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2019-05-20
|
Quantum parameter-estimation of frequency and damping of a harmonic-oscillator
|
We determine the quantum Cram\'er-Rao bound for the precision with which the
oscillator frequency and damping constant of a damped quantum harmonic
oscillator in an arbitrary Gaussian state can be estimated. This goes beyond
standard quantum parameter estimation of a single mode Gaussian state for which
typically a mode of fixed frequency is assumed. We present a scheme through
which the frequency estimation can nevertheless be based on the known results
for single-mode quantum parameter estimation with Gaussian states. Based on
these results, we investigate the optimal measurement time. For measuring the
oscillator frequency, our results unify previously known partial results and
constitute an explicit solution for a general single-mode Gaussian state.
Furthermore, we show that with existing carbon nanotube resonators (see J.
Chaste et al.~Nature Nanotechnology 7, 301 (2012)) it should be possible to
achieve a mass sensitivity of the order of an electron mass $\text{Hz}^{-1/2}$.
|
1905.08288v1
|
2019-11-08
|
Giant anisotropy of Gilbert damping in a Rashba honeycomb antiferromagnet
|
Giant Gilbert damping anisotropy is identified as a signature of strong
Rashba spin-orbit coupling in a two-dimensional antiferromagnet on a honeycomb
lattice. The phenomenon originates in spin-orbit induced splitting of
conduction electron subbands that strongly suppresses certain spin-flip
processes. As a result, the spin-orbit interaction is shown to support an
undamped non-equilibrium dynamical mode that corresponds to an ultrafast
in-plane N\'eel vector precession and a constant perpendicular-to-the-plane
magnetization. The phenomenon is illustrated on the basis of a two dimensional
$s$-$d$ like model. Spin-orbit torques and conductivity are also computed
microscopically for this model. Unlike Gilbert damping these quantities are
shown to reveal only a weak anisotropy that is limited to the semiconductor
regime corresponding to the Fermi energy staying in a close vicinity of
antiferromagnetic gap.
|
1911.03408v1
|
2020-03-25
|
Sharp ultimate velocity bounds for the general solution of some linear second order evolution equation with damping and bounded forcing
|
We consider a class of linear second order differential equations with
damping and external force. We investigate the link between a uniform bound on
the forcing term and the corresponding ultimate bound on the velocity of
solutions, and we study the dependence of that bound on the damping and on the
"elastic force".
We prove three results. First of all, in a rather general setting we show
that different notions of bound are actually equivalent. Then we compute the
optimal constants in the scalar case. Finally, we extend the results of the
scalar case to abstract dissipative wave-type equations in Hilbert spaces. In
that setting we obtain rather sharp estimates that are quite different from the
scalar case, in both finite and infinite dimensional frameworks.
The abstract theory applies, in particular, to dissipative wave, plate and
beam equations.
|
2003.11579v1
|
2020-08-18
|
Survey of 360$^{\circ}$ domain walls in magnetic heterostructures: topology, chirality and current-driven dynamics
|
Chirality and current-driven dynamics of topologically nontrivial
360$^{\circ}$ domain walls (360DWs) in magnetic heterostructures (MHs) are
systematically investigated. For MHs with normal substrates, the static 360DWs
are N\'{e}el-type with no chirality. While for those with heavy-metal
substrates, the interfacial Dzyaloshinskii-Moriya interaction (iDMI) therein
makes 360DWs prefer specific chirality. Under in-plane driving charge currents,
as the direct result of "full-circle" topology a certain 360DW does not undergo
the "Walker breakdown"-type process like a well-studied 180$^{\circ}$ domain
wall as the current density increases. Alternatively, it keeps a fixed
propagating mode (either steady-flow or precessional-flow, depending on the
effective damping constant of the MH) until it collapses or changes to other
types of solition when the current density becomes too high. Similarly, the
field-like spin-orbit torque (SOT) has no effects on the dynamics of 360DWs,
while the anti-damping SOT has. For both modes, modifications to the mobility
of 360DWs by iDMI and anti-damping SOT are provided.
|
2008.08196v1
|
2021-11-26
|
Transition from order to chaos in reduced quantum dynamics
|
We study a damped kicked top dynamics of a large number of qubits ($N
\rightarrow \infty$) and focus on an evolution of a reduced single-qubit
subsystem. Each subsystem is subjected to the amplitude damping channel
controlled by the damping constant $r\in [0,1]$, which plays the role of the
single control parameter. In the parameter range for which the classical
dynamics is chaotic, while varying $r$ we find the universal period-doubling
behavior characteristic to one-dimensional maps: period-two dynamics starts at
$r_1 \approx 0.3181$, while the next bifurcation occurs at $ r_2 \approx
0.5387$. In parallel with period-four oscillations observed for $r \leq r_3
\approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx
0.544$, responsible for a small-scale chaotic dynamics inside the attractor.
The doubling of the principal bifurcation tree continues until $r \leq
r_{\infty} \sim 0.578$, which marks the onset of the full scale chaos
interrupted by the windows of the oscillatory dynamics corresponding to the
Sharkovsky order.
|
2111.13477v1
|
2022-01-12
|
Local Well-Posedness of the Gravity-Capillary Water Waves System in the Presence of Geometry and Damping
|
We consider the gravity-capillary water waves problem in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features.
Namely, we consider a variable bottom, smooth obstacles in the flow and a
constant background current. We utilize a vortex sheet model introduced by
Ambrose, et. al. in arXiv:2108.01786. We show that the water waves problem is
locally-in-time well-posed in this geometric setting and study the lifespan of
solutions. We then add a damping term and derive evolution equations that
account for the damper. Ultimately, we show that the same well-posedness and
lifespan results apply to the damped system. We primarily utilize energy
methods.
|
2201.04713v2
|
2023-05-09
|
Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain
|
Lifespan estimates for semilinear damped wave equations of the form
$\partial_t^2u-\Delta u+\partial_tu=|u|^p$ in a two dimensional exterior domain
endowed with the Dirichlet boundary condition are dealt with. For the critical
case of the semilinear heat equation $\partial_tv-\Delta v=v^2$ with the
Dirichlet boundary condition and the initial condition $v(0)=\varepsilon f$,
the corresponding lifespan can be estimated from below and above by
$\exp(\exp(C\varepsilon^{-1}))$ with different constants $C$. This paper
clarifies that the same estimates hold even for the critical semilinear damped
wave equation in the exterior of the unit ball under the restriction of radial
symmetry. To achieve this result, a new technique to control $L^1$-type norm
and a new Gagliardo--Nirenberg type estimate with logarithmic weight are
introduced.
|
2305.05124v1
|
2023-09-25
|
Linearly implicit exponential integrators for damped Hamiltonian PDEs
|
Structure-preserving linearly implicit exponential integrators are
constructed for Hamiltonian partial differential equations with linear constant
damping. Linearly implicit integrators are derived by polarizing the polynomial
terms of the Hamiltonian function and portioning out the nonlinearly of
consecutive time steps. They require only a solution of one linear system at
each time step. Therefore they are computationally more advantageous than
implicit integrators. We also construct an exponential version of the
well-known one-step Kahan's method by polarizing the quadratic vector field.
These integrators are applied to one-dimensional damped Burger's,
Korteweg-de-Vries, and nonlinear Schr{\"o}dinger equations. Preservation of the
dissipation rate of linear and quadratic conformal invariants and the
Hamiltonian is illustrated by numerical experiments.
|
2309.14184v2
|
2024-03-10
|
Linear-in-temperature resistivity and Planckian dissipation arise in a stochastic quantization model of Cooper pairs
|
We suppose that a Cooper pair (CP) will experience a damping force exerted by
the condensed matter. A Langevin equation of a CP in two dimensional condensed
matter is established. Following a method similar to Nelson's stochastic
mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is
derived. If the CPs move with a constant velocity, then the corresponding
direct current (DC) electrical conductivity can be calculated. Therefore, a
Drude like formula of resistivity of CPs is derived. We suppose that the
damping coefficient of CPs in two dimensional cuprate superconductors is a
linear function of temperature. Then the resistivity and scattering rate of CPs
turn out to be also linear-in-temperature. The origin of linear-in-temperature
resistivity and Planckian dissipation in cuprate superconductors may be the
linear temperature dependence of the damping coefficient of CPs.
|
2403.09710v1
|
2018-07-31
|
Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
|
Relaxation effects are of primary importance in the description of magnetic
excitations, leading to a myriad of methods addressing the phenomenological
damping parameters. In this work, we consider several well-established forms of
calculating the intrinsic Gilbert damping within a unified theoretical
framework, mapping out their connections and the approximations required to
derive each formula. This scheme enables a direct comparison of the different
methods on the same footing and a consistent evaluation of their range of
validity. Most methods lead to very similar results for the bulk ferromagnets
Fe, Co and Ni, due to the low spin-orbit interaction strength and the absence
of the spin pumping mechanism. The effects of inhomogeneities, temperature and
other sources of finite electronic lifetime are often accounted for by an
empirical broadening of the electronic energy levels. We show that the
contribution to the damping introduced by this broadening is additive, and so
can be extracted by comparing the results of the calculations performed with
and without spin-orbit interaction. Starting from simulated ferromagnetic
resonance spectra based on the underlying electronic structure, we
unambiguously demonstrate that the damping parameter obtained within the
constant broadening approximation diverges for three-dimensional bulk magnets
in the clean limit, while it remains finite for monolayers. Our work puts into
perspective the several methods available to describe and compute the Gilbert
damping, building a solid foundation for future investigations of magnetic
relaxation effects in any kind of material.
|
1807.11808v3
|
2019-11-05
|
Observation of Nanoscale Opto-Mechanical Molecular Damping; Origin of Spectroscopic Contrast in Photo Induced Force Microscopy
|
We experimentally investigated the contrast mechanism of infrared
photoinduced force microscopy (PiFM) for recording vibrational resonances.
Extensive experiments have demonstrated that spectroscopic contrast in PiFM is
mediated by opto-mechanical damping of the cantilever oscillation as the
optical wavelength is scanned through optical resonance. To our knowledge, this
is the first time opto-mechanical damping has been observed in the AFM. We
hypothesize that this damping force is a consequence of the dissipative
interaction between the sample and the vibrating tip; the modulated light
source in PiFM modulates the effective damping constant of the 2nd eigenmode of
the cantilever which in turn generate side-band signals producing the PiFM
signal at the 1st eigenmode. A series of experiments have eliminated other
mechanisms of contrast. By tracking the frequency shift of the PiFM signal at
the 1st cantilever eigenmode as the excitation wavenumber is tuned through a
mid-infrared absorption band, we showed that the near-field optical interaction
is attractive. By using a vibrating piezoelectric crystal to mimic sample
thermal expansion in a PiFM operating in mixing mode, we determined that the
minimum thermal expansion our system can detect is 30 pm limited by system
noise. We have confirmed that van der Waal mediated thermal-expansion forces
have negligible effect on PiFM signals by detecting the resonant response of a
4-methylbenzenethiol mono molecular layer deposited on template-stripped gold,
where thermal expansion was expected to be < 3 pm, i.e., 10 times lower than
our system noise level. Finally, the basic theory for dissipative tip-sample
interactions was introduced to model the photoinduced opto-mechanical damping.
Theoretical simulations are in excellent agreement with experiment.
|
1911.05190v1
|
2024-03-28
|
Constants of Motion for Conserved and Non-conserved Dynamics
|
This paper begins with a dynamical model that was obtained by applying a
machine learning technique (FJet) to time-series data; this dynamical model is
then analyzed with Lie symmetry techniques to obtain constants of motion. This
analysis is performed on both the conserved and non-conserved cases of the 1D
and 2D harmonic oscillators. For the 1D oscillator, constants are found in the
cases where the system is underdamped, overdamped, and critically damped. The
novel existence of such a constant for a non-conserved model is interpreted as
a manifestation of the conservation of energy of the {\em total} system (i.e.,
oscillator plus dissipative environment). For the 2D oscillator, constants are
found for the isotropic and anisotropic cases, including when the frequencies
are incommensurate; it is also generalized to arbitrary dimensions. In
addition, a constant is identified which generalizes angular momentum for all
ratios of the frequencies. The approach presented here can produce {\em
multiple} constants of motion from a {\em single}, generic data set.
|
2403.19418v1
|
2003-06-30
|
Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces
|
We study the boundedness problem for maximal operators in 3-dimensional
Euclidean space associated to hypersurfaces given as the graph of $c+f$, where
$f$ is a mixed homogeneous function which is smooth away from the origin and
$c$ is a constant. Our result generalizes a corresponding theorem on mixed
homogeneous polynomial functions by A. Iosevich and E. Sawyer.
|
0306429v1
|
2005-07-26
|
On simulations of the classical harmonic oscillator equation by difference equations
|
We show that any second order linear ordinary diffrential equation with
constant coefficients (including the damped and undumped harmonic oscillator
equation) admits an exact discretization, i.e., there exists a difference
equation whose solutions exactly coincide with solutions of the corresponding
differential equation evaluated at a discrete sequence of points (a lattice).
Such exact discretization is found for an arbitrary lattice spacing.
|
0507182v1
|
2012-09-08
|
Evidence for anisotropic polar nanoregions in relaxor PMN: A neutron study of the elastic constants and anomalous TA phonon damping
|
We use neutron scattering to characterize the acoustic phonons in the relaxor
PMN and demonstrate the presence of an anisotropic damping mechanism directly
related to short-range, polar correlations. For a large range of temperatures
above Tc ~ 210, K, where dynamic polar correlations exist, acoustic phonons
propagating along [1\bar{1}0] and polarized along [110] (TA2 phonons) are
overdamped and softened across most of the Brillouin zone. By contrast,
acoustic phonons propagating along [100] and polarized along [001] (TA1
phonons) are overdamped and softened for only a limited range of wavevectors.
The anisotropy and temperature dependence of the acoustic phonon energy
linewidth are directly correlated with the elastic diffuse scattering,
indicating that polar nanoregions are the cause of the anomalous behavior. The
damping and softening vanish for q -> 0, i.e. for long-wavelength acoustic
phonons, which supports the notion that the anomalous damping is a result of
the coupling between the relaxational component of the diffuse scattering and
the harmonic TA phonons. Therefore, these effects are not due to large changes
in the elastic constants with temperature because the elastic constants
correspond to the long-wavelength limit. We compare the elastic constants we
measure to those from Brillouin scattering and to values reported for pure PT.
We show that while the values of C44 are quite similar, those for C11 and C12
are significantly less in PMN and result in a softening of (C11-C12) over PT.
There is also an increased elastic anisotropy (2C44/(C11-C12)) versus that in
PT. These results suggest an instability to TA2 acoustic fluctuations in
relaxors. We discuss our results in the context of the debate over the
"waterfall" effect and show that they are inconsistent with TA-TO phonon
coupling or other models that invoke the presence of a second optic mode.
|
1209.1736v1
|
2015-11-12
|
Global weak solutions to 3D compressible Navier-Stokes-Poisson equations with density-dependent viscosity
|
Global-in-time weak solutions to the Compressible Navier-Stokes-Poisson
equations in a three-dimensional torus for large data are considered in this
paper. The system takes into account density-dependent viscosity and
non-monotone presseur. We prove the existence of global weak solutions to NSP
equations with damping term by using the Faedo-Galerkin method and the
compactness arguments on the condition that the adiabatic constant satisfies
$\gamma>\frac{4}{3}$.
|
1511.03841v1
|
2015-12-03
|
Lieb-Thirring inequalities on the torus
|
We consider the Lieb-Thirring inequalities on the d-dimensional torus with
arbitrary periods. In the space of functions with zero average with respect to
the shortest coordinate we prove the Lieb-Thirring inequalities for the
$\gamma$-moments of the negative eigenvalues with constants independent of
ratio of the periods. Applications to the attractors of the damped
Navier-Stokes system are given.
|
1512.01160v1
|
2017-09-24
|
Exceptional points in two simple textbook examples
|
We propose to introduce the concept of exceptional points in intermediate
courses on mathematics and classical mechanics by means of simple textbook
examples. The first one is an ordinary second-order differential equation with
constant coefficients. The second one is the well known damped harmonic
oscillator. They enable one to connect the occurrence of linearly dependent
exponential solutions with a defective matrix that cannot be diagonalized but
can be transformed into a Jordan canonical form.
|
1710.00067v1
|
2021-07-21
|
Convergence rates for the Heavy-Ball continuous dynamics for non-convex optimization, under Polyak-Łojasiewicz condition
|
We study convergence of the trajectories of the Heavy Ball dynamical system,
with constant damping coefficient, in the framework of convex and non-convex
smooth optimization. By using the Polyak-{\L}ojasiewicz condition, we derive
new linear convergence rates for the associated trajectory, in terms of
objective function values, without assuming uniqueness of the minimizer.
|
2107.10123v2
|
2022-05-06
|
Quaternion-based attitude stabilization via discrete-time IDA-PBC
|
In this paper, we propose a new sampled-data controller for stabilization of
the attitude dynamics at a desired constant configuration. The design is based
on discrete-time interconnection and damping assignment (IDA) passivity-based
control (PBC) and the recently proposed Hamiltonian representation of
discrete-time nonlinear dynamics. Approximate solutions are provided with
simulations illustrating performances.
|
2205.03086v1
|
2024-04-03
|
Comment on "Machine learning conservation laws from differential equations"
|
In lieu of abstract, first paragraph reads: Six months after the author
derived a constant of motion for a 1D damped harmonic oscillator [1], a similar
result appeared by Liu, Madhavan, and Tegmark [2, 3], without citing the
author. However, their derivation contained six serious errors, causing both
their method and result to be incorrect. In this Comment, those errors are
reviewed.
|
2404.02896v1
|
2003-03-13
|
Vibrational sidebands and dissipative tunneling in molecular transistors
|
Transport through molecular devices with strong coupling to a single
vibrational mode is considered in the case where the vibration is damped by
coupling to the environment. We focus on the weak tunneling limit, for which a
rate equation approach is valid. The role of the environment can be
characterized by a frictional damping term $\mysig(\omega)$ and corresponding
frequency shift. We consider a molecule that is attached to a substrate,
leading to frequency-dependent frictional damping of the single oscillator mode
of the molecule, and compare it to a reference model with frequency-independent
damping featuring a constant quality factor $Q$. For large values of $Q$, the
transport is governed by tunneling between displaced oscillator states giving
rise to the well-known series of the Frank-Condon steps, while at small $Q$,
there is a crossover to the classical regime with an energy gap given by the
classical displacement energy. Using realistic values for the elastic
properties of the substrate and the size of the molecule, we calculate $I$-$V$
curves and find qualitative agreement between our theory and recent experiments
on $C_{60}$ single-molecule devices.
|
0303236v3
|
2001-01-16
|
Nonlinear Landau damping of a plasmino in the quark-gluon plasma
|
On the basis of the Blaizot-Iancu equations, which are a local formulation of
the hard thermal loop (HTL) equations of motion for soft fluctuating quark and
gluon fields and their induced sources, the coupled kinetic equations for
plasminos and plasmons are obtained. The equality of matrix elements for
nonlinear scattering of a plasmino by hard particles in covariant and temporal
gauges is established by using effective Ward identities. The model problem of
the interaction of two infinitely narrow packets with fermion and boson quantum
numbers is considered. The kinematical relations between wave vectors of the
plasmino and plasmon are derived, when the effective pumping over of the plasma
excitation energy from the fermion branch of plasma excitations to the boson
branch and vice versa occur. The expression for the nonlinear Landau damping
rate of a plasmino at rest is found, and a comparison with a plasmino damping
constant obtained within the framework of the hard thermal loop approximation
is made. The nonlinear Landau damping rate for normal quark excitations is
shown to diverge like $1/\sqrt{q^2}$ near the light cone where $q$ is a
four-momentum of excitations, and the improved Blaizot-Iancu equations removing
this divergence are proposed.
|
0101167v2
|
2005-10-21
|
Non-contact atomic force microscopy: Stability criterion and dynamical responses of the shift of frequency and damping signal
|
The aim of this article is to provide a complete analysis of the behavior of
a noncontact atomic force microscope (NC-AFM). We start with a review of the
equations of motion of a tip interacting with a surface in which the stability
conditions are first revisited for tapping mode. Adding the equations of
automatic gain control (AGC), which insures constant amplitude of the
oscillations in the NC-AFM, to the equations of motion of the tip, a new
analytical stability criterion that involves proportional and integral gains of
AGC is deduced. Stationary solutions for the shift of frequency and for the
damping signal are obtained. Special attention is paid to the damping signal in
order to clarify its physical origin. The theoretical results are then compared
to those given by a virtual machine. The virtual machine is a set of equations
solved numerically without any approximation. The virtual machine is of great
help in understanding the dynamical behavior of the NC-AFM as images are
recorded. Transient responses of the shift in frequency and of the damping
signal are discussed in relation to the values of proportional and integral
gains of AGC.
|
0510192v1
|
2008-06-09
|
Relaxation Time and Relaxation Function of Quark-Gluon Plasma with Lattice QCD
|
We propose a method which enables a QCD-based calculation of a relaxation
time for a dissipative current in the causal and dissipative hydrodynamic
equation derived by Israel and Stewart. We point out that the Israel-Stewart
equation is not unique as a causal and dissipative hydrodynamic equation, and
the form of the causal and dissipative hydrodynamic equation is determined by
the shape of a spectral function reflecting the properties of elementary
excitations in the system we consider. Our method utilizes a relaxation
function, which can be calculated from QCD using the linear response theory. We
show that the relaxation function can be derived from a spectral function for a
microscopic representation of the dissipative current. We also show that the
Israel-Stewart equation is acceptable only as long as the calculated relaxation
function is approximated well by a exponentially damping function, and the
relaxation time can be obtained as its damping time constant. Taking a
baryon-number dissipative current of a plasma consisting of charm quarks and
gluons as a simple example, we present the first calculation of the relaxation
function with use of the spectral function derived employing the quenched
lattice QCD together with the maximum entropy method. The calculated relaxation
function shows a strongly-oscillation damping behaviour due to the charmed
vector hadron $J/\Psi$ surviving above the deconfinement phase transition
temperature in QCD. This result suggests that the applicability of the
Israel-Stewart equation to the baryon-number dissipative current of the charm
quark-gluon plasma is quite doubtful. We present an idea for the improvement of
the Israel-Stewart equation by deriving the hydrodynamic equation consistent
with the strongly-oscillation damping relaxation function.
|
0806.1481v1
|
2018-02-18
|
On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation
|
We develop a provably energy stable discontinuous Galerkin spectral element
method (DGSEM) approximation of the perfectly matched layer (PML) for the three
and two space dimensional (3D and 2D) linear acoustic wave equations, in first
order form, subject to well-posed linear boundary conditions. First, using the
well-known complex coordinate stretching, we derive an efficient un-split modal
PML for the 3D acoustic wave equation. Second, we prove asymptotic stability of
the continuous PML by deriving energy estimates in the Laplace space, for the
3D PML in a heterogeneous acoustic medium, assuming piece-wise constant PML
damping. Third, we develop a DGSEM for the wave equation using physically
motivated numerical flux, with penalty weights, which are compatible with all
well-posed, internal and external, boundary conditions. When the PML damping
vanishes, by construction, our choice of penalty parameters yield an upwind
scheme and a discrete energy estimate analogous to the continuous energy
estimate. Fourth, to ensure numerical stability when PML damping is present, it
is necessary to systematically extend the numerical numerical fluxes, and the
inter-element and boundary procedures, to the PML auxiliary differential
equations. This is critical for deriving discrete energy estimates analogous to
the continuous energy estimates. Finally, we propose a procedure to compute PML
damping coefficients such that the PML error converges to zero, at the optimal
convergence rate of the underlying numerical method. Numerical experiments are
presented in 2D and 3D corroborating the theoretical results.
|
1802.06388v1
|
2018-11-15
|
Damping rate of a fermion in ultradegenerate chiral matter
|
We compute the damping rate of a fermion propagating in a chiral plasma when
there is an imbalance between the densities of left- and right-handed fermions,
after generalizing the hard thermal loop resummation techniques for these
systems. In the ultradegenerate limit, for very high energies the damping rate
of this external fermion approaches a constant value. Closer to the two Fermi
surfaces, however, we find that the rate depends on both the energy and the
chirality of the fermion, being higher for the predominant chirality. This
comes out as a result of its scattering with the particles of the plasma,
mediated by the exchange of Landau damped photons. In particular, we find that
the chiral imbalance is responsible for a different propagation of the left and
right circular polarised transverse modes of the photon, and that a chiral
fermion interacts differently with these two transverse modes. We argue that
spontaneous radiation of energetic fermions is kinematically forbidden, and
discuss the time regime where our computation is valid.
|
1811.06394v3
|
2020-07-19
|
Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping
|
In this paper, the smooth solution of the physical vacuum problem for the one
dimensional compressible Euler equations with time-dependent damping is
considered. Near the vacuum boundary, the sound speed is $C^{1/2}$-H\"{o}lder
continuous. The coefficient of the damping depends on time, given by this form
$\frac{\mu}{(1+t)^\lambda}$, $\lambda$, $\mu>0$, which decays by order
$-\lambda$ in time. Under the assumption that $0<\lambda<1$, $0<\mu$ or
$\lambda=1$, $2<\mu$, we will prove the global existence of smooth solutions
and convergence to the modified Barenblatt solution of the related porous media
equation with time-dependent dissipation and the same total mass when the
initial data of the Euler equations is a small perturbation of that of the
Barenblatt solution. The pointwise convergence rates of the density, velocity
and the expanding rate of the physical vacuum boundary are also given. The
proof is based on space-time weighted energy estimates, elliptic estimates and
Hardy inequality in the Lagrangian coordinates. Our result is an extension of
that in Luo-Zeng [Comm. Pure Appl. Math. 69 (2016), no. 7, 1354-1396], where
the authors considered the physical vacuum free boundary problem of the
compressible Euler equations with constant-coefficient damping.
|
2007.14802v2
|
2020-11-16
|
Thresholds for loss of Landau damping in longitudinal plane
|
Landau damping mechanism plays a crucial role in providing single-bunch
stability in LHC, High-Luminosity LHC, other existing as well as previous and
future (like FCC) circular hadron accelerators. In this paper, the thresholds
for the loss of Landau damping (LLD) in the longitudinal plane are derived
analytically using the Lebedev matrix equation (1968) and the concept of the
emerged van Kampen modes (1983). We have found that for the commonly-used
particle distribution functions from a binomial family, the LLD threshold
vanishes in the presence of the constant inductive impedance Im$Z/k$ above
transition energy. Thus, the effect of the cutoff frequency or the resonant
frequency of a broad-band impedance on beam dynamics is studied in detail. The
findings are confirmed by direct numerical solutions of the Lebedev equation as
well as using the Oide-Yokoya method (1990). Moreover, the characteristics,
which are important for beam operation, as the amplitude of residual
oscillations and the damping time after a kick (or injection errors) are
considered both above and below the threshold. Dependence of the threshold on
particle distribution in the longitudinal phase space is also analyzed,
including some special cases with a non-zero threshold for Im$Z/k = const$. All
main results are confirmed by macro-particle simulations and consistent with
available beam measurements in the LHC.
|
2011.07985v1
|
2021-11-15
|
Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters
|
A second order accurate, linear numerical method is analyzed for the
Landau-Lifshitz equation with large damping parameters. This equation describes
the dynamics of magnetization, with a non-convexity constraint of unit length
of the magnetization. The numerical method is based on the second-order
backward differentiation formula in time, combined with an implicit treatment
of the linear diffusion term and explicit extrapolation for the nonlinear
terms. Afterward, a projection step is applied to normalize the numerical
solution at a point-wise level. This numerical scheme has shown extensive
advantages in the practical computations for the physical model with large
damping parameters, which comes from the fact that only a linear system with
constant coefficients (independent of both time and the updated magnetization)
needs to be solved at each time step, and has greatly improved the numerical
efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme
has not been available. In this paper, we provide a rigorous error estimate of
the numerical scheme, in the discrete $\ell^{\infty}(0,T; \ell^2) \cap
\ell^2(0,T; H_h^1)$ norm, under suitable regularity assumptions and reasonable
ratio between the time step-size and the spatial mesh-size. In particular, the
projection operation is nonlinear, and a stability estimate for the projection
step turns out to be highly challenging. Such a stability estimate is derived
in details, which will play an essential role in the convergence analysis for
the numerical scheme, if the damping parameter is greater than 3.
|
2111.07537v1
|
2005-05-11
|
Social Behaviour of Agents: Capital Markets and Their Small Perturbations
|
We study social behaviour of agents on capital markets when these are
perturbed by small perturbations. We use the mean field method. Social
behaviour of agents on capital markets is described: volatility of the market,
aversion constant and equilibrium states are discussed. Relaxation behaviour of
agents on the capital market is studied. Equation of motion for the agent
average number is of the relaxation type. Development of the group of agents in
the states corresponding to minimum of the aim function is either linear either
exponentially damped. There exist characteristic volatility constants $ V_{c3}
$ and $ V_{c3} $. The constant b of verification of information contribution to
the aversion constant A and the $ A_{0} $ constant of aversion are
distinguishing three types of dependencies of the minimum of the aim function
on the expected volatility EV and on the expected returns E. Arbitrage trades
and group forces lead the group into the equilibrium state. Verification of
information intensity influences return back to the equilibrium state. The
linear in time damping to the equilibrium state is characterized with the
characteristic time $ T_{3}$ and $ T_{6} $, the exponential with a
characteristic time $ \tau $. Their dependence on the expected volatility, on
the expected profit and characteristics of agents is discussed.
|
0505086v2
|
2017-06-18
|
Diffusion constant of slowly rotating black three-brane
|
In this paper, we take the slowly rotating black three-brane background and
perturb it by introducing a vector gauge field. We find the components of the
gauge field through Maxwell equations and Bianchi identities. Using currents
and some ansatz we find Fick's first law at long wavelength regime. An
interesting result for this non-trivial supergravity background is that the
diffusion constant on the stretched horizon which emerges from Fick's first law
is a complex constant. The pure imaginary part of the diffusion constant
appears because the black three-brane has angular momentum. By taking the
static limit of the corresponding black brane the well known diffusion constant
will be recovered. On the other hand, from the point of view of the Fick's
second law, we have the dispersion relation $\omega=-iDq^{2}$ and we found a
damping of hydrodynamical flow in the holographically dual theory. Existence of
imaginary term in the diffusion constant introduces an oscillating propagation
of the gauge field in the dual field theory.
|
1706.05669v2
|
2023-04-24
|
On elastic constants of zero-temperature amorphous solids
|
Elastic constants of zero-temperature amorphous solids are given as the
difference between the Born term, which results from a hypothetical affine
deformation of an amorphous solid, and a correction term which originates from
the fact that the deformation of an amorphous solid due to an applied stress
is, at the microscopic level, non-affine. Both terms are non-negative and thus
it is a priori not obvious that the resulting elastic constants are
non-negative. In particular, theories that approximate the correction term may
spuriously predict negative elastic constants and thus an instability of an
amorphous solid. Here we derive alternative expressions for elastic constants
of zero-temperature amorphous solids that are explicitly non-negative. These
expressions provide a useful blueprint for approximate theories for elastic
constants and sound damping in zero temperature amorphous solids.
|
2304.12374v1
|
2003-08-24
|
Numerical analysis of quasinormal modes in nearly extremal Schwarzschild-de Sitter spacetimes
|
We calculate high-order quasinormal modes with large imaginary frequencies
for electromagnetic and gravitational perturbations in nearly extremal
Schwarzschild-de Sitter spacetimes. Our results show that for low-order
quasinormal modes, the analytical approximation formula in the extremal limit
derived by Cardoso and Lemos is a quite good approximation for the quasinormal
frequencies as long as the model parameter $r_1\kappa_1$ is small enough, where
$r_1$ and $\kappa_1$ are the black hole horizon radius and the surface gravity,
respectively. For high-order quasinormal modes, to which corresponds
quasinormal frequencies with large imaginary parts, on the other hand, this
formula becomes inaccurate even for small values of $r_1\kappa_1$. We also find
that the real parts of the quasinormal frequencies have oscillating behaviors
in the limit of highly damped modes, which are similar to those observed in the
case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating
${\rm Re(\omega)}$ as a function of ${\rm Im}(\omega)$ approaches a non-zero
constant value for gravitational perturbations and zero for electromagnetic
perturbations in the limit of highly damped modes, where $\omega$ denotes the
quasinormal frequency. This means that for gravitational perturbations, the
real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter
spacetime appears not to approach any constant value in the limit of highly
damped modes. On the other hand, for electromagnetic perturbations, the real
part of frequency seems to go to zero in the limit.
|
0308077v4
|
2010-12-08
|
Nonequilibrium dynamics of the Holstein polaron driven by external electric field
|
This work represents a fundamental study of a Holstein polaron in one
dimension driven away from the ground state by a constant electric field.
Taking fully into account quantum effects we follow the time-evolution of the
system from its ground state as the constant electric field is switched on at t
= 0, until it reaches a steady state. At weak electron phonon coupling (EP) the
system experiences damped Bloch oscillations (BO) characteristic for
noninteracting electron band. An analytic expression of the steady state
current is proposed in terms of weak EP coupling and large electric field. For
moderate values of EP coupling the oscillations are almost critically damped
and the system reaches the steady state after a short time. In the strong
coupling limit weakly damped BO, consistent with nearly adiabatic evolution
within the polaron band, persist up to extremely large electric fields. A
traveling polaron under the influence of the electric field leaves behind a
trail of phonon excitations absorbing the excess energy gained from the
electric field. The shape of the traveling polaron is investigated in details.
|
1012.1716v3
|
2015-06-23
|
Resonant absorption of kink magnetohydrodynamic waves by a magnetic twist in coronal loops
|
There is ample evidence of twisted magnetic structures in the solar corona.
This motivates us to consider the magnetic twist as the cause of Alfven
frequency continuum in the coronal loops, which can support the resonant
absorption as a rapid damping mechanism for the observed coronal kink
magnetohydrodynamic (MHD) oscillations. We model a coronal loop with a straight
cylindrical magnetic flux tube which has constant but different densities in
the interior and exterior regions. The magnetic field is assumed to be constant
and aligned with the cylinder axis everywhere except a thin layer near the
boundary of the flux tube which has an additional small magnetic field twist.
Then, we investigate a number of possible instabilities that may arise in our
model. In the thin tube thin boundary approximation, we derive the dispersion
relation and solve it analytically to obtain the frequencies and damping rates
of the fundamental (l=1) and first/second overtone (l=2,3) kink (m=1) MHD
modes. We conclude that the resonant absorption by the magnetic twist can
justify the rapid damping of kink MHD waves observed in coronal loops.
Furthermore, the magnetic twist in the inhomogeneous layer can cause deviations
from P1/P2=2 and P1/P3=3 which are comparable with the observations.
|
1507.02653v4
|
2002-07-19
|
Gilbert Damping in Magnetic Multilayers
|
We study the enhancement of the ferromagnetic relaxation rate in thin films
due to the adjacent normal metal layers. Using linear response theory, we
derive the dissipative torque produced by the s-d exchange interaction at the
ferromagnet-normal metal interface. For a slow precession, the enhancement of
Gilbert damping constant is proportional to the square of the s-d exchange
constant times the zero-frequency limit of the frequency derivative of the
local dynamic spin susceptibility of the normal metal at the interface.
Electron-electron interactions increase the relaxation rate by the Stoner
factor squared. We attribute the large anisotropic enhancements of the
relaxation rate observed recently in multilayers containing palladium to this
mechanism. For free electrons, the present theory compares favorably with
recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett.
\textbf{88},117601 (2002)].
|
0207471v1
|
2003-05-21
|
Magnetoresistive response of a high mobility 2DES under electromagnetic wave excitation
|
Oscillations of the resistance observed under electromagnetic wave excitation
in the high mobility GaAs/AlGaAs 2DES are examined as a function of the
radiation frequency and the power, utilizing an empirical lineshape based on
exponentially damped sinusoids. The fit-analysis indicates the resistance
oscillation frequency, F, increases with the radiation frequency, n, at the
rate dF/dn = 2.37 mTesla/GHz; the damping parameter, a, is approximately
independent of n at constant power; and the amplitude, A, of the oscillations
grows slowly with the incident power, at a constant temperature and frequency.
The lineshape appears to provide a good description of the data.
|
0305507v2
|
2005-10-26
|
Multiple electron-hole scattering effect on quasiparticle properties in a homogeneous electron gas
|
We present a detailed study of a contribution of the T matrix accounting for
multiple scattering between an electron and a hole to the quasiparticle
self-energy. This contribution is considered as an additional term to the GW
self-energy. The study is based on a variational solution of the T-matrix
integral equation within a local approximation. A key quantity of such a
solution, the local electron-hole interaction, is obtained at the small
four-momentum transfer limit. Performed by making use of this limit form,
extensive calculations of quasiparticle properties in the homogeneous electron
gas over a broad range of electron densities are reported. We carry out an
analysis of how the T-matrix contribution affects the quasiparticle damping
rate, the quasiparticle energy, the renormalization constant, and the effective
mass enhancement. We find that in comparison with the GW approximation the
inclusion of the T matrix leads to an essential increase of the damping rate, a
slight reduction of the GW band narrowing, a decrease of the renormalization
constant at the Fermi wave vector, and some "weighting" of quasiparticles at
the Fermi surface.
|
0510684v2
|
1995-01-03
|
High temperature QCD and QED with unstable excitations
|
We consider the partition functions of QCD and QED at high temperature
assuming small coupling constants, and present arguments in favor of an
improved perturbative expansion in terms of unstable excitations. Our effective
propagators are derived from spectral functions with a constant width. These
spectral functions describe screening and damping of gluons (photons) as well
as ``Brownian'' motion of quarks (electrons). BRST-invariance allows us to
reduce the number of independent width parameters to three. These are
determined in a self-consistent way from the one-loop self energy and
polarization tensor in the infrared limit thus rendering this limit finite. All
spectral width parameters are found to be proportional to $g T$. We reproduce
the well known expression for the electric ``Debye''-screening mass. The
transverse (magnetic) gluons (photons) are found to interact only at nonzero
momentum or energy, at least to leading order. As a consequence their spectral
function acquires a width only away from the infrared limit. Finally, plasmon
modes are determined and found to be strongly damped.
|
9501203v1
|
2002-06-22
|
Yank and Hooke's constant group theoretically
|
We study the second central extension of the (1+1) Aristotle Lie.We find that
the first central extension admit four orbits on the dual of second central
extension of the (1+1) Aristotle Lie group.The generic orbit is characterised
by a Hooke's constant k and a yank y.If the physics of the orbit is studied
with respect the evolution in time,it represents an elementary system with
internal energy U in a posotion-momentum under the conjugation of a Hooke's
force and a damping one proportional to the velocity as in particle
mechanics.If the physics of the orbit is studied with respect the evolution in
space, it represents an elementary system with an internal momentum P under the
conjugation of a kind of Hooke's force and a damping one proportional to a
slowness, slowness usually used in time travel waves.
|
0206038v1
|
2010-11-21
|
Regular and chaotic transport of discrete solitons in asymmetric potentials
|
Ratchet dynamics of topological solitons of the forced and damped discrete
double sine-Gordon system are studied. Directed transport occurring both in
regular and in chaotic regions of the phase space and its dependence on
damping, amplitude and frequency of the driving, asymmetry parameter, coupling
constant, has been extensively investigated. We show that the passage from
ratchet phase-locked regime to chaotic ratchets occurs via a period doubling
route to chaos and that, quite surprisingly, pinned states can exist inside
phase-locking and chaotic transport regions for intermediate values of the
coupling constant. The possibility to control chaotic discrete soliton ratchets
by means of both small subharmonic signals and more general periodic drivings,
has also been investigated.
|
1011.4707v1
|
2011-07-13
|
q-damped Oscillator and degenerate roots of constant coefficients q-difference ODE
|
The classical model of q-damped oscillator is introduced and solved in terms
of Jackson q-exponential function for three different cases, under-damped,
over-damped and the critical one. It is shown that in all three cases solution
is oscillating in time but is unbounded and non-periodic. By q-periodic
function modulation, the self-similar micro-structure of the solution for small
time intervals is derived. In the critical case with degenerate roots, the
second linearly independent solution is obtained as a limiting case of two
infinitesimally close roots. It appears as standard derivative of q-exponential
and is rewritten in terms of the q-logarithmic function. We extend our result
by constructing n linearly independent set of solutions to a generic constant
coefficient q-difference equation degree N with n degenerate roots.
|
1107.2518v1
|
2012-02-07
|
The Fine Structure Constant and the CMB Damping Scale
|
The recent measurements of the Cosmic Microwave Background anisotropies at
arcminute angular scales performed by the ACT and SPT experiments are probing
the damping regime of CMB fluctuations. The analysis of these datasets
unexpectedly suggests that the effective number of relativistic degrees of
freedom is larger than the standard value of Neff = 3.04, and inconsistent with
it at more than two standard deviations. In this paper we study the role of a
mechanism that could affect the shape of the CMB angular fluctuations at those
scales, namely a change in the recombination process through variations in the
fine structure constant. We show that the new CMB data significantly improve
the previous constraints on variations of {\alpha}, with {\alpha}/{\alpha}0 =
0.984 \pm 0.005, i.e. hinting also to a more than two standard deviation from
the current, local, value {\alpha}0. A significant degeneracy is present
between {\alpha} and Neff, and when variations in the latter are allowed the
constraints on {\alpha} are relaxed and again consistent with the standard
value. Deviations of either parameter from their standard values would imply
the presence of new, currently unknown physics.
|
1202.1476v1
|
2013-04-24
|
Finite amplitude inhomogeneous waves in Mooney-Rivlin viscoelastic solids
|
New exact solutions are exhibited within the framework of finite
viscoelasticity. More precisely, the solutions correspond to finite-amplitude,
transverse, linearly-polarized, inhomogeneous motions superposed upon a finite
homogeneous static deformation. The viscoelastic body is composed of a
Mooney-Rivlin viscoelastic solid, whose constitutive equation consists in the
sum of an elastic part (Mooney-Rivlin hyperelastic model) and a viscous part
(Newtonian viscous fluid model). The analysis shows that the results are
similar to those obtained for the purely elastic case; inter alia, the normals
to the planes of constant phase and to the planes of constant amplitude must be
orthogonal and conjugate with respect to the B-ellipsoid, where B is the left
Cauchy-Green strain tensor associated with the initial large static
deformation. However, when the constitutive equation is specialized either to
the case of a neo-Hookean viscoelastic solid or to the case of a Newtonian
viscous fluid, a greater variety of solutions arises, with no counterpart in
the purely elastic case. These solutions include travelling inhomogeneous
finite-amplitude damped waves and standing damped waves.
|
1304.6748v1
|
2014-10-02
|
Investigation of the temperature-dependence of ferromagnetic resonance and spin waves in Co2FeAl0.5Si0.5
|
Co2FeAl0.5Si0.5 (CFAS) is a Heusler compound that is of interest for
spintronics applications, due to its high spin polarization and relatively low
Gilbert damping constant. In this study, the behavior of ferromagnetic
resonance as a function of temperature was investigated in CFAS, yielding a
decreasing trend of damping constant as the temperature was increased from 13
to 300 K. Furthermore, we studied spin waves in CFAS using both frequency
domain and time domain techniques, obtaining group velocities and attenuation
lengths as high as 26 km/s and 23.3 um, respectively, at room temperature.
|
1410.0439v1
|
2015-12-02
|
Flow of colloidal solids and fluids through constrictions: dynamical density functional theory versus simulation
|
Using both dynamical density functional theory and particle-resolved Brownian
dynamics simulations, we explore the flow of two-dimensional colloidal solids
and fluids driven through a linear channel with a geometric constriction. The
flow is generated by a constant external force acting on all colloids. The
initial configuration is equilibrated in the absence of flow and then the
external force is switched on instantaneously. Upon starting the flow, we
observe four different scenarios: a complete blockade, a monotonic decay to a
constant particle flux (typical for a fluid), a damped oscillatory behaviour in
the particle flux, and a long-lived stop-and-go behaviour in the flow (typical
for a solid). The dynamical density functional theory describes all four
situations but predicts infinitely long undamped oscillations in the flow which
are always damped in the simulations. We attribute the mechanisms of the
underlying stop-and-go flow to symmetry conditions on the flowing solid. Our
predictions are verifiable in real-space experiments on magnetic colloidal
monolayers which are driven through structured microchannels and can be
exploited to steer the flow throughput in microfluidics.
|
1512.00751v1
|
2017-02-14
|
Electron-nuclear coherent spin oscillations probed by spin dependent recombination
|
We demonstrate the detection of coherent electron-nuclear spin oscillations
related to the hyperfine interaction and revealed by the band-to-band
photoluminescence (PL) in zero external magnetic field. On the base of a
pump-probe PL experiment we measure, directly in the temporal domain, the
hyperfine constant of an electron coupled to a gallium defect in GaAsN by
tracing the dynamical behavior of the conduction electron spin-dependent
recombination to the defect site. The hyperfine constants and the relative
abundance of the nuclei isotopes involved can be determined without the need of
electron spin resonance technique and in the absence of any magnetic field.
Information on the nuclear and electron spin relaxation damping parameters can
also be estimated from the oscillations damping and the long delay behavior.
|
1702.04129v1
|
2017-03-08
|
System-Theoretic Performance Metrics for Low-Inertia Stability of Power Networks
|
As bulk synchronous generators in the power grid are replaced by distributed
generation interfaced through power electronics, inertia is removed from the
system, prompting concerns over grid stability. Different metrics are available
for quantifying grid stability and performance; however, no theoretical results
are available comparing and contrasting these metrics. This paper presents a
rigorous system-theoretic study of performance metrics for low-inertia
stability. For networks with uniform parameters, we derive explicit expressions
for the eigenvalue damping ratios, and for the $\mathcal{H}_{2}$ and
$\mathcal{H}_{\infty}$ norms of the linearized swing dynamics, from external
power disturbances to different phase/frequency performance outputs.These
expressions show the dependence of system performance on inertia constants,
damping constants, and on the grid topology. Surprisingly, we find that the
$\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ norms can display contradictory
behavior as functions of the system inertia, indicating that low-inertia
performance depends strongly on the chosen performance metric.
|
1703.02646v1
|
2017-03-30
|
Study of spin pumping in Co thin film vis-a-vis seed and capping layer using ferromagnetic resonance spectroscopy
|
We investigated the dependence of the seed [Ta/Pt, Ta/Au] and capping [Pt/Ta,
Au/Ta] layers on spin pumping effect in the ferromagnetic 3 nm thick Co thin
film using ferromagnetic resonance spectroscopy. The data is fitted with Kittel
equation to evaluate damping constant and g-factor. A strong dependence of seed
and capping layers on spin pumping has been discussed. The value of damping
constant {alpha} is found to be relatively large i.e. 0.0326 for the
Ta{3}/Pt{3}/Co{3}/Pt{3}/Ta{3} {nm} multi-layer structure, while it is 0.0104
for Ta{3}/Co{3}/Ta{3} {nm}. Increase in {alpha} is observed due to Pt layer
that works as a good sink for spins due to high spin orbit coupling. In
addition, we measured the effective spin conductance = 2.0e18 m-2 for the
trilayer structure Pt{3}/Co{3}/Pt{3} {nm} as a result of the enhancement in
{alpha} relative to its bulk value. We observed that the evaluated g-factor
decreases as effective demagnetizing magnetic field increases in all the
studied samples. The azimuthal dependence of magnetic resonance field and line
width showed relatively high anisotropy in the trilayer Ta{3}/Co{3}/Ta{3} {nm}
structure.
|
1703.10630v1
|
2017-05-02
|
The response of a Unruh-deWitt particle detector in a thin-shell wormhole spacetime
|
We investigate the transition probability of a Unruh-deWitt particle detector
evolving in flat space and in a wormhole spacetime, in various scenarios. In
Minkowski space, we look at the response of the detector on trajectories having
discontinuities and rapid variations, as well as the effect of finite-time
coupling. It is found that these features induce spurious oscillations in the
probability and rate of transition. At large times the oscillations are damped
and the probability tends to a constant value. Next, we look at the response of
an inertial detector on a radial trajectory that passes through a thin-shell
wormhole. After finding the appropriate modes, we look at the renormalized
detector response, defined by subtracting the flat space analogues from the
partial probabilities. The resulting curve has a peak around the wormhole
throat followed by a period of damped oscillations, before stabilizing to a
constant value. This is very similar to the flat space results, which is
surprising given that in this case the trajectory is continuous. The features
of the transition probability are due entirely to the nontrivial topology
induced by the wormhole.
|
1705.00890v1
|
2017-08-11
|
On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
|
We study the small mass limit (or: the Smoluchowski-Kramers limit) of a class
of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic
bath spectral density with a Lorentz-Drude cutoff, we derive the
Heisenberg-Langevin equations for the particle's observables using a quantum
stochastic calculus approach. We set the mass of the particle to equal $m =
m_{0} \epsilon$, the reduced Planck constant to equal $\hbar = \epsilon$ and
the cutoff frequency to equal $\Lambda = E_{\Lambda}/\epsilon$, where $m_0$ and
$E_{\Lambda}$ are positive constants, so that the particle's de Broglie
wavelength and the largest energy scale of the bath are fixed as $\epsilon \to
0$. We study the limit as $\epsilon \to 0$ of the rescaled model and derive a
limiting equation for the (slow) particle's position variable. We find that the
limiting equation contains several drift correction terms, the quantum
noise-induced drifts, including terms of purely quantum nature, with no
classical counterparts.
|
1708.03685v1
|
2018-10-11
|
Propagating spin waves in nanometer-thick yttrium iron garnet films: Dependence on wave vector, magnetic field strength and angle
|
We present a comprehensive investigation of propagating spin waves in
nanometer-thick yttrium iron garnet (YIG) films. We use broadband spin-wave
spectroscopy with integrated coplanar waveguides (CPWs) and microstrip antennas
on top of continuous and patterned YIG films to characterize spin waves with
wave vectors up to 10 rad/$\mu$m. All films are grown by pulsed laser
deposition. From spin-wave transmission spectra, parameters such as the Gilbert
damping constant, spin-wave dispersion relation, group velocity, relaxation
time, and decay length are derived and their dependence on magnetic bias field
strength and angle is systematically gauged. For a 40-nm-thick YIG film, we
obtain a damping constant of $3.5 \times 10^{-4}$ and a maximum decay length of
1.2 mm. Our experiments reveal a strong variation of spin-wave parameters with
magnetic bias field and wave vector. Spin-wave properties change considerably
up to a magnetic bias field of about 30 mT and above a field angle of
$\theta_{H} = 20^{\circ}$, where $\theta_{H} = 0^{\circ}$ corresponds to the
Damon-Eshbach configuration.
|
1810.04973v1
|
2018-10-17
|
Perpendicularly magnetized YIG films with small Gilbert damping constant and anomalous spin transport properties
|
The Y3Fe5O12 (YIG) films with perpendicular magnetic anisotropy (PMA) have
recently attracted a great deal of attention for spintronics applications.
Here, we report the induced PMA in the ultrathin YIG films grown on
(Gd2.6Ca0.4)(Ga4.1Mg0.25Zr0.65)O12 (SGGG) substrates by epitaxial strain
without preprocessing. Reciprocal space mapping shows that the films are
lattice-matched to the substrates without strain relaxation. Through
ferromagnetic resonance and polarized neutron reflectometry measurements, we
find that these YIG films have ultra-low Gilbert damping constant with a
magnetic dead layer as thin as about 0.3 nm at the YIG/SGGG interfaces.
Moreover, the transport behavior of the Pt/YIG/SGGG films reveals an
enhancement of spin mixing conductance and a large non-monotonic magnetic field
dependence of anomalous Hall effect as compared with the Pt/YIG/Gd3Ga5O12 (GGG)
films. The non-monotonic anomalous Hall signal is extracted in the temperature
range from 150 to 350 K, which has been ascribed to the possible non-collinear
magnetic order at the Pt/YIG interface induced by uniaxial strain.
|
1810.07384v2
|
2023-09-27
|
Exploring antisymmetric tensor effects on black hole shadows and quasinormal frequencies
|
This study explores the impact of antisymmetric tensor effects on spherically
symmetric black holes, investigating photon spheres, shadows, emission rate and
quasinormal frequencies in relation to a parameter which triggers the Lorentz
symmetry breaking. We examine these configurations without and with the
presence of a cosmological constant. In the first scenario, the Lorentz
violation parameter, denoted as $\lambda$, plays a pivotal role in reducing
both the photon sphere and the shadow radius, while also leading to a damping
effect on quasinormal frequencies. Conversely, in the second scenario, as the
values of the cosmological constant ($\Lambda$) increase, we observe an
expansion in the shadow radius. Also, we provide the constraints of the shadows
based on the analysis observational data obtained from the Event Horizon
Telescope (EHT) focusing on Sagittarius $A^{*}$ shadow images. Additionally,
with the increasing $\Lambda$, the associated gravitational wave frequencies
exhibit reduced damping modes.
|
2309.15778v3
|
2006-01-11
|
Ab initio calculations of inelastic losses and optical constants
|
Ab initio approaches are introduced for calculations of inelastic losses and
vibrational damping in core level x-ray and electron spectroscopies. From the
dielectric response function we obtain system-dependent self-energies,
inelastic mean free paths, and losses due to multiple-electron excitations,
while from the dynamical matrix we obtain phonon spectra and Debye-Waller
factors. These developments yield various spectra and optical constants from
the UV to x-ray energies in aperiodic materials, and significantly improve both
the near edge and extended fine structure.
|
0601241v1
|
2006-04-06
|
Measurement of the complex dielectric constant of a single gold nanoparticle
|
A differential interference contrast microscopy technique, which employs a
photonic crystal fiber as a white-light source, is used to measure both the
real and imaginary parts of the complex dielectric constant of single 10 and 15
nm gold nanoparticles over a wavelength range of 480 to 610 nm. Noticeable
deviations from bulk gold measurements are observed at short wavelengths and
for individual particles even after taking into account finite-size surface
damping effects.
|
0604174v2
|
1998-03-08
|
Wormholes in spacetimes with cosmological horizons
|
A generalisation of the asymptotic wormhole boundary condition for the case
of spacetimes with a cosmological horizon is proposed. In particular, we
consider de Sitter spacetime with small cosmological constant. The wave
functions selected by this proposal are exponentially damped in WKB
approximation when the scale factor is large but still much smaller than the
horizon size. In addition, they only include outgoing gravitational modes in
the region beyond the horizon. We argue that these wave functions represent
quantum wormholes and compute the local effective interactions induced by them
in low-energy field theory. These effective interactions differ from those for
flat spacetime in terms that explicitly depend on the cosmological constant.
|
9803029v1
|
2003-08-01
|
The pushing force of a propagating electromagnetic wave
|
The effect of the electrodynamic forces on a charged particle in a
propagating plane electromagnetic wave is investigated. First it is pointed out
that for constant fields fulfilling the radiation condition there will be an
acceleration in the direction of the Poynting vector. When oscillating fields
are considered the Lorentz force on the particle only causes a drift, with
constant average velocity, in the direction of propagation of the wave, i.e.\
the direction of the Poynting vector. Finally, when the radiative reaction
(radiation damping) force is added the result is again an acceleration in the
direction of wave propagation. PACS classification numbers: 03.50.De, 41.60.-m,
41.75.Jv
|
0308007v1
|
2002-05-20
|
Selection of Squeezed States via Decoherence
|
In the framework of Lindblad theory for open quantum systems, we calculate
the entropy of a damped quantum harmonic oscillator which is initially in a
quasi-free state. The maximally predictable states are identified as those
states producing the minimum entropy increase after a long enough time. In
general, the states with a squeezing parameter depending on the environment's
diffusion coefficients and friction constant are singled out, but if the
friction constant is much smaller than the oscillator's frequency, coherent
states
(or thermalized coherent states) are obtained as the preferred classical
states.
|
0205127v1
|
2007-12-17
|
A single-time two-point closure based on fluid particle displacements
|
A new single-time two-point closure is proposed, in which the equation for
the two-point correlation between the displacement of a fluid particle and the
velocity allows one to estimate a Lagrangian timescale. This timescale is used
to specify the nonlinear damping of triple correlations in the closure. A
closed set of equations is obtained without ad hoc constants. Taking advantage
of the analogy between particle displacements and scalar fluctuations in
isotropic turbulence subjected to a mean scalar gradient, the model is
numerically integrated. Results for the energy spectrum are in agreement with
classical scaling predictions. An estimate for the Kolmogorov constant is
obtained.
|
0712.2496v1
|
2011-02-14
|
Non-gaussianity in the strong regime of warm inflation
|
The bispectrum of scalar mode density perturbations is analysed for the
strong regime of warm inflationary models. This analysis generalises previous
results by allowing damping terms in the inflaton equation of motion that are
dependent on temperature. A significant amount of non-gaussianity emerges with
constant (or local) non-linearity parameter $f_{NL}\sim 20$, in addition to the
terms with non-constant $f_{NL}$ which are characteristic of warm inflation.
|
1102.2833v2
|
2012-11-15
|
Bondi accretion onto cosmological black holes
|
In this paper we investigate a steady accretion within the Einstein-Straus
vacuole, in the presence of the cosmological constant. The dark energy damps
the mass accretion rate and --- above certain limit --- completely stops the
steady accretion onto black holes, which in particular is prohibited in the
inflation era and after (roughly) $10^{12}$ years from Big Bang (assuming the
presently known value of the cosmological constant). Steady accretion would not
exist in the late phases of the Penrose's scenario - known as the Weyl
curvature hypothesis - of the evolution of the Universe.
|
1211.3618v2
|
2015-02-10
|
Tunable subwavelength strong absorption by graphene wrapped dielectric particles
|
The optical absorption properties of graphene wrapped dielectric particles
have been investigated by using Mie scattering theory and exact
multi-scattering method. It is shown that subwavelength strong absorption in
infrared spectra can take place in such systems due to the excitation of
plasmon resonance in graphene. The absorption characteristics and efficiency
are tunable by varying Fermi level and damping constant of graphene, or by
changing size and dielectric constant of small particles. For a cluster of
these particles, the absorption characteristics are also affected by the
separation distance between them. These extreme light resonances and
absorptions in graphene wrapped nanostructures have great potential for
opto-electronic devices.
|
1502.02913v1
|
2015-02-25
|
Barotropic FRW cosmologies with Chiellini damping in comoving time
|
For non-zero cosmological constant Lambda, we show that the barotropic FRW
cosmologies as worked out in the comoving time lead in the radiation-dominated
case to scale factors of identical form as for the Chiellini dissipative scale
factors in conformal time obtained recently by us in Phys. Lett. A 379 (2015)
882-887. This is due to the Ermakov equation which is obtained in this case.
For zero cosmological constant, several textbook solutions are provided as
particular cases of Lambda different from zero.
|
1502.07033v2
|
2022-01-27
|
Thermodynamics of the classical spin triangle
|
The classical spin system consisting of three spins with Heisenberg
interaction is an example of a completely integrable mechanical system. In this
paper we explicitly calculate thermodynamic quantities as density of states,
specific heat, susceptibility and spin autocorrelation functions. These
calculations are performed (semi-)analytically and shown to agree with
corresponding Monte Carlo simulations. For the long-time autocorrelation
function, we find, for certain values of the coupling constants, a decay to
constant values in the form of an $1/t$ damped harmonic oscillation and propose
a theoretical explanation.
|
2201.11401v1
|
2009-10-28
|
Nonlinear envelope equation and nonlinear Landau damping rate for a driven electron plasma wave
|
In this paper, we provide a theoretical description, and calculate, the
nonlinear frequency shift, group velocity and collionless damping rate, $\nu$,
of a driven electron plasma wave (EPW). All these quantities, whose physical
content will be discussed, are identified as terms of an envelope equation
allowing one to predict how efficiently an EPW may be externally driven. This
envelope equation is derived directly from Gauss law and from the investigation
of the nonlinear electron motion, provided that the time and space rates of
variation of the EPW amplitude, $E_p$, are small compared to the plasma
frequency or the inverse of the Debye length. $\nu$ arises within the EPW
envelope equation as more complicated an operator than a plain damping rate,
and may only be viewed as such because $(\nu E_p)/E_p$ remains nearly constant
before abruptly dropping to zero. We provide a practical analytic formula for
$\nu$ and show, without resorting to complex contour deformation, that in the
limit $E_p \to 0$, $\nu$ is nothing but the Landau damping rate. We then term
$\nu$ the "nonlinear Landau damping rate" of the driven plasma wave. As for the
nonlinear frequency shift of the EPW, it is also derived theoretically and
found to assume values significantly different from previously published ones,
assuming that the wave is freely propagating. Moreover, we find no limitation
in $k \lambda_D$, $k$ being the plasma wavenumber and $\lambda_D$ the Debye
length, for a solution to the dispertion relation to exist, and want to stress
here the importance of specifying how an EPW is generated to discuss its
properties. Our theoretical predictions are in excellent agreement with results
inferred from Vlasov simulations of stimulated Raman scattering (SRS), and an
application of our theory to the study of SRS is presented.
|
0910.5289v1
|
2014-10-17
|
Hunting down systematics in baryon acoustic oscillations after cosmic high noon
|
Future dark energy experiments will require better and more accurate
theoretical predictions for the baryonic acoustic oscillations (BAO) signature
in the spectrum of cosmological perturbations. Here, we use large N-body
simulations of the \LambdaCDM Planck cosmology to study any possible systematic
shifts and damping in BAO due to the impact of nonlinear gravitational growth
of structure, scale dependent and non-local bias, and redshift-space
distortions. The effect of cosmic variance is largely reduced by dividing the
tracer power spectrum by that from a BAO-free simulation starting with the same
phases. This permits us to study with unprecedented accuracy (better than 0.02%
for dark matter and 0.07% for low-bias halos) small shifts of the pristine BAO
wavenumbers towards larger k, and non-linear damping of BAO wiggles in the
power spectrum of dark matter and halo populations in the redshift range z=0-1.
For dark matter, we provide an accurate parametrization of the evolution of
\alpha as a function of the linear growth factor D(z). For halo samples, with
bias ranging from 1.2 to 2.8, we measure a typical BAO shift of ~0.25%,
observed in real-space, which does not show an appreciable evolution with
redshift within the uncertainties. Moreover, we report a constant shift as a
function of halo bias. We find a different evolution of the damping of the
acoustic feature in all halo samples as compared to dark matter with haloes
suffering less damping, and also find some weak dependence on bias. A larger
BAO shift and damping is measured in redshift-space which can be well explained
by linear theory due to redshift-space distortions. A clear modulation in phase
with the acoustic scale is observed in the scale-dependent halo bias due to the
presence of the baryonic acoustic oscillations.
|
1410.4684v2
|
2020-06-08
|
Hysteretic depinning of a particle in a periodic potential: Phase diagram and criticality
|
We consider a massive particle driven with a constant force in a periodic
potential and subjected to a dissipative friction. As a function of the drive
and damping, the phase diagram of this paradigmatic model is well known to
present a pinned, a sliding, and a bistable regime separated by three distinct
bifurcation lines. In physical terms, the average velocity $v$ of the particle
is nonzero only if either (i) the driving force is large enough to remove any
stable point, forcing the particle to slide, or (ii) there are local minima but
the damping is small enough, below a critical damping, for the inertia to allow
the particle to cross barriers and follow a limit cycle; this regime is
bistable and whether $v > 0$ or $v = 0$ depends on the initial state. In this
paper, we focus on the asymptotes of the critical line separating the bistable
and the pinned regimes. First, we study its behavior near the "triple point"
where the pinned, the bistable, and the sliding dynamical regimes meet. Just
below the critical damping we uncover a critical regime, where the line
approaches the triple point following a power-law behavior. We show that its
exponent is controlled by the normal form of the tilted potential close to its
critical force. Second, in the opposite regime of very low damping, we revisit
existing results by providing a simple method to determine analytically the
exact behavior of the line in the case of a generic potential. The analytical
estimates, accurately confirmed numerically, are obtained by exploiting exact
soliton solutions describing the orbit in a modified tilted potential which can
be mapped to the original tilted washboard potential. Our methods and results
are particularly useful for an accurate description of underdamped nonuniform
oscillators driven near their triple point.
|
2006.04912v2
|
2021-06-18
|
Sloshing dynamics of liquid tank with built-in buoys for wave energy harvesting
|
This paper proposes a novel design of liquid tank with built-in buoys for
wave energy harvesting, named the 'sloshing wave energy converter (S-WEC)'.
When the tank is oscillated by external loads (such as ocean waves), internal
liquid sloshing is activated, and the mechanical energy of sloshing waves can
be absorbed by the power take-off (PTO) system attached to these buoys. A
fully-nonlinear numerical model is established based on the boundary element
method for a systematic investigation on dynamic properties of the proposed
S-WEC. A motion decoupling algorithm based on auxiliary functions is developed
to solve the nonlinear interaction of sloshing waves and floating buoys in the
tank. An artificial damping model is introduced to reflect viscous effects of
the sloshing liquid. Physical experiments are carried out on a scaled S-WEC
model to validate the mathematical and numerical methodologies. Natural
frequencies of the S-WEC system are first investigated through spectrum
analyses on motion histories of the buoy and sloshing liquid. The viscous
damping strength is identified through comparisons with experimental
measurements. Effects of the PTO damping on power generation characteristics of
S-WEC is further explored. An optimal PTO damping can be found for each
excitation frequency, leading to the maximisation of both the power generation
and conversion efficiency of the buoy. To determine a constant PTO damping for
engineering design, a practical approach based on diagram analyses is proposed.
Effects of the buoy's geometry on power generation characteristics of the S-WEC
are also investigated. In engineering practice, the present design of S-WEC can
be a promising technical solution of ocean wave energy harvesting, based on its
comprehensive advantages on survivability enhancement, metal corrosion or
fouling organism inhibition, power generation stability and efficiency, and so
on.
|
2106.10005v1
|
2017-04-13
|
Stochastic Gradient Descent as Approximate Bayesian Inference
|
Stochastic Gradient Descent with a constant learning rate (constant SGD)
simulates a Markov chain with a stationary distribution. With this perspective,
we derive several new results. (1) We show that constant SGD can be used as an
approximate Bayesian posterior inference algorithm. Specifically, we show how
to adjust the tuning parameters of constant SGD to best match the stationary
distribution to a posterior, minimizing the Kullback-Leibler divergence between
these two distributions. (2) We demonstrate that constant SGD gives rise to a
new variational EM algorithm that optimizes hyperparameters in complex
probabilistic models. (3) We also propose SGD with momentum for sampling and
show how to adjust the damping coefficient accordingly. (4) We analyze MCMC
algorithms. For Langevin Dynamics and Stochastic Gradient Fisher Scoring, we
quantify the approximation errors due to finite learning rates. Finally (5), we
use the stochastic process perspective to give a short proof of why Polyak
averaging is optimal. Based on this idea, we propose a scalable approximate
MCMC algorithm, the Averaged Stochastic Gradient Sampler.
|
1704.04289v2
|
2004-04-13
|
The Fine-structure Constant as a Probe of Chemical Evolution and AGB Nucleosynthesis in Damped Lyman-alpha Systems
|
Evidence from a large sample of quasar absorption-line spectra in damped
Lyman-alpha systems has suggested a possible time variation of the fine
structure constant alpha. The most statistically significant portion of this
sample involves the comparison of Mg and Fe wavelength shifts using the
many-multiplet (MM) method. However, the sensitivity of this method to the
abundance of heavy isotopes, especially Mg, is enough to imitate an apparent
variation in alpha in the redshift range 0.5 < z < 1.8. We implement recent
yields of intermediate mass (IM) stars into a chemical evolution model and show
that the ensuing isotope distribution of Mg can account for the observed
variation in alpha provided the early IMF was particularly rich in intermediate
mass stars (or the heavy Mg isotope yields from AGB stars are even higher than
in present-day models). As such, these observations of quasar absorption
spectra can be used to probe the nucleosynthetic history of low-metallicity
damped Lyman-alpha systems in the redshift range 0.5 < z < 1.8. This analysis,
in conjunction with other abundance measurements of low-metallicity systems,
reinforces the mounting evidence that star formation at low metallicities may
have been strongly influenced by a population of IM stars. Such IM stars have a
significant influence on other abundances, particularly nitrogen. We constrain
our models with independent measurements of N, Si, and Fe in damped Lyman-alpha
systems as well as C/O in low-metallicity stars. In this way, we obtain
consistent model parameters for this chemical-evolution interpretation of the
MM method results.
|
0404257v2
|
2017-12-05
|
Harnessing Electrical Power from Vortex-Induced Vibration of a Circular Cylinder
|
The generation of electrical power from Vortex-Induced Vibration (VIV) of a
cylinder is investigated numerically. The cylinder is free to oscillate in the
direction transverse to the incoming flow. The cylinder is attached to a magnet
that can move along the axis of a coil made from conducting wire. The magnet
and the coil together constitute a basic electrical generator. When the
cylinder undergoes VIV, the motion of the magnet creates a voltage across the
coil, which is connected to a resistive load. By Lenz's law, induced current in
the coil applies a retarding force to the magnet. Effectively, the electrical
generator applies a damping force on the cylinder with a spatially varying
damping coefficient. For the initial investigation reported here, the Reynolds
number is restricted to Re < 200, so that the flow is laminar and
two-dimensional (2D). The incompressible 2D Navier-Stokes equations are solved
using an extensively validated spectral-element based solver. The effects of
the electromagnetic (EM) damping constant xi_m, coil dimensions (radius a,
length L), and mass ratio on the electrical power extracted are quantified. It
is found that there is an optimal value of xi_m (xi_opt) at which maximum
electrical power is generated. As the radius or length of the coil is
increased, the value of xi_opt is observed to increase. Although the maximum
average power remains the same, a larger coil radius or length results in a
more robust system in the sense that a relatively large amount of power can be
extracted when xi_m is far from xi_opt, unlike the constant damping ratio case.
The average power output is also a function of Reynolds number, primarily
through the increased maximum oscillation amplitude that occurs with increased
Reynolds number at least within the laminar range, although the general
qualitative findings seem likely to carry across to high Reynolds number VIV.
|
1712.01588v1
|
2023-12-25
|
IMEX-RK methods for Landau-Lifshitz equation with arbitrary damping
|
Magnetization dynamics in ferromagnetic materials is modeled by the
Landau-Lifshitz (LL) equation, a nonlinear system of partial differential
equations. Among the numerical approaches, semi-implicit schemes are widely
used in the micromagnetics simulation, due to a nice compromise between
accuracy and efficiency. At each time step, only a linear system needs to be
solved and a projection is then applied to preserve the length of
magnetization. However, this linear system contains variable coefficients and a
non-symmetric structure, and thus an efficient linear solver is highly desired.
If the damping parameter becomes large, it has been realized that efficient
solvers are only available to a linear system with constant, symmetric, and
positive definite (SPD) structure. In this work, based on the implicit-explicit
Runge-Kutta (IMEX-RK) time discretization, we introduce an artificial damping
term, which is treated implicitly. The remaining terms are treated explicitly.
This strategy leads to a semi-implicit scheme with the following properties:
(1) only a few linear system with constant and SPD structure needs to be solved
at each time step; (2) it works for the LL equation with arbitrary damping
parameter; (3) high-order accuracy can be obtained with high-order IMEX-RK time
discretization. Numerically, second-order and third-order IMEX-RK methods are
designed in both the 1-D and 3-D domains. A comparison with the backward
differentiation formula scheme is undertaken, in terms of accuracy and
efficiency. The robustness of both numerical methods is tested on the first
benchmark problem from National Institute of Standards and Technology. The
linearized stability estimate and optimal rate convergence analysis are
provided for an alternate IMEX-RK2 numerical scheme as well.
|
2312.15654v1
|
2006-11-01
|
Ferromagnetic resonance study of sputtered Co|Ni multilayers
|
We report on room temperature ferromagnetic resonance (FMR) studies of [$t$
Co$|2t$ Ni]$\times$N sputtered films, where $0.1 \leq t \leq 0.6$ nm. Two
series of films were investigated: films with same number of Co$|$Ni bilayer
repeats (N=12), and samples in which the overall magnetic layer thickness is
kept constant at 3.6 nm (N=1.2/$t$). The FMR measurements were conducted with a
high frequency broadband coplanar waveguide up to 50 GHz using a flip-chip
method. The resonance field and the full width at half maximum were measured as
a function of frequency for the field in-plane and field normal to the plane,
and as a function of angle to the plane for several frequencies. For both sets
of films, we find evidence for the presence of first and second order
anisotropy constants, $K_1$ and $K_2$. The anisotropy constants are strongly
dependent on the thickness $t$, and to a lesser extent on the total thickness
of the magnetic multilayer. The Land\'e g-factor increases with decreasing $t$
and is practically independent of the multilayer thickness. The magnetic
damping parameter $\alpha$, estimated from the linear dependence of the
linewidth, $\triangle H$, on frequency, in the field in-plane geometry,
increases with decreasing $t$. This behaviour is attributed to an enhancement
of spin-orbit interactions with $t$ decreasing and in thinner films, to a
spin-pumping contribution to the damping.
|
0611027v2
|
1996-04-10
|
A Keck HIRES Investigation of the Metal Abundances and Kinematics of the z=2.46 Damped Lya System Toward Q0201+365
|
We present high resolution ($\approx 8$ \kms) spectra of the QSO Q0201+365
obtained with HIRES, the echelle spectrograph on the 10m W.M. Keck Telescope.
Although we identify over $80\%$ of the absorption features and analyze several
of the more complex metal-line systems, we focus our analysis on the damped
\Lya system at $z=2.462$. Ionization simulations suggest the hydrogen in this
system is significantly neutral and all of the observed metals are
predominantly singly ionized. We measure accurate abundances for Fe, Cr, Si, Ni
and place a lower limit on the abundance of Zn: [Fe/H] = $-0.830 \pm 0.051$,
[Cr/H] = $-0.902 \pm 0.064$, [Si/H] = $-0.376 \pm 0.052$, [Ni/H] = $-1.002 \pm
0.054$ and [Zn/H] $> -0.562 \pm 0.064$. We give evidence suggesting the actual
Zn abundance is [Zn/H] $\approx -0.262$, implying the highest metallicity
observed at a redshift $z \geq 2$. The relative abundances of these elements
remains constant over essentially the entire system ($\approx 150$ \kms in
velocity space), suggesting it is well mixed. Furthermore, we use the lack of
abundance variations to infer properties of the dust responsible for element
depletion. Finally, we discuss the kinematic characteristics of this damped
\Lya system, comparing and contrasting it with other systems. The low-ion line
profiles span $\approx 200$ \kms in velocity space and have an asymmetric shape
with the strongest feature on the red edge. These kinematic characteristics are
consistent with a rotating disk model.
|
9604042v1
|
2005-07-06
|
The free precession and libration of Mercury
|
An analysis based on the direct torque equations including tidal dissipation
and a viscous core-mantle coupling is used to determine the damping time scales
of O(10^5) years for free precession of the spin about the Cassini state and
free libration in longitude for Mercury. The core-mantle coupling dominates the
damping over the tides by one to two orders of magnitude for the plausible
parameters chosen. The short damping times compared with the age of the solar
system means we must find recent or on-going excitation mechanisms if such free
motions are found by the current radar experiments or the future measurement by
the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show
that the average precession rate is increased by about 30% over that obtained
from the traditional precession constant because of a spin-orbit resonance
induced contribution by the C_{22} term in the expansion of the gravitational
field. The C_{22} contribution also causes the path of the spin during the
precession to be slightly elliptical with a variation in the precession rate
that is a maximum when the obliquity is a minimum. An observable free
precession will compromise the determination of obliquity of the Cassini state
and hence of C/MR^2 for Mercury, but a detected free libration will not
compromise the determination of the forced libration amplitude and thus the
verification of a liquid core
|
0507117v1
|
1994-09-29
|
Avalanches in the Weakly Driven Frenkel-Kontorova Model
|
A damped chain of particles with harmonic nearest-neighbor interactions in a
spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is
studied numerically. One end of the chain is pulled slowly which acts as a weak
driving mechanism. The numerical study was performed in the limit of infinitely
weak driving. The model exhibits avalanches starting at the pulled end of the
chain. The dynamics of the avalanches and their size and strength distributions
are studied in detail. The behavior depends on the value of the damping
constant. For moderate values a erratic sequence of avalanches of all sizes
occurs. The avalanche distributions are power-laws which is a key feature of
self-organized criticality (SOC). It will be shown that the system selects a
state where perturbations are just able to propagate through the whole system.
For strong damping a regular behavior occurs where a sequence of states
reappears periodically but shifted by an integer multiple of the period of the
external potential. There is a broad transition regime between regular and
irregular behavior, which is characterized by multistability between regular
and irregular behavior. The avalanches are build up by sound waves and shock
waves. Shock waves can turn their direction of propagation, or they can split
into two pulses propagating in opposite directions leading to transient
spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+z
|
9409006v1
|
2004-12-18
|
Fluctuations of the Magnetization in Thin Films due to Conduction Electrons
|
A detailed analysis of damping and noise due to a {\it sd}-interaction in a
thin ferromagnetic film sandwiched between two large normal metal layers is
carried out. The magnetization is shown to obey in general a non-local equation
of motion which differs from the the Gilbert equation and is extended to the
non-adiabatic regime. To lowest order in the exchange interaction and in the
limit where the Gilbert equation applies, we show that the damping term is
enhanced due to interfacial effects but it also shows oscillations as a
function of the film thickness. The noise calculation is however carried out to
all orders in the exchange coupling constant. The ellipticity of the precession
of the magnetization is taken into account. The damping is shown to have a
Gilbert form only in the adiabatic limit while the relaxation time becomes
strongly dependent on the geometry of the thin film. It is also shown that the
induced noise characteristic of sd-exchange is inherently colored in character
and depends on the symmetry of the Hamiltonian of the magnetization in the
film. We show that the sd-noise can be represented in terms of an external
stochastic field which is white only in the adiabatic regime. The temperature
is also renormalized by the spin accumulation in the system. For large
intra-atomic exchange interactions, the Gilbert-Brown equation is no longer
valid.
|
0412510v1
|
2009-04-29
|
Synthetic electric fields and phonon damping in carbon nanotubes and graphene
|
Smoothly varying lattice strain in graphene affects the Dirac carriers
through a synthetic gauge field. When the lattice strain is time dependent, as
in connection with phononic excitations, the gauge field becomes time dependent
and the synthetic vector potential is also associated with an electric field.
We show that this synthetic electric field has observable consequences. Joule
heating associated with the currents driven by the synthetic electric field
dominates the intrinsic damping, caused by the electron-phonon interaction, of
many acoustic phonon modes of graphene and metallic carbon nanotubes when
including the effects of disorder and Coulomb interactions. Several important
consequences follow from the observation that by time-reversal symmetry, the
synthetic electric field associated with the vector potential has opposite
signs for the two valleys. First, this implies that the synthetic electric
field drives charge-neutral valley currents and is therefore unaffected by
screening. This frequently makes the effects of the synthetic vector potential
more relevant than a competing effect of the scalar deformation potential which
has a much larger bare coupling constant. Second, valley currents decay by
electron-electron scattering (valley Coulomb drag) which causes interesting
temperature dependence of the damping rates. While our theory pertains first
and foremost to metallic systems such as doped graphene and metallic carbon
nanotubes, the underlying mechanisms should also be relevant for semiconducting
carbon nanotubes when they are doped.
|
0904.4660v1
|
2010-08-12
|
Dynamical damping terms for symmetry-seeking shift conditions
|
Suitable gauge conditions are fundamental for stable and accurate
numerical-relativity simulations of inspiralling compact binaries. A number of
well-studied conditions have been developed over the last decade for both the
lapse and the shift and these have been successfully used both in vacuum and
non-vacuum spacetimes when simulating binaries with comparable masses. At the
same time, recent evidence has emerged that the standard "Gamma-driver" shift
condition requires a careful and non-trivial tuning of its parameters to ensure
long-term stable evolutions of unequal-mass binaries. We present a novel gauge
condition in which the damping constant is promoted to be a dynamical variable
and the solution of an evolution equation. We show that this choice removes the
need for special tuning and provides a shift damping term which is free of
instabilities in our simulations and dynamically adapts to the individual
positions and masses of the binary black-hole system. Our gauge condition also
reduces the variations in the coordinate size of the apparent horizon of the
larger black hole and could therefore be useful when simulating binaries with
very small mass ratios.
|
1008.2212v2
|
2011-11-06
|
The various manifestations of collisionless dissipation in wave propagation
|
The propagation of an electrostatic wave packet inside a collisionless and
initially Maxwellian plasma is always dissipative because of the irreversible
acceleration of the electrons by the wave. Then, in the linear regime, the wave
packet is Landau damped, so that in the reference frame moving at the group
velocity, the wave amplitude decays exponentially with time. In the nonlinear
regime, once phase mixing has occurred and when the electron motion is nearly
adiabatic, the damping rate is strongly reduced compared to the Landau one, so
that the wave amplitude remains nearly constant along the characteristics. Yet,
we show here that the electrons are still globally accelerated by the wave
packet, and, in one dimension, this leads to a non local amplitude dependence
of the group velocity. As a result, a freely propagating wave packet would
shrink, and, therefore, so would its total energy. In more than one dimension,
not only does the magnitude of the group velocity nonlinearly vary, but also
its direction. In the weakly nonlinear regime, when the collisionless damping
rate is still significant compared to its linear value, this leads to an
effective defocussing effect which we quantify, and which we compare to the
self-focussing induced by wave front bowing.
|
1111.1391v2
|
2012-11-14
|
New algorithm for footstep localization using seismic sensors in an indoor environment
|
In this study, we consider the use of seismic sensors for footstep
localization in indoor environments. A popular strategy of localization is to
use the measured differences in arrival times of source signals at multiple
pairs of receivers. In the literature, most algorithms that are based on time
differences of arrival (TDOA) assume that the propagation velocity is a
constant as a function of the source position, which is valid for air
propagation or even for narrow band signals. However a bounded medium such as a
concrete slab (encountered in indoor environement) is usually dispersive and
damped. In this study, we demonstrate that under such conditions, the concrete
slab can be assimilated to a thin plate; considering a Kelvin-Voigt damping
model, we introduce the notion of {\em perceived propagation velocity}, which
decreases when the source-sensor distance increases. This peculiar behaviour
precludes any possibility to rely on existing localization methods in indoor
environment. Therefore, a new localization algorithm that is adapted to a
damped and dispersive medium is proposed, using only on the sign of the
measured TDOA (SO-TDOA). A simulation and some experimental results are
included, to define the performance of this SO-TDOA algorithm.
|
1211.3233v2
|
2014-05-19
|
Comparison of micromagnetic parameters of ferromagnetic semiconductors (Ga,Mn)(As,P) and (Ga,Mn)As
|
We report on the determination of micromagnetic parameters of epilayers of
the ferromagnetic semiconductor (Ga,Mn)As, which has easy axis in the sample
plane, and (Ga,Mn)(As,P) which has easy axis perpendicular to the sample plane.
We use an optical analog of ferromagnetic resonance where the
laser-pulse-induced precession of magnetization is measured directly in the
time domain. By the analysis of a single set of pump-and-probe magneto-optical
data we determined the magnetic anisotropy fields, the spin stiffness and the
Gilbert damping constant in these two materials. We show that incorporation of
10% of phosphorus in (Ga,Mn)As with 6% of manganese leads not only to the
expected sign change of the perpendicular to plane anisotropy field but also to
an increase of the Gilbert damping and to a reduction of the spin stiffness.
The observed changes in the micromagnetic parameters upon incorporating P in
(Ga,Mn)As are consistent with the reduced hole density, conductivity, and Curie
temperature of the (Ga,Mn)(As,P) material. We report that the magnetization
precession damping is stronger for the n = 1 spin wave resonance mode than for
the n = 0 uniform magnetization precession mode.
|
1405.4677v1
|
2014-08-20
|
Josephson junction ratchet: effects of finite capacitances
|
We study transport in an asymmetric SQUID which is composed of a loop with
three capacitively and resistively shunted Josephson junctions: two in series
in one arm and the remaining one in the other arm. The loop is threaded by an
external magnetic flux and the system is subjected to both a time-periodic and
a constant current. We formulate the deterministic and, as well, the stochastic
dynamics of the SQUID in terms of the Stewart-McCumber model and derive an
equation for the phase difference across one arm, in which an effective
periodic potential is of the ratchet type, i.e. its reflection symmetry is
broken. In doing so, we extend and generalize earlier study by Zapata et al.
[Phys. Rev. Lett. 77, 2292 (1996)] and analyze directed transport in wide
parameter regimes: covering the over-damped to moderate damping regime up to
its fully under-damped regime. As a result we detect the intriguing features of
a negative (differential) conductance, repeated voltage reversals, noise
induced voltage reversals and solely thermal noise-induced ratchet currents. We
identify a set of parameters for which the ratchet effect is most pronounced
and show how the direction of transport can be controlled by tailoring the
external magnetic flux.
|
1408.4607v1
|
2015-03-24
|
Spin dynamics and frequency dependence of magnetic damping study in soft ferromagnetic FeTaC film with a stripe domain structure
|
Perpendicular magnetic anisotropy (PMA) and low magnetic damping are the key
factors for the free layer magnetization switching by spin transfer torque
technique in magnetic tunnel junction devices. The magnetization precessional
dynamics in soft ferromagnetic FeTaC thin film with a stripe domain structure
was explored in broad band frequency range by employing micro-strip
ferromagnetic resonance technique. The polar angular variation of resonance
field and linewidth at different frequencies have been analyzed numerically
using Landau-Lifshitz-Gilbert equation by taking into account the total free
energy density of the film. The numerically estimated parameters Land\'{e}
$g$-factor, PMA constant, and effective magnetization are found to be 2.1,
2$\times10^{5}$ erg/cm$^{3}$ and 7145 Oe, respectively. The frequency
dependence of Gilbert damping parameter ($\alpha$) is evaluated by considering
both intrinsic and extrinsic effects into the total linewidth analysis. The
value of $\alpha$ is found to be 0.006 at 10 GHz and it increases with
decreasing precessional frequency.
|
1503.07043v5
|
2015-09-07
|
Spectral inequality and resolvent estimate for the bi-Laplace operator
|
On a compact Riemannian manifold with boundary, we prove a spectral
inequality for the bi-Laplace operator in the case of so-called "clamped"
boundary conditions , that is, homogeneous Dirichlet and Neumann conditions
simultaneously. We also prove a resolvent estimate for the generator of the
damped plate semigroup associated with these boundary conditions. The spectral
inequality allows one to observe finite sums of eigenfunctions for this
fourth-order elliptic operator, from an arbitrary open subset of the manifold.
Moreover, the constant that appears in the inequality grows as exp(C$\mu$ 1/4)
where $\mu$ is the largest eigenvalue associated with the eigenfunctions
appearing in the sum. This type of inequality is known for the Laplace
operator. As an application, we obtain a null-controllability result for a
higher-order parabolic equation. The resolvent estimate provides the spectral
behavior of the plate semigroup generator on the imaginary axis. This type of
estimate is known in the case of the damped wave semigroup. As an application ,
we deduce a stabilization result for the damped plate equation, with a log-type
decay. The proofs of both the spectral inequality and the resolvent estimate
are based on the derivation of different types of Carleman estimates for an
elliptic operator related to the bi-Laplace operator: in the interior and at
some boundaries. One of these estimates exhibits a loss of one full derivative.
Its proof requires the introduction of an appropriate semi-classical calculus
and a delicate microlocal argument.
|
1509.02098v5
|
2016-06-29
|
On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping
|
In this paper, we are concerned with the global existence and blowup of
smooth solutions to the multi-dimensional compressible Euler equations with
time-depending damping \begin{equation*}
\partial_t\rho+\operatorname{div}(\rho u)=0, \quad
\partial_t(\rho u)+\operatorname{div}\left(\rho u\otimes
u+p\,I_d\right)=-\alpha(t)\rho u, \quad
\rho(0,x)=\bar \rho+\varepsilon\rho_0(x),\quad u(0,x)=\varepsilon u_0(x),
\end{equation*} where $x=(x_1, \cdots, x_d)\in\Bbb R^d$ $(d=2,3)$, the
frictional coefficient is $\alpha(t)=\frac{\mu}{(1+t)^\lambda}$ with
$\lambda\ge0$ and $\mu>0$, $\bar\rho>0$ is a constant, $\rho_0,u_0 \in
C_0^\infty(\Bbb R^d)$, $(\rho_0,u_0)\not\equiv 0$, $\rho(0,x)>0$, and
$\varepsilon>0$ is sufficiently small. One can totally divide the range of
$\lambda\ge0$ and $\mu>0$ into the following four cases:
Case 1: $0\le\lambda<1$, $\mu>0$ for $d=2,3$;
Case 2: $\lambda=1$, $\mu>3-d$ for $d=2,3$;
Case 3: $\lambda=1$, $\mu\le 3-d$ for $d=2$;
Case 4: $\lambda>1$, $\mu>0$ for $d=2,3$.
\noindent We show that there exists a global $C^{\infty}-$smooth solution
$(\rho, u)$ in Case 1, and Case 2 with $\operatorname{curl} u_0\equiv 0$, while
in Case 3 and Case 4, in general, the solution $(\rho, u)$ blows up in finite
time. Therefore, $\lambda=1$ and $\mu=3-d$ appear to be the critical power and
critical value, respectively, for the global existence of small amplitude
smooth solution $(\rho, u)$ in $d-$dimensional compressible Euler equations
with time-depending damping.
|
1606.08935v1
|
2017-02-16
|
Effects of Landau damping on ion-acoustic solitary waves in a semiclassical plasma
|
We study the nonlinear propagation of ion-acoustic waves (IAWs) in an
unmagnetized collisionless plasma with the effects of electron and ion Landau
damping in the weak quantum (semiclassical) regime, i.e., when the typical
ion-acoustic (IA) length scale is larger than the thermal de Broglie
wavelength. Starting from a set of classical and semiclassical Vlasov equations
for ions and electrons, coupled to the Poisson equation, we derive a modified
(by the particle dispersion) Korteweg-de Vries (KdV) equation which governs the
evolution of IAWs with the effects of wave-particle resonance. It is found that
in contrast to the classical results, the nonlinear IAW speed $(\lambda)$ and
the linear Landau damping rate $(\gamma)$ are no longer constants, but can vary
with the wave number $(k)$ due to the quantum particle dispersion. The effects
of the quantum parameter $H$ (the ratio of the plasmon energy to the thermal
energy) and the electron to ion temperature ratio $(T)$ on the profiles of
$\lambda$, $\gamma$ and the solitary wave amplitude are also studied. It is
shown that the decay rate of the wave amplitude is reduced by the effects of
$H$.
|
1702.05035v2
|
2017-08-16
|
Effects of group velocity and multi-plasmon resonances on the modulation of Langmuir waves in a degenerate plasma
|
We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully
degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson
equation and the multiple scale expansion technique, a modified nonlocal
nonlinear Schr{\"{o}}dinger (NLS) equation is derived which governs the
evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in
the NLS equation appears due to the group velocity and multi-plasmon
resonances, i.e., resonances induced by the simultaneous particle absorption of
multiple wave quanta. We focus on the regime where the resonant velocity of
electrons is larger than the Fermi velocity and thereby the linear Landau
damping is forbidden. As a result, the nonlinear wave-particle resonances due
to the group velocity and multi-plasmon processes are the dominant mechanisms
for wave-particle interaction. It is found that in contrast to classical or
semiclassical plasmas, the group velocity resonance does not necessarily give
rise the wave damping in the strong quantum regime where $ \hbar k\sim mv_{F}$
with $\hbar$ denoting the reduced Planck's constant, $m$ the electron mass and
$v_F$ the Fermi velocity, however, the three-plasmon process plays a dominant
role in the nonlinear Landau damping of wave envelopes. In this regime, the
decay rate of the wave amplitude is also found to be higher compared to that in
the modest quantum regime where the multi-plasmon effects are forbidden.
|
1708.04965v3
|
2020-01-13
|
Modelling Stochastic Signatures in Classical Pulsators
|
We consider the impact of stochastic perturbations on otherwise coherent
oscillations of classical pulsators. The resulting dynamics are modelled by a
driven damped harmonic oscillator subject to either an external or an internal
forcing and white noise velocity fluctuations. We characterize the phase and
relative amplitude variations using analytical and numerical tools. When the
forcing is internal the phase variation displays a random walk behaviour and a
red noise power spectrum with a ragged erratic appearance. We determine the
dependence of the root mean square phase and relative amplitude variations
($\sigma_{\Delta \varphi}$ and $\sigma_{\Delta A/A}$, respectively) on the
amplitude of the stochastic perturbations, the damping constant $\eta$, and the
total observation time $t_{\rm obs}$ for this case, under the assumption that
the relative amplitude variations remain small, showing that $\sigma_{\Delta
\varphi}$ increases with $t_{\rm obs}^{1/2}$ becoming much larger than
$\sigma_{\Delta A/A}$ for $t_{\rm obs} \gg \eta^{-1}$. In the case of an
external forcing the phase and relative amplitude variations remain of the same
order, independent of the observing time. In the case of an internal forcing,
we find that $\sigma_{\Delta \varphi}$ does not depend on $\eta$. Hence, the
damping time cannot be inferred from fitting the power of the signal, as done
for solar-like pulsators, but the amplitude of the stochastic perturbations may
be constrained from the observations. Our results imply that, given sufficient
time, the variation of the phase associated to the stochastic perturbations in
internally driven classical pulsators will become sufficiently large to be
probed observationally.
|
2001.04558v1
|
2020-03-03
|
Linear stability analysis for 2D shear flows near Couette in the isentropic Compressible Euler equations
|
In this paper, we investigate linear stability properties of the 2D
isentropic compressible Euler equations linearized around a shear flow given by
a monotone profile, close to the Couette flow, with constant density, in the
domain $\mathbb{T}\times \mathbb{R}$. We begin by directly investigating the
Couette shear flow, where we characterize the linear growth of the compressible
part of the fluid while proving time decay for the incompressible part
(inviscid damping with slower rates). Then we extend the analysis to monotone
shear flows near Couette, where we are able to give an upper bound, superlinear
in time, for the compressible part of the fluid. The incompressible part enjoys
an inviscid damping property, analogous to the Couette case. In the pure
Couette case, we exploit the presence of an additional conservation law (which
connects the vorticity and the density on the moving frame) in order to reduce
the number of degrees of freedom of the system. The result then follows by
using weighted energy estimates. In the general case, unfortunately, this
conservation law no longer holds. Therefore we define a suitable weighted
energy functional for the whole system, which can be used to estimate the
irrotational component of the velocity but does not provide sharp bounds on the
solenoidal component. However, even in the absence of the aforementioned
additional conservation law, we are still able to show the existence of a
functional relation which allows us to recover somehow the vorticity from the
density, on the moving frame. By combining the weighted energy estimates with
the functional relation we also recover the inviscid damping for the solenoidal
component of the velocity.
|
2003.01694v1
|
2020-05-27
|
Role of diffusive surface scattering in nonlocal plasmonics
|
The recent generalised nonlocal optical response (GNOR) theory for plasmonics
is analysed, and its main input parameter, namely the complex hydrodynamic
convection-diffusion constant, is quantified in terms of enhanced Landau
damping due to diffusive surface scattering of electrons at the surface of the
metal. GNOR has been successful in describing plasmon damping effects, in
addition to the frequency shifts originating from induced-charge screening,
through a phenomenological electron diffusion term implemented into the
traditional hydrodynamic Drude model of nonlocal plasmonics. Nevertheless, its
microscopic derivation and justification is still missing. Here we discuss how
the inclusion of a diffusion-like term in standard hydrodynamics can serve as
an efficient vehicle to describe Landau damping without resorting to
computationally demanding quantum-mechanical calculations, and establish a
direct link between this term and the Feibelman $d$ parameter for the centroid
of charge. Our approach provides a recipe to connect the phenomenological
fundamental GNOR parameter to a frequency-dependent microscopic
surface-response function. We therefore tackle one of the principal limitations
of the model, and further elucidate its range of validity and limitations, thus
facilitating its proper application in the framework of nonclassical
plasmonics.
|
2005.13218v2
|
2021-01-28
|
Vortex-induced Vibrations of a Confined Circular Cylinder for Efficient Flow Power Extraction
|
A simple method to increase the flow power extraction efficiency of a
circular cylinder, undergoing vortex-induced vibration (VIV), by confining it
between two parallel plates is proposed. A two-dimensional numerical study was
performed on VIV of a circular cylinder inside a parallel plate channel of
height H at Reynolds number 150 to quantify the improvement. The cylinder is
elastically mounted with a spring such that it is only free to vibrate in the
direction transverse to the channel flow and has a fixed mass ratio (m*) of 10.
The energy extraction process is modelled as a damper, with spatially constant
damping ration ((), attached to the cylinder. The simulations are performed by
varying the reduced velocity for a set of fixed mass-damping ({\alpha} = m*()
values ranging between 0 to 1. The blockage ratio (b = D/H) is varied from 0.25
to 0.5 by changing the channel height. The quasi-periodic initial branch found
for the unconfined cylinder shrinks with the increasing blockage. The extracted
power is found to increase rapidly with the blockage. For maximum blockage (b =
0.2), the maximum flow power extracted by the cylinder is an order of magnitude
larger as compared to what it would extract in an open domain with free stream
velocity equal to the channel mean velocity. The optimal mass-damping
({\alpha}c ) for extracting maximum power is found to lie between 0.2 to 0.3.
An expression is derived to predict the maximum extracted power from the
undamped response of a confined/unconfined cylinder. With the assumption
{\alpha}c = 0.25, the derived expression can predict the maximum power
extraction within +-20% of the actual values obtained from present and previous
numerical and experimental studies.
|
2101.11803v1
|
2021-03-26
|
First-order strong-field QED processes including the damping of particles states
|
Volkov states are exact solutions of the Dirac equation in the presence of an
arbitrary plane wave. Volkov states, as well as free photon states, are not
stable in the presence of the background plane-wave field but "decay" as
electrons/positrons can emit photons and photons can transform into
electron-positron pairs. By using the solutions of the corresponding
Schwinger-Dyson equations within the locally-constant field approximation, we
compute the probabilities of nonlinear single Compton scattering and nonlinear
Breit-Wheeler pair production by including the effects of the decay of
electron, positron, and photon states. As a result, we find that the
probabilities of these processes can be expressed as the integral over the
light-cone time of the known probabilities valid for stable states per unit of
light-cone time times a light-cone time-dependent exponential damping function
for each interacting particle. The exponential function for an incoming
(outgoing) either electron/positron or photon at each light-cone time
corresponds to the total probability that either the electron/positron emits a
photon via nonlinear Compton scattering or the photon transforms into an
electron-positron pair via nonlinear Breit-Wheeler pair production until that
light-cone time (from that light-cone time on). It is interesting that the
exponential damping terms depend not only on the particles momentum but also on
their spin (for electrons/positrons) and polarization (for photons). This
additional dependence on the discrete quantum numbers prevents the application
of the electron/positron spin and photon polarization sum-rules, which
significantly simplify the computations in the perturbative regime.
|
2103.14637v1
|
2021-08-11
|
Numerical investigation of the formation and stability of homogeneous pairs of soft particles in inertial microfluidics
|
We investigate the formation and stability of a pair of identical soft
capsules in channel flow under mild inertia. We employ a combination of the
lattice Boltzmann, finite element and immersed boundary methods to simulate the
elastic particles in flow. Validation tests show excellent agreement with
numerical results obtained by other research groups. Our results reveal new
trajectory types that have not been observed for pairs of rigid particles.
While particle softness increases the likelihood of a stable pair forming, the
pair stability is determined by the lateral position of the particles. A key
finding is that stabilisation of the axial distance occurs after lateral
migration of the particles. During the later phase of pair formation, particles
undergo damped oscillations that are independent of initial conditions. These
damped oscillations are driven by a strong hydrodynamic coupling of the
particle dynamics, particle inertia and viscous dissipation. While the
frequency and damping coefficient of the oscillations depend on particle
softness, the pair formation time is largely determined by the initial particle
positions: the time to form a stable pair grows exponentially with the initial
axial distance. Our results demonstrate that particle softness has a strong
impact on the behaviour of particle pairs. The findings could have significant
ramifications for microfluidic applications where a constant and reliable axial
distance between particles is required, such as flow cytometry.
|
2108.05277v1
|
2021-11-27
|
Rate of Entropy Production in Stochastic Mechanical Systems
|
Entropy production in stochastic mechanical systems is examined here with
strict bounds on its rate. Stochastic mechanical systems include pure
diffusions in Euclidean space or on Lie groups, as well as systems evolving on
phase space for which the fluctuation-dissipation theorem applies, i.e.,
return-to-equilibrium processes. Two separate ways for ensembles of such
mechanical systems forced by noise to reach equilibrium are examined here.
First, a restorative potential and damping can be applied, leading to a
classical return-to-equilibrium process wherein energy taken out by damping can
balance the energy going in from the noise. Second, the process evolves on a
compact configuration space (such as random walks on spheres, torsion angles in
chain molecules, and rotational Brownian motion) lead to long-time solutions
that are constant over the configuration space, regardless of whether or not
damping and random forcing balance. This is a kind of potential-free
equilibrium distribution resulting from topological constraints. Inertial and
noninertial (kinematic) systems are considered. These systems can consist of
unconstrained particles or more complex systems with constraints, such as
rigid-bodies or linkages. These more complicated systems evolve on Lie groups
and model phenomena such as rotational Brownian motion and nonholonomic robotic
systems. In all cases, it is shown that the rate of entropy production is
closely related to the appropriate concept of Fisher information matrix of the
probability density defined by the Fokker-Planck equation. Classical results
from information theory are then repurposed to provide computable bounds on the
rate of entropy production in stochastic mechanical systems.
|
2111.13930v1
|
2022-04-20
|
Ferrimagnet GdFeCo characterization for spin-orbitronics: large field-like and damping-like torques
|
Spintronics is showing promising results in the search for new materials and
effects to reduce energy consumption in information technology. Among these
materials, ferrimagnets are of special interest, since they can produce large
spin currents that trigger the magnetization dynamics of adjacent layers or
even their own magnetization. Here, we present a study of the generation of
spin current by GdFeCo in a GdFeCo/Cu/NiFe trilayer where the FeCo sublattice
magnetization is dominant at room temperature. Magnetic properties such as the
saturation magnetization are deduced from magnetometry measurements while
damping constant is estimated from spin-torque ferromagnetic resonance
(ST-FMR). We show that the overall damping-like (DL) and field-like (FL)
effective fields as well as the associated spin Hall angles can be reliably
obtained by performing the dependence of ST-FMR by an added dc current. The sum
of the spin Hall angles for both the spin Hall effect (SHE) and the spin
anomalous Hall effect (SAHE) symmetries are: $\theta_{DL}^{SAHE} +
\theta_{DL}^{SHE}=-0.15 \pm 0.05$ and $\theta_{FL}^{SAHE} +
\theta_{FL}^{SHE}=0.026 \pm 0.005$. From the symmetry of ST-FMR signals we find
that $\theta_{DL}^{SHE}$ is positive and dominated by the negative
$\theta_{DL}^{SAHE}$. The present study paves the way for tuning the different
symmetries in spin conversion in highly efficient ferrimagnetic systems.
|
2204.09776v1
|
2022-11-28
|
Exciting the TTV Phases of Resonant Sub-Neptunes
|
There are excesses of sub-Neptunes just wide of period commensurabilities
like the 3:2 and 2:1, and corresponding deficits narrow of them. Any theory
that explains this period ratio structure must also explain the strong transit
timing variations (TTVs) observed near resonance. Besides an amplitude and a
period, a sinusoidal TTV has a phase. Often overlooked, TTV phases are
effectively integration constants, encoding information about initial
conditions or the environment. Many TTVs near resonance exhibit non-zero
phases. This observation is surprising because dissipative processes that
capture planets into resonance also damp TTV phases to zero. We show how both
the period ratio structure and the non-zero TTV phases can be reproduced if
pairs of sub-Neptunes capture into resonance in a gas disc while accompanied by
a third eccentric non-resonant body. Convergent migration and eccentricity
damping by the disc drives pairs to orbital period ratios wide of
commensurability; then, after the disc clears, secular forcing by the third
body phase-shifts the TTVs. The scenario predicts that resonant planets are
apsidally aligned and possess eccentricities up to an order of magnitude larger
than previously thought.
|
2211.15701v2
|
2023-01-23
|
Estimation of turbulent proton and electron heating rates via Landau damping constrained by Parker Solar Probe observations
|
The heating of ions and electrons due to turbulent dissipation plays a
crucial role in the thermodynamics of the solar wind and other plasma
environments. Using magnetic field and thermal plasma observations from the
first two perihelia of the Parker Solar Probe (PSP), we model the relative
heating rates as a function of radial distance, magnetic spectra, and plasma
conditions, enabling us to better characterize the thermodynamics of the inner
heliosphere. We employ the Howes et al. 2008 steady-state cascade model, which
considers the behavior of turbulent, low-frequency, wavevector-anisotropic,
critically balanced Alfv\'enic fluctuations that dissipate via Landau damping
to determine proton-to-electron heating rates $Q_p/Q_e$. We distinguish
ion-cyclotron frequency circularly polarized waves from low-frequency
turbulence and constrain the cascade model using spectra constructed from the
latter. We find that the model accurately describes the observed energy
spectrum from over 39.4 percent of the intervals from Encounters 1 and 2,
indicating the possibility for Landau damping to heat the young solar wind. The
ability of the model to describe the observed turbulent spectra increases with
the ratio of thermal-to-magnetic pressure, $\beta_p$, indicating that the model
contains the necessary physics at higher $\beta_p$. We estimate high magnitudes
for the Kolmogorov constant which is inversely proportional to the non-linear
energy cascade rate. We verify the expected strong dependency of $Q_p/Q_e$ on
$\beta_p$ and the consistency of the critical balance assumption.
|
2301.09713v1
|
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