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2020-05-11
|
Manipulating 1-dimensinal skyrmion motion by external magnetic field gradient
|
We have investigated an analytic formula of the 1-dimensional magnetic
skyrmion dynamics under external magnetic field gradient. We find excellent
agreement between the analytical model and micromagnetic simulation results for
various magnetic parameters such as the magnetic field gradient, Gilbert
damping constant. We also observe much faster velocity of the chiral domain
wall (DW) motion. The chiral DW is exist with smaller interfacial
Dzyaloshinskii-Moriya interaction energy density cases. These results provide
to develop efficient control of skyrmion for spintronic devices.
|
2005.05011v1
|
2020-06-28
|
Physical pendulum model: Fractional differential equation and memory effects
|
A detailed analysis of three pendular motion models is presented. Inertial
effects, self-oscillation, and memory, together with non-constant moment of
inertia, hysteresis and negative damping are shown to be required for the
comprehensive description of the free pendulum oscillatory regime. The effects
of very high initial amplitudes, friction in the roller bearing axle, drag, and
pendulum geometry are also analysed and discussed. The model that consists of a
fractional differential equation provides both the best explanation of, and the
best fits to, experimental high resolution and long-time data gathered from
standard action-camera videos.
|
2006.15665v3
|
2020-08-01
|
Equilibration of the chiral asymmetry due to finite electron mass in electron-positron plasma
|
We calculate the rate of collisional decay of the axial charge in an
ultrarelativistic electron-positron plasma, also known as the chirality
flipping rate. We find that contrary to the existing estimates, the chirality
flipping rate appears already in the first order in the fine-structure constant
$\alpha$ and is therefore orders of magnitude greater than previously believed.
The main channels for the rapid relaxation of the axial charge are the
collinear emission of a weakly damped photon and the Compton scattering. The
latter contributes to the $\mathcal{O}(\alpha)$ result because of the infrared
divergence in its cross section, which is regularized on the soft scale $\sim
eT$ due to the thermal corrections. Our results are important for the
description of the early Universe processes (such as leptogenesis or
magnetogenesis) that affect differently left- and right-chiral fermions of the
Standard Model, as discussed in more details in the companion Letter.
|
2008.00360v2
|
2020-08-12
|
Effective Field Theory for Quasicrystals and Phasons Dynamics
|
We build an effective field theory (EFT) for quasicrystals -- aperiodic
incommensurate lattice structures -- at finite temperature, entirely based on
symmetry arguments and a well-define action principle. By means of
Schwinger-Keldysh techniques, we derive the full dissipative dynamics of the
system and we recover the experimentally observed diffusion-to-propagation
crossover of the phason mode. From a symmetry point of view, the diffusive
nature of the phason at long wavelengths is due to the fact that the internal
translations, or phason shifts, are symmetries of the system with no associated
Noether currents. The latter feature is compatible with the EFT description
only because of the presence of dissipation (finite temperature) and the lack
of periodic order. Finally, we comment on the similarities with certain
homogeneous holographic models and we formally derive the universal relation
between the pinning frequency of the phonons and the damping and diffusion
constant of the phason.
|
2008.05339v2
|
2020-08-18
|
Research on rolling friction's dependence on ball bearings' radius
|
There are two alternative historical laws of rolling resistance formulated by
French scientist Coulomb and Dupuit. It has been decided to verify
experimentally again, which of these laws describes freely rolling ball
bearings on a hard surface better. An inducement to carrying out the
measurements was the idea of the constant thickness of roadbed, which is
consistent with Dupuit's theory. Measurements have been done using the damped
oscillations in the pendulum bearings. Results have shown better consistency
with the Coulomb's theory with small, but measurable deviations. These
deviations were successfully explained by the so called "Cobblestones model".
Parameters designated by this model have been successfully verified by the
surface roughness's profile measurement. An additional theoretical aspect of
this work is distinguishing two types of rolling friction force: dynamical and
kinematical in an analogy to two types of specific heat capacity in the
thermodynamics of gases.
|
2008.08127v1
|
2020-08-28
|
Finding Small and Large k-Clique Instances on a Quantum Computer
|
Algorithms for triangle-finding, the smallest nontrivial instance of the
k-clique problem, have been proposed for quantum computers. Still, those
algorithms assume the use of fixed access time quantum RAM (QRAM). We present a
practical gate-based approach to both the triangle-finding problem and its
NP-hard k-clique generalization. We examine both constant factors for near-term
implementation on a Noisy Intermediate Scale Quantum computer (NISQ) device,
and the scaling of the problem to evaluate long-term use of quantum computers.
We compare the time complexity and circuit practicality of the theoretical
approach and actual implementation. We propose and apply two different
strategies to the k-clique problem, examining the circuit size of Qiskit
implementations. We analyze our implementations by simulating triangle finding
with various error models, observing the effect on damping the amplitude of the
correct answer, and compare to execution on six real IBMQ machines. Finally, we
estimate the date when the methods proposed can run effectively on an actual
device based on IBM's quantum volume exponential growth forecast and the
results of our error analysis.
|
2008.12525v1
|
2020-09-02
|
Frustrated bearings
|
In a bearing state, touching spheres (disks in two dimensions) roll on each
other without slip. Here we frustrate a system of touching spheres by imposing
two different bearing states on opposite sides and search for the
configurations of lowest energy dissipation. If the dissipation between
contacts of spheres is viscous (with random damping constants), the angular
momentum continuously changes from one bearing state to the other. For Coulomb
friction (with random friction coefficients) in two dimensions, a sharp line
separates the two bearing states and we show that this line corresponds to the
minimum cut. Astonishingly however, in three dimensions, intermediate bearing
domains, that are not synchronized with either side, are energetically more
favorable than the minimum-cut surface. Instead of a sharp cut, the steady
state displays a fragmented structure. This novel type of state of minimum
dissipation is characterized by a spanning network of slipless contacts that
reaches every sphere. Such a situation becomes possible because in three
dimensions bearing states have four degrees of freedom.
|
2009.01295v1
|
2020-09-04
|
Scalar Perturbations of a Single-Horizon Regular Black Hole
|
We investigate the massless scalar field perturbations, including the
quasinormal mode spectrum and the ringdown waveform, of a regular black hole
spacetime that was derived via the Loop Quantum Gravity inspired polymer
quantization of spherical $4$D black holes. In contrast to most, if not all, of
the other regular black holes considered in the literature, the resulting
nonsingular spacetime has a single bifurcative horizon and hence no mass
inflation. In the interior, the areal radius decreases to a minimum given by
the Polymerization constant, $k$, and then re-expands into a Kantowski-Sachs
universe. We find indications that this black hole model is stable against
small scalar perturbations. We also show that an increase in the magnitude of
$k$ will decrease the height of the QNM potential and gives oscillations with
lower frequency and less damping.
|
2009.02367v2
|
2020-09-22
|
Quasinormal modes of dirty black holes in the two-loop renormalizable effective gravity
|
We consider gravitational quasinormal modes of the static and
spherically-symmetric dirty black holes in the effective theory of gravity
which is renormalizable at the two-loop level. It is demonstrated that using
the WKB-Pad\'e summation proposed in \cite{jaOp} one can achieve sufficient
accuracy to calculate corrections to the complex frequencies of the quasinormal
modes caused by the Goroff-Sagnotti curvature terms. It is shown that the
Goroff-Sagnotti correction (with our choice of the sign of the coupling
constant) increases damping of the fundamental modes (except for the lowest
fundamental mode) and decreases their frequencies. We argue that the methods
adopted in this paper can be used in the analysis of the influence of the
higher-order curvature terms upon the quasinormal modes and in a number of
related problems that require high accuracy.
|
2009.10793v1
|
2020-10-04
|
On the interaction problem between a compressible viscous fluid and a nonlinear thermoelastic plate
|
In this paper we study the interaction problem between a nonlinear
thermoelastic plate and a compressible viscous fluid with the adiabatic
constant $\gamma>12/7$. The existence of a weak solution for this problem is
obtained by constructing a time-continuous operator splitting scheme that
decouples the fluid and the structure. The fluid sub-problem is given on a
fixed reference domain in the arbitrary Lagrangian-Eulerian (ALE) formulation,
and the continuity equation is damped on this domain as well. This allows the
majority of the analysis to be performed on the fixed reference domain, while
the convergence of the approximate pressure is obtained on the physical domain.
|
2010.01639v1
|
2020-10-08
|
On the cost of Bayesian posterior mean strategy for log-concave models
|
In this paper, we investigate the problem of computing Bayesian estimators
using Langevin Monte-Carlo type approximation. The novelty of this paper is to
consider together the statistical and numerical counterparts (in a general
log-concave setting). More precisely, we address the following question: given
$n$ observations in $\mathbb{R}^q$ distributed under an unknown probability
$\mathbb{P}_{\theta^\star}$ with $\theta^\star \in \mathbb{R}^d$ , what is the
optimal numerical strategy and its cost for the approximation of $\theta^\star$
with the Bayesian posterior mean? To answer this question, we establish some
quantitative statistical bounds related to the underlying Poincar\'e constant
of the model and establish new results about the numerical approximation of
Gibbs measures by Cesaro averages of Euler schemes of (over-damped) Langevin
diffusions. These last results include in particular some quantitative controls
in the weakly convex case based on new bounds on the solution of the related
Poisson equation of the diffusion.
|
2010.06420v2
|
2020-10-28
|
Tunable plasmon modes in doped AA-stacked bilayer graphene
|
We study plasmon modes in doped AA-stacked bilayer graphene (BLG) within the
nearest-neighbor tight-binding and the random phase approximation. We obtain
closed analytical expressions for the polarizability function which are used to
obtain the low-energy dispersion relations of and the numerical results for
both acoustic and optical plasmon modes. Our result reveal the potential of
AA-stacked BLG to be used as a tunable plasmonic device. In particular we find
that the long-wavelength acoustic plasmon disperse as
$\omega_{+}\approx\sqrt{max(|\mu|,t_{1})q}$ with a phase space which shrinks
and vanishes as the chemical potential approaches the interlayer hopping
energy, preventing the existence of long-lived acoustic plasmon. Furthermore,
we show that AA-stacked BLG support coherent optical plasmon only when the
condition $(1+\frac{g_{\sigma}g_{v}e^{2}t_{1}d}{\kappa
v_{F}^{2}}\frac{|\mu|}{t_{1}})^{1/2}<\frac{|\mu|}{t_{1}}$ is satisfied,
specially indicating Landau damping of the optical plasmon in undoped AA-staked
BLG even at long-wavelength limit. We also find that the optical plasmon mode
disperses as $\omega_{-}\approx \Delta+Cq^{2}$ with constants that can be tuned
by tuning the chemical potential.
|
2010.14999v3
|
2020-11-04
|
EAdam Optimizer: How $ε$ Impact Adam
|
Many adaptive optimization methods have been proposed and used in deep
learning, in which Adam is regarded as the default algorithm and widely used in
many deep learning frameworks. Recently, many variants of Adam, such as
Adabound, RAdam and Adabelief, have been proposed and show better performance
than Adam. However, these variants mainly focus on changing the stepsize by
making differences on the gradient or the square of it. Motivated by the fact
that suitable damping is important for the success of powerful second-order
optimizers, we discuss the impact of the constant $\epsilon$ for Adam in this
paper. Surprisingly, we can obtain better performance than Adam simply changing
the position of $\epsilon$. Based on this finding, we propose a new variant of
Adam called EAdam, which doesn't need extra hyper-parameters or computational
costs. We also discuss the relationships and differences between our method and
Adam. Finally, we conduct extensive experiments on various popular tasks and
models. Experimental results show that our method can bring significant
improvement compared with Adam. Our code is available at
https://github.com/yuanwei2019/EAdam-optimizer.
|
2011.02150v1
|
2020-11-16
|
Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell
|
We perform Hamiltonian reduction of a model in which 2+1 dimensional gravity
with negative cosmological constant is coupled to a cylindrically symmetric
dust shell. The resulting action contains only a finite number of degrees of
freedom. The phase space consists of two copies of $ADS^2$ -- both coordinate
and momentum space are curved. Different regions in the Penrose diagram can be
identified with different patches of $ADS^2$ momentum space. Quantization in
the momentum representation becomes particularly simple in the vicinity of the
horizon, where one can neglect momentum non-commutativity. In this region, we
calculate the spectrum of the shell radius. This spectrum turns out to be
continuous outside the horizon and becomes discrete inside the horizon with
eigenvalue spacing proportional to the square root of the black hole mass. We
also calculate numerically quantum transition amplitudes between different
regions of the Penrose diagram in the vicinity of the horizon. This calculation
shows a possibility of quantum tunneling of the shell into classically
forbidden regions of the Penrose diagram, although with an exponentially damped
rate away from the horizon.
|
2011.07971v2
|
2020-11-23
|
Energy decay rates of solutions to a viscoelastic wave equation with variable exponents and weak damping
|
The goal of the present paper is to study the asymptotic behavior of
solutions for the viscoelastic wave equation with variable exponents \[
u_{tt}-\Delta u+\int_0^tg(t-s)\Delta u(s)ds+a|u_t|^{m(x)-2}u_t=b|u|^{p(x)-2}u\]
under initial-boundary condition, where the exponents $p(x)$ and $m(x)$ are
given functions, and $a,~b>0$ are constants. More precisely, under the
condition $g'(t)\le -\xi(t)g(t)$, here $\xi(t):\mathbb{R}^+\to\mathbb{R}^+$ is
a non-increasing differential function with
$\xi(0)>0,~\int_0^\infty\xi(s)ds=+\infty$, general decay results are derived.
In addition, when $g$ decays polynomially, the exponential and polynomial decay
rates are obtained as well, respectively. This work generalizes and improves
earlier results in the literature.
|
2011.11185v1
|
2020-11-27
|
Eigenvalue-corrected Natural Gradient Based on a New Approximation
|
Using second-order optimization methods for training deep neural networks
(DNNs) has attracted many researchers. A recently proposed method,
Eigenvalue-corrected Kronecker Factorization (EKFAC) (George et al., 2018),
proposes an interpretation of viewing natural gradient update as a diagonal
method, and corrects the inaccurate re-scaling factor in the Kronecker-factored
eigenbasis. Gao et al. (2020) considers a new approximation to the natural
gradient, which approximates the Fisher information matrix (FIM) to a constant
multiplied by the Kronecker product of two matrices and keeps the trace equal
before and after the approximation. In this work, we combine the ideas of these
two methods and propose Trace-restricted Eigenvalue-corrected Kronecker
Factorization (TEKFAC). The proposed method not only corrects the inexact
re-scaling factor under the Kronecker-factored eigenbasis, but also considers
the new approximation method and the effective damping technique proposed in
Gao et al. (2020). We also discuss the differences and relationships among the
Kronecker-factored approximations. Empirically, our method outperforms SGD with
momentum, Adam, EKFAC and TKFAC on several DNNs.
|
2011.13609v1
|
2020-12-12
|
Stabilized explicit Adams-type methods
|
In this work we present explicit Adams-type multistep methods with extended
stability interval, which are analogous to the stabilized Chebyshev
Runge--Kutta methods. It is proved that for any $k\geq 1$ there exists an
explicit $k$-step Adams-type method of order one with stability interval of
length $2k$. The first order methods have remarkably simple expressions for
their coefficients and error constant. A damped modification of these methods
is derived. In general case to construct a $k$-step method of order $p$ it is
necessary to solve a constrained optimization problem in which the objective
function and $p$ constraints are second degree polynomials in $k$ variables. We
calculate higher-order methods up to order six numerically and perform some
numerical experiments to confirm the accuracy and stability of the methods.
|
2012.06767v1
|
2020-12-18
|
Quantum friction in the Hydrodynamic Model
|
We study the phenomenon of quantum friction in a system consisting of a
polarizable atom moving at a constant speed parallel to a metallic plate. The
metal is described using a charged hydrodynamic model for the electrons. This
model featuring long-range interactions is appropriate for a clean metal in a
temperature range where scattering due to Coulomb interactions dominates over
the scattering of electron by impurities. We find that a quantum friction force
between the atom and the metal surface exists even in the absence of intrinsic
damping in the metal, but that it only starts once the velocity of the atom
exceeds the effective speed of sound in the metal. We argue that this condition
can be fulfilled most easily in metals with nearly empty or nearly filled
bands. We make quantitative predictions for the friction force to the second
and fourth order in the atomic polarizability, and show that the threshold
behavior persists to all orders of the perturbation theory.
|
2012.10204v1
|
2020-12-20
|
A new model with solitary waves: solution, stability and quasinormal modes
|
We construct solitary wave solutions in a $1+1$ dimensional massless scalar
($\phi$) field theory with a specially chosen potential $V(\phi)$. The equation
governing perturbations about this solitary wave has an effective potential
which is a simple harmonic well over a region, and a constant beyond. This
feature allows us to ensure the stability of the solitary wave through the
existence of bound states in the well, which can be found by semi-analytical
methods. A further check on stability is performed through our search for
quasi-normal modes (QNM) which are defined for purely outgoing boundary
conditions. The time-domain profiles of the perturbations and the parametric
variation of the QNM values are presented and discussed in some detail.
Expectedly, a damped oscillatory temporal behaviour (ringdown) of the
fluctuations is clearly seen through our analysis of the quasi-normal modes.
|
2012.10967v2
|
2020-12-29
|
Strongly modulated ultrafast demagnetization and magnetization precession dynamics in ferrimagnetic Gdx(CoFe)1-x alloys via 3d-4f intersublattice exchange coupling
|
Manipulation of the intersublattice interaction strengh (JRE-TM) in rare
earth (RE)-transition metal (TM) alloys is a key issue to understand how
efficiently the laser-induced angular momentum transfers from 3d to 4f spins
and to have a better control of the ultrafast spin dynamics. In this work, the
relationships between laser-induced demagnetization process and the
intersublattice 3d-4f interaction for the GdCoFe alloys were systematically
studied. The ultrafast two-stage demagnetization process could change into a
one-stage mode as the angular momentum transferring channel between 3d and 4f
spins is switched off, which could be modulated by JRE-TM. Furthermore, both
the effective g-factor and damping constant deduced by the subsequently
laser-induced magnetization precession process diverge at the angular momentum
compensation point based on the ferromagnetic resonance method with the LLG
equations. The results provide an alternative way to efficiently manipulate the
ultrafast demagnetization time for practical applications.
|
2012.14620v1
|
2021-02-01
|
Contour Dynamics for One-Dimensional Vlasov-Poisson Plasma with the Periodic Boundary
|
We revisit the contour dynamics (CD) simulation method which is applicable to
large deformation of distribution function in the Vlasov-Poisson plasma with
the periodic boundary, where contours of distribution function are traced
without using spatial grids. Novelty of this study lies in application of CD to
the one-dimensional Vlasov-Poisson plasma with the periodic boundary condition.
A major difficulty in application of the periodic boundary is how to deal with
contours when they cross the boundaries. It has been overcome by virtue of a
periodic Green's function, which effectively introduces the periodic boundary
condition without cutting nor reallocating the contours. The simulation results
are confirmed by comparing with an analytical solution for the piece-wise
constant distribution function in the linear regime and a linear analysis of
the Landau damping. Also, particle trapping by Langmuir wave is successfully
reproduced in the nonlinear regime.
|
2102.00866v1
|
2021-02-01
|
Strong coupling of Fe-Co alloy with ultralow damping to superconducting co-planar waveguide resonators
|
We report on the strong coupling between a metallic ferromagnetic Fe75Co25
thin film patterned element and a range of superconducting Nb half-wavelength
co-planar waveguide (CPW) resonators. By varying the volume of the ferromagnet
we demonstrate that the coupling rate scales linearly with the square root of
the number of spins and achieve a coupling rate over 700 MHz, approaching the
ultrastrong coupling regime. Experiments varying the center conductor width
while maintaining constant magnetic volume verify that decreasing the center
conductor width increases coupling and cooperativity. Our results show that the
frequency dependence of the coupling rate is linear with the fundamental and
higher order odd harmonics of the CPW, but with differing efficiencies. The
results show promise for scaling planar superconducting resonator/magnetic
hybrid systems to smaller dimensions.
|
2102.01129v1
|
2021-02-15
|
Magnetodynamic properties of dipole-coupled 1D magnonic crystals
|
Magnonic crystals are magnetic metamaterials, that provide a promising way to
manipulate magnetodynamic properties by controlling the geometry of the
patterned structures. Here, we study the magnetodynamic properties of 1D
magnonic crystals consisting of parallel NiFe strips with different strip
widths and separations. The strips couple via dipole-dipole interactions. As an
alternative to experiments and/or micromagnetic simulations, we investigate the
accuracy of a simple macrospin model. For the case of simple strips, a model
with a single free parameter to account for an overestimation of the
out-of-plane demagnetization of the magnonic lattice is described. By adjusting
this parameter a good fit with experimental as well as micromagnetic results is
obtained. Moreover, the Gilbert damping is found independent of the lattice
constant however the inhomogeneous linewidth broadening found to increase with
decreasing stripe separation.
|
2102.07712v2
|
2021-03-11
|
The Debye Length and the Running Coupling of QCD: a Potential and Phenomenological Approach
|
In this paper, one uses a damped potential to present a description of the
running coupling constant of QCD in the confinement phase. Based on a
phenomenological perspective for the Debye screening length, one compares the
running coupling obtained here with both the Brodsky-de T\'eramond-Deur and the
Richardson approaches. The results seem to indicate the model introduced here
corroborate the Richardson approach. Moreover, the Debye screening mass in the
confinement phase depends on a small parameter, which tends to vanish in the
non-confinement phase of QCD.
|
2103.06642v2
|
2021-03-16
|
Adapted gauge to small mass ratio binary black hole evolutions
|
We explore the benefits of adapted gauges to small mass ratio binary black
hole evolutions in the moving puncture formulation. We find expressions that
approximate the late time behavior of the lapse and shift,
$(\alpha_0,\beta_0)$, and use them as initial values for their evolutions. We
also use a position and black hole mass dependent damping term,
$\eta[\vec{x}_1(t),\vec{x}_2(t),m_1,m_2]$, in the shift evolution, rather than
a constant or conformal-factor dependent choice. We have found that this
substantially reduces noise generation at the start of the numerical
integration and keeps the numerical grid stable around both black holes,
allowing for more accuracy with lower resolutions. We test our choices for this
gauge in detail in a case study of a binary with a 7:1 mass ratio, and then use
15:1 and 32:1 binaries for a convergence study. Finally, we apply our new gauge
to a 64:1 binary and a 128:1 binary to well cover the comparable and small mass
ratio regimes.
|
2103.09326v1
|
2021-03-24
|
"Second-Order Primal'' + "First-Order Dual'' Dynamical Systems with Time Scaling for Linear Equality Constrained Convex Optimization Problems
|
Second-order dynamical systems are important tools for solving optimization
problems, and most of existing works in this field have focused on
unconstrained optimization problems. In this paper, we propose an inertial
primal-dual dynamical system with constant viscous damping and time scaling for
the linear equality constrained convex optimization problem, which consists of
a second-order ODE for the primal variable and a first-order ODE for the dual
variable. When the scaling satisfies certain conditions, we prove its
convergence property without assuming strong convexity. Even the convergence
rate can become exponential when the scaling grows exponentially. We also show
that the obtained convergence property of the dynamical system is preserved
under a small perturbation.
|
2103.12931v3
|
2021-04-15
|
Evolution of Anti-de Sitter black holes in Einstein-Maxwell-dilaton theory
|
We study the nonlinear evolution of the spherical symmetric black holes under
a small neutral scalar field perturbation in Einstein-Maxwell-dilaton theory
with coupling function $f(\phi)=e^{-b\phi}$ in asymptotic anti-de Sitter
spacetime. The non-minimal coupling between scalar and Maxwell fields allows
the transmission of the energy from the Maxwell field to the scalar field, but
also behaves as a repulsive force for the scalar. The scalar field oscillates
with damping amplitude and converges to a final value by a power law. The
irreducible mass of the black hole increases abruptly at initial times and then
saturates to the final value exponentially. The saturating rate is twice the
decaying rate of the dominant mode of the scalar. The effects of the black hole
charge, the cosmological constant and the coupling parameter on the evolution
are studied in detail. When the initial configuration is a naked singularity
spacetime with a large charge to mass ratio, a horizon will form soon and hide
the singularity.
|
2104.07281v1
|
2021-04-23
|
Well-posedness of a nonlinear shallow water model for an oscillating water column with time-dependent air pressure
|
We propose in this paper a new nonlinear mathematical model of an oscillating
water column (OWC). The one-dimensional shallow water equations in the presence
of this device is reformulated as a transmission problem related to the
interaction between waves and a fixed partially-immersed structure. By imposing
the conservation of the total fluid-OWC energy in the non-damped scenario, we
are able to derive a transmission condition that involves a time-dependent air
pressure inside the chamber of the device, instead of a constant atmospheric
pressure as in \cite{bocchihevergara2021}. We then show that the transmission
problem can be reduced to a quasilinear hyperbolic initial boundary value
problem with a semi-linear boundary condition determined by an ODE depending on
the trace of the solution to the PDE at the boundary. Local well-posedness for
general problems of this type is established via an iterative scheme by using
linear estimates for the PDE and nonlinear estimates for the ODE.
|
2104.11570v3
|
2021-04-27
|
Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation
|
We consider the Cauchy problem for the Burgers hierarchy with general time
dependent coefficients. The closed form for the Green's function of the
corresponding linear equation of arbitrary order $N$ is shown to be a sum of
generalised hypergeometric functions. For suitably damped initial conditions we
plot the time dependence of the Cauchy problem over a range of $N$ values. For
$N=1$, we introduce a spatial forcing term. Using connections between the
associated second order linear Schr\"{o}dinger and Fokker-Planck equations, we
give closed form expressions for the corresponding Green's functions of the
sinked Bessel process with constant drift. We then apply the Green's function
to give time dependent profiles for the corresponding forced Burgers Cauchy
problem.
|
2104.12976v1
|
2021-05-16
|
Time-dependent conformal transformations and the propagator for quadratic systems
|
The method proposed by Inomata and his collaborators allows us to transform a
damped Caldiroli-Kanai oscillator with time-dependent frequency to one with
constant frequency and no friction by redefining the time variable, obtained by
solving a Ermakov-Milne-Pinney equation. Their mapping ``Eisenhart-Duval''
lifts as a conformal transformation between two appropriate Bargmann spaces.
The quantum propagator is calculated also by bringing the quadratic system to
free form by another time-dependent Bargmann-conformal transformation which
generalizes the one introduced before by Niederer and is related to the mapping
proposed by Arnold. Our approach allows us to extend the Maslov phase
correction to arbitrary time-dependent frequency. The method is illustrated by
the Mathieu profile.
|
2105.07374v4
|
2021-06-21
|
Universal many-body diffusion from momentum dephasing
|
The open dynamics of quantum many-body systems involve not only the exchange
of energy, but also of other conserved quantities, such as momentum. This leads
to additional decoherence, which may have a profound impact in the dynamics.
Motivated by this, we consider a many-body system subject to total momentum
dephasing and show that under very general conditions this leads to a diffusive
component in the dynamics of any local density, even far from equilibrium. Such
component will usually have an intricate interplay with the unitary dynamics.
To illustrate this, we consider the case of a superfluid and show that momentum
dephasing introduces a damping in the sound-wave dispersion relation, similar
to that predicted by the Navier-Stokes equation for ordinary fluids. Finally,
we also study the effects of dephasing in linear response, and show that it
leads to a universal additive contribution to the diffusion constant, which can
be obtained from a Kubo formula.
|
2106.10984v1
|
2021-06-23
|
The MGT-Fourier model in the supercritical case
|
We address the energy transfer in the differential system $$ \begin{cases}
u_{ttt}+\alpha u_{tt} - \beta \Delta u_t - \gamma \Delta u = -\eta \Delta
\theta \\ \theta_t - \kappa \Delta \theta =\eta \Delta u_{tt}+ \alpha\eta
\Delta u_t \end{cases} $$ made by a Moore-Gibson-Thompson equation in the
supercritical regime, hence antidissipative, coupled with the classical heat
equation. The asymptotic properties of the related solution semigroup depend on
the strength of the coupling, ruling the competition between the Fourier
damping and the MGT antidamping. Exponential stability will be shown always to
occur, provided that the coupling constant is sufficiently large with respect
to the other structural parameters. A fact of general interest will be also
discussed, namely, the impossibility of attaining the optimal exponential decay
rate of a given dissipative system via energy estimates.
|
2106.12402v2
|
2021-07-07
|
Amplification of light scattering in arrays of nanoholes by plasmonic absorption-induced transparency
|
Absorption induced transparency is an optical phenomenon that occurs in
metallic arrays of nanoholes when materials featuring narrow lines in their
absorption spectra are deposited on top of it. First reported in the visible
range, using dye lasers as cover materials, it has been described as
transmission peaks unexpectedly close to the absorption energies of the dye
laser. In this work, amplification of light is demonstrated in the active
regime of absorption induced transparency. Amplification of stimulated emission
can be achieved when the dye laser behaves as a gain material. Intense
illumination can modify the dielectric constant of the gain material, which in
turn, changes the propagation properties of the plasmonic modes excited in the
hole arrays, providing both less damping to light and further feedback,
enhancing the stimulated emission process.
|
2107.03135v1
|
2021-08-26
|
The Anomalous Transport of Tracers in Active Baths
|
We derive the long-time dynamics of a tracer immersed in a one-dimensional
active bath. In contrast to previous studies, we find that the damping and
noise correlations possess long-time tails with exponents that depend on the
tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects
that alter fluctuations and lead to superdiffusion and friction that grows with
time when the tracer is dragged at a constant speed. In the singular limit of a
completely symmetric tracer, we recover normal diffusion and finite friction.
Furthermore, for small symmetric tracers, the active contribution to the
friction becomes negative: active particles enhance motion rather than oppose
it. These results show that, in low-dimensional systems, the motion of a
passive tracer in an active bath cannot be modeled as a persistent random
walker with a finite correlation time.
|
2108.11970v3
|
2021-09-23
|
Constraining Time Dependent Dark Matter Signals from the Sun
|
Dark matter (DM) particles captured by the Sun can produce high energy
electrons outside the Sun through annihilating into meta-stable mediators. The
corresponding cosmic-ray electron signals observed by the space-based
experiments will be time dependent due to the orbital motion of the space-based
detectors. The shape of this time dependence is predictable given the orbital
information of the detectors. Since the high-energy CR electron (with energy
E>100 GeV) fluxes are expected to be constant in time, non-observation of such
time variation can be used to place upper limits on the DM annihilation cross
section. We analyze the time dependence of dark matter cosmic-ray signals in
three space-based experiments: AMS-02, DAMPE and CALET. Under the assumption
that no time dependent signal is observed, we derive the 95% C.L. exclusion
limits on the signal strength from the current data. We map our limits onto the
parameter space of the dark photon model and find that the constraints are
comparable with that derived from the supernova SN1987A.
|
2109.11662v3
|
2021-11-01
|
Magnon-driven dynamics of frustrated skyrmion in synthetic antiferromagnets: Effect of skyrmion precession
|
A theoretical study on the interplay of frustrated skyrmion and magnons is
useful for revealing new physics and future experiments design. In this work,
we investigated the magnon-driven dynamics of frustrated skyrmion in synthetic
antiferromagnets, focusing on the effect of skyrmion precession. It is
theoretically revealed that the scattering cross section of the injected
magnons depends on the skyrmion precession, which in turn effectively modulates
the skyrmion Hall motion. Specifically, the Hall angle decreases as the
precession speed increases, which is also verified by the atomistic
micromagnetic simulations. Moreover, the precession speed and the Hall angle of
the frustrated skyrmion depending on the magnon intensity and damping constant
are simulated, demonstrating the effective suppression of the Hall motion by
the skyrmion precession. This work provides a comprehensive understanding of
the magnon-skyrmion scattering in frustrated magnets, benefiting future
spintronic and magnonic applications.
|
2111.00738v1
|
2021-11-01
|
Safe Online Gain Optimization for Variable Impedance Control
|
Smooth behaviors are preferable for many contact-rich manipulation tasks.
Impedance control arises as an effective way to regulate robot movements by
mimicking a mass-spring-damping system. Consequently, the robot behavior can be
determined by the impedance gains. However, tuning the impedance gains for
different tasks is tricky, especially for unstructured environments. Moreover,
online adapting the optimal gains to meet the time-varying performance index is
even more challenging. In this paper, we present Safe Online Gain Optimization
for Variable Impedance Control (Safe OnGO-VIC). By reformulating the dynamics
of impedance control as a control-affine system, in which the impedance gains
are the inputs, we provide a novel perspective to understand variable impedance
control. Additionally, we innovatively formulate an optimization problem with
online collected force information to obtain the optimal impedance gains in
real-time. Safety constraints are also embedded in the proposed framework to
avoid unwanted collisions. We experimentally validated the proposed algorithm
on three manipulation tasks. Comparison results with a constant gain baseline
and an adaptive control method prove that the proposed algorithm is effective
and generalizable to different scenarios.
|
2111.01258v1
|
2021-11-15
|
Extremely confined gap plasmon modes: when nonlocality matters
|
Historically, the field of plasmonics has been relying on the framework of
classical electrodynamics, with the local-response approximation of material
response being applied even when dealing with nanoscale metallic structures.
However, when approaching the atomic-scale confinement of the electromagnetic
radiation, mesoscopic effects are anticipated to become observable, e.g., those
associated with the nonlocal electrodynamic surface response of the electron
gas. We investigate nonlocal effects in propagating gap surface plasmon modes
in ultrathin metal--dielectric--metal planar waveguides, exploiting
monocrystalline gold flakes separated by atomic-layer-deposited aluminum oxide.
We use scanning near-field optical microscopy to directly access the near-field
of such confined gap plasmon modes and measure their dispersion relation (via
their complex-valued propagation constants). We compare our experimental
findings with the predictions of the generalized nonlocal optical response
theory to unveil signatures of nonlocal damping, which becomes appreciable for
smaller dielectric gaps.
|
2111.07561v1
|
2021-11-16
|
Flow around topological defects in active nematic films
|
We study the active flow around isolated defects and the self-propulsion
velocity of $+1/2$ defects in an active nematic film with both viscous
dissipation (with viscosity $\eta$) and frictional damping $\Gamma$ with a
substrate. The interplay between these two dissipation mechanisms is controlled
by the hydrodynamic dissipation length $\ell_d=\sqrt{\eta/\Gamma}$ that screens
the flows. For an isolated defect, in the absence of screening from other
defects, the size of the vortical flows around the defect is controlled by the
system size $R$. In the presence of friction that leads to a finite value of
$\ell_d$, the vorticity field decays to zero on the lengthscales larger than
$\ell_d$. We show that the self-propulsion velocity of $+1/2$ defects grows
with $R$ in small systems where $R<\ell_d$, while in the infinite system limit
or when $R\gg \ell_d$, it approaches a constant value determined by $\ell_d$.
|
2111.08537v2
|
2021-12-01
|
Axial perturbations of hairy Gauss-Bonnet black holes with massive self-interacting scalar field
|
We study the axial quasinormal modes of hairy black holes in Gauss-Bonnet
gravity with massive self-interacting scalar field. Two coupling functions of
the scalar field to the Gauss-Bonnet invariant are adopted with one of them
leading to black hole scalarization. The axial perturbations are studied via
time evolution of the perturbation equation, and the effect of the scalar field
mass and the self-interaction constant on the oscillation frequency and damping
time is examined. We study as well the effect of nonzero scalar field potential
on the critical point at which the perturbation equation loses hyperbolicity in
the case of black hole scalarization. The results show that the non-zero scalar
field potential extends the range of parameters where such loss of
hyperbolicity is observed thus shrinking the region of stable black hole
existence. This will have an important effect on the nonlinear dynamical
simulation studies in massive scalar Gauss-Bonnet gravity.
|
2112.00703v1
|
2021-12-20
|
Adversarially Robust Stability Certificates can be Sample-Efficient
|
Motivated by bridging the simulation to reality gap in the context of
safety-critical systems, we consider learning adversarially robust stability
certificates for unknown nonlinear dynamical systems. In line with approaches
from robust control, we consider additive and Lipschitz bounded adversaries
that perturb the system dynamics. We show that under suitable assumptions of
incremental stability on the underlying system, the statistical cost of
learning an adversarial stability certificate is equivalent, up to constant
factors, to that of learning a nominal stability certificate. Our results hinge
on novel bounds for the Rademacher complexity of the resulting adversarial loss
class, which may be of independent interest. To the best of our knowledge, this
is the first characterization of sample-complexity bounds when performing
adversarial learning over data generated by a dynamical system. We further
provide a practical algorithm for approximating the adversarial training
algorithm, and validate our findings on a damped pendulum example.
|
2112.10690v1
|
2022-02-10
|
Amplifying spin waves along Néel domain wall by spin-orbit torque
|
Traveling spin waves in magnonic waveguides undergo severe attenuation, which
tends to result in a finite propagation length of spin waves, even in magnetic
materials with the accessible lowest damping constant, heavily restricting the
development of magnonic devices. Compared with the spin waves in traditional
waveguides, propagating spin waves along strip domain wall are expected to
exhibit enhanced transmission. Here, we demonstrate, theoretically and through
micromagnetic simulations, that spin-orbit torque associated with a
ferromagnet/heavy metal bilayer can efficiently control the attenuation of spin
waves along a N\'eel-type strip domain wall, despite the complexity in the
ground-state magnetization configuration. The direction of the electric current
applied to the heavy-metal layer determines whether these spin waves are
amplified or further attenuated otherwise. Remarkably, our simulations reveal
that the effective current densities required to efficiently tune the decay of
such spin waves are just ~10^10 Am-2, roughly an order smaller than those
required in conventional spin waveguides. Our results will enrich the toolset
for magnonic technologies.
|
2202.05181v1
|
2022-03-06
|
Elongated Skyrmion as Spin Torque Nano-Oscillator and Magnonic Waveguide
|
Spin torque nano-oscillator has been extensively studied both theoretically
and experimentally in recent decades due to its potential applications in
future microwave communication technology and neuromorphic computing. In this
work, we present a skyrmion-based spin torque nano-oscillator driven by a
spatially uniform direct current, where the skyrmion is confined by two pinning
sites. Different from other skyrmion-based oscillators that arise from the
circular motion or the breathing mode of a skyrmion, the steady-state
oscillatory motions are produced by the periodic deformation of an elongated
skyrmion. Through micromagnetic simulations, we find that the oscillation
frequency depends on the driving current, the damping constant as well as the
characteristics of pinning sites. This nonlinear response to direct current
turns out to be universal and can also appear in the case of antiskyrmions,
skyrmioniums and domain walls. Furthermore, the elongated skyrmion possesses a
rectangle-like domain wall, which could also serve as a magnonic waveguide.
Utilizing the propagation of spin waves in this waveguide, we propose a device
design of logic gate and demonstrate its performance.
|
2203.02969v2
|
2022-03-11
|
Absence of Walker breakdown in the dynamics of chiral Neel domain walls driven by in-plane strain gradients
|
We investigate theoretically the motion of chiral N\'eel domain walls in
perpendicularly magnetized systems driven by in-plane strain gradients. We show
that such strain drives domain walls efficiently towards increasing tensile
(compressive) strain for positive (negative) magnetostrictive materials. During
their motion a local damping torque that opposes the precessional torque due to
the strain gradient arises. This torque prevents the onset of turbulent
dynamics, and steady domain wall motion with constant velocity is
asymptotically reached for any arbitrary large strain gradient. Withal,
velocities in the range of 500 m/s can be obtained using voltage-induced strain
under realistic conditions.
|
2203.05826v1
|
2022-06-28
|
Origin of the spontaneous oscillations in a simplified coagulation-fragmentation system driven by a source
|
We consider a system of aggregated clusters of particles, subjected to
coagulation and fragmentation processes with mass dependent rates. Each monomer
particle can aggregate with larger clusters, and each cluster can fragment into
individual monomers with a rate directly proportional to the aggregation rate.
The dynamics of the cluster densities is governed by a set of Smoluchowski
equations, and we consider the addition of a source of monomers at constant
rate. The whole dynamics can be reduced to solving a unique non-linear
differential equation which displays self-oscillations in a specific range of
parameters, and for a number of distinct clusters in the system large enough.
This collective phenomenon is due to the presence of a fluctuating damping
coefficient and is closely related to the Li\'enard self-oscillation mechanism
observed in a more general class of physical systems such as the van der Pol
oscillator.
|
2206.13884v1
|
2022-06-29
|
Strongly coupled quantum Otto cycle with single qubit bath
|
We discuss a model of a closed quantum evolution of two-qubits where the
joint Hamiltonian is so chosen that one of the qubits acts as a bath and
thermalize the other qubit which is acting as the system. The corresponding
exact master equation for the system is derived. Interestingly, for a specific
choice of parameters the master equation takes the
Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients,
representing pumping and damping of a single qubit system. Based on this model
we construct an Otto cycle connected to a single qubit bath and study its
thermodynamic properties. Our analysis goes beyond the conventional weak
coupling scenario and illustrates the effects of finite bath including
non-Markovianity. We find closed form expressions for efficiency (coefficient
of performance), power (cooling power) for heat engine regime (refrigerator
regime) for different modifications of the joint Hamiltonian.
|
2206.14751v1
|
2022-07-24
|
Revisiting the central limit theorems for the SGD-type methods
|
We revisited the central limit theorem (CLT) for stochastic gradient descent
(SGD) type methods, including the vanilla SGD, momentum SGD and Nesterov
accelerated SGD methods with constant or vanishing damping parameters. By
taking advantage of Lyapunov function technique and $L^p$ bound estimates, we
established the CLT under more general conditions on learning rates for broader
classes of SGD methods compared with previous results. The CLT for the time
average was also investigated, and we found that it held in the linear case,
while it was not generally true in nonlinear situation. Numerical tests were
also carried out to verify our theoretical analysis.
|
2207.11755v3
|
2022-08-09
|
Parameter Estimation in Ill-conditioned Low-inertia Power Systems
|
This paper examines model parameter estimation in dynamic power systems whose
governing electro-mechanical equations are ill-conditioned or singular. This
ill-conditioning is because of converter-interfaced power systems generators'
zero or small inertia contribution. Consequently, the overall system inertia
decreases, resulting in low-inertia power systems. We show that the standard
state-space model based on least squares or subspace estimators fails to exist
for these models. We overcome this challenge by considering a least-squares
estimator directly on the coupled swing-equation model but not on its
transformed first-order state-space form. We specifically focus on estimating
inertia (mechanical and virtual) and damping constants, although our method is
general enough for estimating other parameters. Our theoretical analysis
highlights the role of network topology on the parameter estimates of an
individual generator. For generators with greater connectivity, estimation of
the associated parameters is more susceptible to variations in other generator
states. Furthermore, we numerically show that estimating the parameters by
ignoring their ill-conditioning aspects yields highly unreliable results.
|
2208.04471v1
|
2022-08-09
|
Driven particle dispersion in narrow disordered racetracks
|
We study the disorder-induced deterministic dispersion of particles uniformly
driven in an array of narrow tracks. For different toy models with quenched
disorder we obtain exact analytical expressions for the steady-state mean
velocity $v$ and the dispersion constant $D$ for any driving force $f$ above a
putative depinning threshold. For short-range correlated pinning forces we find
that at large drives $D\sim 1/v$ for random-field type of disorder while $D
\sim 1/v^3$ for the random-bond type. We show numerically that these results
are robust: the same scaling holds for models of massive damped particles, soft
particles, particles in quasi-one dimensional or two dimensional tracks, and
for a model of a magnetic domain wall with two degrees of freedom driven either
by electrical current or magnetic field. Crossover and finite temperature
effects are discussed. The universal features we identify may be relevant for
describing the fluctuating dynamics of stable localized objects such solitons,
superconducting vortices, magnetic domain walls and skyrmions, and colloids
driven in quasi one-dimensional track arrays. In particular, the drive
dependence of $D$ appears as a sensitive tool for characterizing and assessing
the nature of disorder in the host materials.
|
2208.05031v2
|
2022-09-19
|
Stationary states of an active Brownian particle in a harmonic trap
|
We study the stationary states of an over-damped active Brownian particle
(ABP) in a harmonic trap in two dimensions, via mathematical calculations and
numerical simulations. In addition to translational diffusion, the ABP
self-propels with a certain velocity, whose magnitude is constant, but its
direction is subject to Brownian rotation. In the limit where translational
diffusion is negligible, the stationary distribution of the particle's position
shows a transition between two different shapes, one with maximum and the other
with minimum density at the centre, as the trap stiffness is increased. We show
that this non-intuitive behaviour is captured by the relevant Fokker-Planck
equation, which, under minimal assumptions, predicts a continuous ``phase
transition" between the two different shapes. As the translational diffusion
coefficient is increased, both these distributions converge into the
equilibrium, Boltzmann form. Our simulations support the analytical
predictions, and also show that the probability distribution of the orientation
angle of the self-propulsion velocity undergoes a transition from unimodal to
bimodal forms in this limit. We also extend our simulations to a three
dimensional trap, and find similar behaviour.
|
2209.09184v2
|
2022-09-25
|
The Design of Observational Longitudinal Studies
|
This paper considers the design of observational longitudinal studies with a
continuous response and a binary time-invariant exposure, where, typically, the
exposure is unbalanced, the mean response in the two groups differs at baseline
and the measurement times might not be the same for all participants. We
consider group differences that are constant and those that increase linearly
with time. We study power, number of study participants (N) and number of
repeated measures (r), and provide formulas for each quantity when the other
two are fixed, for compound symmetry, damped exponential and random intercepts
and slopes covariances. When both N and r can be chosen by the investigator, we
study the optimal combination for maximizing power subject to a cost constraint
and minimizing cost for fixed power. Intuitive parameterizations are used for
all quantities. All calculations are implemented in freely available software.
|
2209.12129v1
|
2022-10-09
|
How general is the strong cosmic censorship bound for quasinormal modes?
|
Hod's proposal claims that the least damped quasinormal mode of a black hole
must have the imaginary part smaller than half of the surface gravity at the
event horizon. The Strong Cosmic Censorship in General Relativity implies that
this bound must be even weaker: half of the surface gravity at the Cauchy
horizon. The appealing question is whether these bounds are limited by the
Einstein theory only? Here we will present numerical evidence that once the
black hole size is much smaller than then the radius of the cosmological
horizon, both the Hod's proposal and the strong cosmic censorship bound for
quasinormal modes are satisfied for general spherically symmetric black holes
in an arbitrary metric theory of gravity. The low-lying quasinormal frequencies
have the universal behavior in this regime and do not depend on the
near-horizon geometry, but only on the asymptotic parameters: the value of the
cosmological constant and black hole mass.
|
2210.04314v2
|
2022-12-12
|
Solving the Teukolsky equation with physics-informed neural networks
|
We use physics-informed neural networks (PINNs) to compute the first
quasi-normal modes of the Kerr geometry via the Teukolsky equation. This
technique allows us to extract the complex frequencies and separation constants
of the equation without the need for sophisticated numerical techniques, and
with an almost immediate implementation under the \texttt{PyTorch} framework.
We are able to compute the oscillation frequencies and damping times for
arbitrary black hole spins and masses, with accuracy typically below the
percentual level as compared to the accepted values in the literature. We find
that PINN-computed quasi-normal modes are indistinguishable from those obtained
through existing methods at signal-to-noise ratios (SNRs) larger than 100,
making the former reliable for gravitational-wave data analysis in the mid
term, before the arrival of third-generation detectors like LISA or the
Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved.
|
2212.06103v2
|
2023-01-27
|
Thermal curvature perturbations in thermal inflation
|
We compute the power spectrum of super-horizon curvature perturbations
generated during a late period of thermal inflation, taking into account
fluctuation-dissipation effects resulting from the scalar flaton field's
interactions with the ambient radiation bath. We find that, at the onset of
thermal inflation, the flaton field may reach an equilibrium with the radiation
bath even for relatively small coupling constants, maintaining a spectrum of
thermal fluctuations until the critical temperature $T_c$, below which thermal
effects stop holding the field at the false potential minimum. This enhances
the field variance compared to purely quantum fluctuations, therefore
increasing the average energy density during thermal inflation and damping the
induced curvature perturbations. In particular, we find that this inhibits the
later formation of primordial black holes, at least on scales that leave the
horizon for $T>T_c$. The larger thermal field variance also reduces the
duration of a period of fast-roll inflation below $T_c$, as the field rolls to
the true potential minimum, which should also affect the generation of (large)
curvature perturbations on even smaller scales.
|
2301.11666v1
|
2023-02-20
|
Adiabatic computing for optimal thermodynamic efficiency of information processing
|
Landauer's principle makes a strong connection between information theory and
thermodynamics by stating that erasing a one-bit memory at temperature $T_0$
requires an average energy larger than $W_{LB}=k_BT_0 \ln2$, with $k_B$
Boltzmann's constant. This tiny limit has been saturated in model experiments
using quasi-static processes. For faster operations, an overhead proportional
to the processing speed and to the memory damping appears. In this article, we
show that underdamped systems are a winning strategy to reduce this extra
energetic cost. We prove both experimentally and theoretically that, in the
limit of vanishing dissipation mechanisms in the memory, the physical system is
thermally insulated from its environment during fast erasures, i.e. fast
protocols are adiabatic as no heat is exchanged with the bath. Using a fast
optimal erasure protocol we also show that these adiabatic processes produce a
maximum adiabatic temperature $T_a=2T_0$, and that Landauer's bound for fast
erasures in underdamped systems becomes the adiabatic bound: $W_a = k_B T_0$.
|
2302.09957v2
|
2023-03-12
|
Can gravitational vacuum condensate stars be a dark energy source?
|
Gravitational vacuum condensate stars, also known as gravastars, have been
proposed as an alternative to black holes. Their interior contains a perfect
fluid with an equation of state akin to that of a cosmological constant. For
this reason, they have recently been considered as a possible astrophysical
source of dark energy. In this work we argue that gravitational vacuum
condensate stars cannot be the source of dark energy and highlight that a
direct coupling of their mass to the dynamics of the Universe would lead to an
additional velocity dependent acceleration, damping their motion with respect
to the cosmological frame. We briefly discuss the potential impact of this
additional acceleration in the context of a recent proposal that the observed
mass growth of compact objects at the core of elliptical galaxies might result
from such a cosmological coupling.
|
2303.06630v1
|
2023-03-23
|
A Computational Study of Cluster Dynamics in Structural Lubricity: Role of Cluster Rotation
|
We present a computational study of sliding between gold clusters and a
highly oriented pyrolytic graphite substrate, a material system that exhibits
ultra-low friction due to structural lubricity. By means of molecular dynamics,
it is found that clusters may undergo spontaneous rotations during manipulation
as a result of elastic instability, leading to attenuated friction due to
enhanced interfacial incommensurability. In the case of a free cluster, shear
stresses exhibit a non-monotonic dependency on the strength of the tip-cluster
interaction, whereby rigid clusters experience nearly constant shear stresses.
Finally, it is shown that the suppression of the translational degrees of
freedom of a cluster's outermost-layer can partially annihilate out-of-plane
phonon vibrations, which leads to a reduction of energy dissipation that is in
compliance with Stokesian damping. It is projected that the physical insight
attained by the study presented here will result in enhanced control and
interpretation of manipulation experiments at structurally lubric contacts.
|
2303.13707v1
|
2023-04-12
|
Using Demand Response to Improve Power System Small-Signal Stability
|
With the increase of uncertain and intermittent renewable energy supply on
the grid, the power system has become more vulnerable to instability. In this
paper, we develop a demand response strategy to improve power system
small-signal stability. We pose the problem as an optimization problem wherein
the total demand-responsive load is held constant at each time instance but
shifted between different buses to improve small-signal stability, which is
measured by small-signal stability metrics that are functions of subsets of the
system's eigenvalues, such as the smallest damping ratio. To solve the problem,
we use iterative linear programming and generalized eigenvalue sensitivities.
We demonstrate the approach via a case study that uses the IEEE 14-bus system.
Our results show that shifting the load between buses, can improve a
small-signal stability margin. We explore the use of models of different
fidelity and find that it is important to include models of the automatic
voltage regulators and power system stabilizers. In addition, we show that load
shifting can achieve similar improvements to generation shifting and better
improvement than simply tuning power system stabilizers.
|
2304.05573v2
|
2023-04-19
|
Memory-induced oscillations of a driven particle in a dissipative correlated medium
|
The overdamped dynamics of a particle is in general affected by its
interaction with the surrounding medium, especially out of equilibrium, and
when the latter develops spatial and temporal correlations. Here we consider
the case in which the medium is modeled by a scalar Gaussian field with
relaxational dynamics, and the particle is dragged at constant velocity through
the medium by a moving harmonic trap. This mimics the setting of an active
microrheology experiment conducted in a near-critical medium. When the particle
is displaced from its average position in the nonequilibrium steady state, its
subsequent relaxation is shown to feature damped oscillations. This is similar
to what has been recently predicted and observed in viscoelastic fluids, but
differs from what happens in the absence of driving or for an overdamped
Markovian dynamics, in which cases oscillations cannot occur. We characterize
these oscillating modes in terms of the parameters of the underlying mesoscopic
model for the particle and the medium, confirming our analytical predictions
via numerical simulations.
|
2304.09684v2
|
2023-05-03
|
Solving irreducible stochastic mean-payoff games and entropy games by relative Krasnoselskii-Mann iteration
|
We analyse an algorithm solving stochastic mean-payoff games, combining the
ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive
parameterized complexity bounds for several classes of games satisfying
irreducibility conditions. We show in particular that an
$\epsilon$-approximation of the value of an irreducible concurrent stochastic
game can be computed in a number of iterations in $O(|\log\epsilon|)$ where the
constant in the $O(\cdot)$ is explicit, depending on the smallest non-zero
transition probabilities. This should be compared with a bound in
$O(|\epsilon|^{-1}|\log(\epsilon)|)$ obtained by Chatterjee and Ibsen-Jensen
(ICALP 2014) for the same class of games, and to a $O(|\epsilon|^{-1})$ bound
by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We
also establish parameterized complexity bounds for entropy games, a class of
matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn
and Kozyakin. We derive these results by methods of variational analysis,
establishing contraction properties of the relative Krasnoselskii-Mann
iteration with respect to Hilbert's semi-norm.
|
2305.02458v1
|
2023-05-14
|
Adiabatic manipulation of a system interacting with a spin-bath
|
Stimulated Raman Adiabatic Passage, a very efficient technique for
manipulating a quantum system based on the adiabatic theorem, is analyzed in
the case where the manipulated physical system is interacting with a spin bath.
Exploitation of the rotating wave approximation allows for the identification
of a constant of motion which simplifies both the analytical and the numerical
treatment, which allows for evaluating the total unitary evolution of system
and bath. The efficiency of the population transfer process is investigated in
several regimes, including the weak and strong coupling with the environment
and the off-resonance. The formation of appropriate Zeno subspaces explains the
lowering of the efficiency in the strong damping regime.
|
2305.08209v3
|
2023-06-08
|
Energy Efficient Skyrmion based Oscillator on Thermocoupled Nanotrack
|
The magnetic skyrmion-based spin transfer nano-oscillators (STNO) are the
potential candidates for next-generation microwave signal generator and has
gained popularity due to their performance, integrability and compatibility
with existing CMOS technology. However, these devices suffer from the Joule
heating problem that neglects their non-volatility advantage in spintronic
devices. Therefore, it is necessary to investigate the alternative driving
mechanisms for the development of energy-efficient skyrmion based
nano-oscillators. In this paper, a skyrmion-based nano-oscillator has been
designed that utilizes thermal power to drive skyrmion on a thermocoupled
nanotrack. The thermocoupled nanotrack is designed in such a way that both the
upper and lower nanotracks have different values of damping constants and a
temperature difference is maintained between the extreme ends, in order to
create a temperature gradient in the two nanotracks. By employing this
technique, skyrmion is able to exhibit the periodic motion on the nanotrack
with the maximum achievable frequency of 2.5GHz without any external stimuli.
Moreover, the proposed device offers low thermal energy consumption of
0.84fJ/oscillation. Hence, this work provides the pathway for the development
of energy-efficient future spintronic devices.
|
2306.05164v1
|
2023-08-31
|
Apply Non-Hermitian Physics to Realize Ultra-High-Quality Factors of Optically Trapped Particles
|
Optical trapping and binding systems are non-Hermitian. On one hand, the
optical force is non-Hermitian and may pump energy into the trapped particle
when the non-Hermiticity is sufficiently large. On the other hand, the ambient
damping constitutes a loss to the particle. Here, we show that in a
low-friction environment, the interplay between the energy pumped-in by light
and the ambient dissipation can give rise to either instability or a periodic
vibration characterized by a finite quality factor (Q-factor). Through a
comprehensive exploration, we analyze the influence of various parameters on
the non-Hermitian force field. Our investigation reveals several strategies for
enhancing the non-Hermitian force field, such as augmenting particle radius and
refractive index, utilizing triangular lattice optical clusters, and reducing
lattice constants.
|
2308.16502v1
|
2023-09-06
|
BV solutions to a hyperbolic system of balance laws with logistic growth
|
We study BV solutions for a $2\times2$ system of hyperbolic balance laws. We
show that when initial data have small total variation on $(-\infty,\infty)$
and small amplitude, and decay sufficiently fast to a constant equilibrium
state as $|x|\rightarrow\infty$, a Cauchy problem (with generic data) has a
unique admissible BV solution defined globally in time. Here the solution is
admissible in the sense that its shock waves satisfy the Lax entropy condition.
We also study asymptotic behavior of solutions. In particular, we obtain a time
decay rate for the total variation of the solution, and a convergence rate of
the solution to its time asymptotic solution. Our system is a modification of a
Keller-Segel type chemotaxis model. Its flux function possesses new features
when comparing to the well-known model of Euler equations with damping. This
may help to shed light on how to extend the study to a general system of
hyperbolic balance laws in the future.
|
2309.03129v1
|
2023-10-09
|
Anomaly and Brownian fluid particle in Navier-Stokes turbulence
|
We investigate the Navier-Stokes turbulence driven by a stochastic random
Gaussian force. Using a field-theoretic approach, we uncover an anomaly that
brings hidden structure to the theory. The anomaly is generated by a
non-self-adjoint operator of the Jacobian and it follows the symmetries of the
stochastic Navier-Stokes equation. We calculate the anomaly and demonstrate
that by forcing the anomaly to vanish, the velocity field is constrained and a
monopole-type object with a constant charge is formed. When the viscosity is
zero, the anomaly can be interpreted as the Brownian damping coefficient of a
random fluid particle. We provide the Brownian particle equation and its
solution in the presence of a pump and viscosity. Our results suggest that the
anomaly is an inherent feature of stochastic turbulence and must be taken into
account in all stochastic turbulence calculations. This constitutes an
additional law for the original set of stochastic Navier-Stokes equations.
|
2310.06007v3
|
2023-11-02
|
A Novel Adaptive Inertia Strategy in Large-Scale Electric Power Grids
|
The increasing penetration of new renewable sources of energy in today's
power grids is accompanied by a decrease in available electromechanical
inertia. This leads to a reduced dynamical stability. To counterbalance this
effect, virtual synchronous generators have been proposed to emulate
conventional generators and provide inertia to power systems. The high
flexibility of these devices makes it possible to control the synthetic inertia
they provide and to have them operate even more efficiently than the
electromechanical inertia they replace. Here, we propose a novel control scheme
for virtual synchronous generators, where the amount of inertia provided is
large at short times - thereby absorbing local faults and disturbances as
efficiently as conventional generators - but decreases over a tunable time
interval to prevent long-time coherent oscillations from setting in. This new
model is used to investigate the effect of adaptive inertia on large-scale
power grids. Our model outperforms conventional constant inertia in all
scenarios and for all performance measures considered. We show how an optimized
geographical distribution of adaptive inertia devices not only effectively
absorbs local faults, but also significantly improves the damping of inter-area
oscillations.
|
2311.01350v1
|
2023-11-19
|
Two-step BEC coming from a temperature dependent energy gap
|
We report the effects on the thermodynamic properties of a 3D Bose gas caused
by a temperature dependent energy gap $\Delta (T)$ at the lower edge of the
energy spectrum of the particles constituting the Bose gas which behaves like
an ideal Bose gas when the gap is removed. Explicit formulae are given for the
critical temperature, the condensate fraction, the internal energy and the
isochoric specific heat, which are calculated for three different gaps that
abruptly go to zero at temperature $T_B$, as well as for the damped
counterparts whose drop to zero we have smoothed. In particular, for the
undamped BCS (Bardeen, Cooper and Schrieffer) gap it is observed that the
Bose-Einstein condensation (BEC) critical temperature $T_c$ is equal to that of
the ideal Bose gas $T_0$, for all $T_B \leq T_0$; surprisingly, the condensate
fraction presents two different filling rates of the ground state at $T_c =
T_0$ and at $T_B < T_0$; while the specific heat shows a finite jump at $T_c$
as well as a divergence at $T_B$. Three-dimensional infinite Bose gas results
are recovered when the temperature independent gap is either a constant or
equal to zero.
|
2311.11447v1
|
2024-02-08
|
Numerical solution of the Newtonian plane Couette flow with linear dynamic wall slip
|
An efficient numerical approach based on weighted average finite differences
is used to solve the Newtonian plane Couette flow with wall slip, obeying a
dynamic slip law that generalizes the Navier slip law with the inclusion of a
relaxation term. Slip is exhibited only along the fixed plate, and the motion
is triggered by the motion of the other plate. Three different cases are
considered for the motion of the moving plate, i.e., constant speed,
oscillating speed, and a single-period sinusoidal speed. The velocity and the
volumetric flow rate are calculated in all cases and comparisons are made with
the results of other methods and available results in the literature. The
numerical outcomes confirm the damping with time and the lagging effects
arising from the Navier and dynamic wall slip conditions and demonstrate the
hysteretic behavior of the slip velocity in following the harmonic boundary
motion.
|
2402.05736v1
|
2024-02-09
|
Local exact controllability to the trajectories of the convective Brinkman-Forchheimer equations
|
In this article, we discuss the local exact controllability to trajectories
of the following convective Brinkman-Forchheimer (CBF) equations (or damped
Navier-Stokes equations) defined in a bounded domain $\Omega
\subset\mathbb{R}^d$ ($d=2,3$) with smooth boundary:
\begin{align*}
\frac{\partial\boldsymbol{u}}{\partial t}-\mu
\Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{2}\boldsymbol{u}+\nabla
p=\boldsymbol{f}+\boldsymbol{\vartheta}, \ \ \ \nabla\cdot\boldsymbol{u}=0,
\end{align*}
where the control $\boldsymbol{\vartheta}$ is distributed in a subdomain
$\omega \subset \Omega$, and the parameters $\alpha,\beta,\mu>0$ are constants.
We first present global Carleman estimates and observability inequality for the
adjoint problem of a linearized version of CBF equations by using a global
Carleman estimate for the Stokes system. This allows us to obtain its null
controllability at any time $T>0$. We then use the inverse mapping theorem to
deduce local results concerning the exact controllability to the trajectories
of CBF equations.
|
2402.06335v1
|
2024-03-15
|
Beam Dynamics Framework Incorporating Acceleration to Define the Minimum Aperture in Two Focusing Schemes for Proton Radiotherapy Linac
|
In this paper, a self-consistent transverse beam dynamics framework is
demonstrated, that incorporates acceleration into the transverse beam dynamics
studies for a proton linac machine. Two focusing schemes are developed and
discussed; the FODO-like scheme, and the minimum aperture scheme. The FODO-like
scheme is a simple scheme, requiring only one quadrupole per cavity. The scheme
is analytically solved to minimise the beam size at the cavity entrance/exit
and ensures a constant beam size along the lattice, with respect to adiabatic
damping due to longitudinally accelerating rf cavities. The minimum aperture
scheme describes the regime that matches the beam ellipse to the acceptance
ellipse of a cavity, allowing for the smallest possible aperture, for a given
cavity length. A simple approximation of an rf cavity map is determined to
allow changes in particle energy along a lattice, and acceleration is assumed
only in the longitudinal direction.
|
2403.10212v1
|
2024-03-19
|
Unraveling the dynamics of magnetization in topological insulator-ferromagnet heterostructures via spin-orbit torque
|
Spin-orbit coupling stands as a pivotal determinant in the realm of condensed
matter physics. In recent, its profound influence on spin dynamics opens up a
captivating arena with promising applications. Notably, the topological
insulator-ferromagnet heterostructure has been recognized for inducing spin
dynamics through applied current, driven by spin-orbit torque. Building upon
recent observations revealing spin flip signals within this heterostructure,
our study elucidates the conditions governing spin flips by studying the
magnetization dynamics. We establish that the interplay between spin-anisotropy
and spin-orbit torque plays a crucial role in shaping the physics of
magnetization dynamics within the heterostructure. Furthermore, we categorize
various modes of magnetization dynamics, constructing a comprehensive phase
diagram across distinct energy scales, damping constants, and applied
frequencies. This research not only offers insights into controlling spin
direction but also charts a new pathway to the practical application of
spin-orbit coupled systems.
|
2403.12701v1
|
2024-03-25
|
Detection of spin pumping free of rectification and thermal artefacts in molecular-based ferromagnetic insulator V[TCNE]x~2
|
The molecular-based ferrimagnetic insulator V(TCNE)x has gained recent
interest for efficient spin-wave excitation due to its low Gilbert damping
ratio a=4E-5, and narrow ferromagnetic resonance linewidth f=1Oe. Here we
report a clean spin pumping signal detected on V(TCNE)x/metal bilayer
structures, free from spin rectification or thermal artifacts. On-chip coupling
of microwave power is achieved via a coplanar waveguide to measure the in-plane
angle-dependence of the inverse spin-Hall effect under ferromagnetic resonance
conditions with respect to a constant external magnetic field. A signature of
pure spin current from V(TCNE)x is observed in both platinum and permalloy
metal layers, demonstrating the utility of V(TCNE)x for magnon spintronics
studies in molecule/solid-state heterostructures.
|
2403.16429v2
|
2024-03-28
|
Quantum asymptotic amplitude for quantum oscillatory systems from the Koopman operator viewpoint
|
We have recently proposed a fully quantum-mechanical definition of the
asymptotic phase for quantum nonlinear oscillators, which is also applicable in
the strong quantum regime [Kato and Nakao 2022 Chaos 32 063133]. In this study,
we propose a definition of the quantum asymptotic amplitude for quantum
oscillatory systems, which extends naturally the definition of the asymptotic
amplitude for classical nonlinear oscillators on the basis of the Koopman
operator theory. We introduce the asymptotic amplitude for quantum oscillatory
systems by using the eigenoperator of the backward Liouville operator
associated with the largest non-zero real eigenvalue. Using examples of the
quantum van der Pol oscillator with the quantum Kerr effect, exhibiting quantum
limit-cycle oscillations, and the quantum van der Pol model with the quantum
squeezing and degenerate parametric oscillator with nonlinear damping,
exhibiting quantum noise-induced oscillations, we illustrate that the proposed
quantum asymptotic amplitude appropriately yields isostable amplitude values
that decay exponentially with a constant rate.
|
2403.19297v1
|
2024-04-05
|
Stability Analysis of Adaptive Model Predictive Control Using the Circle and Tsypkin Criteria
|
Absolute stability is a technique for analyzing the stability of Lur'e
systems, which arise in diverse applications, such as oscillators with
nonlinear damping or nonlinear stiffness. A special class of Lur'e systems
consists of self-excited systems (SES), in which bounded oscillations arise
from constant inputs. In many cases, SES can be stabilized by linear
controllers, which motivates the present work, where the goal is to evaluate
the effectiveness of adaptive model predictive control for Lur'e systems. In
particular, the present paper considers predictive cost adaptive control
(PCAC), which is equivalent to a linear, time-variant (LTV) controller. A
closed-loop Lur'e system comprised of the positive feedback interconnection of
the Lur'e system and the PCAC-based controller can thus be derived at each
step. In this work, the circle and Tsypkin criteria are used to evaluate the
absolute stability of the closed-loop Lur'e system, where the adaptive
controller is viewed as instantaneously linear time-invariant. When the
controller converges, the absolute stability criteria guarantee global
asymptotic stability of the asymptotic closed-loop dynamics.
|
2404.04170v1
|
1999-08-16
|
Thermal Equilibrium Curves and Turbulent Mixing in Keplerian Accretion Disks
|
We consider vertical heat transport in Keplerian accretion disks, including
the effects of radiation, convection, and turbulent mixing driven by the
Balbus-Hawley instability, in astronomical systems ranging from dwarf novae
(DNe), and soft X-ray transients (SXTs), to active galactic nuclei (AGN). We
propose a modified, anisotropic form of mixing-length theory, which includes
radiative and turbulent damping. We also include turbulent heat transport,
which acts everywhere within disks, regardless of whether or not they are
stably stratified, and can move entropy in either direction. We have generated
a series of vertical structure models and thermal equilibrium curves using the
scaling law for the viscosity parameter $\alpha$ suggested by the exponential
decay of the X-ray luminosity in SXTs. We have also included equilibrium curves
for DNe using an $\alpha$ which is constant down to a small magnetic Reynolds
number ($\sim 10^4$). Our models indicate that weak convection is usually
eliminated by turbulent radial mixing. The substitution of turbulent heat
transport for convection is more important on the unstable branches of thermal
equilibrium S-curves when $\alpha$ is larger. The low temperature turnover
points $\Sigma_{max}$ on the equilibrium S-curves are significantly reduced by
turbulent mixing in DNe and SXT disks. However, in AGN disks the standard
mixing-length theory for convection is still a useful approximation when we use
the scaling law for $\alpha$, since these disks are very thin at the relevant
radii. In accordance with previous work, we find that constant $\alpha$ models
give almost vertical S-curves in the $\Sigma-T$ plane and consequently imply
very slow, possibly oscillating, cooling waves.
|
9908166v1
|
2005-01-10
|
On variations in the fine-structure constant and stellar pollution of quasar absorption systems
|
At redshifts z_abs < 2, quasar absorption-line constraints on space-time
variations in the fine-structure constant, alpha, rely on the comparison of
MgII and FeII transition wavelengths. One potentially important uncertainty is
the relative abundance of Mg isotopes in the absorbers which, if different from
solar, can cause spurious shifts in the measured wavelengths and, therefore,
alpha. Here we explore chemical evolution models with enhanced populations of
intermediate-mass (IM) stars which, in their asymptotic giant branch (AGB)
phase, are thought to be the dominant factories for heavy Mg isotopes at the
low metallicities typical of quasar absorption systems. By design, these models
partially explain recent Keck/HIRES evidence for a smaller alpha in z_abs < 2
absorption clouds than on Earth. However, such models also over-produce N,
violating observed abundance trends in high-z_abs damped Lyman-alpha systems
(DLAs). Our results do not support the recent claim of Ashenfelter, Mathews &
Olive (2004b) that similar models of IM-enhanced initial mass functions (IMFs)
may simultaneously explain the HIRES varying-alpha data and DLA N abundances.
We explore the effect of the IM-enhanced model on Si, Al and P abundances,
finding it to be much-less pronounced than for N. We also show that the 13C/12C
ratio, as measured in absorption systems, could constitute a future diagnostic
of non-standard models of the high-redshift IMF.
|
0501168v2
|
1994-04-11
|
Nonlinear Viscous Vortex Motion in Two-Dimensional Josephson-Junction Arrays
|
When a vortex in a two-dimensional Josephson junction array is driven by a
constant external current it may move as a particle in a viscous medium. Here
we study the nature of this viscous motion. We model the junctions in a square
array as resistively and capacitively shunted Josephson junctions and carry out
numerical calculations of the current-voltage characteristics. We find that the
current-voltage characteristics in the damped regime are well described by a
model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot
y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity,
$\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are
constants for a fixed value of the Stewart-McCumber parameter. This result is
found to apply also for triangular lattices in the overdamped regime. Further
qualitative understanding of the nature of the nonlinear friction on the vortex
motion is obtained from a graphic analysis of the microscopic vortex dynamics
in the array. The consequences of having this type of nonlinear friction law
are discussed and compared to previous theoretical and experimental studies.
|
9404022v1
|
2002-09-20
|
Onset of Convection in a Very Compressible Fluid : The Transient Toward Steady State
|
We analyze the time profile $\Delta T(t)$ of the temperature difference,
measured across a very compressible supercritical $^3$He fluid layer in its
convective state. The experiments were done along the critical isochore in a
Rayleigh-B\'{e}nard cell after starting the vertical constant heat flow $q$.
For $q$ sufficiently well above that needed for the convection onset, the
transient $\Delta T(t)$ for a given $\epsilon\equiv(T-T_c)/T_c$, with $T_c$ =
3.318K, shows a damped oscillatory profile with period $t_{osc}$ modulating a
smooth base profile. The smooth profile forms the exponential tail of the
transient which tends to the steady-state $\Delta T(\infty)$ with a time
constant $\tau_{tail}$. The scaled times $t_{osc}/t_D$ and $\tau_{tail}/t_D$
from all the data could be collapsed onto two curves as a function of the
Rayleigh number over $\sim$ 3.5 decades. Here $t_D$ is the characteristic
thermal diffusion time. Furthermore comparisons are made between measurements
of a third characteristic time $t_m$ between the first peak and the first
minimum in the $\Delta T(t)$ profile and its estimation by Onuki et al. Also
comparisons are made between the observed oscillations and the 2D simulations
by Onuki et al. and by Amiroudine and Zappoli. For $\epsilon < 9\times 10^{-3}$
the experiments show a crossover to a different transient regime. This new
regime, which we briefly describe, is not understood at present.
|
0209495v1
|
2004-10-14
|
Cold Strongly Coupled Atoms Make a Near-perfect Liquid
|
Feshbach resonances of trapped ultracold alkali atoms allow to vary the
atomic scattering length a. At very large values of a the system enters an
universal strongly coupled regime in which its properties--the ground state
energy, pressure {\it etc.}--become independent of a. We discuss transport
properties of such systems. In particular, the universality arguments imply
that the shear viscosity of ultracold Fermi atoms at the Feschbach resonance is
proportional to the particle number density n, and the Plank constant \hbar
\eta=\hbar n \alpha_\eta, where \alpha_\eta is a universal constant. Using
Heisenberg uncertainty principle and Einstein's relation between diffusion and
viscosity we argue that the viscosity has the lower bound given by
\alpha_{\eta} \leq (6\pi)^{-1}. We relate the damping of low-frequency density
oscillations of ultracold optically trapped ^{6}Li atoms to viscosity and find
that the value of the coefficient \alpha_\eta is about 0.3. We also show that
such a small viscosity can not be explained by kinetic theory based on binary
scattering. We conclude that the system of ultracold atoms near the Feshbach
resonance is a near-ideal liquid.
|
0410067v2
|
2004-09-24
|
Oscillator model for dissipative QED in an inhomogeneous dielectric
|
The Ullersma model for the damped harmonic oscillator is coupled to the
quantised electromagnetic field. All material parameters and interaction
strengths are allowed to depend on position. The ensuing Hamiltonian is
expressed in terms of canonical fields, and diagonalised by performing a
normal-mode expansion. The commutation relations of the diagonalising operators
are in agreement with the canonical commutation relations. For the proof we
replace all sums of normal modes by complex integrals with the help of the
residue theorem. The same technique helps us to explicitly calculate the
quantum evolution of all canonical and electromagnetic fields. We identify the
dielectric constant and the Green function of the wave equation for the
electric field. Both functions are meromorphic in the complex frequency plane.
The solution of the extended Ullersma model is in keeping with well-known
phenomenological rules for setting up quantum electrodynamics in an absorptive
and spatially inhomogeneous dielectric. To establish this fundamental
justification, we subject the reservoir of independent harmonic oscillators to
a continuum limit. The resonant frequencies of the reservoir are smeared out
over the real axis. Consequently, the poles of both the dielectric constant and
the Green function unite to form a branch cut. Performing an analytic
continuation beyond this branch cut, we find that the long-time behaviour of
the quantised electric field is completely determined by the sources of the
reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field
itself tends to zero, whereas its quantum fluctuations stay alive. We argue
that the last feature may have important consequences for application of
entanglement and related processes in quantum devices.
|
0409161v1
|
2007-07-30
|
Extended Quintessence with non-minimally coupled phantom scalar field
|
We investigate evolutional paths of an extended quintessence with a
non-minimally coupled phantom scalar field $\psi$ to the Ricci curvature. The
dynamical system methods are used to investigate typical regimes of dynamics at
the late time. We demonstrate that there are two generic types of evolutional
scenarios which approach the attractor (a focus or a node type critical point)
in the phase space: the quasi-oscillatory and monotonic trajectories approach
to the attractor which represents the FRW model with the cosmological constant.
We demonstrate that dynamical system admits invariant two-dimensional
submanifold and discussion that which cosmological scenario is realized depends
on behavior of the system on the phase plane $(\psi, \psi')$. We formulate
simple conditions on the value of coupling constant $\xi$ for which
trajectories tend to the focus in the phase plane and hence damping
oscillations around the mysterious value $w=-1$. We describe this condition in
terms of slow-roll parameters calculated at the critical point. We discover
that the generic trajectories in the focus-attractor scenario come from the
unstable node. It is also investigated the exact form of the parametrization of
the equation of state parameter $w(z)$ (directly determined from dynamics)
which assumes a different form for both scenarios.
|
0707.4471v2
|
2009-07-14
|
Nonlinear Schrödinger Equation with Spatio-Temporal Perturbations
|
We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger
Equation (NLSE) with the following perturbations: non-parametric
spatio-temporal driving of the form $f(x,t) = a \exp[i K(t) x]$, damping, and a
linear term which serves to stabilize the driven soliton. Using the time
evolution of norm, momentum and energy, or, alternatively, a Lagrangian
approach, we develop a Collective-Coordinate-Theory which yields a set of ODEs
for our four collective coordinates. These ODEs are solved analytically and
numerically for the case of a constant, spatially periodic force $f(x)$. The
soliton position exhibits oscillations around a mean trajectory with constant
velocity. This means that the soliton performs, on the average, a
unidirectional motion although the spatial average of the force vanishes. The
amplitude of the oscillations is much smaller than the period of $f(x)$. In
order to find out for which regions the above solutions are stable, we
calculate the time evolution of the soliton momentum $P(t)$ and soliton
velocity $V(t)$: This is a parameter representation of a curve $P(V)$ which is
visited by the soliton while time evolves. Our conjecture is that the soliton
becomes unstable, if this curve has a branch with negative slope. This
conjecture is fully confirmed by our simulations for the perturbed NLSE.
Moreover, this curve also yields a good estimate for the soliton lifetime: the
soliton lives longer, the shorter the branch with negative slope is.
|
0907.2438v2
|
2012-09-11
|
Macroscopic quantum tunneling of two coupled particles in the presence of a transverse magnetic field
|
Two coupled particles of identical masses but opposite charges, with a
constant transverse external magnetic field and an external potential,
interacting with a bath of harmonic oscillators are studied. We show that the
problem cannot be mapped to a one-dimensional problem like the one in Ref.
\cite{pa}, it strictly remains two-dimensional. We calculate the effective
action both for the case of linear coupling to the bath and without a linear
coupling using imaginary time path integral at finite temperature. At zero
temperature we use Leggett's prescription to derive the effective action. In
the limit of zero magnetic field we recover a two dimensional version of the
result derived in Ref. \cite{em1} for the case of two identical particles. We
find that in the limit of strong dissipation, the effective action reduces to a
two dimensional version of the Caldeira-Leggett form in terms of the reduced
mass and the magnetic field. The case of Ohmic dissipation with the motion of
the two particles damped by the Ohmic frictional constant $\eta$ is studied in
detail.
|
1209.2307v4
|
2013-08-28
|
On the evolution of the momentarily static radiation free data in the Apostolatos - Thorne cylindrical shell model
|
We study the evolution of the "Momentarily Static and Radiation Free" (MSRF)
initial data for the Apostolatos - Thorne cylindrical shell model. We analyze
the relation between the parameters characterizing the MSRF data those for the
corresponding final static configuration, and show that there is a priori no
conflict for any choice of initial MSRF data, in contrast with some recent
results of Nakao, Ida and Kurita. We also consider the problem in the linear
approximation, and show that the evolution is stable in all cases. We find that
the approach to the final state is very slow, with an inverse logarithmic
dependence on time at fixed radius. To complement these results we introduce a
numerical computation procedure that allows us to visualize the explicit form
of the evolution of the shell and of the gravitational field up to large times.
The results are in agreement with the qualitative behaviour conjectured by
Apostolatos and Thorne, with an initial damped oscillatory stage, but with
oscillations about a position that approaches slowly that of the static final
state, as indicated by our analysis. We also include an Appendix, where we
prove the existence of solutions of the cylindrical wave equation with
vanishing initial value for $r > R_0$, ($R_0 > 0$ some finite constant), that
approach a constant value for large times. This result is crucial for the proof
of compatibility of arbitrary MSRF initial data and a final static
configuration for the system.
|
1308.6296v1
|
2014-01-17
|
Co2FeAl Heusler thin films grown on Si and MgO substrates: annealing temperature effect
|
10 nm and 50 nm Co$_{2}$FeAl (CFA) thin films have been deposited on MgO(001)
and Si(001) substrates by magnetron sputtering and annealed at different
temperatures. X-rays diffraction revealed polycrystalline or epitaxial growth
(according to the relation CFA(001)[110]//MgO(001)[100] epitaxial relation),
respectively for CFA films grown on a Si and on a MgO substrate. For these
later, the chemical order varies from the A2 phase to the B2 phase when
increasing the annealing temperature (Ta) while only the A2 disorder type has
been observed for CFA grown on Si. Microstrip ferromagnetic resonance (MS-FMR)
measurements revealed that the in-plane anisotropy results from the
superposition of a uniaxial and of a fourfold symmetry term for CFA grown on
MgO substrates. This fourfold anisotropy, which disappears completely for
samples grown on Si, is in accord with the crystal structure of the samples.
The fourfold anisotropy field decreases when increasing Ta while the uniaxial
anisotropy field is nearly unaffected by Ta within the investigated range. The
MS-FMR data also allow for concluding that the gyromagnetic factor remains
constant and that the exchange stiffness constant increases with $T_{a}$.
Finally, the FMR linewidth decreases when increasing Ta, due to the enhancement
of the chemical order. We derive a very low intrinsic damping parameter
(1.3*10^-3 and 1.1*10^-3 for films of 50 nm thickness annealed at 615 {\deg}C
grown on MgO and on Si, respectively).
|
1401.4397v1
|
2014-02-04
|
Complete Tidal Evolution of Pluto-Charon
|
Both Pluto and its satellite Charon have rotation rates synchronous with
their orbital mean motion. This is the theoretical end point of tidal evolution
where transfer of angular momentum has ceased. Here we follow Pluto's tidal
evolution from an initial state having the current total angular momentum of
the system but with Charon in an eccentric orbit with semimajor axis $a \approx
4R_P$ (where $R_P$ is the radius of Pluto), consistent with its impact origin.
Two tidal models are used, where the tidal dissipation function $Q \propto$
1/frequency and $Q=$ constant, where details of the evolution are strongly
model dependent. The inclusion of the gravitational harmonic coefficient
$C_{22}$ of both bodies in the analysis allows smooth, self consistent
evolution to the dual synchronous state, whereas its omission frustrates
successful evolution in some cases. The zonal harmonic $J_2$ can also be
included, but does not cause a significant effect on the overall evolution. The
ratio of dissipation in Charon to that in Pluto controls the behavior of the
orbital eccentricity, where a judicious choice leads to a nearly constant
eccentricity until the final approach to dual synchronous rotation. The tidal
models are complete in the sense that every nuance of tidal evolution is
realized while conserving total angular momentum - including temporary capture
into spin-orbit resonances as Charon's spin decreases and damped librations
about the same.
|
1402.0625v1
|
2014-05-22
|
Tagged particle diffusion in one-dimensional systems with Hamiltonian dynamics - II
|
We study various temporal correlation functions of a tagged particle in
one-dimensional systems of interacting point particles evolving with
Hamiltonian dynamics. Initial conditions of the particles are chosen from the
canonical thermal distribution. The correlation functions are studied in finite
systems, and their forms examined at short and long times. Various
one-dimensional systems are studied. Results of numerical simulations for the
Fermi-Pasta-Ulam chain are qualitatively similar to results for the harmonic
chain, and agree unexpectedly well with a simple description in terms of
linearized equations for damped fluctuating sound waves. Simulation results for
the alternate mass hard particle gas reveal that - in contradiction to our
earlier results [1] with smaller system sizes - the diffusion constant slowly
converges to a constant value, in a manner consistent with mode coupling
theories. Our simulations also show that the behaviour of the Lennard-Jones gas
depends on its density. At low densities, it behaves like a hard-particle gas,
and at high densities like an anharmonic chain. In all the systems studied, the
tagged particle was found to show normal diffusion asymptotically, with
convergence times depending on the system under study. Finite size effects show
up at time scales larger than sound traversal times, their nature being
system-specific.
|
1405.5718v2
|
2014-09-01
|
Nitric Oxide as stress inducer and synchronizer of p53 dynamics
|
We study how the temporal behaviours of p53 and MDM2 are affected by stress
inducing bioactive molecules NO (Nitric Oxide) in the p53-MDM2-NO regulatory
network. We also study synchronization among a group of identical stress
systems arranged in a three dimensional array with nearest neighbour diffusive
coupling. The role of NO and effect of noise are investigated. In the single
system study, we have found three distinct types of temporal behaviour of p53,
namely, oscillation death, damped oscillation and sustain oscillation,
depending on the amount of stress induced by the NO concentration, indicating
how p53 responds to the incoming stress. The correlation among the coupled
systems increases as the value of coupling constant (\epsilon) is increased
(\gamma increases) and becomes constant after certain value of \epsilon. The
permutation entropy spectra H(\epsilon) for p53 and MDM2 as a function of
\epsilon are found to be different due to direct and indirect interaction of NO
with the respective proteins. \gamma versus \epsilon for p53 and MDM2 are found
to be similar in deterministic approach, but different in stochastic approach
and the separation between \gamma of the respective proteins as a function of
\epsilon decreases as system size increases. The role of NO is found to be
twofold: stress induced by it is prominent at small and large values of
\epsilon but synchrony inducing by it dominates in moderate range of \epsilon.
Excess stress induce apoptosis to the system.
|
1409.0528v1
|
2015-10-15
|
Markov Chain Analysis of Cumulative Step-size Adaptation on a Linear Constrained Problem
|
This paper analyzes a (1, $\lambda$)-Evolution Strategy, a randomized
comparison-based adaptive search algorithm, optimizing a linear function with a
linear constraint. The algorithm uses resampling to handle the constraint. Two
cases are investigated: first the case where the step-size is constant, and
second the case where the step-size is adapted using cumulative step-size
adaptation. We exhibit for each case a Markov chain describing the behaviour of
the algorithm. Stability of the chain implies, by applying a law of large
numbers, either convergence or divergence of the algorithm. Divergence is the
desired behaviour. In the constant step-size case, we show stability of the
Markov chain and prove the divergence of the algorithm. In the cumulative
step-size adaptation case, we prove stability of the Markov chain in the
simplified case where the cumulation parameter equals 1, and discuss steps to
obtain similar results for the full (default) algorithm where the cumulation
parameter is smaller than 1. The stability of the Markov chain allows us to
deduce geometric divergence or convergence , depending on the dimension,
constraint angle, population size and damping parameter, at a rate that we
estimate. Our results complement previous studies where stability was assumed.
|
1510.04409v1
|
2016-02-02
|
Planck constraints on scalar-tensor cosmology and the variation of the gravitational constant
|
Cosmological constraints on the scalar-tensor theory of gravity by analyzing
the angular power spectrum data of the cosmic microwave background (CMB)
obtained from the Planck 2015 results are presented. We consider the harmonic
attractor model, in which the scalar field has a harmonic potential with
curvature ($\beta$) in the Einstein frame and the theory relaxes toward the
Einstein gravity with time. Analyzing the {\it TT}, {\it EE}, {\it TE} and
lensing CMB data from Planck by the Markov chain Monte Carlo method, we find
that the present-day deviation from the Einstein gravity (${\alpha_0}^2$) is
constrained as ${\alpha_0}^2<2.5\times10^{-4-4.5\beta^2}\ (95.45\% {\rm\
C.L.})$ and ${\alpha_0}^2<6.3\times10^{-4-4.5\beta^2}\ (99.99\%\ {\rm C.L.})$
for $0<\beta<0.4$. The time variation of the effective gravitational constant
between the recombination and the present epochs is constrained as $G_{\rm
rec}/G_0<1.0056\ (95.45\% {\rm\ C.L.})$ and $G_{\rm rec}/G_0<1.0115\ (99.99
\%{\rm\ C.L.})$. We also find that the constraints are little affected by
extending to nonflat cosmological models because the diffusion damping effect
revealed by Planck breaks the degeneracy of the projection effect.
|
1602.00809v2
|
2016-05-06
|
Eisenhart lifts and symmetries of time-dependent systems
|
Certain dissipative systems, such as Caldirola and Kannai's damped simple
harmonic oscillator, may be modelled by time-dependent Lagrangian and hence
time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper
we treat these systems, their projective and conformal symmetries as well as
their quantisation from the point of view of the Eisenhart lift to a Bargmann
spacetime in $n+2$ dimensions, equipped with its covariantly constant null
Killing vector field. Reparametrization of the time variable corresponds to
conformal rescalings of the Bargmann metric. We show how the Arnold map lifts
to Bargmann spacetime. We contrast the greater generality of the
Caldirola-Kannai approach with that of Arnold and Bateman. At the level of
quantum mechanics, we are able to show how the relevant Schr\"odinger equation
emerges naturally using the techniques of quantum field theory in curved
spacetimes, since a covariantly constant null Killing vector field gives rise
to well defined one particle Hilbert space. Time-dependent Lagrangians arise
naturally also in cosmology and give rise to the phenomenon of Hubble friction.
We provide an account of this for Friedmann-Lemaitre and Bianchi cosmologies
and how it fits in with our previous discussion in the non-relativistic limit.
|
1605.01932v2
|
2016-05-24
|
Coherent magneto-elastic oscillations in superfluid magnetars
|
We study the effect of superfluidity on torsional oscillations of highly
magnetised neutron stars (magnetars) with a microphysical equation of state by
means of two-dimensional, magnetohydrodynamical- elastic simulations. The
superfluid properties of the neutrons in the neutron star core are treated in a
parametric way in which we effectively decouple part of the core matter from
the oscillations. Our simulations confirm the existence of two groups of
oscillations, namely continuum oscillations that are confined to the neutron
star core and are of Alfv\'enic character, and global oscillations with
constant phase and that are of mixed magneto-elastic type. The latter might
explain the quasi-periodic oscillations observed in magnetar giant flares,
since they do not suffer from the additional damping mechanism due to phase
mixing, contrary to what happens for continuum oscillations. However, we cannot
prove rigorously that the coherent oscillations with constant phase are normal
modes. Moreover, we find no crustal shear modes for the magnetic field
strengths typical for magnetars.We provide fits to our numerical simulations
that give the oscillation frequencies as functions of magnetic field strength
and proton fraction in the core.
|
1605.07638v1
|
2016-06-28
|
Negative stiffness and modulated states in active nematics
|
We examine the dynamics of a compressible active nematic liquid crystal on a
frictional substrate. When frictional damping dominates over viscous
dissipation, we eliminate flow in favor of active stresses to obtain a minimal
dynamical model for the nematic order parameter, with elastic constants
renormalized by activity. The renormalized elastic constants can become
negative at large activity, leading to the selection of spatially inhomogeneous
patterns via a mechanism analogous to that responsible for modulated phases
arising at an equilibrium Lifshitz point. Tuning activity and the degree of
nematic order in the passive system, we obtain a linear stability phase diagram
that exhibits a nonequilibrium tricritical point where ordered, modulated and
disordered phases meet. Numerical solution of the nonlinear equations yields a
succession of spatial structures of increasing complexity with increasing
activity, including kink walls and active turbulence, as observed in
experiments on microtubule bundles confined at an oil-water interface. Our work
provides a minimal model for an overdamped active nematic that reproduces all
the nonequilibrium structures seen in simulations of the full active nematic
hydrodynamics and provides a framework for understanding some of the mechanisms
for selection of the nonequilibrium patterns in the language of equilibrium
critical phenomena.
|
1606.08786v2
|
2017-03-11
|
Magnonic crystals - prospective structures for shaping spin waves in nanoscale
|
We have investigated theoretically band structure of spin waves in magnonic
crystals with periodicity in one-(1D), two- (2D) and three-dimensions (3D). We
have solved Landau-Lifshitz equation with the use of plane wave method, finite
element method in frequency domain and micromagnetic simulations in time domain
to find the dynamics of spin waves and spectrum of their eigenmodes. The spin
wave spectra were calculated in linear approximation. In this paper we show
usefulness of these methods in calculations of various types of spin waves. We
demonstrate the surface character of the Damon-Eshbach spin wave in 1D magnonic
crystals and change of its surface localization with the band number and
wavenumber in the first Brillouin zone. The surface property of the spin wave
excitation is further exploited by covering plate of the magnonic crystal with
conductor. The band structure in 2D magnonic crystals is complex due to
additional spatial inhomogeneity introduced by the demagnetizing field. This
modifies spin wave dispersion, makes the band structure of magnonic crystals
strongly dependent on shape of the inclusions and type of the lattice. The
inhomogeneity of the internal magnetic field becomes unimportant for magnonic
crystals with small lattice constant, where exchange interactions dominate. For
3D magnonic crystals, characterized by small lattice constant, wide magnonic
band gap is found. We show that the spatial distribution of different materials
in magnonic crystals can be explored for tailored effective damping of spin
waves.
|
1703.04012v1
|
2018-02-17
|
Superconductivity induced by flexural modes in non $σ_{\rm h}$-symmetric Dirac-like two-dimensional materials: A theoretical study for silicene and germanene
|
In two-dimensional crystals that lack symmetry under reflections on the
horizontal plane of the lattice (non-$\sigma_{\rm h}$-symmetric), electrons can
couple to flexural modes (ZA phonons) at first order. We show that in materials
of this type that also exhibit a Dirac-like electron dispersion, the strong
coupling can result in electron pairing mediated by these phonons, as long as
the flexural modes are not damped or suppressed by additional interactions with
a supporting substrate or gate insulator. We consider several models: The
weak-coupling limit, which is applicable only in the case of gapped and
parabolic materials, like stanene and HfSe$_{2}$, thanks to the weak coupling;
the full gap-equation, solved using the constant-gap approximation and
considering statically screened interactions; its extensions to
energy-dependent gap and to dynamic screening. We argue that in the case of
silicene and germanene superconductivity mediated by this process can exhibit a
critical temperature of a few degrees K, or even a few tens of degrees K when
accounting for the effect of a high-dielectric-constant environment. We
conclude that the electron/flexural-modes coupling should be included in
studies of possible superconductivity in non-$\sigma_{\rm h}$-symmetric
two-dimensional crystals, even if alternative forms of coupling are considered.
|
1802.06272v1
|
2019-04-29
|
A nonlinear subgrid-scale model for large-eddy simulations of rotating turbulent flows
|
Rotating turbulent flows form a challenging test case for large-eddy
simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS)
model for such flows. The proposed SGS model consists of a dissipative eddy
viscosity term as well as a nondissipative term that is nonlinear in the
rate-of-strain and rate-of-rotation tensors. The two corresponding model
coefficients are a function of the vortex stretching magnitude. Therefore, the
model is consistent with many physical and mathematical properties of the
Navier-Stokes equations and turbulent stresses, and is easy to implement. We
determine the two model constants using a nondynamic procedure that takes into
account the interaction between the model terms. Using detailed direct
numerical simulations (DNSs) and LESs of rotating decaying turbulence and
spanwise-rotating plane-channel flow, we reveal that the two model terms
respectively account for dissipation and backscatter of energy, and that the
nonlinear term improves predictions of the Reynolds stress anisotropy near
solid walls. We also show that the new SGS model provides good predictions of
rotating decaying turbulence and leads to outstanding predictions of
spanwise-rotating plane-channel flow over a large range of rotation rates for
both fine and coarse grid resolutions. Moreover, the new nonlinear model
performs as well as the dynamic Smagorinsky and scaled anisotropic
minimum-dissipation models in LESs of rotating decaying turbulence and
outperforms these models in LESs of spanwise-rotating plane-channel flow,
without requiring (dynamic) adaptation or near-wall damping of the model
constants.
|
1904.12748v1
|
2020-04-03
|
Probing modified gravity theories and cosmology using gravitational-waves and associated electromagnetic counterparts
|
The direct detection of gravitational waves by the LIGO-Virgo collaboration
has opened a new window with which to measure cosmological parameters such as
the Hubble constant $H_0$, and also probe general relativity on large scales.
In this paper we present a new phenomenological approach, together with its
inferencial implementation, for measuring deviations from general relativity
(GR) on cosmological scales concurrently with a determination of $H_0$. We
consider gravitational waves (GWs) propagating in an expanding homogeneous and
isotropic background, but with a modified friction term and dispersion relation
relative to that of GR. We find that a single binary neutron star GW detection
will poorly constrain the GW friction term. However, a joint analysis including
the GW phase and GW-GRB detection delay could improve constraints on some GW
dispersion relations provided the delay is measured with millisecond precision.
We also show that, for massive gravity, by combining 100 binary neutron stars
detections with observed electromagnetic counterparts and hosting galaxy
identification, we will be able to constrain the Hubble constant, the GW
damping term and the GW dispersion relation with 2\%, 15\% and 2 \% accuracy,
respectively. We emphasise that these three parameters should be measured
together in order avoid biases. Finally we apply the method to GW170817, and
demonstrate that for all the GW dispersions relations we consider, including
massive gravity, the GW must be emitted $\sim$ 1.74s before the Gamma-ray burst
(GRB). Furthermore, at the GW merger peak frequency, we show that the
fractional difference between the GW group velocity and $c$ is $\lesssim
10^{-17}$.
|
2004.01632v2
|
2021-08-18
|
Velocity auto correlation function of a confined Brownian particle
|
Motivated by the simple models of molecular motor obeying a linear
force-velocity relation, we have studied the stochastic dynamics of a Brownian
particle in the presence of a linear velocity dependent force,
$f_s(1-\frac{v}{v_0})$ where $f_{s}$ is a constant. The position and velocity
auto correlation functions in different situations of the dynamics are
calculated exactly. We observed that the velocity auto correlation function
shows an exponentially decaying behaviour with time and saturates to a constant
value in the time asymptotic limit, for a fixed $f_s$. It attains saturation
faster with increase in the $f_{s}$ value. When the particle is confined in a
harmonic well, the spectral density exhibits a symmetric behaviour and the
corresponding velocity auto correlation function shows a damped oscillatory
behaviour before decaying to zero in the long time limit. With viscous
coefficient, a non-systematic variation of the velocity auto correlation
function is observed. Further, in the presence of a sinusoidal driving force,
the correlation in velocities increases with increase in the amplitude of
driving in the transient regime. For the particle confined in a harmonic well,
the correlation corresponding to the shift relative to the average position is
basically the thermal contribution to the total position correlation. Moreover,
in the athermal regime, the total correlation is entirely due to the velocity
dependent force.
|
2108.07922v1
|
2021-12-21
|
Fast long-wavelength exchange spin waves in partially-compensated Ga:YIG
|
Spin waves in yttrium iron garnet (YIG) nano-structures attract increasing
attention from the perspective of novel magnon-based data processing
applications. For short wavelengths needed in small-scale devices, the group
velocity is directly proportional to the spin-wave exchange stiffness constant
$\lambda_\mathrm{ex}$. Using wave vector resolved Brillouin Light Scattering
(BLS) spectroscopy, we directly measure $\lambda_\mathrm{ex}$ in Ga-substituted
YIG thin films and show that it is about three times larger than for pure YIG.
Consequently, the spin-wave group velocity overcomes the one in pure YIG for
wavenumbers $k > 4$ rad/$\mu$m, and the ratio between the velocities reaches a
constant value of around 3.4 for all $k > 20$ rad/$\mu$m. As revealed by
vibrating-sample magnetometry (VSM) and ferromagnetic resonance (FMR)
spectroscopy, Ga:YIG films with thicknesses down to 59 nm have a low Gilbert
damping ($\alpha < 10^{-3}$), a decreased saturation magnetization $\mu_0
M_\mathrm{S}~\approx~20~$mT and a pronounced out-of-plane uniaxial anisotropy
of about $\mu_0 H_{\textrm{u1}} \approx 95 $ mT which leads to an out-of-plane
easy axis. Thus, Ga:YIG opens access to fast and isotropic spin-wave transport
for all wavelengths in nano-scale systems independently of dipolar effects.
|
2112.11348v1
|
2022-04-11
|
Forecast and backcast of the solar cycles
|
Solar cycle is modeled as a forced and damped harmonic oscillator and the
amplitudes, frequencies, phases and decay factors of such a harmonic oscillator
are estimated by non-linear fitting the equation of sinusoidal and transient
parts to the sunspot and irradiance (proxy for the sunspot) data for the years
1700-2008. We find that:(i) amplitude and frequency (or period of $\sim$11 yr)
of the sinusoidal part remain constant for all the solar cycles; (ii) the
amplitude of the transient part is phase locked with the phase of the
sinusoidal part; (iii) for all the cycles, the period and decay factor (that is
much less than 1) of the transient part remain approximately constant. The
constancy of the amplitudes and the frequencies of the sinusoidal part and a
very small decay factor from the transient part suggests that the solar
activity cycle mainly consists of a persistent oscillatory part that might be
compatible with long-period ($\sim$22 yr) Alfven oscillations. For all the
cycles, with the estimated physical parameters (amplitudes, phases and periods)
and, by an autoregressive model, we forecast (especially for coming solar cycle
25) and backcast (to check whether Maunder minimum type solar activity exists
or not) the solar cycles. We find that amplitude of coming solar cycle 25 is
almost same as the amplitude of the previous solar cycle 24. We also find that
sun might not have experienced a deep Maunder minimum (MM) type of activity
during 1645-1700 AD corroborating some of the paleoclimatic inferences and, MM
type of activity will not be imminent in near future, until at least 200 years.
|
2204.04818v1
|
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