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2023-08-05
|
The isometric immersion of surfaces with finite total curvature
|
In this paper, we study the smooth isometric immersion of a complete simply
connected surface with a negative Gauss curvature in the three-dimensional
Euclidean space. For a surface with a finite total Gauss curvature and
appropriate oscillations of the Gauss curvature, we prove the global existence
of a smooth solution to the Gauss-Codazzi system and thus establish a global
smooth isometric immersion of the surface into the three-dimensional Euclidean
space. Based on a crucial observation that some linear combinations of the
Riemann invariants decay faster than others, we reformulate the Gauss-Codazzi
system as a symmetric hyperbolic system with a partial damping. Such a damping
effect and an energy approach permit us to derive global decay estimates and
meanwhile control the non-integrable coefficients of nonlinear terms.
|
2308.02832v2
|
2023-08-25
|
The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients
|
This paper aims to reconstruct the initial condition of a hyperbolic equation
with an unknown damping coefficient. Our approach involves approximating the
hyperbolic equation's solution by its truncated Fourier expansion in the time
domain and using a polynomial-exponential basis. This truncation process
facilitates the elimination of the time variable, consequently, yielding a
system of quasi-linear elliptic equations. To globally solve the system without
needing an accurate initial guess, we employ the Carleman contraction
principle. We provide several numerical examples to illustrate the efficacy of
our method. The method not only delivers precise solutions but also showcases
remarkable computational efficiency.
|
2308.13152v1
|
2023-08-25
|
A Game of Bundle Adjustment -- Learning Efficient Convergence
|
Bundle adjustment is the common way to solve localization and mapping. It is
an iterative process in which a system of non-linear equations is solved using
two optimization methods, weighted by a damping factor. In the classic
approach, the latter is chosen heuristically by the Levenberg-Marquardt
algorithm on each iteration. This might take many iterations, making the
process computationally expensive, which might be harmful to real-time
applications. We propose to replace this heuristic by viewing the problem in a
holistic manner, as a game, and formulating it as a reinforcement-learning
task. We set an environment which solves the non-linear equations and train an
agent to choose the damping factor in a learned manner. We demonstrate that our
approach considerably reduces the number of iterations required to reach the
bundle adjustment's convergence, on both synthetic and real-life scenarios. We
show that this reduction benefits the classic approach and can be integrated
with other bundle adjustment acceleration methods.
|
2308.13270v1
|
2023-08-30
|
Stochastic Thermodynamics of Brownian motion in Temperature Gradient
|
We study stochastic thermodynamics of a Brownian particle which is subjected
to a temperature gradient and is confined by an external potential. We first
formulate an over-damped Ito-Langevin theory in terms of local temperature,
friction coefficient, and steady state distribution, all of which are
experimentally measurable. We then study the associated stochastic
thermodynamics theory. We analyze the excess entropy production (EP) both at
trajectory level and at ensemble level, and derive the Clausius inequality as
well as the transient fluctuation theorem (FT). We also use molecular dynamics
to simulate a Brownian particle inside a Lennard-Jones fluid and verify the FT.
Remarkably we find that the FT remains valid even in the under-damped regime.
We explain the possible mechanism underlying this surprising result.
|
2308.15764v3
|
2023-09-04
|
Sphaleron damping and effects on vector and axial charge transport in high-temperature QCD plasmas
|
We modify the anomalous hydrodynamic equations of motion to account for
dissipative effects due to QCD sphaleron transitions. By investigating the
linearized hydrodynamic equations, we show that sphaleron transitions lead to
nontrivial effects on vector and axial charge transport phenomena in the
presence of a magnetic field. Due to the dissipative effects of sphaleron
transitions, a wavenumber threshold $k_{\rm CMW}$ emerges characterizing the
onset of chiral magnetic waves. Sphaleron damping also significantly impacts
the time evolution of both axial and vector charge perturbations in a QCD
plasma in the presence of a magnetic field. Based on our analysis of the
linearized hydrodynamic equations, we also investigate the dependence of the
vector charge separation on the sphaleron transition rate, which may have
implications for the experimental search for the Chiral Magnetic Effect in
Heavy Ion Collisions.
|
2309.01726v1
|
2023-09-05
|
Signatures and characterization of dominating Kerr nonlinearity between two driven systems with application to a suspended magnetic beam
|
We consider a model of two harmonically driven damped harmonic oscillators
that are coupled linearly and with a cross-Kerr coupling. We show how to
distinguish this combination of coupling types from the case where a coupling
of optomechanical type is present. This can be useful for the characterization
of various nonlinear systems, such as mechanical oscillators, qubits, and
hybrid systems. We then consider a hybrid system with linear and cross-Kerr
interactions and a relatively high damping in one of the modes. We derive a
quantum Hamiltonian of a doubly clamped magnetic beam, showing that the
cross-Kerr coupling is prominent there. We discuss, in the classical limit,
measurements of its linear response as well as the specific higher-harmonic
responses. These frequency-domain measurements can allow estimating the
magnitude of the cross-Kerr coupling or its magnon population.
|
2309.02204v2
|
2023-09-07
|
Strong coupling between WS$_2$ monolayer excitons and a hybrid plasmon polariton at room temperature
|
Light-matter interactions in solid-state systems have attracted considerable
interest in recent years. Here, we report on a room-temperature study on the
interaction of tungsten disulfide (WS$_2$) monolayer excitons with a hybrid
plasmon polariton (HPP) mode supported by nanogroove grating structures milled
into single-crystalline silver flakes. By engineering the depth of the
nanogroove grating, we can modify the HPP mode at the A-exciton energy from
propagating surface plasmon polariton-like (SPP-like) to localized surface
plasmon resonance-like (LSPR-like). Using reflection spectroscopy, we
demonstrate strong coupling between the A-exciton mode and the lower branch of
the HPP for a SPP-like configuration with a Rabi splitting of 68 meV. In
contrast, only weak coupling between the constituents is observed for LSPR-like
configurations. These findings demonstrate the importance to consider both the
plasmonic near-field enhancement and the plasmonic damping during the design of
the composite structure since a possible benefit from increasing the coupling
strength can be easily foiled by larger damping.
|
2309.03560v1
|
2023-09-07
|
Neutron spin echo is a "quantum tale of two paths''
|
We describe an experiment that strongly supports a two-path interferometric
model in which the spin-up and spin-down components of each neutron propagate
coherently along spatially separated parallel paths in a typical neutron spin
echo small angle scattering (SESANS) experiment. Specifically, we show that the
usual semi-classical, single-path treatment of Larmor precession of a polarized
neutron in an external magnetic field predicts a damping as a function of the
spin echo length of the SESANS signal obtained with a periodic phase grating
when the transverse width of the neutron wave packet is finite. However, no
such damping is observed experimentally, implying either that the Larmor model
is incorrect or that the transverse extent of the wave packet is very large. In
contrast, we demonstrate theoretically that a quantum-mechanical
interferometric model in which the two mode-entangled (i.e. intraparticle
entangled) spin states of a single neutron are separated in space when they
interact with the grating accurately predicts the measured SESANS signal, which
is independent of the wave packet width.
|
2309.03987v2
|
2023-09-07
|
An explicit multi-time stepping algorithm for multi-time scale coupling problems in SPH
|
Simulating physical problems involving multi-time scale coupling is
challenging due to the need of solving these multi-time scale processes
simultaneously. In response to this challenge, this paper proposed an explicit
multi-time step algorithm coupled with a solid dynamic relaxation scheme. The
explicit scheme simplifies the equation system in contrast to the implicit
scheme, while the multi-time step algorithm allows the equations of different
physical processes to be solved under different time step sizes. Furthermore,
an implicit viscous damping relaxation technique is applied to significantly
reduce computational iterations required to achieve equilibrium in the
comparatively fast solid response process. To validate the accuracy and
efficiency of the proposed algorithm, two distinct scenarios, i.e., a nonlinear
hardening bar stretching and a fluid diffusion coupled with Nafion membrane
flexure, are simulated. The results show good agreement with experimental data
and results from other numerical methods, and the simulation time is reduced
firstly by independently addressing different processes with the multi-time
step algorithm and secondly decreasing solid dynamic relaxation time through
the incorporation of damping techniques.
|
2309.04010v1
|
2023-09-15
|
Limiting absorption principles and linear inviscid damping in the Euler-Boussinesq system in the periodic channel
|
We consider the long-time behavior of solutions to the two dimensional
non-homogeneous Euler equations under the Boussinesq approximation posed on a
periodic channel. We study the linearized system near a linearly stratified
Couette flow and prove inviscid damping of the perturbed density and velocity
field for any positive Richardson number, with optimal rates. Our methods are
based on time-decay properties of oscillatory integrals obtained using a
limiting absorption principle, and require a careful understanding of the
asymptotic expansion of the generalized eigenfunction near the critical layer.
As a by-product of our analysis, we provide a precise description of the
spectrum of the linearized operator, which, for sufficiently large Richardson
number, consists of an essential spectrum (as expected according to classical
hydrodynamic problems) as well as discrete neutral eigenvalues (giving rise to
oscillatory modes) accumulating towards the endpoints of the essential
spectrum.
|
2309.08445v2
|
2023-09-15
|
Breakdown of sound in superfluid helium
|
Like elementary particles carry energy and momentum in the Universe,
quasiparticles are the elementary carriers of energy and momentum quanta in
condensed matter. And, like elementary particles, under certain conditions
quasiparticles can be unstable and decay, emitting pairs of less energetic
ones. Pitaevskii proposed that such processes exist in superfluid helium, a
quantum fluid where the very concept of quasiparticles was borne, and which
provided the first spectacular triumph of that concept. Pitaevskii's decays
have important consequences, including possible breakdown of a quasiparticle.
Here, we present neutron scattering experiments, which provide evidence that
such decays explain the collapsing lifetime (strong damping) of higher-energy
phonon-roton sound-wave quasiparticles in superfluid helium. This damping
develops when helium is pressurized towards crystallization or warmed towards
approaching the superfluid transition. Our results resolve a number of puzzles
posed by previous experiments and reveal the ubiquity of quasiparticle decays
and their importance for understanding quantum matter.
|
2309.08790v1
|
2023-09-18
|
Nonlinear dynamics and magneto-elasticity of nanodrums near the phase transition
|
Nanomechanical resonances of two-dimensional (2D) materials are sensitive
probes for condensed-matter physics, offering new insights into magnetic and
electronic phase transitions. Despite extensive research, the influence of the
spin dynamics near a second-order phase transition on the nonlinear dynamics of
2D membranes has remained largely unexplored. Here, we investigate nonlinear
magneto-mechanical coupling to antiferromagnetic order in suspended
FePS$_3$-based heterostructure membranes. By monitoring the motion of these
membranes as a function of temperature, we observe characteristic features in
both nonlinear stiffness and damping close to the N\'{e}el temperature
$T_{\rm{N}}$. We account for these experimental observations with an analytical
magnetostriction model in which these nonlinearities emerge from a coupling
between mechanical and magnetic oscillations, demonstrating that
magneto-elasticity can lead to nonlinear damping. Our findings thus provide
insights into the thermodynamics and magneto-mechanical energy dissipation
mechanisms in nanomechanical resonators due to the material's phase change and
magnetic order relaxation.
|
2309.09672v1
|
2023-09-21
|
Quantum State Reconstruction in a Noisy Environment via Deep Learning
|
Quantum noise is currently limiting efficient quantum information processing
and computation. In this work, we consider the tasks of reconstructing and
classifying quantum states corrupted by the action of an unknown noisy channel
using classical feedforward neural networks. By framing reconstruction as a
regression problem, we show how such an approach can be used to recover with
fidelities exceeding 99% the noiseless density matrices of quantum states of up
to three qubits undergoing noisy evolution, and we test its performance with
both single-qubit (bit-flip, phase-flip, depolarising, and amplitude damping)
and two-qubit quantum channels (correlated amplitude damping). Moreover, we
also consider the task of distinguishing between different quantum noisy
channels, and show how a neural network-based classifier is able to solve such
a classification problem with perfect accuracy.
|
2309.11949v1
|
2023-09-27
|
Exploring antisymmetric tensor effects on black hole shadows and quasinormal frequencies
|
This study explores the impact of antisymmetric tensor effects on spherically
symmetric black holes, investigating photon spheres, shadows, emission rate and
quasinormal frequencies in relation to a parameter which triggers the Lorentz
symmetry breaking. We examine these configurations without and with the
presence of a cosmological constant. In the first scenario, the Lorentz
violation parameter, denoted as $\lambda$, plays a pivotal role in reducing
both the photon sphere and the shadow radius, while also leading to a damping
effect on quasinormal frequencies. Conversely, in the second scenario, as the
values of the cosmological constant ($\Lambda$) increase, we observe an
expansion in the shadow radius. Also, we provide the constraints of the shadows
based on the analysis observational data obtained from the Event Horizon
Telescope (EHT) focusing on Sagittarius $A^{*}$ shadow images. Additionally,
with the increasing $\Lambda$, the associated gravitational wave frequencies
exhibit reduced damping modes.
|
2309.15778v3
|
2023-10-20
|
Exponential weight averaging as damped harmonic motion
|
The exponential moving average (EMA) is a commonly used statistic for
providing stable estimates of stochastic quantities in deep learning
optimization. Recently, EMA has seen considerable use in generative models,
where it is computed with respect to the model weights, and significantly
improves the stability of the inference model during and after training. While
the practice of weight averaging at the end of training is well-studied and
known to improve estimates of local optima, the benefits of EMA over the course
of training is less understood. In this paper, we derive an explicit connection
between EMA and a damped harmonic system between two particles, where one
particle (the EMA weights) is drawn to the other (the model weights) via an
idealized zero-length spring. We then leverage this physical analogy to analyze
the effectiveness of EMA, and propose an improved training algorithm, which we
call BELAY. Finally, we demonstrate theoretically and empirically several
advantages enjoyed by BELAY over standard EMA.
|
2310.13854v1
|
2023-10-23
|
Adam through a Second-Order Lens
|
Research into optimisation for deep learning is characterised by a tension
between the computational efficiency of first-order, gradient-based methods
(such as SGD and Adam) and the theoretical efficiency of second-order,
curvature-based methods (such as quasi-Newton methods and K-FAC). We seek to
combine the benefits of both approaches into a single computationally-efficient
algorithm. Noting that second-order methods often depend on stabilising
heuristics (such as Levenberg-Marquardt damping), we propose AdamQLR: an
optimiser combining damping and learning rate selection techniques from K-FAC
(Martens and Grosse, 2015) with the update directions proposed by Adam,
inspired by considering Adam through a second-order lens. We evaluate AdamQLR
on a range of regression and classification tasks at various scales, achieving
competitive generalisation performance vs runtime.
|
2310.14963v1
|
2023-10-24
|
Observation of Damped Oscillations in Chemical-Quantum-Magnetic Interactions
|
Fundamental interactions are the basis of the most diverse phenomena in
science that allow the dazzling of possible applications. In this work, we
report a new interaction, which we call chemical-quantum-magnetic interaction.
This interaction arises due to the difference in valence that the Fe3O4/PANI
nanostructure acquires under certain conditions. In this study, PANI activates
the chemical part of the oscillations, leaving the quantum and magnetic part
for the double valence effect and consequently for changing the number of spins
of the nanostructure sites. We also observed using interaction measurements
that chemical-quantum-magnetic interactions oscillate in a subcritical regime
satisfying the behavior of a damped harmonic oscillator.
|
2310.15775v1
|
2023-10-26
|
Do Graph Neural Networks Dream of Landau Damping? Insights from Kinetic Simulations of a Plasma Sheet Model
|
We explore the possibility of fully replacing a plasma physics kinetic
simulator with a graph neural network-based simulator. We focus on this class
of surrogate models given the similarity between their message-passing update
mechanism and the traditional physics solver update, and the possibility of
enforcing known physical priors into the graph construction and update. We show
that our model learns the kinetic plasma dynamics of the one-dimensional plasma
model, a predecessor of contemporary kinetic plasma simulation codes, and
recovers a wide range of well-known kinetic plasma processes, including plasma
thermalization, electrostatic fluctuations about thermal equilibrium, and the
drag on a fast sheet and Landau damping. We compare the performance against the
original plasma model in terms of run-time, conservation laws, and temporal
evolution of key physical quantities. The limitations of the model are
presented and possible directions for higher-dimensional surrogate models for
kinetic plasmas are discussed.
|
2310.17646v2
|
2023-10-29
|
Impact of Medium Anisotropy on Quarkonium Dissociation and Regeneration
|
Quarkonium production in ultra-relativistic collisions plays a crucial role
in probing the existence of hot QCD matter. This study explores quarkonia
states dissociation and regeneration in the hot QCD medium while considering
momentum anisotropy. The net quarkonia decay width ($\Gamma_{D}$) arises from
two essential processes: collisional damping and gluonic dissociation. The
quarkonia regeneration includes the transition from octet to singlet states
within the anisotropic medium. Our study utilizes a medium-modified potential
that incorporates anisotropy via particle distribution functions. This modified
potential gives rise to collisional damping for quarkonia due to the
surrounding medium, as well as the transition of quarkonia from singlet to
octet states due to interactions with gluons. Furthermore, we employ the
detailed balance approach to investigate the regeneration of quarkonia within
this medium. Our comprehensive analysis spans various temperature settings,
transverse momentum values, and anisotropic strengths. Notably, we find that,
in addition to medium temperatures and heavy quark transverse momentum,
anisotropy significantly influences the dissociation and regeneration of
various quarkonia states.
|
2310.18909v1
|
2023-10-31
|
Stability threshold of nearly-Couette shear flows with Navier boundary conditions in 2D
|
In this work, we prove a threshold theorem for the 2D Navier-Stokes equations
posed on the periodic channel, $\mathbb{T} \times [-1,1]$, supplemented with
Navier boundary conditions $\omega|_{y = \pm 1} = 0$. Initial datum is taken to
be a perturbation of Couette in the following sense: the shear component of the
perturbation is assumed small (in an appropriate Sobolev space) but importantly
is independent of $\nu$. On the other hand, the nonzero modes are assumed size
$O(\nu^{\frac12})$ in an anisotropic Sobolev space. For such datum, we prove
nonlinear enhanced dissipation and inviscid damping for the resulting solution.
The principal innovation is to capture quantitatively the \textit{inviscid
damping}, for which we introduce a new Singular Integral Operator which is a
physical space analogue of the usual Fourier multipliers which are used to
prove damping. We then include this SIO in the context of a nonlinear
hypocoercivity framework.
|
2311.00141v1
|
2023-11-10
|
Moment expansion method for composite open quantum systems including a damped oscillator mode
|
We consider a damped oscillator mode that is resonantly driven and is coupled
to an arbitrary target system via the position quadrature operator. For such a
composite open quantum system, we develop a numerical method to compute the
reduced density matrix of the target system and the low-order moments of the
quadrature operators. In this method, we solve the evolution equations for
quantities related to moments of the quadrature operators, rather than for the
density matrix elements as in the conventional approach. The application to an
optomechanical setting shows that the new method can compute the correlation
functions accurately with a significant reduction in the computational cost.
Since the method does not involve any approximation in its abstract formulation
itself, we investigate the numerical accuracy closely. This study reveals the
numerical sensitivity of the new approach in certain parameter regimes. We find
that this issue can be alleviated by using the position basis instead of the
commonly used Fock basis.
|
2311.06113v1
|
2023-11-22
|
Analytic formulas for the D-mode Robinson instability
|
The passive superconducting harmonic cavity (PSHC) scheme is adopted by
several existing and future synchrotron light source storage rings, as it has a
relatively smaller R/Q and a relatively larger quality factor (Q), which can
effectively reduce the beam-loading effect and suppress the mode-one
instability. Based on the mode-zero Robinson instability equation of uniformly
filled rigid bunches and a search algorithm for minimum, we have revealed that
the PSHC fundamental mode with a large loaded-Q possibly triggers the D-mode
Robinson instability [T. He, et al., Mode-zero Robinson instability in the
presence of passive superconducting harmonic cavities, PRAB 26, 064403 (2023)].
This D-mode Robinson instability is unique because it is anti-damped by the
radiation-damping effect. In this paper, analytical formulas for the frequency
and growth rate of the D-mode Robinson instability are derived with several
appropriate approximations. These analytical formulas will facilitate analyzing
and understanding the D-mode Robinson instability. Most importantly, useful
formulas for the D-mode threshold detuning calculation have finally been found.
|
2311.13205v1
|
2023-11-27
|
Learning Reionization History from Quasars with Simulation-Based Inference
|
Understanding the entire history of the ionization state of the intergalactic
medium (IGM) is at the frontier of astrophysics and cosmology. A promising
method to achieve this is by extracting the damping wing signal from the
neutral IGM. As hundreds of redshift $z>6$ quasars are observed, we anticipate
determining the detailed time evolution of the ionization fraction with
unprecedented fidelity. However, traditional approaches to parameter inference
are not sufficiently accurate. We assess the performance of a simulation-based
inference (SBI) method to infer the neutral fraction of the universe from
quasar spectra. The SBI method adeptly exploits the shape information of the
damping wing, enabling precise estimations of the neutral fraction
$\left<x_{\rm HI}\right>_{\rm v}$ and the wing position $w_p$. Importantly, the
SBI framework successfully breaks the degeneracy between these two parameters,
offering unbiased estimates of both. This makes the SBI superior to the
traditional method using a pseudo-likelihood function. We anticipate that SBI
will be essential to determine robustly the ionization history of the Universe
through joint inference from the hundreds of high-$z$ spectra we will observe.
|
2311.16238v1
|
2023-12-05
|
DemaFormer: Damped Exponential Moving Average Transformer with Energy-Based Modeling for Temporal Language Grounding
|
Temporal Language Grounding seeks to localize video moments that semantically
correspond to a natural language query. Recent advances employ the attention
mechanism to learn the relations between video moments and the text query.
However, naive attention might not be able to appropriately capture such
relations, resulting in ineffective distributions where target video moments
are difficult to separate from the remaining ones. To resolve the issue, we
propose an energy-based model framework to explicitly learn moment-query
distributions. Moreover, we propose DemaFormer, a novel Transformer-based
architecture that utilizes exponential moving average with a learnable damping
factor to effectively encode moment-query inputs. Comprehensive experiments on
four public temporal language grounding datasets showcase the superiority of
our methods over the state-of-the-art baselines.
|
2312.02549v1
|
2023-12-05
|
THz-Driven Coherent Magnetization Dynamics in a Labyrinth Domain State
|
Terahertz (THz) light pulses can be used for an ultrafast coherent
manipulation of the magnetization. Driving the magnetization at THz frequencies
is currently the fastest way of writing magnetic information in ferromagnets.
Using time-resolved resonant magnetic scattering, we gain new insights to the
THz-driven coherent magnetization dynamics on nanometer length scales. We
observe ultrafast demagnetization and coherent magnetization oscillations that
are governed by a time-dependent damping. This damping is determined by the
interplay of lattice heating and magnetic anisotropy reduction revealing an
upper speed limit for THz-induced magnetization switching. We show that in the
presence of nanometer-sized magnetic domains, the ultrafast magnetization
oscillations are associated with a correlated beating of the domain walls. The
overall domain structure thereby remains largely unaffected which highlights
the applicability of THz-induced switching on the nanoscale.
|
2312.02654v1
|
2023-12-07
|
Enhanced high-dimensional teleportation in correlated amplitude damping noise by weak measurement and environment-assisted measurement
|
High-dimensional teleportation provides various benefits in quantum networks
and repeaters, but all these advantages rely on the high-quality distribution
of high-dimensional entanglement over a noisy channel. It is essential to
consider correlation effects when two entangled qutrits travel consecutively
through the same channel. In this paper, we present two strategies for
enhancing qutrit teleportation in correlated amplitude damping (CAD) noise by
weak measurement (WM) and environment-assisted measurement (EAM). The fidelity
of both approaches has been dramatically improved due to the probabilistic
nature of WM and EAM. We have observed that the correlation effects of CAD
noise result in an increase in the probability of success. A comparison has
demonstrated that the EAM scheme consistently outperforms the WM scheme in
regard to fidelity. Our research expands the capabilities of WM and EAM as
quantum techniques to combat CAD noise in qutrit teleportation, facilitating
the development of advanced quantum technologies in high-dimensional systems.
|
2312.03988v1
|
2023-12-11
|
Collisions and collective flavor conversion: Integrating out the fast dynamics
|
In dense astrophysical environments, notably core-collapse supernovae and
neutron star mergers, neutrino-neutrino forward scattering can spawn flavor
conversion on very short scales. Scattering with the background medium can
impact collective flavor conversion in various ways, either damping
oscillations or possibly setting off novel collisional flavor instabilities
(CFIs). A key feature in this process is the slowness of collisions compared to
the much faster dynamics of neutrino-neutrino refraction. Assuming spatial
homogeneity, we leverage this hierarchy of scales to simplify the description
accounting only for the slow dynamics driven by collisions. We illustrate our
new approach both in the case of CFIs and in the case of fast instabilities
damped by collisions. In both cases, our strategy provides new equations, the
slow-dynamics equations, that simplify the description of flavor conversion and
allow us to qualitatively understand the final state of the system after the
instability, either collisional or fast, has saturated.
|
2312.07612v2
|
2023-12-15
|
Position-momentum conditioning, relative entropy decomposition and convergence to equilibrium in stochastic Hamiltonian systems
|
This paper is concerned with a class of multivariable stochastic Hamiltonian
systems whose generalised position is related by an ordinary differential
equation to the momentum governed by an Ito stochastic differential equation.
The latter is driven by a standard Wiener process and involves both
conservative and viscous damping forces. With the mass, diffusion and damping
matrices being position-dependent, the resulting nonlinear model of Langevin
dynamics describes dissipative mechanical systems (possibly with rotational
degrees of freedom) or their electromechanical analogues subject to external
random forcing. We study the time evolution of the joint position-momentum
probability distribution for the system and its convergence to equilibrium by
decomposing the Fokker-Planck-Kolmogorov equation (FPKE) and the
Kullback-Leibler relative entropy with respect to the invariant measure into
those for the position distribution and the momentum distribution conditioned
on the position. This decomposition reveals a manifestation of the
Barbashin-Krasovskii-LaSalle principle and higher-order dissipation
inequalities for the relative entropy as a Lyapunov functional for the FPKE.
|
2312.09475v1
|
2023-12-16
|
Continuous Phase Transition in Anyonic-PT Symmetric Systems
|
We reveal the continuous phase transition in anyonic-PT symmetric systems,
contrasting with the discontinuous phase transition corresponding to the
discrete (anti-) PT symmetry. The continuous phase transition originates from
the continuity of anyonic-PT symmetry. We find there are three
information-dynamics patterns for anyonic-PT symmetric systems: damped
oscillations with an overall decrease (increase) and asymptotically stable
damped oscillations, which are three-fold degenerate and distorted using the
Hermitian quantum R\'enyi entropy or distinguishability. It is the
normalization of the non-unitary evolved density matrix causes the degeneracy
and distortion. We give a justification for non-Hermitian quantum R\'enyi
entropy being negative. By exploring the mathematics and physical meaning of
the negative entropy in open quantum systems, we connect the negative
non-Hermitian quantum R\'enyi entropy and negative quantum conditional entropy,
opening up a new journey to rigorously investigate the negative entropy in open
quantum systems.
|
2312.10350v4
|
2023-12-20
|
Quadrature squeezing enhances Wigner negativity in a mechanical Duffing oscillator
|
Generating macroscopic non-classical quantum states is a long-standing
challenge in physics. Anharmonic dynamics is an essential ingredient to
generate these states, but for large mechanical systems, the effect of the
anharmonicity tends to become negligible compared to decoherence. As a possible
solution to this challenge, we propose to use a motional squeezed state as a
resource to effectively enhance the anharmonicity. We analyze the production of
negativity in the Wigner distribution of a quantum anharmonic resonator
initially in a squeezed state. We find that initial squeezing enhances the rate
at which negativity is generated. We also analyze the effect of two common
sources of decoherence, namely energy damping and dephasing, and find that the
detrimental effects of energy damping are suppressed by strong squeezing. In
the limit of large squeezing, which is needed for state-of-the-art systems, we
find good approximations for the Wigner function. Our analysis is significant
for current experiments attempting to prepare macroscopic mechanical systems in
genuine quantum states. We provide an overview of several experimental
platforms featuring nonlinear behaviors and low levels of decoherence. In
particular, we discuss the feasibility of our proposal with carbon nanotubes
and levitated nanoparticles.
|
2312.12986v1
|
2023-12-21
|
Subsonic time-periodic solution to damped compressible Euler equations with large entropy
|
In this paper, one-dimensional nonisentropic compressible Euler equations
with linear damping $\alpha(x)\rho u$ are analyzed.~We want to explore the
conditions under which a subsonic temporal periodic boundary can trigger a
time-periodic $C^{1}$ solution. To achieve this aim, we use a technically
constructed iteration scheme and give the sufficient conditions to guarantee
the existence, uniqueness and stability of the $C^{1}$ time-periodic solutions
on the perturbation of a subsonic Fanno flow.~It is worthy to be pointed out
that the entropy exhibits large amplitude under the assumption that the inflow
sound speed is small.~However, it is crucial to assume that the boundary
conditions possess a kind of dissipative structure at least on one side, which
is used to cancel the nonlinear accelerating effect in the system.~The results
indicate that the time-periodic feedback boundary control with dissipation can
stabilize the nonisentropic compressible Euler equations around the Fanno
flows.
|
2312.13546v1
|
2023-12-27
|
Universal orbital and magnetic structures in infinite-layer nickelates
|
We conducted a comparative study of the rare-earth infinite-layer nickelates
films, RNiO2 (R = La, Pr, and Nd) using resonant inelastic X-ray scattering
(RIXS). We found that the gross features of the orbital configurations are
essentially the same, with minor variations in the detailed hybridization. For
low-energy excitations, we unambiguously confirm the presence of damped
magnetic excitations in all three compounds. By fitting to a linear spin-wave
theory, comparable spin exchange coupling strengths and damping coefficients
are extracted, indicating a universal magnetic structure in the infinite-layer
nickelates. Interestingly, while signatures of a charge order are observed in
LaNiO2 in the quasi-elastic region of the RIXS spectrum, it is absent in NdNiO2
and PrNiO2. This prompts further investigation into the universality and the
origins of charge order within the infinite-layer inickelates.
|
2312.16444v1
|
2024-01-05
|
Response solutions for beam equations with nonlocal nonlinear damping and Liouvillean frequencies
|
Response solutions are quasi-periodic ones with the same frequency as the
forcing term. The present work is devoted to the construction of response
solutions for $d$-dimensional beam equations with nonlocal nonlinear damping,
which model frictional mechanisms affecting the bodies based on the average. By
considering $\epsilon$ in a domain that does not include the origin and
imposing a small quasi-periodic forcing with Liouvillean frequency vector,
which is weaker than the Diophantine or Brjuno one, we can show the existence
of the response solution for such a model. We present an alternative approach
to the contraction mapping principle (cf. [5,33]) through a combination of
reduction and the Nash--Moser iteration technique. The reason behind this
approach lies in the derivative losses caused by the nonlocal nonlinearity.
|
2401.02628v1
|
2024-01-10
|
Stochastic modelling of blob-like plasma filaments in the scrape-off layer: Continuous velocity distributions
|
A stochastic model for a superposition of uncorrelated pulses with a random
distribution of amplitudes, sizes, and velocities is analyzed. The pulses are
assumed to move radially with fixed shape and amplitudes decreasing
exponentially in time due to linear damping. The pulse velocities are taken to
be time-independent but randomly distributed. The implications of a broad
distribution of pulse amplitudes and velocities, as well as correlations
between these, are investigated. Fast and large-amplitude pulses lead to broad
and flat average radial profiles with order unity relative fluctuations in the
scrape-off layer. For theoretically predicted blob velocity scaling relations,
the stochastic model reveals average radial profiles similar to the case of a
degenerate distribution of pulse velocities but with more intermittent
fluctuations. The average profile e-folding length is given by the product of
the average pulse velocity and the linear damping time due to losses along
magnetic field lines. The model describes numerous common features from
experimental measurements and underlines the role of large-amplitude
fluctuations for plasma-wall interactions in magnetically confined fusion
plasmas.
|
2401.05198v1
|
2024-01-11
|
Optical and acoustic plasmons in the layered material Sr$_2$RuO$_4$
|
We use momentum-dependent electron energy-loss spectroscopy in transmission
to study collective charge excitations in the "strange" layer metal
Sr$_2$RuO$_4$. We cover a complete range between in-plane and out-of-plane
oscillations. Outside of the classical range of electron-hole excitations,
leading to a Landau damping, we observe well defined plasmons. The optical
(acoustic) plasmon due to an in-phase (out-of-phase) charge oscillation of
neighbouring layers exhibits a quadratic (linear) dispersion. Using a model for
the Coulomb interaction of the charges in a layered system, it is possible to
describe the complete range of plasmon excitations in a mean-field random phase
approximation without taking correlation effects into account. There are no
signs of over-damped plasmons predicted by holographic theories. This indicates
that long wavelength charge excitations are not influenced by local correlation
effects such as on-site Coulomb interaction and Hund's exchange interaction.
|
2401.05880v1
|
2024-01-12
|
Robust fully discrete error bounds for the Kuznetsov equation in the inviscid limit
|
The Kuznetsov equation is a classical wave model of acoustics that
incorporates quadratic gradient nonlinearities. When its strong damping
vanishes, it undergoes a singular behavior change, switching from a
parabolic-like to a hyperbolic quasilinear evolution. In this work, we
establish for the first time the optimal error bounds for its finite element
approximation as well as a semi-implicit fully discrete approximation that are
robust with respect to the vanishing damping parameter. The core of the new
arguments lies in devising energy estimates directly for the error equation
where one can more easily exploit the polynomial structure of the
nonlinearities and compensate inverse estimates with smallness conditions on
the error. Numerical experiments are included to illustrate the theoretical
results.
|
2401.06492v1
|
2024-01-12
|
Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order
|
In this paper, we focus on studying the Cauchy problem for semilinear damped
wave equations involving the sub-Laplacian $\mathcal{L}$ on the Heisenberg
group $\mathbb{H}^n$ with power type nonlinearity $|u|^p$ and initial data
taken from Sobolev spaces of negative order homogeneous Sobolev space $\dot
H^{-\gamma}_{\mathcal{L}}(\mathbb{H}^n), \gamma>0$, on $\mathbb{H}^n$. In
particular, in the framework of Sobolev spaces of negative order, we prove that
the critical exponent is the exponent $p_{\text{crit}}(Q,
\gamma)=1+\frac{4}{Q+2\gamma},$ for some $\gamma\in (0, \frac{Q}{2})$, where
$Q:=2n+2$ is the homogeneous dimension of $\mathbb{H}^n$. More precisely, we
establish
a global-in-time existence of small data Sobolev solutions of lower
regularity for $p>p_{\text{crit}}(Q, \gamma)$ in the energy evolution space;
a finite time blow-up of weak solutions for $1<p<p_{\text{crit}}(Q, \gamma)$
under certain conditions on the initial data by using the test function method.
Furthermore, to precisely characterize the blow-up time, we derive sharp
upper bound and lower bound estimates for the lifespan in the subcritical case.
|
2401.06565v1
|
2024-01-12
|
Universal Modelling of Emergent Oscillations in Fractional Quantum Hall Fluids
|
Density oscillations in quantum fluids can reveal their fundamental
characteristic features. In this work, we study the density oscillation of
incompressible fractional quantum Hall (FQH) fluids created by flux insertion.
For the model Laughlin state, we find that the complex oscillations seen in
various density profiles in real space can be universally captured by a simple
damped oscillator model in the occupation-number space. It requires only two
independent fitting parameters or characteristic length scales: the decay
length and the oscillation wave number. Realistic Coulomb quasiholes can be
viewed as Laughlin quasiholes dressed by magnetorotons which can be modeled by
a generalized damped oscillator model. Our work reveals the fundamental
connections between the oscillations seen in various aspects of FQH fluids such
as in the density of quasiholes, edge, and the pair correlation function. The
presented model is useful for the study of quasihole sizes for their control
and braiding in experiments and large-scale numerical computation of
variational energies.
|
2401.06856v1
|
2024-01-19
|
Quantum circuit model for discrete-time three-state quantum walks on Cayley graphs
|
We develop qutrit circuit models for discrete-time three-state quantum walks
on Cayley graphs corresponding to Dihedral groups $D_N$ and the additive groups
of integers modulo any positive integer $N$. The proposed circuits comprise of
elementary qutrit gates such as qutrit rotation gates, qutrit-$X$ gates and
two-qutrit controlled-$X$ gates. First, we propose qutrit circuit
representation of special unitary matrices of order three, and the block
diagonal special unitary matrices with $3\times 3$ diagonal blocks, which
correspond to multi-controlled $X$ gates and permutations of qutrit Toffoli
gates. We show that one-layer qutrit circuit model need $O(3nN)$ two-qutrit
control gates and $O(3N)$ one-qutrit rotation gates for these quantum walks
when $N=3^n$. Finally, we numerically simulate these circuits to mimic its
performance such as time-averaged probability of finding the walker at any
vertex on noisy quantum computers. The simulated results for the time-averaged
probability distributions for noisy and noiseless walks are further compared
using KL-divergence and total variation distance. These results show that noise
in gates in the circuits significantly impacts the distributions than amplitude
damping or phase damping errors.
|
2401.11023v1
|
2024-01-22
|
Exact Normal Modes of Quantum Plasmas
|
The normal modes, i.e., the eigen solutions to the dispersion relation
equation, are the most fundamental properties of a plasma, which also of key
importance to many nonlinear effects such as parametric and two-plasmon decay,
and Raman scattering. The real part indicates the intrinsic oscillation
frequency while the imaginary part the Landau damping rate. In most of the
literatures, the normal modes of quantum plasmas are obtained by means of small
damping approximation (SDA), which is invalid for high-$k$ modes. In this
paper, we solve the exact dispersion relations via the analytical continuation
(AC) scheme, and, due to the multi-value nature of the Fermi-Dirac
distribution, reformation of the complex Riemann surface is required. It is
found that the change of the topological shape of the root locus in quantum
plasmas is quite different from classical plasmas, in which both real and
imaginary frequencies of high-$k$ modes increase with $k$ in a steeper way than
the typical linear behaviour as appears in classical plasmas. As a result, the
temporal evolution of a high-$k$ perturbation in quantum plasmas is dominated
by the ballistic modes.
|
2401.11894v1
|
2024-01-23
|
On the stability and emittance growth of different particle phase-space distributions in a long magnetic quadrupole channel
|
The behavior of K-V, waterbag, parabolic, conical and Gaussian distributions
in periodic quadrupole channels is studied by particle simulations. It is found
that all these different distributions exhibit the known K-V instabilities. But
the action of the K-V type modes becomes more and more damped in the order of
the types of distributions quoted above. This damping is so strong for the
Gaussian distribution that the emittance growth factor after a large number of
periods is considerably lower than in the case of an equivalent K-V
distribution. In addition, the non K-V distributions experience in only one
period of the channel a rapid initial emittance growth, which becomes very
significant at high beam intensities. This growth is attributed to the
homogenization of the space-charge density, resulting in a conversion of
electric-field energy into transverse kinetic and potential energy. Two simple
analytical formulae are derived to estimate the upper and lower boundary values
for this effect and are compared with the results obtained from particle
simulations.
|
2401.12595v1
|
2024-01-26
|
Double pulse all-optical coherent control of ultrafast spin-reorientation in antiferromagnetic rare-earth orthoferrite
|
A pair of circularly polarized laser pulses of opposite helicities are shown
to control the route of spin reorientation phase transition in rare-earth
antiferromagnetic orthoferrite SmTbFeO$_3$. The route can be efficiently
controlled by the delay between the pulses and the sample temperature.
Simulations employing earlier published models of laserinduced spin dynamics in
orthoferrites failed to reproduce the experimental results. It is suggested
that the failure is due to neglected temperature dependence of the
antiferromagnetic resonance damping in the material. Taking into account the
experimentally deduced temperature dependence of the damping, we have been able
to obtain a good agreement between the simulations and the experimental
results.
|
2401.15009v1
|
2024-01-31
|
Observer-based Controller Design for Oscillation Damping of a Novel Suspended Underactuated Aerial Platform
|
In this work, we present a novel actuation strategy for a suspended aerial
platform. By utilizing an underactuation approach, we demonstrate the
successful oscillation damping of the proposed platform, modeled as a spherical
double pendulum. A state estimator is designed in order to obtain the
deflection angles of the platform, which uses only onboard IMU measurements.
The state estimator is an extended Kalman filter (EKF) with intermittent
measurements obtained at different frequencies. An optimal state feedback
controller and a PD+ controller are designed in order to dampen the
oscillations of the platform in the joint space and task space respectively.
The proposed underactuated platform is found to be more energy-efficient than
an omnidirectional platform and requires fewer actuators. The effectiveness of
our proposed system is validated using both simulations and experimental
studies.
|
2401.17676v1
|
2024-02-02
|
Long-time dynamics of stochastic wave equation with dissipative damping and its full discretization: exponential ergodicity and strong law of large numbers
|
For stochastic wave equation, when the dissipative damping is a non-globally
Lipschitz function of the velocity, there are few results on the long-time
dynamics, in particular, the exponential ergodicity and strong law of large
numbers, for the equation and its numerical discretization to our knowledge.
Focus on this issue, the main contributions of this paper are as follows.
First, based on constructing novel Lyapunov functionals, we show the unique
invariant measure and exponential ergodicity of the underlying equation and its
full discretization. Second, the error estimates of invariant measures both in
Wasserstein distance and in the weak sense are obtained. Third, the strong laws
of large numbers of the equation and the full discretization are obtained,
which states that the time averages of the exact and numerical solutions are
shown to converge to the ergodic limit almost surely.
|
2402.01137v1
|
2024-02-05
|
Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping
|
A fifth-order KdV equation with time dependent coefficients and linear
damping has been studied. Symmetry groups have several different applications
in the context of nonlinear differential equations. For instance, they can be
used to determine conservation laws. We obtain the symmetries of the model
applying Lie's classical method. The choice of some arbitrary functions of the
equation by the equivalence transformation enhances the study of Lie symmetries
of the equation. We have determined the subclasses of the equation which are
nonlinearly self-adjoint. This allow us to obtain conservation laws by using a
theorem proved by Ibragimov which is based on the concept of adjoint equation
for nonlinear differential equations.
|
2402.03265v1
|
2024-02-07
|
Curvature-Informed SGD via General Purpose Lie-Group Preconditioners
|
We present a novel approach to accelerate stochastic gradient descent (SGD)
by utilizing curvature information obtained from Hessian-vector products or
finite differences of parameters and gradients, similar to the BFGS algorithm.
Our approach involves two preconditioners: a matrix-free preconditioner and a
low-rank approximation preconditioner. We update both preconditioners online
using a criterion that is robust to stochastic gradient noise and does not
require line search or damping. To preserve the corresponding symmetry or
invariance, our preconditioners are constrained to certain connected Lie
groups. The Lie group's equivariance property simplifies the preconditioner
fitting process, while its invariance property eliminates the need for damping,
which is commonly required in second-order optimizers. As a result, the
learning rate for parameter updating and the step size for preconditioner
fitting are naturally normalized, and their default values work well in most
scenarios. Our proposed approach offers a promising direction for improving the
convergence of SGD with low computational overhead. We demonstrate that
Preconditioned SGD (PSGD) outperforms SoTA on Vision, NLP, and RL tasks across
multiple modern deep-learning architectures. We have provided code for
reproducing toy and large scale experiments in this paper.
|
2402.04553v1
|
2024-02-08
|
A non-damped stabilization algorithm for multibody dynamics
|
The stability of integrators dealing with high order Differential Algebraic
Equations (DAEs) is a major issue. The usual procedures give rise to
instabilities that are not predicted by the usual linear analysis, rendering
the common checks (developed for ODEs) unusable. The appearance of these
difficult-toexplain and unexpected problems leads to methods that arise heavy
numerical damping for avoiding them. This has the undesired consequences of
lack of convergence of the methods, along with a need of smaller stepsizes. In
this paper a new approach is presented. The algorithm presented here allows us
to avoid the interference of the constraints in the integration, thus allowing
the linear criteria to be applied. In order to do so, the integrator is applied
to a set of instantaneous minimal coordinates that are obtained through the
application of the null space. The new approach can be utilized along with any
integration method. Some experiments using the Newmark method have been carried
out, which validate the methodology and also show that the method behaves in a
predictable way if one considers linear stability criteria.
|
2402.05768v1
|
2024-02-09
|
Constraints on Quasinormal modes from Black Hole Shadows in regular non-minimal Einstein Yang-Mills Gravity
|
This work deals with the scalar quasinormal modes using higher order WKB
method and black hole shadow in non-minimal Einstein Yang-Mills theory. To
validate the results of quasinormal modes, time domain profiles are also
investigated. We found that with an increase in the magnetic charge of the
black hole, the ring-down gravitational wave increases non-linearly and damping
rate decreases non-linearly. The presence of magnetic charge also results in a
decrease in the black hole shadow non-linearly. It is found that for large
values of the coupling parameter, the black hole changes to a solitonic
solution and the corresponding ring-down gravitational wave frequency increases
slowly with a decrease in the damping rate. For the solitonic solutions, the
shadow is also smaller. The constraints on the model parameters calculated
using shadow observations of M87* and Sgr A* and an approximate analytic
relation between quasinormal modes and shadow at the eikonal limit is
discussed.
|
2402.06186v1
|
2024-02-14
|
The impact of load placement on grid resonances during grid restoration
|
As inverter-based generation is being massively deployed in the grid, these
type of units have to take over the current roles of conventional generation,
including the capability of restoring the grid. In this context, the resonances
of the grid during the first steps of a black start can be concerning, given
that the grid is lightly loaded. Especially relevant are the low frequency
resonances, that may be excited by the harmonic components of the inverter. A
typical strategy to avoid or minimize the effect of such resonances relies on
connecting load banks. This was fairly feasible with conventional generation,
but given the limited ratings of inverters, the amount of load that can be
connected at the beginning is very limited. In this paper we consider the
energization of a transmission line, and investigate the optimal location of a
load along a line in order to maximize the damping in the system. By analysing
the spectral properties as a function of the load location, we formally prove
that placing the load in the middle of the transmission line maximizes the
damping ratio of the first resonance of the system.
|
2402.09294v1
|
2024-02-19
|
Gravitational wave asteroseismology of dark matter hadronic stars
|
The influence of the dark matter mass~($M_{\chi}$) and the Fermi
momentum~($k_{F}^{\dm}$) on the $f_0$-mode oscillation frequency, damping time
parameter, and tidal deformability of hadronic stars are studied by employing a
numerical integration of hydrostatic equilibrium, nonradial oscillation, and
tidal deformability equations. The matter inside the hadronic stars follows the
NL3* equation of state. We obtain that the influence of $M_{\chi}$ and
$k_F^{\dm}$ is observed in the $f_0$-mode, damping tome parameter, and tidal
deformability. Finally, the correlation between the tidal deformability of the
GW$170817$ event with $M_{\chi}$ and $k_F^{\dm}$ are also investigated.
|
2402.12600v1
|
2024-02-21
|
Landau damping, collisionless limit, and stability threshold for the Vlasov-Poisson equation with nonlinear Fokker-Planck collisions
|
In this paper, we study the Vlasov-Poisson-Fokker-Planck (VPFP) equation with
a small collision frequency $0 < \nu \ll 1$, exploring the interplay between
the regularity and size of perturbations in the context of the asymptotic
stability of the global Maxwellian. Our main result establishes the Landau
damping and enhanced dissipation phenomena under the condition that the
perturbation of the global Maxwellian falls within the Gevrey-$\frac{1}{s}$
class and obtain that the stability threshold for the Gevrey-$\frac{1}{s}$
class with $s>s_{\mathrm{k}}$ can not be larger than
$\gamma=\frac{1-3s_{\mathrm{k}}}{3-3s_{\mathrm{k}}}$ for $s_{\mathrm{k}}\in
[0,\frac{1}{3}]$. Moreover, we show that for Gevrey-$\frac{1}{s}$ with $s>3$,
and for $t\ll \nu^{\frac13}$, the solution to VPFP converges to the solution to
Vlasov-Poisson equation without collision.
|
2402.14082v2
|
2024-02-22
|
Long-time asymptotics of the damped nonlinear Klein-Gordon equation with a delta potential
|
We consider the damped nonlinear Klein-Gordon equation with a delta potential
\begin{align*} \partial_{t}^2u-\partial_{x}^2u+2\alpha \partial_{t}u+u-\gamma
{\delta}_0u-|u|^{p-1}u=0, \ & (t,x) \in \mathbb{R} \times \mathbb{R},
\end{align*} where $p>2$, $\alpha>0,\ \gamma<2$, and $\delta_0=\delta_0 (x)$
denotes the Dirac delta with the mass at the origin. When $\gamma=0$, C\^{o}te,
Martel and Yuan proved that any global solution either converges to 0 or to the
sum of $K\geq 1$ decoupled solitary waves which have alternative signs. In this
paper, we first prove that any global solution either converges to 0 or to the
sum of $K\geq 1$ decoupled solitary waves. Next we construct a single solitary
wave solution that moves away from the origin when $\gamma<0$ and construct an
even 2-solitary wave solution when $\gamma\leq -2$. Last we give single
solitary wave solutions and even 2-solitary wave solutions an upper bound for
the distance between the origin and the solitary wave.
|
2402.14381v2
|
2024-02-22
|
Low-frequency Resonances in Grid-Forming Converters: Causes and Damping Control
|
Grid-forming voltage-source converter (GFM-VSC) may experience low-frequency
resonances, such as synchronous resonance (SR) and sub-synchronous resonance
(SSR), in the output power. This paper offers a comprehensive study on the root
causes of low-frequency resonances with GFM-VSC systems and the damping control
methods. The typical GFM control structures are introduced first, along with a
mapping between the resonances and control loops. Then, the causes of SR and
SSR are discussed, highlighting the impacts of control interactions on the
resonances. Further, the recent advancements in stabilizing control methods for
SR and SSR are critically reviewed with experimental tests of a GFM-VSC under
different grid conditions.
|
2402.14543v1
|
2024-02-27
|
Unified study of viscoelasticity and sound damping in hard and soft amorphous solids
|
Recent research has made significant progress in understanding the non-phonon
vibrational states present in amorphous materials. It has been established that
their vibrational density of states follows non-Debye scaling laws. Here, we
show that the non-Debye scaling laws play a crucial role in determining
material properties of a broad range of amorphous solids, from ``hard"
amorphous solids like structural glasses to ``soft" amorphous solids such as
foams and emulsions. We propose a unified framework of viscoelasticity and
sound damping for these materials. Although these properties differ
significantly between hard and soft amorphous solids, they are determined by
the non-Debye scaling laws. We also validate our framework using numerical
simulations.
|
2402.17335v1
|
2024-02-29
|
Quantum coherence and entanglement under the influence of decoherence
|
In this work, we delve into the dynamic traits of the relative entropy of
quantum coherence (REQC) as the quantum system interacts with the different
noisy channels, drawing comparisons with entanglement (concurrence). The
research results demonstrate the broader prevalence and stronger robustness of
the REQC as opposed to concurrence. It's worth noting that the bit flip channel
cannot uphold a constant nonzero frozen the REQC, besides, the concurrence
follows a pattern of temporary reduction to zero, followed by recovery after a
certain time span. More importantly, the REQC maintains its presence
consistently until reaching a critical threshold, whereas concurrence
experiences completely attenuation to zero under the influence of phase damping
and amplitude damping channels.
|
2402.19055v1
|
2024-03-02
|
Diffusive Decay of Collective Quantum Excitations in Electron Gas
|
In this work the multistream quasiparticle model of collective electron
excitations is used to study the energy-density distribution of collective
quantum excitations in an interacting electron gas with arbitrary degree of
degeneracy. Generalized relations for the probability current and energy
density distributions is obtained which reveals a new interesting quantum
phenomenon of diffusive decay of pure quasiparticle states at microscopic
level. The effects is studied for various cases of free quasiparticles,
quasiparticle in an infinite square-well potential and half-space collective
excitations. It is shown that plasmon excitations have the intrinsic tendency
to decay into equilibrium state with uniform energy density spacial
distribution. It is found that plasmon levels of quasipaticle in a square-well
potential are unstable decaying into equilibrium state due to the fundamental
property of collective excitations. The decay rates of pure plasmon states are
determined analytically. Moreover, for damped quasiparticle excitations the
non-vanishing probability current divergence leads to imaginary energy density
resulting in damping instability of energy density dynamic. The pronounced
energy density valley close to half-space boundary at low level excitations
predicts attractive force close to the surface. Current research can have
implications with applications in plasmonics and related fields. Current
analysis can be readily generalized to include external potential and magnetic
field effects.
|
2403.01099v1
|
2024-03-04
|
Successive quasienergy collapse and the driven Dicke phase transition in the few-emitter limit
|
The emergent behavior that arises in many-body systems of increasing size
follows universal laws that become apparent in order-to-disorder transitions.
While this behavior has been traditionally explored for large numbers of
emitters, recent progress allows for the exploration of the few-emitter limit,
where correlations can be measured and connected to microscopic models to gain
further insight into order-to-disorder transitions. We explore this few-body
limit in the driven and damped Tavis--Cummings model, which describes a
collection of atoms interacting with a driven and damped cavity mode. Our
exploration revolves around the dressed states of the atomic ensemble and
field, whose energies are shown to collapse as the driving field is increased
to mark the onset of a dissipative quantum phase transition. The collapse
occurs in stages and is an effect of light-matter correlations that are
overlooked for single atoms and neglected in mean-field models. The
implications of these correlations over the macroscopic observables of the
system are presented. We encounter a shift in the expected transition point and
an increased number of parity-broken states to choose from once the ordered
phase is reached.
|
2403.02417v1
|
2024-03-05
|
Domain-Agnostic Mutual Prompting for Unsupervised Domain Adaptation
|
Conventional Unsupervised Domain Adaptation (UDA) strives to minimize
distribution discrepancy between domains, which neglects to harness rich
semantics from data and struggles to handle complex domain shifts. A promising
technique is to leverage the knowledge of large-scale pre-trained
vision-language models for more guided adaptation. Despite some endeavors,
current methods often learn textual prompts to embed domain semantics for
source and target domains separately and perform classification within each
domain, limiting cross-domain knowledge transfer. Moreover, prompting only the
language branch lacks flexibility to adapt both modalities dynamically. To
bridge this gap, we propose Domain-Agnostic Mutual Prompting (DAMP) to exploit
domain-invariant semantics by mutually aligning visual and textual embeddings.
Specifically, the image contextual information is utilized to prompt the
language branch in a domain-agnostic and instance-conditioned way. Meanwhile,
visual prompts are imposed based on the domain-agnostic textual prompt to
elicit domain-invariant visual embeddings. These two branches of prompts are
learned mutually with a cross-attention module and regularized with a
semantic-consistency loss and an instance-discrimination contrastive loss.
Experiments on three UDA benchmarks demonstrate the superiority of DAMP over
state-of-the-art approaches.
|
2403.02899v1
|
2024-03-12
|
Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
|
In this work, we demonstrate that the mixing of scalar and vector condensates
produces spatially oscillating, but exponentially damped correlation functions
in fermionic theories at finite density and temperature. We find a regime
exhibiting this oscillatory behavior in a Gross-Neveu-type model that also
features vector interactions within the mean-field approximation. The existence
of this regime aligns with expectations based on symmetry arguments, that are
also applicable to QCD at finite baryon density. We compute the phase diagram
including both homogeneous phases and regions with spatially oscillating,
exponentially damped correlation functions at finite temperature and chemical
potential for different strengths of the vector coupling. Furthermore, we find
that inhomogeneous condensates are disfavored compared to homogeneous ones akin
to previous findings without vector interactions. We show that our results are
valid for a broad class of $\left(2+1\right)$-dimensional models with local
four-fermion interactions.
|
2403.07430v1
|
2024-03-13
|
Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System
|
We consider a modified damped version of H\'enon-Heiles system and
investigate its integrability. By extending the Painlev\'e analysis of ordinary
differential equations we find that the modified H\'enon-Heiles system
possesses the Painlev\'e property for three distinct parametric restrictions.
For each of the identified cases, we construct two independent integrals of
motion using the well known Prelle-Singer method. We then derive a set of
nontrivial non-point symmetries for each of the identified integrable cases of
the modified H\'enon-Heiles system. We infer that the modified H\'enon-Heiles
system is integrable for three distinct parametric restrictions. Exact
solutions are given explicitly for two integrable cases.
|
2403.08410v1
|
2024-03-15
|
Delayed interactions in the noisy voter model through the periodic polling mechanism
|
We investigate the effects of delayed interactions on the stationary
distribution of the noisy voter model. We assume that the delayed interactions
occur through the periodic polling mechanism and replace the original
instantaneous two-agent interactions. In our analysis, we require that the
polling period aligns with the delay in announcing poll outcomes. As expected,
when the polling period is relatively short, the model with delayed
interactions is effectively identical to the original model. As the polling
period increases, oscillatory behavior emerges, but the model with delayed
interactions still converges to stationary distribution. The stationary
distribution resembles a Beta-binomial distribution, with its shape parameters
scaling with the polling period. The observed scaling behavior is non-trivial.
As the polling period increases, fluctuation damping also intensifies, yet
there is a critical intermediate polling period for which fluctuation damping
reaches its maximum intensity.
|
2403.10277v1
|
2024-03-16
|
CETASim: A numerical tool for beam collective effect study in storage rings
|
We developed a 6D multi-particle tracking program CETASim in C++ programming
language to simulate intensity-dependent effects in electron storage rings. The
program can simulate the beam collective effects due to short-range/long-range
wakefields for single/coupled-bunch instability studies. It also features to
simulate interactions among charged ions and the trains of electron bunches,
including both fast ion and ion trapping effects. The bunch-by-bunch feedback
is also included so that the user can simulate the damping of the unstable
motion when its growth rate is faster than the radiation damping rate. The
particle dynamics is based on the one-turn map, including the nonlinear effects
of amplitude-dependent tune shift, high-order chromaticity, and second-order
momentum compaction factor. A skew quadrupole can also be introduced by the
users, which is very useful for the emittance sharing and the emittance
exchange studies. This paper describes the code structure, the physics models,
and the algorithms used in CETASim. We also present the results of its
application to PETRA-IV storage ring.
|
2403.10973v1
|
2024-03-18
|
Mitigation of the Microbunching Instability Through Transverse Landau Damping
|
The microbunching instability has been a long-standing issue for
high-brightness free-electron lasers (FELs), and is a significant show-stopper
to achieving full longitudinal coherence in the x-ray regime. This paper
reports the first experimental demonstration of microbunching instability
mitigation through transverse Landau damping, based on linear optics control in
a dispersive region. Analytical predictions for the microbunching content are
supported by numerical calculations of the instability gain and confirmed
through the experimental characterization of the spectral brightness of the
FERMI FEL under different transverse optics configurations of the transfer line
between the linear accelerator and the FEL.
|
2403.11594v1
|
2024-03-19
|
Calculating quasinormal modes of extremal and non-extremal Reissner-Nordström black holes with the continued fraction method
|
We use the numerical continued fraction method to investigate quasinormal
mode spectra of extremal and non-extremal Reissner-Nordstr\"om black holes in
the low and intermediate damping regions. In the extremal case, we develop
techniques that significantly expand the calculated spectrum from what had
previously appeared in the literature. This allows us to determine the
asymptotic behavior of the extremal spectrum in the high damping limit, where
there are conflicting published results. Our investigation further supports the
idea that the extremal limit of the non-extremal case, where the charge
approaches the mass of the black hole in natural units, leads to the same
vibrational spectrum as in the extremal case despite the qualitative
differences in their topology. In addition, we numerically explore the
quasinormal mode spectrum for a Reissner-Nordstr\"om black hole in the small
charge limit.
|
2403.13074v1
|
2024-03-19
|
Uniform vorticity depletion and inviscid damping for periodic shear flows in the high Reynolds number regime
|
We study the dynamics of the two dimensional Navier-Stokes equations
linearized around a shear flow on a (non-square) torus which possesses exactly
two non-degenerate critical points. We obtain linear inviscid damping and
vorticity depletion estimates for the linearized flow that are uniform with
respect to the viscosity, and enhanced dissipation type decay estimates. The
main task is to understand the associated Rayleigh and Orr-Sommerfeld
equations, under the natural assumption that the linearized operator around the
shear flow in the inviscid case has no discrete eigenvalues. The key difficulty
is to understand the behavior of the solution to Orr-Sommerfeld equations in
three distinct regimes depending on the spectral parameter: the non-degenerate
case when the spectral parameter is away from the critical values, the
intermediate case when the spectral parameter is close to but still separated
from the critical values, and the most singular case when the spectral
parameter is inside the viscous layer.
|
2403.13104v1
|
2024-03-26
|
Greybody Factors Imprinted on Black Hole Ringdowns. II. Merging Binary Black Holes
|
The spectral amplitude of the merger-ringdown gravitational wave (GW) emitted
by a comparable mass-ratio black hole merger is modeled by the greybody factor
of the remnant black hole. Our model does not include fitting parameters except
for a single overall spectral amplitude. We perform the mass-spin inference
from the SXS data without introducing fitting parameters and without tuning the
data range of each SXS template. Also, we find that the exponential damping in
the ringdown spectral amplitude can be modeled well with the exponential
damping in the greybody factor at high frequencies. Based on the findings, we
propose a conjecture that the light ring of the remnant black hole, which
sources the ringdown, forms as early as during the merger stage. We discuss the
formation of the light ring in the static binary solution as a first step
towards the understanding of how the separation of merging black holes may
affect the formation of the light ring.
|
2403.17487v1
|
2024-03-27
|
Fractional variational integrators based on convolution quadrature
|
Fractional dissipation is a powerful tool to study non-local physical
phenomena such as damping models. The design of geometric, in particular,
variational integrators for the numerical simulation of such systems relies on
a variational formulation of the model. In [19], a new approach is proposed to
deal with dissipative systems including fractionally damped systems in a
variational way for both, the continuous and discrete setting. It is based on
the doubling of variables and their fractional derivatives. The aim of this
work is to derive higher-order fractional variational integrators by means of
convolution quadrature (CQ) based on backward difference formulas. We then
provide numerical methods that are of order 2 improving a previous result in
[19]. The convergence properties of the fractional variational integrators and
saturation effects due to the approximation of the fractional derivatives by CQ
are studied numerically.
|
2403.18362v1
|
2024-04-02
|
High-energy neutrinos flavour composition as a probe of neutrino magnetic moments
|
Neutrino propagation in the Galactic magnetic field is considered. To
describe neutrino flavour and spin oscillations on the galactic scale baselines
an approach using wave packets is developed. Evolution equations for the
neutrino wave packets in a uniform and non-uniform magnetic field are derived.
Analytical expressions for neutrino flavour and spin oscillations probabilities
accounting for damping due to wave packet separation are obtained for the case
of uniform magnetic field. It is shown that for oscillations on magnetic
frequencies $\omega_i^B = \mu_i B_\perp$ the coherence lengths that
characterizes the damping scale is proportional to the cube of neutrino average
momentum $p_0^3$. Probabilities of flavour and spin oscillations are calculated
numerically for neutrino interacting with the non-uniform Galactic magnetic
field. Flavour compositions of high-energy neutrino flux coming from the
Galactic centre are calculated accounting for neutrino interaction with the
magnetic field. It is shown that for neutrino magnetic moments $\sim 10^{-13}
\mu_B$ and larger these flavour compositions significantly differ from ones
predicted by the vacuum neutrino oscillations scenario.
|
2404.02027v1
|
2018-06-27
|
Deterministics descriptions of the turbulence in the Navier-Stokes equations
|
This PhD thesis is devoted to deterministic study of the turbulence in the
Navier- Stokes equations. The thesis is divided in four independent
chapters.The first chapter involves a rigorous discussion about the energy's
dissipation law, proposed by theory of the turbulence K41, in the deterministic
setting of the homogeneous and incompressible Navier-Stokes equations, with a
stationary external force (the force only depends of the spatial variable) and
on the whole space R3. The energy's dissipation law, also called the
Kolmogorov's dissipation law, characterizes the energy's dissipation rate (in
the form of heat) of a turbulent fluid and this law was developed by A.N.
Kolmogorov in 1941. However, its deduction (which uses mainly tools of
statistics) is not fully understood until our days and then an active research
area consists in studying this law in the rigorous framework of the
Navier-Stokes equations which describe in a mathematical way the fluids motion
and in particular the movement of turbulent fluids. In this setting, the
purpose of this chapter is to highlight the fact that if we consider the
Navier-Stokes equations on R3 then certain physical quantities, necessary for
the study of the Kolmogorov's dissipation law, have no a rigorous definition
and then to give a sense to these quantities we suggest to consider the
Navier-Stokes equations with an additional damping term. In the framework of
these damped equations, we obtain some estimates for the energy's dissipation
rate according to the Kolmogorov's dissipation law.In the second chapter we are
interested in study the stationary solutions of the damped Navier- Stokes
introduced in the previous chapter. These stationary solutions are a particular
type of solutions which do not depend of the temporal variable and their study
is motivated by the fact that we always consider the Navier-Stokes equations
with a stationary external force. In this chapter we study two properties of
the stationary solutions : the first property concerns the stability of these
solutions where we prove that if we have a control on the external force then
all non stationary solution (with depends of both spatial and temporal
variables) converges toward a stationary solution. The second property concerns
the decay in spatial variable of the stationary solutions. These properties of
stationary solutions are a consequence of the damping term introduced in the
Navier-Stokes equations.In the third chapter we still study the stationary
solutions of Navier-Stokes equations but now we consider the classical
equations (without any additional damping term). The purpose of this chapter is
to study an other problem related to the deterministic description of the
turbulence : the frequency decay of the stationary solutions. Indeed, according
to the K41 theory, if the fluid is in a laminar setting then the stationary
solutions of the Navier-Stokes equations must exhibit a exponential frequency
decay which starts at lows frequencies. But, if the fluid is in a turbulent
setting then this exponential frequency decay must be observed only at highs
frequencies. In this chapter, using some Fourier analysis tools, we give a
precise description of this exponential frequency decay in the laminar and in
the turbulent setting.In the fourth and last chapter we return to the
stationary solutions of the classical Navier-Stokes equations and we study the
uniqueness of these solutions in the particular case without any external
force. Following some ideas of G. Seregin, we study the uniqueness of these
solutions first in the framework of Lebesgue spaces of and then in the a
general framework of Morrey spaces.
|
1806.10430v2
|
1996-10-28
|
QSO Absorbing Galaxies at z<~1: Deep Imaging and Spectroscopy in the Field of 3C 336
|
We present very deep WFPC2 images and FOS spectroscopy from the Hubble Space
Telescope (HST) together with numerous supporting ground-based observations of
the field of the quasar 3C 336 ($z_{em}=0.927$). The observations are designed
to investigate the nature of galaxies producing metal line absorption systems
in the spectrum of the QSO. Along a single line of sight, we find at least 6
metal line absorption systems (of which 3 are newly discovered) ranging in
redshift from 0.317 to 0.892. Through an extensive program of optical and IR
imaging, QSO spectroscopy, and faint galaxy spectroscopy, we have identified 5
of the 6 metal line absorption systems with luminous (L_K > 0.1 L*_K) galaxies.
These have morphologies ranging from very late-type spiral to S0, and exhibit a
wide range of inclination and position angles with respect to the QSO
sightline. The only unidentified absorber, despite our intensive search, is a
damped Lyman $\alpha$ system at $z_{abs}=0.656$. Analysis of the absorption
spectrum suggests that the metal abundances ([Fe/H]$=-1.2$) in this system are
similar to those in damped systems at $z \sim 2$, and to the two other damped
systems for which abundances have been determined at $z <1$. We have found no
examples of intrinsically faint galaxies ($L < 0.1 L^{\ast}$) at small impact
parameters that might have been missed as absorber candidates in our previous
ground-based imaging and spectroscopic programs on MgII absorbing galaxies.
There are no bright galaxies (L > 0.1 L_K) within 50h^{-1} kpc which do not
produce detectable metal lines (of Mg II 2796, 2803 and/or C IV 1548, 1550) in
the QSO spectrum. All of these results generally support the inferences which
we have previously reached from a larger survey for absorption-selected
galaxies at $z\simlt 1$.
|
9610230v1
|
1996-11-05
|
The nature of intermediate-redshift damped Ly-alpha absorbers
|
We present HST/WFPC2 high-spatial resolution images in the R and B bands of
the close environment of the sightlines to seven quasars which spectra show
either a damped Ly-alpha absorption line, 21cm absorption, or a very strong
MgII/FeII absorption system at intermediate redshifts (0.4 < z < 1). Objects
down to about 0.3", or 2.0 kpc at z=0.6 (H0 = 50 kms/s/Mpc, q0=0), and to a
limiting magnitude m(702, lim)=25.9 could be detected for seven fields
comprising eight absorbers (one at higher redshift z=1.78 towards MC 1331+170)
with high HI column densities of at least 1x10^20 cm^-2. In each case, a
candidate absorber with absolute magnitude Mb =-19.0 or much brighter has been
detected. This small sample of gas-rich galaxies at intermediate redshifts
covers a wide range in morphological types. There are three spiral galaxies of
various sizes and luminosities (towards 3C 196, Q 1209+107 and MC 1331+170),
three compact objects (towards EX 0302-223, PKS 0454+039 and, at high redshift,
MC 1331+170), and two amorphous, low surface brightness galaxies (towards PKS
1229-021 and 3C 286). In the fields around 3C 196, PKS 1229-021 and Q 1209+107,
there is an excess of galaxies in the PC2 images, suggestive of the presence of
a group of galaxies associated with the damped Ly-alpha absorber, or maybe with
the quasar itself for the two z = 1.0 cases. For 3C 196 and 3C 286, the quasar
host galaxies have also tentatively been discovered.
|
9611031v1
|
1997-07-08
|
The Formation of Galactic Disks
|
We study the population of galactic disks expected in current hierarchical
clustering models for structure formation. A rotationally supported disk with
exponential surface density profile is assumed to form with a mass and angular
momentum which are fixed fractions of those of its surrounding dark halo. We
assume that haloes respond adiabatically to disk formation, and that only
stable disks can correspond to real systems. With these assumptions the
predicted population can match both present-day disks and the damped Lyman
alpha absorbers in QSO spectra. Good agreement is found provided: (i) the
masses of disks are a few percent of those of their haloes; (ii) the specific
angular momenta of disks are similar to those of their haloes; (iii)
present-day disks were assembled recently (at z<1). In particular, the observed
scatter in the size-rotation velocity plane is reproduced, as is the slope and
scatter of the Tully-Fisher relation. The zero-point of the TF relation is
matched for a stellar mass-to-light ratio of 1 to 2 h in the I-band, consistent
with observational values derived from disk dynamics. High redshift disks are
predicted to be small and dense, and could plausibly merge together to form the
observed population of elliptical galaxies. In many (but not all) currently
popular cosmogonies, disks with rotation velocities exceeding 200 km/s can
account for a third or more of the observed damped Lyman alpha systems at
z=2.5. Half of the lines-of-sight to such systems are predicted to intersect
the absorber at r>3kpc/h and about 10% at r>10kpc/h. The cross-section for
absorption is strongly weighted towards disks with large angular momentum and
so large size for their mass. The galaxy population associated with damped
absorbers should thus be biased towards low surface brightness systems.
|
9707093v1
|
1997-09-26
|
No C+ emission from the z=3.137 damped Lyman-alpha absorber towards PC1643+4631A
|
We describe a search for redshifted [C II] in a z=3.137 damped Ly-alpha
absorption system that has a large neutral hydrogen column density and which
was controversially reported to be a source of CO emission, indicative of rapid
star-formation (Frayer, Brown & Vanden Bout 1994; Braine, Downes & Guilloteau
1996). There is no sign of [C II] emission in our spectrum, which was obtained
during excellent observing conditions at the James Clerk Maxwell Telescope
(JCMT) and covers 1890 km/s. The upper limit we have placed on the integrated
line intensity (3 sigma(T_MB) < 5.9 K km/s for a profile akin to that of the CO
lines) constrains the [C II]/CO(1-0) line-intensity ratio to 3 sigma < 8300,
based on the line intensity reported by Frayer et al. (1994), or to 3 sigma <
58700 based on the data obtained by Braine et al. (1996). These limits are
consistent with values measured in the Galactic plane and for nearby starburst
nuclei; the former, however, is significantly lower than the ratio found in
low-metallicity systems such as the Large Magellanic Cloud (which might be
expected to have much in common with a damped Ly-alpha absorption system at
high redshift). This can be taken as evidence against the reality of the CO
line detections, with the proviso that a system significantly larger than
present-day disk galaxies would NOT have been fully covered by our small beam
whereas it WOULD have been properly sampled by the Frayer et al. observations.
Finally, we demonstate (as did Ivison et al. 1996) that knitting together
overlapping bands can generate erroneous results - specifically, an emission
feature that has a width, profile and central velocity consistent with the
controversial CO emission lines and which could have drawn us to entirely the
wrong conclusions.
|
9709266v1
|
1998-04-06
|
Three-dimensional waves generated at Lindblad resonances in thermally stratified disks
|
We analyze the linear, 3D response to tidal forcing of a disk that is thin
and thermally stratified in the direction normal to the disk plane. We model
the vertical disk structure locally as a polytrope which represents a disk of
high optical depth. We solve the 3D gas-dynamic equations semi-analytically in
the neighborhood of a Lindblad resonance. These solutions match asymptotically
on to those valid away from resonances and provide solutions valid at all
radii. We obtain the following results. 1) A variety of waves are launched at
resonance. However, the f mode carries more than 95% of the torque exerted at
the resonance. 2) These 3D waves collectively transport exactly the amount of
angular momentum predicted by the 2D torque formula. 3) Near resonance, the f
mode occupies the full vertical extent of the disk. Away from resonance, the f
mode becomes confined near the surface of the disk, and, in the absence of
other dissipation mechanisms, damps via shocks. The radial length scale for
this process is roughly r_L/m (for resonant radius r_L and azimuthal wavenumber
m), independent of the disk thickness H. This wave channeling process is due to
the variations of physical quantities in r and is not due to wave refraction.
4) However, the inwardly propagating f mode launched from an m=2 inner Lindblad
resonance experiences relatively minor channeling.
We conclude that for binary stars, tidally generated waves in highly
optically thick circumbinary disks are subject to strong nonlinear damping by
the channeling mechanism, while those in circumstellar accretion disks are
subject to weaker nonlinear effects. We also apply our results to waves excited
by young planets for which m is approximately r/H and conclude that the waves
are damped on the scale of a few H.
|
9804063v1
|
2000-11-23
|
Near-Infrared Integral Field Spectroscopy of Damped Lyman-alpha Systems
|
We assess the feasibility of detecting star formation in damped Lyman-alpha
systems (DLAs) at z>1 through near-infrared spectroscopy using the forthcoming
integral field units on 8m-class telescopes. Although their relation to
galaxies is not well established, high-z DLAs contain most of the neutral gas
in the Universe, and this reservoir is depleted with time - presumably through
star formation. Line emission should be an indicator of star formation
activity, but searches based on Lyman-alpha are unreliable because of the
selective extinction of this resonant UV line. Using more robust lines such as
H-alpha forces a move to the near-infrared at z>1. For line emission searches,
spectroscopy is more sensitive than imaging, but previous long-slit
spectroscopic searches have been hampered by the likelihood that any star
forming region in the DLA galaxy disk would fall outside the narrow slit. The
new integral field units such as CIRPASS on Gemini will cover sufficient solid
angles to intercept these, even in the extreme case of large galactic disks at
high redshift. On an 8m-class telescope, star formation rates of <1M_sun/yr
will be reached at z~1.4 with H-alpha in the H-band. Such star formation rates
are well below L* for the high-z Lyman-break population, and are comparable
locally to the luminous giant HII complexes in M101. It appears that
instruments such as CIRPASS on Gemini will have both the sensitivity and the
survey area to measure star formation rates in z>1 DLAs. These observations
will probe the nature of damped Lyman-alpha systems and address their relation
to galaxies.
|
0011421v1
|
2001-08-07
|
Dynamics and Origin of the 2:1 Orbital Resonances of the GJ 876 Planets
|
(Abridged) A dynamical fit has placed the two planets about the star GJ 876
in coplanar orbits deep in 3 resonances at the 2:1 mean-motion commensurability
with small libration amplitudes. The libration of both lowest order mean-motion
resonance variables, theta_1 and theta_2, and the secular resonance variable,
theta_3, about 0 deg. differs from the familiar geometry of the Io-Europa pair,
where theta_2 and theta_3 librate about 180 deg. By considering a condition for
stable simultaneous librations of theta_1 and theta_2, we show that the GJ 876
geometry results because of the large orbital eccentricities e_i, whereas the
very small e_i in the Io-Europa system lead to the latter's geometry.
Surprisingly, the GJ 876 resonance configuration remains stable for e_1 up to
0.86 and for amplitude of libration of theta_1 approaching 45 deg. with the
current e_i. We find that inward migration of the outer planet of the GJ 876
system results in certain capture into the observed resonances if initially e_1
<0.06 and e_2<0.03 and the migration rate |(da_2/dt)/a_2| < 0.03(a_2/AU)^{-3/2}
yr^{-1}. The bound on the migration rate is easily satisfied by migration due
to planet-nebula interaction. If there is no eccentricity damping, eccentricity
growth is rapid with continued migration within the resonance, with e_i
exceeding the observed values after a further reduction in the semi-major axes
a_i of only 7%. With eccentricity damping (de_i/dt)/e_i = -K|(da_i/dt)/a_i|,
the e_i reach equilibrium values that remain constant for arbitrarily long
migration within the resonances. The equilibrium e_i are close to the observed
e_i for K=100 (K=10) if there is migration and damping of the outer planet only
(of both planets). It is as yet unclear that planet-nebula interaction can
produce the large value of K required to obtain the observed eccentricities.
|
0108104v2
|
2001-12-03
|
Euler, Jacobi, and Missions to Comets and Asteroids
|
Whenever a freely spinning body is found in a complex rotational state, this
means that either the body is a recent victim of an impact or a tidal
interaction, or is a fragment of a recently disrupted progenitor. Another
factor (relevant for comets) is outgassing. Due to impacts, tidal forces and
outgassing, the asteroidal and cometary precession must be a generic
phenomenon: while some rotators are in the state of visible tumbling, a much
larger amount of objects must be performing narrow-cone precession not so
easily observable from the Earth. The internal dissipation in a freely
precessing top leads to relaxation (gradual damping of the precession) and
sometimes to spontaneous changes in the rotation axis. Recently developed
theory of dissipative precession of a rigid body reveals that this is a highly
nonlinear process: while the body is precessing at an angular rate $ \omega$,
the precession-caused stresses and strains in the body contain components
oscillating at other frequencies. Dependent upon the spin state, those
frequencies may be higher or, most remarkably, lower than the precession rate.
In many states dissipation at the harmonics is comparable to or even exceeds
that at the principal frequency. For this and other reasons, in many spin
states the damping of asteroidal and cometary wobble happens faster, by several
orders, than believed previously. This makes it possible to measure the
precession-damping rate. The narrowing of the precession cone through the
period of about a year can be registered by the currently available
spacecraft-based observational means. However, in the near-separatrix spin
states a precessing rotator can considerably slow down its relaxation.
|
0112054v3
|
2002-06-17
|
The UCSD HIRES/KECK I Damped Lya Abundance Database: IV. Probing Galactic Enrichment Histories with Nitrogen
|
We present 14 N^0 measurements from our HIRES/Keck database of damped Lya
abundances. These data are combined with measurements from the recent and past
literature to build an homogeneous, uniform set of observations. We examine
photoionization diagnostics like Fe^++ and Ar^0 in the majority of the complete
sample and assess the impact of ionization corrections on N/alpha and alpha/H
values derived from observed ionic column densities of N^0, Si^+, H^0, and S^+.
Our final sample of 19 N/alpha, alpha/H pairs appears bimodal; the majority of
systems show N/alpha values consistent with metal-poor emission regions in the
local universe but a small sub-sample exhibit significantly lower N/alpha
ratios. Contrary to previous studies of N/alpha in the damped systems, our
sample shows little scatter within each sub-sample. We consider various
scenarios to explain the presence of the low N/alpha sightlines and account for
the apparent bimodality. We favor a model where at least some galaxies undergo
an initial burst of star formation with suppressed formation of
intermediate-mass stars. We found a power-law IMF with slope 0.10 or a mass cut
of ~5-8 Msolar would successfully reproduce the observed LN-DLA values. If the
bimodal distribution is confirmed by a larger sample of measurements, this may
present the first observational evidence for a top heavy initial mass function
in some early stellar populations.
|
0206296v1
|
2003-08-11
|
The Nature of Damped Ly-alpha Absorbing Galaxies at z<=1--A Photometric Redshift Survey of Damped Ly-alpha Absorbers
|
We study the nature of damped Lya absorption (DLA) systems at z<=1 using a
sample of 11 DLA galaxies, for which accurate redshift measurements are
available. We demonstrate that the precision of photometric redshifts is
sufficient for identifying DLA galaxies, because DLAs are rare and their
intrinsically high column density implies a small impact parameter of the host
galaxy to the QSO line of sight. We adopt this first large DLA galaxy sample to
study the neutral gas cross section of intermediate-redshift galaxies and
examine the optical properties of DLA galaxies at z<=1. The results of our
study are: (1) the extent of neutral gas around intermediate-redshift galaxies
scales with B-band luminosity as R/R_* = [L_B/L_{B_*}]^{\beta} with R_*=24-30
h^{-1} kpc and \beta = 0.26_{-0.06}^{+0.24} at N(HI)=10^{20} cm^{-2}; (2) the
observed incidence of the DLAs versus the B-band luminosity of the DLA galaxies
is consistent with models derived from adopting a known galaxy B-band
luminosity function and the best-fit scaling relation of the neutral gas cross
section at M_B - 5\log h <= -17; (3) comparison of the observed and predicted
number density of DLAs supports that luminous galaxies can explain most of the
DLAs found in QSO absorption line surveys and a large contribution of dwarfs
(M_B - 5\log h >= -17) to the total neutral gas cross section is not necessary;
(4) of the 11 DLAs studied, 45% are disk dominated, 22% are bulge dominated,
11% are irregular, and 22% are in galaxy groups, indicating that galaxies that
give rise to the DLAs span a wide range of morphological types and arise in a
variety of galaxy environment; (Abridged)
|
0308190v1
|
2004-07-21
|
Discovery of a Primitive Damped Lyman alpha Absorber Near an X-ray Bright Galaxy Group in the Virgo Cluster
|
We present a new UV echelle spectrum of PG1216+069, obtained with HST+STIS,
which reveals damped Lya (DLA) absorption as well as O I, C II, Si II, and Fe
II absorption lines at z(abs) = 0.00632 near the NGC4261 group. The absorber
shows no evidence of highly-ionized gas, which places constraints on "warm-hot"
missing baryons in the NGC4261 group. The well-developed damping wings of the
Lya line tightly constrain the H I column density; we find log N(H I) =
19.32+/-0.03. The metallicity of this sub-DLA is remarkably low, [O/H] =
-1.60^{+0.09}_{-0.11}, which is comparable to many analogous high-redshift
systems, and the iron abundance indicates that this absorber contains little or
no dust. Nitrogen is underabundant; we detect neither N I or N II, and we show
that this is not due to ionization effects but rather indicates that [N/O] <
-0.28 (3sigma). Despite the proximity to NGC4261 group, there are no bright
galaxies close to the sight line at the absorption redshift. The nearest known
galaxy is a sub-L* galaxy with a projected distance rho = 86 kpc; the closest
L* galaxy is NGC4260 at rho = 246 kpc. The low metallicity and [N/O] indicate
that this low-z sub-DLA is a relatively primitive gas cloud. We consider the
nature and origin of the sub-DLA, and we find several possibilities. The
properties of the sub-DLA are similar to those of the interstellar media in
blue compact dwarf galaxies and are also reminiscent of Milky Way HVCs. Or, the
object could simply be a small dark-matter halo, self-enriched by a small
amount of internal star formation but mostly undisturbed since its initial
formation. In this case, the small halo would likely be an ancient building
block of galaxy formation that formed before the epoch of reionization.
|
0407465v2
|
2004-08-27
|
Detection of 21 Centimeter HI Absorption at z = 0.78 in a Survey of Radio Continuum Sources
|
We report the detection of a deep broad HI 21 cm absorption system at z =
0.78 toward the radio source [HB89] 2351+456 (4C+45.51) at z = 1.992. The HI
absorption was identified in a blind spectral line survey conducted at the
Green Bank Telescope spanning 0.63 < z < 1.10 toward a large sample of radio
continuum sources. The HI column density is N(HI) = 2.35 x 10^19 (T_s/f) cm^-2,
where T_s is the spin temperature and f is the continuum covering factor of the
absorbing gas. For T_s/f > 8.5 K, this system is by definition a damped Ly
alpha absorption system (N(HI) >= 2 x 10^20 cm^-2). The line is unusually
broad, with a FWHM of 53 km/s and a full span of 163 km/s, suggesting a
physically extended HI gas structure. Radio surveys identify damped Ly alpha
systems in a manner that bypasses many of the selection effects present in
optical/UV surveys, including dust extinction and the atmospheric cutoff for z
< 1.65. The smooth broad profile of this HI 21 cm absorption system is similar
to the z = 0.89 HI absorption toward PKS 1830-211, which suggests that the
absorber toward [HB89] 2351+456 is also a gravitational lens and a molecular
absorption system. However, very long baseline interferometry and Hubble Space
Telescope observations show little evidence for gravitational lensing, and BIMA
millimeter observations show no HCO+ (1-2) or HCN (1-2) absorption down to tau
= 0.15 (3 sigma) in 5 km/s channels. Although this radio damped Ly alpha
selection technique would include dusty, molecule-rich systems, [HB89] 2351+456
appears to be a ``vanilla'' HI 21 cm absorber.
|
0408531v1
|
2005-03-17
|
The first WIMPy halos
|
Dark matter direct and indirect detection signals depend crucially on the
dark matter distribution. While the formation of large scale structure is
independent of the nature of the cold dark matter (CDM), the fate of
inhomogeneities on sub-galactic scales, and hence the present day CDM
distribution on these scales, depends on the micro-physics of the CDM
particles. We study the density contrast of Weakly Interacting Massive
Particles (WIMPs) on sub-galactic scales. We calculate the damping of the
primordial power spectrum due to collisional damping and free-streaming of
WIMPy CDM and show that free-streaming leads to a CDM power spectrum with a
sharp cut-off at about $10^{-6} M_\odot$. We also calculate the transfer
function for the growth of the inhomogeneities in the linear regime, taking
into account the suppression in the growth of the CDM density contrast after
matter-radiation equality due to baryons and show that our analytic results are
in good agreement with numerical calculations. Combining the transfer function
with the damping of the primordial fluctuations we produce a WMAP normalized
primordial CDM power spectrum, which can serve as an input for high resolution
CDM simulations. We find that the smallest inhomogeneities typically have
co-moving radius of about 1 pc and enter the non-linear regime at a redshift of
$60 \pm 20$. We study the effect of scale dependence of the primordial power
spectrum on these numbers and also use the spherical collapse model to make
simple estimates of the properties of the first generation of WIMP halos to
form. We find that the very first WIMPy halos may have a significant impact on
indirect dark matter searches.
|
0503387v2
|
2005-06-30
|
Molecular Hydrogen in the Damped Ly alpha Absorber of Q1331+170
|
We used HST/STIS to obtain the spectrum of molecular hydrogen associated with
the damped Ly$\alpha$ system at $z_{\rm abs}=1.7765$ toward the quasar
Q1331+170 at $z_{\rm em}=2.084$. Strong ${\rm H}_2$ absorption was detected,
with a total ${\rm H}_2$ column density of $N({\rm H}_2)=(4.45\pm 0.36)\times
10^{19} {\rm cm^{-2}}$.The molecular hydrogen fraction is $f_{{\rm
H}_2}=\frac{2N_{\rm H_2}}{N_{\rm HI}+2N_{\rm H_2}}=(5.6\pm 0.7)%$, which is the
greatest value reported so far in any redshifted damped Ly$\alpha$ system. This
results from the combined effect of a relatively high dust-to-gas ratio, a low
gas temperature, and an extremely low ambient UV radiation field. Based on the
observed population of $J$ states, we estimate the photo-absorption rate to be
$R_{\rm abs}=(7.6\pm 2.4)\times 10^{-13} {\rm s^{-1}}$, corresponding to a
local UV radiation field of $J(1000{\rm \AA})\approx 2.1\times 10^{-3}
J_{1000{\rm \AA},\odot}$, where $J_{1000{\rm \AA},\odot}$ is the UV intensity
at $1000 \AA$ in the solar neighborhood. This is comparable with the
metagalactic UV background intensity at this redshift, and implies an extremely
low star formation rate in the absorber's environment. The observed CO-to-H$_2$
column density ratio is $\frac{N_{\rm CO}}{N_{\rm H_2}}<2.5\times 10^{-7}$,
which is similar to the value measured for diffuse molecular clouds in the
Galactic ISM. Finally, applying the inferred physical conditions to the
observed C I fine structure excitation (Songaila {\it et al.} 1994), we
estimate the cosmic microwave background temperature to be $T_{\rm CMB}=(7.2\pm
0.8) {\rm K}$ at $z=1.77654$, consistent with the predicted value of $7.566
{\rm K}$ from the standard cosmology.
|
0506766v1
|
1997-05-06
|
Resonant Raman Scattering in Antiferromagnets
|
Two-magnon Raman scattering provides important information about electronic
correlations in the insulating parent compounds of high-$T_c$ materials. Recent
experiments have shown a strong dependence of the Raman signal in $B_{1g}$
geometry on the frequency of the incoming photon. We present an analytical and
numerical study of the Raman intensity in the resonant regime. It has been
previously argued by one of us (A.Ch) and D. Frenkel that the most relevant
contribution to the Raman vertex at resonance is given by the triple resonance
diagram. We derive an expression for the Raman intensity in which we
simultaneously include the enhancement due to the triple resonance and a final
state interaction. We compute the two-magnon peak height (TMPH) as a function
of incident frequency and find two maxima at $\omega^{(1)}_{res} \approx
2\Delta + 3J$ and $\omega^{(2)}_{res} \approx 2\Delta + 8J$. We argue that the
high-frequency maximum is cut only by a quasiparticle damping, while the
low-frequency maximum has a finite amplitude even in the absence of damping. We
also obtain an evolution of the Raman profile from an asymmetric form around
$\omega^{(1)}_{res}$ to a symmetric form around $\omega^{(2)}_{res}$. We
further show that the TMPH depends on the fermionic quasiparticle damping, the
next-nearest neighbor hopping term $t^{\prime}$ and the corrections to the
interaction vertex between light and the fermionic current. We discuss our
results in the context of recent experiments by Blumberg et al. on
$Sr_2CuO_2Cl_2$ and $YBa_2Cu_3O_{6.1}$ and R\"{u}bhausen et al. on
$PrBa_2Cu_3O_7$ and show that the triple resonance theory yields a qualitative
and to some extent also quantitative understanding of the experimental data.
|
9705051v1
|
1998-09-15
|
Solid friction at high sliding velocities: an explicit 3D dynamical SPH approach
|
We present realistic 3D numerical simulations of elastic bodies sliding on
top of each other in a regime of velocities ranging from meters to tens of
meters per second using the so-called Smoothed Particle Hydrodynamics (SPH)
method. Our investigations are restricted to regimes of pressure and roughness
where only elastic deformations occur between asperities at the contact surface
between the slider block and the substrate. In this regime, solid friction is
due to the generation of vibrational radiations which are subsequently damped
out. We study periodic commensurate and incommensurate asperities and various
types of disordered surfaces. We report the evidence of a transition from zero
(or non-measurable $\mu < 0.001$) friction to a finite friction as the normal
pressure increases above about $10^6~Pa$. For larger normal pressures (up to
$10^9~Pa$), we find a remarkably universal value for the friction coefficient
$\mu \approx 0.06$, which is independent of the internal dissipation strength
over three order of magnitudes, and independent of the detailled nature of the
slider block-substrate interactions. We find that disorder may either decrease
or increase $\mu$ due to the competition between two effects: disorder detunes
the coherent vibrations of the asperties that occur in the periodic case,
leading to weaker acoustic radiation and thus weaker damping. On the other
hand, large disorder leads to stronger vibration amplitudes at local asperities
and thus stronger damping. Our simulations have confirmed the existence of
jumps over steps or asperities of the slider blocks occurring at the largest
velocities studied ($10~m/s$). These jumps lead to chaotic motions similar to
the bouncing-ball problem. We find a velocity strengthening with a doubling of
the friction coefficient as the velocity increases from $1~m/s$ to $10~m/s$.
|
9809213v1
|
2000-03-10
|
Competing orders and quantum criticality in doped antiferromagnets
|
We use a number of large-N limits to explore the competition between ground
states of square lattice doped antiferromagnets which break electromagnetic
U(1), time-reversal, or square lattice space group symmetries. Among the states
we find are d-, (s+id)-, and (d+id)-wave superconductors, Wigner crystals,
Wigner crystals of hole pairs, orbital antiferromagnets (or staggered-flux
states), and states with spin-Peierls and bond-centered charge stripe order. In
the vicinity of second-order quantum phase transitions between the states, we
go beyond the large-N limit by identifying the universal quantum field theories
for the critical points, and computing the finite temperature, quantum-critical
damping of fermion spectral functions. We identify candidate critical points
for the recently observed quantum-critical behavior in photoemission
experiments on BSCCO by Valla et al. (Science 285, 2110 (1999)). These involve
onset of a charge density wave, or of broken time-reversal symmetry with (d+id)
or (s+id) pairing, in a d-wave superconductor. It is not required (although it
is allowed) that the stable state in the doped cuprates to be anything other
than the d-wave superconductor--the other states need only be stable nearby in
parameter space. At finite temperatures, fluctuations associated with these
nearby states lead to the observed fermion damping in the vicinity of the nodal
points in the Brillouin zone. The cases with broken time-reversal symmetry are
appealing because the order parameter is not required to satisfy any special
commensurability conditions. The observed absence of inelastic damping of
quasiparticles with momenta (pi,k), (k,pi) (with 0 < k < pi) also appears very
naturally for the case of a transition to (d+id) order.
|
0003163v7
|
2001-12-03
|
Theory of proximity effect in superconductor/ferromagnet heterostructures
|
We present a microscopic theory of proximity effect in the
ferromagnet/superconductor/ferromagnet (F/S/F) nanostructures where S is s-wave
low-T_c superconductor and F's are layers of 3d transition ferromagnetic metal.
Our approach is based on the solution of Gor'kov equations for the normal and
anomalous Green's functions together with a self-consistent evaluation of the
superconducting order parameter. We take into account the elastic
spin-conserving scattering of the electrons assuming s-wave scattering in the S
layer and s-d scattering in the F layers. In accordance with the previous
quasiclassical theories, we found that due to exchange field in the ferromagnet
the anomalous Green's function F(z) exhibits the damping oscillations in the
F-layer as a function of distance z from the S/F interface. In the given model
a half of period of oscillations is determined by the length \xi_m^0 = \pi
v_F/E_ex, where v_F is the Fermi velocity and E_ex is the exchange field, while
damping is governed by the length l_0 = (1/l_{\uparrow} +
1/l_{\downarrow})^{-1} with l_{\uparrow} and l_{\downarrow} being
spin-dependent mean free paths in the ferromagnet. The superconducting
transition temperature T_c(d_F) of the F/S/F trilayer shows the damping
oscillations as a function of the F-layer thickness d_F with period \xi_F =
\pi/\sqrt{m E_ex}, where m is the effective electron mass. We show that strong
spin-conserving scattering either in the superconductor or in the ferromagnet
significantly suppresses these oscillations. The calculated T_c(d_F)
dependences are compared with existing experimental data for Fe/Nb/Fe trilayers
and Nb/Co multilayers.
|
0112034v3
|
2007-07-27
|
C IV absorption in damped and sub-damped Lyman-alpha systems: correlations with metallicity and implications for galactic winds at z~2-3
|
We present a study of C IV absorption in a sample of 63 damped Lyman-alpha
(DLA) systems and 11 sub-DLAs in the redshift range 1.75<z_abs<3.61, using a
dataset of high-resolution (6.6 km/s FWHM), high signal-to-noise VLT/UVES
spectra. Narrow and broad C IV absorption line components indicate the presence
of both warm, photoionized and hot, collisionally ionized gas. We report new
correlations between the metallicity (measured in the neutral-phase) and each
of the C IV column density, the C IV total line width, and the maximum C IV
velocity. We explore the effect on these correlations of the sub-DLAs, the
proximate DLAs (defined as those within 5 000 km/s of the quasar), the
saturated absorbers, and the metal line used to measure the metallicity, and we
find the correlations to be robust. There is no evidence for any difference
between the measured properties of DLA C IV and sub-DLA C IV. In 25 DLAs and 4
sub-DLAs, covering 2.5 dex in [Z/H], we directly observe C IV moving above the
escape speed, where v_esc is derived from the total line width of the neutral
gas profiles. These high-velocity C IV clouds, unbound from the central
potential well, can be interpreted as highly ionized outflowing winds, which
are predicted by numerical simulations of galaxy feedback. The distribution of
C IV column density in DLAs and sub-DLAs is similar to the distribution in
Lyman Break galaxies, where winds are directly observed, supporting the idea
that supernova feedback creates the ionized gas in DLAs. The unbound C IV
absorbers show a median mass flow rate of ~22(r/40 kpc) solar masses per year,
where r is the characteristic C IV radius. Their kinetic energy fluxes are
large enough that a star formation rate (SFR) of ~2 solar masses per year is
required to power them.
|
0707.4065v2
|
2007-09-25
|
On the Structure of Dark Matter Halos at the Damping Scale of the Power Spectrum with and without Relict Velocities
|
We report a series of high-resolution cosmological N-body simulations
designed to explore the formation and properties of dark matter halos with
masses close to the damping scale of the primordial power spectrum of density
fluctuations. We further investigate the effect that the addition of a random
component, v_rms, into the particle velocity field has on the structure of
halos. We adopted as a fiducial model the Lambda Warm Dark Matter cosmology
with a non-thermal sterile neutrino mass of 0.5 keV. The filtering mass
corresponds then to M_f = 2.6x10^12 M_sun/h. Halos of masses close to M_f were
simulated with several million of particles. The results show that, on one
hand, the inner density slope of these halos (at radii <~0.02 the virial radius
Rvir) is systematically steeper than the one corresponding to the NFW fit or to
the CDM counterpart. On the other hand, the overall density profile (radii
larger than 0.02Rvir) is less curved and less concentrated than the NFW fit,
with an outer slope shallower than -3. For simulations with v_rms, the inner
halo density profiles flatten significantly at radii smaller than 2-3 kpc/h
(<~0.010-0.015Rvir). A constant density core is not detected in our
simulations, with the exception of one halo for which the flat core radius is
~1 kpc/h. Nevertheless, if ``cored'' density profiles are used to fit the halo
profiles, the inferred core radii are ~0.1-0.8 kpc/h, in rough agreement with
theoretical predictions based on phase-space constrains, and on dynamical
models of warm gravitational collapse. A reduction of v_rms by a factor of 3
produces a modest decrease in core radii, less than a factor of 1.5. We discuss
the extension of our results into several contexts, for example, to the
structure of the cold DM micro-halos at the damping scale of this model.
|
0709.4027v1
|
2008-10-01
|
Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations
|
We study the global stability of non-axisymmetric p-modes (also called
inertial-acoustic modes) trapped in the inner-most regions of accretion discs
around black holes. We show that the lowest-order (highest-frequency) p-modes,
with frequencies $\omega=(0.5-0.7) m\Omega_{\rm ISCO}$, can be overstable due
to general relativistic effects, according to which the radial epicyclic
frequency is a non-monotonic function of radius near the black hole. The mode
is trapped inside the corotation resonance radius and carries a negative
energy. The mode growth arises primarily from wave absorption at the corotation
resonance, and the sign of the wave absorption depends on the gradient of the
disc vortensity. When the mode frequency is sufficiently high, such that the
slope of the vortensity is positive at corotation positive wave energy is
absorbed at the resonance, leading to the growth of mode amplitude. We also
study how the rapid radial inflow at the inner edge of the disc affects the
mode trapping and growth. Our analysis of the behavior of the fluid
perturbations in the transonic flow near the ISCO indicates that, while the
inflow tends to damp the mode, the damping effect is sufficiently small under
some conditions so that net mode growth can still be achieved. We further
clarify the role of the Rossby wave instability and show that it does not
operate for black hole accretion discs with smooth-varying vortensity profiles.
Overstable non-axisymmetric p-modes driven by the corotational instability
provide a plausible explanation for the high-frequency (> 100 Hz)
quasi-periodic oscillations (HFQPOs) observed from a number of black-hole X-ray
binaries in the very high state. The absence of HFQPOs in the soft (thermal)
state may result from mode damping due to the radial infall at the ISCO.
|
0810.0203v2
|
2008-10-03
|
Stochastic excitation of nonradial modes II. Are solar asymptotic gravity modes detectable?
|
Detection of solar gravity modes remains a major challenge to our
understanding of the innerparts of the Sun. Their frequencies would enable the
derivation of constraints on the core physical properties while their
amplitudes can put severe constraints on the properties of the inner convective
region. Our purpose is to determine accurate theoretical amplitudes of solar g
modes and estimate the SOHO observation duration for an unambiguous detection.
We investigate the stochastic excitation of modes by turbulent convection as
well as their damping. Input from a 3D global simulation of the solar
convective zone is used for the kinetic turbulent energy spectrum. Damping is
computed using a parametric description of the nonlocal time-dependent
convection-pulsation interaction. We then provide a theoretical estimation of
the intrinsic, as well as apparent, surface velocity. Asymptotic g-mode
velocity amplitudes are found to be orders of magnitude higher than previous
works. Using a 3D numerical simulation, from the ASH code, we attribute this to
the temporal-correlation between the modes and the turbulent eddies which is
found to follow a Lorentzian law rather than a Gaussian one as previously used.
We also find that damping rates of asymptotic gravity modes are dominated by
radiative losses, with a typical life-time of $3 \times 10^5$ years for the
$\ell=1$ mode at $\nu=60 \mu$Hz. The maximum velocity in the considered
frequency range (10-100 $\mu$Hz) is obtained for the $\ell=1$ mode at $\nu=60
\mu$Hz and for the $\ell=2$ at $\nu=100 \mu$Hz. Due to uncertainties in the
modeling, amplitudes at maximum i.e. for $\ell=1$ at 60 $\mu$Hz can range from
3 to 6 mm s$^{-1}$.
|
0810.0602v2
|
2008-10-20
|
The kinematic signature of damped Lyman alpha systems: Using the D-index to screen for high column density HI absorbers
|
Using a sample of 21 damped Lyman alpha systems (DLAs) and 35 sub-DLAs, we
evaluate the D-index = EW / Delta v x 1000 from high resolution spectra of the
MgII lambda 2796 profile. This sample represents an increase in sub-DLA D-index
statistics by a factor of four over the sample used by Ellison (2006). We
investigate various techniques to define the velocity spread (Delta v) of the
MgII line to determine an optimal D-index for the identification of DLAs. The
success rate of DLA identification is 50 -- 55%, depending on the velocity
limits used, improving by a few percent when the column density of FeII is
included in the D-index calculation. We recommend the set of parameters that is
judged to be most robust, have a combination of high DLA identification rate
(57%) and low DLA miss rate (6%) and most cleanly separate the DLAs and
sub-DLAs (Kolmogorov-Smirnov probability 0.5%). These statistics demonstrate
that the D-index is the most efficient technique for selecting low redshift DLA
candidates: 65% more efficient than selecting DLAs based on the equivalent
widths of MgII and FeII alone. We also investigate the effect of resolution on
determining the N(HI) of sub-DLAs. We convolve echelle spectra of sub-DLA Lya
profiles with Gaussians typical of the spectral resolution of instruments on
the Hubble Space Telescope and compare the best fit N(HI) values at both
resolutions. We find that the fitted HI column density is systematically
over-estimated by ~ 0.1 dex in the moderate resolution spectra compared to the
best fits to the original echelle spectra. This offset is due to blending of
nearby Lya clouds that are included in the damping wing fit at low resolution.
|
0810.3700v1
|
2009-01-24
|
Dynamic migration of rotating neutron stars due to a phase transition instability
|
Using numerical simulations based on solving the general relativistic
hydrodynamic equations, we study the dynamics of a phase transition in the
dense core of isolated rotating neutron stars, triggered by the back bending
instability reached via angular momentum loss. In particular, we investigate
the dynamics of a migration from an unstable configuration into a stable one,
which leads to a mini-collapse of the neutron star and excites sizeable
pulsations in its bulk until it acquires a new stable equilibrium state. We
consider equations of state with softening at high densities, a simple analytic
one with a mixed hadron-quark phase in an intermediate pressure interval and
pure quark matter at very high densities, and a microphysical one that has a
first-order phase transition, originating from kaon condensation. Although the
marginally stable initial models are rigidly rotating, we observe that during
the collapse (albeit little) differential rotation is created. We analyze the
emission of gravitational radiation, which in some models is amplified by mode
resonance effects, and assess its prospective detectability by interferometric
detectors. We expect that the most favorable conditions for dynamic migration
exist in very young magnetars. We find that the damping of the post-migration
pulsations strongly depends on the character of the equation of state
softening. The damping of pulsations in the models with the microphysical
equation of state is caused by dissipation associated with matter flowing
through the density jump at the edge of the dense core. If at work, this
mechanism dominates over all other types of dissipation, like bulk viscosity in
the exotic-phase core, gravitational radiation damping, or numerical viscosity.
|
0901.3819v2
|
2009-02-12
|
New Magellan Inamori Kyocera Echelle Observations of z<1.5 sub-damped Lyman-alpha systems
|
The Damped and sub-Damped Lyman-alpha (DLA and sub-DLA) systems seen in the
spectra of QSOs offer a unique way to study the interstellar medium of high
redshift galaxies. In this paper we report on new abundance determinations in a
sample of 10 new systems, nine of the lesser studied sub-DLAs and one DLA,
along the line of sight to seven QSOs from spectra taken with the MIKE
spectrograph. Lines of Mg I, Mg II, Al II, Al III, Ca II, Mn II, Fe II, and Zn
II were detected. Here, we give the column densities and equivalent widths of
the observed absorption lines, as well as the abundances determined for these
systems. Zn, a relatively undepleted element in the local interstellar medium
(ISM) is detected in one system with a high metallicity of [Zn/H]=+0.27\pm0.18.
In one other system, a high abundance based on the more depleted element Fe is
seen with [Fe/H]=-0.37\pm0.13, although Zn is not detected. The N(HI)-weighted
mean metallicity of these sub-DLA systems based on Fe is <[Fe/H]>=-0.76\pm0.11,
nearly ~0.7 dex higher (a factor of 5) than what is seen in DLAs in this
redshift range. The relative abundance of [Mn/Fe] is also investigated. A clear
trend is visible for these systems as well as systems from the literature, with
[Mn/Fe] increasing with increasing metallicity in good agreement with with
Milky Way stellar abundances.
|
0902.2022v2
|
2009-04-16
|
Revisiting the origin of the high metallicities of sub-damped Lyman-alpha systems
|
Sub-damped Lyman-alpha systems (sub-DLAs) have previously been found to
exhibit a steeper metallicity evolution than the classical damped Lyman-alpha
systems (DLAs), evolving to close to solar metallicity by z~1. From new
high-resolution spectra of 17 sub-DLAs we have increased the number of
measurements of [Fe/H] at z<1.7 by 25% and compiled the most complete
literature sample of sub-DLA and DLA abundances to date. We find that sub-DLAs
are indeed significantly more metal-rich than DLAs, but only at z<1.7; the
metallicity distributions of sub-DLAs and DLAs at z>1.7 are statistically
consistent. We also present the first evidence that sub-DLAs follow a velocity
width-metallicity correlation over the same velocity range as DLAs, but the
relation is offset to higher metallicities than the DLA relation. On the basis
of these results, we revisit the previous explanation that the systematically
higher metallicities observed in sub-DLAs are indicative of higher host galaxy
masses. We discuss the various problems that this interpretation encounters and
conclude that in general sub-DLAs are not uniquely synonymous with massive
galaxies. We rule out physically related sources of bias (dust, environment,
ionization effects) and examine systematics associated with the selection and
analysis of low-redshift sub-DLAs. We propose that the high metallicities of
sub-DLAs at z<1.7 that drives an apparently steep evolution may be due to the
selection of most low-redshift sub-DLAs based on their high MgII equivalent
widths.
|
0904.2531v1
|
2009-05-27
|
A MIKE + UVES survey of Sub-Damped Lyman-Alpha Systems at z<1.5
|
We have combined the results from our recent observations of Damped and
sub-Damped Lyman-alpha systems with the MIKE and UVES spectrographs on the
Magellan Clay and VLT Kueyen telescopes with ones from the literature to
determine the N(HI)-weighted mean metallicity of these systems based both on
Fe, a depleted element in QSO absorbers and the local ISM, and Zn a relatively
undepleted element. In each case, the N(HI)-weighted mean metallicity is higher
and shows faster evolution in sub-DLAs than the classical DLA systems. Large
grids of photoionisation models over the sub-DLA \nhI range with CLOUDY show
that the ionisation corrections to the abundances are in general small, however
the fraction of ionized H can be up to ~90 per cent. The individual spectra
have been shifted to the rest frame of the absorber and averaged together to
determine the average properties of these systems at z<1.5. We find that the
average abundance pattern of the Sub-DLA systems is similar to the gas in the
halo of the Milky Way, with an offset of ~0.3 dex in the overall metallicity.
Both DLAs and Sub-DLAs show similar characteristics in their relative
abundances patterns, although the DLAs have smaller <[Mn/Zn]> as well as higher
<[Ti/Zn]> and <[Cr/Zn]>. We calculate the contribution of sub-DLAs to the metal
budget of the Universe, and find that the sub-DLA systems at z<1.5 contain a
comoving density of metals Omega_met (3.5-15.8)x10^{5} M_sun Mpc^{-3}, at least
twice the comoving density of metals in the DLA systems. The sub-DLAs do
however track global chemical evolution models much more closely than do the
DLAs, perhaps indicating that they are a less dust biased metallicity indicator
of galaxies at high redshifts than the DLA systems.
|
0905.4473v2
|
2009-11-18
|
Slow Diffusive Gravitational Instability Before Decoupling
|
Radiative diffusion damps acoustic modes at large comoving wavenumber (k)
before decoupling (``Silk damping''). In a simple WKB analysis, neglecting
moments of the temperature distribution beyond the quadrupole, damping appears
in the acoustic mode as a term of order ik^2/(taudot) where taudot is the
scattering rate per unit conformal time. Although the Jeans instability is
stabilized on scales smaller than the adiabatic Jeans length, I show that the
medium is linearly unstable to first order in (1/taudot) to a slow diffusive
mode. At large comoving wavenumber, the characteristic growth rate becomes
independent of spatial scale and constant: (t_{KH}a)^-1 ~ (128 pi G/9 kappa_T
c)(rho_m/rho_b), where "a" is the scale factor, rho_m and rho_b are the matter
and baryon energy density, respectively, and kappa_T is the Thomson opacity.
This is the characteristic timescale for a fluid parcel to radiate away its
thermal energy content at the Eddington limit, analogous to the Kelvin-Helmholz
(KH) time for a massive star or the Salpeter time for black hole growth.
Although this mode grows at all times prior to decoupling and on scales smaller
than the horizon, the growth time is long, about 100 times the age of the
universe at decoupling. Thus, it modifies the density and temperature
perturbations on small scales only at the percent level. The physics of this
mode is already accounted for in the popular codes CMBFAST and CAMB, but is
typically neglected in analytic studies of the growth of primordial
perturbations. This work clarifies the physics of this instability in the epoch
before decoupling, and emphasizes that the universe is formally unstable on
scales below the horizon, even in the limit of large taudot. Analogous
instabilities at yet earlier epochs are also mentioned. (Abridged)
|
0911.3665v1
|
2009-12-14
|
Using 21cm Absorption in Small Impact Parameter Galaxy-QSO Pairs to Probe Low-Redshift Damped and Sub-Damped Lyman-alpha System
|
To search for low-redshift damped Lyman-alpha (DLA) and sub-DLA quasar
absorbers, we have conducted a 21cm absorption survey of radio-loud quasars at
small impact parameters to foreground galaxies selected from the Sloan Digital
Sky Survey (SDSS). Here we present the first results from this survey based on
observations of SDSS J104257.58+074850.5 ($z_{QSO}$ = 2.66521), a quasar at an
angular separation from a foreground galaxy ($z_{gal}$ = 0.03321) of 2.5" (1.7
kpc in projection). The foreground galaxy is a low-luminosity spiral with
on-going star formation (0.004 M$_{\odot}$ yr$^{-1}$ kpc$^{-2}$) and a
metallicity of $-0.27 \pm 0.05$ dex. We detect 21cm absorption from the galaxy
with the Green Bank Telescope (GBT), the Very Large Array (VLA), and the Very
Long Baseline Array (VLBA). The absorption appears to be quiescent disk gas
corotating with the galaxy and we do not find any evidence for outflowing cold
neutral gas. The width of the main absorption line indicates that the gas is
cold, $T_{k} < 283$ K, and the HI column is surprisingly low given the impact
parameter of 1.7 kpc; we find that N(HI) $\leq 9.6 \times 10^{19}$ cm$^{-2}$
(GBT) and N(HI) $\leq 1.5 \times 10^{20}$ cm$^{-2}$ (VLBA). VLBA marginally
resolves the continuum source and the absorber, and a lower limit of 27.1
$\times$ 13.9 pc is derived for the size of the absorbing cloud. In turn, this
indicates a low density for a cold cloud, n(HI) $<$ 3.5 cm$^{-3}$. We
hypothesize that this galaxy, which is relatively isolated, is becoming
depleted in HI because it is converting its interstellar matter into stars
without a replenishing source of gas, and we suggest future observations to
probe this and similar galaxies.
|
0912.2575v2
|
2010-04-02
|
Modeling the Time Variability of SDSS Stripe 82 Quasars as a Damped Random Walk
|
We model the time variability of ~9,000 spectroscopically confirmed quasars
in SDSS Stripe 82 as a damped random walk. Using 2.7 million photometric
measurements collected over 10 years, we confirm the results of Kelly et al.
(2009) and Koz{\l}owski et al. (2010) that this model can explain quasar light
curves at an impressive fidelity level (0.01-0.02 mag). The damped random walk
model provides a simple, fast [O(N) for N data points], and powerful
statistical description of quasar light curves by a characteristic time scale
(tau) and an asymptotic rms variability on long time scales (SF_inf). We
searched for correlations between these two variability parameters and physical
parameters such as luminosity and black hole mass, and rest-frame wavelength.
We find that tau increases with increasing wavelength with a power law index of
0.17, remains nearly constant with redshift and luminosity, and increases with
increasing black hole mass with power law index of 0.21+/-0.07. The amplitude
of variability is anti-correlated with the Eddington ratio, which suggests a
scenario where optical fluctuations are tied to variations in the accretion
rate. The radio-loudest quasars have systematically larger variability
amplitudes by about 30%, when corrected for the other observed trends, while
the distribution of their characteristic time scale is indistinguishable from
that of the full sample. We do not detect any statistically robust differences
in the characteristic time scale and variability amplitude between the full
sample and the small subsample of quasars detected by ROSAT. Our results
provide a simple quantitative framework for generating mock quasar light
curves, such as currently used in LSST image simulations. (abridged)
|
1004.0276v2
|
2010-04-21
|
Kadanoff-Baym description of Hubbard clusters out of equilibrium: performance of many-body schemes, correlation-induced damping and multiple steady states
|
We present in detail a method we recently introduced (PRL. 103, 176404
(2009)) to describe finite systems in and out of equilibrium, where the
evolution in time is performed via the Kadanoff-Baym Equations (KBE) within
Many-Body Perturbation Theory (MBPT). The main property we analyze is the
time-dependent density. We also study is the exchange-correlation potential of
TDDFT, obtained via reverse engineering from the time-dependent density. Our
systems consist of small, strongly correlated clusters, described by a Hubbard
Hamiltonian within the Hartree-Fock, second Born, GW and T-matrix
approximations. We compare the results from the KBE dynamics to those from
exact numerical solutions. The outcome of our comparisons is that, among the
many-body schemes considered, the T-matrix approximation is overall superior at
all electron densities. Such comparisons permit a general assessment of the
whole idea of applying MBPT, in the KBE sense, to finite systems. A striking
outcome of our analysis is that when the system evolves under a strong external
field, the KBE develop a steady-state solution as a consequence of a
correlation-induced damping. This damping is present both in isolated (finite)
systems, where it is purely artificial, as well as in clusters contacted to
(infinite) macroscopic leads. To illustrate this point we present selected
results for a system coupled to contacts within the T-matrix and second Born
approximation. The extensive characterization we performed indicates that this
behavior is present whenever approximate self energies, based upon infinite
partial summations, are used. A second important result is that, for isolated
clusters, the steady state reached is not unique but depends on how one
switches on the external field. This may also true for clusters connected to
leads.
|
1004.3662v1
|
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