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2022-07-01
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Particle acceleration and radiation reaction in a strongly magnetized rotating dipole
|
Abridged. Neutron stars are surrounded by ultra-relativistic particles
efficiently accelerated by ultra strong electromagnetic fields. However so far,
no numerical simulations were able to handle such extreme regimes of very high
Lorentz factors and magnetic field strengths. It is the purpose of this paper
to study particle acceleration and radiation reaction damping in a rotating
magnetic dipole with realistic field strengths typical of millisecond and young
pulsars as well as of magnetars. To this end, we implemented an exact
analytical particle pusher including radiation reaction in the reduced
Landau-Lifshitz approximation where the electromagnetic field is assumed
constant in time and uniform in space during one time step integration. The
position update is performed using a velocity Verlet method. We extensively
tested our algorithm against time independent background electromagnetic fields
like the electric drift in cross electric and magnetic fields and the magnetic
drift and mirror motion in a dipole. Eventually, we apply it to realistic
neutron star environments. We investigated particle acceleration and the impact
of radiation reaction for electrons, protons and iron nuclei plunged around
millisecond pulsars, young pulsars and magnetars, comparing it to situations
without radiation reaction. We found that the maximum Lorentz factor depends on
the particle species but only weakly on the neutron star type. Electrons reach
energies up to $\gamma_e \approx 10^8-10^9$ whereas protons energies up to
$\gamma_p \approx 10^5-10^6$ and iron up to $\gamma \approx 10^4-10^5$. While
protons and irons are not affected by radiation reaction, electrons are
drastically decelerated, reducing their maximum Lorentz factor by 2 orders of
magnitude. We also found that the radiation reaction limit trajectories fairly
agree with the reduced Landau-Lifshitz approximation in almost all cases.
|
2207.00624v1
|
2022-07-04
|
Selectivity of Protein Interactions Stimulated by Terahertz Signals
|
It has been established that Terahertz (THz) band signals can interact with
biomolecules through resonant modes. Specifically, of interest here, protein
activation. Our research goal is to show how directing the mechanical signaling
inside protein molecules using THz signals can control changes in their
structure and activate associated biochemical and biomechanical events. To
establish that, we formulate a selectivity metric that quantifies the system
performance and captures the capability of the nanoantenna to induce a
conformational change in the desired protein molecule/population. The metric
provides a score between -1 and 1 that indicates the degree of control we have
over the system to achieve targeted protein interactions. To develop the
selectivity measure, we first use the Langevin stochastic equation driven by an
external force to model the protein behavior. We then determine the probability
of protein folding by computing the steady-state energy of the driven protein
and then generalize our model to account for protein populations. Our numerical
analysis results indicate that a maximum selectivity score is attained when
only the targeted population experiences a folding behavior due to the
impinging THz signal. From the achieved selectivity values, we conclude that
the system response not only depends on the resonant frequency but also on the
system controlling parameters namely, the nanoantenna force, the damping
constant, and the abundance of each protein population. The presented work
sheds light on the potential associated with the electromagnetic-based control
of protein networks, which could lead to a plethora of applications in the
medical field ranging from bio-sensing to targeted therapy.
|
2207.01572v1
|
2022-07-10
|
Revealing the drag instability in one-fluid nonideal MHD simulations of a 1D isothermal C-shock
|
C-type shocks are believed to be ubiquitous in turbulent molecular clouds
thanks to ambipolar diffusion. We investigate whether the drag instability in
1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can
appear in non-ideal magnetohydrodynamic simulations. Two C-shock models (with
narrow and broad steady-state shock widths) are considered to represent the
typical environment of star-forming clouds. The ionization-recombination
equilibrium is adopted for the one-fluid approach. In the 1D simulation, the
inflow gas is continuously perturbed by a sinusoidal density fluctuation with a
constant frequency. The perturbations clearly grow after entering the C-shock
region until they start being damped at the transition to the postshock region.
We show that the profiles of a predominant Fourier mode extracted locally from
the simulated growing perturbation match those of the growing mode derived from
the linear analysis. Moreover, the local growth rate and wave frequency derived
from the predominant mode generally agree with those from the linear theory.
Therefore, we confirm the presence of the drag instability in simulated 1D
isothermal C-shocks. We also explore the nonlinear behavior of the instability
by imposing larger-amplitude perturbations to the simulation. We find that the
drag instability is subject to wave steepening, leading to saturated
perturbation growth. Issues concerning local analysis, nonlinear effects,
one-fluid approach, and astrophysical applications are discussed.
|
2207.04355v2
|
2022-08-10
|
Theoretical model of a new type tunneling transistor
|
A tunneling transistor without heterojunction as a theoretical design, or
more precisely controlled electron current transmission by barrier potential,
is under consideration.
The electrons from the conduction band of the source tunnel through the
forbidden gap $E_g$ of the channel to the conduction band of the drain. The
tunneling current $J$ calculations made at helium temperature for the example
InAs-InAs-InAs, Au-GaSe-Au and Al-AlN-Al structures show that for a constant
source-drain voltage, $V_C$, of several mV, changes in the gate voltage, $V_G$,
applied to the channel within the voltage range of 0 - $E_g/$2e change $J$ by
even 10 orders of magnitude. Unlike the existing solutions such as tunnel
field-effect-transistor (TFET), the proposed device uses the change of $V_G$
(gate voltage), i.e. the change of the electrostatic potential in the channel,
to modify the imaginary wave vector $k_z$ of tunnel current electrons.
Consequently, the gate voltage controls the damping force of the electrons wave
functions and thus the magnitude of the tunneling current, $J$. The effect of
increasing temperature, T, on $J(V_G)$ relation was also tested. It was found
that only in structures with a wide forbidden channel gap this effect is
insignificant (at least up to T=300 K).
|
2208.05188v3
|
2022-08-11
|
Statistical distribution of HI 21cm intervening absorbers as potential cosmic acceleration probes
|
Damped Lyman-$\alpha$ Absorber (DLA), or HI 21cm Absorber (H21A), is an
important probe to model-independently measure the acceleration of
spectroscopic velocity ($v_\mathrm{S}$) via the Sandage-Loeb (SL) effect.
Confined by the shortage of DLAs and Background Radio Sources (BRSs) with
adequate information, the detectable amount of DLAs is ambiguous in the bulk of
previous work. After differing the acceleration of scale factor ($\ddot{a}$)
from the first order time derivative of spectroscopic velocity
($\dot{v}_\mathrm{S}$), we make a statistical investigation of the amount of
potential DLAs in the most of this paper. Using Kernel Density Estimation (KDE)
to depict general redshift distributions of BRSs, observed DLAs and a DLA
detection rate with different limitations (1.4GHz flux, HI column density and
spin temperature), we provide fitted multi-Gaussian expressions of the three
components and their 1$\sigma$ regions by bootstrap, with a proportional
constant of H21As in detected DLAs, leading to the measurable number
predictions of H21As for FAST, ASKAP and SKA1-Mid in HI absorption blind
survey. In our most optimistic condition ($F_\mathrm{1.4GHz}$>10mJy,
$N_\mathrm{HI}>2\times10^{20}\mathrm{cm^{-2}}$ and $T_\mathrm{S}$>500K), the
FAST, AKSAP and SKA1-Mid would probe about 80, 500 and 600 H21As respectively.
|
2208.05639v3
|
2022-10-03
|
Quintom fields from chiral anisotropic cosmology
|
In this paper we present an analysis of a chiral anisotropic cosmological
scenario from the perspective of quintom fields. In this setup quintessence and
phantom fields interact in a non-standard (chiral) way within an anisotropic
Bianchi type I background. We present our examination from two fronts:
classical and quantum approaches. In the classical program we find analytical
solutions given by a particular choice of the emerged relevant parameters.
Remarkably, we present an explanation of the ''big-bang'' singularity by means
of a ''big-bounce''. Moreover, isotropization is in fact reached as the time
evolves. On the quantum counterpart the Wheeler-DeWitt equation is analytically
solved for various instances given by the same parameter space from the
classical study, and we also include the factor ordering $\rm Q$. Having
solutions in this scheme we compute the probability density, which is in effect
damped as the volume function and the scalar fields evolve; and it also tends
towards a flat FLRW framework when the factor ordering constant $\rm Q \ll 0$.
This result might indicate that for a fixed set of parameters, the anisotropies
quantum-mechanically vanish for very small values of the parameter $\rm Q$.
Finally, classical and quantum solutions reduce to their flat FLRW counterparts
when the anisotropies vanish.
|
2210.01186v2
|
2022-10-06
|
Effects of a Pre-inflationary de Sitter Bounce on the Primordial Gravitational Waves in $f(R)$ Gravity Theories
|
In this work we examine the effects of a pre-inflationary de Sitter bounce on
the energy spectrum of the primordial gravitational waves. Specifically we
assume that the Universe is described by several evolution patches, starting
with a de Sitter pre-inflationary bounce which is followed by an quasi-de
Sitter slow-roll inflationary era, followed by a constant equation of state
parameter abnormal reheating era, which is followed by the radiation and matter
domination eras and the late-time acceleration eras. The bounce and the
inflationary era can be realized by vacuum $f(R)$ gravity and the abnormal
reheating and the late-time acceleration eras by the synergy of $f(R)$ gravity
and the prefect matter fluids present. Using well-known reconstruction
techniques we find which $f(R)$ gravity can realize each evolution patch,
except from the matter and radiation domination eras which are realized by the
corresponding matter fluids. Accordingly, we calculate the damping factor of
the primordial de Sitter bounce, and as we show, the signal can be detected by
only one gravitational wave future experiment, in contrast to the case in which
the bounce is absent. We discuss in detail the consequences of our results and
the future perspectives.
|
2210.02861v1
|
2022-10-11
|
Switching Dynamics of Shallow Arches
|
This paper presents an analytical method to predict the delayed switching
dynamics of nonlinear shallow arches while switching from one state to another
state for different loading cases. We study an elastic arch subject to static
loading and time-dependent loading separately. In particular, we consider a
time-dependent loading that evolves linearly with time at a constant rate. In
both cases, we observed that the switching does not occur abruptly when the
load exceeds the static switching load, rather the time scale of the dynamics
drastically slows down; hence there is a delay in switching. For
time-independent loading, this delay increases as the applied load approach the
static switching load. Whereas for a time-dependent loading, the delay is
proportional to the rate of the applied load. Other than the loading
parameters, the delay switching time also depends on the local curvature of the
force-displacement function at the static switching point and the damping
coefficient of the arch material. The delay switching occurs due to the
flatness of the energy curve at static switching load. Therefore, we linearize
the arch near the static switching point and get a reduced nonlinear ordinary
differential equation to study the switching dynamics of the arch. This reduced
equation allows us to derive analytical expressions for the delay switching
time of the. We further compare the derived analytical results with the
numerical solutions and observed a good agreement between them. Finally, the
derived analytical formulae can be used to design arches for self-offloading
dynamic footwear for diabetics.
|
2210.05734v2
|
2022-10-17
|
Pion dynamics in a soft-wall AdS-QCD model
|
Pseudo-Goldstone modes appear in many physical systems and display robust
universal features. First, their mass $m$ obeys the so-called
Gell-Mann-Oakes-Renner (GMOR) relation $f^2\,m^2=H\,\bar{\sigma}$, with $f$ the
Goldstone stiffness, $H$ the explicit breaking scale and $\bar{\sigma}$ the
spontaneous condensate. More recently, it has been shown that their damping
$\Omega$ is constrained to follow the relation $\Omega=m^2 D_\varphi$, where
$D_\varphi$ is the Goldstone diffusivity in the purely spontaneous phase. Pions
are the most paradigmatic example of pseudo-Goldstone modes and they are
related to chiral symmetry breaking in QCD. In this work, we consider a
bottom-up soft-wall AdS-QCD model with broken ${\rm{SU}}(2)_L \times
{\rm{SU}}(2)_R$ symmetry and we study the nature of the associated
pseudo-Goldstone modes -- the pions. In particular, we perform a detailed
investigation of their dispersion relation in presence of dissipation, of the
role of the explicit breaking induced by the quark masses and of the dynamics
near the critical point. Taking advantage of the microscopic information
provided by the holographic model, we give quantitative predictions for all the
coefficients appearing in the effective description. In particular, we estimate
the finite temperature behavior of the kinetic parameter $\mathfrak{r^2}$
defined as the ration between the Goldstone diffusivity $D_\varphi$ and the
pion attenuation constant $D_A$. Interestingly, we observe important deviations
from the value $\mathfrak{r^2}=3/4$ computed in chiral perturbation theory in
the limit of zero temperature.
|
2210.09088v1
|
2022-10-23
|
Robust Adaptive Prescribed-Time Control for Parameter-Varying Nonlinear Systems
|
It is an interesting open problem to achieve adaptive prescribed-time control
for strict-feedback systems with unknown and fast or even abrupt time-varying
parameters. In this paper we present a solution with the aid of several design
and analysis innovations. First, by using a spatiotemporal transformation, we
convert the original system operational over finite time interval into one
operational over infinite time interval, allowing for Lyapunov asymptotic
design and recasting prescribed-time stabilization on finite time domain into
asymptotic stabilization on infinite time domain. Second, to deal with
time-varying parameters with unknown variation boundaries, we use congelation
of variables method and establish three separate adaptive laws for parameter
estimation (two for the unknown parameters in the feedback path and one for the
unknown parameter in the input path), in doing so we utilize two tuning
functions to eliminate over-parametrization. Third, to achieve asymptotic
convergence for the transformed system, we make use of nonlinear damping design
and non-regressor-based design to cope with time-varying perturbations, and
finally, we derive the prescribed-time control scheme from the asymptotic
controller via inverse temporal-scale transformation. The boundedness of all
closed-loop signals and control input is proved rigorously through Lyapunov
analysis, squeeze theorem, and two novel lemmas built upon the method of
variation of constants. Numerical simulation verifies the effectiveness of the
proposed method.
|
2210.12706v1
|
2022-11-22
|
Possible enhancement of the superconducting $T_c$ due to sharp Kohn-like soft phonon anomalies
|
Phonon softening is a ubiquitous phenomenon in condensed matter systems which
is often associated with charge density wave (CDW) instabilities and
anharmonicity. The interplay between phonon softening, CDW and
superconductivity is a topic of intense debate. In this work, the effects of
anomalous soft phonon instabilities on superconductivity are studied based on a
recently developed theoretical framework that accounts for phonon damping and
softening within the Migdal-Eliashberg theory. Model calculations show that the
phonon softening in the form of a sharp dip in the phonon dispersion relation,
either acoustic or optical (including the case of Kohn-type anomalies typically
associated with CDW), can cause a manifold increase of the electron-phonon
coupling constant $\lambda$. This, under certain conditions, which are
consistent with the concept of optimal frequency introduced by Bergmann and
Rainer, can produce a large increase of the superconducting transition
temperature $T_c$. In summary, our results suggest the possibility of reaching
high-temperature superconductivity by exploiting soft phonon anomalies
restricted in momentum space.
|
2211.12015v3
|
2022-11-22
|
Understanding Sparse Feature Updates in Deep Networks using Iterative Linearisation
|
Larger and deeper networks generalise well despite their increased capacity
to overfit. Understanding why this happens is theoretically and practically
important. One recent approach looks at the infinitely wide limits of such
networks and their corresponding kernels. However, these theoretical tools
cannot fully explain finite networks as the empirical kernel changes
significantly during gradient-descent-based training in contrast to infinite
networks. In this work, we derive an iterative linearised training method as a
novel empirical tool to further investigate this distinction, allowing us to
control for sparse (i.e. infrequent) feature updates and quantify the frequency
of feature learning needed to achieve comparable performance. We justify
iterative linearisation as an interpolation between a finite analog of the
infinite width regime, which does not learn features, and standard gradient
descent training, which does. Informally, we also show that it is analogous to
a damped version of the Gauss-Newton algorithm -- a second-order method. We
show that in a variety of cases, iterative linearised training surprisingly
performs on par with standard training, noting in particular how much less
frequent feature learning is required to achieve comparable performance. We
also show that feature learning is essential for good performance. Since such
feature learning inevitably causes changes in the NTK kernel, we provide direct
negative evidence for the NTK theory, which states the NTK kernel remains
constant during training.
|
2211.12345v4
|
2023-01-23
|
(Non)-penalized Multilevel methods for non-uniformly log-concave distributions
|
We study and develop multilevel methods for the numerical approximation of a
log-concave probability $\pi$ on $\mathbb{R}^d$, based on (over-damped)
Langevin diffusion. In the continuity of \cite{art:egeapanloup2021multilevel}
concentrated on the uniformly log-concave setting, we here study the procedure
in the absence of the uniformity assumption. More precisely, we first adapt an
idea of \cite{art:DalalyanRiouKaragulyan} by adding a penalization term to the
potential to recover the uniformly convex setting. Such approach leads to an
\textit{$\varepsilon$-complexity} of the order $\varepsilon^{-5} \pi(|.|^2)^{3}
d$ (up to logarithmic terms). Then, in the spirit of \cite{art:gadat2020cost},
we propose to explore the robustness of the method in a weakly convex
parametric setting where the lowest eigenvalue of the Hessian of the potential
$U$ is controlled by the function $U(x)^{-r}$ for $r \in (0,1)$. In this
intermediary framework between the strongly convex setting ($r=0$) and the
``Laplace case'' ($r=1$), we show that with the help of the control of
exponential moments of the Euler scheme, we can adapt some fundamental
properties for the efficiency of the method. In the ``best'' setting where $U$
is ${\mathcal{C}}^3$ and $U(x)^{-r}$ control the largest eigenvalue of the
Hessian, we obtain an $\varepsilon$-complexity of the order
$c_{\rho,\delta}\varepsilon^{-2-\rho} d^{1+\frac{\rho}{2}+(4-\rho+\delta) r}$
for any $\rho>0$ (but with a constant $c_{\rho,\delta}$ which increases when
$\rho$ and $\delta$ go to $0$).
|
2301.09471v1
|
2023-02-02
|
The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing
|
We propose $\textsf{ScaledGD($\lambda$)}$, a preconditioned gradient descent
method to tackle the low-rank matrix sensing problem when the true rank is
unknown, and when the matrix is possibly ill-conditioned. Using
overparametrized factor representations, $\textsf{ScaledGD($\lambda$)}$ starts
from a small random initialization, and proceeds by gradient descent with a
specific form of damped preconditioning to combat bad curvatures induced by
overparameterization and ill-conditioning. At the expense of light
computational overhead incurred by preconditioners,
$\textsf{ScaledGD($\lambda$)}$ is remarkably robust to ill-conditioning
compared to vanilla gradient descent ($\textsf{GD}$) even with
overprameterization. Specifically, we show that, under the Gaussian design,
$\textsf{ScaledGD($\lambda$)}$ converges to the true low-rank matrix at a
constant linear rate after a small number of iterations that scales only
logarithmically with respect to the condition number and the problem dimension.
This significantly improves over the convergence rate of vanilla $\textsf{GD}$
which suffers from a polynomial dependency on the condition number. Our work
provides evidence on the power of preconditioning in accelerating the
convergence without hurting generalization in overparameterized learning.
|
2302.01186v3
|
2023-03-28
|
Nonlocal Nonholonomic Source Seeking Despite Local Extrema
|
In this paper, we investigate the problem of source seeking with a unicycle
in the presence of local extrema. Our study is motivated by the fact that most
of the existing source seeking methods follow the gradient direction of the
signal function and thus only lead to local convergence into a neighborhood of
the nearest local extremum. So far, only a few studies present ideas on how to
overcome local extrema in order to reach a global extremum. None of them apply
to second-order (force- and torque-actuated) nonholonomic vehicles. We consider
what is possibly the simplest conceivable algorithm for such vehicles, which
employs a constant torque and a translational/surge force in proportion to an
approximately differentiated measured signal. We show that the algorithm steers
the unicycle through local extrema towards a global extremum. In contrast to
the previous extremum-seeking studies, in our analysis we do not approximate
the gradient of the objective function but of the objective function's local
spatial average. Such a spatially averaged objective function is expected to
have fewer critical points than the original objective function. Under suitable
assumptions on the averaged objective function and on sufficiently strong
translational damping, we show that the control law achieves practical uniform
asymptotic stability and robustness to sufficiently weak measurement noise and
disturbances to the force and torque inputs.
|
2303.16027v1
|
2023-04-18
|
A blue depression in the optical spectra of M dwarfs
|
A blue depression is found in the spectra of M dwarfs from 4000 to 4500A.
This depression shows an increase toward lower temperatures though is
particularly sensitive to gravity and metallicity. It is the single most
sensitive feature in the optical spectra of M dwarfs. The depression appears as
centered on the neutral calcium resonance line at 4227A and leads to nearby
features being weaker by about two orders of magnitude than predicted. We
consider a variety of possible causes for the depression including temperature,
gravity, metallicity, dust, damping constants, and atmospheric stratification.
We also consider relevant molecular opacities which might be the cause
identifying AlH, SiH, and NaH in the spectral region. However, none of these
solutions are satisfactory. In the absence of a more accurate determination of
the broadening of the calcium line perturbed by molecular hydrogen, we find a
promising empirical fit using a modified Lorentzian line profile for the
calcium resonance line. Such fits provide a simplistic line-broadening
description for this calcium resonance line and potentially other un-modelled
resonance lines in cool high-pressure atmospheres. Thus we claim the most
plausible cause of the blue depression in the optical spectra of M dwarfs is a
lack of appropriate treatment of line broadening for atomic calcium. The broad
wings of the calcium resonance line develop at temperatures below about 4000K
and are analogous to the neutral sodium and potassium features which dominate
the red optical spectra of L dwarfs.
|
2304.09219v2
|
2023-04-19
|
Thickness-dependent magnetic properties in Pt[CoNi]n multilayers with perpendicular magnetic anisotropy
|
We systematically investigated the Ni and Co thickness-dependent
perpendicular magnetic anisotropy (PMA) coefficient, magnetic domain
structures, and magnetization dynamics of Pt(5 nm)/[Co(t_Co nm)/Ni(t_Ni
nm)]5/Pt(1 nm) multilayers by combining the four standard magnetic
characterization techniques. The magnetic-related hysteresis loops obtained
from the field-dependent magnetization M and anomalous Hall resistivity (AHR)
\r{ho}_xy found that the two serial multilayers with t_Co = 0.2 and 0.3 nm have
the optimum PMA coefficient K_U well as the highest coercivity H_C at the Ni
thickness t_Ni = 0.6 nm. Additionally, the magnetic domain structures obtained
by Magneto-optic Kerr effect (MOKE) microscopy also significantly depend on the
thickness and K_U of the films. Furthermore, the thickness-dependent linewidth
of ferromagnetic resonance is inversely proportional to K_U and H_C, indicating
that inhomogeneous magnetic properties dominate the linewidth. However, the
intrinsic Gilbert damping constant determined by a linear fitting of
frequency-dependent linewidth does not depend on Ni thickness and K_U. Our
results could help promote the PMA [Co/Ni] multilayer applications in various
spintronic and spin-orbitronic devices.
|
2304.09366v1
|
2023-04-25
|
Flow-induced oscillations of pitching swept wings: Stability boundary, vortex dynamics and force partitioning
|
We experimentally study the aeroelastic instability boundaries and
three-dimensional vortex dynamics of pitching swept wings, with the sweep angle
ranging from 0 to 25 degrees. The structural dynamics of the wings are
simulated using a cyber-physical control system. With a constant flow speed, a
prescribed high inertia and a small structural damping, we show that the system
undergoes a subcritical Hopf bifurcation to large-amplitude limit-cycle
oscillations (LCOs) for all the sweep angles. The onset of LCOs depends largely
on the static characteristics of the wing. The saddle-node point is found to
change non-monotonically with the sweep angle, which we attribute to the
non-monotonic power transfer between the ambient fluid and the elastic mount.
An optimal sweep angle is observed to enhance the power extraction performance
and thus promote LCOs and destabilize the aeroelastic system. The frequency
response of the system reveals a structural-hydrodynamic oscillation mode for
wings with relatively high sweep angles. Force, moment, and three-dimensional
flow structures measured using multi-layer stereoscopic particle image
velocimetry are analyzed to explain the differences in power extraction for
different swept wings. Finally, we employ a physics-based Force and Moment
Partitioning Method (FMPM) to quantitatively correlate the three-dimensional
vortex dynamics with the resultant unsteady aerodynamic moment.
|
2304.12544v2
|
2023-07-04
|
Exponential stability of Euler-Bernoulli beam under boundary controls in rotation and angular velocity
|
This paper addresses the analysis of a boundary feedback system involving a
non-homogeneous Euler-Bernoulli beam governed by the equation
$m(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the
initial $u(x,0)=u_0(x)$, $u_t(x,0)=v_0(x)$ and boundary conditions $u(0,t)=0$,
$\left (-r(x)u_{xx}(x,t)\right )_{x=0}=-k^{-}_r u_{x}(0,t)-k^{-}_a
u_{xt}(0,t)$, $u(\ell,t)=0$, $\left (-r(x)u_{xx}(x,t)\right )_{x=\ell}=-k^{+}_r
u_{x}(\ell,t)-k^{+}_a u_{xt}(\ell,t)$, with boundary control at both ends
resulting from the rotation and angular velocity. The approach proposed in this
study relies on the utilization of regular weak solutions, energy identity, and
a physically motivated Lyapunov function. By imposing natural assumptions
concerning physical parameters and other inputs, which ensure the existence of
a regular weak solution, we successfully derive a uniform exponential decay
estimate for the system's energy. The decay rate constant featured in this
estimate is solely dependent on the physical and geometric properties of the
beam. These properties encompass crucial parameters such as the viscous
external damping coefficient $\mu(x)$, as well as the boundary springs
$k^{-}_r,k^+_r $ and dampers $k^{-}_a,k^+_a$. To illustrate the practical
effectiveness of our theoretical findings, numerical examples are provided.
These examples serve to demonstrate the applicability and relevance of our
derived results in real-world scenarios.
|
2307.01518v1
|
2023-07-13
|
Exciton-polaritons in CsPbBr$_3$ crystals revealed by optical reflectivity in high magnetic fields and two-photon spectroscopy
|
Cesium lead bromide (CsPbBr$_3$) is a representative material of the emerging
class of lead halide perovskite semiconductors that possess remarkable
optoelectronic properties. Its optical properties in the vicinity of the band
gap energy are greatly contributed by excitons, which form exciton-polaritons
due to strong light-matter interactions. We examine exciton-polaritons in
solution-grown CsPbBr$_3$ crystals by means of circularly-polarized reflection
spectroscopy measured in high magnetic fields up to 60 T. The excited 2P
exciton state is measured by two-photon absorption. Comprehensive modeling and
analysis provides detailed quantitative information about the exciton-polariton
parameters: exciton binding energy of 32.5 meV, oscillator strength
characterized by longitudinal-tranverse splitting of 5.3 meV, damping of 6.7
meV, reduced exciton mass of $0.18 m_0$, exciton diamagnetic shift of 1.6
$\mu$eV/T$^2$, and exciton Land\'e factor $g_X=+2.35$. We show that the exciton
states can be well described within a hydrogen-like model with an effective
dielectric constant of 8.7. From the measured exciton longitudinal-transverse
splitting we evaluate the Kane energy of $E_p=15$ eV, which is in reasonable
agreement with values of $11.8-12.5$ eV derived from the carrier effective
masses.
|
2307.07035v1
|
2023-07-19
|
Impact of bulk viscosity on the post-merger gravitational-wave signal from merging neutron stars
|
In the violent post-merger of binary neutron-star mergers strong oscillations
are present that impact the emitted gravitational-wave (GW) signal. The
frequencies, temperatures and densities involved in these oscillations allow
for violations of the chemical equilibrium promoted by weak-interactions, thus
leading to a nonzero bulk viscosity that can impact dynamics and GW signals. We
present the first simulations of binary neutron-star mergers employing the
self-consistent and second-order formulation of the equations of relativistic
hydrodynamics for dissipative fluids proposed by M\"uller, Israel and Stewart.
With the spirit of obtaining a first assessment of the impact of bulk viscosity
on the structure and radiative efficiency of the merger remnant we adopt a
simplified approach for the viscosity, which we assume to be constant within
the stars, but which we vary in strength for different binaries, thus exploring
the possible behaviours and obtaining strict upper limits. In this way, we find
that large bulk viscosities are very effective at damping the
collision-and-bounce oscillations that characterize the dynamics of the stellar
cores right after the merger. As a result, the $m=2$ deformations and the
gravitational-radiation efficiency of the remnant are considerably reduced,
with qualitative and quantitative changes in the post-merger spectrum that can
be large in the case of the most extreme configurations. Overall, our crude but
self-consistent results indicate that bulk viscosity reduces the energy
radiated in GWs by $\lesssim 1\%$ in the (realistic) scenario of small
viscosity, and by $\lesssim 15\%$ in the (unrealistic) scenario of large
viscosity.
|
2307.10464v1
|
2023-07-21
|
Non-ideal magnetohydrodynamics on a moving mesh I: Ohmic and ambipolar diffusion
|
Especially in cold and high-density regions, the assumptions of ideal
magnetohydrodynamics (MHD) can break down, making first order non-ideal terms
such as Ohmic and ambipolar diffusion as well as the Hall effect important. In
this study we present a new numerical scheme for the first two resistive terms,
which we implement in the moving-mesh code AREPO using the single-fluid
approximation combined with a new gradient estimation technique based on a
least-squares fit per interface. Through various test calculations including
the diffusion of a magnetic peak, the structure of a magnetic C-shock, and the
damping of an Alfv\'en wave, we show that we can achieve an accuracy comparable
to the state-of-the-art code ATHENA++. We apply the scheme to the linear growth
of the magnetorotational instability and find good agreement with the
analytical growth rates. By simulating the collapse of a magnetised cloud with
constant magnetic diffusion, we show that the new scheme is stable even for
large density contrasts. Thanks to the Lagrangian nature of the moving mesh
method the new scheme is thus well suited for intended future applications
where a high resolution in the dense cores of collapsing protostellar clouds
needs to be achieved. In a forthcoming work we will extend the scheme to the
Hall effect.
|
2307.11814v1
|
2023-09-14
|
The cost of solving linear differential equations on a quantum computer: fast-forwarding to explicit resource counts
|
How well can quantum computers simulate classical dynamical systems? There is
increasing effort in developing quantum algorithms to efficiently simulate
dynamics beyond Hamiltonian simulation, but so far exact resource estimates are
not known. In this work, we provide two significant contributions. First, we
give the first non-asymptotic computation of the cost of encoding the solution
to general linear ordinary differential equations into quantum states -- either
the solution at a final time, or an encoding of the whole history within a time
interval. Second, we show that the stability properties of a large class of
classical dynamics allow their fast-forwarding, making their quantum simulation
much more time-efficient. From this point of view, quantum Hamiltonian dynamics
is a boundary case that does not allow this form of stability-induced
fast-forwarding. In particular, we find that the history state can always be
output with complexity $O(T^{1/2})$ for any stable linear system. We present a
range of asymptotic improvements over state-of-the-art in various regimes. We
illustrate our results with a family of dynamics including linearized
collisional plasma problems, coupled, damped, forced harmonic oscillators and
dissipative nonlinear problems. In this case the scaling is quadratically
improved, and leads to significant reductions in the query counts after
inclusion of all relevant constant prefactors.
|
2309.07881v2
|
2023-09-18
|
Coherent Tunneling and Strain Sensitivity of an All Heusler Alloy Magnetic Tunneling Junction: A First-Principles Study
|
Half-metallic Co-based full Heusler alloys have captured considerable
attention of the researchers in the realm of spintronic applications, owing to
their remarkable characteristics such as exceptionally high spin polarization
at Fermi level, ultra-low Gilbert damping, and high Curie temperature. In this
comprehensive study, employing density functional theory, we delve into the
stability and electron transport properties of a magnetic tunneling junction
(MTJ) comprising a Co$_2$MnSb/HfIrSb interface. Utilizing a standard model
given by Julliere, we estimate the tunnel magnetoresistance (TMR) ratio of this
heterojunction under external electric field, revealing a significantly high
TMR ratio (500%) that remains almost unaltered for electric field magnitudes up
to 0.5 V/A. In-depth investigation of K-dependent majority spin transmissions
uncovers the occurrence of coherent tunneling for the Mn-Mn/Ir interface,
particularly when a spacer layer beyond a certain thickness is employed.
Additionally, we explore the impact of bi-axial strain on the MTJ by varying
the in-plane lattice constants between -4% and +4%. Our spin-dependent
transmission calculations demonstrate that the Mn-Mn/Ir interface manifests
strain-sensitive transmission properties under both compressive and tensile
strain, and yields a remarkable three-fold increase in majority spin
transmission under tensile strain conditions. These compelling outcomes place
the Co2MnSb/HfIrSb junction among the highly promising candidates for nanoscale
spintronic devices, emphasizing the potential significance of the system in the
advancement of the field.
|
2309.09755v1
|
2023-09-25
|
Domain wall dynamics driven by a transient laser-induced magnetisation
|
One of the fundamental effects of the laser-matter interaction is the
appearance of an induced transient magnetisation. While the underlying
phenomena differ in their microscopic origin and cover a diverse array of
materials, here we address a fundamental question about the possibility to
drive domain-wall dynamics on the femtosecond timescale of the exchange
interactions solely by longitudinal changes of the magnetic moments. We verify
the viability of this hypothesis in the case of a generic ferromagnetic system
described in the framework of the high-temperature micromagnetic model based on
the Landau-Lifshitz-Bloch equation. The effect is investigated in a 1D model at
constant temperature as well as in a full micromagnetic framework considering
realistic laser-induced heating. Our results demonstrate that domain-wall
deformation in a femtosecond timeframe leads to the displacement of the wall on
a larger timescale up to nanoseconds accompanied by a release of excess energy
in the form of spin waves. The domain wall deformation leads to the appearance
of a magnetisation gradient across the wall which promotes the motion towards
the region consisting of spins with decreased magnetisation length. The total
displacement is enhanced at larger temperatures and smaller damping due to an
increase of the longitudinal relaxation time which ensures the longer presence
of the induced magnetisation gradient. We also demonstrate an enhanced domain
wall motion in the presence of the Dzyaloshinskii-Moriya interaction attributed
to augmented magnonic torques. Our results are important towards the
understanding of ultrafast magnetism phenomena on the sub-picosecond timescale.
|
2309.14287v1
|
2023-10-03
|
Controlled Quasi-Latitudinal Solutions for ultra-fast Spin-Torque Precessional Magnetization Switching
|
The aim of the paper is to present a novel class of time-dependent controls
to realize ultra-fast magnetization switching in nanomagnets driven by
spin-torques produced by spin-polarized electric currents. Magnetization
dynamics in such systems is governed by the Landau-Lifshitz-Slonczewski
equation which describes the precessional motion of (dimensionless)
magnetization vector on the unit-sphere. The relevant case of nanoparticles
with uniaxial anisotropy having in-plane easy and intermediate axes and
out-of-plane hard axis is considered. By exploiting the characteristic
smallness of damping and spin-torque intensity, the aforementioned controls are
constructed via suitable perturbative tools in a way to realise approximate
\emph{latitudinal solutions} (i.e. motions on a sphere in which the
out-of-plane magnetization component stays constant) with the effect to fast
``switch'' the system from one stationary state to another. The possibility to
keep a (``small'') bounded value of the out-of-plane coordinate throughout this
process of ``transfer'', turns out to be advantageous in the applications as it
sensibly reduces the post-switching relaxation oscillations that may cause the
failure of switching in real samples. Further relevant quantitative results on
the behaviour of the solutions during the pre- and post-switching stages
(termed ``expulsion'' and ``attraction'', respectively), are given as a
byproduct. A selection of validating numerical experiments is presented
alongside the corresponding theoretical results.
|
2310.02070v1
|
2023-09-29
|
A Fast second-order solver for stiff multifluid dust and gas hydrodynamics
|
We present MDIRK: a Multifluid second-order Diagonally-Implicit Runge-Kutta
method to study momentum transfer between gas and an arbitrary number ($N$) of
dust species. The method integrates the equations of hydrodynamics with an
Implicit Explicit (IMEX) scheme and solves the stiff source term in the
momentum equation with a diagonally-implicit asymptotically stable Runge-Kutta
method (DIRK). In particular, DIRK admits a simple analytical solution that can
be evaluated with $\mathcal{O}(N)$ operations, instead of standard matrix
inversion, which is $\mathcal{O}(N)^3$. Therefore the analytical solution
significantly reduces the computational cost of the multifluid method, making
it suitable for studying the dynamics of systems with particle-size
distributions. We demonstrate that the method conserves momentum to machine
precision and converges to the correct equilibrium solution with constant
external acceleration. To validate our numerical method we present a series of
simple hydrodynamic tests, including damping of sound waves, dusty shocks, a
multi-fluid dusty Jeans instability, and a steady-state gas-dust drift
calculation. The simplicity of MDIRK lays the groundwork to build fast
high-order asymptotically stable multifluid methods.
|
2310.04435v3
|
2023-10-19
|
Error-mitigated fermionic classical shadows on noisy quantum devices
|
Efficiently estimating the expectation values of fermionic Hamiltonians,
including $k$-particle reduced density matrices ($k$-RDMs) of an $n$-mode
fermionic state, is crucial for quantum simulations of a wealth of physical
systems from the fields of many-body physics, chemistry, and materials. Yet,
conventional quantum state tomography methods are too costly in terms of their
resource requirements. Classical shadow (CS) algorithms have been proposed as a
solution to address this task by substantially reducing the number of copies of
quantum states. However, the implementation of these algorithms faces a
significant challenge due to the inherent noise in near-term quantum devices,
leading to inaccuracies in gate operations. To address this challenge, we
propose an error-mitigated CS algorithm for fermionic systems. For $n$-qubit
quantum systems, our algorithm, which employs the easily prepared initial state
$|0^n\rangle\!\langle 0^n|$ assumed to be noiseless, provably efficiently
estimates all elements of $k$-RDMs with $\widetilde{\mathcal O}(kn^k)$ scaled
copies of quantum states and $\widetilde{\mathcal O}(\sqrt{n})$ scaled
calibration measurements. It does so even in the presence of gate or
measurement noise such as depolarizing, amplitude damping, or $X$-rotation
noise with at most a constant noise strength. Furthermore, our algorithm
exhibits scaling comparable to previous CS algorithms for fermionic systems
with respect to the number of quantum state copies, while also demonstrating
enhanced resilience to noise. We numerically demonstrate the performance of our
algorithm in the presence of these noise sources, and its performance under
Gaussian unitary noise. Our results underscore the potential utility of
implementing our algorithm on near-term quantum devices.
|
2310.12726v2
|
2023-11-02
|
Phase space noncommutativity, power-law inflation and quantum cosmology
|
Considering an arbitrary dimensional FLRW universe in the framework of a
generalized S\'{a}ez--Ballester (SB) theory, we establish a noncommutative (NC)
cosmological model. We concentrate on the predictions of NC model and compare
them with their commutative counterparts in both the classical and quantum
regimes. For the classic case, taking a very small NC parameter, we apply two
different methods to analyze the model features. First, we show through
numerical analysis that our NC model is a successful inflationary model capable
of overcoming the graceful exit and horizon problems. Furthermore, the NC
traces are visible the late time, which supports the UV/IR mixing
characteristic of the NC models. In the second method, we show that our NC
model can correspond to the previously developed NC inflationary models. In the
commutative quantum case, we obtain an exact wave function and then use the WKB
approximation to show that the solutions of the corresponding classical regime
are recovered. Finally, with regard to the NC quantum level, we focus on the
special case for which we show that a constant of motion exists. The latter
helps us to conveniently transform the corresponding complicated NC-WDW
equation into an ordinary differential equation, which can be easily solved
numerically for the general case or analytically for some special cases. The
resultant solutions show a damping behavior in the wave function associated
with the proposed NC model, which may be important in determining the viable
initial states for the very early universe.
|
2311.01627v1
|
2023-11-04
|
Electronic quantum wires in extended quasiparticle picture
|
A one-dimensional quantum wire of Fermions is considered and ground state
properties are calculated in the high density regime within the extended
quasiparticle picture and Born approximation. Expanding the two-particle Green
functions determines the selfenergy and the polarization as well as the
response function on the same footing. While the on-shell selfenergies are
strictly zero due to Pauli-blocking of elastic scattering, the off-shell
behaviour shows a rich structure of a gap in the damping of excitation which is
closed when the momentum approaches the Fermi one. The consistent spectral
function is presented completing the first two energy-weighted sum rules. The
excitation spectrum shows a splitting due to holons and antiholons as non-Fermi
liquid behaviour. A renormalization procedure is proposed by subtracting an
energy constant to render the Fock exchange energy finite. The effective mass
derived from meanfield shows a dip as onset of Peierls instability. The
correlation energy is calculated with the help of the extended quasiparticle
picture which accounts for off-shell effects. The corresponding response
function leads to the same correlation energy as the selfenergy in agreement
with perturbation theory. The reduced density matrix or momentum distribution
is calculated with the help of a Pad\'e regularization repairing deficiencies
of the perturbation theory. A seemingly finite step at the Fermi energy
indicating Fermi-liquid behaviour is repaired in this way.
|
2311.02414v1
|
2023-11-14
|
Berry curvature induced giant intrinsic spin-orbit torque in single layer magnetic Weyl semimetal thin films
|
Topological quantum materials can exhibit unconventional surface states and
anomalous transport properties, but their applications to spintronic devices
are restricted as they require the growth of high-quality thin films with
bulk-like properties. Here, we study 10--30 nm thick epitaxial ferromagnetic
Co$_{\rm 2}$MnGa films with high structural order. Very high values of the
anomalous Hall conductivity, $\sigma_{\rm xy}=1.35\times10^{5}$ $\Omega^{-1}
m^{-1}$, and the anomalous Hall angle, $\theta_{\rm H}=15.8\%$, both comparable
to bulk values. We observe a dramatic crystalline orientation dependence of the
Gilbert damping constant of a factor of two and a giant intrinsic spin Hall
conductivity, $\mathit{\sigma_{\rm SHC}}=(6.08\pm 0.02)\times 10^{5}$
($\hbar/2e$) $\Omega^{-1} m^{-1}$, which is an order of magnitude higher than
literature values of single-layer Ni$_{\rm 80}$Fe$_{\rm 20}$, Ni, Co, Fe, and
multilayer Co$_{\rm 2}$MnGa stacks. Theoretical calculations of the intrinsic
spin Hall conductivity, originating from a strong Berry curvature, corroborate
the results and yield values comparable to the experiment. Our results open up
for the design of spintronic devices based on single layers of topological
quantum materials.
|
2311.08145v2
|
2023-12-26
|
All solution grown epitaxial magnonic crystal of thulium iron garnet thin film
|
Magnonics has shown the immense potential of compatibility with CMOS devices
and the ability to be utilized in futuristic quantum computing. Therefore, the
magnonic crystals, both metallic and insulating, are under extensive
exploration. The presence of high spin-orbit interaction induced by the
presence of rare-earth elements in thulium iron garnet (TmIG) increases its
potential in magnonic applications. Previously, TmIG thin films were grown
using ultra-high vacuum-based techniques. Here, we present a cost-effective
solution-based approach that enables the excellent quality interface and
surface roughness of the epitaxial TmIG/GGG. The deposited TmIG (12.2 nm) thin
film's physical and spin dynamic properties are investigated in detail. The
confirmation of the epitaxy using X-ray diffraction in $\phi$-scan geometry
along with the X-ray reflectivity and atomic force for the thickness and
roughness analysis and topography, respectively. The epitaxial TmIG/GGG have
confirmed the perpendicular magnetic anisotropy utilizing the
polar-magneto-optic Kerr effect. Analyzing the ferromagnetic resonance study of
TmIG/GGG thin films provides the anisotropy constant K$_U$ = 20.6$\times$10$^3$
$\pm$ 0.2$\times$10$^3$ N/m$^2$ and the Gilbert damping parameter $\alpha$ =
0.0216 $\pm$ 0.0028. The experimental findings suggest that the
solution-processed TmIG/GGG thin films have the potential to be utilized in
device applications.
|
2312.15973v1
|
2023-12-01
|
Large enhancement of spin-orbit torques under a MHz modulation due to phonon-magnon coupling
|
The discovery of spin-orbit torques (SOTs) generated through the spin Hall or
Rashba effects provides an alternative write approach for magnetic
random-access memory (MRAM), igniting the development of spin-orbitronics in
recent years. Quantitative characterization of SOTs highly relies on the
SOT-driven ferromagnetic resonance (ST-FMR), where a modulated microwave
current is used to generate ac SOTs and the modulation-frequency is usually
less than 100 kHz (the limit of conventional lock-in amplifiers). Here we have
investigated the SOT of typical SOT material/ferromagnet bilayers in an
extended modulation-frequency range, up to MHz, by developing the ST-FMR
measurement. Remarkably, we found that the measured SOTs are enhanced about
three times in the MHz range, which cannot be explained according to present
SOT theory. We attribute the enhancement of SOT to additional magnon
excitations due to phonon-magnon coupling, which is also reflected in the
slight changes of resonant field and linewidth in the acquired ST-FMR spectra,
corresponding to the modifications of effective magnetization and damping
constant, respectively. Our results indicate that the write current of SOT-MRAM
may be reduced with the assistant of phonon-magnon coupling.
|
2401.02967v1
|
2024-01-25
|
Photon propagation in a charged Bose-Einstein condensate
|
We consider the propagation of photons in the background of a Bose-Einstein
(BE) condensate of a charged scalar field, by extending a method recently
proposed to treat the propagation of fermions in a BE condensate. We determine
the dispersion relations of the collective modes of the system, as well as the
photon polarization tensor and the dielectric constant that result after the
symmetry breaking associated with the BE condensation in the model. Two modes
correspond to the transverse photon polarizations, and their dispersion
relations have the usual form of the transverse photons in a plasma. The other
two modes, which we denote as the $(\pm)$ modes, are combinations of the
longitudinal photon and the massive scalar field. The dispersion relation of
the $(-)$ mode decreases as a function of the momentum in a given range, and
the corresponding group velocity is negative in that range. We also determine
the wavefunctions of the $(\pm)$ modes, which can be used to obtain the
corrections to the dispersion relations (e.g., imaginary parts due the damping
effects) and/or the effects of scattering, due to the interactions with the
excitations of the system. The results can be useful in various physical
contexts that have been considered in the literature involving the
electrodynamics of a charged scalar BE condensate.
|
2401.13896v1
|
2024-01-26
|
Well-posedness and stability of the Navier-Stokes-Maxwell equations
|
The paper is devoted to studying the well-posedness and stability of the
generalized Navier-Stokes-Maxwell (NSM) equations with the standard Ohm's law
in $\mathbb{R}^d$ for $d \in \{2,3\}$. More precisely, the global
well-posedness is established in case of fractional Laplacian velocity
$(-\Delta)^\alpha v$ with $\alpha = \frac{d}{2}$ for suitable data. In
addition, the local well-posedness in the inviscid case is also provided for
sufficient smooth data, which allows us to study the inviscid limit of
associated positive viscosity solutions in the case $\alpha = 1$, where an
explicit bound on the difference is given. On the other hand, in the case
$\alpha = 0$ the stability near a magnetohydrostatic equilibrium with a
constant (or equivalently bounded) magnetic field is also obtained in which
nonhomogeneous Sobolev norms of the velocity and electric fields, and the
$L^\infty$ norm of the magnetic field converge to zero as time goes to infinity
with an implicit rate. In this velocity damping case, the situation is
different both in case of the two and a half, and three-dimensional
magnetohydrodynamics (MHD) system, where an explicit rate of convergence in
infinite time is computed for both the velocity and magnetic fields in
nonhomogeneous Sobolev norms. Therefore, there is a gap between NSM and MHD in
terms of the norm convergence of the magnetic field and the rate of decaying in
time, even the latter equations can be proved as a limiting system of the
former one in the sense of distributions as the speed of light tends to
infinity.
|
2401.14839v2
|
2024-03-14
|
The effect of spatially-varying collision frequency on the development of the Rayleigh-Taylor instability
|
The Rayleigh-Taylor (RT) instability is ubiquitously observed, yet has
traditionally been studied using ideal fluid models. Collisionality can vary
strongly across the fluid interface, and previous work demonstrates the
necessity of kinetic models to completely capture dynamics in certain
collisional regimes. Where previous kinetic simulations used spatially- and
temporally-constant collision frequency, this work presents 5-dimensional (two
spatial, three velocity dimensions) continuum-kinetic simulations of the RT
instability using a more realistic spatially-varying collision frequency. Three
cases of collisional variation are explored for two Atwood numbers: low to
intermediate, intermediate to high, and low to high. The low to intermediate
case exhibits no RT instability growth, while the intermediate to high case is
similar to a fluid limit kinetic case with interface widening biased towards
the lower collisionality region. A novel contribution of this work is the low
to high collisionality case that shows significantly altered instability growth
through upward movement of the interface and damped spike growth due to
increased free-streaming particle diffusion in the lower region. Contributions
to the energy-flux from the non-Maxwellian portions of the distribution
function are not accessible to fluid models and are greatest in magnitude in
the spike and regions of low collisionality. Increasing the Atwood number
results in greater RT instability growth and reduced upward interface movement.
Deviation of the distribution function from Maxwellian is inversely
proportional to collision frequency and concentrated around the fluid
interface. The linear phase of RT instability growth is well-described by
theoretical linear growth rates accounting for viscosity and diffusion.
|
2403.09591v1
|
2024-04-11
|
The Cattaneo-Christov approximation of Fourier heat-conductive compressible fluids
|
We investigate the Navier-Stokes-Cattaneo-Christov (NSC) system in
$\mathbb{R}^d$ ($d\geq3$), a model of heat-conductive compressible flows
serving as a finite speed of propagation approximation of the
Navier-Stokes-Fourier (NSF) system. Due to the presence of Oldroyd's
upper-convected derivatives, the system (NSC) exhibits a \textit{lack of
hyperbolicity} which makes it challenging to establish its well-posedness,
especially in multi-dimensional contexts. In this paper, within a critical
regularity functional framework, we prove the global-in-time well-posedness of
(NSC) for initial data that are small perturbations of constant equilibria,
uniformly with respect to the approximation parameter $\varepsilon>0$. Then,
building upon this result, we obtain the sharp large-time asymptotic behaviour
of (NSC) and, for all time $t>0$, we derive quantitative error estimates
between the solutions of (NSC) and (NSF). To the best of our knowledge, our
work provides the first strong convergence result for this relaxation procedure
in the three-dimensional setting and for ill-prepared data.
The (NSC) system is partially dissipative and incorporates both partial
diffusion and partial damping mechanisms. To address these aspects and ensure
the large-time stability of the solutions, we construct localized-in-frequency
perturbed energy functionals based on the hypocoercivity theory. More
precisely, our analysis relies on partitioning the frequency space into
\textit{three} distinct regimes: low, medium and high frequencies. Within each
frequency regime, we introduce effective unknowns and Lyapunov functionals,
revealing the spectrally expected dissipative structures.
|
2404.07809v1
|
2003-10-29
|
Comparing Chemical Abundances of the Damped Lya Systems and Metal-Poor Stars
|
I briefly draw comparisons between the fields of damped Lya and metal-poor
stellar abundances. In particular, I examine their complementary
age-metallicity relations and comparisons between the damped Lya and dwarf
galaxy abundance patterns. Regarding the latter, I describe a series of
problems concerning associating high z damped Lya systems with present-day
dwarfs.
|
0310850v1
|
2006-12-01
|
Stochastic excitation and damping of solar-type oscillations
|
A review on acoustic mode damping and excitation in solar-type stars is
presented. Current models for linear damping rates are discussed in the light
of recent low-degree solar linewidth measurements with emphasis on the
frequency-dependence of damping rates of low-order modes. Recent developments
in stochastic excitation models are reviewed and tested against the latest
high-quality data of solar-like oscillations, such as from alpha Cen A, and
against results obtained from hydrodynamical simulations.
|
0612024v1
|
1997-08-11
|
A theoretical study on the damping of collective excitations in a Bose-Einstein condensate
|
We study the damping of low-lying collective excitations of condensates in a
weakly interacting Bose gas model within the framework of imaginary time path
integral. A general expression of the damping rate has been obtained in the low
momentum limit for both the very low temperature regime and the higher
temperature regime. For the latter, the result is new and applicable to recent
experiments. Theoretical predictions for the damping rate are compared with the
experimental values.
|
9708080v3
|
1997-09-24
|
Damping in dilute Bose gases: a mean-field approach
|
Damping in a dilute Bose gas is investigated using a mean-field approximation
which describes the coupled oscillations of condensate and non-condensate atoms
in the collisionless regime. Explicit results for both Landau and Beliaev
damping rates are given for non-uniform gases. In the case of uniform systems
we obtain results for the damping of phonons both at zero and finite
temperature. The isothermal compressibility of a uniform gas is also discussed.
|
9709259v1
|
2000-09-01
|
Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud
|
We calculate the damping of condensate collective excitations at finite
temperatures arising from the lack of equilibrium between the condensate and
thermal atoms. We neglect the non-condensate dynamics by fixing the thermal
cloud in static equilibrium. We derive a set of generalized Bogoliubov
equations for finite temperatures that contain an explicit damping term due to
collisional exchange of atoms between the two components. We have numerically
solved these Bogoliubov equations to obtain the temperature dependence of the
damping of the condensate modes in a harmonic trap. We compare these results
with our recent work based on the Thomas-Fermi approximation.
|
0009021v2
|
2000-11-20
|
Cavity assisted quasiparticle damping in a Bose-Einstein condensate
|
We consider an atomic Bose-Einstein condensate held within an optical cavity
and interacting with laser fields. We show how the interaction of the cavity
mode with the condensate can cause energy due to excitations to be coupled to a
lossy cavity mode, which then decays, thus damping the condensate, how to
choose parameters for damping specific excitations, and how to target a range
of different excitations to potentially produce extremely cold condensates.
|
0011341v2
|
2002-12-16
|
The nonlinear damping of Bose-Einstein condensate oscillations at ultra-low temperatures
|
We analyze the damping of the transverse breathing mode in an elongated trap
at ultralow temperatures. The damping occurs due to the parametric resonance
entailing the energy transfer to the longitudinal degrees of freedom. It is
found that the nonlinear coupling between the transverse and discrete
longitudinal modes can result in an anomalous behavior of the damping as a
function of time with the partially reversed pumping of the breathing mode. The
picture revealed explains the results observed in [16].
|
0212377v2
|
2004-08-27
|
Tunable magnetization damping in transition metal ternary alloys
|
We show that magnetization damping in Permalloy, Ni80Fe20 (``Py''), can be
enhanced sufficiently to reduce post-switching magnetization precession to an
acceptable level by alloying with the transition metal osmium (Os). The damping
increases monotonically upon raising the Os-concentration in Py, at least up to
9% of Os. Other effects of alloying with Os are suppression of magnetization
and enhancement of in-plane anisotropy. Magnetization damping also increases
significantly upon alloying with the five other transition metals included in
this study (4d-elements: Nb, Ru, Rh; 5d-elements: Ta, Pt) but never as strongly
as with Os.
|
0408608v1
|
2005-03-06
|
Nonlinear damping in nanomechanical beam oscillator
|
We investigate the impact of nonlinear damping on the dynamics of a
nanomechanical doubly clamped beam. The beam is driven into nonlinear regime
and the response is measured by a displacement detector. For data analysis we
introduce a nonlinear damping term to Duffing equation. The experiment shows
conclusively that accounting for nonlinear damping effects is needed for
correct modeling of the nanomechanical resonators under study.
|
0503130v2
|
2006-05-23
|
The origin of increase of damping in transition metals with rare earth impurities
|
The damping due to rare earth impurities in transition metals is discussed in
the low concentration limit. It is shown that the increase in damping is mainly
due to the coupling of the orbital moments of the rare earth impurities and the
conduction $p$-electrons. It is shown that an itinerant picture for the host
transition ions is needed to reproduce the observed dependence of the damping
on the total angular moment of the rare earths.
|
0605583v1
|
2001-05-14
|
Simplified models of electromagnetic and gravitational radiation damping
|
In previous work the authors analysed the global properties of an approximate
model of radiation damping for charged particles. This work is put into context
and related to the original motivation of understanding approximations used in
the study of gravitational radiation damping. It is examined to what extent the
results obtained previously depend on the particular model chosen. Comparisons
are made with other models for gravitational and electromagnetic fields. The
relation of the kinetic model for which theorems were proved to certain
many-particle models with radiation damping is exhibited.
|
0105045v1
|
1994-06-07
|
Damping Rate of a Yukawa Fermion at Finite Temperature
|
The damping of a massless fermion coupled to a massless scalar particle at
finite temperature is considered using the Braaten-Pisarski resummation
technique. First the hard thermal loop diagrams of this theory are extracted
and effective Green's functions are constructed. Using these effective Green's
functions the damping rate of a soft Yukawa fermion is calculated. This rate
provides the most simple example for the damping of a soft particle. To leading
order it is proportional to $g^2T$, whereas the one of a hard fermion is of
higher order.
|
9406242v1
|
2006-05-02
|
Moduli decay in the hot early Universe
|
We consider moduli fields interacting with thermalized relativistic matter.
We determine the temperature dependence of their damping rate and find it is
dominated by thermal effects in the high temperature regime, i.e. for
temperatures larger than their mass. For a simple scalar model the damping rate
is expressed through the known matter bulk viscosity. The high temperature
damping rate is always smaller than the Hubble rate, so that thermal effects
are not sufficient for solving the cosmological moduli problem.
|
0605030v2
|
2006-11-27
|
Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${{\mathbb R}^2}$
|
We consider the zero viscosity limit of long time averages of solutions of
damped and driven Navier-Stokes equations in ${\mathbb R}^2$. We prove that the
rate of dissipation of enstrophy vanishes. Stationary statistical solutions of
the damped and driven Navier-Stokes equations converge to renormalized
stationary statistical solutions of the damped and driven Euler equations.
These solutions obey the enstrophy balance.
|
0611782v1
|
2001-11-25
|
The Landau Damping Effect and Complex-valued Nature of Physical Quantities
|
Within the framework of the hypothesis offered by authors about
complex-valued nature of physical quantities, the effect of the Landau damping
has been explored with assumption that not only frequency can be a small
imaginary component but also a wave vector. The numerical solution of the
obtained dispersion equation testifies that uncollisional damping is
accompanied in a certain region of space by antidumping of waves, and in
particular situations antidumping may prevail over damping. It is possible that
this effect may explain the experimental difficulties connected with inhibition
of instabilities of plasma in the problem of controllable thermonuclear fusion.
|
0111176v1
|
2005-10-14
|
Nontrapping arrest of Langmuir wave damping near the threshold amplitude
|
Evolution of a Langmuir wave is studied numerically for finite amplitudes
slightly above the threshold which separates damping from nondamping cases.
Arrest of linear damping is found to be a second-order effect due to ballistic
evolution of perturbations, resonant power transfer between field and
particles, and organization of phase space into a positive slope for the
average distribution function $f_{av}$ around the resonant wave phase speed
$v_\phi$. Near the threshold trapping in the wave potential does not arrest
damping or saturate the subsequent growth phase.
|
0510131v3
|
2000-06-22
|
Decoherence and Entanglement in Two-mode Squeezed Vacuum States
|
I investigate the decoherence of two-mode squeezed vacuum states by analyzing
the relative entropy of entanglement. I consider two sources of decoherence:
(i) the phase damping and (ii) the amplitude damping due to the coupling to the
thermal environment. In particular, I give the exact value of the relative
entropy of entanglement for the phase damping model. For the amplitude damping
model, I give an upper bound for the relative entropy of entanglement, which
turns out to be a good approximation for the entanglement measure in usual
experimental situations.
|
0006100v1
|
2006-08-02
|
Damped Population Oscillation in a Spontaneously Decaying Two-Level Atom Coupled to a Monochromatic Field
|
We investigate the time evolution of atomic population in a two-level atom
driven by a monochromatic radiation field, taking spontaneous emission into
account. The Rabi oscillation exhibits amplitude damping in time caused by
spontaneous emission. We show that the semiclassical master equation leads in
general to an overestimation of the damping rate and that a correct
quantitative description of the damped Rabi oscillation can thus be obtained
only with a full quantum mechanical theory.
|
0608020v1
|
2006-11-23
|
Analytical solutions for two-level systems with damping
|
A method is proposed to transform any analytic solution of the Bloch equation
into an analytic solution of the Landau-Lifshitz-Gilbert equation. This allows
for the analytical description of the dynamics of a two level system with
damping. This method shows that damping turns the linear Schr\"{o}dinger
equation of a two-level system into a nonlinear Schr\"{o}dinger equation. As
applications, it is shown that damping has a relatively mild influence on
self-induced transparency but destroys dynamical localization.
|
0611238v1
|
2007-06-12
|
Gilbert and Landau-Lifshitz damping in the presense of spin-torque
|
A recent article by Stiles et al. (cond-mat/0702020) argued in favor of the
Landau-Lifshitz damping term in the micromagnetic equations of motion over that
of the more commonly accepted Gilbert damping form. Much of their argument
revolved around spin-torque driven domain wall motion in narrow magnetic wires,
since the presence of spin-torques can more acutely draw a distinction between
the two forms of damping. In this article, the author uses simple arguments and
examples to offer an alternative point of view favoring Gilbert.
|
0706.1736v1
|
2008-04-04
|
Inhomogeneous Gilbert damping from impurities and electron-electron interactions
|
We present a unified theory of magnetic damping in itinerant electron
ferromagnets at order $q^2$ including electron-electron interactions and
disorder scattering. We show that the Gilbert damping coefficient can be
expressed in terms of the spin conductivity, leading to a Matthiessen-type
formula in which disorder and interaction contributions are additive. In a weak
ferromagnet regime, electron-electron interactions lead to a strong enhancement
of the Gilbert damping.
|
0804.0820v2
|
2008-12-18
|
Dipole Oscillations of a Fermi Gas in a Disordered Trap: Damping and Localization
|
We theoretically study the dipole oscillations of an ideal Fermi gas in a
disordered trap. We show that even weak disorder induces strong damping of the
oscillations and we identify a metal-insulator crossover. For very weak
disorder, we show that damping results from a dephasing effect related to weak
random perturbations of the energy spectrum. For increasing disorder, we show
that the Fermi gas crosses over to an insulating regime characterized by
strong-damping due to the proliferation of localized states.
|
0812.3501v2
|
2009-03-11
|
Confronting the damping of the baryon acoustic oscillations with observation
|
We investigate the damping of the baryon acoustic oscillations in the matter
power spectrum due to the quasinonlinear clustering and redshift-space
distortions by confronting the models with the observations of the Sloan
Digital Sky Survey luminous red galaxy sample. The chi-squared test suggests
that the observed power spectrum is better matched by models with the damping
of the baryon acoustic oscillations rather than the ones without the damping.
|
0903.1883v1
|
2009-04-10
|
Spectral deviations for the damped wave equation
|
We prove a Weyl-type fractal upper bound for the spectrum of the damped wave
equation, on a negatively curved compact manifold. It is known that most of the
eigenvalues have an imaginary part close to the average of the damping
function. We count the number of eigenvalues in a given horizontal strip
deviating from this typical behaviour; the exponent that appears naturally is
the `entropy' that gives the deviation rate from the Birkhoff ergodic theorem
for the geodesic flow. A Weyl-type lower bound is still far from reach; but in
the particular case of arithmetic surfaces, and for a strong enough damping, we
can use the trace formula to prove a result going in this direction.
|
0904.1736v1
|
2009-10-26
|
Pressure Fronts in 1D Damped Nonlinear Lattices
|
The propagation of pressure fronts (impact solutions) in 1D chains of atoms
coupled by anharmonic potentials between nearest neighbor and submitted to
damping forces preserving uniform motion, is investigated. Travelling fronts
between two regions at different uniform pressures are found numerically and
well approximate analytically. It is proven that there are three analytical
relations between the impact velocity, the compression, the front velocity and
the energy dissipation which only depend on the coupling potential and are
\textit{independent} of the damping. Such travelling front solutions cannot
exist without damping.
|
0910.4890v1
|
2010-01-12
|
Decoherence and damping in ideal gases
|
The particle and current densities are shown to display damping and undergo
decoherence in ideal quantum gases. The damping is read off from the equations
of motion reminiscent of the Navier-Stokes equations and shows some formal
similarity with Landau damping. The decoherence leads to consistent density and
current histories with characteristic length and time scales given by the ideal
gas.
|
1001.1803v2
|
2010-05-14
|
The effect of spin magnetization in the damping of electron plasma oscillations
|
The effect of spin of particles in the propagation of plasma waves is studied
using a semi-classical kinetic theory for a magnetized plasma. We focus in the
simple damping effects for the electrostatic wave modes besides Landau damping.
Without taking into account more quantum effects than spin contribution to
Vlasov's equation, we show that spin produces a new damping or instability
which is proportional to the zeroth order magnetization of the system. This
correction depends on the electromagnetic part of the wave which is coupled
with the spin vector.
|
1005.2573v1
|
2010-06-01
|
Recent Progress on a Manifold Damped and Detuned Structure for CLIC
|
A damped detuned structure for the main X-band linacs of CLIC is being
investigated as an alternative design to the present baseline heavily damped
structure. In our earlier designs we studied detuned structures, operating at
11.994 GHz, with a range of dipole bandwidths in order to ensure the structure
satisfies beam dynamics and rf breakdown constraints. Here we report on the
development of a damped and detuned structure which satisfies both constraints.
Preparations for high power testing of the structure are also discussed
|
1006.0087v1
|
2010-07-21
|
Finite temperature damping of collective modes of a BCS-BEC crossover superfluid
|
A new mechanism is proposed to explain the puzzling damping of collective
excitations, which was recently observed in the experiments of strongly
interacting Fermi gases below the superfluid critical temperature on the
fermionic (BCS) side of Feshbach resonance. Sound velocity, superfluid density
and damping rate are calculated with effective field theory. We find that a
dominant damping process is due to the interaction between superfluid phonons
and thermally excited fermionic quasiparticles, in contrast to the previously
proposed pair-breaking mechanism. Results from our effective model are compared
quantitatively with recent experimental findings, showing a good agreement.
|
1007.3694v2
|
2010-08-04
|
Confinement induced by fermion damping in three-dimensional QED
|
The three-dimensional non-compact QED is known to exhibit weak confinement
when fermions acquire a finite mass via the mechanism of dynamical chiral
symmetry breaking. In this paper, we study the effect of fermion damping caused
by elastic scattering on the classical potential between fermions. By
calculating the vacuum polarization function that incorporates the fermion
damping effect, we show that fermion damping can induce a weak confinement even
when the fermions are massless and the chiral symmetry is not broken.
|
1008.0736v2
|
2011-06-22
|
Highly Damped Quasinormal Modes and the Small Scale Structure of Quantum Corrected Black Hole Exteriors
|
Quasinormal modes provide valuable information about the structure of
spacetime outside a black hole. There is also a conjectured relationship
between the highly damped quasinormal modes and the semi-classical spectrum of
the horizon area/entropy. In this paper, we show that for spacetimes
characterized by more than one scale, the "infinitely damped" modes in
principle probe the structure of spacetime outside the horizon at the shortest
length scales. We demonstrate this with the calculation of the highly damped
quasinormal modes of the non-singular, single horizon, quantum corrected black
hole derived in [14].
|
1106.4357v1
|
2012-02-20
|
Simple Non-Markovian Microscopic Models for the Depolarizing Channel of a Single Qubit
|
The archetypal one-qubit noisy channels ---depolarizing, phase-damping and
amplitude-damping channels--- describe both Markovian and non-Markovian
evolution. Simple microscopic models for the depolarizing channel, both
classical and quantum, are considered. Microscopic models which describe phase
damping and amplitude damping channels are briefly reviewed.
|
1202.4210v4
|
2012-06-14
|
Damping of optomechanical disks resonators vibrating in air
|
We report on miniature GaAs disk optomechanical resonators vibrating in air
in the radiofrequency range. The flexural modes of the disks are studied by
scanning electron microscopy and optical interferometry, and correctly modeled
with the elasticity theory for annular plates. The mechanical damping is
systematically measured, and confronted with original analytical models for air
damping. Formulas are derived that correctly reproduce both the mechanical
modes and the damping behavior, and can serve as design tools for
optomechanical applications in fluidic environment.
|
1206.3032v1
|
2012-07-09
|
A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations
|
In this paper, we establish a generalized H{\"o}lder's or interpolation
inequality for weighted spaces in which the weights are non-necessarily
homogeneous. We apply it to the stabilization of some damped wave-like
evolution equations. This allows obtaining explicit decay rates for smooth
solutions for more general classes of damping operators. In particular, for
$1-d$ models, we can give an explicit decay estimate for pointwise damping
mechanisms supported on any strategic point.
|
1207.2030v2
|
2012-07-10
|
Conformation dependent damping and generalization of fluctuation-dissipation relation
|
Damping on an object generally depends on its conformation (shape size etc.).
We consider the Langevin dynamics of a model system with a conformation
dependent damping and generalize the fluctuation dissipation relation to fit in
such a situation. We derive equilibrium distribution function for such a case
which converges to the standard Boltzmann form at the limit of uniform damping.
The results can have implications, in general, for barrier overcoming processes
where standard Boltzmann statistics is slow.
|
1207.2218v2
|
2012-10-30
|
On algebraic damping close to inhomogeneous Vlasov equilibria in multi-dimensional spaces
|
We investigate the asymptotic damping of a perturbation around inhomogeneous
stable stationary states of the Vlasov equation in spatially multi-dimensional
systems. We show that branch singularities of the Fourier-Laplace transform of
the perturbation yield algebraic dampings. In two spatial dimensions, we
classify the singularities and compute the associated damping rate and
frequency. This 2D setting also applies to spherically symmetric
self-gravitating systems. We validate the theory using a toy model and an
advection equation associated with the isochrone model, a model of spherical
self-gravitating systems.
|
1210.8040v1
|
2013-04-07
|
Phenomenological model of anomalous magnon softening and damping in half-metallic manganites
|
To describe anomalous zone-boundary softening and damping of magnons in
manganites we present a phenomenological two-fluid model containing
ferromagnetic Fermi-liquid and non-Fermi-liquid components. The Fermi-liquid
component accounts for softening of zone-boundary magnons and for the Landau
damping of magnons in the Stoner continuum arising at low frequencies due to
zero-point effects. Coupling of the Fermi-liquid and non-Fermi-liquid fluids
yields conventional long wavelength magnons damped due to their coupling with
longitudinal spin fluctuations.
|
1304.1983v1
|
2013-04-25
|
Determination of Transverse Density Structuring from Propagating MHD Waves in the Solar Atmosphere
|
We present a Bayesian seismology inversion technique for propagating
magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The
technique uses theoretical predictions for the spatial damping of propagating
kink waves in transversely inhomogeneous coronal waveguides. It combines wave
amplitude damping length scales along the waveguide with theoretical results
for resonantly damped propagating kink waves to infer the plasma density
variation across the oscillating structures. Provided the spatial dependence of
the velocity amplitude along the propagation direction is measured and the
existence of two different damping regimes is identified, the technique would
enable us to fully constrain the transverse density structuring, providing
estimates for the density contrast and its transverse inhomogeneity length
scale.
|
1304.6869v1
|
2013-07-08
|
Optimal decay rate of the bipolar Euler-Poisson system with damping in $\mathbb{R}^3$
|
By rewriting a bipolar Euler-Poisson equations with damping into an Euler
equation with damping coupled with an Euler-Poisson equation with damping, and
using a new spectral analysis, we obtain the optimal decay results of the
solutions in $L^2$-norm, which improve theose in \cite{Li3, Wu3}. More
precisely, the velocities $u_1,u_2$ decay at the $L^2-$rate $(1+t)^{-{5}{4}}$,
which is faster than the normal $L^2-$rate $(1+t)^{-{3}{4}}$ for the Heat
equation and the Navier-Stokes equations. In addition, the disparity of two
densities $\rho_1-\rho_2$ and the disparity of two velocities $u_1-u_2$ decay
at the $L^2$-rate $(1+t)^{-2}$.
|
1307.2081v1
|
2013-07-27
|
Symmetry considerations on radiation damping
|
It is well known that a direct Lagrangian description of radiation damping is
still missing. In this paper we will use a specific approach of this problem
which is the standard way to treat the radiation damping problem. The
objectives here are to construct: a N=2 supersymmetric extension for the model
describing the radiation damping on the noncommutative plane with electric and
magnetic interactions; a dualization analysis of the original action; the
supercharge algebra and the total Hamiltonian for the system.
|
1307.7319v1
|
2014-02-10
|
Damping of a nanocantilever by paramagnetic spins
|
We compute damping of mechanical oscillations of a cantilever that contains
flipping paramagnetic spins. This kind of damping is mandated by the dynamics
of the total angular momentum, spin + mechanical. Rigorous expression for the
damping rate is derived in terms of measurable parameters. The effect of spins
on the quality factor of the cantilever can be significant in cantilevers of
small length that have large concentration of paramagnetic spins of atomic
and/or nuclear origin.
|
1402.2326v1
|
2014-02-20
|
Long-time behavior of solutions of a BBM equation with generalized damping
|
We study the long-time behavior of the solution of a damped BBM equation $u_t
+ u_x - u_{xxt} + uu_x + \mathscr{L}_{\gamma}(u) = 0$. The proposed dampings
$\mathscr{L}_{\gamma}$ generalize standards ones, as parabolic
($\mathscr{L}_{\gamma}(u)=-\Delta u$) or weak damping
($\mathscr{L}_{\gamma}(u)=\gamma u$) and allows us to consider a greater range.
After establish the local well-posedness in the energy space, we investigate
some numerical properties.
|
1402.5009v1
|
2014-02-24
|
N=2 supersymmetric radiation damping problem on a noncommutative plane
|
It is well known that a direct Lagrangian description of radiation damping is
still missing. In this paper a specific approach of this problem was used,
which is the standard way to treat the radiation damping problem. A $N=2$
supersymmetric extension for the model describing the radiation damping on the
noncommutative plane with electric and magnetic interactions was obtained. The
entire supercharge algebra and the total Hamiltonian for the system were
analyzed. Finally, noncommutativity features were introduced and its
consequences were explored..
|
1402.6996v1
|
2014-11-03
|
Renormalized solutions to the continuity equation with an integrable damping term
|
We consider the continuity equation with a nonsmooth vector field and a
damping term. In their fundamental paper, DiPerna and Lions proved that, when
the damping term is bounded in space and time, the equation is well posed in
the class of distributional solutions and the solution is transported by
suitable characteristics of the vector field. In this paper, we prove existence
and uniqueness of renormalized solutions in the case of an integrable damping
term, employing a new logarithmic estimate inspired by analogous ideas of
Ambrosio, Lecumberry, and Maniglia, Crippa and De Lellis in the Lagrangian
case.
|
1411.0451v1
|
2015-02-07
|
Landau Damping in a Mixture of Bose and Fermi Superfluids
|
We study the Landau damping in Bose-Fermi superfluid mixture at finite
temperature. We find that at low temperature, the Landau damping rate will be
exponentially suppressed at both the BCS side and the BEC side of Fermi
superfluid. The momentum dependence of the damping rate is obtained, and it is
quite different from the BCS side to the BEC side. The relations between our
result and collective mode experiment in the recently realized Bose-Fermi
superfluid mixture are also discussed.
|
1502.02116v1
|
2015-03-20
|
Applying a formula for generator redispatch to damp interarea oscillations using synchrophasors
|
If an interarea oscillatory mode has insufficient damping, generator
redispatch can be used to improve its damping. We explain and apply a new
analytic formula for the modal sensitivity to rank the best pairs of generators
to redispatch. The formula requires some dynamic power system data and we show
how to obtain that data from synchrophasor measurements. The application of the
formula to damp interarea modes is explained and illustrated with interarea
modes of the New England 10-machine power system.
|
1503.06144v2
|
2016-01-21
|
Codeword Stabilized Quantum Codes for Asymmetric Channels
|
We discuss a method to adapt the codeword stabilized (CWS) quantum code
framework to the problem of finding asymmetric quantum codes. We focus on the
corresponding Pauli error models for amplitude damping noise and phase damping
noise. In particular, we look at codes for Pauli error models that correct one
or two amplitude damping errors. Applying local Clifford operations on graph
states, we are able to exhaustively search for all possible codes up to length
$9$. With a similar method, we also look at codes for the Pauli error model
that detect a single amplitude error and detect multiple phase damping errors.
Many new codes with good parameters are found, including nonadditive codes and
degenerate codes.
|
1601.05763v1
|
2016-02-08
|
On Boundary Damped Inhomogeneous Timoshenko Beams and Related Problems
|
We consider the model equations for the Timoshenko beam as a first order
system in the framework of evolutionary equations. The focus is on boundary
damping, which is implemented as a dynamic boundary condition. A change of
material laws allows to include a large class of cases of boundary damping. By
choosing a particular material law, it is shown that the first order approach
to Sturm-Liouville problems with boundary damping is also covered.
|
1602.02521v1
|
2016-02-13
|
Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain
|
In this paper, we consider the asymptotic behavior of solutions to the wave
equation with space-dependent damping in an exterior domain. We prove that when
the damping is effective, the solution is approximated by that of the
corresponding heat equation as time tends to infinity. Our proof is based on
semigroup estimates for the corresponding heat equation and weighted energy
estimates for the damped wave equation. The optimality of the decay late for
solutions is also established.
|
1602.04318v1
|
2016-02-29
|
Robust quantum state recovery from amplitude damping within a mixed states framework
|
Due to the interaction with the environment, a quantum state is subjected to
decoherence which becomes one of the biggest problems for practical quantum
computation. Amplitude damping is one of the most important decoherence
processes. Here, we show that general two-qubit mixed states undergoing an
amplitude damping can be almost completely restored using a reversal procedure.
This reversal procedure through CNOT and Hadamard gates, could also protect the
entanglement of two-qubit mixed states, when it undergoes general amplitude
damping. Moreover, in the presence of uncertainty in the underlying system, we
propose a robust recovering method with optimal characteristics of the problem.
|
1602.08865v1
|
2016-07-21
|
Protecting and enhancing spin squeezing under decoherence using weak measurement
|
We propose an efficient method to protect spin squeezing under the action of
amplitude-damping, depolarizing and phase-damping channels based on measurement
reversal from weak measurement, and consider an ensemble of N independent
spin-1/2 particles with exchange symmetry. We find that spin squeezing can be
enhanced greatly under three different decoherence channels and spin-squeezing
sudden death (SSSD) can be avoided undergoing amplitude damping and
phase-damping channels.
|
1607.06530v2
|
2016-08-02
|
Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical surface; A Non-Equilibrium Keldysh Green Function Approach
|
In this paper, we investigate theoretically the spin-orbit torque as well as
the Gilbert damping for a two band model of a 2D helical surface state with a
Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the
Fermi sea and Fermi surface components and obtain their contributions to the
electronic transport as well as the spin-orbit torque (SOT). Furthermore, we
obtain the expression for the Gilbert damping due to the surface state of a 3D
Topological Insulator (TI) and predicted its dependence on the direction of the
magnetization precession axis.
|
1608.00984v2
|
2016-09-05
|
Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain
|
This paper is concerned with weighted energy estimates and diffusion
phenomena for the initial-boundary problem of the wave equation with
space-dependent damping term in an exterior domain. In this analysis, an
elliptic problem was introduced by Todorova and Yordanov. This attempt was
quite useful when the coefficient of the damping term is radially symmetric. In
this paper, by modifying their elliptic problem, we establish weighted energy
estimates and diffusion phenomena even when the coefficient of the damping term
is not radially symmetric.
|
1609.01063v2
|
2016-11-16
|
Finite-orbit-width effects on the geodesic acoustic mode in the toroidally rotating tokamak plasma
|
The Landau damping of geodesic acoustic mode (GAM) in a torodial rotating
tokamak plasma is analytically investigated by taking into account the
finite-orbit-width (FOW) resonance effect to the 3rd order. The analytical
result is shown to agree well with the numerical solution. The dependence of
the damping rate on the toroidal Mach number $M$ relies on $k_r \rho_i$. For
sufficiently small $k_r \rho_i$, the damping rate monotonically decreases with
$M$. For relatively large $k_r \rho_i$, the damping rate increases with $M$
until approaching the maximum and then decreases with $M$.
|
1611.05168v1
|
2017-03-09
|
Long-time dynamics of the strongly damped semilinear plate equation in $\mathbb{R}^{n}$
|
We investigate the initial-value problem for the semilinear plate equation
containing localized strong damping, localized weak damping and nonlocal
nonlinearity. We prove that if nonnegative damping coefficients are strictly
positive almost everywhere in the exterior of some ball and the sum of these
coefficients is positive a.e. in $%
\mathbb{R}
^{n}$, then the semigroup generated by the considered problem possesses a
global attractor in $H^{2}\left(
\mathbb{R}
^{n}\right) \times L^{2}\left(
\mathbb{R}
^{n}\right) $. We also establish boundedness of this attractor in $
H^{3}\left(
\mathbb{R}
^{n}\right) \times H^{2}\left(
\mathbb{R} ^{n}\right) $.
|
1703.03485v2
|
2017-04-21
|
The Effects of Rolling Deformation and Annealing Treatment on Damping Capacity of 1200 Aluminium Alloy
|
Annealing treatment is an important step of rolling deformation that
contributes to microstructural evolution and leads to the significant changes
in damping capacity. Damping capacities were analyzed in the parallel to
rolling direction at 1 and 10 Hz respectively. It was found that severe plastic
deformation at 40 percent reduction has lower damping capacity compared to that
of 30 percent and 20 percent reductions respectively. The microstructural
results show that the grains of as rolled alloys were changed to almost
equiaxed structures after a rolling reduction at 40 percent reduction.
|
1704.07362v1
|
2017-07-12
|
Isolated resonances and nonlinear damping
|
We analyze isolated resonance curves (IRCs) in a single-degree-of-freedom
system with nonlinear damping. The adopted procedure exploits singularity
theory in conjunction with the harmonic balance method. The analysis unveils a
geometrical connection between the topology of the damping force and IRCs.
Specifically, we demonstrate that extremas and zeros of the damping force
correspond to the appearance and merging of IRCs.
|
1707.03561v2
|
2017-07-25
|
Best exponential decay rate of energy for the vectorial damped wave equation
|
The energy of solutions of the scalar damped wave equation decays uniformly
exponentially fast when the geometric control condition is satisfied. A theorem
of Lebeau [leb93] gives an expression of this exponential decay rate in terms
of the average value of the damping terms along geodesics and of the spectrum
of the infinitesimal generator of the equation. The aim of this text is to
generalize this result in the setting of a vectorial damped wave equation on a
Riemannian manifold with no boundary. We obtain an expression analogous to
Lebeau's one but new phenomena like high frequency overdamping arise in
comparison to the scalar setting. We also prove a necessary and sufficient
condition for the strong stabilization of the vectorial wave equation.
|
1707.07893v1
|
2017-08-20
|
Radiation Damping of a Polarizable Particle
|
A polarizable body moving in an external electromagnetic field will slow
down. This effect is referred to as radiation damping and is analogous to
Doppler cooling in atomic physics. Using the principles of special relativity
we derive an expression for the radiation damping force and find that it solely
depends on the scattered power. The cooling of the particle's center-of-mass
motion is balanced by heating due to radiation pressure shot noise, giving rise
to an equilibrium that depends on the ratio of the field's frequency and the
particle's mass. While damping is of relativistic nature heating has it's roots
in quantum mechanics.
|
1708.06628v1
|
2017-09-13
|
Energy decay for the Klein-Gordon equation with highly oscillating damping
|
We consider the free Klein-Gordon equation with periodic damping. We show on
this simple model that if the usual geometric condition holds then the decay of
the energy is uniform with respect to the oscillations of the damping, and in
particular the size of the derivatives do not play any role. We also show that
without geometric condition the polynomial decay of the energy is even slightly
better for a highly oscillating damping. To prove these estimates we provide a
parameter dependent version of well known results of semigroup theory.
|
1709.04197v1
|
2017-11-01
|
Analysis of A Splitting Scheme for Damped Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise
|
In this paper, we investigate the damped stochastic nonlinear
Schr\"odinger(NLS) equation with multiplicative noise and its splitting-based
approximation. When the damped effect is large enough, we prove that the
solutions of the damped stochastic NLS equation and the splitting scheme are
exponential stable and possess some exponential integrability.
These properties lead that the strong order of the scheme is $\frac 12$ and
independent of time. Meanwhile, we analyze the regularity of the Kolmogorov
equation with respect to the equation. As a consequence, the weak order of the
scheme is shown to be twice the strong order and independent of time.
|
1711.00516v2
|
2017-12-31
|
Stabilization of the weakly coupled wave-plate system with one internal damping
|
This paper is addressed to a stabilization problem of a system coupled by a
wave and a Euler-Bernoulli plate equation. Only one equation is supposed to be
damped. Under some assumption about the damping and the coupling terms, it is
shown that sufficiently smooth solutions of the system decay logarithmically at
infinity without any geometric conditions on the effective damping domain. The
proofs of these decay results rely on the interpolation inequalities for the
coupled elliptic-parabolic systems and make use of the estimate of the
resolvent operator for the coupled system. The main tools to derive the desired
interpolation inequalities are global Carleman estimates.
|
1801.00232v1
|
2018-05-10
|
Dynamics of coherence-induced state ordering under Markovian channels
|
We study the dynamics of coherence-induced state ordering under incoherent
channels, particularly four specific Markovian channels: $-$ amplitude damping
channel, phase damping channel, depolarizing channel and bit flit channel for
single-qubit states. We show that the amplitude damping channel, phase damping
channel, and depolarizing channel do not change the coherence-induced state
ordering by $l_1$ norm of coherence, relative entropy of coherence, geometric
measure of coherence, and Tsallis relative $\alpha$-entropies, while the bit
flit channel does change for some special cases.
|
1805.03898v1
|
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