publicationDate
stringlengths 1
2.79k
| title
stringlengths 1
36.5k
⌀ | abstract
stringlengths 1
37.3k
⌀ | id
stringlengths 9
47
|
|---|---|---|---|
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
|
2018-03-06
|
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
|
2018-04-04
|
Stabilizable Gaussian states
|
The unavoidable interaction of quantum systems with their environment usually
results in the loss of desired quantum resources. Suitably chosen system
Hamiltonians, however, can, to some extent, counteract such detrimental decay,
giving rise to the set of stabilizable states. Here, we discuss the possibility
to stabilize Gaussian states in continuous-variable systems. We identify
necessary and sufficient conditions for such stabilizability and elaborate
these on two benchmark examples, a single, damped mode and two locally damped
modes. The obtained stabilizability conditions, which are formulated in terms
of the states' covariance matrices, are, more generally, also applicable to
non-Gaussian states, where they may similarly help to, e.g., discuss
entanglement preservation and/or detection up to the second moments.
|
1804.01315v2
|
2018-04-11
|
Collisionless sound in a uniform two-dimensional Bose gas
|
Using linear response theory within the Random Phase Approximation, we
investigate the propagation of sound in a uniform two dimensional (2D) Bose gas
in the collisionless regime. We show that the sudden removal of a static
density perturbation produces a damped oscillatory behavior revealing that
sound can propagate also in the absence of collisions, due to mean-field
interaction effects. Our analysis points out the crucial role played by Landau
damping. We support our predictions by performing numerical simulations with
the stochastic (projected) Gross-Pitaevskii equation. The results are
consistent with the recent experimental observation of sound in a weakly
interacting 2D Bose gas both below and above the superfluid
Berezinskii-Kosterlitz-Thouless transition.
|
1804.04032v2
|
2018-04-11
|
Sound propagation in a uniform superfluid two-dimensional Bose gas
|
In superfluid systems several sound modes can be excited, as for example
first and second sound in liquid helium. Here, we excite propagating and
standing waves in a uniform two-dimensional Bose gas and we characterize the
propagation of sound in both the superfluid and normal regime. In the
superfluid phase, the measured speed of sound is well described by a two-fluid
hydrodynamic model, and the weak damping rate is well explained by the
scattering with thermal excitations. In the normal phase the sound becomes
strongly damped due to a departure from hydrodynamic behavior.
|
1804.04037v1
|
2018-04-14
|
Theory of plasmon reflection by a 1D junction
|
We present a comprehensive study of the reflection of normally incident
plasmon waves from a low-conductivity 1D junction in a 2D conductive sheet.
Rigorous analytical results are derived in the limits of wide and narrow
junctions. Two types of phenomena determine the reflectance, the cavity
resonances within the junction and the capacitive coupling between the leads.
The resonances give rise to alternating strong and weak reflection but are
vulnerable to plasmonic damping. The capacitive coupling, which is immune to
damping, induces a near perfect plasmon reflection in junctions narrower than
$1/10$ of the plasmon wavelength. Our results are important for infrared 2D
plasmonic circuits utilizing slot antennas, split gates or nanowire gates. They
are also relevant for the implementation of nanoscale terahertz detectors,
where optimal light absorption coincides with the maximal junction reflectance.
|
1804.05256v1
|
2018-03-25
|
Nonlinear effect of forced harmonic oscillator subject to sliding friction and simulation by a simple nonlinear circuit
|
We study the nonlinear behaviors of mass-spring systems damped by dry
friction using simulation by a nonlinear LC circuit damped by anti-parallel
diodes. We show that the differential equation for the electric oscillator is
equivalent to the mechanical one's when a piecewise linear model is used to
simplify the diodes I-V curve. We derive series solutions to the differential
equation under weak nonlinear approximation which can describe the resonant
response as well as amplitudes of superharmonic components. Experimental
results are consistent with series solutions. We also present the phenomenon of
hysteresis. Theoretical analysis along with numerical simulations are conducted
to explore the stick-slip boundary.
The correspondence between the mechanical and electric oscillators makes it
easy to demonstrate the behaviors of this nonlinear oscillator on a digital
oscilloscope. It can be used to extend the linear RLC experiment at the
undergraduate level.
|
1804.05762v1
|
2018-04-17
|
Asymmetric fitting function for condensed-phase Raman spectroscopy
|
Asymmetric lineshapes are experimentally observed in Raman spectra of
different classes of condensed matter. Determination of the peak parameters,
typically done with symmetric pseudo-Voigt functions, in such situations yields
unreliable results. While wide choice of asymmetric fitting functions is
possible, for the function to be practically useful, it should satisfy several
criteria: simple analytic form, minimum of parameters, description of the
symmetric shape as "zero case", estimation of the desired peak parameters in a
straightforward way and, above all, adequate description of the experimental
data. In this work we formulate the asymmetric pseudo-Voigt function by damped
perturbation of the original symmetric shapes with one asymmetry-related
parameter. The damped character of the perturbation ensures by construction the
consistent behavior of the line tails. We test the asymmetric function by
fitting the experimental Raman spectra. The results show that the function is
able to describe a wide range of experimentally observed asymmetries for
different nature of asymmetric broadening, including 3D and 2D crystals,
nanoparticles, polymer, molecular solid and liquid.
|
1804.06083v2
|
2018-04-23
|
Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method
|
We study the large time behavior of solutions to two-dimensional Euler and
Navier-Stokes equations linearized about shear flows of the mixing layer type
in the unbounded channel $\mathbb{T} \times \mathbb{R}$. Under a simple
spectral stability assumption on a self-adjoint operator, we prove a local form
of the linear inviscid damping that is uniform with respect to small viscosity.
We also prove a local form of the enhanced viscous dissipation that takes place
at times of order $\nu^{-1/3}$, $\nu$ being the small viscosity. To prove these
results, we use a Hamiltonian approach, following the conjugate operator method
developed in the study of Schr\"odinger operators, combined with a
hypocoercivity argument to handle the viscous case.
|
1804.08291v1
|
2018-04-23
|
Capillary waves with surface viscosity
|
Experiments over the last 50 years have suggested a tentative correlation
between the surface (shear) viscosity and the stability of a foam or emulsion.
We examine this link theoretically using small-amplitude capillary waves in the
presence of a surfactant solution of dilute concentrations where the associated
Marangoni and surface viscosity effects are modelled via the Boussinesq-Scriven
formulation. The resulting integro-differential initial value problem is solved
analytically and surface viscosity is found to contribute an overall damping
effect on the amplitude of the capillary wave with varying degrees depending on
the lengthscale of the system. Numerically, we find the critical damping
wavelength to increase for increasing surface concentration but the rate of
increase remains different for both the surface viscosity and the Marangoni
effect.
|
1804.08389v1
|
2018-04-23
|
The Multidimensional Damped Wave Equation: Maximal Weak Solutions for Nonlinear Forcing via Semigroups and Approximation
|
The damped nonlinear wave equation, also known as the nonlinear telegraph
equation, is studied within the framework of semigroups and eigenfunction
approximation. The linear semigroup assumes a central role: it is bounded on
the domain of its generator for all time t > 0. This permits eigenfunction
approximation within the semigroup framework as a tool for the study of weak
solutions. The semigroup convolution formula, known to be rigorous on the
generator domain, is extended to the interpretation of weak solution on an
arbitrary time interval. A separate approximation theory can be developed by
using the invariance of the semigroup on eigenspaces of the Laplacian as the
system evolves. For (locally) bounded continuous L^2 forcing, this permits a
natural derivation of a maximal solution, which can logically include a
constraint on the solution as well. Operator forcing allows for the
incorporation of concurrent physical processes. A significant feature of the
proof in the nonlinear case is verification of successive approximation without
standard fixed point analysis.
|
1804.08394v3
|
2018-04-24
|
Bidirectional Controlled Quantum Teleportation Using Eight-Qubit Quantum Channel in Noisy Environments
|
In this work, a novel protocol is proposed for bidirectional controlled
quantum teleportation (BCQT) in which a quantum channel is used with the
eight-qubit entangled state. Using the protocol, two users can teleport an
arbitrary entangled state and a pure two-qubit state (QBS) to each other
simultaneously under the permission of a third party in the role of controller.
This protocol is based on the controlled-not operation, appropriate
single-qubit (SIQ) UOs and SIQ measurements in the Z and X-basis. Reduction of
the predictability of the controller's qubit (QB) by the eavesdropper and also,
an increasing degree of freedom of controller for controlling one of the users
or both are other features of this protocol. Then, the proposed protocol is
investigated in two typical noisy channels include the amplitude-damping noise
(ADN) and the phase-damping noise (PDN). And finally, analysis of the protocol
shows that it only depends on the amplitude of the initial state and the
decoherence noisy rate (DR).
|
1804.08876v3
|
2018-04-25
|
Type II Seesaw with scalar dark matter in light of AMS-02, DAMPE and Fermi-LAT
|
The Standard Model (SM) supplemented by Type II Seesaw and a SM gauge-singlet
scalar dark matter (DM) is a very simple framework to incorporate the observed
neutrino oscillations and provide a plausible DM candidate. In this framework,
the scalar DM naturally has a leptophilic nature with a pair annihilating
mainly into the SM SU(2)$_L$ triplet Higgs scalar of Type II Seesaw which, in
turn, decay into leptons. In this work, we consider indirect signatures of this
leptophilic DM and examine the spectrum of the cosmic ray electron/positron
flux from DM pair annihilations in the Galactic halo. Given an astrophysical
background spectrum of the cosmic ray electron/positron flux, we find that the
contributions from DM annihilations can nicely fit the observed data from the
AMS-02, DAMPE and Fermi-LAT collaborations, with a multi-TeV range of DM mass
and a boost factor for the DM annihilation cross section of ${\cal O}(1000)$.
The boost factor has a slight tension with the Fermi-LAT data for gamma-ray
from dwarf spheroidal galaxies, which can be ameliorated with an enhanced local
DM density by a factor of about 2.
|
1804.09835v1
|
2018-05-17
|
Viscous damping of gravity-capillary waves: Dispersion relations and nonlinear corrections
|
We discuss the impact of viscosity on nonlinear propagation of surface waves
at the interface of air and a fluid of large depth. After a survey of the
available approximations of the dispersion relation, we propose to modify the
hydrodynamic boundary conditions to model both short and long waves. From them,
we derive a nonlinear Schr\"odinger equation where both linear and nonlinear
parts are modified by dissipation and show that the former plays the main role
in both gravity and capillary-gravity waves while, in most situations, the
latter represents only small corrections. This provides a justification of the
conventional approaches to damped propagation found in the literature.
|
1805.06777v2
|
2018-05-25
|
Calculating the transport properties of magnetic materials from first-principles including thermal and alloy disorder, non-collinearity and spin-orbit coupling
|
A density functional theory based two-terminal scattering formalism that
includes spin-orbit coupling and spin non-collinearity is described. An
implementation using tight-binding muffin-tin orbitals combined with extensive
use of sparse matrix techniques allows a wide variety of inhomogeneous
structures to be flexibly modelled with various types of disorder including
temperature induced lattice and spin disorder. The methodology is illustrated
with calculations of the temperature dependent resistivity and magnetization
damping for the important substitutional disordered magnetic alloy Permalloy
(Py), Ni$_{80}$Fe$_{20}$. Comparison of calculated results with recent
experimental measurements of the damping (including its temperature dependence)
indicates that the scattering approach captures the most important
contributions to this important property.
|
1805.10062v1
|
2018-05-28
|
The linearized Vlasov and Vlasov-Fokker-Planck equations in a uniform magnetic field
|
We study the linearized Vlasov equations and the linearized
Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform
magnetic field. In both cases, we consider periodic confinement and Maxwellian
(or close to Maxwellian) backgrounds. In the collisionless case, for modes
transverse to the magnetic field, we provide a precise decomposition into a
countably infinite family of standing waves for each spatial mode. These are
known as Bernstein modes in the physics literature, though the decomposition is
not an obvious consequence of any existing arguments that we are aware of. We
show that other modes undergo Landau damping. In the presence of collisions
with collision frequency $\nu \ll 1$, we show that these modes undergo
uniform-in-$\nu$ Landau damping and enhanced collisional relaxation at the
time-scale $O(\nu^{-1/3})$. The modes transverse to the field are uniformly
stable and exponentially thermalize on the time-scale $O(\nu^{-1})$. Most of
the results are proved using Laplace transform analysis of the associated
Volterra equations, whereas a simple case of Yan Guo's energy method for
hypocoercivity of collision operators is applied for stability in the
collisional case.
|
1805.10756v1
|
2018-06-08
|
Can Star Products be Augmented by Classical Physics?
|
It has been suggested that star products in phase-space quantization may be
augmented to describe additional, classical effects. That proposal is examined
critically here. Two known star products that introduce classical effects are:
the generalized Husimi product of coarse-grained quantization, and a
non-Hermitian damped star product for the harmonic oscillator. Following these
examples, we consider products related by transition differential operators to
the classic Moyal star product. We restrict to Hermitian star products,
avoiding problems already pointed out for the original damped product. It is
shown, however, that with such star products, augmented quantization is
impossible, since an appropriate classical limit does not result.
For a more complete study, we then also consider generalized, or local,
transition operators, that depend on the local phase-space coordinates, as well
as their derivatives. In this framework, one example of possible physical
interest is constructed. Because of its limited validity and complicated form,
however, it cannot be concluded that augmented quantization with local
transition operators is practical.
|
1806.03309v2
|
2018-06-20
|
Large-Scale Demonstration of Precise Demand Response Provided by Residential Heating Systems
|
Being able to adjust the demand of electricity can be an effective means for
power system operators to compensate fluctuating renewable generation, to avoid
grid congestion, and to cope with other contingencies. Electric heating and
cooling systems of buildings can provide different demand response services
because their electricity consumption is inherently flexible because of their
thermal inertia. This paper reports on the results of a large-scale demand
response demonstration involving a population of more than 300 residential
buildings with heat pump installations. We show how the energetic behavior and
flexibility of individual systems can be identified autonomously based only on
energy meter data and outdoor air temperature measurements, and how the
aggregate demand response potential of the population can be quantified.
Various load reduction and rebound damping experiments illustrate the
effectiveness of the approach: the load reductions can be predicted precisely
and amount to 40-65% of the aggregate load, and the rebound can be damped
efficiently.
|
1806.07670v1
|
2018-06-22
|
Weakly coupled systems of semi-linear elastic waves with different damping mechanisms in 3D
|
We consider the following Cauchy problem for weakly coupled systems of
semi-linear damped elastic waves with a power source non-linearity in
three-dimensions: \begin{equation*}
U_{tt}-a^2\Delta U-\big(b^2-a^2\big)\nabla\text{div }
U+(-\Delta)^{\theta}U_t=F(U),\,\, (t,x)\in[0,\infty)\times\mathbb{R}^3,
\end{equation*} where
$U=U(t,x)=\big(U^{(1)}(t,x),U^{(2)}(t,x),U^{(3)}(t,x)\big)^{\mathrm{T}}$ with
$b^2>a^2>0$ and $\theta\in[0,1]$. Our interests are some qualitative properties
of solutions to the corresponding linear model with vanishing right-hand side
and the influence of the value of $\theta$ on the exponents $p_1,p_2,p_3$ in
$F(U)=\big(|U^{(3)}|^{p_1},|U^{(1)}|^{p_2},|U^{(2)}|^{p_3}\big)^{\mathrm{T}}$
to get results for the global (in time) existence of small data solutions.
|
1806.08543v2
|
2018-07-02
|
Global Existence of Solutions to the Compressible Euler Equations with Time-dependent Damping and Logarithmic State Equation
|
In mathematical physics, the pressure function is determined by the equation
of state. There are two existing barotropic state equations: the state equation
for polytropic gas with adiabatic index greater than or equal to 1 and the
state equation for generalized Chaplygin gas in cosmology. In this paper, a
logarithmic pressure is derived naturally with the coexistence of the two
existing state equations through an equivalent symmetric hyperbolic
transformation. On the study of the logarithmic pressure, global existence of
solutions with small initial data to the one-dimensional compressible Euler
equations with time-dependent damping is established.
|
1807.00550v2
|
2018-07-02
|
On wave equations of the $p$-Laplacian type with supercritical nonlinearities
|
This article focuses on a quasilinear wave equation of $p$-Laplacian type: \[
u_{tt} - \Delta_p u -\Delta u_t = f(u) \] in a bounded domain $\Omega \subset
\mathbb{R}^3$ with a sufficiently smooth boundary $\Gamma=\partial \Omega$
subject to a generalized Robin boundary condition featuring boundary damping
and a nonlinear source term. The operator $\Delta_p$, $2<p<3$, denotes the
classical $p$-Laplacian. The interior and boundary terms $f(u)$, $h(u)$ are
sources that are allowed to have a supercritical exponent, in the sense that
their associated Nemytskii operators are not locally Lipschitz from
$W^{1,p}(\Omega)$ into $L^2(\Omega)$ or $L^2(\Gamma)$. Under suitable
assumptions on the parameters we provide a rigorous proof of existence of a
local weak solution which can be extended globally in time, provided the
damping terms dominates the corresponding sources in an appropriate sense.
Moreover, a blow-up result is proved for solutions with negative initial total
energy.
|
1807.00650v1
|
2018-06-30
|
Efficient $p$-multigrid method based on an exponential time discretization for compressible steady flows
|
An efficient multigrid framework is developed for the time marching of
steady-state compressible flows with a spatially high-order ($p$-order
polynomial) modal discontinuous Galerkin method. The core algorithm that based
on a global coupling, exponential time integration scheme provides strong
damping effects to accelerate the convergence towards the steady state, while
high-frequency, high-order spatial error modes are smoothed out with a
$s$-stage preconditioned Runge-Kutta method. Numerical studies show that the
exponential time integration substantially improves the damping and propagative
efficiency of Runge-Kutta time-stepping for use with the $p$-multigrid method,
yielding rapid and $p$-independent convergences to steady flows in both two and
three dimensions.
|
1807.01151v1
|
2018-07-04
|
Structural crossover in a model fluid exhibiting two length scales: repercussions for quasicrystal formation
|
We investigate the liquid state structure of the two-dimensional (2D) model
introduced by Barkan et al. [Phys. Rev. Lett. 113, 098304 (2014)], which
exhibits quasicrystalline and other unusual solid phases, focussing on the
radial distribution function $g(r)$ and its asymptotic decay $r\to\infty$. For
this particular model system, we find that as the density is increased there is
a structural crossover from damped oscillatory asymptotic decay with one
wavelength to damped oscillatory asymptotic decay with another distinct
wavelength. The ratio of these wavelengths is $\approx1.932$. Following the
locus in the phase diagram of this structural crossover leads directly to the
region where quasicrystals are found. We argue that identifying and following
such a crossover line in the phase diagram towards higher densities where the
solid phase(s) occur is a good strategy for finding quasicrystals in a wide
variety of systems. We also show how the pole analysis of the asymptotic decay
of equilibrium fluid correlations is intimately connected with the
non-equilibrium growth or decay of small amplitude density fluctuations in a
bulk fluid.
|
1807.01467v1
|
2018-07-04
|
Dirac's Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space
|
The system of two-dimensional damped harmonic oscillator is revisited in the
extended phase space. It is an old problem already addressed by many authors
that we present here in some fresh points of view and carry on smoothly a whole
discussion. We show that the system is singular. The classical Hamiltonian is
proportional to the first-class constraint. We pursue with the Dirac's
canonical quantization procedure by fixing the gauge and provide a reduced
phase space description of the system. As result the quantum system is simply
modeled by the original quantum Hamiltonian.
|
1807.01539v2
|
2018-07-05
|
Decay of approximate solutions for the damped semilinear wave equation on a bounded 1d domain
|
In this paper we study the long time behavior for a semilinear wave equation
with space-dependent and nonlinear damping term. After rewriting the equation
as a first order system, we define a class of approximate solutions that employ
tipical tools of hyperbolic systems of conservation laws, such as the Riemann
problem. By recasting the problem as a discrete-time nonhomogeneous system,
which is related to a probabilistic interpretation of the solution, we provide
a strategy to study its long-time behavior uniformly with respect to the mesh
size parameter $\Delta x=1/N\to 0$. The proof makes use of the Birkhoff
decomposition of doubly stochastic matrices and of accurate estimates on the
iteration system as $N\to\infty$.
Under appropriate assumptions on the nonlinearity, we prove the exponential
convergence in $L^\infty$ of the solution to the first order system towards a
stationary solution, as $t\to+\infty$, as well as uniform error estimates for
the approximate solutions.
|
1807.01968v3
|
2018-07-07
|
Axial Quasi-Normal Modes of Scalarized Neutron Stars with Realistic Equations of State
|
We compute the axial quasi-normal modes of static neutron stars in scalar
tensor theory. In particular, we employ various realistic equations of state
including nuclear, hyperonic and hybrid matter. We investigate the fundamental
curvature mode and compare the results with those of General Relativity. We
find that the frequency of the modes and the damping time are reduced for the
scalarized neutron stars. In addition, we confirm and extend the universal
relations for quasi-normal modes known in General Relativity to this wide range
of realistic equations of state for scalarized neutron stars and confirm the
universality of the scaled frequency and damping time in terms of the scaled
moment of inertia as well as compactness for neutron stars with and without
scalarization.
|
1807.02598v1
|
2018-07-09
|
DLA and sub-DLA metallicity evolution: A case study of absorbers towards Q0338-0005
|
The damped and sub-damped Lyman alpha systems (DLAs and sub-DLAs) traced in
absorption against bright background quasars represent the main reserve of
neutral hydrogen at high redshifts. We used the archival Very Large Telescope
(VLT) instrument Ultraviolet and Visual Echelle Spectrograph (UVES)
high-resolution data of Q0338-0005 (zem = 3.049) to study abundances of the DLA
(zabs = 2.2298) and sub-DLA (zabs =2.7457) along the line of sight. We
estimated column densities of HI and various elements present in the DLA and
sub-DLA through Voigt profile fitting. The DLA trough shows the Lyman alpha
emission from its host galaxy. We derive the metallicities of the DLA and
sub-DLA with [Zn/H] = -0.67 +/- 0.18 and [S/H] = -1.45 +/-0.17, respectively.
We compared our abundances of the DLA and sub-DLA with other high resolution
DLA and sub-DLA metallicities and find that both populations show an overall
increase of metallicity with decreasing redshift. However, sub-DLAs usually
have higher metallicities than the DLAs.
|
1807.04189v1
|
2018-07-15
|
Asymptotic profile of solutions for semilinear wave equations with structural damping
|
This paper is concerned with the initial value problem for semilinear wave
equation with structural damping $u_{tt}+(-\Delta)^{\sigma}u_t -\Delta u
=f(u)$, where $\sigma \in (0,\frac{1}{2})$ and $f(u) \sim |u|^p$ or $u
|u|^{p-1}$ with $p> 1 + {2}/(n - 2 \sigma)$. We first show the global existence
for initial data small in some weighted Sobolev spaces on $\mathcal R^n$ ($n
\ge 2$). Next, we show that the asymptotic profile of the solution above is
given by a constant multiple of the fundamental solution of the corresponding
parabolic equation, provided the initial data belong to weighted $L^1$ spaces.
|
1807.05509v3
|
2018-07-19
|
Vibrational damping effects on electronic energy relaxation in molecular aggregates
|
Representation of molecular vibrational degrees of freedom by independent
harmonic oscillators, when describing electronic spectra or electronic
excitation energy transport, raises unfavourable effects as vibrational energy
relaxation becomes inaccessible. A standard theoretical description is extended
in this paper by including both electronic-phonon and vibrational-phonon
couplings. Using this approach we have simulated a model pigment-protein system
and have shown that intermode coupling leads to the quenching of pigment
vibrational modes, and to the redistribution of fluctuation spectral density
with respect to the electronic excitations. Moreover, new energy relaxation
pathways, opened by the vibrational-phonon interaction, allow to reach the
electronic excited state equilibrium quicker in the naturally occurring water
soluble chlorophyll binding protein (WSCP) aggregate, demonstrating the
significance that the damping of molecular vibrations has for the
intrarmolecular energy relaxation process rate.
|
1807.07314v1
|
2018-07-24
|
Role of stable modes in driven shear-flow turbulence
|
A linearly unstable, sinusoidal $E \times B$ shear flow is examined in the
gyrokinetic framework in both the linear and nonlinear regimes. In the linear
regime, it is shown that the eigenmode spectrum is nearly identical to
hydrodynamic shear flows, with a conjugate stable mode found at every unstable
wavenumber. In the nonlinear regime, turbulent saturation of the instability is
examined with and without the inclusion of a driving term that prevents
nonlinear flattening of the mean flow, and a scale-independent radiative
damping term that suppresses the excitation of conjugate stable modes. A simple
fluid model for how momentum transport and partial flattening of the mean flow
scale with the driving term is constructed, from which it is shown that, except
at high radiative damping, stable modes play an important role in the turbulent
state and yield significantly improved quantitative predictions when compared
with corresponding models neglecting stable modes.
|
1807.09280v1
|
2018-08-08
|
An application of $L^1$ estimates for oscillating integrals to parabolic like semi-linear structurally damped $σ$-evolution models
|
We study the following Cauchy problems for semi-linear structurally damped
$\sigma$-evolution models: \begin{equation*} u_{tt}+ (-\Delta)^\sigma u+ \mu
(-\Delta)^\delta u_t = f(u,u_t),\, u(0,x)= u_0(x),\, u_t(0,x)=u_1(x)
\end{equation*} with $\sigma \ge 1$, $\mu>0$ and $\delta \in
(0,\frac{\sigma}{2})$. Here the function $f(u,u_t)$ stands for the power
nonlinearities $|u|^{p}$ and $|u_t|^{p}$ with a given number $p>1$. We are
interested in investigating $L^{1}$ estimates for oscillating integrals in the
presentation of the solutions to the corresponding linear models with vanishing
right-hand sides by applying the theory of modified Bessel functions and
Fa\`{a} di Bruno's formula. By assuming additional $L^{m}$ regularity on the
initial data, we use $(L^{m}\cap L^{q})- L^{q}$ and $L^{q}- L^{q}$ estimates
with $q\in (1,\infty)$ and $m\in [1,q)$, to prove the global (in time)
existence of small data Sobolev solutions to the above semi-linear models from
suitable function spaces basing on $L^q$ spaces.
|
1808.02706v2
|
2018-08-09
|
Two-qubit state recovery from amplitude damping based on weak measurement
|
In the quantum control process, arbitrary pure or mixed initial states need
to be protected from amplitude damping through the noise channel using
measurements and quantum control. However, how to achieve it on a two-qubit
quantum system remains a challenge. In this paper, we propose a feed-forward
control approach to protect arbitrary two-qubit pure or mixed initial states
using the weak measurement. A feed-forward operation and measurements are used
before the noise channel, and afterwards a reversed operation and measurements
are applied to recover the state back to its initial state. In the case of
two-qubit pure states, we use the unravelling trick to describe the state of
the system in each step of the control procedure. For two-qubit mixed states, a
completely-positive trace-preserving (CPTP) map is implemented. Finally, the
fidelity and success probability are used to evaluate the effect of protection.
The complete recovery conditions for the measurement strengths are derived,
under which we achieve the optimal fidelity and the success probability of
recovering the initial pure or mixed states.
|
1808.03094v1
|
2018-08-10
|
Dynamical polarization and the optical response of silicene and related materials
|
We discuss the dynamical polarization, optical response in low-frequency
regime under in-plane polarized driving field of the silicene. The dynamical
polarization, dielectric function, and absorption of radiation in infrared
region are obtained and shown in the ${\bf q}\sim\omega$ space, and they are
distinguishing for the cases of chemical potential larger than the band gap and
smaller than the band gap. The optical properties of silicene and the related
group-V and group-VI materials: MoS$_{2}$ and black phosphorus are explored
through the first-principle study. The plasmon which damped into the
electron-hole pair in the single-particle excitation regime is also mentioned.
The spin/valley polarized electron-hole pairs can be formed through that way,
especially for the high-energy $\pi$-plasmon which begin to damp at the small
${\bf q}$-limit. The anisotropic effects induced by the warping structure or
charged impurity, and the anisotropic polarization induced by the polarized
incident light are also discussed. Our result exhibits the great potential in
the optoelectronic applications of the materials we discussed.
|
1808.03442v1
|
2018-08-19
|
Reconstruction algorithms for photoacoustic tomography in heterogenous damping media
|
In this article, we study several reconstruction methods for the inverse
source problem of photoacoustic tomography (PAT) with spatially variable sound
speed and damping. The backbone of these methods is the adjoint operators,
which we thoroughly analyze in both the $L^2$- and $H^1$-settings. They are
casted in the form of a nonstandard wave equation. We derive the well-pawedness
of the aforementioned wave equation in a natural functional space, and also
prove the finite speed of propagation. Under the uniqueness and visibility
condition, our formulations of the standard iterative reconstruction methods,
such as Landweber's and conjugate gradients (CG), achieve a linear rate of
convergence in either $L^2$- or $H^1$-norm. When the visibility condition is
not satisfied, the problem is severely ill-posed and one must apply a
regularization technique to stabilize the solutions. To that end, we study two
classes of regularization methods: (i) iterative, and (ii) variational
regularization. In the case of full data, our simulations show that the CG
method works best; it is very fast and robust. In the ill-posed case, the CG
method behaves unstably. Total variation regularization method (TV), in this
case, significantly improves the reconstruction quality.
|
1808.06176v1
|
2018-08-27
|
Landau damping of Alfvénic modes in stellarators
|
It is found that the presence of the so-called non-axisymmetric resonances of
wave-particle interaction in stellarators [which are associated with the lack
of axial symmetry of the magnetic configuration, Kolesnichenko et al., Phys.
Plasmas 9 (2002) 517] may have a strong stabilizing influence through Landau
mechanism on the Toroidicity-induced Alfv\'en Eigenmodes (TAE) and isomon modes
(Alfv\'enic modes with equal poloidal and toroidal mode numbers and frequencies
in the continuum region) destabilized by the energetic ions. These resonances
involve largest harmonics of the equilibrium magnetic field of stellarators and
lead to absorption of the mode energy by thermal ions in medium pressure
plasma, in which case the effect is large. On the other hand, at the high
pressure attributed to, e.g., a Helias reactor, thermal ions can interact also
with high frequency Alfv\'en gap modes [Helicity-induced Alfv\'en Eigenmodes
(HAE) and mirror-induced Alfv\'en Eigenmodes (MAE)], leading to a considerable
damping of these modes. Only resonances with passing particles are considered.
The developed theory is applied to various modes in the Wendelstein 7-X
stellarator and a Helias reactor, and to two TAE modes in the LHD helical
device.
|
1808.08862v1
|
2018-09-04
|
Linear Wave Propagation for Resistive Relativistic Magnetohydrodynamics
|
We present a linear mode analysis of the relativistic MHD equations in the
presence of finite electrical conductivity. Starting from the fully
relativistic covariant formulation, we derive the dispersion relation in the
limit of small linear perturbations. It is found that the system supports ten
wave modes which can be easily identified in the limits of small or large
conductivities. In the resistive limit, matter and electromagnetic fields
decouple and solution modes approach pairs of light and acoustic waves as well
as a number of purely damped (non-propagating) modes. In the opposite (ideal)
limit, the frozen-in condition applies and the modes of propagation coincide
with a pair of fast magnetosonic, a pair of slow and Alfv\'en modes, as
expected. In addition, the contact mode is always present and it is unaffected
by the conductivity. For finite values of the conductivity, the dispersion
relation gives rise to either pairs of opposite complex conjugate roots or
purely imaginary (damped) modes. In all cases, the system is dissipative and
also dispersive as the phase velocity depends nonlineary on the wavenumber.
Occasionally, the group velocity may exceed the speed of light although this
does not lead to superluminal signal propagation.
|
1809.01115v1
|
2018-09-05
|
NMR-like effect on Anisotropic Magnetic Moment of Surface Bound States in Topological Superfluid $^3$He-B
|
We present experimental observation of a new phenomenon, that we interpret as
NMR-like effect on anisotropic magnetic moment of the surface Andreev bound
states in topological superfluid $^3$He-B at zero temperature limit. We show
that an anisotropic magnetic moment formed near the horizontal surface of a
mechanical resonator due to symmetry violation of the superfluid $^3$He-B order
parameter by the resonator's surface may lead to anomalous damping of the
resonator motion in magnetic field. In difference to classical NMR technique,
here NMR was excited using own harmonic motion of the mechanical resonator, and
nuclear magnetic resonance was detected as a maximum in damping when
resonator's angular frequency satisfied the Larmor resonance condition.
|
1809.01402v3
|
2018-09-11
|
Optomechanical damping basis
|
We present a closed-form analytical solution to the eigenvalue problem of the
Liouville operator generating the dissipative dynamics of the standard
optomechanical system. The corresponding Lindblad master equation describes the
dynamics of a single-mode field inside an optical cavity coupled by radiation
pressure to its moving mirror. The optical field and the mirror are in contact
with separate environments, which are assumed at zero and finite temperature,
respectively. The optomechanical damping basis refers to the exact set of
eigenvectors of the generator that, together with the exact eigenvalues, are
explicitly derived. Both the weak- and the strong-coupling regime, which
includes combined decay mechanisms, are solved in this work.
|
1809.03693v2
|
2018-09-13
|
Active Damping of a DC Network with a Constant Power Load: An Adaptive Passivity-based Control Approach
|
This paper proposes a nonlinear, adaptive controller to increase the
stability margin of a direct-current (DC) small-scale electrical network
containing a constant power load, whose value is unknown. Due to their negative
incremental impedance, constant power loads are known to reduce the effective
damping of a network, leading to voltage oscillations and even to network
collapse. To tackle this problem, we consider the incorporation of a controlled
DC-DC power converter between the feeder and the constant power load. The
design of the control law for the converter is based on the use of standard
Passivity-Based Control and Immersion and Invariance theories. The good
performance of the controller is evaluated with numerical simulations.
|
1809.04920v1
|
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
|
2018-09-29
|
Uniform stabilization for the Klein-Gordon system in a inhomogeneous medium with locally distributed damping
|
We consider the Klein-Gordon system posed in an inhomogeneous medium with
smooth boundary subject to a local viscoelastic damping distributed around a
neighborhoodof the boundary according to the Geometric Control Condition. We
show that the energy of the system goes uniformly and exponentially to zero for
all initial data of finite energy taken in bounded sets of finite energy
phase-space. For this purpose, refined microlocal analysis arguments are
considered by exploiting ideas due to Burq and Gerard . By using sharp Carleman
estimates we prove a unique continuation property for coupled systems.
|
1810.00247v1
|
2018-10-09
|
Lévy-walk-like Langevin dynamics
|
Continuous time random walks and Langevin equations are two classes of
stochastic models for describing the dynamics of particles in the natural
world. While some of the processes can be conveniently characterized by both of
them, more often one model has significant advantages (or has to be used)
compared with the other one. In this paper, we consider the weakly damped
Langevin system coupled with a new subordinator|$\alpha$-dependent subordinator
with $1<\alpha<2$. We pay attention to the diffusion behaviour of the
stochastic process described by this coupled Langevin system, and find the
super-ballistic diffusion phenomena for the system with an unconfined potential
on velocity but sub-ballistic superdiffusion phenomenon with a confined
potential, which is like L\'{e}vy walk for long times. One can further note
that the two-point distribution of inverse subordinator affects mean square
displacement of this coupled weakly damped Langevin system in essential.
|
1810.04332v1
|
2018-10-18
|
Analysis of the controllability from the exterior of strong damping nonlocal wave equations
|
We make a complete analysis of the controllability properties from the
exterior of the (possible) strong damping wave equation with the fractional
Laplace operator subject to the nonhomogeneous Dirichlet type exterior
condition. In the first part, we show that if $0<s<1$, $\Omega\subset\RR^N$
($N\ge 1$) is a bounded Lipschitz domain and the parameter $\delta> 0$, then
there is no control function $g$ such that the following system
\begin{equation*} \begin{cases} u_{tt} + (-\Delta)^{s} u + \delta(-\Delta)^{s}
u_{t}=0 & \mbox{ in }\; \Omega\times(0,T),\\ u=g\chi_{\mathcal O\times (0,T)}
&\mbox{ in }\; (\Omc)\times (0,T) ,\\ u(\cdot,0) = u_0, u_t(\cdot,0) = u_1
&\mbox{ in }\; \Omega, \end{cases} \end{equation*} is exact or null
controllable at time $T>0$. In the second part, we prove that for every
$\delta\ge 0$ and $0<s<1$, the system is indeed approximately controllable for
any $T>0$ and $g\in \mathcal D(\mathcal O\times(0,T))$, where $\mathcal
O\subset\Omc$ is any non-empty open set.
|
1810.08060v1
|
2018-10-20
|
Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments
|
Many practically relevant materials combine properties of viscous fluids and
elastic solids to viscoelastic behavior. Our focus is on the induced dynamic
behavior of damped finite-sized particulate inclusions in such substances. We
explicitly describe history-dependent interactions that emerge between the
embedded particles. These interactions are mediated by the viscoelastic
surroundings. They result from the flows and distortions of the viscoelastic
medium when induced by the rigid inclusions. Both, viscoelastic environments of
terminal fluid-like flow or of completely reversible damped elastic behavior,
are covered. For illustration and to highlight the role of the formalism in
potential applications, we briefly address the relevant examples of dragging a
rigid sphere through a viscoelastic environment together with subsequent
relaxation dynamics, the switching dynamics of magnetic fillers in elastic gel
matrices, and the swimming behavior of active microswimmers in viscoelastic
solutions. The approach provides a basis for more quantitative and extended
investigations of these and related systems in the future.
|
1810.08832v1
|
2018-10-22
|
Dynamical instability towards finite-momentum pairing in quenched BCS superconducting phases
|
In this work we numerically investigate the fate of the
Bardeen-Cooper-Schrieffer (BCS) pairing in the presence of quenched phase under
Peierls substitution using time-dependent real space and momentum space
Bogoliubov-de Gennes equation methods and Anderson pseudospin representation
method. This kind of phase imprint can be realized by modulating electric field
in ultracold atoms and illumining of THz optical pump pulse in solids with
conventional and unconventional superconductors. In the case of weak phase
imprint, the BCS pairing is stable; while in the strong phase imprint,
instability towards finite-momentum pairing is allowed, in which the real space
and momentum space methods yield different results. In the pulsed gauge
potential, we find that this instability will not happen even with much
stronger vector potential. We also show that the uniform and staggered gauge
potentials yield different behaviors. While the staggered potential induces
transition from the BCS pairing to over-damped phase, the uniform gauge may
enhance the pairing and will not induce to the over-damped phase. These result
may shade light on the realization of finite momentum pairing, such as
Fulde-Ferrell-Larkin-Ovchinnikov phase with dynamical modulation.
|
1810.09125v1
|
2018-10-21
|
A note on a weakly coupled system of semi-linear visco-elastic damped $σ$-evolution models with different power nonlinearities and different $σ$ values
|
In this article, we prove the global (in time) existence of small data
solutions from energy spaces basing on $L^q$ spaces, with $q \in (1,\infty)$,
to the Cauchy problems for a weakly coupled system of semi-linear visco-elastic
damped $\sigma$-evolution models. Here we consider different power
nonlinearities and different $\sigma$ values in the comparison between two
single equations. To do this, we use $(L^m \cap L^q)- L^q$ and $L^q- L^q$
estimates, i.e., by mixing additional $L^m$ regularity for the data on the
basis of $L^q- L^q$ estimates for solutions, with $m \in [1,q)$, to the
corresponding linear Cauchy problems. In addition, allowing loss of decay and
the flexible choice of parameters $\sigma$, $m$ and $q$ bring some benefits to
relax the restrictions to the admissible exponents $p$.
|
1810.09664v1
|
2018-10-25
|
First-principles calculation of spin-orbit torque in a Co/Pt bilayer
|
The angular dependence of spin-orbit torque in a disordered Co/Pt bilayer is
calculated using a first-principles non-equilibrium Green's function formalism
with an explicit supercell averaging over Anderson disorder. In addition to the
usual dampinglike and fieldlike terms, the odd torque contains a sizeable
planar Hall-like term $(\mathbf{m\cdot
E})\mathbf{m}\times(\mathbf{z}\times\mathbf{m})$ whose contribution to
current-induced damping is consistent with experimental observations. The
dampinglike and planar Hall-like torquances depend weakly on disorder strength,
while the fieldlike torquance declines with increasing disorder. The torques
that contribute to damping are almost entirely due to spin-orbit coupling on
the Pt atoms, but the fieldlike torque does not require it.
|
1810.11003v2
|
2018-10-29
|
Optimal identification of non-Markovian environments for spin chains
|
Correlations of an environment are crucial for the dynamics of non-Markovian
quantum systems, which may not be known in advance. In this paper, we propose a
gradient algorithm for identifying the correlations in terms of time-varying
damping rate functions in a time-convolution-less master equation for spin
chains. By measuring time trace observables of the system, the identification
procedure can be formulated as an optimization problem. The gradient algorithm
is designed based on a calculation of the derivative of an objective function
with respect to the damping rate functions, whose effectiveness is shown in a
comparison to a differential approach for a two-qubit spin chain.
|
1810.11923v1
|
2018-10-29
|
Existence and uniqueness of dynamic evolutions for a one-dimensional debonding model with damping
|
In this paper we analyse a one-dimensional debonding model for a thin film
peeled from a substrate when viscosity is taken into account. It is described
by the weakly damped wave equation whose domain, the debonded region, grows
according to a Griffith's criterion. Firstly we prove that the equation admits
a unique solution when the evolution of the debonding front is assigned.
Finally we provide an existence and uniqueness result for the coupled problem
given by the wave equation together with Griffith's criterion.
|
1810.12006v3
|
2018-10-29
|
A Graceful Exit for the Cosmological Constant Damping Scenario
|
We present a broad and simple class of scalar-tensor scenarios that
successfully realize dynamical damping of the effective cosmological constant,
therefore providing a viable dynamical solution to the fine-tuning or "old"
cosmological constant problem. In contrast to early versions of this approach,
pioneered in the works of A. Dolgov in the 1980es, these do not suffer from
unacceptable variations of Newton's constant, as one aims at a small but
strictly positive (rather than zero) late-time curvature. In our approach, the
original fine-tuning issue is traded for a hierarchy of couplings, and we
further suggest a way to naturally generate this hierarchy based on fermion
condensation and softly broken field shift symmetry.
|
1810.12336v2
|
2018-10-31
|
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
|
2018-12-28
|
Axion Misalignment Driven to the Bottom
|
Several theoretical motivations point to ultralight QCD axions with large
decay constants $f_a \simeq \mathcal{O}(10^{16}-10^{17})$ GeV, to which
experimental proposals are dedicated. This regime is known to face the problem
of overproduction of axion dark matter from the misalignment mechanism unless
the misalignment angle $\theta_{\rm mis}$ is as small as
$\mathcal{O}(10^{-3}-10^{-4})$, which is generally considered a fine-tuning
problem. We investigate a dynamical explanation for a small $\theta_{\rm mis}$.
The axion mass arises from strong dynamics and may be sufficiently enhanced by
early dynamics so as to overcome Hubble friction and drive the field value to
the bottom of the potential long before the QCD phase transition. Together with
an approximate CP symmetry in the theory, this minimum is very closely related
to today's value and thus $\theta_{\rm mis}$ can automatically be well under
unity. Owing to such efficient relaxation, the isocurvature perturbations are
essentially damped. As an existence proof, using supersymmetric theories we
illustrate that the Higgs coupling with the inflaton energy can successfully
achieve this axion damping in a consistent inflationary cosmology.
|
1812.11186v2
|
2019-01-03
|
Calibration and Status of the 3D Imaging Calorimeter of DAMPE for Cosmic Ray Physics on Orbit
|
The DArk Matter Particle Explorer (DAMPE) developed in China was designed to
search for evidence of dark matter particles by observing primary cosmic rays
and gamma rays in the energy range from 5 GeV to 10 TeV. Since its launch in
December 2015, a large quantity of data has been recorded. With the data set
acquired during more than a year of operation in space, a precise
time-dependent calibration for the energy measured by the BGO ECAL has been
developed. In this report, the instrumentation and development of the BGO
Electromagnetic Calorimeter (BGO ECAL) are briefly described. The calibration
on orbit, including that of the pedestal, attenuation length, minimum ionizing
particle peak, and dynode ratio, is discussed, and additional details about the
calibration methods and performance in space are presented.
|
1901.00734v1
|
2019-01-08
|
Atom-only descriptions of the driven-dissipative Dicke model
|
We investigate how to describe the dissipative spin dynamics of the
driven-dissipative Dicke model, describing $N$ two-level atoms coupled to a
cavity mode, after adiabatic elimination of the cavity mode. To this end, we
derive a Redfield master equation which goes beyond the standard secular
approximation and large detuning limits. We show that the secular (or rotating
wave) approximation and the large detuning approximation both lead to
inadequate master equations, that fail to predict the Dicke transition or the
damping rates of the atomic dynamics. In contrast, the full Redfield theory
correctly predicts the phase transition and the effective atomic damping rates.
Our work provides a reliable framework to study the full quantum dynamics of
atoms in a multimode cavity, where a quantum description of the full model
becomes intractable.
|
1901.02473v2
|
2019-01-10
|
Stability and Controllability results for a Timoshenko system
|
In this paper, we study the indirect boundary stability and exact
controllability of a one-dimensional Timoshenko system. In the first part of
the paper, we consider the Timoshenko system with only one boundary fractional
damping. We first show that the system is strongly stable but not uniformly
stable. Hence, we look for a polynomial decay rate for smooth initial data.
Using frequency domain arguments combined with the multiplier method, we prove
that the energy decay rate depends on coefficients appearing in the PDE and on
the order of the fractional damping. Moreover, under the equal speed
propagation condition, we obtain the optimal polynomial energy decay rate. In
the second part of this paper, we study the indirect boundary exact
controllability of the Timoshenko system with mixed Dirichlet-Neumann boundary
conditions and boundary control. Using non-harmonic analysis, we first
establish a weak observability inequality, which depends on the ratio of the
waves propagation speeds. Next, using the HUM method, we prove that the system
is exactly controllable in appropriate spaces and that the control time can be
small.
|
1901.03303v2
|
2019-01-13
|
Dueling Dynamical Backaction in a Cryogenic Optomechanical Cavity
|
Dynamical backaction has proven to be a versatile tool in cavity
optomechanics, allowing for precise manipulation of a mechanical resonator's
motion using confined optical photons. In this work, we present measurements of
a silicon whispering-gallery-mode optomechanical cavity where backaction
originates from opposing radiation pressure and photothermal forces, with the
former dictating the optomechanical spring effect and the latter governing the
optomechanical damping. At high enough optical input powers, we show that the
photothermal force drives the mechanical resonator into self-oscillations for a
pump beam detuned to the lower-frequency side of the optical resonance,
contrary to what one would expect for a radiation-pressure-dominated
optomechanical device. Using a fully nonlinear model, we fit the hysteretic
response of the optomechanical cavity to extract its properties, demonstrating
that this non-sideband-resolved device exists in a regime where photothermal
damping could be used to cool its motion to the quantum ground state.
|
1901.03950v1
|
2019-01-22
|
Coupling between superfluid neutrons and superfluid protons in the elementary excitations of neutron star matter
|
Several phenomena occurring in neutron stars are affected by the elementary
excitations that characterize the stellar matter. In particular, low-energy
excitations can play a major role in the emission and propagation of neutrinos,
neutron star cooling and transport processes. In this paper, we consider the
elementary modes in the star region where both proton and neutron components
are superfluid.
We study the overall spectral functions of protons, neutrons and electrons on
the basis of the Coulomb and nuclear interactions.
This study is performed in the framework of the Random Phase Approximation,
generalized to superfluid systems. The formalism we use ensures that the
Generalized Ward's Identities are satisfied. We focus on the coupling between
neutrons and protons. On one hand this coupling results in collective modes
that involve simultaneously neutrons and protons, on the other hand it produces
a damping of the excitations. Both effects are especially visible in the
spectral functions of the different components of the matter. At high density
while the neutrons and protons tend to develop independent excitations, as
indicated by the spectral functions, the neutron-proton coupling still produces
a strong damping of the modes.
|
1901.07550v1
|
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
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.