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2020-02-27 | Ultrafast magnetization dynamics in half-metallic Co$_2$FeAl Heusler alloy | We report on optically induced, ultrafast magnetization dynamics in the
Heusler alloy $\mathrm{Co_{2}FeAl}$, probed by time-resolved magneto-optical
Kerr effect. Experimental results are compared to results from electronic
structure theory and atomistic spin-dynamics simulations. Experimentally, we
find that the demagnetization time ($\tau_{M}$) in films of
$\mathrm{Co_{2}FeAl}$ is almost independent of varying structural order, and
that it is similar to that in elemental 3d ferromagnets. In contrast, the
slower process of magnetization recovery, specified by $\tau_{R}$, is found to
occur on picosecond time scales, and is demonstrated to correlate strongly with
the Gilbert damping parameter ($\alpha$). Our results show that
$\mathrm{Co_{2}FeAl}$ is unique, in that it is the first material that clearly
demonstrates the importance of the damping parameter in the remagnetization
process. Based on these results we argue that for $\mathrm{Co_{2}FeAl}$ the
remagnetization process is dominated by magnon dynamics, something which might
have general applicability. | 2002.12255v1 |
2020-06-05 | Controlling the nonlinear relaxation of quantized propagating magnons in nanodevices | Relaxation of linear magnetization dynamics is well described by the viscous
Gilbert damping processes. However, for strong excitations, nonlinear damping
processes such as the decay via magnon-magnon interactions emerge and trigger
additional relaxation channels. Here, we use space- and time-resolved
microfocused Brillouin light scattering spectroscopy and micromagnetic
simulations to investigate the nonlinear relaxation of strongly driven
propagating spin waves in yttrium iron garnet nanoconduits. We show that the
nonlinear magnon relaxation in this highly quantized system possesses
intermodal features, i.e., magnons scatter to higher-order quantized modes
through a cascade of scattering events. We further show how to control such
intermodal dissipation processes by quantization of the magnon band in
single-mode devices, where this phenomenon approaches its fundamental limit.
Our study extends the knowledge about nonlinear propagating spin waves in
nanostructures which is essential for the construction of advanced spin-wave
elements as well as the realization of Bose-Einstein condensates in scaled
systems. | 2006.03400v2 |
2021-05-16 | Anatomy of inertial magnons in ferromagnets | We analyze dispersion relations of magnons in ferromagnetic nanostructures
with uniaxial anisotropy taking into account inertial terms, i.e. magnetic
nutation. Inertial effects are parametrized by damping-independent parameter
$\beta$, which allows for an unambiguous discrimination of inertial effects
from Gilbert damping parameter $\alpha$. The analysis of magnon dispersion
relation shows its two branches are modified by the inertial effect, albeit in
different ways. The upper nutation branch starts at $\omega=1/ \beta$, the
lower branch coincides with FMR in the long-wavelength limit and deviates from
the zero-inertia parabolic dependence $\simeq\omega_{FMR}+Dk^2$ of the exchange
magnon. Taking a realistic experimental geometry of magnetic thin films,
nanowires and nanodiscs, magnon eigenfrequencies, eigenvectors and $Q$-factors
are found to depend on the shape anisotropy. The possibility of phase-matched
magneto-elastic excitation of nutation magnons is discussed and the condition
was found to depend on $\beta$, exchange stiffness $D$ and the acoustic
velocity. | 2105.07376v1 |
2021-11-16 | Ultrathin ferrimagnetic GdFeCo films with very low damping | Ferromagnetic materials dominate as the magnetically active element in
spintronic devices, but come with drawbacks such as large stray fields, and low
operational frequencies. Compensated ferrimagnets provide an alternative as
they combine the ultrafast magnetization dynamics of antiferromagnets with a
ferromagnet-like spin-orbit-torque (SOT) behavior. However to use ferrimagnets
in spintronic devices their advantageous properties must be retained also in
ultrathin films (t < 10 nm). In this study, ferrimagnetic Gdx(Fe87.5Co12.5)1-x
thin films in the thickness range t = 2-20 nm were grown on high resistance
Si(100) substrates and studied using broadband ferromagnetic resonance
measurements at room temperature. By tuning their stoichiometry, a nearly
compensated behavior is observed in 2 nm Gdx(Fe87.5Co12.5)1-x ultrathin films
for the first time, with an effective magnetization of Meff = 0.02 T and a low
effective Gilbert damping constant of {\alpha} = 0.0078, comparable to the
lowest values reported so far in 30 nm films. These results show great promise
for the development of ultrafast and energy efficient ferrimagnetic spintronic
devices. | 2111.08768v1 |
2021-11-30 | First and second order magnetic anisotropy and damping of europium iron garnet under high strain | Understanding and tailoring static and dynamic properties of magnetic
insulator thin films is important for spintronic device applications. Here, we
grow atomically flat epitaxial europium iron garnet (EuIG) thin films by pulsed
laser deposition on (111)-oriented garnet substrates with a range of lattice
parameters. By controlling the lattice mismatch between EuIG and the
substrates, we tune the strain in EuIG films from compressive to tensile
regime, which is characterized by X-ray diffraction. Using ferromagnetic
resonance, we find that in addition to the first-order perpendicular magnetic
anisotropy which depends linearly on the strain, there is a significant
second-order one that has a quadratic strain dependence. Inhomogeneous
linewidth of the ferromagnetic resonance increases notably with increasing
strain, while the Gilbert damping parameter remains nearly constant (~
2x10^-2). These results provide valuable insight into the spin dynamics in
ferrimagnetic insulators and useful guidance for material synthesis and
engineering of next-generation spintronics applications. | 2111.15142v1 |
2022-10-01 | Nonlinear features of the superconductor--ferromagnet--superconductor $\varphi_0$ Josephson junction in ferromagnetic resonance region | We demonstrate the manifestations of the nonlinear features in magnetic
dynamics and IV-characteristics of the $\varphi_0$ Josephson junction in the
ferromagnetic resonance region. We show that at small values of system
parameters, namely, damping, spin-orbit interaction, and Josephson to magnetic
energy ratio, the magnetic dynamics is reduced to the dynamics of the scalar
Duffing oscillator, driven by the Josephson oscillations. The role of
increasing superconducting current in the resonance region is clarified.
Shifting of the ferromagnetic resonant frequency and the reversal of its
damping dependence due to nonlinearity are demonstrated by the full
Landau-Lifshitz-Gilbert-Josephson system of equations, and in its different
approximations. Finally, we demonstrate the negative differential resistance in
the IV--characteristics, and its correlation with the foldover effect. | 2210.00366v1 |
2023-12-16 | Spin-torque nano-oscillator based on two in-plane magnetized synthetic ferrimagnets | We report the dynamic characterization of the spin-torque-driven in-plane
precession modes of a spin-torque nano-oscillator based on two different
synthetic ferrimagnets: a pinned one characterized by a strong RKKY interaction
which is exchange coupled to an antiferromagnetic layer; and a second one,
non-pinned characterized by weak RKKY coupling. The microwave properties
associated with the steady-state precession of both SyFs are characterized by
high spectral purity and power spectral density. However, frequency dispersion
diagrams of the damped and spin transfer torque modes reveal drastically
different dynamical behavior and microwave emission properties in both SyFs. In
particular, the weak coupling between the magnetic layers of the non-pinned SyF
raises discontinuous dispersion diagrams suggesting a strong influence of mode
crossing. An interpretation of the different dynamical features observed in the
damped and spin torque modes of both SyF systems was obtained by solving
simultaneously, in a macrospin approach, a linearized version of the
Landau-Lifshitz-Gilbert equation including the spin transfer torque term. | 2312.10451v2 |
2020-10-02 | Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: Regularity and error analysis | Stochastic PDE eigenvalue problems are useful models for quantifying the
uncertainty in several applications from the physical sciences and engineering,
e.g., structural vibration analysis, the criticality of a nuclear reactor or
photonic crystal structures. In this paper we present a multilevel quasi-Monte
Carlo (MLQMC) method for approximating the expectation of the minimal
eigenvalue of an elliptic eigenvalue problem with coefficients that are given
as a series expansion of countably-many stochastic parameters. The MLQMC
algorithm is based on a hierarchy of discretisations of the spatial domain and
truncations of the dimension of the stochastic parameter domain. To approximate
the expectations, randomly shifted lattice rules are employed. This paper is
primarily dedicated to giving a rigorous analysis of the error of this
algorithm. A key step in the error analysis requires bounds on the mixed
derivatives of the eigenfunction with respect to both the stochastic and
spatial variables simultaneously. Under stronger smoothness assumptions on the
parametric dependence, our analysis also extends to multilevel higher-order
quasi-Monte Carlo rules. An accompanying paper [Gilbert and Scheichl, 2022],
focusses on practical extensions of the MLQMC algorithm to improve efficiency,
and presents numerical results. | 2010.01044v4 |
2021-03-05 | Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: Efficient algorithms and numerical results | Stochastic PDE eigenvalue problems often arise in the field of uncertainty
quantification, whereby one seeks to quantify the uncertainty in an eigenvalue,
or its eigenfunction. In this paper we present an efficient multilevel
quasi-Monte Carlo (MLQMC) algorithm for computing the expectation of the
smallest eigenvalue of an elliptic eigenvalue problem with stochastic
coefficients. Each sample evaluation requires the solution of a PDE eigenvalue
problem, and so tackling this problem in practice is notoriously
computationally difficult. We speed up the approximation of this expectation in
four ways: we use a multilevel variance reduction scheme to spread the work
over a hierarchy of FE meshes and truncation dimensions; we use QMC methods to
efficiently compute the expectations on each level; we exploit the smoothness
in parameter space and reuse the eigenvector from a nearby QMC point to reduce
the number of iterations of the eigensolver; and we utilise a two-grid
discretisation scheme to obtain the eigenvalue on the fine mesh with a single
linear solve. The full error analysis of a basic MLQMC algorithm is given in
the companion paper [Gilbert and Scheichl, 2022], and so in this paper we focus
on how to further improve the efficiency and provide theoretical justification
for using nearby QMC points and two-grid methods. Numerical results are
presented that show the efficiency of our algorithm, and also show that the
four strategies we employ are complementary. | 2103.03407v3 |
2014-08-15 | Linear hyperbolic equations with time-dependent propagation speed and strong damping | We consider a second order linear equation with a time-dependent coefficient
c(t) in front of the "elastic" operator. For these equations it is well-known
that a higher space-regularity of initial data compensates a lower
time-regularity of c(t).
In this paper we investigate the influence of a strong dissipation, namely a
friction term which depends on a power of the elastic operator.
What we discover is a threshold effect. When the exponent of the elastic
operator in the friction term is greater than 1/2, the damping prevails and the
equation behaves as if the coefficient c(t) were constant. When the exponent is
less than 1/2, the time-regularity of c(t) comes into play. If c(t) is regular
enough, once again the damping prevails. On the contrary, when c(t) is not
regular enough the damping might be ineffective, and there are examples in
which the dissipative equation behaves as the non-dissipative one. As expected,
the stronger is the damping, the lower is the time-regularity threshold.
We also provide counterexamples showing the optimality of our results. | 1408.3499v1 |
2019-10-24 | Topological damping Rashba spin orbit torque in ballistic magnetic domain walls | Rashba spin orbit torque derived from the broken inversion symmetry at
ferromagnet/heavy metal interfaces has potential application in spintronic
devices. In conventional description of the precessional and damping components
of the Rashba spin orbit torque in magnetization textures, the decomposition
coefficients are assumed to be independent of the topology of the underlying
structure. Contrary to this common wisdom, for Schr\"{o}dinger electrons
trespassing ballistically across a magnetic domain wall, we found that the
decomposition coefficient of the damping component is determined by the
topology of the domain wall. The resultant damping Rashba spin orbit torque is
protected by the topology of the underlying magnetic domain wall and robust
against small deviations from the ideal domain wall profile. Our identification
of a topological damping Rashba spin orbit torque component in magnetic domain
walls will help to understand experiments on current driven domain wall motion
in ferromagnet/heavy metal systems with broken inversion symmetry and to
facilitate its utilization in innovative device designs. | 1910.10977v2 |
2023-10-14 | Exploring Damping Effect of Inner Control Loops for Grid-Forming VSCs | This paper presents an analytical approach to explore the damping effect of
inner loops on grid-forming converters. First, an impedance model is proposed
to characterize the behaviors of inner loops, thereby illustrating their
influence on output impedance shaping. Then, based on the impedance
representation, the complex torque coefficient method is employed to assess the
contribution of inner loops to system damping. The interactions among inner
loops, outer loops, and the ac grid are analyzed. It reveals that inner loops
shape the electrical damping torque coefficient and consequently influence both
synchronous and sub-synchronous oscillation modes. The virtual admittance and
current control-based inner-loop scheme is employed to illustrate the proposed
analytical approach. The case study comprises the analysis of impedance
profiles, the analysis of damping torque contributed by inner loops under
various grid strengths, and the comparison between dq-frame and
{\alpha}\b{eta}-frame realizations of inner loops. Finally, simulation and
experimental tests collaborate with theoretical approaches and findings. | 2310.09660v1 |
2003-01-30 | Dynamic effects of electromagnetic wave on a damped two-level atom | We studied the dynamic effects of an electromagnetic(EM) wave with circular
polarization on a two-level damped atom. The results demonstrate interesting ac
Stark split of energy levels of damped atom. The split levels have different
energies and lifetimes, both of which depend on the interaction and the damping
rate of atom. When the frequency of the EM wave is tuned to satisfy the
resonance condition in the strong coupling limit, the transition probability
exhibits Rabi oscillation. Momentum transfer between atom and EM wave shows
similar properties as the transition probability under resonance condition. For
a damped atom interacting with EM field, there exists no longer stable state.
More importantly, if the angular frequency of the EM wave is tuned the same as
the atomic transition frequency and its amplitude is adjusted appropriately
according to the damping coefficients, we can prepare a particular 'Dressed
State' of the coupled system between atom and EM field and can keep the system
coherently in this 'Dressed state' for a very long time. This opens another way
to prepare coherent atomic states. | 0301166v1 |
2014-03-13 | The best decay rate of the damped plate equation in a square | In this paper we study the best decay rate of the solutions of a damped plate
equation in a square and with a homogeneous Dirichlet boundary conditions. We
show that the fastest decay rate is given by the supremum of the real part of
the spectrum of the infinitesimal generator of the underlying semigroup, if the
damping coefficient is in $L^\infty(\Omega).$ Moreover, we give some numerical
illustrations by spectral computation of the spectrum associated to the damped
plate equation. The numerical results obtained for various cases of damping are
in a good agreement with theoretical ones. Computation of the spectrum and
energy of discrete solution of damped plate show that the best decay rate is
given by spectral abscissa of numerical solution. | 1403.3199v1 |
2015-02-16 | Role of nonlinear anisotropic damping in the magnetization dynamics of topological solitons | The consequences of nonlinear anisotropic damping, driven by the presence of
Rashba spin-orbit coupling in thin ferromagnetic metals, are examined for the
dynamics of topological magnetic solitons such as domain walls, vortices, and
skyrmions. The damping is found to affect Bloch and N\'eel walls differently in
the steady state regime below Walker breakdown and leads to a monotonic
increase in the wall velocity above this transition for large values of the
Rashba coefficient. For vortices and skyrmions, a generalization of the damping
tensor within the Thiele formalism is presented. It is found that chiral
components of the damping affect vortex- and hedgehog-like skyrmions in
different ways, but the dominant effect is an overall increase in the
viscous-like damping. | 1502.04695v2 |
2016-05-29 | Damped Infinite Energy Solutions of the 3D Euler and Boussinesq Equations | We revisit a family of infinite-energy solutions of the 3D incompressible
Euler equations proposed by Gibbon et al. [9] and shown to blowup in finite
time by Constantin [6]. By adding a damping term to the momentum equation we
examine how the damping coefficient can arrest this blowup. Further, we show
that similar infinite-energy solutions of the inviscid 3D Boussinesq system
with damping can develop a singularity in finite time as long as the damping
effects are insufficient to arrest the (undamped) 3D Euler blowup in the
associated damped 3D Euler system. | 1605.08965v3 |
2016-06-14 | Anomalous Damping of a Micro-electro-mechanical Oscillator in Superfluid $^3$He-B | The mechanical resonance properties of a micro-electro-mechanical oscillator
with a gap of 1.25 $\mu$m was studied in superfluid $^3$He-B at various
pressures. The oscillator was driven in the linear damping regime where the
damping coefficient is independent of the oscillator velocity. The quality
factor of the oscillator remains low ($Q\approx 80$) down to 0.1 $T_c$, 4
orders of magnitude less than the intrinsic quality factor measured in vacuum
at 4 K. In addition to the Boltzmann temperature dependent contribution to the
damping, a damping proportional to temperature was found to dominate at low
temperatures. We propose a multiple scattering mechanism of the surface Andreev
bound states to be a possible cause for the anomalous damping. | 1606.04483v2 |
2019-09-21 | Stability for coupled waves with locally disturbed Kelvin-Voigt damping | We consider a coupled wave system with partial Kelvin-Voigt damping in the
interval (-1,1), where one wave is dissipative and the other does not. When the
damping is effective in the whole domain (-1,1) it was proven in H.Portillo
Oquendo and P.Sanez Pacheco, optimal decay for coupled waves with Kelvin-voigt
damping, Applied Mathematics Letters 67 (2017), 16-20. That the energy is
decreasing over the time with a rate equal to $t^{-\frac{1}{2}}$. In this
paper, using the frequency domain method we show the effect of the coupling and
the non smoothness of the damping coefficient on the energy decay. Actually, as
expected we show the lack of exponential stability, that the semigroup loses
speed and it decays polynomially with a slower rate then given in, H.Portillo
Oquendo and P.Sanez Pacheco, optimal decay for coupled waves with Kelvin-voigt
damping, Applied Mathematics Letters 67 (2017), 16-20, down to zero at least as
$t^{-\frac{1}{12}}$. | 1909.09838v1 |
2020-06-30 | Polynomial stabilization of non-smooth direct/indirect elastic/viscoelastic damping problem involving Bresse system | We consider an elastic/viscoelastic transmission problem for the Bresse
system with fully Dirichlet or Dirichlet-Neumann-Neumann boundary conditions.
The physical model consists of three wave equations coupled in certain pattern.
The system is damped directly or indirectly by global or local Kelvin-Voigt
damping. Actually, the number of the dampings, their nature of distribution
(locally or globally) and the smoothness of the damping coefficient at the
interface play a crucial role in the type of the stabilization of the
corresponding semigroup. Indeed, using frequency domain approach combined with
multiplier techniques and the construction of a new multiplier function, we
establish different types of energy decay rate (see the table of stability
results below). Our results generalize and improve many earlier ones in the
literature and in particular some studies done on the Timoshenko system with
Kelvin-Voigt damping. | 2006.16595v2 |
2021-12-13 | Cosmic ray streaming in the turbulent interstellar medium | We study the streaming instability of GeV$-100~$GeV cosmic rays (CRs) and its
damping in the turbulent interstellar medium (ISM). We find that the damping of
streaming instability is dominated by ion-neutral collisional damping in weakly
ionized molecular clouds, turbulent damping in the highly ionized warm medium,
and nonlinear Landau damping in the Galactic halo. Only in the Galactic halo,
is the streaming speed of CRs close to the Alfv\'{e}n speed. Alfv\'{e}nic
turbulence plays an important role in both suppressing the streaming
instability and regulating the diffusion of streaming CRs via magnetic field
line tangling, with the effective mean free path of streaming CRs in the
observer frame determined by the Alfv\'{e}nic scale in super-Alfv\'{e}nic
turbulence. The resulting diffusion coefficient is sensitive to Alfv\'{e}n Mach
number, which has a large range of values in the multi-phase ISM.
Super-Alfv\'{e}nic turbulence contributes to additional confinement of
streaming CRs, irrespective of the dominant damping mechanism. | 2112.06941v2 |
2023-12-07 | Probing levitodynamics with multi-stochastic forces and the simple applications on the dark matter detection in optical levitation experiment | If the terrestrial environment is permeated by dark matter, the levitation
experiences damping forces and fluctuations attributed to dark matter. This
paper investigates levitodynamics with multiple stochastic forces, including
thermal drag, photon recoil, feedback, etc., assuming that all of these forces
adhere to the fluctuation-dissipation theorem. The ratio of total damping to
the stochastic damping coefficient distinguishes the levitodynamics from cases
involving only one single stochastic force. The heating and cooling processes
are formulated to determine the limits of temperature change. All sources of
stochastic forces are comprehensively examined, revealing that dark matter
collisions cannot be treated analogously to fluid dynamics. Additionally, a
meticulous analysis is presented, elucidating the intricate relationship
between the fundamental transfer cross-section and the macroscopic transfer
cross-section. While the dark damping coefficient is suppressed by the mass of
the levitated particle, scattering can be coherently enhanced based on the
scale of the component microscopic particle, the atomic form factor, and the
static structure factor. Hence, dark damping holds the potential to provide
valuable insights into the detection of the macroscopic strength of fundamental
particles. We propose experimental procedures for levitation and employ linear
estimation to extract the dark damping coefficient. Utilizing current
levitation results, we demonstrate that the fundamental transfer cross section
of dark matter can be of the order $\sigma^{\rm D}_{T}\lsim {\cal
O}(10^{-26})\rm cm^2$. | 2312.04202v2 |
2013-08-17 | Thickness and power dependence of the spin-pumping effect in Y3Fe5O12/Pt heterostructures measured by the inverse spin Hall effect | The dependence of the spin-pumping effect on the yttrium iron garnet
(Y3Fe5O12, YIG) thickness detected by the inverse spin Hall effect (ISHE) has
been investigated quantitatively. Due to the spin-pumping effect driven by the
magnetization precession in the ferrimagnetic insulator YIG film a
spin-polarized electron current is injected into the Pt layer. This spin
current is transformed into electrical charge current by means of the ISHE. An
increase of the ISHE-voltage with increasing film thickness is observed and
compared to the theoretically expected behavior. The effective damping
parameter of the YIG/Pt samples is found to be enhanced with decreasing YIG
film thickness. The investigated samples exhibit a spin mixing conductance of
g=(7.43 \pm 0.36) \times 10^{18} m^{-2} and a spin Hall angle of theta_{ISHE} =
0.009 \pm 0.0008. Furthermore, the influence of nonlinear effects on the
generated voltage and on the Gilbert damping parameter at high excitation
powers are revealed. It is shown that for small YIG film thicknesses a
broadening of the linewidth due to nonlinear effects at high excitation powers
is suppressed because of a lack of nonlinear multi-magnon scattering channels.
We have found that the variation of the spin-pumping efficiency for thick YIG
samples exhibiting pronounced nonlinear effects is much smaller than the
nonlinear enhancement of the damping. | 1308.3787v1 |
2020-05-28 | Spintronics meets nonadiabatic molecular dynamics: Geometric spin torque and damping on noncollinear classical magnetism due to electronic open quantum system | We analyze a quantum-classical hybrid system of steadily precessing slow
classical localized magnetic moments, forming a head-to-head domain wall,
embedded into an open quantum system of fast nonequilibrium electrons. The
electrons reside within a metallic wire connected to macroscopic reservoirs.
The model captures the essence of dynamical noncollinear and noncoplanar
magnetic textures in spintronics, while making it possible to obtain the exact
time-dependent nonequilibrium density matrix of electronic system and split it
into four contributions. The Fermi surface contribution generates dissipative
(or damping-like in spintronics terminology) spin torque on the moments, and
one of the two Fermi sea contributions generates geometric torque dominating in
the adiabatic regime. When the coupling to the reservoirs is reduced, the
geometric torque is the only nonzero contribution. Locally it has both
nondissipative (or field-like in spintronics terminology) and damping-like
components, but with the sum of latter being zero, which act as the
counterparts of geometric magnetism force and electronic friction in
nonadiabatic molecular dynamics. Such current-independent geometric torque is
absent from widely used micromagnetics or atomistic spin dynamics modeling of
magnetization dynamics based on the Landau-Lifshitz-Gilbert equation, where
previous analysis of Fermi surface-type torque has severely underestimated its
magnitude. | 2005.14153v2 |
2020-09-29 | Structural Phase Dependent Giant Interfacial Spin Transparency in W/CoFeB Thin Film Heterostructure | Pure spin current has transfigured the energy-efficient spintronic devices
and it has the salient characteristic of transport of the spin angular
momentum. Spin pumping is a potent method to generate pure spin current and for
its increased efficiency high effective spin-mixing conductance (Geff) and
interfacial spin transparency (T) are essential. Here, a giant T is reported in
Sub/W(t)/Co20Fe60B20(d)/SiO2(2 nm) heterostructures in \beta-tungsten (\beta-W)
phase by employing all-optical time-resolved magneto-optical Kerr effect
technique. From the variation of Gilbert damping with W and CoFeB thicknesses,
the spin diffusion length of W and spin-mixing conductances are extracted.
Subsequently, T is derived as 0.81 \pm 0.03 for the \beta-W/CoFeB interface. A
sharp variation of Geff and T with W thickness is observed in consonance with
the thickness-dependent structural phase transition and resistivity of W. The
spin memory loss and two-magnon scattering effects are found to have negligible
contributions to damping modulation as opposed to spin pumping effect which is
reconfirmed from the invariance of damping with Cu spacer layer thickness
inserted between W and CoFeB. The observation of giant interfacial spin
transparency and its strong dependence on crystal structures of W will be
important for pure spin current based spin-orbitronic devices. | 2009.14143v1 |
2023-12-31 | Molecular Hybridization Induced Antidamping and Sizable Enhanced Spin-to-Charge Conversion in Co20Fe60B20/$β$-W/C60 Heterostructures | Development of power efficient spintronics devices has been the compelling
need in the post-CMOS technology era. The effective tunability of
spin-orbit-coupling (SOC) in bulk and at the interfaces of hybrid materials
stacking is a prerequisite for scaling down the dimension and power consumption
of these devices. In this work, we demonstrate the strong chemisorption of C60
molecules when grown on the high SOC $\beta$-W layer. The parent CFB/$\beta$-W
bilayer exhibits large spin-to-charge interconversion efficiency, which can be
ascribed to the interfacial SOC observed at the Ferromagnet/Heavy metal
interface. Further, the adsorption of C60 molecules on $\beta$-W reduces the
effective Gilbert damping by $\sim$15% in the CFB/$\beta$-W/C60
heterostructures. The anti-damping is accompanied by a gigantic $\sim$115%
enhancement in the spin-pumping induced output voltage owing to the molecular
hybridization. The non-collinear Density Functional Theory calculations confirm
the long-range enhancement of SOC of $\beta$-W upon the chemisorption of C60
molecules, which in turn can also enhance the SOC at the CFB/$\beta$-W
interface in CFB/$\beta$-W/C60 heterostructures. The combined amplification of
bulk as well interfacial SOC upon molecular hybridization stabilizes the
anti-damping and enhanced spin-to-charge conversion, which can pave the way for
the fabrication of power efficient spintronics devices. | 2401.00486v1 |
2011-01-28 | Entanglement between two atoms in a damping Jaynes-Cummings model | The entanglement between two atoms in a damping Jaynes-Cummings model is
investigated with different decay coefficients of the atoms from the upper
level to other levels under detuning between the atomic frequency and the
quantized light field frequency. The results indicate that the larger the decay
coefficient is, the more quickly the entanglement decays. The detuning enhances
the entanglement's average value at long times. More importantly, the results
show that the so-called sudden death effect can be avoided by enhancing the
detuning or the decay coefficient. | 1101.5522v1 |
2015-05-27 | Logarithmic stability in determining a boundary coefficient in an ibvp for the wave equation | In [2] we introduced a method combining together an observability inequality
and a spectral decomposition to get a logarithmic stability estimate for the
inverse problem of determining both the potential and the damping coefficient
in a dissipative wave equation from boundary measurements. The present work
deals with an adaptation of that method to obtain a logarithmic stability
estimate for the inverse problem of determining a boundary damping coefficient
from boundary measurements. As in our preceding work, the different boundary
measurements are generated by varying one of the initial conditions. | 1505.07248v1 |
2021-05-20 | On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity | In this note, we derive a blow-up result for a semilinear generalized Tricomi
equation with damping and mass terms having time-dependent coefficients. We
consider these coefficients with critical decay rates. Due to this threshold
nature of the time-dependent coefficients (both for the damping and for the
mass), the multiplicative constants appearing in these lower-order terms
strongly influence the value of the critical exponent, determining a
competition between a Fujita-type exponent and a Strauss-type exponent. | 2105.09879v2 |
2021-07-11 | Space-time arithmetic quasi-periodic homogenization for damped wave equations | This paper is concerned with space-time homogenization problems for damped
wave equations with spatially periodic oscillating elliptic coefficients and
temporally (arithmetic) quasi-periodic oscillating viscosity coefficients. Main
results consist of a homogenization theorem, qualitative properties of
homogenized matrices which appear in homogenized equations and a corrector
result for gradients of solutions. In particular, homogenized equations and
cell problems will turn out to deeply depend on the quasi-periodicity as well
as the log ratio of spatial and temporal periods of the coefficients. Even
types of equations will change depending on the log ratio and
quasi-periodicity. Proofs of the main results are based on a (very weak)
space-time two-scale convergence theory. | 2107.04966v1 |
2014-08-26 | Stability of an abstract-wave equation with delay and a Kelvin-Voigt damping | In this paper we consider a stabilization problem for the abstract-wave
equation with delay. We prove an exponential stability result for appropriate
damping coefficient. The proof of the main result is based on a
frequency-domain approach. | 1408.6261v2 |
2015-10-14 | The General Solution to Vlasov Equation and Linear Landau Damping | A general solution to linearized Vlasov equation for an electron
electrostatic wave in a homogeneous unmagnetized plasma is derived. The
quasi-linear diffusion coefficient resulting from this solution is a continuous
function of omega in contrast to that derived from the traditional Vlasov
treatment. The general solution is also equivalent to the Landau treatment of
the plasma normal oscillations, and hence leads to the well-known Landau
damping. | 1510.03949v1 |
2017-08-24 | Nonlinear network dynamics for interconnected micro-grids | This paper deals with transient stability in interconnected micro-grids. The
main contribution involves i) robust classification of transient dynamics for
different intervals of the micro-grid parameters (synchronization, inertia, and
damping); ii) exploration of the analogies with consensus dynamics and bounds
on the damping coefficient separating underdamped and overdamped dynamics iii)
the extension to the case of disturbed measurements due to hackering or
parameter uncertainties. | 1708.07296v1 |
2020-09-16 | Exponential decay for semilinear wave equations with viscoelastic damping and delay feedback | In this paper we study a class of semilinear wave type equations with
viscoelastic damping and delay feedback with time variable coefficient. By
combining semigroup arguments, careful energy estimates and an iterative
approach we are able to prove, under suitable assumptions, a well-posedness
result and an exponential decay estimate for solutions corresponding to small
initial data. This extends and concludes the analysis initiated in [16] and
then developed in [13, 17]. | 2009.07777v1 |
2022-12-04 | Inverse problem of recovering the time-dependent damping and nonlinear terms for wave equations | In this paper, we consider the inverse boundary problems of recovering the
time-dependent nonlinearity and damping term for a semilinear wave equation on
a Riemannian manifold. The Carleman estimate and the construction of Gaussian
beams together with the higher order linearization are respectively used to
derive the uniqueness results of recovering the coefficients. | 2212.01815v2 |
2022-10-08 | Recover all Coefficients in Second-Order Hyperbolic Equations from Finite Sets of Boundary Measurements | We consider the inverse hyperbolic problem of recovering all spatial
dependent coefficients, which are the wave speed, the damping coefficient,
potential coefficient and gradient coefficient, in a second-order hyperbolic
equation defined on an open bounded domain with smooth enough boundary. We show
that by appropriately selecting finite pairs of initial conditions we can
uniquely and Lipschitz stably recover all those coefficients from the
corresponding boundary measurements of their solutions. The proofs are based on
sharp Carleman estimate, continuous observability inequality and regularity
theory for general second-order hyperbolic equations. | 2210.03865v1 |
2002-04-25 | Statics and Fast Dynamics of Nanomagnets with Vortex Structure | Within the framework of the Landau-Lifshitz-Gilbert equation, using permalloy
parameters, we study the statics and dynamics of flat circular magnetic
nano-structures with an in-plane magnetic vortex configuration, putting
particular emphasis on the (planar) vorticity of the magnetic state and on the
(perpendicular) polarisation of the vortex center (which may be shifted with
respect to the center of the circle). These binary degrees of freedom can in
principle be used to manipulate two independent bits of information.
Studying switching processes induced by in-plane and out-of plane field
pulses we find that it is possible to switch the vorticity of the magnetic dot
on a time scale of 40 ps in strong enough and short enough perpendicular
external field pulses (B_z^ext \approx 0.5 T, duration \approx 40 ps). But for
realistically small values of the Gilbert damping, only the vorticity can be
switched this fast, and it turns out that it is better to dismiss the center of
the circle totally, concentrating on flat 'nano-rings' with an inner radius R_1
and an outer radius R_2. On these 'nano-rings' the vortex state is more stable,
and with respect to the switching of the vorticity these structures have
similar properties as circular dots. | 0204541v3 |
2007-03-15 | Functional Keldysh Theory of Spin Torques | We present a microscopic treatment of current-induced torques and thermal
fluctuations in itinerant ferromagnets based on a functional formulation of the
Keldysh formalism. We find that the nonequilibrium magnetization dynamics is
governed by a stochastic Landau-Lifschitz-Gilbert equation with spin transfer
torques. We calculate the Gilbert damping parameter $\alpha$ and the
non-adiabatic spin transfer torque parameter $\beta$ for a model ferromagnet.
We find that $\beta \neq \alpha$, in agreement with the results obtained using
imaginary-time methods of Kohno, Tatara and Shibata [J. Phys. Soc. Japan 75,
113706 (2006)]. We comment on the relationship between $s-d$ and
isotropic-Stoner toy models of ferromagnetism and more realistic
density-functional-theory models, and on the implications of these
relationships for predictions of the $\beta/\alpha$ ratio which plays a central
role in domain wall motion. Only for a single-parabolic-band isotropic-Stoner
model with an exchange splitting that is small compared to the Fermi energy
does $\beta/\alpha$ approach one. In addition, our microscopic formalism
incorporates naturally the fluctuations needed in a nonzero-temperature
description of the magnetization. We find that to first order in the applied
electric field, the usual form of thermal fluctuations via a phenomenological
stochastic magnetic field holds. | 0703414v2 |
2010-10-04 | Thermal fluctuation field for current-induced domain wall motion | Current-induced domain wall motion in magnetic nanowires is affected by
thermal fluctuation. In order to account for this effect, the
Landau-Lifshitz-Gilbert equation includes a thermal fluctuation field and
literature often utilizes the fluctuation-dissipation theorem to characterize
statistical properties of the thermal fluctuation field. However, the theorem
is not applicable to the system under finite current since it is not in
equilibrium. To examine the effect of finite current on the thermal
fluctuation, we adopt the influence functional formalism developed by Feynman
and Vernon, which is known to be a useful tool to analyze effects of
dissipation and thermal fluctuation. For this purpose, we construct a quantum
mechanical effective Hamiltonian describing current-induced domain wall motion
by generalizing the Caldeira-Leggett description of quantum dissipation. We
find that even for the current-induced domain wall motion, the statistical
properties of the thermal noise is still described by the
fluctuation-dissipation theorem if the current density is sufficiently lower
than the intrinsic critical current density and thus the domain wall tilting
angle is sufficiently lower than pi/4. The relation between our result and a
recent result, which also addresses the thermal fluctuation, is discussed. We
also find interesting physical meanings of the Gilbert damping alpha and the
nonadiabaticy parameter beta; while alpha characterizes the coupling strength
between the magnetization dynamics (the domain wall motion in this paper) and
the thermal reservoir (or environment), beta characterizes the coupling
strength between the spin current and the thermal reservoir. | 1010.0478v2 |
2015-06-03 | Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach | Motivated by recent experiments observing spin-orbit torque (SOT) acting on
the magnetization $\vec{m}$ of a ferromagnetic (F) overlayer on the surface of
a three-dimensional topological insulator (TI), we investigate the origin of
the SOT and the magnetization dynamics in such systems. We predict that lateral
F/TI bilayers of finite length, sandwiched between two normal metal leads, will
generate a large antidamping-like SOT per very low charge current injected
parallel to the interface. The large values of antidamping-like SOT are {\it
spatially localized} around the transverse edges of the F overlayer. Our
analysis is based on adiabatic expansion (to first order in $\partial
\vec{m}/\partial t$) of time-dependent nonequilibrium Green functions (NEGFs),
describing electrons pushed out of equilibrium both by the applied bias voltage
and by the slow variation of a classical degree of freedom [such as
$\vec{m}(t)$]. From it we extract formulas for spin torque and charge pumping,
which show that they are reciprocal effects to each other, as well as Gilbert
damping in the presence of SO coupling. The NEGF-based formula for SOT
naturally splits into four components, determined by their behavior (even or
odd) under the time and bias voltage reversal. Their complex angular dependence
is delineated and employed within Landau-Lifshitz-Gilbert simulations of
magnetization dynamics in order to demonstrate capability of the predicted SOT
to efficiently switch $\vec{m}$ of a perpendicularly magnetized F overlayer. | 1506.01303v3 |
2015-07-11 | Realization of the thermal equilibrium in inhomogeneous magnetic systems by the Landau-Lifshitz-Gilbert equation with stochastic noise, and its dynamical aspects | It is crucially important to investigate effects of temperature on magnetic
properties such as critical phenomena, nucleation, pinning, domain wall motion,
coercivity, etc. The Landau-Lifshitz-Gilbert (LLG) equation has been applied
extensively to study dynamics of magnetic properties. Approaches of Langevin
noises have been developed to introduce the temperature effect into the LLG
equation. To have the thermal equilibrium state (canonical distribution) as the
steady state, the system parameters must satisfy some condition known as the
fluctuation-dissipation relation. In inhomogeneous magnetic systems in which
spin magnitudes are different at sites, the condition requires that the ratio
between the amplitude of the random noise and the damping parameter depends on
the magnitude of the magnetic moment at each site. Focused on inhomogeneous
magnetic systems, we systematically showed agreement between the stationary
state of the stochastic LLG equation and the corresponding equilibrium state
obtained by Monte Carlo simulations in various magnetic systems including
dipole-dipole interactions. We demonstrated how violations of the condition
result in deviations from the true equilibrium state. We also studied the
characteristic features of the dynamics depending on the choice of the
parameter set. All the parameter sets satisfying the condition realize the same
stationary state (equilibrium state). In contrast, different choices of
parameter set cause seriously different relaxation processes. We show two
relaxation types, i.e., magnetization reversals with uniform rotation and with
nucleation. | 1507.03075v1 |
2017-01-12 | Dynamic coupling of ferromagnets via spin Hall magnetoresistance | The synchronized magnetization dynamics in ferromagnets on a nonmagnetic
heavy metal caused by the spin Hall effect is investigated theoretically. The
direct and inverse spin Hall effects near the ferromagnetic/nonmagnetic
interface generate longitudinal and transverse electric currents. The
phenomenon is known as the spin Hall magnetoresistance effect, whose magnitude
depends on the magnetization direction in the ferromagnet due to the spin
transfer effect. When another ferromagnet is placed onto the same nonmagnet,
these currents are again converted to the spin current by the spin Hall effect
and excite the spin torque to this additional ferromagnet, resulting in the
excitation of the coupled motions of the magnetizations. The in-phase or
antiphase synchronization of the magnetization oscillations, depending on the
value of the Gilbert damping constant and the field-like torque strength, is
found in the transverse geometry by solving the Landau-Lifshitz-Gilbert
equation numerically. On the other hand, in addition to these synchronizations,
the synchronization having a phase difference of a quarter of a period is also
found in the longitudinal geometry. The analytical theory clarifying the
relation among the current, frequency, and phase difference is also developed,
where it is shown that the phase differences observed in the numerical
simulations correspond to that giving the fixed points of the energy supplied
by the coupling torque. | 1701.03201v2 |
2018-10-16 | Superfluid spin transport in ferro- and antiferromagnets | This paper focuses on spin superfluid transport, observation of which was
recently reported in antiferromagnet Cr$_2$O$_3$ [Yuan et al., Sci. Adv. 4,
eaat1098 (2018)]. This paper analyzes the role of dissipation in transformation
of spin current injected with incoherent magnons to a superfluid spin current
near the interface where spin is injected. The Gilbert damping parameter in the
Landau-Lifshitz-Gilbert theory does not describe dissipation properly, and the
dissipation parameters are calculated from the Boltzmann equation for magnons
scattered by defects. The two-fluid theory is developed similar to the
two-fluid theory for superfluids. This theory shows that the influence of
temperature variation in bulk on the superfluid spin transport (bulk Seebeck
effect) is weak at low temperatures. The scenario that the results of Yuan et
al. are connected with the Seebeck effect at the interface between the spin
detector and the sample is also discussed.
The Landau criterion for an antiferromagnet put in a magnetic field is
derived from the spectrum of collective spin modes. The Landau instability
starts in the gapped mode earlier than in the Goldstone gapless mode, in
contrast to easy-plane ferromagnets where the Goldstone mode becomes unstable.
The structure of the magnetic vortex in the geometry of the experiment is
determined. The vortex core has the skyrmion structure with finite
magnetization component normal to the magnetic field. This magnetization
creates stray magnetic fields around the exit point of the vortex line from the
sample, which can be used for experimental detection of vortices. | 1810.07020v4 |
2020-02-20 | Stoner-Wohlfarth switching of the condensate magnetization in a dipolar spinor gas and the metrology of excitation damping | We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in
the homogeneous-local-spin-orientation approximation, that is with
unidirectional local magnetization. By analytically calculating the exact
effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert
equation for the dissipative condensate magnetization dynamics, and show how it
leads to the Stoner-Wohlfarth model of a uni-axial ferro-magnetic particle,
where the latter model determines the stable magnetization patterns and
hysteresis curves for switching between them. For an external magnetic field
pointing along the axial, long direction, we analytically solve the
Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the
magnetic dipole-dipole interaction {\it accelerates} the dissipative dynamics
of the magnetic moment distribution and the associated dephasing of the
magnetic moment direction. Under suitable conditions, dephasing of the
magnetization direction due to dipole-dipole interactions occurs within time
scales up to two orders of magnitude smaller than the lifetime of currently
experimentally realized dipolar spinor condensates, e.g., produced with the
large magnetic-dipole-moment atoms ${}^{166} \textrm{Er}$. This enables
experimental access to the dissipation parameter $\Gamma$ in the
Gross-Pitaevski\v\i~mean-field equation, for a system currently lacking a
complete quantum kinetic treatment of dissipative processes and, in particular,
an experimental check of the commonly used assumption that $\Gamma$ is a single
scalar independent of spin indices. | 2002.08723v2 |
2022-06-20 | First-principles calculation of the parameters used by atomistic magnetic simulations | While the ground state of magnetic materials is in general well described on
the basis of spin density functional theory (SDFT), the theoretical description
of finite-temperature and non-equilibrium properties require an extension
beyond the standard SDFT. Time-dependent SDFT (TD-SDFT), which give for example
access to dynamical properties are computationally very demanding and can
currently be hardly applied to complex solids. Here we focus on the alternative
approach based on the combination of a parameterized phenomenological spin
Hamiltonian and SDFT-based electronic structure calculations, giving access to
the dynamical and finite-temperature properties for example via spin-dynamics
simulations using the Landau-Lifshitz-Gilbert (LLG) equation or Monte Carlo
simulations. We present an overview on the various methods to calculate the
parameters of the various phenomenological Hamiltonians with an emphasis on the
KKR Green function method as one of the most flexible band structure methods
giving access to practically all relevant parameters. Concerning these, it is
crucial to account for the spin-orbit coupling (SOC) by performing relativistic
SDFT-based calculations as it plays a key role for magnetic anisotropy and
chiral exchange interactions represented by the DMI parameters in the spin
Hamiltonian. This concerns also the Gilbert damping parameters characterizing
magnetization dissipation in the LLG equation, chiral multispin interaction
parameters of the extended Heisenberg Hamiltonian, as well as spin-lattice
interaction parameters describing the interplay of spin and lattice dynamics
processes, for which an efficient computational scheme has been developed
recently by the present authors. | 2206.09969v1 |
2023-09-25 | Ultrafast Demagnetization through Femtosecond Generation of Non-thermal Magnons | Ultrafast laser excitation of ferromagnetic metals gives rise to correlated,
highly non-equilibrium dynamics of electrons, spins and lattice, which are,
however, poorly described by the widely-used three-temperature model (3TM).
Here, we develop a fully ab-initio parameterized out-of-equilibrium theory
based on a quantum kinetic approach--termed (N+2) temperature model--that
describes magnon occupation dynamics due to electron-magnon scattering. We
apply this model to perform quantitative simulations on the ultrafast,
laser-induced generation of magnons in iron and demonstrate that on these
timescales the magnon distribution is non-thermal: predominantly high-energy
magnons are created, while the magnon occupation close to the center of the
Brillouin zone even decreases, due to a repopulation towards higher energy
states via a so-far-overlooked scattering term. We demonstrate that the simple
relation between magnetization and temperature computed at equilibrium does not
hold in the ultrafast regime and that the 3TM greatly overestimates the
demagnetization. The ensuing Gilbert damping becomes strongly magnon wavevector
dependent and requires a description beyond the conventional
Landau-Lifshitz-Gilbert spin dynamics. Our ab-initio-parameterized calculations
show that ultrafast generation of non-thermal magnons provides a sizable
demagnetization within 200fs in excellent comparison with experimentally
observed laser-induced demagnetizations. Our investigation emphasizes the
importance of non-thermal magnon excitations for the ultrafast demagnetization
process. | 2309.14167v3 |
2023-12-12 | Sliding Dynamics of Current-Driven Skyrmion Crystal and Helix in Chiral Magnets | The skyrmion crystal (SkX) and helix (HL) phases, present in typical chiral
magnets, can each be considered as forms of density waves but with distinct
topologies. The SkX exhibits gyrodynamics analogous to electrons under a
magnetic field, while the HL state resembles topological trivial spin density
waves. However, unlike the charge density waves, the theoretical analysis of
the sliding motion of SkX and HL remains unclear, especially regarding the
similarities and differences in sliding dynamics between these two spin density
waves. In this work, we systematically explore the sliding dynamics of SkX and
HL in chiral magnets in the limit of large current density. We demonstrate that
the sliding dynamics of both SkX and HL can be unified within the same
theoretical framework as density waves, despite their distinct microscopic
orders. Furthermore, we highlight the significant role of gyrotropic sliding
induced by impurity effects in the SkX state, underscoring the impact of
nontrivial topology on the sliding motion of density waves. Our theoretical
analysis shows that the effect of impurity pinning is much stronger in HL
compared with SkX, i.e., $\chi^{SkX}/\chi^{HL}\sim \alpha^2$ ($\chi^{SkX}$,
$\chi^{HL}$: susceptibility to the impurity potential, $\alpha$ ($\ll 1$) is
the Gilbert damping). Moreover, the velocity correction is mostly in the
transverse direction to the current in SkX. These results are further
substantiated by realistic Landau-Lifshitz-Gilbert simulations. | 2312.07116v2 |
2007-01-08 | Coefficient of restitution for viscoelastic disks | The dissipative collision of two identical viscoelastic disks is studied. By
using a known law for the elastic part of the interaction force and the
viscoelastic damping model an analytical solution for the coefficient of
restitution shall be given. The coefficient of restitution depends
significantly on the impact velocity. It approaches one for small velocities
and decreases for increasing velocities. | 0701142v1 |
2008-02-29 | Heat conduction and Fourier's law in a class of many particle dispersing billiards | We consider the motion of many confined billiard balls in interaction and
discuss their transport and chaotic properties. In spite of the absence of mass
transport, due to confinement, energy transport can take place through binary
collisions between neighbouring particles. We explore the conditions under
which relaxation to local equilibrium occurs on time scales much shorter than
that of binary collisions, which characterize the transport of energy, and
subsequent relaxation to local thermal equilibrium. Starting from the
pseudo-Liouville equation for the time evolution of phase-space distributions,
we derive a master equation which governs the energy exchange between the
system constituents. We thus obtain analytical results relating the transport
coefficient of thermal conductivity to the frequency of collision events and
compute these quantities. We also provide estimates of the Lyapunov exponents
and Kolmogorov-Sinai entropy under the assumption of scale separation. The
validity of our results is confirmed by extensive numerical studies. | 0802.4455v3 |
2014-07-01 | Transport properties of Lévy walks: an analysis in terms of multistate processes | Continuous time random walks combining diffusive and ballistic regimes are
introduced to describe a class of L\'evy walks on lattices. By including
exponentially-distributed waiting times separating the successive jump events
of a walker, we are led to a description of such L\'evy walks in terms of
multistate processes whose time-evolution is shown to obey a set of coupled
delay differential equations. Using simple arguments, we obtain asymptotic
solutions to these equations and rederive the scaling laws for the mean squared
displacement of such processes. Our calculation includes the computation of all
relevant transport coefficients in terms of the parameters of the models. | 1407.0227v2 |
2015-01-21 | Lévy walks on lattices as multi-state processes | Continuous-time random walks combining diffusive scattering and ballistic
propagation on lattices model a class of L\'evy walks. The assumption that
transitions in the scattering phase occur with exponentially-distributed
waiting times leads to a description of the process in terms of multiple
states, whose distributions evolve according to a set of delay differential
equations, amenable to analytic treatment. We obtain an exact expression of the
mean squared displacement associated with such processes and discuss the
emergence of asymptotic scaling laws in regimes of diffusive and superdiffusive
(subballistic) transport, emphasizing, in the latter case, the effect of
initial conditions on the transport coefficients. Of particular interest is the
case of rare ballistic propagation, in which case a regime of superdiffusion
may lurk underneath one of normal diffusion. | 1501.05216v1 |
2015-01-31 | Bases and Structure Constants of Generalized Splines with Integer Coefficients on Cycles | An integer generalized spline is a set of vertex labels on an edge-labeled
graph that satisfy the condition that if two vertices are joined by an edge,
the vertex labels are congruent modulo the edge label. Foundational work on
these objects comes from Gilbert, Polster, and Tymoczko, who generalize ideas
from geometry/topology (equivariant cohomology rings) and algebra (algebraic
splines) to develop the notion of generalized splines. Gilbert, Polster, and
Tymoczko prove that the ring of splines on a graph can be decomposed in terms
of splines on its subgraphs (in particular, on trees and cycles), and then
fully analyze splines on trees. Following Handschy-Melnick-Reinders and Rose,
we analyze splines on cycles, in our case integer generalized splines. The
primary goal of this paper is to establish two new bases for the module of
integer generalized splines on cycles: the triangulation basis and the King
basis. Unlike bases in previous work, we are able to characterize each basis
element completely in terms of the edge labels of the underlying cycle. As an
application we explicitly construct the multiplication table for the ring of
integer generalized splines in terms of the King basis. | 1502.00176v1 |
2019-05-31 | Characterizing the mod-$\ell$ local Langlands correspondence by nilpotent gamma factors | Let $F$ be a $p$-adic field and choose $k$ an algebraic closure of
$\mathbb{F}_{\ell}$, with $\ell$ different from $p$. We define ``nilpotent
lifts'' of irreducible generic $k$-representations of $GL_n(F)$, which take
coefficients in Artin local $k$-algebras. We show that an irreducible generic
$\ell$-modular representation $\pi$ of $GL_n(F)$ is uniquely determined by its
collection of Rankin--Selberg gamma factors $\gamma(\pi\times
\widetilde{\tau},X,\psi)$ as $\widetilde{\tau}$ varies over nilpotent lifts of
irreducible generic $k$-representations $\tau$ of $GL_t(F)$ for $t=1,\dots,
\lfloor \frac{n}{2}\rfloor$. This gives a characterization of the mod-$\ell$
local Langlands correspondence in terms of gamma factors, assuming it can be
extended to a surjective local Langlands correspondence on nilpotent lifts. | 1905.13487v2 |
2020-01-31 | An efficient automated data analytics approach to large scale computational comparative linguistics | This research project aimed to overcome the challenge of analysing human
language relationships, facilitate the grouping of languages and formation of
genealogical relationship between them by developing automated comparison
techniques. Techniques were based on the phonetic representation of certain key
words and concept. Example word sets included numbers 1-10 (curated), large
database of numbers 1-10 and sheep counting numbers 1-10 (other sources),
colours (curated), basic words (curated).
To enable comparison within the sets the measure of Edit distance was
calculated based on Levenshtein distance metric. This metric between two
strings is the minimum number of single-character edits, operations including:
insertions, deletions or substitutions. To explore which words exhibit more or
less variation, which words are more preserved and examine how languages could
be grouped based on linguistic distances within sets, several data analytics
techniques were involved. Those included density evaluation, hierarchical
clustering, silhouette, mean, standard deviation and Bhattacharya coefficient
calculations. These techniques lead to the development of a workflow which was
later implemented by combining Unix shell scripts, a developed R package and
SWI Prolog. This proved to be computationally efficient and permitted the fast
exploration of large language sets and their analysis. | 2001.11899v1 |
2022-06-22 | Homogenization of the Landau-Lifshitz-Gilbert equation with natural boundary condition | The full Landau-Lifshitz-Gilbert equation with periodic material coefficients
and natural boundary condition is employed to model the magnetization dynamics
in composite ferromagnets. In this work, we establish the convergence between
the homogenized solution and the original solution via a Lax equivalence
theorem kind of argument. There are a few technical difficulties, including: 1)
it is proven the classic choice of corrector to homogenization cannot provide
the convergence result in the $H^1$ norm; 2) a boundary layer is induced due to
the natural boundary condition; 3) the presence of stray field give rise to a
multiscale potential problem. To keep the convergence rates near the boundary,
we introduce the Neumann corrector with a high-order modification. Estimates on
singular integral for disturbed functions and boundary layer are deduced, to
conduct consistency analysis of stray field. Furthermore, inspired by length
conservation of magnetization, we choose proper correctors in specific
geometric space. These, together with a uniform $W^{1,6}$ estimate on original
solution, provide the convergence rates in the $H^1$ sense. | 2206.10948v1 |
2023-10-13 | Unified framework of the microscopic Landau-Lifshitz-Gilbert equation and its application to Skyrmion dynamics | The Landau-Lifshitz-Gilbert (LLG) equation is widely used to describe
magnetization dynamics. We develop a unified framework of the microscopic LLG
equation based on the nonequilibrium Green's function formalism. We present a
unified treatment for expressing the microscopic LLG equation in several
limiting cases, including the adiabatic, inertial, and nonadiabatic limits with
respect to the precession frequency for a magnetization with fixed magnitude,
as well as the spatial adiabatic limit for the magnetization with slow
variation in both its magnitude and direction. The coefficients of those terms
in the microscopic LLG equation are explicitly expressed in terms of
nonequilibrium Green's functions. As a concrete example, this microscopic
theory is applied to simulate the dynamics of a magnetic Skyrmion driven by
quantum parametric pumping. Our work provides a practical formalism of the
microscopic LLG equation for exploring magnetization dynamics. | 2310.08807v1 |
2004-04-19 | Nonlinear response of superparamagnets with finite damping: an analytical approach | The strongly damping-dependent nonlinear dynamical response of classical
superparamagnets is investigated by means of an analytical approach. Using
rigorous balance equations for the spin occupation numbers a simple approximate
expression is derived for the nonlinear susceptibility. The results are in good
agreement with those obtained from the exact (continued-fraction) solution of
the Fokker-Planck equation. The formula obtained could be of assistance in the
modelling of the experimental data and the determination of the damping
coefficient in superparamagnets. | 0404445v1 |
2005-05-10 | Highly Damped Quasinormal Modes of Generic Single Horizon Black Holes | We calculate analytically the highly damped quasinormal mode spectra of
generic single-horizon black holes using the rigorous WKB techniques of
Andersson and Howls\cite{Andersson}. We thereby provide a firm foundation for
previous analysis, and point out some of their possible limitations. The
numerical coefficient in the real part of the highly damped frequency is
generically determined by the behavior of coupling of the perturbation to the
gravitational field near the origin, as expressed in tortoise coordinates. This
fact makes it difficult to understand how the famous $ln(3)$ could be related
to the quantum gravitational microstates near the horizon. | 0505044v1 |
2003-09-15 | Eigenfrequencies and expansions for damped wave equations | We study eigenfrequencies and propagator expansions for damped wave equations
on compact manifolds. Under the assumption of geometric control, the propagator
is shown to admit an expansion in terms of finitely many eigenmodes near the
real axis, with an error term exponentially decaying in time. In the presence
of a nondegenerate elliptic closed geodesic not meeting the support of the
damping coefficient, we show that there exists a sequence of eigenfrequencies
converging rapidly to the real axis. In the case of Zoll manifolds, we show
that the propagator can be expanded in terms of clusters of the
eigenfrequencies in the entire spectral band. | 0309250v1 |
2010-03-08 | A single-ion nonlinear mechanical oscillator | We study the steady state motion of a single trapped ion oscillator driven to
the nonlinear regime. Damping is achieved via Doppler laser-cooling. The ion
motion is found to be well described by the Duffing oscillator model with an
additional nonlinear damping term. We demonstrate a unique ability of tuning
both the linear as well as the nonlinear damping coefficients by controlling
the cooling laser parameters. Our observations open a way for the investigation
of nonlinear dynamics on the quantum-to-classical interface as well as
mechanical noise squeezing in laser-cooling dynamics. | 1003.1577v1 |
2012-02-24 | Small data global existence for the semilinear wave equation with space-time dependent damping | In this paper we consider the critical exponent problem for the semilinear
wave equation with space-time dependent damping. When the damping is effective,
it is expected that the critical exponent agrees with that of only space
dependent coefficient case. We shall prove that there exists a unique global
solution for small data if the power of nonlinearity is larger than the
expected exponent. Moreover, we do not assume that the data are compactly
supported. However, it is still open whether there exists a blow-up solution if
the power of nonlinearity is smaller than the expected exponent. | 1202.5379v1 |
2012-03-21 | Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves | We consider the effect of the wind and the dissipation on the nonlinear
stages of the modulational instability. By applying a suitable transformation,
we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the
standard NLS with constant coefficients. The transformation is valid as long as
|{\Gamma}t| \ll 1, with {\Gamma} the growth/damping rate of the waves due to
the wind/dissipation. Approximate rogue wave solutions of the equation are
presented and discussed. The results shed some lights on the effects of wind
and dissipation on the formation of rogue waves. | 1203.4735v1 |
2013-11-16 | Shear viscosity due to the Landau damping from quark-pion interaction | We have calculated the shear viscosity coefficient $\eta$ of the strongly
interacting matter in the relaxation time approximation, where a quasi particle
description of quarks with its dynamical mass is considered from NJL model. Due
to the thermodynamic scattering of quarks with pseudo scalar type condensate
(i.e. pion), a non zero Landau damping will be acquired by the propagating
quarks. This Landau damping may be obtained from the Landau cut contribution of
the in-medium self-energy of quark-pion loop, which is evaluated in the
framework of real-time thermal field theory. | 1311.4070v1 |
2014-03-24 | Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations | In this paper we make a subtle use of operator theory techniques and the
well-known Schauder fixed-point principle to establish the existence of
pseudo-almost automorphic solutions to some second-order damped
integro-differential equations with pseudo-almost automorphic coefficients. In
order to illustrate our main results, we will study the existence of
pseudo-almost automorphic solutions to a structurally damped plate-like
boundary value problem. | 1403.5955v1 |
2014-08-09 | Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions | We investigate the Westervelt equation with several versions of nonlinear
damping and lower order damping terms and Neumann as well as absorbing boundary
conditions. We prove local in time existence of weak solutions under the
assumption that the initial and boundary data are sufficiently small.
Additionally, we prove local well-posedness in the case of spatially varying
$L^{\infty}$ coefficients, a model relevant in high intensity focused
ultrasound (HIFU) applications. | 1408.2160v1 |
2015-03-03 | Large Deviations for the Langevin equation with strong damping | We study large deviations in the Langevin dynamics, with damping of order
$\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient
is assumed to be state dependent. We proceed first with a change of time and
then, we use a weak convergence approach to large deviations and their
equivalent formulation in terms of the Laplace principle, to determine the good
action functional.
Some applications of these results to the exit problem from a domain and to
the wave front propagation for a suitable class of reaction diffusion equations
are considered. | 1503.01027v1 |
2017-06-15 | Fractional Driven Damped Oscillator | The resonances associated with a fractional damped oscillator which is driven
by an oscillatory external force are studied. It is shown that such resonances
can be manipulated by tuning up either the coefficient of the fractional
damping or the order of the corresponding fractional derivatives. | 1706.08596v1 |
2017-09-13 | Life-span of blowup solutions to semilinear wave equation with space-dependent critical damping | This paper is concerned with the blowup phenomena for initial value problem
of semilinear wave equation with critical space-dependent damping term
(DW:$V$). The main result of the present paper is to give a solution of the
problem and to provide a sharp estimate for lifespan for such a solution when
$\frac{N}{N-1}<p\leq p_S(N+V_0)$, where $p_S(N)$ is the Strauss exponent for
(DW:$0$). The main idea of the proof is due to the technique of test functions
for (DW:$0$) originated by Zhou--Han (2014, MR3169791). Moreover, we find a new
threshold value $V_0=\frac{(N-1)^2}{N+1}$ for the coefficient of critical and
singular damping $|x|^{-1}$. | 1709.04401v1 |
2018-06-08 | Brownian motion of magnetic domain walls and skyrmions, and their diffusion constants | Extended numerical simulations enable to ascertain the diffusive behavior at
finite temperatures of chiral walls and skyrmions in ultra-thin model Co layers
exhibiting symmetric - Heisenberg - as well as antisymmetric -
Dzyaloshinskii-Moriya - exchange interactions. The Brownian motion of walls and
skyrmions is shown to obey markedly different diffusion laws as a function of
the damping parameter. Topology related skyrmion diffusion suppression with
vanishing damping parameter, albeit already documented, is shown to be
restricted to ultra-small skyrmion sizes or, equivalently, to ultra-low damping
coefficients, possibly hampering observation. | 1806.03172v1 |
2020-02-09 | Fujita modified exponent for scale invariant damped semilinear wave equations | The aim of this paper is to prove a blow up result of the solution for a
semilinear scale invariant damped wave equation under a suitable decay
condition on radial initial data. The admissible range for the power of the
nonlinear term depends both on the damping coefficient and on the pointwise
decay order of the initial data. In addition we give an upper bound estimate
for the lifespan of the solution, in terms of the power of the nonlinearity,
size and growth of initial data. | 2002.03418v2 |
2020-05-24 | A transmission problem for the Timoshenko system with one local Kelvin-Voigt damping and non-smooth coefficient at the interface | In this paper, we study the indirect stability of Timoshenko system with
local or global Kelvin-Voigt damping, under fully Dirichlet or mixed boundary
conditions. Unlike the results of H. L. Zhao, K. S. Liu, and C. G. Zhang and of
X. Tian and Q. Zhang, in this paper, we consider the Timoshenko system with
only one locally or globally distributed Kelvin-Voigt damping. Indeed, we prove
that the energy of the system decays polynomially and that the obtained decay
rate is in some sense optimal. The method is based on the frequency domain
approach combining with multiplier method. | 2005.12756v1 |
2020-08-11 | An inverse spectral problem for a damped wave operator | This paper proposes a new and efficient numerical algorithm for recovering
the damping coefficient from the spectrum of a damped wave operator, which is a
classical Borg-Levinson inverse spectral problem. The algorithm is based on
inverting a sequence of trace formulas, which are deduced by a recursive
formula, bridging geometrical and spectrum information explicitly in terms of
Fredholm integral equations. Numerical examples are presented to illustrate the
efficiency of the proposed algorithm. | 2008.04523v1 |
2020-08-18 | A class of Finite difference Methods for solving inhomogeneous damped wave equations | In this paper, a class of finite difference numerical techniques is presented
to solve the second-order linear inhomogeneous damped wave equation. The
consistency, stability, and convergences of these numerical schemes are
discussed. The results obtained are compared to the exact solution, ordinary
explicit, implicit finite difference methods, and the fourth-order compact
method (FOCM). The general idea of these methods is developed by using the
C0-semigroups operator theory. We also showed that the stability region for the
explicit finite difference scheme depends on the damping coefficient. | 2008.08043v2 |
2020-09-10 | Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime | We prove by using an iteration argument some blow-up results for a semilinear
damped wave equation in generalized Einstein-de Sitter spacetime with a
time-dependent coefficient for the damping term and power nonlinearity. Then,
we conjecture an expression for the critical exponent due to the main blow-up
results, which is consistent with many special cases of the considered model
and provides a natural generalization of Strauss exponent. In the critical
case, we consider a non-autonomous and parameter-dependent Cauchy problem for a
linear ODE of second-order, whose explicit solutions are determined by means of
special functions' theory. | 2009.05372v1 |
2021-06-16 | Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations | The dependence of the fractal dimension of global attractors for the damped
3D Euler--Bardina equations on the regularization parameter $\alpha>0$ and
Ekman damping coefficient $\gamma>0$ is studied. We present explicit upper
bounds for this dimension for the case of the whole space, periodic boundary
conditions, and the case of bounded domain with Dirichlet boundary conditions.
The sharpness of these estimates when $\alpha\to0$ and $\gamma\to0$ (which
corresponds in the limit to the classical Euler equations) is demonstrated on
the 3D Kolmogorov flows on a torus. | 2106.09077v1 |
2022-03-12 | Stability for nonlinear wave motions damped by time-dependent frictions | We are concerned with the dynamical behavior of solutions to semilinear wave
systems with time-varying damping and nonconvex force potential. Our result
shows that the dynamical behavior of solution is asymptotically stable without
any bifurcation and chaos. And it is a sharp condition on the damping
coefficient for the solution to converge to some equilibrium. To illustrate our
theoretical results, we provide some numerical simulations for dissipative
sine-Gordon equation and dissipative Klein-Gordon equation. | 2203.06312v1 |
2022-06-07 | Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data | We study the large time behavior of solutions to the semilinear wave equation
with space-dependent damping and absorbing nonlinearity in the whole space or
exterior domains. Our result shows how the amplitude of the damping
coefficient, the power of the nonlinearity, and the decay rate of the initial
data at the spatial infinity determine the decay rates of the energy and the
$L^2$-norm of the solution. In Appendix, we also give a survey of basic results
on the local and global existence of solutions and the properties of weight
functions used in the energy method. | 2206.03218v2 |
2022-12-18 | Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions | We establish the decay of the solutions of the damped wave equations in one
dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions
where the damping coefficient is a function of space and time. The analysis is
based on the study of the corresponding hyperbolic systems associated with the
Riemann invariants. The key ingredient in the study of these systems is the use
of the internal dissipation energy to estimate the difference of solutions with
their mean values in an average sense. | 2212.09164v1 |
2023-05-03 | Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions | We establish the exponential decay of the solutions of the damped wave
equations in one-dimensional space where the damping coefficient is a
nowhere-vanishing function of space. The considered PDE is associated with
several dynamic boundary conditions, also referred to as Wentzell/Ventzel
boundary conditions in the literature. The analysis is based on the
determination of appropriate Lyapunov functions and some further analysis. This
result is associated with a regulation problem inspired by a real experiment
with a proportional-integral control. Some numerical simulations and additional
results on closed wave equations are also provided. | 2305.01969v2 |
2023-07-12 | Asymptotic behavior of solutions to the Cauchy problem for 1-D p-system with space dependent damping | We consider the Cauchy problem for one-dimensional p-system with damping of
space-dependent coefficient. This system models the compressible flow through
porous media in the Lagrangean coordinate. Our concern is an asymptotic
behavior of solutions, which is expected to be the diffusion wave based on the
Darcy law. To show this expectation, the problem is reformulated to the Cauchy
problem for the second order quasilinear hyperbolic equation with space
dependent damping, which is analyzed by the energy method. | 2307.05865v1 |
2023-07-12 | Parabolic-elliptic Keller-Segel's system | We study on the whole space R d the compressible Euler system with damping
coupled to the Poisson equation when the damping coefficient tends towards
infinity. We first prove a result of global existence for the Euler-Poisson
system in the case where the damping is large enough, then, in a second step,
we rigorously justify the passage to the limit to the parabolic-elliptic
Keller-Segel after performing a diffusive rescaling, and get an explicit
convergence rate. The overall study is carried out in 'critical' Besov spaces,
in the spirit of the recent survey [16] by R. Danchin devoted to partially
dissipative systems. | 2307.05981v1 |
2021-07-29 | Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects | Sound attenuation in low temperature amorphous solids originates from their
disordered structure. However, its detailed mechanism is still being debated.
Here we analyze sound attenuation starting directly from the microscopic
equations of motion. We derive an exact expression for the zero-temperature
sound damping coefficient. We verify that the sound damping coefficients
calculated from our expression agree very well with results from independent
simulations of sound attenuation. The small wavevector analysis of our
expression shows that sound attenuation is primarily determined by the
non-affine displacements' contribution to the sound wave propagation
coefficient coming from the frequency shell of the sound wave. Our expression
involves only quantities that pertain to solids' static configurations. It can
be used to evaluate the low temperature sound damping coefficients without
directly simulating sound attenuation. | 2107.14254v2 |
2023-10-29 | Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity | In this article we investigate the asymptotic profile of solutions for the
Cauchy problem of the nonlinear damped beam equation with two variable
coefficients: \[ \partial_t^2 u + b(t) \partial_t u - a(t) \partial_x^2 u +
\partial_x^4 u
= \partial_x \left( N(\partial_x u) \right). \] In the authors' previous
article [17], the asymptotic profile of solutions for linearized problem ($N
\equiv 0$) was classified depending on the assumptions for the coefficients
$a(t)$ and $b(t)$ and proved the asymptotic behavior in effective damping
cases. We here give the conditions of the coefficients and the nonlinear term
in order that the solution behaves as the solution for the heat equation: $b(t)
\partial_t u - a(t) \partial_x^2 u=0$ asymptotically as $t \to \infty$. | 2310.18878v1 |
2023-08-14 | Temperature Evolution of Magnon Propagation Length in Tm$_3$Fe$_5$O$_{12}$ Thin Films: Roles of Magnetic Anisotropy and Gilbert Damping | The magnon propagation length ($\langle\xi\rangle$) of a ferro/ferrimagnet
(FM) is one of the key factors that controls the generation and propagation of
thermally-driven spin current in FM/heavy metal (HM) bilayer based
spincaloritronic devices. Theory predicts that for the FM layer,
$\langle\xi\rangle$ is inversely proportional to the Gilbert damping ($\alpha$)
and the square root of the effective magnetic anisotropy constant ($K_{\rm
eff}$). However, direct experimental evidence of this relationship is lacking.
To experimentally confirm this prediction, we employ a combination of
longitudinal spin Seebeck effect (LSSE), transverse susceptibility, and
ferromagnetic resonance experiments to investigate the temperature evolution of
$\langle\xi\rangle$ and establish its correlation with the effective magnetic
anisotropy field, $H_K^{\rm eff}$ ($\propto K_{\rm eff}$) and $\alpha$ in
Tm$_3$Fe$_5$O$_{12}$ (TmIG)/Pt bilayers. We observe concurrent drops in the
LSSE voltage and $\langle\xi\rangle$ below 200$^\circ$K in TmIG/Pt bilayers
regardless of TmIG film thickness and substrate choice and attribute it to the
noticeable increases in $H_K^{\rm eff}$ and $\alpha$ that occur within the same
temperature range. From the TmIG thickness dependence of the LSSE voltage, we
determined the temperature dependence of $\langle\xi\rangle$ and highlighted
its correlation with the temperature-dependent $H_K^{\rm eff}$ and $\alpha$ in
TmIG/Pt bilayers, which will be beneficial for the development of rare-earth
iron garnet-based efficient spincaloritronic nanodevices. | 2308.07236v3 |
2015-06-23 | The remarkable effectiveness of time-dependent damping terms for second order evolution equations | We consider a second order linear evolution equation with a dissipative term
multiplied by a time-dependent coefficient. Our aim is to design the
coefficient in such a way that all solutions decay in time as fast as possible.
We discover that constant coefficients do not achieve the goal, as well as
time-dependent coefficients that are too big. On the contrary, pulsating
coefficients which alternate big and small values in a suitable way prove to be
more effective.
Our theory applies to ordinary differential equations, systems of ordinary
differential equations, and partial differential equations of hyperbolic type. | 1506.06915v1 |
2018-04-20 | A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings | In this paper we address the stability of resonantly forced density waves in
dense planetary rings.
Already by Goldreich & Tremaine (1978) it has been argued that density waves
might be unstable, depending on the relationship between the ring's viscosity
and the surface mass density.
In the recent paper Schmidt et al. (2016) we have pointed out that when -
within a fluid description of the ring dynamics - the criterion for viscous
overstability is satisfied, forced spiral density waves become unstable as
well.
In this case, linear theory fails to describe the damping, but nonlinearity
of the underlying equations guarantees a finite amplitude and eventually a
damping of the wave.
We apply the multiple scale formalism to derive a weakly nonlinear damping
relation from a hydrodynamical model.
This relation describes the resonant excitation and nonlinear viscous damping
of spiral density waves in a vertically integrated fluid disk with density
dependent transport coefficients.
The model consistently predicts density waves to be (linearly) unstable in a
ring region where the conditions for viscous overstability are met.
Sufficiently far away from the Lindblad resonance, the surface mass density
perturbation is predicted to saturate to a constant value due to nonlinear
viscous damping.
The wave's damping lengths of the model depend on certain input parameters,
such as the distance to the threshold for viscous overstability in parameter
space and the ground state surface mass density. | 1804.07674v1 |
2006-02-17 | Damped quantum harmonic oscillator | In the framework of the Lindblad theory for open quantum systems the damping
of the harmonic oscillator is studied. A generalization of the fundamental
constraints on quantum mechanical diffusion coefficients which appear in the
master equation for the damped quantum oscillator is presented; the
Schr\"odinger and Heisenberg representations of the Lindblad equation are given
explicitly. On the basis of these representations it is shown that various
master equations for the damped quantum oscillator used in the literature are
particular cases of the Lindblad equation and that the majority of these
equations are not satisfying the constraints on quantum mechanical diffusion
coefficients. Analytical expressions for the first two moments of coordinate
and momentum are also obtained by using the characteristic function of the
Lindblad master equation. The master equation is transformed into Fokker-Planck
equations for quasiprobability distributions. A comparative study is made for
the Glauber $P$ representation, the antinormal ordering $Q$ representation and
the Wigner $W$ representation. It is proven that the variances for the damped
harmonic oscillator found with these representations are the same. By solving
the Fokker-Planck equations in the steady state, it is shown that the
quasiprobability distributions are two-dimensional Gaussians with widths
determined by the diffusion coefficients. The density matrix is represented via
a generating function, which is obtained by solving a time-dependent linear
partial differential equation derived from the master equation. Illustrative
examples for specific initial conditions of the density matrix are provided. | 0602149v1 |
2006-05-25 | Time Quantified Monte Carlo Algorithm for Interacting Spin Array Micromagnetic Dynamics | In this paper, we reexamine the validity of using time quantified Monte Carlo
(TQMC) method [Phys. Rev. Lett. 84, 163 (2000); Phys. Rev. Lett. 96, 067208
(2006)] in simulating the stochastic dynamics of interacting magnetic
nanoparticles. The Fokker-Planck coefficients corresponding to both TQMC and
Langevin dynamical equation (Landau-Lifshitz-Gilbert, LLG) are derived and
compared in the presence of interparticle interactions. The time quantification
factor is obtained and justified. Numerical verification is shown by using TQMC
and Langevin methods in analyzing spin-wave dispersion in a linear array of
magnetic nanoparticles. | 0605621v1 |
2000-07-10 | Fractal Dimensions of the Hydrodynamic Modes of Diffusion | We consider the time-dependent statistical distributions of diffusive
processes in relaxation to a stationary state for simple, two dimensional
chaotic models based upon random walks on a line. We show that the cumulative
functions of the hydrodynamic modes of diffusion form fractal curves in the
complex plane, with a Hausdorff dimension larger than one. In the limit of
vanishing wavenumber, we derive a simple expression of the diffusion
coefficient in terms of this Hausdorff dimension and the positive Lyapunov
exponent of the chaotic model. | 0007008v1 |
2000-10-06 | The Fractality of the Hydrodynamic Modes of Diffusion | Transport by normal diffusion can be decomposed into the so-called
hydrodynamic modes which relax exponentially toward the equilibrium state. In
chaotic systems with two degrees of freedom, the fine scale structure of these
hydrodynamic modes is singular and fractal. We characterize them by their
Hausdorff dimension which is given in terms of Ruelle's topological pressure.
For long-wavelength modes, we derive a striking relation between the Hausdorff
dimension, the diffusion coefficient, and the positive Lyapunov exponent of the
system. This relation is tested numerically on two chaotic systems exhibiting
diffusion, both periodic Lorentz gases, one with hard repulsive forces, the
other with attractive, Yukawa forces. The agreement of the data with the theory
is excellent. | 0010017v1 |
1998-05-29 | Atom cooling and trapping by disorder | We demonstrate the possibility of three-dimensional cooling of neutral atoms
by illuminating them with two counterpropagating laser beams of mutually
orthogonal linear polarization, where one of the lasers is a speckle field,
i.e. a highly disordered but stationary coherent light field. This
configuration gives rise to atom cooling in the transverse plane via a Sisyphus
cooling mechanism similar to the one known in standard two-dimensional optical
lattices formed by several plane laser waves. However, striking differences
occur in the spatial diffusion coefficients as well as in local properties of
the trapped atoms. | 9805037v1 |
2014-08-11 | An optimal irrigation network with infinitely many branching points | The Gilbert-Steiner problem is a mass transportation problem, where the cost
of the transportation depends on the network used to move the mass and it is
proportional to a certain power of the "flow". In this paper, we introduce a
new formulation of the problem, which turns it into the minimization of a
convex functional in a class of currents with coefficients in a group. This
framework allows us to define calibrations, which can be used to prove the
optimality of concrete configurations. We apply this technique to prove the
optimality of a certain irrigation network, having the topological property
mentioned in the title. | 1408.2406v1 |
2023-03-15 | Algebraic Geometry codes in the sum-rank metric | We introduce the first geometric construction of codes in the sum-rank
metric, which we called linearized Algebraic Geometry codes, using quotients of
the ring of Ore polynomials with coefficients in the function field of an
algebraic curve. We study the parameters of these codes and give lower bounds
for their dimension and minimum distance. Our codes exhibit quite good
parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry
codes in the Hamming metric. Furthermore, our construction yields codes
asymptotically better than the sum-rank version of the Gilbert-Varshamov bound. | 2303.08903v2 |
2023-05-31 | Codes from Goppa codes | On a Goppa code whose structure polynomial has coefficients in the symbol
field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the
naturally occurred redundance, we obtain a new code. It is proved that these
new codes approach the Gilbert-Varshamov bound. It is also proved that these
codes can be decoded within $O(n^2(\logn)^a)$ operations in the symbol field,
which is usually much small than the location field, where $n$ is the codeword
length, and $a$ a constant determined by the polynomial factorization
algorithm. | 2305.19565v5 |
2023-07-21 | Thermomechanics of ferri-antiferromagnetic phase transition in finitely-strained rocks towards paleomagnetism | The thermodynamic model of visco-elastic deformable magnetic materials at
finite strains is formulated in a fully Eulerian way in rates with the aim to
describe thermoremanent paleomagnetism in crustal rocks. The Landau theory
applied to a ferro-to-para-magnetic phase transition, the gradient theory for
magnetization (leading to exchange energy) with general mechanically dependent
coefficient, hysteresis in magnetization evolution by Gilbert equation
involving objective corotational time derivative of magnetization, and
demagnetizing field are considered in the model. The Jeffreys viscoelastic
rheology is used with temperature-dependent creep to model solidification or
melting transition. The model complies with energy conservation and the
Clausius-Duhem entropy inequality. | 2307.11826v2 |
2011-06-23 | Ratchet effect on a relativistic particle driven by external forces | We study the ratchet effect of a damped relativistic particle driven by both
asymmetric temporal bi-harmonic and time-periodic piecewise constant forces.
This system can be formally solved for any external force, providing the
ratchet velocity as a non-linear functional of the driving force. This allows
us to explicitly illustrate the functional Taylor expansion formalism recently
proposed for this kind of systems. The Taylor expansion reveals particularly
useful to obtain the shape of the current when the force is periodic, piecewise
constant. We also illustrate the somewhat counterintuitive effect that
introducing damping may induce a ratchet effect. When the force is symmetric
under time-reversal and the system is undamped, under symmetry principles no
ratchet effect is possible. In this situation increasing damping generates a
ratchet current which, upon increasing the damping coefficient eventually
reaches a maximum and decreases toward zero. We argue that this effect is not
specific of this example and should appear in any ratchet system with tunable
damping driven by a time-reversible external force. | 1106.4861v1 |
2011-07-17 | Nonlinear-damping continuation of the nonlinear Schrödinger equation - a numerical study | We study the nonlinear-damping continuation of singular solutions of the
critical and supercritical NLS. Our simulations suggest that for generic
initial conditions that lead to collapse in the undamped NLS, the solution of
the weakly-damped NLS $$
i\psi_t(t,\X)+\Delta\psi+|\psi|^{p-1}\psi+i\delta|\psi|^{q-1}\psi=0,\qquad0<\delta
\ll 1, $$ is highly asymmetric with respect to the singularity time, and the
post-collapse defocusing velocity of the singular core goes to infinity as the
damping coefficient $\delta$ goes to zero. In the special case of the
minimal-power blowup solutions of the critical NLS, the continuation is a
minimal-power solution with a higher (but finite) defocusing velocity, whose
magnitude increases monotonically with the nonlinear damping exponent $q$. | 1107.3281v1 |
2018-04-06 | Exponential Integrators Preserving Local Conservation Laws of PDEs with Time-Dependent Damping/Driving Forces | Structure-preserving algorithms for solving conservative PDEs with added
linear dissipation are generalized to systems with time-dependent
damping/driving terms. This study is motivated by several PDE models of
physical phenomena, such as Korteweg-de Vries, Klein-Gordon, Schr\"{o}dinger,
and Camassa-Holm equations, all with damping/driving terms and time-dependent
coefficients. Since key features of the PDEs under consideration are described
by local conservation laws, which are independent of the boundary conditions,
the proposed (second-order in time) discretizations are developed with the
intent of preserving those local conservation laws. The methods are
respectively applied to a damped-driven nonlinear Schr\"{o}dinger equation and
a damped Camassa-Holm equation. Numerical experiments illustrate the
structure-preserving properties of the methods, as well as favorable results
over other competitive schemes. | 1804.02266v1 |
2019-11-13 | Dipole oscillations of fermionic superfluids along the BEC-BCS crossover in disordered potentials | We investigate dipole oscillations of ultracold Fermi gases along the BEC-BCS
crossover through disordered potentials. We observe a disorder-induced damping
of oscillations as well as a change of the fundamental Kohn-mode frequency. The
measurement results are compared to numerical density matrix renormalization
group calculations as well as to a three-dimensional simulation of
non-interacting fermions. Experimentally, we find a disorder-dependent damping,
which grows approximately with the second power of the disorder strength.
Moreover, we observe experimentally a change of oscillation frequency which
deviates from the expected behavior of a damped harmonic oscillator on a
percent level. While this behavior is qualitatively expected from the
theoretical models used, quantitatively the experimental observations show a
significantly stronger effect than predicted by theory. Furthermore, while the
frequency shift seems to scale differently with interaction strength in the BEC
versus BCS regime, the damping coefficient apparently decreases with the
strength of interaction, but not with the sign, which changes for BEC and BCS
type Fermi gases. This is surprising, as the dominant damping mechanisms are
expected to be different in the two regimes. | 1911.05638v1 |
2020-05-16 | Simultaneous observation of anti-damping and inverse spin Hall effect in La$_{0.67}$Sr$_{0.33}$MnO$_{3}$/Pt bilayer system | Manganites have shown potential in spintronics because they exhibit high spin
polarization. Here, by ferromagnetic resonance we have studied the damping
properties of La$_{0.67}$Sr$_{0.33}$MnO$_{3}$/Pt bilayers which are prepared by
oxide molecular beam epitaxy. The damping coefficient ($\alpha$) of
La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO) single layer is found to be 0.0104.
However the LSMO/Pt bilayers exhibit decrease in $\alpha$ with increase in Pt
thickness. This decrease in the value of $\alpha$ is probably due to high
anti-damping like torque. Further, we have investigated the angle dependent
inverse spin Hall effect (ISHE) to quantify the spin pumping voltage from other
spin rectification effects such as anomalous Hall effect and anisotropic
magnetoresistance. We have observed high spin pumping voltage ($\sim$~20 $ \mu
V$). The results indicate that both anti-damping and spin pumping phenomena are
occuring simultaneously. | 2005.07848v3 |
2021-10-26 | Theory of sound attenuation in amorphous solids from nonaffine motions | We present a theoretical derivation of acoustic phonon damping in amorphous
solids based on the nonaffine response formalism for the viscoelasticity of
amorphous solids. The analytical theory takes into account the nonaffine
displacements in transverse waves and is able to predict both the ubiquitous
low-energy diffusive damping $\sim k^{2}$, as well as a novel contribution to
the Rayleigh damping $\sim k^{4}$ at higher wavevectors and the crossover
between the two regimes observed experimentally. The coefficient of the
diffusive term is proportional to the microscopic viscous (Langevin-type)
damping in particle motion (which arises from anharmonicity), and to the
nonaffine correction to the static shear modulus, whereas the Rayleigh damping
emerges in the limit of low anharmonicity, consistent with previous
observations and macroscopic models. Importantly, the $k^4$ Rayleigh
contribution derived here does not arise from harmonic disorder or elastic
heterogeneity effects and it is the dominant mechanism for sound attenuation in
amorphous solids as recently suggested by molecular simulations. | 2110.13446v2 |
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