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2021-11-20 | Skyrmionics in correlated oxides | While chiral magnets, metal-based magnetic multilayers, or Heusler compounds
have been considered as the material workhorses in the field of skyrmionics,
oxides are now emerging as promising alternatives, as they host special
correlations between the spin-orbital-charge-lattice degrees of freedom and/or
coupled ferroic order parameters. These interactions open new possibilities for
practically exploiting skyrmionics. In this article, we review the recent
advances in the observation and control of topological spin textures in various
oxide systems. We start with the discovery of skyrmions and related
quasiparticles in bulk and heterostructure ferromagnetic oxides. Next, we
emphasize the shortcomings of implementing ferromagnetic textures, which have
led to the recent explorations of ferrimagnetic and antiferromagnetic oxide
counterparts, with higher Curie temperatures, stray-field immunity, low Gilbert
damping, ultrafast magnetic dynamics, and/or absence of skyrmion deflection.
Then, we highlight the development of novel pathways to control the stability,
motion, and detection of topological textures using electric fields and
currents. Finally, we present the outstanding challenges that need to be
overcome to achieve all-electrical, nonvolatile, low-power oxide skyrmionic
devices. | 2111.10562v2 |
2021-12-01 | Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics | Recently, Kim & Wilkening (Convergence of a mass-lumped finite element method
for the Landau-Lifshitz equation, Quart. Appl. Math., 76, 383-405, 2018)
proposed two novel predictor-corrector methods for the Landau-Lifshitz-Gilbert
equation (LLG) in micromagnetics, which models the dynamics of the
magnetization in ferromagnetic materials. Both integrators are based on the
so-called Landau-Lifshitz form of LLG, use mass-lumped variational formulations
discretized by first-order finite elements, and only require the solution of
linear systems, despite the nonlinearity of LLG. The first(-order in time)
method combines a linear update with an explicit projection of an intermediate
approximation onto the unit sphere in order to fulfill the LLG-inherent
unit-length constraint at the discrete level. In the second(-order in time)
integrator, the projection step is replaced by a linear constraint-preserving
variational formulation. In this paper, we extend the analysis of the
integrators by proving unconditional well-posedness and by establishing a close
connection of the methods with other approaches available in the literature.
Moreover, the new analysis also provides a well-posed integrator for the
Schr\"odinger map equation (which is the limit case of LLG for vanishing
damping). Finally, we design an implicit-explicit strategy for the treatment of
the lower-order field contributions, which significantly reduces the
computational cost of the schemes, while preserving their theoretical
properties. | 2112.00451v1 |
2021-12-21 | Fast long-wavelength exchange spin waves in partially-compensated Ga:YIG | Spin waves in yttrium iron garnet (YIG) nano-structures attract increasing
attention from the perspective of novel magnon-based data processing
applications. For short wavelengths needed in small-scale devices, the group
velocity is directly proportional to the spin-wave exchange stiffness constant
$\lambda_\mathrm{ex}$. Using wave vector resolved Brillouin Light Scattering
(BLS) spectroscopy, we directly measure $\lambda_\mathrm{ex}$ in Ga-substituted
YIG thin films and show that it is about three times larger than for pure YIG.
Consequently, the spin-wave group velocity overcomes the one in pure YIG for
wavenumbers $k > 4$ rad/$\mu$m, and the ratio between the velocities reaches a
constant value of around 3.4 for all $k > 20$ rad/$\mu$m. As revealed by
vibrating-sample magnetometry (VSM) and ferromagnetic resonance (FMR)
spectroscopy, Ga:YIG films with thicknesses down to 59 nm have a low Gilbert
damping ($\alpha < 10^{-3}$), a decreased saturation magnetization $\mu_0
M_\mathrm{S}~\approx~20~$mT and a pronounced out-of-plane uniaxial anisotropy
of about $\mu_0 H_{\textrm{u1}} \approx 95 $ mT which leads to an out-of-plane
easy axis. Thus, Ga:YIG opens access to fast and isotropic spin-wave transport
for all wavelengths in nano-scale systems independently of dipolar effects. | 2112.11348v1 |
2022-01-27 | Magnon transport and thermoelectric effects in ultrathin Tm3Fe5O12/Pt nonlocal devices | The possibility of electrically exciting and detecting magnon currents in
magnetic insulators has opened exciting perspectives for transporting spin
information in electronic devices. However, the role of the magnetic field and
the nonlocal thermal gradients on the magnon transport remain unclear. Here, by
performing nonlocal harmonic voltage measurements, we investigate magnon
transport in perpendicularly magnetized ultrathin Tm3Fe5O12 (TmIG) films
coupled to Pt electrodes. We show that the first harmonic nonlocal voltage
captures spin-driven magnon transport in TmIG, as expected, and the second
harmonic is dominated by thermoelectric voltages driven by current-induced
thermal gradients at the detector. The magnon diffusion length in TmIG is found
to be on the order of 0.3 {\mu}m at 0.5 T and gradually decays to 0.2 {\mu}m at
0.8 T, which we attribute to the suppression of the magnon relaxation time due
to the increase of the Gilbert damping with field. By performing current,
magnetic field, and distance dependent nonlocal and local measurements we
demonstrate that the second harmonic nonlocal voltage exhibits five
thermoelectric contributions, which originate from the nonlocal spin Seebeck
effect and the ordinary, planar, spin, and anomalous Nernst effects. Our work
provides a guide on how to disentangle magnon signals from diverse
thermoelectric voltages of spin and magnetic origin in nonlocal magnon devices,
and establish the scaling laws of the thermoelectric voltages in
metal/insulator bilayers. | 2201.11353v1 |
2022-01-31 | Tuning spin-orbit torques across the phase transition in VO$_2$/NiFe heterostructure | The emergence of spin-orbit torques as a promising approach to
energy-efficient magnetic switching has generated large interest in material
systems with easily and fully tunable spin-orbit torques. Here, current-induced
spin-orbit torques in VO$_2$/NiFe heterostructures were investigated using
spin-torque ferromagnetic resonance, where the VO$_2$ layer undergoes a
prominent insulator-metal transition. A roughly two-fold increase in the
Gilbert damping parameter, $\alpha$, with temperature was attributed to the
change in the VO$_2$/NiFe interface spin absorption across the VO$_2$ phase
transition. More remarkably, a large modulation ($\pm$100%) and a sign change
of the current-induced spin-orbit torque across the VO$_2$ phase transition
suggest two competing spin-orbit torque generating mechanisms. The bulk spin
Hall effect in metallic VO$_2$, corroborated by our first-principles
calculation of spin Hall conductivity, $\sigma_{SH} \approx 10^4
\frac{\hbar}{e} \Omega^{-1} m^{-1}$, is verified as the main source of the
spin-orbit torque in the metallic phase. The self-induced/anomalous torque in
NiFe, of the opposite sign and a similar magnitude to the bulk spin Hall effect
in metallic VO$_2$, could be the other competing mechanism that dominates as
temperature decreases. For applications, the strong tunability of the torque
strength and direction opens a new route to tailor spin-orbit torques of
materials which undergo phase transitions for new device functionalities. | 2201.12984v1 |
2022-02-03 | Controlling spin pumping into superconducting Nb by proximity-induced spin-triplet Cooper pairs | Proximity-induced long-range spin-triplet supercurrents, important for the
field of superconducting spintronics, are generated in
superconducting/ferromagnetic heterostructures when interfacial magnetic
inhomogeneities responsible for spin mixing and spin flip scattering are
present. The multilayer stack Nb/Cr/Fe/Cr/Nb has been shown to support such
exotic currents when fabricated into Josephson junction devices. However,
creating pure spin currents controllably in superconductors outside of the
Josephson junction architecture is a bottleneck to progress. Recently,
ferromagnetic resonance was proposed as a possible direction, the signature of
pure supercurrent creation being an enhancement of the Gilbert damping below
the superconducting critical temperature, but the necessary conditions are
still poorly established. Consistent with theoretical prediction, we
demonstrate conclusively that pumping pure spin currents into a superconductor
is only possible when conditions supporting proximity-induced spin-triplet
effects are satisfied. Our study is an important step forward for
superconducting pure spin current creation and manipulation, considerably
advancing the field of superconducting spintronics. | 2202.01520v1 |
2022-06-17 | Multiscale Modelling of the Antiferromagnet Mn2Au: From ab-initio to Micromagnetics | Antiferromagnets (AFMs) are strong candidates for the future spintronic and
memory applications largely because of their inherently fast dynamics and lack
of stray fields, with Mn2Au being one of the most promising. For the numerical
modelling of magnetic material properties, it is common to use ab-initio
methods, atomistic models and micromagnetics. However, each method alone
describes the physics within certain limits. Multiscale methods bridging the
gap between these three approaches have been already proposed for ferromagnetic
materials. Here, we present a complete multiscale model of the AFM Mn2Au as an
exemplar material, starting with results from ab-initio methods going via
atomistic spin dynamics (ASD) to an AFM Landau-Lifshitz-Bloch (AFM-LLB) model.
Firstly, bulk is modelled using a classical spin Hamiltonian constructed based
on earlier first-principles calculations. Secondly, this spin model is used in
the stochastic Landau-Lifshitz-Gilbert (LLG) to calculate temperature-dependent
equilibrium properties, such as magnetization and magnetic susceptibilities.
Thirdly, the temperature dependent micromagnetic parameters are used in the
AFM-LLB. We validate our approach by comparing the ASD and AFM-LLB models for
three paradigmatic cases; (i) Damped magnetic oscillations, (ii) magnetization
dynamics following a heat pulse resembling pump-probe experiments, (iii)
magnetic domain wall motion under thermal gradients. | 2206.08625v1 |
2022-10-29 | Micromagnetic frequency-domain simulation methods for magnonic systems | We present efficient numerical methods for the simulation of small
magnetization oscillations in three-dimensional micromagnetic systems.
Magnetization dynamics is described by the Landau-Lifshitz-Gilbert (LLG)
equation, linearized in the frequency domain around a generic equilibrium
configuration, and formulated in a special operator form that allows leveraging
large-scale techniques commonly used to evaluate the effective field in
time-domain micromagnetic simulations. By using this formulation, we derive
numerical algorithms to compute the free magnetization oscillations (i.e., spin
wave eigenmodes) as well as magnetization oscillations driven by ac
radio-frequency fields for arbitrarily shaped nanomagnets. Moreover,
semi-analytical perturbation techniques based on the computation of a reduced
set of eigenmodes are provided for fast evaluation of magnetization frequency
response and absorption spectra as a function of damping and ac field. We
present both finite difference and finite element implementations and
demonstrate their effectiveness on a test case. These techniques open the
possibility to study generic magnonic systems discretized with several hundred
thousand (or even millions) of computational cells in a reasonably short time. | 2210.16564v3 |
2023-03-07 | Magnon currents excited by the spin Seebeck effect in ferromagnetic EuS thin films | A magnetic insulator is an ideal platform to propagate spin information by
exploiting magnon currents. However, until now, most studies have focused on
Y$_3$Fe$_5$O$_{12}$ (YIG) and a few other ferri- and antiferromagnetic
insulators, but not on pure ferromagnets. In this study, we demonstrate for the
first time that magnon currents can propagate in ferromagnetic insulating thin
films of EuS. By performing both local and non-local transport measurements in
18-nm-thick films of EuS using Pt electrodes, we detect magnon currents arising
from thermal generation by the spin Seebeck effect. By comparing the dependence
of the local and non-local signals with the temperature (< 30 K) and magnetic
field (< 9 T), we confirm the magnon transport origin of the non-local signal.
Finally, we extract the magnon diffusion length in the EuS film (~140 nm), a
short value in good correspondence with the large Gilbert damping measured in
the same film. | 2303.03833v2 |
2023-04-01 | A coupled magneto-structural continuum model for multiferroic $\mathrm{BiFeO}_3$ | A continuum approach to study magnetoelectric multiferroic $\mathrm{BiFeO}_3$
(BFO) is proposed. Our modeling effort marries the ferroelectric (FE) phase
field method and micromagnetic simulations in order to describe the entire
multiferroic order parameter sector (polarization, oxygen antiphase tilts,
strain, and magnetism) self-consistently on the same time and length scale. In
this paper, we discuss our choice of ferroelectric and magnetic energy terms
and demonstrate benchmarks against known behavior. We parameterize the lowest
order couplings of the structural distortions against previous predictions from
density functional theory calculations giving access to simulations of the FE
domain wall (DW) topology. This allows us to estimate the energetic hierarchy
and thicknesses of the numerous structural DWs. We then extend the model to the
canted antiferromagnetic order and demonstrate how the ferroelectric domain
boundaries influence the resulting magnetic DWs. We also highlight some
capabilities of this model by providing two examples relevant for applications.
We demonstrate spin wave transmission through the multiferroic domain
boundaries which identify rectification in qualitative agreement with recent
experimental observations. As a second example of application, we model
fully-dynamical magnetoelectric switching, where we find a sensitivity on the
Gilbert damping with respect to switching pathways. We envision that this
modeling effort will set the basis for further work on properties of arbitrary
3D nanostructures of BFO (and related multiferroics) at the mesoscale. | 2304.00270v1 |
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 |
2023-10-27 | Effect of interfacial Dzyaloshinskii-Moriya interaction in spin dynamics of an Antiferromagnet coupled Ferromagnetic double-barrier Magnetic Tunnel Junction | In this work, we have studied the spin dynamics of a synthethic
Antiferromagnet (SAFM)$|$Heavy Metal (HM)$|$Ferromagnet (FM) double barrier
magnetic tunnel junction (MTJ) in presence of Ruderman-Kittel-Kasuya-Yoside
interaction (RKKYI), interfacial Dzyaloshinskii-Moriya interaction (iDMI),
N\'eel field and Spin-Orbit Coupling (SOC) with different Spin Transfer Torque
(STT). We employ Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation to
investigate the AFM dynamics of the proposed system. We found that the system
exhibits a transition from regular to damped oscillations with the increase in
strength of STT for systems with weaker iDMI than RKKYI while display sustained
oscillatons for system having same order of iDMI and RKKYI. On the other hand
the iDMI dominating system exhibits self-similar but aperiodic patterns in
absence of N\'eel field. In the presence of N\'eel field, the RKKYI dominating
systems exhibit chaotic oscillations for low STT but display sustained
oscillation under moderate STT. Our results suggest that the decay time of
oscillations can be controlled via SOC. The system can works as an oscillator
for low SOC but display nonlinear characteristics with the rise in SOC for
systems having weaker iDMI than RKKYI while an opposite characteristic are
noticed for iDMI dominating systems. We found periodic oscillations under low
external magnetic field in RKKYI dominating systems while moderate field are
necessary for sustained oscillation in iDMI dominating systems. Moreover, the
system exhibits saddle-node bifurcation and chaos under moderate N\'eel field
and SOC with suitable iDMI and RKKYI. In addition, our results indicate that
the magnon lifetime can be enhanced by increasing the strength of iDMI for both
optical and acoustic modes. | 2310.18175v1 |
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 |
2024-03-01 | Spin current control of magnetism | Exploring novel strategies to manipulate the order parameter of magnetic
materials by electrical means is of great importance, not only for advancing
our understanding of fundamental magnetism, but also for unlocking potential
practical applications. A well-established concept to date uses gate voltages
to control magnetic properties, such as saturation magnetization, magnetic
anisotropies, coercive field, Curie temperature and Gilbert damping, by
modulating the charge carrier population within a capacitor structure. Note
that the induced carriers are non-spin-polarized, so the control via the
electric-field is independent of the direction of the magnetization. Here, we
show that the magnetocrystalline anisotropy (MCA) of ultrathin Fe films can be
reversibly modified by a spin current generated in Pt by the spin Hall effect.
The effect decreases with increasing Fe thickness, indicating that the origin
of the modification can be traced back to the interface. Uniquely, the change
in MCA due to the spin current depends not only on the polarity of the charge
current but also on the direction of magnetization, i.e. the change in MCA has
opposite sign when the direction of magnetization is reversed. The control of
magnetism by the spin current results from the modified exchange splitting of
majority- and minority-spin bands, and differs significantly from the
manipulation by gate voltages via a capacitor structure, providing a
functionality that was previously unavailable and could be useful in advanced
spintronic devices. | 2403.00709v1 |
2004-04-06 | Bounds for contractive semigroups and second order systems | We derive a uniform bound for the difference of two contractive semigroups,
if the difference of their generators is form-bounded by the Hermitian parts of
the generators themselves. We construct a semigroup dynamics for second order
systems with fairly general operator coefficients and apply our bound to the
perturbation of the damping term. The result is illustrated on a dissipative
wave equation. As a consequence the exponential decay of some second order
systems is proved. | 0404120v1 |
1998-05-29 | Magnetic Faraday-Instability | In a magnetic fluid parametrically driven surface waves can be excited by an
external oscillating magnetic field. A static magnetic field changes the
restoring forces and damping coefficients of the various surface waves. This
property enables the excitation of both subharmonic and harmonic responses of
the standing waves. | 9806001v1 |
2003-12-10 | Charge Fluctuation of Dust Grains and its Impact on Dusty Wave Propagation | In this paper we consider the influence of dust charge fluctuations on
damping of the dust-ion-acoustic waves. Fluid approximation of longitudinal
electrostatic waves in unmagnetized plasmas is considered. We show that for a
weak acoustic wave the attenuation depends on a phenomenological charging
coefficient. | 0312067v1 |
2005-07-26 | On simulations of the classical harmonic oscillator equation by difference equations | We show that any second order linear ordinary diffrential equation with
constant coefficients (including the damped and undumped harmonic oscillator
equation) admits an exact discretization, i.e., there exists a difference
equation whose solutions exactly coincide with solutions of the corresponding
differential equation evaluated at a discrete sequence of points (a lattice).
Such exact discretization is found for an arbitrary lattice spacing. | 0507182v1 |
1998-02-16 | Classical states via decoherence | The initial states which minimize the predictability loss for a damped
harmonic oscillator are identified as quasi-free states with a symmetry
dictated by the environment's diffusion coefficients. For an isotropic
diffusion in phase space, coherent states (or mixtures of coherent states) are
selected as the most stable ones. | 9802044v1 |
2007-11-15 | $C^m$-theory of damped wave equations with stabilisation | The aim of this note is to extend the energy decay estimates from [J. Wirth,
J. Differential Equations 222 (2006) 487--514] to a broader class of
time-dependent dissipation including very fast oscillations. This is achieved
using stabilisation conditions on the coefficient in the spirit of [F.
Hirosawa, Math. Ann. 339/4 (2007) 819--839]. | 0711.2403v1 |
2014-04-22 | A unique continuation result for the plate equation and an application | In this paper, we prove the unique continuation property for the weak
solution of the plate equation with non-smooth coefficients. Then, we apply
this result to study the global attractor for the semilinear plate equation
with a localized damping. | 1404.5586v3 |
2017-09-24 | Exceptional points in two simple textbook examples | We propose to introduce the concept of exceptional points in intermediate
courses on mathematics and classical mechanics by means of simple textbook
examples. The first one is an ordinary second-order differential equation with
constant coefficients. The second one is the well known damped harmonic
oscillator. They enable one to connect the occurrence of linearly dependent
exponential solutions with a defective matrix that cannot be diagonalized but
can be transformed into a Jordan canonical form. | 1710.00067v1 |
2019-06-06 | Well-posedness and exponential decay estimates for a Korteweg-de Vries-Burgers equation with time-delay | We consider the KdV-Burgers equation and its linear version in presence of a
delay feedback. We prove well-posedness of the models and exponential decay
estimates under appropriate conditions on the damping coefficients. Our
arguments rely on a Lyapunov functional approach combined with a step by step
procedure and semigroup theory. | 1906.02488v1 |
2021-07-21 | Convergence rates for the Heavy-Ball continuous dynamics for non-convex optimization, under Polyak-Łojasiewicz condition | We study convergence of the trajectories of the Heavy Ball dynamical system,
with constant damping coefficient, in the framework of convex and non-convex
smooth optimization. By using the Polyak-{\L}ojasiewicz condition, we derive
new linear convergence rates for the associated trajectory, in terms of
objective function values, without assuming uniqueness of the minimizer. | 2107.10123v2 |
2021-08-29 | Well-posedness and stability for semilinear wave-type equations with time delay | In this paper we analyze a semilinear abstract damped wave-type equation with
time delay. We assume that the delay feedback coefficient is variable in time
and belonging to $L^1_{loc}([0, +\infty)).$ Under suitable assumptions, we show
well-posedness and exponential stability for small initial data. Our strategy
combines careful energy estimates and continuity arguments. Some examples
illustrate the abstract results. | 2108.12786v1 |
2021-10-22 | p-Laplacian wave equations in non-cylindrical domains | This paper is devoted to studying the stability of p-Laplacian wave equations
with strong damping in non-cylindrical domains. The method of proof based on
some estimates for time-varying coefficients rising from moving boundary and a
modified Kormonik inequality. Meanwhile, by selecting appropriate auxiliary
functions, finally we obtain the polynomial stability (p > 2) and exponential
stability (p = 2) for such systems in some unbounded development domains. | 2110.11547v1 |
2022-07-25 | Inviscid limit for the compressible Navier-Stokes equations with density dependent viscosity | We consider the compressible Navier-Stokes system describing the motion of a
barotropic fluid with density dependent viscosity confined in a
three-dimensional bounded domain $\Omega$. We show the convergence of the weak
solution to the compressible Navier-Stokes system to the strong solution to the
compressible Euler system when the viscosity and the damping coefficients tend
to zero. | 2207.12222v1 |
2018-05-08 | Effect of transport coefficients on excitation of flare-induced standing slow-mode waves in coronal loops | Standing slow-mode waves have been recently observed in flaring loops by the
Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). By
means of the coronal seismology technique transport coefficients in hot
($\sim$10 MK) plasma were determined by Wang et al.(2015, Paper I), revealing
that thermal conductivity is nearly suppressed and compressive viscosity is
enhanced by more than an order of magnitude. In this study we use 1D nonlinear
MHD simulations to validate the predicted results from the linear theory and
investigate the standing slow-mode wave excitation mechanism. We first explore
the wave trigger based on the magnetic field extrapolation and flare emission
features. Using a flow pulse driven at one footpoint we simulate the wave
excitation in two types of loop models: model 1 with the classical transport
coefficients and model 2 with the seismology-determined transport coefficients.
We find that model 2 can form the standing wave pattern (within about one
period) from initial propagating disturbances much faster than model 1, in
better agreement with the observations. Simulations of the harmonic waves and
the Fourier decomposition analysis show that the scaling law between damping
time ($\tau$) and wave period ($P$) follows $\tau\propto{P^2}$ in model 2,
while $\tau\propto{P}$ in model 1. This indicates that the largely enhanced
viscosity efficiently increases the dissipation of higher harmonic components,
favoring the quick formation of the fundamental standing mode. Our study
suggests that observational constraints on the transport coefficients are
important in understanding both, the wave excitation and damping mechanisms. | 1805.03282v1 |
2005-01-02 | Effect of dipolar interactions on the magnetization of a cubic array of nanomagnets | We investigated the effect of intermolecular dipolar interactions on a cubic
3D ensemble of 5X5X4=100 nanomagnets, each with spin $S = 5$. We employed the
Landau-Lifshitz-Gilbert equation to solve for the magnetization $M(B)$ curves
for several values of the damping constant $\alpha$, the induction sweep rate,
the lattice constant $a$, the temperature $T$, and the magnetic anisotropy
field $H_A$. We find that the smaller the $\alpha$, the stronger the maximum
induction required to produce hysteresis. The shape of the hysteresis loops
also depends on the damping constant. We find further that the system
magnetizes and demagnetizes at decreasing magnetic field strengths with
decreasing sweep rates, resulting in smaller hysteresis loops. Variations of
$a$ within realistic values (1.5 nm - 2.5 nm) show that the dipolar interaction
plays an important role in the magnetic hysteresis by controlling the
relaxation process. The $T$ dependencies of $\alpha$ and of $M$ are presented
and discussed with regard to recent experimental data on nanomagnets. $H_A$
enhances the size of the hysteresis loops for external fields parallel to the
anisotropy axis, but decreases it for perpendicular external fields. Finally,
we reproduce and test an $M(B)$ curve for a 2D-system [M. Kayali and W. Saslow,
Phys. Rev. B {\bf 70}, 174404 (2004)]. We show that its hysteretic behavior is
only weakly dependent on the shape anisotropy field and the sweep rate, but
depends sensitively upon the dipolar interactions. Although in 3D systems,
dipole-dipole interactions generally diminish the hysteresis, in 2D systems,
they strongly enhance it. For both square 2D and rectangular 3D lattices with
${\bm B}||(\hat{\bm x}+\hat{\bm y})$, dipole-dipole interactions can cause
large jumps in the magnetization. | 0501006v2 |
2019-03-07 | Uniaxial anisotropy, intrinsic and extrinsic damping in Co$_{2}$FeSi Heusler alloy thin films | Ferromagnetic resonance (FMR) technique has been used to study the
magnetization relaxation processes and magnetic anisotropy in two different
series of the Co2FeSi (CFS) Heusler alloy thin films, deposited on the Si(111)
substrate by UHV sputtering. While the CFS films of fixed (50 nm) thickness,
deposited at different substrate temperatures (TS) ranging from room
temperature (RT) to 600^C, constitute the series-I, the CFS films with
thickness t varying from 12 nm to 100 nm and deposited at 550^C make up the
series-II. In series-I, the CFS films deposited at TS = RT and 200^C are
completely amorphous, the one at TS = 300^C is partially crystalline, and those
at TS equal 450^C, 550^C and 600^C are completely crystalline with B2 order. By
contrast, all the CFS films in series-II are in the fully-developed B2
crystalline state. Irrespective of the strength of disorder and film thickness,
angular variation of the resonance field in the film plane unambiguously
establishes the presence of global in-plane uniaxial anisotropy. Angular
variation of the linewidth in the film plane reveals that, in the CFS thin
films of varying thickness, a crossover from the in-plane local four-fold
symmetry (cubic anisotropy) to local two-fold symmetry (uniaxial anisotropy)
occurs as t exceeds 50 nm. Gilbert damping parameter {\alpha} decreases
monotonously from 0.047 to 0.0078 with decreasing disorder strength (increasing
TS) and jumps from 0.008 for the CFS film with t = 50 nm to 0.024 for the film
with t equal 75 nm. Such variations of {\alpha} with TS and t are understood in
terms of the changes in the total (spin-up and spin-down) density of states at
the Fermi level caused by the disorder and film thickness. | 1903.02976v1 |
2023-09-19 | Impact of strain on the SOT-driven dynamics of thin film Mn$_3$Sn | Mn$_3$Sn, a metallic antiferromagnet with an anti-chiral 120$^\circ$ spin
structure, generates intriguing magneto-transport signatures such as a large
anomalous Hall effect, spin-polarized current with novel symmetries, anomalous
Nernst effect, and magneto-optic Kerr effect. When grown epitaxially as
MgO(110)[001]$\parallel$ Mn$_3$Sn($0\bar{1}\bar{1}0$)[0001], Mn$_3$Sn
experiences a uniaxial tensile strain, which changes the bulk six-fold
anisotropy landscape to a perpendicular magnetic anisotropy with two stable
states. In this work, we investigate the field-assisted spin orbit-torque
(SOT)-driven response of the order parameter in single-domain Mn$_3$Sn with
uniaxial tensile strain. We find that for a non-zero external magnetic field,
the order parameter can be switched between the two stable states if the
magnitude of the input current is between two field-dependent critical
currents. Below the lower critical current, the order parameter exhibits a
stationary state in the vicinity of the initial stable state. On the other
hand, above the higher critical current, the order parameter shows oscillatory
dynamics which could be tuned from the 100's of megahertz to the gigahertz
range. We obtain approximate expressions of the two critical currents and find
them to agree very well with the numerical simulations for experimentally
relevant magnetic fields. We also obtain unified functional form of the
switching time versus the input current for different magnetic fields. Finally,
we show that for lower values of Gilbert damping ($\alpha \leq 2\times
10^{-3}$), the critical currents and the final steady states depend
significantly on the damping constant. The numerical and analytic results
presented in our work can be used by both theorists and experimentalists to
understand the SOT-driven order dynamics in PMA Mn$_3$Sn and design future
experiments and devices. | 2309.10246v2 |
2009-04-16 | Good Concatenated Code Ensembles for the Binary Erasure Channel | In this work, we give good concatenated code ensembles for the binary erasure
channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code
ensembles formed by the serial concatenation of a repetition code with multiple
accumulators, and the hybrid concatenated code (HCC) ensembles recently
introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics,
Lausanne, Switzerland) consisting of an outer multiple parallel concatenated
code serially concatenated with an inner accumulator. We introduce stopping
sets for iterative constituent code oriented decoding using maximum a
posteriori erasure correction in the constituent codes. We then analyze the
asymptotic stopping set distribution for RMA and HCC ensembles and show that
their stopping distance hmin, defined as the size of the smallest nonempty
stopping set, asymptotically grows linearly with the block length. Thus, these
code ensembles are good for the BEC. It is shown that for RMA code ensembles,
contrary to the asymptotic minimum distance dmin, whose growth rate coefficient
increases with the number of accumulate codes, the hmin growth rate coefficient
diminishes with the number of accumulators. We also consider random puncturing
of RMA code ensembles and show that for sufficiently high code rates, the
asymptotic hmin does not grow linearly with the block length, contrary to the
asymptotic dmin, whose growth rate coefficient approaches the Gilbert-Varshamov
bound as the rate increases. Finally, we give iterative decoding thresholds for
the different code ensembles to compare the convergence properties. | 0904.2482v1 |
2004-08-10 | Cosmic Ray Scattering and Streaming in Compressible Magnetohydrodynamic Turbulence | Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call
for revisions in the picture of cosmic ray transport. In this paper we use
recently obtained scaling laws for MHD modes to obtain the scattering frequency
for cosmic rays. Using quasilinear theory we calculate gyroresonance with MHD
modes (Alfv\'{e}nic, slow and fast) and transit-time damping (TTD) by fast
modes. We provide calculations of cosmic ray scattering for various phases of
interstellar medium with realistic interstellar turbulence driving that is
consistent with the velocity dispersions observed in diffuse gas. We account
for the turbulence cutoff arising from both collisional and collisionless
damping. We obtain analytical expressions for diffusion coefficients that enter
Fokker-Planck equation describing cosmic ray evolution. We obtain the
scattering rate and show that fast modes provide the dominant contribution to
cosmic ray scattering for the typical interstellar conditions in spite of the
fact that fast modes are subjected to damping. We determine how the efficiency
of the scattering depends on the characteristics of ionized media, e.g. plasma
$\beta$. We calculate the range of energies for which the streaming instability
is suppressed by the ambient MHD turbulence. | 0408172v1 |
1999-11-22 | Two-fluid hydrodynamics of a Bose gas including damping from normal fluid transport coefficients | We extend our recent work on the two-fluid hydrodynamics of the condensate
and non-condensate in a trapped Bose gas by including the dissipation
associated with viscosity and thermal conduction. For purposes of illustration,
we consider the hydrodynamic modes in the case of a uniform Bose gas. A finite
thermal conductivity and shear viscosity give rise to a damping of the first
and second sound modes in addition to that found previously due to the lack of
diffusive equilibrium between the condensate and non-condensate. The
relaxational mode associated with this equilibration process is strongly
coupled to thermal fluctuations and reduces to the usual thermal diffusion mode
above the Bose-Einstein transition. In contrast to the standard Landau
two-fluid hydrodynamics, we predict a damped mode centered at zero frequency,
in addition to the usual second sound doublet. | 9911336v1 |
2001-11-14 | Soliton-radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation | We use the Riemann-Hilbert problem to study the interaction of the soliton
with radiation in the parametrically driven, damped nonlinear Schr\"odinger
equation. The analysis is reduced to the study of a finite-dimensional
dynamical system for the amplitude and phase of the soliton and the complex
amplitude of the long-wavelength radiation. In contrast to previously utilised
Inverse Scattering-based perturbation techniques, our approach is valid for
arbitrarily large driving strengths and damping coefficients. We show that,
contrary to suggestions made in literature, the complexity observed in the
soliton's dynamics cannot be accounted for just by its coupling to the
long-wavelength radiation. | 0111034v1 |
1996-12-08 | Towards a Simple Model of Compressible Alfvenic Turbulence | A simple model collisionless, dissipative, compressible MHD (Alfvenic)
turbulence in a magnetized system is investigated. In contrast to more familiar
paradigms of turbulence, dissipation arises from Landau damping, enters via
nonlinearity, and is distributed over all scales. The theory predicts that two
different regimes or phases of turbulence are possible, depending on the ratio
of steepening to damping coefficient (m_1/m_2). For strong damping
(|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For
|m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit.
Rather, spikey, small scale structure is predicted. | 9612005v2 |
2009-01-15 | The sound damping constant for generalized theories of gravity | The near-horizon metric for a black brane in Anti-de Sitter (AdS) space and
the metric near the AdS boundary both exhibit hydrodynamic behavior. We
demonstrate the equivalence of this pair of hydrodynamic systems for the sound
mode of a conformal theory. This is first established for Einstein's gravity,
but we then show how the sound damping constant will be modified, from its
Einstein form, for a generalized theory. The modified damping constant is
expressible as the ratio of a pair of gravitational couplings that are
indicative of the sound-channel class of gravitons. This ratio of couplings
differs from both that of the shear diffusion coefficient and the shear
viscosity to entropy ratio. Our analysis is mostly limited to conformal
theories but suggestions are made as to how this restriction might eventually
be lifted. | 0901.2191v1 |
2009-07-30 | Gas damping force noise on a macroscopic test body in an infinite gas reservoir | We present a simple analysis of the force noise associated with the
mechanical damping of the motion of a test body surrounded by a large volume of
rarefied gas. The calculation is performed considering the momentum imparted by
inelastic collisions against the sides of a cubic test mass, and for other
geometries for which the force noise could be an experimental limitation. In
addition to arriving at an accurated estimate, by two alternative methods, we
discuss the limits of the applicability of this analysis to realistic
experimental configurations in which a test body is surrounded by residual gas
inside an enclosure that is only slightly larger than the test body itself. | 0907.5375v2 |
2011-03-08 | Steady states of the parametric rotator and pendulum | We discuss several steady-state rotation and oscillation modes of the planar
parametric rotator and pendulum with damping. We consider a general elliptic
trajectory of the suspension point for both rotator and pendulum, for the
latter at an arbitrary angle with gravity, with linear and circular
trajectories as particular cases. We treat the damped, non-linear equation of
motion of the parametric rotator and pendulum perturbatively for small
parametric excitation and damping, although our perturbative approach can be
extended to other regimes as well. Our treatment involves only ordinary
second-order differential equations with constant coefficients, and provides
numerically accurate perturbative solutions in terms of elementary functions.
Some of the steady-state rotation and oscillation modes studied here have not
been discussed in the previous literature. Other well-known ones, such as
parametric resonance and the inverted pendulum, are extended to elliptic
parametric excitation tilted with respect to gravity. The results presented
here should be accessible to advanced undergraduates, and of interest to
graduate students and specialists in the field of non-linear mechanics. | 1103.1413v1 |
2011-03-28 | Motion of position-dependent mass as a damping-antidamping process: Application to the Fermi gas and to the Morse potential | The object of this paper is to investigate, classically and quantum
mechanically, the relation existing between the position-dependent effective
mass and damping-antidamping dynamics. The quantization of the equations of
motion is carried out using the geometric interpretation of the motion, and we
compare it with the one based on the ordering ambiguity scheme. Furthermore, we
apply the obtained results to a Fermi gas of damped-antidamped particles, and
we solve the Schr\"odinger equation for an exponentially increasing
(decreasing) mass in the presence of the Morse potential. | 1103.5440v3 |
2011-06-22 | Tunable Magnonic Frequency and Damping in [Co/Pd]8 Multilayers with Variable Co Layer Thickness | We report the experimental observation of collective picosecond magnetization
dynamics in [Co/Pd]8 multilayers with perpendicular magnetic anisotropy. The
precession frequency shows large and systematic variation from about 5 GHz to
about 90 GHz with the decrease in the Co layer thickness from 1.0 nm to 0.22 nm
due to the linear increase in the perpendicular magnetic anisotropy. The
damping coefficient 'alpha' is found to be inversely proportional to the Co
layer thickness and a linear relation between the perpendicular magnetic
anisotropy and 'alpha' is established. We discuss the possible reasons behind
the enhanced damping as the d-d hybridization at the interface and spin
pumping. These observations are significant for the applications of these
materials in spintronics and magnonic crystals. | 1106.4491v1 |
2012-05-14 | Critical viscoelastic response in jammed solids | We determine the linear viscoelastic response of jammed packings of athermal
repulsive viscous spheres, a model for emulsions, wet foams, and soft colloidal
suspensions. We numerically measure the complex shear modulus, a fundamental
characterization of the response, and demonstrate that low frequency response
displays dynamic critical scaling near unjamming. Viscoelastic shear response
is governed by the relaxational eigenmodes of a packing. We use scaling
arguments to explain the distribution of eigenrates, which develops a
divergence at unjamming. We then derive the critical exponents characterizing
response, including a vanishing shear modulus, diverging viscosity, and
critical shear thinning regime. Finally, we demonstrate that macroscopic
rheology is sensitive to details of the local viscous force law. By varying the
ratio of normal and tangential damping coefficients, we identify and explain a
qualitative difference between systems with strong and weak damping of sliding
motion. When sliding is weakly damped there is no diverging time scale, no
diverging viscosity, and no critical shear thinning regime. | 1205.2960v1 |
2012-10-04 | Basic microscopic plasma physics unified and simplified by N-body classical mechanics | Debye shielding, collisional transport, Landau damping of Langmuir waves, and
spontaneous emission of these waves are introduced, in typical plasma physics
textbooks, in different chapters. This paper provides a compact unified
introduction to these phenomena without appealing to fluid or kinetic models,
but by using Newton's second law for a system of $N$ electrons in a periodic
box with a neutralizing ionic background. A rigorous equation is derived for
the electrostatic potential. Its linearization and a first smoothing reveal
this potential to be the sum of the shielded Coulomb potentials of the
individual particles. Smoothing this sum yields the classical Vlasovian
expression including initial conditions in Landau contour calculations of
Langmuir wave growth or damping. The theory is extended to accommodate a
correct description of trapping or chaos due to Langmuir waves. In the linear
regime, the amplitude of such a wave is found to be ruled by Landau growth or
damping and by spontaneous emission. Using the shielded potential, the
collisional diffusion coefficient is computed for the first time by a
convergent expression including the correct calculation of deflections for all
impact parameters. Shielding and collisional transport are found to be two
related aspects of the repulsive deflections of electrons. | 1210.1546v2 |
2015-01-23 | Response solutions for quasi-periodically forced, dissipative wave equations | We consider several models of nonlinear wave equations subject to very strong
damping and quasi-periodic external forcing. This is a singular perturbation,
since the damping is not the highest order term. We study the existence of
response solutions (i.e., quasi-periodic solutions with the same frequency as
the forcing). Under very general non-resonance conditions on the frequency, we
show the existence of asymptotic expansions of the response solution; moreover,
we prove that the response solution indeed exists and depends analytically on
$\varepsilon$ (where $\varepsilon$ is the inverse of the coefficient
multiplying the damping) for $\varepsilon$ in a complex domain, which in some
cases includes disks tangent to the imaginary axis at the origin. In other
models, we prove analyticity in cones of aperture $\pi/2$ and we conjecture it
is optimal. These results have consequences for the asymptotic expansions of
the response solutions considered in the literature. The proof of our results
relies on reformulating the problem as a fixed point problem, constructing an
approximate solution and studying the properties of iterations that converge to
the solutions of the fixed point problem. | 1501.05979v1 |
2015-05-08 | Existence and general stabilization of the Timoshenko system with a thermo-viscoelastic damping and a delay term in the internal feedback | In this paper, we consider a Timoshenko system with a thermo-viscoelastic
damping and a delay term in the internal feedback together with initial datum
and boundary conditions of Dirichlet type, where g is a positive non-increasing
relaxation function and {\mu}1, {\mu}2 are positive constants. Under an
hypothesis between the weight of the delay term in the feedback and the the
weight of the friction damping term, using the Faedo-Galerkin approximations
together with some energy estimates, we prove the global existence of the
solutions. Then, by introducing appropriate Lyapunov functionals, under the
imposed constrain on the weights of the two feedbacks and the coefficients, we
establish the general energy decay result from which the exponential and
polynomial types of decay are only special cases. | 1505.01899v1 |
2015-09-03 | Stability analysis of degenerately-damped oscillations | Presented here is a study of well-posedness and asymptotic stability of a
"degenerately damped" PDE modeling a vibrating elastic string. The coefficient
of the damping may vanish at small amplitudes thus weakening the effect of the
dissipation. It is shown that the resulting dynamical system has strictly
monotonically decreasing energy and uniformly decaying lower-order norms,
however, is not uniformly stable on the associated finite-energy space. These
theoretical findings were motivated by numerical simulations of this model
using a finite element scheme and successive approximations. A description of
the numerical approach and sample plots of energy decay are supplied. In
addition, for certain initial data the solution can be determined in closed
form up to a dissipative nonlinear ordinary differential equation. Such
solutions can be used to assess the accuracy of the numerical examples. | 1509.00917v1 |
2016-07-20 | Envelope equation for the linear and nonlinear propagation of an electron plasma wave, including the effects of Landau damping, trapping, plasma inhomogeneity, and the change in the state of wave | This paper addresses the linear and nonlinear three-dimensional propagation
of an electron wave in a collisionless plasma that may be inhomogeneous,
nonstationary, anisotropic and even weakly magnetized. The wave amplitude,
together with any hydrodynamic quantity characterizing the plasma (density,
temperature,...) are supposed to vary very little within one wavelength or one
wave period. Hence, the geometrical optics limit is assumed, and the wave
propagation is described by a first order differential equation. This equation
explicitly accounts for three-dimensional effects, plasma inhomogeneity, Landau
damping, and the collisionless dissipation and electron acceleration due to
trapping. It is derived by mixing results obtained from a direct resolution of
the Vlasov-Poisson system and from a variational formalism involving a nonlocal
Lagrangian density. In a one-dimensional situation, abrupt transitions are
predicted in the coefficients of the wave equation. They occur when the state
of the electron plasma wave changes, from a linear wave to a wave with trapped
electrons. In a three dimensional geometry, the transitions are smoother,
especially as regards the nonlinear Landau damping rate, for which a very
simple effective and accurate analytic expression is provided. | 1607.05844v2 |
2017-04-07 | Underdamped stochastic harmonic oscillator | We investigate stationary states of the linear damped stochastic oscillator
driven by L\'evy noises. In the long time limit kinetic and potential energies
of the oscillator do not fulfill the equipartition theorem and their
distributions follow the power-law asymptotics. At the same time, partition of
the mechanical energy is controlled by the damping coefficient. We show that in
the limit of vanishing damping a stochastic analogue of the equipartition
theorem can be proposed, namely the statistical properties of potential and
kinetic energies attain distributions characterized by the same width. Finally,
we demonstrate that the ratio of instantaneous kinetic and potential energies
which signifies departure from the mechanical energy equipartition, follows
universal power-law asymptotics. | 1704.02119v2 |
2017-08-30 | Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant | This paper is concerned with the asymptotic behavior of the solution to the
Euler equations with time-depending damping on quadrant $(x,t)\in
\mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v
-
\partial_x u=0, \qquad \partial_t u
+
\partial_x p(v)
=\displaystyle
-\frac{\alpha}{(1+t)^\lambda} u, \end{equation} with null-Dirichlet boundary
condition or null-Neumann boundary condition on $u$. We show that the
corresponding initial-boundary value problem admits a unique global smooth
solution which tends time-asymptotically to the nonlinear diffusion wave.
Compared with the previous work about Euler equations with constant coefficient
damping, studied by Nishihara and Yang (1999, J. Differential Equations, 156,
439-458), and Jiang and Zhu (2009, Discrete Contin. Dyn. Syst., 23, 887-918),
we obtain a general result when the initial perturbation belongs to the same
space. In addition, our main novelty lies in the facts that the cut-off points
of the convergence rates are different from our previous result about the
Cauchy problem. Our proof is based on the classical energy method and the
analyses of the nonlinear diffusion wave. | 1708.09127v1 |
2018-01-23 | The effect of liquid on the vibrational intensity of a wineglass at steady state resonance | As a liquid is inserted into a wineglass, the natural frequency of the
wineglass decreases. This phenomenon, known as pitch lowering, is well
explained in past papers. However, previous literature have not yet mentioned
that pitch lowering also reduces the resonance intensity of a wineglass. Thus,
this present paper aims to extend the body of research on this topic by
describing the relationship between pitch lowering and its effect on resonation
intensity. To do so, we identify the vibrating wineglass wall as a damped
harmonic oscillator, derive a theoretical model, and find that the resonance
intensity of the wineglass is proportional to the square of its natural
frequency, under the assumption that damping stays constant. However, our
experiments showed the coefficient of damping to increase with respect to the
amount of liquid, which caused the data to deviate from its theoretical
predictions. We conclude by discussing the accuracy and limitation of our
proposed model. | 1801.07514v5 |
2018-04-11 | A global existence result for a semilinear wave equation with scale-invariant damping and mass in even space dimension | In the present article a semilinear wave equation with scale-invariant
damping and mass is considered. The global (in time) existence of radial
symmetric solutions in even spatial dimension $n$ is proved using weighted
$L^\infty-L^\infty$ estimates, under the assumption that the multiplicative
constants, which appear in the coefficients of damping and of mass terms,
fulfill an interplay condition which yields somehow a "wave-like" model. In
particular, combining this existence result with a recently proved blow-up
result, a suitable shift of Strauss exponent is proved to be the critical
exponent for the considered model. Moreover, the still open part of a
conjecture done by D'Abbicco - Lucente - Reissig is proved to be true in the
massless case. | 1804.03978v1 |
2018-07-17 | Boundary-to-Displacement Asymptotic Gains for Wave Systems With Kelvin-Voigt Damping | We provide estimates for the asymptotic gains of the displacement of a
vibrating string with endpoint forcing, modeled by the wave equation with
Kelvin-Voigt and viscous damping and a boundary disturbance. Two asymptotic
gains are studied: the gain in the L2 spatial norm and the gain in the spatial
sup norm. It is shown that the asymptotic gain property holds in the L2 norm of
the displacement without any assumption for the damping coefficients. The
derivation of the upper bounds for the asymptotic gains is performed by either
employing an eigenfunction expansion methodology or by means of a small-gain
argument, whereas a novel frequency analysis methodology is employed for the
derivation of the lower bounds for the asymptotic gains. The graphical
illustration of the upper and lower bounds for the gains shows that that the
asymptotic gain in the L2 norm is estimated much more accurately than the
asymptotic gain in the sup norm. | 1807.06549v1 |
2018-07-24 | Stabilization of an unstable wave equation using an infinite dimensional dynamic controller | This paper deals with the stabilization of an anti-stable string equation
with Dirichlet actuation where the instability appears because of the
uncontrolled boundary condition. Then, infinitely many unstable poles are
generated and an infinite dimensional control law is therefore proposed to
exponentially stabilize the system. The idea behind the choice of the
controller is to extend the domain of the PDE so that the anti-damping term is
compensated by a damping at the other boundary condition. Additionally, notice
that the system can then be exponentially stabilized with a chosen decay-rate
and is robust to uncertainties on the wave speed and the anti-damped
coefficient of the wave equation, with the only use of a point-wise boundary
measurement. The efficiency of this new control strategy is then compared to
the backstepping approach. | 1807.08999v2 |
2018-08-30 | The influence of the coefficients of a system of coupled wave equations with fractional damping on its stabilization | In this work, we consider a system of two wave equations coupled by
velocities in one-dimensional space, with one boundary fractional damping.
First, we show that the system is strongly asymptotically stable if and only if
the coupling parameter b of the two equations is outside a discrete set of
exceptional real values. Next, we show that our system is not uniformly stable.
Hence, we look for a polynomial decay rate for smooth initial data. Using
frequency domain approach combining with multiplier method, we prove that the
energy decay rate is greatly influenced by the nature of the coupling parameter
b, the arithmetic property of the ratio of the wave propagation speeds a, the
order of the fractional damping. Indeed, under the equal speed propagation
condition, we establish an optimal polynomial energy decay rate. Furthermore,
when the wave propagate with different speeds, under some arithmetic conditions
on the ratio of the wave propagation speeds, we prove that the energy of our
system decays polynomially to zero. | 1808.10285v4 |
2019-06-10 | Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosity | We study the compressible quantum Navier-Stokes (QNS) equations with
degenerate viscosity in the three dimensional periodic domains. On the one
hand, we consider QNS with additional damping terms. Motivated by the recent
works [Li-Xin, arXiv:1504.06826] and [Antonelli-Spirito, Arch. Ration. Mech.
Anal., 203(2012), 499--527], we construct a suitable approximate system which
has smooth solutions satisfying the energy inequality and the BD entropy
estimate. Using this system, we obtain the global existence of weak solutions
to the compressible QNS equations with damping terms for large initial data.
Moreover, we obtain some new a priori estimates, which can avoid using the
assumption that the gradient of the velocity is a well-defined function, which
is indeed used directly in [Vasseur-Yu, SIAM J. Math. Anal., 48 (2016),
1489--1511; Invent. Math., 206 (2016), 935--974]. On the other hand, in the
absence of damping terms, we also prove the global existence of weak solutions
to the compressible QNS equations without the lower bound assumption on the
dispersive coefficient, which improves the previous result due to
[Antonelli-Spirito, Arch. Ration. Mech. Anal., 203(2012), 499--527]. | 1906.03971v1 |
2019-08-19 | Time Delay in the Swing Equation: A Variety of Bifurcations | The present paper addresses the swing equation with additional delayed
damping as an example for pendulum-like systems. In this context, it is proved
that recurring sub- and supercritical Hopf bifurcations occur if time delay is
increased. To this end, a general formula for the first Lyapunov coefficient in
second order systems with additional delayed damping and delay-free
nonlinearity is given. In so far the paper extends results about stability
switching of equilibria in linear time delay systems from Cooke and Grossman.
In addition to the analytical results, periodic solutions are numerically dealt
with. The numerical results demonstrate how a variety of qualitative behaviors
is generated in the simple swing equation by only introducing time delay in a
damping term. | 1908.07996v3 |
2019-12-30 | A Link Between Relativistic Rest Energy and Fractionary Momentum Operators of Order 1/2 | The solution of a causal fractionary wave equation in an infinite potential
well was obtained. First, the so-called "free particle" case was solved, giving
as normalizable solutions a superposition of damped oscillations similar to a
wave packet. From this results, the infinite potential well case was then
solved. The damping coefficient of the equation obtained was matched with the
exponent appearing in the Yucawa potential or "screened" Coulomb potential.
When this matching was forced, the particle aquires an offset energy of E =
mc^2/2 which then can be increased by each energy level. The expontential
damping of the wave solutions in the box was found to be closely related with
the radius of the proton when the particle has a mass equal to the mass of the
proton. Lastly the fractionary wave equation was expressed in spherical
coordinates and remains to be solved through analytical or numerical methods. | 1912.12770v4 |
2020-08-18 | Singularity formation for compressible Euler equations with time-dependent damping | In this paper, we consider the compressible Euler equations with
time-dependent damping \frac{\a}{(1+t)^\lambda}u in one space dimension. By
constructing 'decoupled' Riccati type equations for smooth solutions, we
provide some sufficient conditions under which the classical solutions must
break down in finite time. As a byproduct, we show that the derivatives blow
up, somewhat like the formation of shock wave, if the derivatives of initial
data are appropriately large at a point even when the damping coefficient goes
to infinity with a algebraic growth rate. We study the case \lambda\neq1 and
\lambda=1 respectively, moreover, our results have no restrictions on the size
of solutions and the positivity/monotonicity of the initial Riemann invariants.
In addition, for 1<\gamma<3 we provide time-dependent lower bounds on density
for arbitrary classical solutions, without any additional assumptions on the
initial data. | 2008.07756v1 |
2020-11-14 | Learning a Reduced Basis of Dynamical Systems using an Autoencoder | Machine learning models have emerged as powerful tools in physics and
engineering. Although flexible, a fundamental challenge remains on how to
connect new machine learning models with known physics. In this work, we
present an autoencoder with latent space penalization, which discovers finite
dimensional manifolds underlying the partial differential equations of physics.
We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV),
and damped KdV equations. We show that the resulting optimal latent space of
the K-S equation is consistent with the dimension of the inertial manifold. The
results for the KdV equation imply that there is no reduced latent space, which
is consistent with the truly infinite dimensional dynamics of the KdV equation.
In the case of the damped KdV equation, we find that the number of active
dimensions decreases with increasing damping coefficient. We then uncover a
nonlinear basis representing the manifold of the latent space for the K-S
equation. | 2011.07346v1 |
2021-01-11 | Damped (linear) response theory within the resolution-of-identity coupled cluster singles and approximate doubles (RI-CC2) method | An implementation of a complex solver for the solution of the response
equations required to compute the complex response functions of damped response
theory is presented for the resolution-of-identity (RI) coupled-cluster singles
and approximate doubles CC2 method. The implementation uses a partitioned
formulation that avoids the storage of double excitation amplitudes to make it
applicable to large molecules. The solver is the keystone element for the
development of the damped coupled-cluster response formalism for linear and
nonlinear effects in resonant frequency regions at the RI-CC2 level of theory.
Illustrative results are reported for the one-photon absorption cross section
of C60, the electronic circular dichroism of $n$-helicenes ($n$ = 5, 6, 7), and
the $C_6$ dispersion coefficients of a set of selected organic molecules and
fullerenes. | 2101.03756v1 |
2021-06-24 | Landau damping of electron-acoustic waves due to multi-plasmon resonances | The linear and nonlinear theories of electron-acoustic waves (EAWs) are
studied in a partially degenerate quantum plasma with two-temperature electrons
and stationary ions. The initial equilibrium of electrons is assumed to be
given by the Fermi-Dirac distribution at finite temperature. By employing the
multi-scale asymptotic expansion technique to the one-dimensional Wigner-Moyal
and Poisson equations, it is shown that the effects of multi-plasmon resonances
lead to a modified complex Korteweg-de Vries (KdV) equation with a new nonlocal
nonlinearity. Besides giving rise to a nonlocal nonlinear term, the
wave-particle resonance also modifies the local nonlinear coupling coefficient
of the KdV equation. The latter is shown to conserve the number of particles,
however, the wave energy decays with time. A careful analysis shows that the
two-plasmon resonance is the dominant mechanism for nonlinear Landau damping of
EAWs. An approximate soliton solution of the KdV equation is also obtained, and
it is shown that the nonlinear Landau damping causes the wave amplitude to
decay slowly with time compared to the classical theory. | 2106.12754v2 |
2021-08-12 | The damping and diffusion of atoms moving in the background electromagnetic environment | The interaction between an atom and the quantized electromagnetic field
depends on the position of the atom. Then the atom experiences a force which is
the minus gradient of this interaction. Through the Heisenberg equations of
motion and the Born-Markov approximation, the mean and correlation of the force
are obtained, showing that the center-of-mass motion of the atom is damped and
diffused. This approach can be easily generalized to multi-level atoms, where
the damping force and diffusion coefficients are just the weighted average of
the contributions from all pairs of energy levels that have nonvanishing dipole
elements. It is shown that these results are invariant under Galilean
transformation, and in principle can be used to determine the velocity of the
lab relative to the background radiation. | 2108.05590v3 |
2021-11-18 | Sharp Stability of a String with Local Degenerate Kelvin-Voigt Damping | This paper is on the asymptotic behavior of the elastic string equation with
localized degenerate Kelvin--Voigt damping $$
u_{tt}(x,t)-[u_{x}(x,t)+b(x)u_{x,t}(x,t)]_{x}=0,\; x\in(-1,1),\; t>0,$$ where
$b(x)=0$ on $x\in (-1,0]$, and $b(x)=x^\alpha>0$ on $x\in (0,1)$ for
$\alpha\in(0,1)$. It is known that the optimal decay rate of solution is
$t^{-2}$ in the limit case $\alpha=0$, and exponential decay rate for
$\alpha\ge 1$. When $\alpha\in (0,1)$, the damping coefficient $b(x)$ is
continuous, but its derivative has a singularity at the interface $x=0$. In
this case, the best known decay rate is $t^{-\frac{3-\alpha}{2(1-\alpha)}}$.
Although this rate is consistent with the exponential one at $\alpha=1$, it
failed to match the optimal one at $\alpha=0$.
In this paper, we obtain a sharper polynomial decay rate
$t^{-\frac{2-\alpha}{1-\alpha}}$. More significantly, it is consistent with the
optimal polynomial decay rate at $\alpha=0$ and the exponential decay rate at
$\alpha = 1$.This is a big step toward the goal of obtaining eventually the
optimal decay rate. | 2111.09500v1 |
2021-11-26 | Damping of Pseudo-Goldstone Fields | Approximate symmetries abound in Nature. If these symmetries are also
spontaneously broken, the would-be Goldstone modes acquire a small mass, or
inverse correlation length, and are referred to as pseudo-Goldstones. At
nonzero temperature, the effects of dissipation can be captured by
hydrodynamics at sufficiently long scales compared to the local equilibrium.
Here we show that in the limit of weak explicit breaking, locality of
hydrodynamics implies that the damping of pseudo-Goldstones is completely
determined by their mass and diffusive transport coefficients. We present many
applications: superfluids, QCD in the chiral limit, Wigner crystal and density
wave phases in the presence of an external magnetic field or not, nematic
phases and (anti-)ferromagnets. For electronic density wave phases,
pseudo-Goldstone damping generates a contribution to the resistivity
independent of the strength of disorder, which can have a linear temperature
dependence provided the associated diffusivity saturates a bound. This is
reminiscent of the phenomenology of strange metal high $T_c$ superconductors,
where charge density waves are observed across the phase diagram. | 2111.13459v2 |
2023-06-26 | Blow-up result for a weakly coupled system of wave equations with a scale-invariant damping, mass term and time derivative nonlinearity | We study in this article the blow-up of solutions to a coupled semilinear
wave equations which are characterized by linear damping terms in the
\textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and
Tricomi terms. The latter are specifically of great interest from both physical
and mathematical points of view since they allow the speeds of propagation to
be time-dependent ones. However, we assume in this work that both waves are
propagating with the same speeds. Employing this fact together with other
hypotheses on the aforementioned parameters (mass and damping coefficients), we
obtain a new blow-up region for the system under consideration, and we show a
lifespan estimate of the maximal existence time. | 2306.14768v1 |
2010-03-11 | Damping of MHD turbulence in partially ionized gas and the observed difference of velocities of neutrals and ions | Theoretical and observational studies on the turbulence of the interstellar
medium developed fast in the past decades. The theory of supersonic magnetized
turbulence, as well as the understanding of projection effects of observed
quantities, are still in progress. In this work we explore the characterization
of the turbulent cascade and its damping from observational spectral line
profiles. We address the difference of ion and neutral velocities by clarifying
the nature of the turbulence damping in the partially ionized. We provide
theoretical arguments in favor of the explanation of the larger Doppler
broadening of lines arising from neutral species compared to ions as arising
from the turbulence damping of ions at larger scales. Also, we compute a number
of MHD numerical simulations for different turbulent regimes and explicit
turbulent damping, and compare both the 3-dimensional distributions of velocity
and the synthetic line profile distributions. From the numerical simulations,
we place constraints on the precision with which one can measure the 3D
dispersion depending on the turbulence sonic Mach number. We show that no
universal correspondence between the 3D velocity dispersions measured in the
turbulent volume and minima of the 2D velocity dispersions available through
observations exist. For instance, for subsonic turbulence the correspondence is
poor at scales much smaller than the turbulence injection scale, while for
supersonic turbulence the correspondence is poor for the scales comparable with
the injection scale. We provide a physical explanation of the existence of such
a 2D-3D correspondence and discuss the uncertainties in evaluating the damping
scale of ions that can be obtained from observations. However, we show that the
statistics of velocity dispersion from observed line profiles can provide the
spectral index and the energy transfer rate of turbulence. Also, comparing two
similar simulations with different viscous coefficients it was possible to
constrain the turbulent cut-off scale. This may especially prove useful since
it is believed that ambipolar diffusion may be one of the dominant dissipative
mechanism in star-forming regions. In this case, the determination of the
ambipolar diffusion scale may be used as a complementary method for the
determination of magnetic field intensity in collapsing cores. We discuss the
implications of our findings in terms of a new approach to magnetic field
measurement proposed by Li & Houde (2008). | 1003.2346v1 |
2012-11-06 | Torsional Alfvén waves in solar partially ionized plasma: effects of neutral helium and stratification | Ion-neutral collisions may lead to the damping of Alfven waves in
chromospheric and prominence plasmas. Neutral helium atoms enhance the damping
in certain temperature interval, where the ratio of neutral helium and neutral
hydrogen atoms is increased. Therefore, the height-dependence of ionization
degrees of hydrogen and helium may influence the damping rate of Alfven waves.
We aim to study the effect of neutral helium in the damping of Alfven waves in
stratified partially ionized plasma of the solar chromosphere. We consider a
magnetic flux tube, which is expanded up to 1000 km height and then becomes
vertical due to merging with neighboring tubes, and study the dynamics of
linear torsional Alfven waves in the presence of neutral hydrogen and neutral
helium atoms. We start with three-fluid description of plasma and consequently
derive single-fluid magnetohydrodynamic (MHD) equations for torsional Alfven
waves. Thin flux tube approximation allows to obtain the dispersion relation of
the waves in the lower part of tubes, while the spatial dependence of
steady-state Alfven waves is governed by Bessel type equation in the upper part
of tubes. Consecutive derivation of single-fluid MHD equations results in a new
Cowling diffusion coefficient in the presence of neutral helium which is
different from previously used one. We found that shorter-period (< 5 s)
torsional Alfven waves damp quickly in the chromospheric network due to
ion-neutral collision. On the other hand, longer-period (> 5 s) waves do not
reach the transition region as they become evanescent at lower heights in the
network cores. Propagation of torsional Alfven waves through the chromosphere
into the solar corona should be considered with caution: low-frequency waves
are evanescent due to the stratification, while high-frequency waves are damped
due to ion neutral collisions. | 1211.1348v2 |
1999-05-29 | Theory of Hall Effect and Electrical Transport in High-Tc Cuprates: Effects of Antiferromagnetic Spin Fluctuations | In the normal state of high-Tc cuprates, the Hall coefficient shows
remarkable temperature dependence, and its absolute value is enhanced in
comparison with that value simply estimated on the basis of band structure. It
has been recognized that this temperature dependence of the Hall coefficient is
due to highly anisotropic quasiparticle damping rate on the Fermi surface. In
this paper we further take account of the vertex correction to the current
vertex arising from quasiparticle interactions. Then the transport current is
transformed to a large extent from the quasiparticle velocity, and is no longer
proportional to the latter. As a consequence some pieces of the Fermi surface
outside of the antiferromagnetic Brillouin zone make negative contribution to
the Hall conductivity, even if the curvature of the Fermi surface is hole-like.
The Hall coefficient is much larger at low temperatures than the estimate made
without the vertex correction. Temperature dependence of the antiferromagnetic
spin correlation length is also crucial to cause remarkable temperature
dependence of the Hall coefficient. In our treatment the Hall coefficient of
the electron-doped cuprates can be negative despite hole-like curvature of the
Fermi surface. | 9905428v1 |
2021-06-02 | In-medium kinetic theory of $D$ mesons and heavy-flavor transport coefficients | We extend the kinetic theory of $D$ mesons to accommodate thermal and
off-shell effects due to the medium modification of the heavy-meson spectral
functions. From the Kadanoff-Baym approach we derive the off-shell
Fokker-Planck equation which encodes the heavy-flavor transport coefficients.
We analyze the thermal width (damping rate) of $D$ mesons due to their
scattering off light mesons, focusing on new in-medium effects: off-shell
corrections, inelastic channels, and the contribution of the Landau cut. We
obtain that the latter effect (absent for vacuum scattering amplitudes) brings
sizable corrections at moderate temperatures. We discuss how the heavy-flavor
transport coefficients, like the drag and diffusion coefficients, are modified
in matter. We find that the $D$-meson spatial diffusion coefficient matches
smoothly to the latest results of lattice-QCD calculations and Bayesian
analyses at higher temperatures. | 2106.01156v2 |
2022-04-08 | Transport coefficients of heavy quarkonia comparing with heavy quark coefficients | We revisit the transport coefficients of heavy quarkonia moving in
high-temperature QCD plasmas. The thermal width and mass shift for heavy
quarkonia are closely related to the momentum diffusion coefficient and its
dispersive counterpart for heavy quarks, respectively. For quarkonium at rest
in plasmas the longitudinal gluon part of the color-singlet self-energy diagram
is sufficient to determine the leading-order thermal width, whereas the
momentum dependence is obtained from the transverse gluon channel. Using the
quarkonium-gluon effective vertex based on the dipole interaction of color
charges, we discuss the damping rate, the effective rest and kinetic mass
shifts of slowly moving quarkonia and compare with the corresponding
coefficients of heavy quarks. | 2204.04180v1 |
2006-06-15 | Purity and decoherence in the theory of a damped harmonic oscillator | For the generalized master equations derived by Karrlein and Grabert for the
microscopic model of a damped harmonic oscillator, the conditions for purity of
states are written, in particular for different initial conditions and
different types of damping, including Ohmic, Drude and weak coupling cases,
Agarwal and Weidlich-Haake models. It is shown that the states which remain
pure are the squeezed states with constant in time variances. For pure states,
the generalized nonlinear Schr\" odinger-type equations corresponding to these
master equations are also obtained. Then the condition for purity of states of
a damped harmonic oscillator is considered in the framework of Lindblad theory
for open quantum systems. For a special choice of the environment coefficients,
the correlated coherent states with constant variances and covariance are shown
to be the only states which remain pure all the time during the evolution of
the considered system. In Karrlein-Grabert and Lindblad models, as well as in
the considered particular models, the expressions of the rate of entropy
production is written and it is shown that the states which preserve their
purity in time are also the states which minimize the entropy production and,
therefore, they are the most stable ones under evolution in the presence of the
environment and play an important role in the description of decoherence
phenomenon. | 0606134v1 |
2009-10-09 | One-way coupled Van der Pol system | The equation of the Van der Pol oscillator, being characterized by a
dissipative term, is non-Lagrangian. Appending an additional degree of freedom
we bring the equation in the frame of action principle and thus introduce a
one-way coupled system. As with the Van der Pol oscillator, the coupled system
also involves only one parameter that controls the dynamics. The response
system is described by a linear differential equation coupled nonlinearly to
the drive system. In the linear approximation the equations of our coupled
system coincide with those of the Bateman dual system (a pair of damped and
anti-damped harmonic oscillators). The critical point of damped and anti-damped
oscillators are stable and unstable for all physical values of the frictional
coefficient $\mu$. Contrarily, the critical points of the drive- (Van der Pol)
and response systems depend crucially on the values of $\mu$. These points are
unstable for $\mu > 0$ while the critical point of the drive system is stable
and that of the response system is unstable for $\mu < 0$. The one-way coupled
system exhibits bifurcations which are different from those of the uncoupled
Van der Pol oscillator. Our system is chaotic and we observe phase
synchronization in the regime of dynamic chaos only for small values of $\mu$. | 0910.1700v1 |
2018-02-18 | On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation | We develop a provably energy stable discontinuous Galerkin spectral element
method (DGSEM) approximation of the perfectly matched layer (PML) for the three
and two space dimensional (3D and 2D) linear acoustic wave equations, in first
order form, subject to well-posed linear boundary conditions. First, using the
well-known complex coordinate stretching, we derive an efficient un-split modal
PML for the 3D acoustic wave equation. Second, we prove asymptotic stability of
the continuous PML by deriving energy estimates in the Laplace space, for the
3D PML in a heterogeneous acoustic medium, assuming piece-wise constant PML
damping. Third, we develop a DGSEM for the wave equation using physically
motivated numerical flux, with penalty weights, which are compatible with all
well-posed, internal and external, boundary conditions. When the PML damping
vanishes, by construction, our choice of penalty parameters yield an upwind
scheme and a discrete energy estimate analogous to the continuous energy
estimate. Fourth, to ensure numerical stability when PML damping is present, it
is necessary to systematically extend the numerical numerical fluxes, and the
inter-element and boundary procedures, to the PML auxiliary differential
equations. This is critical for deriving discrete energy estimates analogous to
the continuous energy estimates. Finally, we propose a procedure to compute PML
damping coefficients such that the PML error converges to zero, at the optimal
convergence rate of the underlying numerical method. Numerical experiments are
presented in 2D and 3D corroborating the theoretical results. | 1802.06388v1 |
2018-09-19 | Critical exponent for the semilinear wave equations with a damping increasing in the far field | We consider the Cauchy problem of the semilinear wave equation with a damping
term \begin{align*}
u_{tt} - \Delta u + c(t,x) u_t = |u|^p, \quad (t,x)\in (0,\infty)\times
\mathbb{R}^N,\quad
u(0,x) = \varepsilon u_0(x), \ u_t(0,x) = \varepsilon u_1(x), \quad x\in
\mathbb{R}^N, \end{align*} where $p>1$ and the coefficient of the damping term
has the form \begin{align*}
c(t,x) = a_0 (1+|x|^2)^{-\alpha/2} (1+t)^{-\beta} \end{align*} with some $a_0
> 0$, $\alpha < 0$, $\beta \in (-1, 1]$. In particular, we mainly consider the
cases $ \alpha < 0, \beta =0$ or $\alpha < 0, \beta = 1$, which imply $\alpha +
\beta < 1$, namely, the damping is spatially increasing and effective. Our aim
is to prove that the critical exponent is given by $ p = 1+
\frac{2}{N-\alpha}$. This shows that the critical exponent is the same as that
of the corresponding parabolic equation $c(t,x) v_t - \Delta v = |v|^p$. The
global existence part is proved by a weighted energy estimates with an
exponential-type weight function and a special case of the
Caffarelli-Kohn-Nirenberg inequality. The blow-up part is proved by a
test-function method introduced by Ikeda and Sobajima (arXiv:1710.06780v1). We
also give an upper estimate of the lifespan. | 1809.06994v1 |
2020-08-03 | Improvement on the blow-up of the wave equation with the scale-invariant damping and combined nonlinearities | We consider in this article the damped wave equation, in the
\textit{scale-invariant case} with combined two nonlinearities, which reads as
follows: \begin{displaymath} \d (E) \hspace{1cm} u_{tt}-\Delta
u+\frac{\mu}{1+t}u_t=|u_t|^p+|u|^q, \quad \mbox{in}\ \R^N\times[0,\infty),
\end{displaymath} with small initial data.\\ Compared to our previous work
\cite{Our}, we show in this article that the first hypothesis on the damping
coefficient $\mu$, namely $\mu < \frac{N(q-1)}{2}$, can be removed, and the
second one can be extended from $(0, \mu_*/2)$ to $(0, \mu_*)$ where $\mu_*>0$
is solution of $(q-1)\left((N+\mu_*-1)p-2\right) = 4$. Indeed, owing to a
better understanding of the influence of the damping term in the global
dynamics of the solution, we think that this new interval for $\mu$ describe
better the threshold between the blow-up and the global existence regions.
Moreover, taking advantage of the techniques employed in the problem $(E)$, we
also improve the result in \cite{LT2,Palmieri} in relationship with the Glassey
conjecture for the solution of $(E)$ but without the nonlinear term $|u|^q$.
More precisely, we extend the blow-up region from $p \in (1, p_G(N+\sigma)]$,
where $\sigma$ is given by \eqref{sigma} below, to $p \in (1, p_G(N+\mu)]$
giving thus a better estimate of the lifespan in this case. | 2008.02109v3 |
2021-07-17 | Theoretical and numerical study of vibrational resonance in a damped softening Duffing oscillator | We study the possibility of occurrence of vibrational resonance in a
softening Duffing oscillator in the underdamped and overdamped cases both
theoretically as well as numerically. The oscillator is driven by two periodic
forces. Numerically we find that in the underdamped case two oscillatory
solutions are obtained in a limited range of the parameters considered (damping
coefficient and amplitude of the high frequency force) for a fixed frequency
and amplitude of the low frequency periodic force depending on the initial
conditions. These solutions have distinct response amplitude to the low
frequency force. When damping is gradually increased, only one oscillatory
solution is observed. Vibrational resonance is observed in both the regions of
oscillation. The analytical approximation yields only one oscillatory solution
for all damping values. Analytically, the peak in the area bounded by the phase
portrait as a function of the amplitude of the high frequency force is
connected to vibrational resonance. Also, the values of the frequency of the
low frequency forcing and the amplitude of the high frequency forcing at which
vibrational resonance is found to occur are obtained. In the overdamped case,
vibrational resonance is not observed for the softening Duffing oscillator thus
showing a marked contrast to the overdamped bistable oscillator | 2107.08302v1 |
2021-11-15 | Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters | A second order accurate, linear numerical method is analyzed for the
Landau-Lifshitz equation with large damping parameters. This equation describes
the dynamics of magnetization, with a non-convexity constraint of unit length
of the magnetization. The numerical method is based on the second-order
backward differentiation formula in time, combined with an implicit treatment
of the linear diffusion term and explicit extrapolation for the nonlinear
terms. Afterward, a projection step is applied to normalize the numerical
solution at a point-wise level. This numerical scheme has shown extensive
advantages in the practical computations for the physical model with large
damping parameters, which comes from the fact that only a linear system with
constant coefficients (independent of both time and the updated magnetization)
needs to be solved at each time step, and has greatly improved the numerical
efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme
has not been available. In this paper, we provide a rigorous error estimate of
the numerical scheme, in the discrete $\ell^{\infty}(0,T; \ell^2) \cap
\ell^2(0,T; H_h^1)$ norm, under suitable regularity assumptions and reasonable
ratio between the time step-size and the spatial mesh-size. In particular, the
projection operation is nonlinear, and a stability estimate for the projection
step turns out to be highly challenging. Such a stability estimate is derived
in details, which will play an essential role in the convergence analysis for
the numerical scheme, if the damping parameter is greater than 3. | 2111.07537v1 |
2022-12-22 | Spin wave dispersion of ultra-low damping hematite ($α\text{-Fe}_2\text{O}_3$) at GHz frequencies | Low magnetic damping and high group velocity of spin waves (SWs) or magnons
are two crucial parameters for functional magnonic devices. Magnonics research
on signal processing and wave-based computation at GHz frequencies focussed on
the artificial ferrimagnetic garnet Y$_3$Fe$_5$O$_{12}$ (YIG) so far. We report
on spin-wave spectroscopy studies performed on the natural mineral hematite
($\alpha\text{-Fe}_2\text{O}_3$) which is a canted antiferromagnet. By means of
broadband GHz spectroscopy and inelastic light scattering, we determine a
damping coefficient of $1.1\times10^{-5}$ and magnon group velocities of a few
10 km/s, respectively, at room temperature. Covering a large regime of wave
vectors up to $k\approx 24~{\rm rad}/\mu$m, we find the exchange stiffness
length to be relatively short and only about 1 \r{A}. In a small magnetic field
of 30 mT, the decay length of SWs is estimated to be 1.1 cm similar to the best
YIG. Still, inelastic light scattering provides surprisingly broad and partly
asymmetric resonance peaks. Their characteristic shape is induced by the large
group velocities, low damping and distribution of incident angles inside the
laser beam. Our results promote hematite as an alternative and sustainable
basis for magnonic devices with fast speeds and low losses based on a stable
natural mineral. | 2212.11887v2 |
2024-02-19 | Global existence for non-homogeneous incompressible inviscid fluids in presence of Ekman pumping | In this paper, we study the global solvability of the density-dependent
incompressible Euler equations, supplemented with a damping term of the form $
\mathfrak{D}_{\alpha}^{\gamma}(\rho, u) = \alpha \rho^{\gamma} u $, where
$\alpha>0$ and $ \gamma \in \{0,1\} $. To some extent, this system can be seen
as a simplified model describing the mean dynamics in the ocean; from this
perspective, the damping term can be interpreted as a term encoding the effects
of the celebrated Ekman pumping in the system.
On the one hand, in the general case of space dimension $d\geq 2$, we
establish global well-posedness in the Besov spaces framework, under a
non-linear smallness condition involving the size of the initial velocity field
$u_0$, of the initial non-homogeneity $\rho_0-1$ and of the damping coefficient
$\alpha$. On the other hand, in the specific situation of planar motions and
damping term with $\gamma=1$, we exhibit a second smallness condition implying
global existence, which in particular yields global well-posedness for
arbitrarily large initial velocity fields, provided the initial density
variations $\rho_0-1$ are small enough. The formulated smallness conditions
rely only on the endpoint Besov norm $B^1_{\infty,1}$ of the initial datum,
whereas, as a byproduct of our analysis, we derive exponential decay of the
velocity field and of the pressure gradient in the high regularity norms
$B^s_{p,r}$. | 2402.12592v1 |
1993-04-01 | Wavelet transforms versus Fourier transforms | This note is a very basic introduction to wavelets. It starts with an
orthogonal basis of piecewise constant functions, constructed by dilation and
translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients
with respect to this basis. The mathematics is simple and the transform is fast
(faster than the Fast Fourier Transform, which we briefly explain), but
approximation by piecewise constants is poor. To improve this first wavelet, we
are led to dilation equations and their unusual solutions. Higher-order
wavelets are constructed, and it is surprisingly quick to compute with them ---
always indirectly and recursively. We comment informally on the contest between
these transforms in signal processing, especially for video and image
compression (including high-definition television). So far the Fourier
Transform --- or its 8 by 8 windowed version, the Discrete Cosine Transform ---
is often chosen. But wavelets are already competitive, and they are ahead for
fingerprints. We present a sample of this developing theory. | 9304214v1 |
2008-01-07 | Magnetization reversal driven by spin-injection : a mesoscopic spin-transfer effect | A mesoscopic description of spin-transfer effect is proposed, based on the
spin-injection mechanism occurring at the junction with a ferromagnet. The
effect of spin-injection is to modify locally, in the ferromagnetic
configuration space, the density of magnetic moments. The corresponding
gradient leads to a current-dependent diffusion process of the magnetization.
In order to describe this effect, the dynamics of the magnetization of a
ferromagnetic single domain is reconsidered in the framework of the
thermokinetic theory of mesoscopic systems. Assuming an Onsager
cross-coefficient that couples the currents, it is shown that spin-dependent
electric transport leads to a correction of the Landau-Lifshitz-Gilbert
equation of the ferromagnetic order parameter with supplementary diffusion
terms. The consequence of spin-injection in terms of activation process of the
ferromagnet is deduced, and the expressions of the effective energy barrier and
of the critical current are derived. Magnetic fluctuations are calculated: the
correction to the fluctuations is similar to that predicted for the activation.
These predictions are consistent with the measurements of spin-transfer
obtained in the activation regime and for ferromagnetic resonance under
spin-injection. | 0801.1019v1 |
2012-07-24 | Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators | We survey various quantized bulk physical observables in two- and
three-dimensional topological band insulators invariant under translational
symmetry and crystallographic point group symmetries (PGS). In two-dimensional
insulators, we show that: (i) the Chern number of a $C_n$-invariant insulator
can be determined, up to a multiple of $n$, by evaluating the eigenvalues of
symmetry operators at high-symmetry points in the Brillouin zone; (ii) the
Chern number of a $C_n$-invariant insulator is also determined, up to a
multiple of $n$, by the $C_n$ eigenvalue of the Slater determinant of a
noninteracting many-body system and (iii) the Chern number vanishes in
insulators with dihedral point groups $D_n$, and the quantized electric
polarization is a topological invariant for these insulators. In
three-dimensional insulators, we show that: (i) only insulators with point
groups $C_n$, $C_{nh}$ and $S_n$ PGS can have nonzero 3D quantum Hall
coefficient and (ii) only insulators with improper rotation symmetries can have
quantized magnetoelectric polarization $P_3$ in the term
$P_3\mathbf{E}\cdot\mathbf{B}$, the axion term in the electrodynamics of the
insulator (medium). | 1207.5767v2 |
2016-08-06 | High current, high efficiency graded band gap perovskite solar cells | Organic-inorganic halide perovskite materials have emerged as attractive
alternatives to conventional solar cell building blocks. Their high light
absorption coefficients and long diffusion lengths suggest high power
conversion efficiencies (PCE),1-5 and indeed perovskite-based single band gap
and tandem solar cell designs have yielded impressive performances.1-16 One
approach to further enhance solar spectrum utilization is the graded band gap,
but this has not been previously achieved for perovskites. In this study, we
demonstrate graded band gap perovskite solar cells with steady-state conversion
efficiencies averaging 18.4%, with a best of 21.7%, all without reflective
coatings. An analysis of the experimental data yields high fill factors of ~75%
and high short circuit current densities up to 42.1 mA/cm2. These cells, which
are based on a novel architecture of two perovskite layers (MASnI3 and
MAPbI3-xBrx), incorporating GaN, monolayer hexagonal boron nitride, and
graphene aerogel, display the highest efficiency ever reported for perovskite
solar cells. | 1608.02150v1 |
2016-08-30 | LiRa: A New Likelihood-Based Similarity Score for Collaborative Filtering | Recommender system data presents unique challenges to the data mining,
machine learning, and algorithms communities. The high missing data rate, in
combination with the large scale and high dimensionality that is typical of
recommender systems data, requires new tools and methods for efficient data
analysis. Here, we address the challenge of evaluating similarity between two
users in a recommender system, where for each user only a small set of ratings
is available. We present a new similarity score, that we call LiRa, based on a
statistical model of user similarity, for large-scale, discrete valued data
with many missing values. We show that this score, based on a ratio of
likelihoods, is more effective at identifying similar users than traditional
similarity scores in user-based collaborative filtering, such as the Pearson
correlation coefficient. We argue that our approach has significant potential
to improve both accuracy and scalability in collaborative filtering. | 1608.08646v2 |
2018-11-01 | Time Quantified Monte Carlo Method for Long-range Interacting Systems | We propose a method for simulating the stochastic dynamics of classical spin
systems with long-range interactions. The method incorporates the stochastic
cutoff (SCO) method, which is originally specialized for simulating equilibrium
state, into time quantified Monte Carlo (TQMC) method. We analytically prove
that the present method gives the same real-time dynamics with the stochastic
Landau-Lifshitz-Gilbert (s-LLG) equation, i.e., both method derives the same
Fokker-Planck coefficients. We demonstrate magnetization reversal processes and
confirm that the result is in good agreement with the result obtained by s-LLG.
Using our method enables us to analyze complicated lattice systems consisting
of many spins in a unit cell. Technical improvement of TQMC is also proposed. | 1811.00237v2 |
2019-01-10 | Multi-Parameter Regression Survival Modelling: An Alternative to Proportional Hazards | It is standard practice for covariates to enter a parametric model through a
single distributional parameter of interest, for example, the scale parameter
in many standard survival models. Indeed, the well-known proportional hazards
model is of this kind. In this paper we discuss a more general approach whereby
covariates enter the model through more than one distributional parameter
simultaneously (e.g., scale and shape parameters). We refer to this practice as
"multi-parameter regression" (MPR) modelling and explore its use in a survival
analysis context. We find that multi-parameter regression leads to more
flexible models which can offer greater insight into the underlying data
generating process. To illustrate the concept, we consider the two-parameter
Weibull model which leads to time-dependent hazard ratios, thus relaxing the
typical proportional hazards assumption and motivating a new test of
proportionality. A novel variable selection strategy is introduced for such
multi-parameter regression models. It accounts for the correlation arising
between the estimated regression coefficients in two or more linear predictors
-- a feature which has not been considered by other authors in similar
settings. The methods discussed have been implemented in the mpr package in R. | 1901.03277v1 |
2019-11-05 | Numerical methods for antiferromagnetics | Compared with ferromagnetic counterparts, antiferromagnetic materials are
considered as the future of spintronic applications since these materials are
robust against the magnetic perturbation, produce no stray field, and display
ultrafast dynamics. There are (at least) two sets of magnetic moments in
antiferromagnets (with magnetization of the same magnitude but antiparallel
directions) and ferrimagnets (with magnetization of the different magnitude).
The coupled dynamics for the bipartite collinear antiferromagnets is modeled by
a coupled system of Landau-Lifshitz-Gilbert equations with an additional term
originated from the antiferromagnetic exchange, which leads to femtosecond
magnetization dynamics. In this paper, we develop three Gauss-Seidel projection
methods for micromagnetics simulation in antiferromagnets and ferrimagnets.
They are first-order accurate in time and second-order in space, and only solve
linear systems of equations with constant coefficients at each step.
Femtosecond dynamics, N\'{e}el wall structure, and phase transition in presence
of an external magnetic field for antiferromagnets are provided with the
femtosecond stepsize. | 1911.01717v1 |
2023-02-06 | Landau theory for ferro-paramagnetic phase transition in finitely-strained viscoelastic magnets | The thermodynamic model of visco-elastic deformable magnetic materials at
finite strains is formulated in a fully Eulerian way in rates. The Landau
theory applies for ferro-to-para-magnetic phase transition, the gradient theory
(leading exchange energy) for magnetization with general mechanically dependent
coefficient, hysteresis in magnetization evolution by Landau-Lifshitz-Gilbert
equation involving objective corotational time derivative of magnetization, and
demagnetizing field are considered in the model. The Kelvin-Voigt viscoelastic
rheology with a higher-order viscosity (exploiting the concept of multipolar
materials) is used, allowing for physically relevant frame-indifferent stored
energies and for local invertibility of deformation. The model complies with
energy conservation and Clausius-Duhem entropy inequality. Existence and a
certain regularity of weak solutions is proved by a Faedo-Galerkin
semi-discretization and a suitable regularization. | 2302.02850v1 |
2000-10-12 | Friction in a solid lubricant film | Molecular dynamics study of a thin (one to five layers) lubricant film
between two substrates in moving contact are performed using Langevin equations
with an external damping coefficient depending on distance and velocity of
atoms relative the substrates, motivated by microscopic configurations. They
show that the minimal friction coefficient is obtained for the solid-sliding
regime. A detailed analysis of the results, the comparison with other
microscopic modeling approaches of friction, and the evaluation of quantities
that can be compared to experiments, such as the velocity of the transition
from stick-slip to smooth sliding, are used to discuss the relevance of the
microscopic simulations of friction. | 0010185v1 |
1993-06-01 | Transport Properties of Solitons | We calculate in this article the transport coefficients which characterize
the dynamics of solitons in quantum field theory using the methods of
dissipative quantum systems. We show how the damping and diffusion coefficients
of soliton-like excitations can be calculated using the integral functional
formalism. The model obtained in this article has new features which cannot be
obtained in the standard models of dissipation in quantum mechanics. | 9306007v1 |
2008-10-01 | Estimating Speed and Damping in the Stochastic Wave Equation | A parameter estimation problem is considered for a one-dimensional stochastic
wave equation driven by additive space-time Gaussian white noise.
The estimator is of spectral type and utilizes a finite number of the spatial
Fourier coefficients of the solution. The asymptotic properties of the
estimator are studied as the number of the Fourier coefficients increases,
while the observation time and the noise intensity are fixed. | 0810.0046v1 |
2009-06-23 | Parameter Estimation in Diagonalizable Stochastic Hyperbolic Equations | A parameter estimation problem is considered for a linear stochastic
hyperbolic equation driven by additive space-time Gaussian white noise. The
damping/amplification operator is allowed to be unbounded.
The estimator is of spectral type and utilizes a finite number of the spatial
Fourier coefficients of the solution. The asymptotic properties of the
estimator are studied as the number of the Fourier coefficients increases,
while the observation time and the noise intensity are fixed. | 0906.4353v1 |
2011-12-11 | Shear viscosity and spin diffusion coefficient of a two-dimensional Fermi gas | Using kinetic theory, we calculate the shear viscosity and the spin diffusion
coefficient as well as the associated relaxation times for a two-component
Fermi gas in two dimensions, as a function of temperature, coupling strength,
polarization, and mass ratio of the two components. It is demonstrated that the
minimum value of the viscosity decreases with the mass ratio, since Fermi
blocking becomes less efficient. We furthermore analyze recent experimental
results for the quadrupole mode of a 2D gas in terms of viscous damping
obtaining a qualitative agreement using no fitting parameters. | 1112.2395v2 |
2014-03-12 | Logarithmic stability in determining two coefficients in a dissipative wave equation. Extensions to clamped Euler-Bernoulli beam and heat equations | We are concerned with the inverse problem of determining both the potential
and the damping coefficient in a dissipative wave equation from boundary
measurements. We establish stability estimates of logarithmic type when the
measurements are given by the operator who maps the initial condition to
Neumann boundary trace of the solution of the corresponding initial-boundary
value problem. We build a method combining an observability inequality together
with a spectral decomposition. We also apply this method to a clamped
Euler-Bernoulli beam equation. Finally, we indicate how the present approach
can be adapted to a heat equation. | 1403.3018v2 |
2015-03-16 | Determining a boundary coefficient in a dissipative wave equation: Uniqueness and directional lipschitz stability | We are concerned with the problem of determining the damping boundary
coefficient appearing in a dissipative wave equation from a single boundary
measurement. We prove that the uniqueness holds at the origin provided that the
initial condition is appropriately chosen. We show that the choice of the
initial condition leading to uniqueness is related to a fine version of unique
continuation property for elliptic operators. We also establish a Lipschitz
directional stability estimate at the origin, which is obtained by a
linearization process. | 1503.04528v1 |
2015-04-28 | Fractional relaxation and fractional oscillation models involving Erdelyi-Kober integrals | We consider fractional relaxation and fractional oscillation equations
involving Erdelyi-Kober integrals. In terms of Riemann-Liouville integrals, the
equations we analyze can be understood as equations with time-varying
coefficients. Replacing Riemann-Liouville integrals with Erdelyi-Kober-type
integrals in certain fractional oscillation models, we obtain some more general
integro-differential equations. The corresponding Cauchy-type problems can be
solved numerically, and, in some cases analytically, in terms of Saigo-Kilbas
Mittag-Leffler functions. The numerical results are obtained by a treatment
similar to that developed by K. Diethelm and N.J. Ford to solve the
Bagley-Torvik equation. Novel results about the numerical approach to the
fractional damped oscillator equation with time-varying coefficients are also
presented. | 1504.07568v1 |
2017-12-28 | On well-posedness of Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow | We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in
compressible flow. Inspired by our study for incompressible case
\cite{Jiang-Luo-arXiv-2017} and some techniques from compressible Navier-Stokes
equations, we prove the local-in-time existence of the classical solution to
the system with finite initial energy, under some constraints on the Leslie
coefficients which ensure the basic energy law is dissipative. Furthermore,
with an additional assumption on the coefficients which provides a damping
effect, and the smallness of the initial energy, the global classical solution
can be established. | 1712.09799v1 |
2018-02-02 | Energy decay and global solutions for a damped free boundary fluid-elastic structure interface model with variable coefficients in elasticity | We cope with a free boundary fluid-structure interaction model. In the model,
the viscous incompressible fluid interacts with elastic body via the common
boundary. The motion of the fluid is governed by Navier-Stokes equations while
the displacement of elastic structure is described by variable coefficient wave
equations. The dissipation is placed on the common boundary between fluid and
elastic body. Given small initial data, the global existence of the solutions
of this system is proved and the exponential decay of solutions are obtained. | 1802.00585v2 |
2020-05-23 | Stability analysis of multi-term fractional-differential equations with three fractional derivatives | Necessary and sufficient stability and instability conditions are obtained
for multi-term homogeneous linear fractional differential equations with three
Caputo derivatives and constant coefficients. In both cases,
fractional-order-dependent as well as fractional-order-independent
characterisations of stability and instability properties are obtained, in
terms of the coefficients of the multi-term fractional differential equation.
The theoretical results are exemplified for the particular cases of the Basset
and Bagley-Torvik equations, as well as for a multi-term fractional
differential equation of an inextensible pendulum with fractional damping
terms, and for a fractional harmonic oscillator. | 2005.11486v1 |
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