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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
|
2023-10-20
|
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
|
2023-10-22
|
The residual flow in well-optimized stellarators
|
The gyrokinetic theory of the residual flow, in the electrostatic limit, is
revisited, with optimized stellarators in mind. We consider general initial
conditions for the problem, and identify cases that lead to a non-zonal
residual electrostatic potential, i.e. one having a significant component that
varies within a flux surface. We investigate the behavior of the ``intermediate
residual'' in stellarators, a measure of the flow that remains after geodesic
acoustic modes have damped away, but before the action of the slower damping
that is caused by unconfined particle orbits. The case of a quasi-isodynamic
stellarator is identified as having a particularly large such residual, owing
to the small orbit width achieved by optimization.
|
2310.14218v2
|
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
|
2023-12-16
|
Spin-torque nano-oscillator based on two in-plane magnetized synthetic ferrimagnets
|
We report the dynamic characterization of the spin-torque-driven in-plane
precession modes of a spin-torque nano-oscillator based on two different
synthetic ferrimagnets: a pinned one characterized by a strong RKKY interaction
which is exchange coupled to an antiferromagnetic layer; and a second one,
non-pinned characterized by weak RKKY coupling. The microwave properties
associated with the steady-state precession of both SyFs are characterized by
high spectral purity and power spectral density. However, frequency dispersion
diagrams of the damped and spin transfer torque modes reveal drastically
different dynamical behavior and microwave emission properties in both SyFs. In
particular, the weak coupling between the magnetic layers of the non-pinned SyF
raises discontinuous dispersion diagrams suggesting a strong influence of mode
crossing. An interpretation of the different dynamical features observed in the
damped and spin torque modes of both SyF systems was obtained by solving
simultaneously, in a macrospin approach, a linearized version of the
Landau-Lifshitz-Gilbert equation including the spin transfer torque term.
|
2312.10451v2
|
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.
|
2401.06565v2
|
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.
|
2401.12595v2
|
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
|
2024-03-02
|
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
|
2024-04-09
|
Calculation of toroidal Alfvén eigenmode mode structure in general axisymmetric toroidal geometry
|
A workflow is developed based on the ideal MHD model to investigate the
linear physics of various Alfv\'en eigenmodes in general axisymmetric toroidal
geometry, by solving the coupled shear Alfv\'en wave (SAW) and ion sound wave
(ISW) equations in ballooning space. The model equations are solved by the
FALCON code in the singular layer, and the corresponding solutions are then
taken as the boundary conditions for calculating parallel mode structures in
the whole ballooning space. As an application of the code, the frequencies and
mode structures of toroidal Alfv\'en eigenmode (TAE) are calculated in the
reference equilibria of the Divertor Tokamak Test facility (DTT) with positive
and negative triangularities, respectively. By properly handling the boundary
conditions, we demonstrate finite TAE damping due to coupling with the local
acoustic continuum, and find that the damping rate is small for typical plasma
parameters.
|
2404.06296v1
|
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
|
2019-03-04
|
Constant angle surfaces in 4-dimensional Minkowski space
|
We first define a complex angle between two oriented spacelike planes in
4-dimensional Minkowski space, and then study the constant angle surfaces in
that space, i.e. the oriented spacelike surfaces whose tangent planes form a
constant complex angle with respect to a fixed spacelike plane. This notion is
the natural Lorentzian analogue of the notion of constant angle surfaces in
4-dimensional Euclidean space. We prove that these surfaces have vanishing
Gauss and normal curvatures, obtain representation formulas for the constant
angle surfaces with regular Gauss maps and construct constant angle surfaces
using PDE's methods. We then describe their invariants of second order and show
that a surface with regular Gauss map and constant angle $\psi\neq 0\ [\pi/2]$
is never complete. We finally study the special cases of surfaces with constant
angle $\pi/2\ [\pi],$ with real or pure imaginary constant angle and describe
the constant angle surfaces in hyperspheres and lightcones.
|
1903.01554v1
|
2020-05-17
|
Universal constants and natural systems of units in a spacetime of arbitrary dimension
|
We study the properties of fundamental physical constants using the threefold
classification of dimensional constants proposed by J.-M. L{\'e}vy-Leblond:
constants of objects (masses, etc.), constants of phenomena (coupling
constants), and "universal constants" (such as $c$ and $\hbar$). We show that
all of the known "natural" systems of units contain at least one non-universal
constant. We discuss the possible consequences of such non-universality, e.g.,
the dependence of some of these systems on the number of spatial dimensions. In
the search for a "fully universal" system of units, we propose a set of
constants that consists of $c$, $\hbar$, and a length parameter and discuss its
origins and the connection to the possible kinematic groups discovered by
L{\'e}vy-Leblond and Bacry. Finally, we give some comments about the
interpretation of these constants.
|
2005.08196v3
|
2020-11-13
|
Losing the trace to find dynamical Newton or Planck constants
|
We show that promoting the trace part of the Einstein equations to a trivial
identity results in the Newton constant being an integration constant. Thus, in
this formulation the Newton constant is a global dynamical degree of freedom
which is also a subject to quantization and quantum fluctuations. This is
similar to what happens to the cosmological constant in the unimodular gravity
where the trace part of the Einstein equations is lost in a different way. We
introduce a constrained variational formulation of these modified Einstein
equations. Then, drawing on analogies with the Henneaux-Teitelboim action for
unimodular gravity, we construct different general-covariant actions resulting
in these dynamics. The inverse of dynamical Newton constant is canonically
conjugated to the Ricci scalar integrated over spacetime. Surprisingly, instead
of the dynamical Newton constant one can formulate an equivalent theory with a
dynamical Planck constant. Finally, we show that an axion-like field can play a
role of the gravitational Newton constant or even of the quantum Planck
constant.
|
2011.07055v2
|
2008-11-24
|
Artificial contradiction between cosmology and particle physics: the lambda problem
|
It is shown that the usual choice of units obtained by taking G = c = Planck
constant = 1, giving the Planck units of mass, length and time, introduces an
artificial contradiction between cosmology and particle physics: the lambda
problem that we associate with Planck constant. We note that the choice of
Planck constant = 1 does not correspond to the scale of quantum physics. For
this scale we prove that the correct value is Planck constant \hbar; 1/10^122,
while the choice of Planck constant = 1 corresponds to the cosmological scale.
This is due to the scale factor of 10^61 that converts the Planck scale to the
cosmological scale. By choosing the ratio G/c^3 = constant = 1, which includes
the choice G = c = 1, and the momentum conservation mc = constant, we preserve
the derivation of the Einstein field equations from the action principle. Then
the product Gm/c^2 = rg, the gravitational radius of m, is constant. For a
quantum black hole we prove that Planck constant \hbar; rg^2 \hbar; (mc)^2. We
also prove that the product lambda x Planck constant is a general constant of
order one, for any scale. The cosmological scale implies lambda \hbar; Planck
constant \hbar; 1, while the Planck scale gives lambda \hbar; 1/Planck constant
\hbar; 10^122. This explains the lambda problem. We get two scales: the
cosmological quantum black hole (QBH), size \Lambda; 10^28 cm, and the quantum
black hole (qbh) that includes the fundamental particles scale, size \Lambda;
10^-13 cm, as well as the Planck scale, size \Lambda; 10^-33 cm.
|
0811.3933v2
|
2003-02-07
|
Lattice constant in diluted magnetic semiconductors (Ga,Mn)As
|
We use the density-functional calculations to investigate the compositional
dependence of the lattice constant of (Ga,Mn)As containing various native
defects. The lattice constant of perfect mixed crystals does not depend much on
the concentration of Mn. The lattice parameter increases if some Mn atoms
occupy interstitial positions. The same happens if As antisite defects are
present. A quantitative agreement with the observed compositional dependence is
obtained for materials close to a complete compensation due to these two
donors. The increase of the lattice constant of (Ga,Mn)As is correlated with
the degree of compensation: the materials with low compensation should have
lattice constants close to the lattice constant of GaAs crystal.
|
0302150v1
|
2002-12-04
|
Implications of a Time-Varying Fine Structure Constant
|
Much work has been done after the possibility of a fine structure constant
being time-varying. It has been taken as an indication of a time-varying speed
of light. Here we prove that this is not the case. We prove that the speed of
light may or may not vary with time, independently of the fine structure
constant being constant or not. Time variations of the speed of light, if
present, have to be derived by some other means and not from the fine structure
constant. No implications based on the possible variations of the fine
structure constant can be imposed on the speed of light.
|
0212020v1
|
2005-12-20
|
Local Experiments See Cosmologically Varying Constants
|
We describe a rigorous construction, using matched asymptotic expansions,
which establishes under very general conditions that local terrestrial and
solar-system experiments will measure the effects of varying `constants' of
Nature occurring on cosmological scales to computable precision. In particular,
`constants' driven by scalar fields will still be found to evolve in time when
observed within virialised structures like clusters, galaxies, and planetary
systems. This provides a justification for combining cosmological and
terrestrial constraints on the possible time variation of many assumed
`constants' of Nature, including the fine structure constant and Newton's
gravitation constant.
|
0512117v2
|
1992-12-22
|
The Third Electromagnetic Constant of an Isotropic Medium:
|
In addition to the dielectric and magnetic permeability constants, another
constant is generally needed to describe the electrodynamic properties of a
linear isotropic medium. We discuss why the need for the third constant arises
and what sort of physical situations can give rise to a non-zero value for it.
This additional constant, which we call the {\em ``Activity Constant''} and
denote by $\zeta$, can explain optical activity and other phenomena from a
purely macroscopic and phenomenological point of view.
|
9212300v2
|
2001-09-15
|
Two-dimensional Finsler metrics of constant curvature
|
A Riemannian metric is of constant curvature if and only if it is locally
projectively flat. There are infinitely many locally projectively flat Finsler
metrics of constant curvature, that are special solutions to the Hilbert's
Fourth Problem.
In this paper, we use the technique in the paper titled "Finsler metrics with
K=0 and S=0" (math.DG/0109060) to construct infinitely many Finsler metrics on
the 2-sphere with constant curvature K=1 and infinitely many Finsler metrics on
the 2-disk with constant curvature K = -1. These metrics are not projectively
flat. So far, the classification of Finsler metrics of constant curvature has
not been completely done yet. These examples are important to the
classification problem.
|
0109097v1
|
2002-09-04
|
Experimental Consequences of Time Variations of the Fundamental Constants
|
We discuss the experimental consequences of hypothetical time variations of
the fundamental constants. We emphasize that from a purely phenomenological
point of view, only dimensionless fundamental constants have significance. Two
classes of experiments are identified that give results that are essentially
independent of the values of all constants. Finally, we show that experiments
that are generally interpreted in terms of time variations of the dimensioned
gravitional constant $G$ are better interpreted as giving limits on the
variation of the dimensionless constant $\alpha_G=Gm_p^2/\hbar c$.
|
0209016v1
|
2008-10-13
|
A note on Artin's constant
|
We suggest a new approach to Artin's constant that leads to its
representation as an infinite sum divided by another infinite sum. The same
approach works well for Stephens' constant and higher rank Artin's constants.
The main results are theoretical but there are interesting experimental and
computational aspects.
|
0810.2325v4
|
2009-03-27
|
Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
|
The influence of an underlying current on 3-wave interactions of capillary
water waves is studied. The fact that in irrotational flow resonant 3-wave
interactions are not possible can be invalidated by the presence of an
underlying current of constant non-zero vorticity. We show that: 1) wave trains
in flows with constant non-zero vorticity are possible only for two-dimensional
flows; 2) only positive constant vorticities can trigger the appearance of
three-wave resonances; 3) the number of positive constant vorticities which do
trigger a resonance is countable; 4) the magnitude of a positive constant
vorticity triggering a resonance can not be too small.
|
0903.4813v1
|
2010-04-09
|
A New Construction for Constant Weight Codes
|
A new construction for constant weight codes is presented. The codes are
constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These
subspaces form a constant dimension code in the Grassmannian space
$\cG_q(n,k)$. Some of the constructed codes are optimal constant weight codes
with parameters not known before. An efficient algorithm for error-correction
is given for the constructed codes. If the constant dimension code has an
efficient encoding and decoding algorithms then also the constructed constant
weight code has an efficient encoding and decoding algorithms.
|
1004.1503v3
|
2011-07-01
|
Mimicking the cosmological constant: constant curvature spherical solutions in a non-minimally coupled model
|
The purpose of this study is to describe a perfect fluid matter distribution
that leads to a constant curvature region, thanks to the effect of a
non-minimal coupling. This distribution exhibits a density profile within the
range found in the interstellar medium and an adequate matching of the metric
components at its boundary. By identifying this constant curvature with the
value of the cosmological constant, and superimposing the spherical
distributions arising from different matter sources throughout the universe,
one is able to mimic a large-scale homogeneous cosmological constant solution.
|
1107.0225v1
|
2013-11-09
|
On Maxwell's and Poincare's Constants
|
We prove that for bounded and convex domains in three dimensions, the Maxwell
constants are bounded from below and above by Friedrichs' and Poincar\'e's
constants. In other words, the second Maxwell eigenvalues lie between the
square roots of the second Neumann-Laplace and the first Dirichlet-Laplace
eigenvalue.
|
1311.2186v4
|
2015-01-08
|
On the optimal constants in Korn's and geometric rigidity estimates, in bounded and unbounded domains, under Neumann boundary conditions
|
We are concerned with the optimal constants: in the Korn inequality under
tangential boundary conditions on bounded sets $\Omega \subset \mathbb{R}^n$,
and in the geometric rigidity estimate on the whole $\mathbb{R}^2$. We prove
that the latter constant equals $\sqrt{2}$, and we discuss the relation of the
former constants with the optimal Korn's constants under Dirichlet boundary
conditions, and in the whole $\mathbb{R}^n$, which are well known to equal
$\sqrt{2}$. We also discuss the attainability of these constants and the
structure of deformations/displacement fields in the optimal sets.
|
1501.01917v1
|
2016-05-16
|
A Constant-Factor Bi-Criteria Approximation Guarantee for $k$-means++
|
This paper studies the $k$-means++ algorithm for clustering as well as the
class of $D^\ell$ sampling algorithms to which $k$-means++ belongs. It is shown
that for any constant factor $\beta > 1$, selecting $\beta k$ cluster centers
by $D^\ell$ sampling yields a constant-factor approximation to the optimal
clustering with $k$ centers, in expectation and without conditions on the
dataset. This result extends the previously known $O(\log k)$ guarantee for the
case $\beta = 1$ to the constant-factor bi-criteria regime. It also improves
upon an existing constant-factor bi-criteria result that holds only with
constant probability.
|
1605.04986v1
|
2016-11-01
|
Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds
|
We study the problem of deforming a Riemannian metric to a conformal one with
nonzero constant scalar curvature and nonzero constant boundary mean curvature
on a compact manifold of dimension $n\geq 3$. We prove the existence of such
conformal metrics in the cases of $n=6,7$ or the manifold is spin and some
other remaining ones left by Escobar. Furthermore, in the positive Yamabe
constant case, by normalizing the scalar curvature to be $1$, there exists a
sequence of conformal metrics such that their constant boundary mean curvatures
go to $+\infty$.
|
1611.00229v2
|
2019-05-31
|
Hyperbolicity constants for pants and relative pants graphs
|
The pants graph has proved to be influential in understanding 3-manifolds
concretely. This stems from a quasi-isometry between the pants graph and the
Teichm\"uller space with the Weil-Petersson metric. Currently, all estimates on
the quasi-isometry constants are dependent on the surface in an undiscovered
way. This paper starts effectivising some constants which begins the
understanding how relevant constants change based on the surface. We do this by
studying the hyperbolicity constant of the pants graph for the five-punctured
sphere and the twice punctured torus. The hyperbolicity constant of the
relative pants graph for complexity 3 surfaces is also calculated. Note, for
higher complexity surfaces, the pants graph is not hyperbolic or even strongly
relatively hyperbolic.
|
1905.13595v1
|
2019-11-28
|
Constant mean curvature Isometric Immersions into $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2 \times \mathbb{R}$ and related results
|
In this article, we study constant mean curvature isometric immersions into
$\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2 \times \mathbb{R}$ and we
classify these isometric immersions when the surface has constant intrinsic
curvature. As applications, we use the sister surface correspondence to
classify the constant mean curvature surfaces with constant intrinsic curvature
in the $3-$dimensional homogenous manifolds $\mathbb{E}(\kappa, \tau)$ and we
use the Torralbo-Urbano correspondence to classify the parallel mean curvature
surfaces in $\mathbb{S}^2 \times \mathbb{S}^2$ and $\mathbb{H}^2 \times
\mathbb{H}^2$ with constant intrinsic curvature. It is worthwhile to point out
that these classifications provide new examples.
|
1911.12630v1
|
2020-12-21
|
A Couple of Transcendental Prime-Representing Constants
|
It is well known that the arithmetic nature of Mills' prime-representing
constant is uncertain: we do not know if Mills' constant is a rational or
irrational number. In the case of other prime-representing constants,
irrationality can be proved, but it is not known whether these constants are
algebraic or transcendental numbers. By using Liouville or Roth's theorems
about approximation by rationals, we find a couple of prime-representing
constants that can be proved to be transcendental numbers.
|
2012.11750v2
|
2021-03-17
|
Complex nilmanifolds with constant holomorphic sectional curvature
|
A well known conjecture in complex geometry states that a compact Hermitian
manifold with constant holomorphic sectional curvature must be K\"ahler if the
constant is non-zero and must be Chern flat if the constant is zero. The
conjecture is confirmed in complex dimension $2$, by the work of
Balas-Gauduchon in 1985 (when the constant is zero or negative) and by
Apostolov-Davidov-Muskarov in 1996 (when the constant is positive). For higher
dimensions, the conjecture is still largely unknown. In this article, we
restrict ourselves to the class of complex nilmanifolds and confirm the
conjecture in that case.
|
2103.09571v1
|
2021-03-25
|
Universal Constants as Manifestations of Relativity
|
We study the possible interpretation of the "universal constants" by the
classification of J.~M.~L\'evy-Leblond. $\hbar$ and $c$ are the most common
example of constants of this type. Using Fock's principle of the relativity
w.r.t. observation means, we show that both $c$ and $\hbar$ can be viewed as
manifestations of certain relativity. We also show that there is a possibility
to interpret the Boltzmann's constant in a similar way, and make some comments
about the relativistic interpretation of the constant spacetime curvature and
gravitational constant $G$.
|
2103.13854v2
|
2022-03-30
|
Convex bodies of constant width in spaces of constant curvature and the extremal area of Reuleaux triangles
|
Extending Blaschke and Lebesgue's classical result in the Euclidean plane, it
has been recently proved in spherical and the hyperbolic cases, as well, that
Reuleaux triangles have the minimal area among convex domains of constant width
$D$. We prove an essentially optimal stability version of this statement in
each of the three types of surfaces of constant curvature. In addition, we
summarize the fundamental properties of convex bodies of constant width in
spaces of constant curvature, and provide a characterization in the hyperbolic
case in terms of horospheres.
|
2203.16636v1
|
2022-05-23
|
On Computing Coercivity Constants in Linear Variational Problems Through Eigenvalue Analysis
|
In this work, we investigate the convergence of numerical approximations to
coercivity constants of variational problems. These constants are essential
components of rigorous error bounds for reduced-order modeling; extension of
these bounds to the error with respect to exact solutions requires an
understanding of convergence rates for discrete coercivity constants. The
results are obtained by characterizing the coercivity constant as a spectral
value of a self-adjoint linear operator; for several differential equations, we
show that the coercivity constant is related to the eigenvalue of a compact
operator. For these applications, convergence rates are derived and verified
with numerical examples.
|
2205.11580v1
|
2022-08-07
|
Spacelike Curves of Constant-Ratio in Pseudo-Galilean Space
|
In the theory of differential geometry curves, a curve is said to be of
constant-ratio if the ratio of the length of the tangential and normal
components of its position vector function is constant. In this paper, we study
and characterize a spacelike admissible curve of constant-ratio in terms of its
curvature functions in pseudo-Galilean space. Some special curves of
constant-ratio such as T and N constant types are investigated. As an
application of our main results, some examples are given.
|
2208.03686v1
|
2022-08-24
|
New Geometric Constant Related to the P-angle Function in Banach Spaces
|
In this paper, combined with the P-angle function of Banach spaces and the
geometric constants that can characterize Hilbert spaces, the new angular
geometric constant is defined. Firstly, this paper explores the basic
properties of the new constant and obtains some inequalities with significant
geometric constants. Then according to the derived inequalities, this paper
studies the relationship between the new constant and the geometric properties
of Banach spaces. Furthermore, the necessary and sufficient condition for
uniform non-squareness, and the sufficient conditions for uniform convexity,
the normal structure and the fixed point property will be established.
|
2208.11239v1
|
2022-09-22
|
Kemeny's constant and Wiener index on trees
|
On trees of fixed order, we show a direct relation between Kemeny's constant
and Wiener index, and provide a new formula of Kemeny's constant from the
relation with a combinatorial interpretation. Moreover, the relation simplifies
proofs of several known results for extremal trees in terms of Kemeny's
constant for random walks on trees. Finally, we provide various families of
co-Kemeny's mates, which are two non-isomorphic connected graphs with the same
Kemeny's constant, and we also give a necessary condition for a tree to attain
maximum Kemeny's constant for trees with fixed diameter.
|
2209.11271v1
|
2023-12-18
|
Asymptotic products of binomial and multinomial coefficients revisited
|
In this note, we consider asymptotic products of binomial and multinomial
coefficients and determine their asymptotic constants and formulas. Among them,
special cases are the central binomial coefficients, the related Catalan
numbers, and binomial coefficients in a row of Pascal's triangle. For the
latter case, we show that it can also be derived from a limiting case of
products of binomial coefficients over the rows. The asymptotic constants are
expressed by known constants, for example, the Glaisher--Kinkelin constant. In
addition, the constants lie in certain intervals that we determine precisely.
Subsequently, we revisit a related result of Hirschhorn and clarify the given
numerical constant by showing the exact expression.
|
2312.11369v1
|
2023-12-23
|
The Table of the Structure Constants for the Complex Simple Lie Algebra of Type G_2 and Chevalley Commutator Formulas in the Chevalley Group of Type G_2 over a Field
|
This article is the second in the series and is devoted to the type G_2. The
work consists of two parts. In the first part we calculate the structure
constants of the complex simple Lie algebra of type G_2. All structure
constants are represented as functions of the structure constants corresponding
to extraspecial pairs. The results obtained are used to calculate the
commutator Chevalley formulas for [x_r(u),x_s(y)], when the sum r+s is a root.
Further, in the second part there is a table of structure constants and
Chevalley commutator formulas in the special case, when all structure constants
corresponding to extraspecial pairs are positive.
|
2312.15226v1
|
2003-10-21
|
Cosmological model with $Ω_M$-dependent cosmological constant
|
The idea here is to set the cosmical constant $\lambda$ proportional to the
scalar of the stress-energy tensor of the ordinary matter. We investigate the
evolution of the scale factor in a cosmological model in which the cosmological
constant is proportional to the scalar of the stress-energy tensor.
|
0310609v1
|
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