present in the DLA
catalog with respect to the parent quasar catalog as caused by the large scale
structure traced by DLAs, we are able to infer the bias of these objects:
$b_{\rm DLA}=2.6\pm0.9$. These results are consistent with previous
measurements made in cross-correlation with the Lyman-$\alpha$ forest, although
the current noise in the lensing data and the low number density of DLAs limits
the constraining power of this measurement. We discuss the robustness of the
analysis with respect to a number different systematic effects and forecast
prospects of carrying out this measurement with data from future experiments.
|
1712.02738v2
|
2017-12-08
|
Viscoelastic optical nonlocality of low-loss epsilon-near-zero nanofilms
|
Optical nonlocalities are elusive and hardly observable in traditional
plasmonic materials like noble and alkali metals. Here we report experimental
observation of viscoelastic nonlocalities in the infrared optical response of
doped cadmium-oxide, epsilon-near-zero nanofilms. The nonlocality is detectable
thanks to the low damping rate of conduction electrons and the virtual absence
of interband transitions at infrared wavelengths. We describe the motion of
conduction electrons using a hydrodynamic model for a viscoelastic fluid, and
find excellent agreement with experimental results. The electrons elasticity
blue-shifts the infrared plasmonic resonance associated with the main
epsilon-near-zero mode, and triggers the onset of higher-order resonances due
to the excitation of electron-pressure modes above the bulk plasma frequency.
We also provide evidence of the existence of nonlocal damping, i.e., viscosity,
in the motion of optically-excited conduction electrons using a combination of
spectroscopic ellipsometry data and predictions based on the viscoelastic
hydrodynamic model.
|
1712.03169v2
|
2017-12-08
|
A Strong Test of the Dark Matter Origin of the 1.4 TeV DAMPE Signal Using IceCube Neutrinos
|
A tentative excess in the electron spectrum at 1.4 TeV was recently reported
by the DArk Matter Particle Explorer (DAMPE). A non-astrophysical scenario in
which dark matter particles annihilate or decay in a local clump has been
invoked to explain the excess. If $e^\pm$ annihilation channels in the final
states are mediated by left-handed leptons as a component in the $SU(2)_L$
doublet, neutrinos with similar energies should have been simultaneously
produced. We demonstrate that generic dark matter models can be decisively
tested by the existing IceCube data. In case of a non-detection, such models
would be excluded at the $5\sigma$ level by the five-year data for a point-like
source and by the ten-year data for an extended source of dark matter particles
with left-handed leptons.
|
1712.03210v2
|
2017-12-11
|
Prospects of type-II seesaw at future colliders in light of the DAMPE $e^+ e^-$ excess
|
The DAMPE $e^+ e^-$ excess at around 1.4 TeV could be explained in the
type-II seesaw model with a scalar dark mater $D$ which is stabilized by a
discrete $Z_2$ symmetry. The simplest scenario is the annihilation $DD \to
H^{++} H^{--}$ followed by the subsequent decay $H^{\pm\pm} \to e^\pm e^\pm$,
with both the DM and triplet scalars roughly 3 TeV with a small mass splitting.
In addition to the Drell-Yan process at future 100 TeV hadron colliders, the
doubly-charged components could also be produced at lepton colliders like ILC
and CLIC in the off-shell mode, and mediate lepton flavor violating processes
$e^+ e^- \to \ell_i^\pm \ell_j^\mp$ (with $i \neq j$). A wide range of
parameter space of the type-II seesaw could be probed, which are well below the
current stringent lepton flavor constraints.
|
1712.03642v3
|
2017-12-12
|
Thermal decoherence in a strongly correlated Bose liquid
|
We compute the single particle spectral function of a Bose liquid on a
lattice, at integer filling, close to the superfluid-Mott transition. We use a
`static path approximation' that retains all the classical thermal fluctuations
in the problem, and a real space implementation of the random phase
approximation (RPA) for the Green's functions on the thermally fluctuating
backgrounds. This leads to the standard RPA answers in the ground state but
captures the progressive damping of the excitations with increasing
temperature. We focus on the momentum resolved lineshape across the superfluid
to Bose liquid thermal transition. In the superfluid regime we observe a gapped
`amplitude' mode, and gapless `phase' modes of positive and negative energy.
The dispersion and weight of these modes changes with interaction but are
almost temperature independent, even into the normal state, except near
critical coupling. The damping of the modes varies roughly as $T^{\alpha}
f_{\bf k}$, where $T$ is the temperature and ${\bf k}$ the momentum, with
$\alpha \sim 0.5$ and $f_{\bf k}$ having non trivial momentum dependence. The
Mott phase has gapped dispersive spectra. Near critical coupling the thermal
Bose `liquid' is gapped, with progressive widening of the gap with increasing
temperature, a feature that it shares with the Mott insulator.
|
1712.04433v1
|
2017-12-17
|
Oscillation energy based sensitivity analysis and control for multi-mode oscillation systems
|
This paper describes a novel approach to analyze and control systems with
multi-mode oscillation problems. Traditional single dominant mode analysis
fails to provide effective control actions when several modes have similar low
damping ratios. This work addresses this problem by considering all modes in
the formulation of the system kinetic oscillation energy. The integral of
energy over time defines the total action as a measure of dynamic performance,
and its sensitivity allows comparing the performance of different
actuators/locations in the system to select the most effective one to damp the
oscillation energy. Time domain simulations in the IEEE 9-bus system and IEEE
39-bus system verify the findings obtained by the oscillation energy based
analysis. Applications of the proposed method in control and system planning
are discussed.
|
1712.06157v1
|
2017-12-19
|
Nonequilibrium quantum solvation with a time-dependent Onsager cavity
|
We formulate a theory of nonequilibrium quantum solvation in which parameters
of the solvent are explicitly depending on time. We assume in a simplest
approach a spherical molecular Onsager cavity with a time-dependent radius. We
analyze the relaxation properties of a test molecular point dipole in a
dielectric solvent and consider two cases: (i) a shrinking Onsager sphere, and,
(ii) a breathing Onsager sphere. Due to the time-dependent solvent, the
frequency-dependent response function of the dipole becomes time-dependent. For
a shrinking Onsager sphere, the dipole relaxation is in general enhanced. This
is reflected in a temporally increasing line width of the absorptive part of
the response. Furthermore, the effective frequency-dependent response function
shows two peaks in the absorptive part which are symmetrically shifted around
the eigenfrequency. In contrast, a breathing sphere reduces damping as compared
to the static sphere. Interestingly, we find a non-monotonous dependence of the
relaxation rate on the breathing rate and a resonant suppression of damping
when both rates are comparable. Moreover, the line width of the absorptive part
of the response function is strongly reduced for times when the breathing
sphere reaches its maximal extension.
|
1712.06973v2
|
2017-12-26
|
Newton's equation of motion with quadratic drag force and Toda's potential as a solvable one
|
The family of exactly solvable potentials for Newton's equation of motion in
the one-dimensional system with quadratic drag force has been determined
completely. The determination is based on the implicit inverse-function
solution valid for any potential shape, and hence exhaustive. This solvable
family includes the exponential potential appearing in the Toda lattice as a
special limit. The global solution is constructed by matching the solutions
applicable for positive and negative velocity, yielding the piecewise analytic
function with a cusp in the third-order derivative, i.e., the jerk. These
procedures and features can be regarded as a generalization of Gorder's
construction [Phys. Scr. 2015, {\bf 90}, 085208] to the energy-dissipating
damped oscillators. We also derive the asymptotic formulae by solving the
matching equation, and prove that the damping of the oscillation amplitude is
proportional to $ t^{-1} $.
|
1712.09189v4
|
2017-12-23
|
Density Fluctuations in the Solar Wind Driven by Alfvén Wave Parametric Decay
|
Measurements and simulations of inertial compressive turbulence in the solar
wind are characterized by anti-correlated magnetic fluctuations parallel to the
mean field and density structures. This signature has been interpreted as
observational evidence for non-propagating pressure balanced structures (PBS),
kinetic ion acoustic waves, as well as the MHD slow-mode. Given the high
damping rates of parallel propagating compressive fluctuations, their ubiquity
in satellite observations is surprising, and suggestive of a local driving
process. One possible candidate for the generation of compressive fluctuations
in the solar wind is Alfv\'en wave parametric instability. Here we test the
parametric decay process as a source of compressive waves in the solar wind by
comparing the collisionless damping rates of compressive fluctuations with the
growth rates of the parametric decay instability daughter waves. Our results
suggest that generation of compressive waves through parametric decay is
overdamped at 1 AU, but that the presence of slow-mode like density
fluctuations is correlated with the parametric decay of Alfv\'en waves.
|
1712.09336v2
|
2018-01-15
|
A radiative neutrino mass model in light of DAMPE excess with hidden gauged $U(1)$ symmetry
|
We propose a one-loop induced neutrino mass model with hidden $U(1)$ gauge
symmetry, in which we successfully involve a bosonic dark matter (DM) candidate
propagating inside a loop diagram in neutrino mass generation to explain the
$e^+e^-$ excess recently reported by the DArk Matter Particle Explorer (DAMPE)
experiment. In our scenario dark matter annihilates into four leptons through
$Z'$ boson as DM DM $\to Z' Z' (Z' \to \ell^+ \ell^-)$ and $Z'$ decays into
leptons via one-loop effect. We then investigate branching ratios of $Z'$
taking into account lepton flavor violations and neutrino oscillation data.
|
1801.04729v2
|
2018-01-22
|
A port-Hamiltonian approach to the control of nonholonomic systems
|
In this paper a method of controlling nonholonomic systems within the
port-Hamiltonian (pH) framework is presented. It is well known that
nonholonomic systems can be represented as pH systems without Lagrange
multipliers by considering a reduced momentum space. Here, we revisit the
modelling of these systems for the purpose of identifying the role that
physical damping plays. Using this representation, a geometric structure
generalising the well known chained form is identified as \textit{chained
structure}. A discontinuous control law is then proposed for pH systems with
chained structure such that the configuration of the system asymptotically
approaches the origin. The proposed control law is robust against the damping
and inertial of the open-loop system. The results are then demonstrated
numerically on a car-like vehicle.
|
1801.06954v1
|
2018-01-23
|
Temperature gradient driven heat flux closure in fluid simulations of collisionless reconnection
|
Recent efforts to include kinetic effects in fluid simulations of plasmas
have been very promising. Concerning collisionless magnetic reconnection, it
has been found before that damping of the pressure tensor to isotropy leads to
good agreement with kinetic runs in certain scenarios. An accurate
representation of kinetic effects in reconnection was achieved in a study by
Wang et al. (Phys. Plasmas, volume 22, 2015, 012108) with a closure derived
from earlier work by Hammett and Perkins (PRL, volume 64, 1990, 3019). Here,
their approach is analyzed on the basis of heat flux data from a Vlasov
simulation. As a result, we propose a new local closure in which heat flux is
driven by temperature gradients. That way, a more realistic approximation of
Landau damping in the collisionless regime is achieved. Previous issues are
addressed and the agreement with kinetic simulations in different reconnection
setups is improved significantly. To the authors' knowledge, the new fluid
model is the first to perform well in simulations of the coalescence of large
magnetic islands.
|
1801.07628v1
|
2018-01-29
|
Oscillatory relaxation of zonal flows in a multi-species stellarator plasma
|
The low frequency oscillatory relaxation of zonal potential perturbations is
studied numerically in the TJ-II stellarator (where it was experimentally
detected for the first time). It is studied in full global gyrokinetic
simulations of multi-species plasmas. The oscillation frequency obtained is
compared with predictions based on single-species simulations using simplified
analytical relations. It is shown that the frequency of this oscillation for a
multi-species plasma can be accurately obtained from single-species
calculations using extrapolation formulas. The damping of the oscillation and
the influence of the different inter-species collisions is studied in detail.
It is concluded that taking into account multiple kinetic ions and electrons
with impurity concentrations realistic for TJ-II plasmas allows to account for
the values of frequency and damping rate in zonal flows relaxations observed
experimentally.
|
1801.09495v1
|
2018-01-30
|
Input / Output Stability of a Damped String Equation coupled with Ordinary Differential System
|
The input/output stability of an interconnected system composed of an
ordinary differential equation and a damped string equation is studied. Issued
from the literature on time-delay systems, an exact stability result is firstly
derived using pole locations. Then, based on the Small-Gain theorem and on the
Quadratic Separation framework, some robust stability criteria are provided.
The latter follows from a projection of the infinite dimensional state on an
orthogonal basis of Legendre polynomials. Numerical examples comparing these
results with the ones in the literature are proposed and a comparison of its
efficiency is made.
|
1801.09916v2
|
2018-02-05
|
Intrinsic spin-orbit torque arising from Berry curvature in metallic-magnet/Cu-oxide interface
|
We report the observation of the intrinsic damping-like spin-orbit torque
(SOT) arising from the Berry curvature in metallic-magnet/CuO$_x$
heterostructures. We show that a robust damping-like SOT, an order of magnitude
larger than a field-like SOT, is generated in the heterostructure despite the
absence of the bulk spin-orbit effect in the CuO$_x$ layer. Furthermore, by
tuning the interface oxidation level, we demonstrate that the field-like SOT
changes drastically and even switches its sign, which originates from oxygen
modulated spin-dependent disorder. These results provide an important
information for fundamental understanding of the physics of the SOTs.
|
1802.01285v2
|
2018-02-12
|
Selective Phonon Damping in Topological Semimetals
|
Topological semimetals are characterized by their intriguing Fermi surfaces
(FSs) such as Weyl and Dirac points, or nodal FS, and their associated surface
states. Among them, topological crystalline semimetals, in the presence of
strong spin-orbit coupling, possess a nodal FS protected by non-symmorphic
lattice symmetries. In particular, it was theoretically proposed that
$\mathrm{SrIrO}_{3}$ exhibits a bulk nodal ring due to glide symmetries, as
well as flat two-dimensional surface states related to chiral and mirror
symmetries. However, due to the semimetallic nature of the bulk, direct
observation of these surface states is difficult. Here we study the effect of
flat-surface states on phonon modes for $\mathrm{SrIrO}_{3}$ side surfaces. We
show that particular phonon modes, based on mirror symmetry, have qualitatively
different damping mechanisms due to the surface states which could be used to
infer their existence. Experimental techniques for such measurements are also
discussed.
|
1802.04300v2
|
2018-02-14
|
Motion of interfaces for a damped hyperbolic Allen-Cahn equation
|
Consider the Allen-Cahn equation $u_t=\varepsilon^2\Delta u-F'(u)$, where $F$
is a double well potential with wells of equal depth, located at $\pm1$. There
are a lot of papers devoted to the study of the limiting behavior of the
solutions as the diffusion coefficient $\varepsilon\to0^+$, and it is well
known that, if the initial datum $u(\cdot,0)$ takes the values $+1$ and $-1$ in
the regions $\Omega_+$ and $\Omega_-$, then the "interface" connecting
$\Omega_+$ and $\Omega_-$ moves with normal velocity equal to the sum of its
principal curvatures, i.e. the interface moves by mean curvature flow.
This paper concerns with the motion of the inteface for a damped hyperbolic
Allen-Cahn equation, in a bounded domain of $\mathbb{R}^n$, for $n=2$ or $n=3$.
In particular, we focus the attention on radially simmetric solutions, studying
in detail the differences with the classic parabolic case, and we prove that,
under appropriate assumptions on the initial data $u(\cdot,0)$ and
$u_t(\cdot,0)$, the interface moves by mean curvature as $\varepsilon\to0^+$
also in the hyperbolic framework.
|
1802.05038v1
|
2018-02-23
|
Blow up of solutions for semilinear wave equations with noneffective damping
|
In this paper, we study the finite-time blow up of solutions to the following
semilinear wave equation with time-dependent damping \[ \partial_t^2u-\Delta
u+\frac{\mu}{1+t}\partial_tu=|u|^p \] in $\mathbb{R}_{+}\times\mathbb{R}^n$.
More precisely, for $0\leq\mu\leq 2,\mu \neq1$ and $n\geq 2$, there is no
global solution for $1<p<p_S(n+\mu)$, where $p_S(k)$ is the $k$-dimensional
Strauss exponent and a life-span of the blow up solution will be obtained. Our
work is an extension of \cite{IS}, where the authors proved a similar blow up
result with a larger range of $\mu$. However, we obtain a better life-span
estimate when $\mu\in(0,1)\cup(1,2)$ by using a different method.
|
1802.08403v2
|
2018-03-04
|
Optimization of Time-Resolved Magneto-optical Kerr Effect Signals for Magnetization Dynamics Measurements
|
Recently magnetic storage and magnetic memory have shifted towards the use of
magnetic thin films with perpendicular magnetic anisotropy (PMA). Understanding
the magnetic damping in these materials is crucial, but normal Ferromagnetic
Resonance (FMR) measurements face some limitations. The desire to quantify the
damping in materials with PMA has resulted in the adoption of Time-Resolved
Magneto-optical Kerr Effect (TR-MOKE) measurements. In this paper, we discuss
the angle and field dependent signals in TR-MOKE, and utilize a numerical
algorithm based on the Landau-Lifshitz-Gilbert (LLG) equation to provide
information on the optimal conditions to run TR-MOKE measurements.
|
1803.01280v2
|
2018-03-06
|
A comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions
|
The purpose of the present paper is to compare two semi-Lagrangian methods in
the context of the four-dimensional Vlasov--Poisson equation. More
specifically, our goal is to compare the performance of the more recently
developed semi-Lagrangian discontinuous Galerkin scheme with the de facto
standard in Eulerian Vlasov simulation (i.e. using cubic spline interpolation).
To that end, we perform simulations for nonlinear Landau damping and a
two-stream instability and provide benchmarks for the SeLaLib and sldg codes
(both on a workstation and using MPI on a cluster).
We find that the semi-Lagrangian discontinuous Galerkin scheme shows a
moderate improvement in run time for nonlinear Landau damping and a substantial
improvement for the two-stream instability. It should be emphasized that these
results are markedly different from results obtained in the asymptotic regime
(which favor spline interpolation). Thus, we conclude that the traditional
approach of evaluating numerical methods is misleading, even for short time
simulations. In addition, the absence of any All-to-All communication in the
semi-Lagrangian discontinuous Galerkin method gives it a decisive advantage for
scaling to more than 256 cores.
|
1803.02143v1
|
2018-03-06
|
Kak's three-stage protocol of secure quantum communication revisited: Hitherto unknown strengths and weaknesses of the protocol
|
Kak's three-stage protocol for quantum key distribution is revisited with
special focus on its hitherto unknown strengths and weaknesses. It is shown
that this protocol can be used for secure direct quantum communication.
Further, the implementability of this protocol in the realistic situation is
analyzed by considering various Markovian noise models. It is found that the
Kak's protocol and its variants in their original form can be implemented only
in a restricted class of noisy channels, where the protocols can be transformed
to corresponding protocols based on logical qubits in decoherence free
subspace. Specifically, it is observed that Kak's protocol can be implemented
in the presence of collective rotation and collective dephasing noise, but
cannot be implemented in its original form in the presence of other types of
noise, like amplitude damping and phase damping noise. Further, the performance
of the protocol in the noisy environment is quantified by computing average
fidelity under various noise models, and subsequently a set of preferred states
for secure communication in noisy environment have also been identified.
|
1803.02157v1
|
2018-03-09
|
Dynamical evolutions in non-Hermitian triple-well system with complex potential
|
We investigate the dynamical properties for non-Hermitian triple-well system
with a loss in the middle well. When chemical potentials in two end wells are
uniform and nonlinear interactions are neglected, there always exists a dark
state, whose eigenenergy becomes zero, and the projections onto which do not
change over time and the loss factor. The increasing of loss factor only makes
the damping form from the oscillating decay to over-damping decay. However,
when the nonlinear interaction is introduced, even interactions in the two end
wells are also uniform, the projection of the dark state will be obviously
diminished. Simultaneously the increasing of loss factor will also aggravate
the loss. In this process the interaction in the middle well plays no role.
When two chemical potentials or interactions in two end wells are not uniform
all disappear with time. In addition, when we extend the triple-well system to
a general (2n + 1)-well, the loss is reduced greatly by the factor 1=2n in the
absence of the nonlinear interaction.
|
1803.03360v1
|
2018-03-11
|
Graph Laplacian Spectrum and Primary Frequency Regulation
|
We present a framework based on spectral graph theory that captures the
interplay among network topology, system inertia, and generator and load
damping in determining the overall grid behavior and performance. Specifically,
we show that the impact of network topology on a power system can be quantified
through the network Laplacian eigenvalues, and such eigenvalues determine the
grid robustness against low frequency disturbances. Moreover, we can explicitly
decompose the frequency signal along scaled Laplacian eigenvectors when
damping-inertia ratios are uniform across buses. The insight revealed by this
framework partially explains why load-side participation in frequency
regulation not only makes the system respond faster, but also helps lower the
system nadir after a disturbance. Finally, by presenting a new controller
specifically tailored to suppress high frequency disturbances, we demonstrate
that our results can provide useful guidelines in the controller design for
load-side primary frequency regulation. This improved controller is simulated
on the IEEE 39-bus New England interconnection system to illustrate its
robustness against high frequency oscillations compared to both the
conventional droop control and a recent controller design.
|
1803.03905v3
|
2018-03-15
|
Control Inversion: A Clustering-Based Method for Distributed Wide-Area Control of Power Systems
|
Wide-area control (WAC) has been shown to be an effective tool for damping
low-frequency oscillations in power systems. In the current state of art, WAC
is challenged by two main factors - namely, scalability of design and
complexity of implementation. In this paper we present a control design called
control inversion that bypasses both of these challenges using the idea of
clustering. The basic philosophy behind this method is to project the original
power system model into a lower-dimensional state-space through clustering and
aggregation of generator states, and then designing an LQR controller for the
lower-dimensional model. This controller is finally projected back to the
original coordinates for wide-area implementation. The main problem is,
therefore, posed as finding the projection which best matches the closed-loop
performance of the WAC controller with that of a reference LQR controller for
damping low-frequency oscillations. We verify the effectiveness of the proposed
design using the NPCC 48-machine power system model.
|
1803.05947v1
|
2018-03-18
|
Damped Anderson acceleration with restarts and monotonicity control for accelerating EM and EM-like algorithms
|
The expectation-maximization (EM) algorithm is a well-known iterative method
for computing maximum likelihood estimates from incomplete data. Despite its
numerous advantages, a main drawback of the EM algorithm is its frequently
observed slow convergence which often hinders the application of EM algorithms
in high-dimensional problems or in other complex settings.To address the need
for more rapidly convergent EM algorithms, we describe a new class of
acceleration schemes that build on the Anderson acceleration technique for
speeding fixed-point iterations. Our approach is effective at greatly
accelerating the convergence of EM algorithms and is automatically scalable to
high dimensional settings. Through the introduction of periodic algorithm
restarts and a damping factor, our acceleration scheme provides faster and more
robust convergence when compared to un-modified Anderson acceleration while
also improving global convergence. Crucially, our method works as an
"off-the-shelf" method in that it may be directly used to accelerate any EM
algorithm without relying on the use of any model-specific features or
insights. Through a series of simulation studies involving five representative
problems, we show that our algorithm is substantially faster than the existing
state-of-art acceleration schemes.
|
1803.06673v2
|
2018-03-21
|
Connectivity-Preserving Coordination Control of Multi-Agent Systems with Time-Varying Delays
|
This paper presents a distributed position synchronization strategy that also
preserves the initial communication links for single-integrator multi-agent
systems with time-varying delays. The strategy employs a coordinating
proportional control derived from a specific type of potential energy,
augmented with damping injected through a dynamic filter. The injected damping
maintains all agents within the communication distances of their neighbours,
and asymptotically stabilizes the multi-agent system, in the presence of time
delays. Regarding the closed-loop single-integrator multi-agent system as a
double-integrator system suggests an extension of the proposed strategy to
connectivity-preserving coordination of Euler-Lagrange networks with
time-varying delays. Lyapunov stability analysis and simulation results
validate the two designs.
|
1803.08152v1
|
2018-03-23
|
A Novel Approach to Resonant Absorption of the Fast MHD Eigenmodes of a Coronal Arcade
|
The arched field lines forming coronal arcades are often observed to undulate
as magnetohydrodynamic (MHD) waves propagate both across and along the magnetic
field. These waves are most likely a combination of resonantly coupled fast
magnetoacoustic waves and Alfv\'en waves. The coupling results in resonant
absorption of the fast waves, converting fast wave energy into Alfv\'en waves.
The fast eigenmodes of the arcade have proven difficult to compute or derive
analytically, largely because of the mathematical complexity that the coupling
introduces. When a traditional spectral decomposition is employed, the discrete
spectrum associated with the fast eigenmodes is often subsumed into the
continuous Alfv\'en spectrum. Thus fast eigenmodes, become collective modes or
quasi-modes. Here we present a spectral decomposition that treats the
eigenmodes as having real frequencies but complex wavenumbers. Using this
procedure we derive dispersion relations, spatial damping rates, and
eigenfunctions for the resonant, fast eigenmodes of the arcade. We demonstrate
that resonant absorption introduces a fast mode that would not exist otherwise.
This new mode is heavily damped by resonant absorption, only travelling a few
wavelengths before losing most of its energy.
|
1803.08948v1
|
2018-03-25
|
Parareal exponential $θ$-scheme for longtime simulation of stochastic Schrödinger equations with weak damping
|
A parareal algorithm based on an exponential $\theta$-scheme is proposed for
the stochastic Schr\"odinger equation with weak damping and additive noise. It
proceeds as a two-level temporal parallelizable integrator with the exponential
$\theta$-scheme as the propagator on the coarse grid. The proposed algorithm in
the linear case increases the convergence order from one to $k$ for
$\theta\in[0,1]\setminus\{\frac12\}$. In particular, the convergence order
increases to $2k$ when $\theta=\frac12$ due to the symmetry of the algorithm.
Furthermore, the algorithm is proved to be suitable for longtime simulation
based on the analysis of the invariant distributions for the exponential
$\theta$-scheme. The convergence condition for longtime simulation is also
established for the proposed algorithm in the nonlinear case, which indicates
the superiority of implicit schemes. Numerical experiments are dedicated to
illustrate the best choice of the iteration number $k$, as well as the
convergence order of the algorithm for different choices of $\theta$.
|
1803.09188v1
|
2018-04-01
|
Aggregated Momentum: Stability Through Passive Damping
|
Momentum is a simple and widely used trick which allows gradient-based
optimizers to pick up speed along low curvature directions. Its performance
depends crucially on a damping coefficient $\beta$. Large $\beta$ values can
potentially deliver much larger speedups, but are prone to oscillations and
instability; hence one typically resorts to small values such as 0.5 or 0.9. We
propose Aggregated Momentum (AggMo), a variant of momentum which combines
multiple velocity vectors with different $\beta$ parameters. AggMo is trivial
to implement, but significantly dampens oscillations, enabling it to remain
stable even for aggressive $\beta$ values such as 0.999. We reinterpret
Nesterov's accelerated gradient descent as a special case of AggMo and analyze
rates of convergence for quadratic objectives. Empirically, we find that AggMo
is a suitable drop-in replacement for other momentum methods, and frequently
delivers faster convergence.
|
1804.00325v3
|
2018-04-03
|
Damped perturbations in the no-boundary state
|
We evaluate the no-boundary path integral exactly in a Bianchi IX
minisuperspace with two scale factors. In this model the no-boundary proposal
can be implemented by requiring one scale factor to be zero initially together
with a judiciously chosen regularity condition on the momentum conjugate to the
second scale factor. Taking into account the non-linear backreaction of the
perturbations we recover the predictions of the original semiclassical
no-boundary proposal. In particular we find that large perturbations are
strongly damped, consistent with vacuum state wave functions.
|
1804.01102v2
|
2018-09-14
|
Nonequilibrium polariton dynamics in a Bose-Einstein condensate coupled to an optical cavity
|
We study quasiparticle scattering effects on the dynamics of a homogeneous
Bose-Einstein condensate of ultracold atoms coupled to a single mode of an
optical cavity. The relevant excitations, which are polariton-like mixed
excitations of photonic and atomic density-wave modes, are identified. All the
first-order correlation functions are presented by means of the Keldysh Green's
function technique. Beyond confirming the existence of the resonant enhancement
of Beliaev damping, we find a very structured spectrum of fluctuations. There
is a spectral hole burning at half of the recoil frequency reflecting the
singularity of the Beliaev scattering process. The effects of the photon-loss
dissipation channel and that of the Beliaev damping due to atom-atom collisions
can be well separated. We show that the Beliaev process does not influence the
properties of the self-organization criticality.
|
1809.05427v2
|
2018-09-26
|
The influence of oscillations on energy estimates for damped wave models with time-dependent propagation speed and dissipation
|
The aim of this paper is to derive higher order energy estimates for
solutions to the Cauchy problem for damped wave models with time-dependent
propagation speed and dissipation. The model of interest is \begin{equation*}
u_{tt}-\lambda^2(t)\omega^2(t)\Delta u +\rho(t)\omega(t)u_t=0, \quad
u(0,x)=u_0(x), \,\, u_t(0,x)=u_1(x). \end{equation*} The coefficients
$\lambda=\lambda(t)$ and $\rho=\rho(t)$ are shape functions and
$\omega=\omega(t)$ is an oscillating function. If $\omega(t)\equiv1$ and
$\rho(t)u_t$ is an "effective" dissipation term, then $L^2-L^2$ energy
estimates are proved in [2]. In contrast, the main goal of the present paper is
to generalize the previous results to coefficients including an oscillating
function in the time-dependent coefficients. We will explain how the interplay
between the shape functions and oscillating behavior of the coefficient will
influence energy estimates.
|
1809.10179v2
|
2018-09-27
|
Non-equilibrium Quantum Langevin dynamics of orbital diamagnetic moment
|
We investigate the time dependent orbital diamagnetic moment of a charged
particle in a magnetic field in a viscous medium via the Quantum Langevin
Equation. We study how the interplay between the cyclotron frequency and the
viscous damping rate governs the dynamics of the orbital magnetic moment in the
high temperature classical domain and the low temperature quantum domain for an
Ohmic bath. These predictions can be tested via state of the art cold atom
experiments with hybrid traps for ions and neutral atoms. We also study the
effect of a confining potential on the dynamics of the magnetic moment. We
obtain the expected Bohr Van Leeuwen limit in the high temperature, asymptotic
time ($ \gamma t\longrightarrow \infty$, where $ \gamma $ is the viscous
damping coefficient) limit.
|
1809.10370v1
|
2018-10-31
|
AGN Variability Analysis Handbook
|
This work develops application techniques for stochastic modelling of Active
Galactic Nuclei (AGN) variability as a probe of accretion disk physics.
Stochastic models, specifically Continuous Auto-Regressive Moving Average
(CARMA) models, characterize lightcurves by estimating delay timescales that
describe movements away from and toward equilibrium (mean flux) as well as an
amplitude and frequency of intrinsic perturbations to the AGN flux. We begin
this tutorial by reviewing discrete auto-regressive (AR) and moving-average
(MA) processes, we bridge these components to their continuous analogs, and
lastly we investigate the significance of timescales from direct stochastic
modelling of a lightcurve projected in power spectrum (PSD) and structure
function (SF) space. We determine that higher order CARMA models, for example
the Damped Harmonic Oscillator (DHO or CARMA(2,1)) are more sensitive to
deviations from a single-slope power-law description of AGN variability; unlike
Damped Random Walks (DRW or CAR(1)) where the PSD slope is fixed, the DHO slope
is not. Higher complexity stochastic models than the DRW capture additional
covariance in data and output additional characteristic timescales that probe
the driving mechanisms of variability.
|
1811.00154v1
|
2018-11-15
|
Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise
|
In this paper, we consider a certain class of second order nonlinear PDEs
with damping and space-time white noise forcing, posed on the $d$-dimensional
torus. This class includes the wave equation for $d=1$ and the beam equation
for $d\le 3$. We show that the Gibbs measure of the equation without forcing
and damping is the unique invariant measure for the flow of this system. Since
the flow does not satisfy the Strong Feller property, we introduce a new
technique for showing unique ergodicity. This approach may be also useful in
situations in which finite-time blowup is possible.
|
1811.06294v4
|
2018-12-04
|
Optical excitation of single- and multi-mode magnetization precession in Galfenol nanolayers
|
We demonstrate a variety of precessional responses of the magnetization to
ultrafast optical excitation in nanolayers of Galfenol (Fe,Ga), which is a
ferromagnetic material with large saturation magnetization and enhanced
magnetostriction. The particular properties of Galfenol, including cubic
magnetic anisotropy and weak damping, allow us to detect up to 6 magnon modes
in a 120-nm layer, and a single mode with effective damping ${\alpha}_{eff}$ =
0.005 and frequency up to 100 GHz in a 4-nm layer. This is the highest
frequency observed to date in time-resolved experiments with metallic
ferromagnets. We predict that detection of magnetization precession approaching
THz frequencies should be possible with Galfenol nanolayers.
|
1812.01237v1
|
2018-12-10
|
Assessment of skin-friction-reduction techniques on a turbulent wing section
|
The scope of the present project is to quantify the effects of uniform
blowing and body-force damping on turbulent boundary layers subjected to a
non-uniform adverse-pressure-gradient distribution. To this end, well-resolved
large-eddy simulations are employed to describe the flow around the NACA4412
airfoil at moderate Reynolds number 200, 000 based on freestream velocity and
chord length. In the present paper we focus on uniform blowing and the
conference presentation will include a comparison with body-force damping
applied in the same region. The inner-scaled profiles of the mean velocity and
of selected components of the Reynolds-stress tensor are examined and compared
with the uncontrolled cases. It is known that uniform blowing and
adverse-pressure gradients share some similarities in their effect on the
boundary layers, and our results will show that these effects are not
independent. The behaviour of the skin-friction coefficient is analyzed through
the FIK decomposition, and the impact of this control strategy on the
aerodynamic efficiency of the airfoil is discussed.
|
1812.03762v1
|
2018-12-18
|
Gravitational quasinormal modes of black holes in Einstein-aether theory
|
The local Lorentz violation (LV) in gravity sector should show itself in
derivation of the characteristic quasinormal modes (QNMs) of black hole mergers
from their general relativity case. In this paper, I study QNMs of the
gravitational field perturbations to Einstein-aether black holes and, at first
compare them to those in Schwarzschild black hole, and then some other known LV
gravity theories. By comparing to Schwarzschild black hole, the first kind
aether black holes have larger damping rate and the second ones have lower
damping rate. And they all have smaller real oscillation frequency of QNMs. By
comparing to some other LV theories, the QNMs of the first kind aether black
hole are similar to that of the QED-extension limit of standard model
extension, non-minimal coupling to Einstein's tensor and massive gravity
theories. While as to the second kind aether black hole, they are similar to
those of the noncommutative gravity theories and Einstein-Born-Infeld theories.
These similarities may imply that LV in gravity sector and LV in matter sector
have some intrinsic connections.
|
1812.07994v1
|
2018-12-19
|
Rain Calms the Sea - The Impact of Entrained Air
|
We propose a mechanism for the damping of short ocean gravity waves during
rainstorms associated with the injection of air bubbles by rain drops. The
mechanism is proposed as one of the possible explanations that ascribe to rain
a calming effect on ocean surface waves. A model is developed that shows how
wave attenuation increases with the presence of air bubbles in the upper
reaches of the ocean. The model makes predictions of the effective wave
dissipation coefficient, as a function of the volumetric ratio of air to water,
as well as to the rainfall rate. The model predicts dissipation rates that are
in line with experimental estimates of the effective wave damping rate.
|
1812.08200v2
|
2018-12-25
|
Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities
|
In this work we study the blow-up of solutions of a weakly coupled system of
damped semilinear wave equations in the scattering case with power
nonlinearities. We apply an iteration method to study both the subcritical case
and the critical case. In the subcritical case our approach is based on lower
bounds for the space averages of the components of local solutions. In the
critical case we use the slicing method and a couple of auxiliary functions,
recently introduced by Wakasa-Yordanov, to modify the definition of the
functionals with the introduction of weight terms. In particular, we find as
critical curve for the pair (p, q) of the exponents in the nonlinear terms the
same one as for the weakly coupled system of semilinear wave equations with
power nonlinearities.
|
1812.10086v1
|
2018-12-27
|
Global existence of solutions to semilinear damped wave equation with slowly decaying inital data in exterior domain
|
In this paper, we discuss the global existence of weak solutions to the
semilinear damped wave equation \begin{equation*} \begin{cases}
\partial_t^2u-\Delta u + \partial_tu = f(u) & \text{in}\ \Omega\times (0,T), \\
u=0 & \text{on}\ \partial\Omega\times (0,T), \\ u(0)=u_0, \partial_tu(0)=u_1 &
\text{in}\ \Omega, \end{cases} \end{equation*} in an exterior domain $\Omega$
in $\mathbb{R}^N$ $(N\geq 2)$, where $f:\mathbb{R}\to \mathbb{R}$ is a smooth
function behaves like $f(u)\sim |u|^p$. From the view point of weighted energy
estimates given by Sobajima--Wakasugi \cite{SoWa4}, the existence of
global-in-time solutions with small initial data in the sense of
$(1+|x|^2)^{\lambda/2}u_0$, $(1+|x|^2)^{\lambda/2}\nabla u_0$,
$(1+|x|^2)^{\lambda/2}u_1\in L^2(\Omega)$ with $\lambda\in (0,\frac{N}{2})$ is
shown under the condition $p\geq 1+\frac{4}{N+2\lambda}$. The sharp lower bound
for the lifespan of blowup solutions with small initial data $(\varepsilon
u_0,\varepsilon u_1)$ is also given.
|
1812.10664v1
|
2019-02-08
|
Milky Way Halo Vibrations and Incommensurate Stream Velocities
|
Collisionless dark matter galactic halos are expected to exhibit damped
oscillations as a result of ongoing late time accretion. An n-body model of the
cosmological assembly of a Milky Way-like halo is used to quantify the time
dependence of its gravitational field. The simulation contains stellar streams
whose incommensurate perpendicular velocities are found to have an
approximately exponential distribution with a scale of 10-20\kms, depending on
how the stars are selected, comparable to those reported for the Orphan stream.
The fluctuations in the quadrupole moment of the dark matter halo are
sufficient to largely explain the tangential velocities. If velocity
measurements of a larger sample of Milky Way streams finds (or does not find)
the expected distribution of transverse velocities it will lead to limits on
the cross-section of self-interacting dark matter, in which kinetic viscosity
can damp the oscillations more rapidly than the mixing processes of
collisionless dark matter alone.
|
1902.03275v2
|
2019-02-20
|
Dark matter gets DAMPE at high energies
|
The DArk Matter Particle Explorer (DAMPE) mission revealed a break in the
spectrum of cosmic-ray electons and positrons. This is associated with an
excess above the expected backgrounds at energies around 1 TeV. Several authors
have argued that such an excess can be explained in terms of dark matter models
that feature heavy leptophilic WIMPs. These models, however, require some form
annihilation enchancement above that expected from the Milky-Way galactic
centre. This can take the form of either a local over-density near to our solar
system or some form of Sommerfeld enhancement of the annihilation rate. In this
work we will explore the detectability of local over-densities using gamma-ray
and neutrino observatories. We conclude that KM3NET may be the only up-coming
high-energy instrument capable of ruling out the presence of such objects.
However, in the case where the local over-density is an Ultra-Compact Mini
Halo, CTA can also explore the parameter space of these proposed dark matter
models.
|
1902.07468v1
|
2019-02-23
|
General symmetry in the reduced dynamics of two-level system
|
We study general transformation on the density matrix of two-level system
that keeps the expectation value of observable invariant. We introduce a set of
generators that yields hermiticity and trace preserving general transformation
which casts the transformation into simple form. The general transformation is
in general not factorized and not completely positive. Consequently, either the
parameter of transformation or the density matrix it acts on needs to be
restricted. It can transform the system in the forward and backward direction
with regard to its parameter, not as a semigroup in the time translation
symmetry of dynamical maps. The general transformation can rotate the Bloch
vector circularly or hyperbolically, dilate it or translate it. We apply the
general transformation to study the general symmetry of amplitude damping and
phase damping in two-level system. We generalize the generators to higher level
systems.
|
1902.08714v2
|
2019-02-25
|
Interpretation of the cosmic ray positron and electron excesses with an annihilating-decaying dark matter scenario
|
The precise measurements of energy spectra of cosmic ray positrons and/or
electrons by recent experiments show clear excesses above 10 GeV. Moreover, a
potential sharp spectral feature was suggested by the Dark Matter Particle
Explorer (DAMPE) data. These results inspire quite a number of discussions on
the connection with either the annihilation/decay of dark matter (DM) or the
astrophysical origins. Here we discuss a DM scenario in which DM particles
could annihilate and decay into standard model particle pairs simultaneously.
In this model, the peak structure is due to the DM annihilation in a nearby
subhalo and the broad positron/electron excesses are due to the decay of DM in
the Milky Way. This model can reasonably explain the DAMPE and AMS-02 data of
the total $e^+e^-$ spectra and the positron fraction, with model parameters
being consistent with existing constraints. A simple realization of such a DM
model is the spin-1 vector DM model.
|
1902.09235v2
|
2019-02-27
|
Necessary and Sufficient Conditions for Passivity of Velocity-Sourced Impedance Control of Series Elastic Actuators
|
Series Elastic Actuation (SEA) has become prevalent in applications involving
physical human-robot interaction as it provides considerable advantages over
traditional stiff actuators in terms of stability robustness and fidelity of
force control. Several impedance control architectures have been proposed for
SEA. Among these alternatives, the cascaded controller with an inner-most
velocity loop, an intermediate torque loop and an outer-most impedance loop is
particularly favoured for its simplicity, robustness, and performance. In this
paper, we derive the \emph{necessary and sufficient conditions} to ensure the
passivity of this cascade-controller architecture for rendering two most common
virtual impedance models. Based on the newly established passivity conditions,
we provide non-conservative design guidelines to haptically display a null
impedance and a pure spring while ensuring the passivity of interaction. We
also demonstrate the importance of including physical damping in the actuator
model during derivation of passivity conditions, when integral controllers are
utilized. In particular, we show the adversary effect of physical damping on
system passivity.
|
1902.10607v2
|
2019-03-01
|
Response to: [Comment on Quantization of the damped harmonic oscillator [Serhan et al, J. Math. Phys. 59, 082105 (2018)]]
|
This is a response to a recently reported comment [1] on paper [J. Math.
Phys.59, 082105 (2018)] regarding the quantization of damped harmonic
oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We
assert here that the calculation of Eq. (29) of [2] is incorrect, and thus the
subsequent steps via the Nikiforov-Uvarov method are affected, and the energy
eigenvalues should have been complex. However, we show here that the
Hermiticity of the Hamiltonian should be firstly achieved to make the correct
transition from classical Hamiltonian to quantum counterpart, and this can be
reached using the symmetrization rule. Applying the canonical quantization on
the resulted Hermitian Hamiltonian and then using the Nikiforov-Uvarov method
correctly, the energy eigenvalues will be real and exactly as given by Eq. (35)
of [2].
|
1903.00352v2
|
2019-03-07
|
Current-induced motion of twisted skyrmions
|
Twisted skyrmions, whose helicity angles are different from that of Bloch
skyrmions and N\'eel skyrmions, have already been demonstrated in experiments
recently. In this work, we first contrast the magnetic structure and origin of
the twisted skyrmion with other three types of skyrmion including Bloch
skyrmion, N\'eel skyrmion and antiskyrmion. Following, we investigate the
dynamics of twisted skyrmions driven by the spin transfer toque (STT) and the
spin Hall effect (SHE) by using micromagnetic simulations. It is found that the
spin Hall angle of the twisted skyrmion is related to the dissipative force
tensor and the Gilbert damping both for the motions induced by the STT and the
SHE, especially for the SHE induced motion, the skyrmion Hall angle depends
substantially on the skyrmion helicity. At last, we demonstrate that the
trajectory of the twisted skyrmion can be controlled in a two dimensional plane
with a Gilbert damping gradient. Our results provide the understanding of
current-induced motion of twisted skyrmions, which may contribute to the
applications of skyrmion-based racetrack memories.
|
1903.02812v1
|
2019-03-08
|
Protecting quantum correlations in presence of generalised amplitude damping channel: the two-qubit case
|
Any kind of quantum resource useful in different information processing tasks
is vulnerable to several types of environmental noise. Here we study the
behaviour of quantum correlations such as entanglement and steering in
two-qubit systems under the application of the generalised amplitude damping
channel and propose some protocols towards preserving them under this type of
noise. First, we employ the technique of weak measurement and reversal for the
purpose of preservation of correlations. We then show how the evolution under
the channel action can be seen as an unitary process. We use the technique of
weak measurement and most general form of selective positive operator valued
measure (POVM) to achieve preservation of correlations for a significantly
large range of parameter values.
|
1903.03550v2
|
2019-03-17
|
Generalized Euler, Smoluchowski and Schrödinger equations admitting self-similar solutions with a Tsallis invariant profile
|
The damped isothermal Euler equations, the Smoluchowski equation and the
damped logarithmic Schr\"odinger equation with a harmonic potential admit
stationary and self-similar solutions with a Gaussian profile. They satisfy an
$H$-theorem for a free energy functional involving the von Weizs\"acker
functional and the Boltzmann functional. We derive generalized forms of these
equations in order to obtain stationary and self-similar solutions with a
Tsallis profile. In particular, we introduce a nonlinear Schr\"odinger equation
involving a generalized kinetic term characterized by an index $q$ and a
power-law nonlinearity characterized by an index $\gamma$. We derive an
$H$-theorem satisfied by a generalized free energy functional involving a
generalized von Weizs\"acker functional (associated with $q$) and a Tsallis
functional (associated with $\gamma$). This leads to a notion of generalized
quantum mechanics and generalized thermodynamics. When $q=2\gamma-1$, our
nonlinear Schr\"odinger equation admits an exact self-similar solution with a
Tsallis invariant profile. Standard quantum mechanics (Schr\"odinger) and
standard thermodynamics (Boltzmann) are recovered for $q=\gamma=1$.
|
1903.07111v1
|
2019-03-21
|
Creating localized plasma wave by ionization of doped semiconductors
|
Localized plasma waves can be generated by suddenly ionizing extrinsic
semiconductors with spatially periodic dopant densities. The built-in
electrostatic potentials at the metallurgical junctions, combined with electron
density ripples, offer the exact initial condition for exciting long-lasting
plasma waves upon ionization. This method can create plasma waves with a
frequency between a few terahertz to sub-petahertz without substantial damping.
The lingering plasma waves can seed backward Raman amplification in a wide
range of resonance frequencies up to the extreme ultraviolet regime. Chirped
wavevectors and curved wavefronts allow focusing the amplified beam in both
longitudinal and transverse dimensions. The main limitation to this method
appears to be obtaining sufficiently low plasma density from solid-state
materials to avoid collisional damping.
|
1903.09013v2
|
2019-03-22
|
Noncommutative approach to diagnose degenerate Higgs bosons at 125 GeV
|
We propose a noncommutative (NC) version for a global O(2) scalar field
theory, whose damping feature is introduced into the scalar field theory
through the NC parameter. In this context, we investigate how noncommutative
drives spontaneous symmetry breaking (SSB) and Higgs-Kibble mechanisms and how
the damping feature workout. Indeed, we show that the noncommutativity plays an
important role in such mechanisms, i.e., the Higgs mass and VEV dependent on NC
parameter. After that, it is explored the consequences of noncommutativity
dependence of Higgs mass and VEV: for the first, it is shown that there are a
mass-degenerate Higgs bosons near 126.5 GeV, parametrized by the
noncommutativity; for the second, the gauge fields gain masses that present a
noncommutativity contribution.
|
1903.09727v2
|
2019-05-02
|
The floatability of aerosols and waves damping on Titan's seas
|
Titan, Saturn's largest moon, has a dense atmosphere, together with lakes and
seas of liquid hydrocarbons. These liquid bodies, which are in polar regions
and up to several hundred kilometres in diameter, generally have smooth
surfaces despite evidence of near-surface winds. Photochemically generated
organic aerosols form a haze that can settle and potentially interact with the
liquid surface. Here we investigate the floatability of these aerosols on
Titan's seas and their potential to dampen waves. We find that the majority of
aerosols are denser than the liquid hydrocarbons, but that some could have
liquid-repelling properties. From calculation of the capillary forces, we
propose that these 'liquidophobic' aerosols could float and form a persistent
film on Titan's seas. We numerically model the wave damping efficiency of such
a film under the conditions on Titan, demonstrating that even a film one
molecule thick may inhibit formation of waves larger than a few centimetres in
wavelength. We conclude that the presence of a floating film of aerosols
deposited on Titan's lakes and seas could explain the remarkable smoothness of
their surfaces.
|
1905.00760v1
|
2019-05-02
|
Holographic Plasmon Relaxation with and without Broken Translations
|
We study the dynamics and the relaxation of bulk plasmons in strongly coupled
and quantum critical systems using the holographic framework. We analyze the
dispersion relation of the plasmonic modes in detail for an illustrative class
of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we
entangle the complicated interplay between the three least damped modes and
shed light on the underlying physical processes. Such as the dependence of the
plasma frequency and the effective relaxation time in terms of the
electromagnetic coupling, the charge and the temperature of the system.
Introducing momentum dissipation, we then identify its additional contribution
to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of
translational invariance. Upon dialing the strength of the SSB, we observe an
increase of the longitudinal sound speed controlled by the elastic moduli and a
decrease in the plasma frequency of the gapped plasmon. We comment on the
condensed matter interpretation of this mechanism.
|
1905.00804v2
|
2019-05-05
|
Effective spin-mixing conductance of heavy-metal-ferromagnet interfaces
|
The effective spin-mixing conductance (G_eff) of a heavy metal/ferromagnet
(HM/FM) interface characterizes the efficiency of the interfacial spin
transport.Accurately determining G_eff is critical to the quantitative
understanding of measurements of direct and inverse spin Hall effects. G_eff is
typically ascertained from the inverse dependence of magnetic damping on the FM
thickness under the assumption that spin pumping is the dominant mechanism
affecting this dependence.Here we report that, this assumption fails badly in
many in-plane magnetized prototypical HM/FM systems in the nm-scale thickness
regime. Instead, the majority of the damping is from two-magnon scattering at
the FM interface, while spin-memory-loss scattering at the interface can also
be significant.If these two effects are neglected, the results will be an
unphysical "giant" apparent G_eff and hence considerable underestimation of
both the spin Hall ratio and the spin Hall conductivity in inverse/direct spin
Hall experiments.
|
1905.01577v2
|
2019-05-07
|
Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case
|
This paper is devoted to derive integral representation formulae for the
solution of an inhomogeneous linear wave equation with time-dependent damping
and mass terms, that are scale-invariant with respect to the so-called
hyperbolic scaling. Yagdjian's integral transform approach is employed for this
purpose. The main step in our argument consists in determining the kernel
functions for the different integral terms, which are related to the source
term and to initial data. We will start with the one dimensional case (in
space). We point out that we may not apply in a straightforward way Duhamel's
principle to deal with the source term since the coefficients of lower order
terms make our model not invariant by time translation. On the contrary, we
shall begin with the representation formula for the inhomogeneous equation with
vanishing data by using a revised Duhamel's principle. Then, we will derive the
representation of the solution in the homogeneous case with nontrivial data.
After deriving the formula in the one dimensional case, the classical approach
by spherical means is used in order to deal with the odd dimensional case.
Finally, using the method of descent, the representation formula in the even
dimensional case is proved.
|
1905.02408v1
|
2019-05-07
|
Optimal decay for the $n$-dimensional incompressible Oldroyd-B model without damping mechanism
|
By a new energy approach involved in the high frequencies and low frequencies
decomposition in the Besov spaces, we obtain the optimal decay for the
incompressible Oldroyd-B model without damping mechanism in $\mathbb{R}^n$
($n\ge 2$). More precisely, let $(u,\tau)$ be the global small solutions
constructed in [18],
we prove for any $(u_0,\tau_0)\in{\dot{B}_{2,1}^{-s}}(\mathbb{R}^n)$ that
\begin{eqnarray*}
\big\|\Lambda^{\alpha}(u,\Lambda^{-1}\mathbb{P}\mathrm{div}\tau)\big\|_{L^q}
\le C (1+t)^{-\frac n4-\frac {(\alpha+s)q-n}{2q}},
\quad\Lambda\stackrel{\mathrm{def}}{=}\sqrt{-\Delta}, \end{eqnarray*}
with $\frac n2-1<s<\frac np, $ $2\leq p \leq \min(4,{2n}/({n-2})),\ p\not=4\
\hbox{ if }\ n=2,$ and $p\leq q\leq\infty$, $\frac nq-\frac np-s<\alpha
\leq\frac nq-1$. The proof relies heavily on the special dissipative structure
of the equations and some commutator estimates and various interpolations
between Besov type spaces. The method also works for other parabolic-hyperbolic
systems in which the Fourier splitting technique is invalid.
|
1905.02604v1
|
2019-05-12
|
Transport and Phonon Damping in $^{\bf 4}$He
|
The dynamic structure function $S(k,\omega)$ informs about the dispersion and
damping of excitations. We have recently (Phys. Rev. B {\bf 97}, 184520 (2018))
compared experimental results for $S(k,\omega)$ from high-precision neutron
scattering experiment and theoretical results using the ``dynamic many-body
theory'' (DMBT), showing excellent agreement over the whole experimentally
accessible pressure regime. This paper focuses on the specific aspect of the
propagation of low-energy phonons. We report calculations of the phonon
mean-free path and phonon life time in liquid \he4 as a function of wave length
and pressure. Historically, the question was of interest for experiments of
quantum evaporation. More recently, there is interest in the potential use of
$^4$He as a detector for low-energy dark matter (K. Schulz and Kathryn M.
Zurek, Phys. Rev. Lett. {\bf 117}, 121302 (2016)). While the mean free path of
long wave length phonons is large, phonons of intermediate energy can have a
short mean free path of the order of $\mu$m. Comparison of different levels of
theory indicate that reliable predictions of the phonon mean free path can be
made only by using the most advanced many--body method available, namely, DMBT.
|
1905.04759v1
|
2019-05-15
|
Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
|
We identify a set of dynamical maps of open quantum system, and refer to them
as "$ \epsilon $-Markovian" maps. It is constituted of maps which, in a higher
dimensional system-environment Hilbert space, possibly violate Born
approximation but only a "little". We characterize the
"$\epsilon$-nonmarkovianity" of a general dynamical map by the minimum distance
of that map from the set of $\epsilon$-Markovian maps. We analytically derive
an inequality which gives a bound on the $ \epsilon$-nonmarkovianity of the
dynamical map, in terms of an entanglement-like resource generated between the
system and its "immediate" environment. In the special case of a vanishing
$\epsilon$, this inequality gives a relation between the
$\epsilon$-nonmarkovianity of the reduced dynamical map on the system and the
entanglement generated between the system and its immediate environment. We
numerically investigate the behavior of the similar distant based measures of
non-Markovianity for classes of amplitude damping and phase damping channels.
|
1905.06198v3
|
2019-05-15
|
A remark on triviality for the two-dimensional stochastic nonlinear wave equation
|
We consider the two-dimensional stochastic damped nonlinear wave equation
(SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In
particular, we investigate the limiting behavior of solutions to SdNLW with
regularized noises and establish triviality results in the spirit of the work
by Hairer, Ryser, and Weber (2012). More precisely, without renormalization of
the nonlinearity, we establish the following two limiting behaviors; (i) in the
strong noise regime, we show that solutions to SdNLW with regularized noises
tend to 0 as the regularization is removed and (ii) in the weak noise regime,
we show that solutions to SdNLW with regularized noises converge to a solution
to a deterministic damped nonlinear wave equation with an additional mass term.
|
1905.06278v3
|
2019-05-17
|
Chiral p-wave superconductors have complex coherence and magnetic field penetration lengths
|
We show that in superconductors that break time reversal symmetry and have
anisotropy, such as p+ip materials, all order parameters and magnetic modes are
mixed. Excitation of the gap fields produces an excitation of the magnetic
field and vice versa. Correspondingly the long-range decay of the magnetic
field and order parameter are in general given by the same exponent. Thus one
cannot characterize p+ip superconductors by the usual coherence and magnetic
field penetration lengths. Instead the system has normal modes that are
associated with linear combinations of magnetic fields, moduli of and phases of
the order parameter components. Each such normal mode has its own decay length
that plays the role of a hybridized coherence/magnetic field penetration
length. On a large part of the parameter space these exponents are complex.
Therefore the system in general has damped oscillatory decay of the magnetic
field accompanied by damped oscillatory variation of the order parameter
fields.
|
1905.07296v2
|
2019-05-20
|
Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping
|
In this paper we study blow-up and lifespan estimate for solutions to the
Cauchy problem with small data for semilinear wave equations with scattering
damping and negative mass term. We show that the negative mass term will play a
dominant role when the decay of its coefficients is not so fast, thus the
solutions will blow up in a finite time. What is more, we establish a lifespan
estimate from above which is much shorter than the usual one.
|
1905.08100v1
|
2019-05-21
|
Low-pass-filter-based shock response spectrum and the evaluation method of transmissibility between equipment and sensitive components interfaces
|
According to the features of the sources of pyroshock and ballistic shock,
this study considers the pyroshock and ballistic shock generated by their
respective impulsive sources as damped harmonic waves with different
frequencies. According to the linear superposition assumption of damped
harmonic waves in a linear elastic structure, a shock analysis method based on
low-pass-filtered shock signals and their corresponding shock response spectrum
(SRS), termed as low-pass-filter-based shock response spectrum (LPSRS), is
proposed. LPSRS contains rich information of the frequency distribution of the
shock excitation signal. A method to calculate shock transmissibility is
proposed based on LPSRS and basic modal information of the equipment structure.
LPSRS and SRS curves can be predicted at any given position of the equipment
structure. The prediction method is validated by finite element method (FEM)
simulation.
|
1905.10190v1
|
2019-05-24
|
Sound damping in glasses: interplay between anharmonicities and elastic heterogeneities
|
Some facets of the way sound waves travel through glasses are still unclear.
Recent works have shown that in the low-temperature harmonic limit a crucial
role in controlling sound damping is played by local elastic heterogeneity.
Sound waves propagation has been demonstrated to be strongly affected by
inhomogeneous mechanical features of the materials, which add to the anharmonic
couplings at finite temperatures. We describe the interplay between these two
effects by molecular dynamics simulation of a model glass. In particular, we
focus on the transverse components of the vibrational excitations in terms of
dynamic structure factors, and characterize the temperature dependence of sound
attenuation rates in an extended frequency range. We provide a complete picture
of all phenomena, in terms encompassing both theory and experiments.
|
1905.10235v2
|
2019-05-27
|
A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type
|
In this note, we prove blow-up results for semilinear wave models with
damping and mass in the scale-invariant case and with nonlinear terms of
derivative type. We consider the single equation and the weakly coupled system.
In the first case we get a blow-up result for exponents below a certain shift
of the Glassey exponent. For the weakly coupled system we find as critical
curve a shift of the corresponding curve for the weakly coupled system of
semilinear wave equations with the same kind of nonlinearities. Our approach
follows the one for the respective classical wave equation by Zhou Yi. In
particular, an explicit integral representation formula for a solution of the
corresponding linear scale-invariant wave equation, which is derived by using
Yagdjian's integral transform approach, is employed in the blow-up argument.
While in the case of the single equation we may use a comparison argument, for
the weakly coupled system an iteration argument is applied.
|
1905.11025v2
|
2019-05-28
|
Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
|
Using methods of stochastic dynamics, we have studied stationary states in
the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape
of stationary states depend both on the potential type and the damping. If the
damping is strong enough, for potential wells which in the overdamped regime
produce multimodal stationary states, stationary states in the underdamped
regime can be multimodal with the same number of modes like in the overdamped
regime. For the parabolic potential, the stationary density is always unimodal
and it is given by the two dimensional $\alpha$-stable density. For the mixture
of quartic and parabolic single-well potentials the stationary density can be
bimodal. Nevertheless, the parabolic addition, which is strong enough, can
destroy bimodlity of the stationary state.
|
1905.12078v2
|
2019-08-01
|
The $J$-method for the Gross-Pitaevskii eigenvalue problem
|
This paper studies the $J$-method of [E. Jarlebring, S. Kvaal, W. Michiels.
SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014] for nonlinear eigenvector problems
in a general Hilbert space framework. This is the basis for variational
discretization techniques and a mesh-independent numerical analysis. A simple
modification of the method mimics an energy-decreasing discrete gradient flow.
In the case of the Gross-Pitaevskii eigenvalue problem, we prove global
convergence towards an eigenfunction for a damped version of the $J$-method.
More importantly, when the iterations are sufficiently close to an
eigenfunction, the damping can be switched off and we recover a local linear
convergence rate previously known from the discrete setting. This quantitative
convergence analysis is closely connected to the~$J$-method's unique feature of
sensitivity with respect to spectral shifts. Contrary to classical gradient
flows, this allows both the selective approximation of excited states as well
as the amplification of convergence beyond linear rates in the spirit of the
Rayleigh quotient iteration for linear eigenvalue problems. These advantageous
convergence properties are demonstrated in a series of numerical experiments
involving exponentially localized states under disorder potentials and vortex
lattices in rotating traps.
|
1908.00333v2
|
2019-08-02
|
How do Conservative Backbone Curves Perturb into Forced Responses? A Melnikov Function Analysis
|
Weakly damped mechanical systems under small periodic forcing tend to exhibit
periodic response in a close vicinity of certain periodic orbits of their
conservative limit. Specifically, amplitude frequency plots for the
conservative limit have often been noted, both numerically and experimentally,
to serve as backbone curves for the near resonance peaks of the forced
response. In other cases, such a relationship between the unforced and forced
response was not observed. Here we provide a systematic mathematical analysis
that predicts which members of conservative periodic orbit families will serve
as backbone curves for the forced-damped response. We also obtain mathematical
conditions under which approximate numerical and experimental approaches, such
as energy balance and force appropriation, are justifiable. Finally, we derive
analytic criteria for the birth of isolated response branches (isolas) whose
identification is otherwise challenging from numerical continuation.
|
1908.00721v3
|
2019-08-05
|
Tunable strong coupling of two adjacent optical λ/2 Fabry-Pérot microresonators
|
Optical half-wave microresonators enable to control the optical mode density
around a quantum system and thus to modify the temporal emission properties. If
the coupling rate exceeds the damping rate, strong coupling between a
microresonator and a quantum system can be achieved, leading to a coherent
energy exchange and the creation of new hybrid modes. Here, we investigate
strong coupling between two adjacent lambda/2 Fabry-P\'erot microresonators,
where the resonance of one microresonator can be actively tuned across the
resonance of the other microresonator. The transmission spectra of the coupled
microresonators show a clear anticrossing behavior, which proves that the two
cavity modes are strongly coupled. Additionally, we can vary the coupling rate
by changing the resonator geometry and thereby investigate the basic principles
of strong coupling with a well-defined model system. Finally, we will show that
such a coupled system can theoretically be modelled by coupled damped harmonic
oscillators.
|
1908.01566v1
|
2019-07-27
|
An extension of the second order dynamical system that models Nesterov's convex gradient method
|
In this paper we deal with a general second order continuous dynamical system
associated to a convex minimization problem with a Fr\`echet differentiable
objective function. We show that inertial algorithms, such as Nesterov's
algorithm, can be obtained via the natural explicit discretization from our
dynamical system. Our dynamical system can be viewed as a perturbed version of
the heavy ball method with vanishing damping, however the perturbation is made
in the argument of the gradient of the objective function. This perturbation
seems to have a smoothing effect for the energy error and eliminates the
oscillations obtained for this error in the case of the heavy ball method with
vanishing damping, as some numerical experiments show. We prove that the value
of the objective function in a generated trajectory converges in order O(1/t^2)
to the global minimum of the objective function. Moreover, we obtain that a
trajectory generated by the dynamical system converges to a minimum point of
the objective function.
|
1908.02574v1
|
2019-08-07
|
Interfacial contributions to spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers
|
The thickness dependence of spin-orbit torque and magnetoresistance in
ferromagnet/heavy-metal bilayers is studied using the first-principles
non-equilibrium Green's function formalism combined with the Anderson disorder
model. A systematic expansion in orthogonal vector spherical harmonics is used
for the angular dependence of the torque. The damping-like torque in Co/Pt and
Co/Au bilayers can be described as a sum of the spin-Hall contribution, which
increases with thickness in agreement with the spin-diffusion model, and a
comparable interfacial contribution. The magnetoconductance in the plane
perpendicular to the current in Co/Pt bilayers is of the order of a conductance
quantum per interfacial atom, exceeding the prediction of the spin-Hall model
by more than an order of magnitude. This suggests that the "spin-Hall
magnetoresistance," similarly to the damping-like torque, has a large
interfacial contribution unrelated to the spin-Hall effect.
|
1908.02680v2
|
2019-08-16
|
Dynamics of Hot Bose-Einstein Condensates: stochastic Ehrenfest relations for number and energy damping
|
Describing partially-condensed Bose gases poses a long-standing theoretical
challenge. We present exact stochastic Ehrenfest relations for the stochastic
projected Gross-Pitaevskii equation, including both number and energy damping
mechanisms, and all projector terms that arise from the energy cutoff
separating system from reservoir. We test the theory by applying it to the
centre of mass fluctuations of a harmonically trapped prolate system, finding
close agreement between c-field simulations and analytical results. The
formalism lays the foundation to analytically explore experimentally accessible
hot Bose-Einstein condensates.
|
1908.05809v3
|
2019-08-12
|
On a simple derivation of the very low damping escape rate for classical spins by modifying the method of Kramers
|
The original perturbative Kramers' method (starting from the phase space
coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion
equation for Newtonian particles with separable and additive Hamiltonians is
generalized to yield the energy-controlled diffusion equation and thus the very
low damping (VLD) escape rate including spin-transfer torque for classical
giant magnetic spins with two degrees of freedom. These have dynamics governed
by the magnetic Langevin and Fokker-Planck equations and thus are generally
based on non-separable and non-additive Hamiltonians. The derivation of the VLD
escape rate directly from the (magnetic) Fokker-Planck equation for the surface
distribution of magnetization orientations in the configuration space of the
polar and azimuthal angles $(\vartheta, \varphi)$ is much simpler than those
previously used.
|
1908.06747v1
|
2019-08-22
|
Improving the dynamics of quantum sensors with reinforcement learning
|
Recently proposed quantum-chaotic sensors achieve quantum enhancements in
measurement precision by applying nonlinear control pulses to the dynamics of
the quantum sensor while using classical initial states that are easy to
prepare. Here, we use the cross-entropy method of reinforcement learning to
optimize the strength and position of control pulses. Compared to the
quantum-chaotic sensors with periodic control pulses in the presence of
superradiant damping, we find that decoherence can be fought even better and
measurement precision can be enhanced further by optimizing the control. In
some examples, we find enhancements in sensitivity by more than an order of
magnitude. By visualizing the evolution of the quantum state, the mechanism
exploited by the reinforcement learning method is identified as a kind of
spin-squeezing strategy that is adapted to the superradiant damping.
|
1908.08416v2
|
2019-08-28
|
Spin functional renormalization group for quantum Heisenberg ferromagnets: Magnetization and magnon damping in two dimensions
|
We use the spin functional renormalization group recently developed by two of
us [J. Krieg and P. Kopietz, Phys. Rev. B $\bf{99}$, 060403(R) (2019)] to
calculate the magnetization $M ( H , T )$ and the damping of magnons due to
classical longitudinal fluctuations of quantum Heisenberg ferromagnets. In
order to guarantee that for vanishing magnetic field $H \rightarrow 0$ the
magnon spectrum is gapless when the spin rotational invariance is spontaneously
broken, we use a Ward identity to express the magnon self-energy in terms of
the magnetization. In two dimensions our approach correctly predicts the
absence of long-range magnetic order for $H=0$ at finite temperature $T$. The
magnon spectrum then exhibits a gap from which we obtain the transverse
correlation length. We also calculate the wave-function renormalization factor
of the magnons. As a mathematical by-product, we derive a recursive form of the
generalized Wick theorem for spin operators in frequency space which
facilitates the calculation of arbitrary time-ordered connected correlation
functions of an isolated spin in a magnetic field.
|
1908.10753v2
|
2019-09-03
|
Learning Elastic Constitutive Material and Damping Models
|
Commonly used linear and nonlinear constitutive material models in
deformation simulation contain many simplifications and only cover a tiny part
of possible material behavior. In this work we propose a framework for learning
customized models of deformable materials from example surface trajectories.
The key idea is to iteratively improve a correction to a nominal model of the
elastic and damping properties of the object, which allows new forward
simulations with the learned correction to more accurately predict the behavior
of a given soft object. Space-time optimization is employed to identify gentle
control forces with which we extract necessary data for model inference and to
finally encapsulate the material correction into a compact parametric form.
Furthermore, a patch based position constraint is proposed to tackle the
challenge of handling incomplete and noisy observations arising in real-world
examples. We demonstrate the effectiveness of our method with a set of
synthetic examples, as well with data captured from real world homogeneous
elastic objects.
|
1909.01875v2
|
2019-09-06
|
Effect of Tantalum spacer thickness and deposition conditions on the properties of MgO/CoFeB/Ta/CoFeB/MgO free layers
|
To get stable perpendicularly magnetized tunnel junctions at small device
dimensions, composite free layers that comprise two MgO/FeCoB interfaces as
sources of interface anisotropy are generally used. Proper cristallisation and
annealing robustness is typically ensured by the insertion of a spacer layer of
the early transition metal series within the FeCoB layer. We study the
influence of the spacer thickness and growth condition on the switching metrics
of tunnel junctions thermally annealed at 400$^\circ$C for the case of 1-4
\r{A} Ta spacers. Thick Ta spacer results in a large anisotropies indicative of
a better defined top FeCoB/MgO interface, but this is achieved at the
systematic expense of a stronger damping. For the best anisotropy-damping
compromise, junctions of diameter 22 nm can still be stable and spin-torque
switched. Coercivity and inhomogeneous linewidth broadening, likely arising
from roughness at the FeCoB/Ta interface, can be reduced if a sacrificial Mg
layer is inserted before the Ta spacer deposition.
|
1909.02741v1
|
2019-09-10
|
Spin Pumping from Permalloy into Uncompensated Antiferromagnetic Co doped Zinc Oxide
|
Heterostructures of Co-doped ZnO and Permalloy were investigated for their
static and dynamic magnetic interaction. The highly Co-doped ZnO is
paramagentic at room temperature and becomes an uncompensated antiferromagnet
at low temperatures, showing a narrowly opened hysteresis and a vertical
exchange bias shift even in the absence of any ferromagnetic layer. At low
temperatures in combination with Permalloy an exchange bias is found causing a
horizontal as well as vertical shift of the hysteresis of the heterostructure
together with an increase in coercive field. Furthermore, an increase in the
Gilbert damping parameter at room temperature was found by multifrequency FMR
evidencing spin pumping. Temperature dependent FMR shows a maximum in magnetic
damping close to the magnetic phase transition. These measurements also
evidence the exchange bias interaction of Permalloy and long-range ordered
Co-O-Co structures in ZnO, that are barely detectable by SQUID due to the
shorter probing times in FMR.
|
1909.04362v3
|
2019-09-19
|
Blow-up for Strauss type wave equation with damping and potential
|
We study a kind of nonlinear wave equations with damping and potential, whose
coefficients are both critical in the sense of the scaling and depend only on
the spatial variables. Based on the earlier works, one may think there are two
kinds of blow-up phenomenons when the exponent of the nonlinear term is small.
It also means there are two kinds of law to determine the critical exponent. In
this paper, we obtain a blow-up result and get the estimate of the upper bound
of the lifespan in critical and sub-critical cases. All of the results support
such a conjecture, although for now, the existence part is still open.
|
1909.08885v3
|
2019-09-23
|
Inference of modes for linear stochastic processes
|
For dynamical systems that can be modelled as asymptotically stable linear
systems forced by Gaussian noise, this paper develops methods to infer or
estimate their modes from observations in real time. The modes can be real or
complex. For a real mode, we wish to infer its damping rate and mode shape. For
a complex mode, we wish to infer its frequency, damping rate and (complex) mode
shape. Their amplitudes and correlations are encoded in a mode covariance
matrix. The work is motivated and illustrated by the problem of detection of
oscillations in power flow in AC electrical networks. Suggestions of other
applications are given.
|
1909.10247v2
|
2019-11-06
|
High spin mixing conductance and spin interface transparency at $Co_2Fe_{0.4}Mn_{0.6}Si$ Heusler alloy and Pt interface
|
Ferromagnetic materials exhibiting low magnetic damping ($\alpha$) and
moderately high saturation magnetization are required from the viewpoints of
generation, transmission and detection of spin wave. Since spin-to-charge
conversion efficiency is another important parameter, high spin mixing
conductance ($g_{r}^{\uparrow \downarrow}$) is the key for efficient
spin-to-charge conversion. Full Heusler alloys e.g. $Co_2Fe_{0.4}Mn_{0.6}Si$
(CFMS), which are predicted to be 100$\%$ spin polarized, possess low $\alpha$.
However, the $g_{r}^{\uparrow \downarrow}$ at the interface between CFMS and a
paramagnet has not fully been understood. Here, we report the investigations of
spin pumping and inverse spin Hall effect in $CFMS/Pt$ bilayers. Damping
analysis indicates the presence of significant spin pumping at the interface of
CFMS and Pt, which is also confirmed by the detection of inverse spin Hall
voltage. We show that in CFMS/Pt the $g_{r}^{\uparrow \downarrow}$
(1.77$\times$10$^{20}$m$^{-2}$) and interface transparency (84$\%$) are higher
compared to values reported for other ferromagnet/heavy metal systems.
|
1911.02230v1
|
2019-11-10
|
Influence of resonances on the noise performance of SQUID susceptometers
|
Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry
simultaneously images the local magnetic fields and susceptibilities above a
sample with sub-micron spatial resolution. Further development of this
technique requires a thorough understanding of the current, voltage, and flux
characteristics of scanning SQUID susceptometers. These sensors often have
striking anomalies in their current-voltage characteristics, which we believe
to be due to electromagnetic resonances. The effect of these resonances on the
performance of these SQUIDs is unknown. To explore the origin and impact of the
resonances, we have developed a model that qualitatively reproduces the
experimentally-determined current-voltage characteristics of our scanning SQUID
susceptometers. We use this model to calculate the noise characteristics of
SQUIDs of different designs. We find that the calculated ultimate flux noise is
better in susceptometers with damping resistors that diminish the resonances
than susceptometers without damping resistors. Such calculations will enable
the optimization of the signal-to-noise characteristics of scanning SQUID
susceptometers.
|
1911.03836v2
|
2019-11-13
|
Impact of the crystal orientation on spin-orbit torques in Fe/Pd bilayers
|
Spin-orbit torques in ferromagnetic (FM)/non-magnetic (NM) heterostructures
offer more energy-efficient means to realize spin-logic devices; however, their
strengths are determined by the heterostructure interface. This work examines
crystal orientation impact on the spin-orbit torque efficiency in different
Fe/Pd bilayer systems. Spin torque ferromagnetic measurements evidence that the
damping-like torque efficiency is higher in epitaxial than in polycrystalline
bilayer structures while the field-like torque is negligible in all bilayer
structures. The strength of the damping-like torque decreases with
deterioration of the bilayer epitaxial quality. The present finding provides
fresh insight for the enhancement of spin-orbit torques in magnetic
heterostructures.
|
1911.05487v1
|
2020-01-04
|
Finite Difference/Galerkin Finite Element Simulation of the Semi-Linear Wave Equation with Scale-Invariant Damping and Mass and Power Non-Linearity
|
This study is concern with the numerical solution of the initial boundary
value problem (IBVP) for the semilinear scale-invariant wave equation with
damping and mass and power non-linearity. Numerical results of the
aforementioned IBVP is obtained by using standart Galerkin finite element
method (GFEM) for the spatial variable and the temporal variable is discretized
with the finite difference method (FDM). The FDM is also used for the
discretization of the spatial variable for the accuracy of the numerical
results. The obtained numerical results with different numerical schemes are
observed compatible. Numerical simulation of the considered problem is given
for the different initial conditions.
|
2001.01075v2
|
2020-01-05
|
Quantifying quantum non-Markovianity based on quantum coherence via skew information
|
Based on the nonincreasing property of quantum coherence via skew information
under incoherent completely positive and trace-preserving maps, we propose a
non-Markovianity measure for open quantum processes. As applications, by
applying the proposed measure to some typical noisy channels, we find that it
is equivalent to the three previous measures of non-Markovianity for phase
damping and amplitude damping channels, i.e., the measures based on the quantum
trace distance, dynamical divisibility, and quantum mutual information. For the
random unitary channel, it is equivalent to the non-Markovianity measure based
on $l_1$ norm of coherence for a class of output states and it is incompletely
equivalent to the measure based on dynamical divisibility. We also use the
modified Tsallis relative $\alpha$ entropy of coherence to detect the
non-Markovianity of dynamics of quantum open systems, the results show that the
modified Tsallis relative $\alpha$ entropy of coherence are more comfortable
than the original Tsallis relative $\alpha$ entropy of coherence for small
$\alpha$.
|
2001.01261v1
|
2020-01-07
|
von Neumann entropy and the entropy production of a damped harmonic oscillator
|
In this paper we analyze the entropy and entropy production of a non-isolated
quantum system described within the quantum Brownian motion framework. This is
a very general and paradigmatic framework for describing non-isolated quantum
systems and can be used in any kind of coupling regime. We start by considering
the application of von Neumann entropy to an arbitrarily damped quantum system
making use of its reduced density operator. We argue that this application is
formally valid and develop a path integral method to evaluate that quantity
analytically. We apply this technique to a harmonic oscillator in contact with
a heat bath and obtain an exact form for its entropy. Then we study the entropy
production of this system and enlighten important characteristics of its
thermodynamical behavior on the pure quantum realm and also address their
transition to the classical limit.
|
2001.02261v1
|
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