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2010-09-15 | A discontinuous Galerkin method for the Vlasov-Poisson system | A discontinuous Galerkin method for approximating the Vlasov-Poisson system
of equations describing the time evolution of a collisionless plasma is
proposed. The method is mass conservative and, in the case that piecewise
constant functions are used as a basis, the method preserves the positivity of
the electron distribution function and weakly enforces continuity of the
electric field through mesh interfaces and boundary conditions. The performance
of the method is investigated by computing several examples and error estimates
associated system's approximation are stated. In particular, computed results
are benchmarked against established theoretical results for linear advection
and the phenomenon of linear Landau damping for both the Maxwell and Lorentz
distributions. Moreover, two nonlinear problems are considered: nonlinear
Landau damping and a version of the two-stream instability are computed. For
the latter, fine scale details of the resulting long-time BGK-like state are
presented. Conservation laws are examined and various comparisons to theory are
made. The results obtained demonstrate that the discontinuous Galerkin method
is a viable option for integrating the Vlasov-Poisson system. | 1009.3046v2 |
2017-03-22 | New versions of Newton method: step-size choice, convergence domain and under-determined equations | Newton method is one of the most powerful methods for finding solutions of
nonlinear equations and for proving their existence. In its "pure" form it has
fast convergence near the solution, but small convergence domain. On the other
hand damped Newton method has slower convergence rate, but weaker conditions on
the initial point. We provide new versions of Newton-like algorithms, resulting
in combinations of Newton and damped Newton method with special step-size
choice, and estimate its convergence domain. Under some assumptions the
convergence is global. Explicit complexity results are also addressed. The
adaptive version of the algorithm (with no a priori constants knowledge) is
presented. The method is applicable for under-determined equations (with $m<n$,
$m$ being the number of equations and $n$ being the number of variables). The
results are specified for systems of quadratic equations, for composite
mappings and for one-dimensional equations and inequalities. | 1703.07810v2 |
2020-08-14 | Testing Dissipative Collapse Models with a Levitated Micromagnet | We present experimental tests of dissipative extensions of spontaneous wave
function collapse models based on a levitated micromagnet with ultralow
dissipation. The spherical micromagnet, with radius $R=27$ $\mu$m, is levitated
by Meissner effect in a lead trap at $4.2$ K and its motion is detected by a
SQUID. We perform accurate ringdown measurements on the vertical translational
mode with frequency $57$ Hz, and infer the residual damping at vanishing
pressure $\gamma/2\pi<9$ $\mu$Hz. From this upper limit we derive improved
bounds on the dissipative versions of the CSL (continuous spontaneous
localization) and the DP (Di\'{o}si-Penrose) models with proper choices of the
reference mass. In particular, dissipative models give rise to an intrinsic
damping of an isolated system with the effect parameterized by a temperature
constant; the dissipative CSL model with temperatures below 1 nK is ruled out,
while the dissipative DP model is excluded for temperatures below $10^{-13}$ K.
Furthermore, we present the first bounds on dissipative effects in a more
recent model, which relates the wave function collapse to fluctuations of a
generalized complex-valued spacetime metric. | 2008.06245v2 |
2012-02-25 | Fractional Order Phase Shaper Design with Routh's Criterion for Iso-damped Control System | Phase curve of an open loop system is flat in nature if the derivative of
phase with respect to frequency is zero. With a flat phase curve, the
corresponding closed-loop system exhibits an iso-damped property i.e. maintains
constant overshoot with the change of gain and with other parametric
variations. In recent past application, fractional order (FO) phase shapers
have been proposed by contemporary researchers to achieve enhanced parametric
robustness. In this paper, a simple Routh tabulation based methodology is
proposed to design an appropriate FO phase shaper to achieve phase flattening
in a control loop, comprising a system, controlled by a classical PID
controller. The method is demonstrated using MATLAB simulation of a second
order DC motor plant and also a first order with time delay system. | 1202.5667v1 |
2014-04-25 | Nonlinear and Linear Timescales near Kinetic Scales in Solar Wind Turbulence | The application of linear kinetic treatments to plasma waves, damping, and
instability requires favorable inequalities between the associated linear
timescales and timescales for nonlinear (e.g., turbulence) evolution. In the
solar wind these two types of timescales may be directly compared using
standard Kolmogorov-style analysis and observational data. The estimated local
nonlinear magnetohydrodynamic cascade times, evaluated as relevant kinetic
scales are approached, remain slower than the cyclotron period, but comparable
to, or faster than, the typical timescales of instabilities, anisotropic waves,
and wave damping. The variation with length scale of the turbulence timescales
is supported by observations and simulations. On this basis the use of linear
theory - which assumes constant parameters to calculate the associated kinetic
rates - may be questioned. It is suggested that the product of proton
gyrofrequency and nonlinear time at the ion gyroscales provides a simple
measure of turbulence influence on proton kinetic behavior. | 1404.6569v1 |
2019-04-09 | Ferromagnetic Resonance Studies of Strain tuned Bi:YIG Films | Bismuth-doped Yttrium iron garnet (Bi:YIG) thin films known for large
Magneto-optical activity with low losses still needs to get probed for its
magnetization dynamics. We demonstrate a controlled tuning of
magnetocrystalline anisotropy in Bi-doped Y_3 Fe_5 O_12 (Bi:YIG) films of high
crystalline quality using growth induced epitaxial strain on [111]-oriented
Gd_3 Ga_5 O_12 (GGG) substrate. We optimize a growth protocol to get thick
highly-strained epitaxial films showing large magneto-crystalline anisotropy,
compare to thin films prepared using a different protocol. Ferromagnetic
resonance measurements establish a linear dependence of the out-of-plane
uniaxial anisotropy on the strain induced rhombohedral distortion of Bi:YIG
lattice. Interestingly, the enhancement in the magnetoelastic constant due to
an optimum substitution of Bi^(3+) ions with strong spin orbit coupling does
not strongly affect the precessional damping (~2x10^(-3) ). Large
magneto-optical activity, reasonably low damping, large magnetocrystalline
anisotropy and large magnetoelastic coupling in BiYIG are the properties that
may help BiYIG emerge as a possible material for photo-magnonics and other
spintronics applications. | 1904.04800v2 |
2019-04-25 | Low damping magnetic properties and perpendicular magnetic anisotropy with strong volume contribution in the Heusler alloy Fe1.5CoGe | We present a study of the dynamic magnetic properties of TiN-buffered
epitaxial thin films of the Heusler alloy Fe$_{1.5}$CoGe. Thickness series
annealed at different temperatures are prepared and the magnetic damping is
measured, a lowest value of $\alpha=2.18\times 10^{-3}$ is obtained. The
perpendicular magnetic anisotropy properties in Fe$_{1.5}$CoGe/MgO are also
characterized. The evolution of the interfacial perpendicular anisotropy
constant $K^{\perp}_{\rm S}$ with the annealing temperature is shown and
compared with the widely used CoFeB/MgO interface. A large volume contribution
to the perpendicular anisotropy of $(4.3\pm0.5)\times 10^{5}$ $\rm J/m^3$ is
also found, in contrast with vanishing bulk contribution in common Co- and
Fe-based Heusler alloys. | 1904.11247v1 |
2019-04-26 | Terahertz spin dynamics driven by a field-derivative torque | Efficient manipulation of magnetization at ultrashort time scales is of
particular interest for future technology. Here, we numerically investigate the
influence of the so-called field-derivative torque, which was derived earlier
based on relativistic Dirac theory [Mondal et al., Phys. Rev. B 94, 144419
(2016)], on the spin dynamics triggered by ultrashort laser pulses. We find
that only considering the THz Zeeman field can underestimate the spin
excitation in antiferromagnetic oxide systems as, e.g., NiO and CoO. However,
accounting for both, the THz Zeeman torque and the field-derivative torque, the
amplitude of the spin excitation increases significantly. Studying the damping
dependence of field-derivative torque we observe larger effects for materials
having larger damping constants. | 1904.11768v2 |
2019-05-30 | Intrinsically Undamped Plasmon Modes in Narrow Electron Bands | Surface plasmons in 2-dimensional electron systems with narrow Bloch bands
feature an interesting regime in which Landau damping (dissipation via
electron-hole pair excitation) is completely quenched. This surprising behavior
is made possible by strong coupling in narrow-band systems characterized by
large values of the "fine structure" constant $\alpha=e^2/\hbar \kappa v_{\rm
F}$. Dissipation quenching occurs when dispersing plasmon modes rise above the
particle-hole continuum, extending into the forbidden energy gap that is free
from particle-hole excitations. The effect is predicted to be prominent in
moir\'e graphene, where at magic twist-angle values, flat bands feature
$\alpha\gg1$. The extinction of Landau damping enhances spatial optical
coherence. Speckle-like interference, arising in the presence of disorder
scattering, can serve as a telltale signature of undamped plasmons directly
accessible in near-field imaging experiments. | 1905.13088v2 |
2019-12-10 | Stability of traveling waves in a driven Frenkel-Kontorova model | In this work we revisit a classical problem of traveling waves in a damped
Frenkel-Kontorova lattice driven by a constant external force. We compute these
solutions as fixed points of a nonlinear map and obtain the corresponding
kinetic relation between the driving force and the velocity of the wave for
different values of the damping coefficient. We show that the kinetic curve can
become non-monotone at small velocities, due to resonances with linear modes,
and also at large velocities where the kinetic relation becomes multivalued.
Exploring the spectral stability of the obtained waveforms, we identify, at the
level of numerical accuracy of our computations, a precise criterion for
instability of the traveling wave solutions: monotonically decreasing portions
of the kinetic curve always bear an unstable eigendirection. We discuss why the
validity of this criterion in the {\it dissipative} setting is a rather
remarkable feature offering connections to the Hamiltonian variant of the model
and of lattice traveling waves more generally. Our stability results are
corroborated by direct numerical simulations which also reveal the possible
outcomes of dynamical instabilities. | 1912.05052v2 |
2020-05-20 | Dynamic Peach-Koehler self-force, inertia, and radiation damping of a regularized dislocation | The elastodynamic Peach-Koehler force is computed for a fully-regularized
straight dislocation with isotropic core in continuum isotropic elastic
elasticity, in compact forms involving partial mass or impulsion functions
relative to shear and compressional waves. The force accounts for both dynamic
radiation damping and inertia. The expressions are valid indifferently for
subsonic or supersonic velocities. Results are compared with the case of a
flat-core dislocation of the Peierls-Eshelby type, for a motion of jump from
rest to constant velocity. In the steady-state limit, the Lagrangian function
relevant to expressing the force in the flat-core case must be replaced by a
related but different function for the regularized dislocation. However, by
suitably defining the regularizing dislocation width, the steady-state limits
of the force for the fully-regularized and flat-core dislocations can be
matched exactly. | 2005.12704v2 |
2020-06-29 | Collective excitations in spin-polarized bilayer graphene | We calculate the plasmon frequency and damping rate of plasma oscillations in
a spin-polarized BLG system. Using the long wavelength approximation for
dynamical dielectric function, we obtain an analytical expression for plasmon
frequency showing that the degree of spin polarization P has negligible effect
on the long wavelength plasmon frequency. Numerical calculations demonstrate
that the degree of spin polarization affects slightly (strongly) plasmon
frequency at small (large) wave-vectors and the maximum value of damping rate
increases with increasing P. We also study the effects of carrier density and
substrate dielectric constant on plasmon properties for different value of spin
polarization. The numerically calculated critical wave-vector, at which the
plasmon dispersion curve hits the edge of electron-hole continuum, decreases
with P and can be used to determine experimentally the degree of spin
polarization. | 2006.16042v2 |
2020-10-28 | Spin-valley collective modes of the electron liquid in graphene | We develop the theory of collective modes supported by a Fermi liquid of
electrons in pristine graphene. Under reasonable assumptions regarding the
electron-electron interaction, all the modes but the plasmon are over-damped.
In addition to the $SU(2)$ symmetric spin mode, these include also the valley
imbalance modes obeying a $U(1)$ symmetry, and a $U(2)$ symmetric valley spin
imbalance mode. We derive the interactions and diffusion constants
characterizing the over-damped modes. The corresponding relaxation rates set
fundamental constraints on graphene valley- and spintronics applications. | 2010.15154v2 |
2020-11-14 | Oscillating charge currents of one-dimensional Hubbard model in an electric field | The time evolution properties of charge current for the one-dimensional
Hubbard model in an electric field have been studied in a rigorous manner. We
find that there is a complete and orthonormal set of time-evolution states for
which the charge current can only keep zero or oscillate constantly, differing
from the possible picture of damped or over-damped Bloch oscillations due to
strong correlations. It is also found that, associated with these states, there
is a set of constant phase factors, which are uniquely determined and are very
useful on discussing the long-time evolution behaviors of the system. | 2011.07220v2 |
2021-01-15 | Efficient Spin-Orbit Torque Generation in Semiconducting WTe2 with Hopping Transport | Spin-orbit torques (SOTs) from transition metal dichalcogenides systems
(TMDs) in conjunction with ferromagnetic materials are recently attractive in
spintronics for their versatile features. However, most of the previously
studied crystalline TMDs are prepared by mechanical exfoliation, which limits
their potentials for industrial applications. Here we show that amorphous WTe2
heterostructures deposited by magnetron sputtering possess a sizable
damping-like SOT efficiency {\xi}_DL^WTe2 ~ 0.20 and low damping constant
{\alpha} = 0.009/pm0.001. Only an extremely low critical switching current
density J_c ~ 7.05\times10^9 A/m^2 is required to achieve SOT-driven
magnetization switching. The SOT efficiency is further proved to depend on the
W and Te relative compositions in the co-sputtered W_100-xTe_x samples, from
which a sign change of {\xi}_DL^WTe2 is observed. Besides, the electronic
transport in amorphous WTe2 is found to be semiconducting and is governed by a
hopping mechanism. With the above advantages and rich tunability, amorphous and
semiconducting WTe2 serves as a unique SOT source for future spintronics
applications. | 2101.06047v1 |
2021-03-13 | Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state | Discrete dissipative coupled systems exhibit complex behavior such as chaos,
spatiotemporal intermittence, chimera among others. We construct and
investigate chimera states, in the form of confined stationary and dynamical
states in a chain of parametrically driven sites with onsite damping and cubic
nonlinearity. The system is modeled by the respective discrete parametrically
driven damped nonlinear Schrodinger equation. Chimeras feature quasi-periodic
or chaotic dynamic in the filled area, quantified by time dependence of the
total norm (along with its power spectrum), and by the largest Lyapunov
exponent. Systematic numerical simulations, in combination with some analytical
results, reveal regions in the parameter space populated by stable localized
states of different types. A phase transition from the stationary disorder
states to spatially confined dynamical chaotic one is identified. Essential
parameters of the system are the strength and detuning of the forcing, as well
as the lattice's coupling constant. | 2103.07748v1 |
2021-05-31 | Machine-Learning Non-Conservative Dynamics for New-Physics Detection | Energy conservation is a basic physics principle, the breakdown of which
often implies new physics. This paper presents a method for data-driven "new
physics" discovery. Specifically, given a trajectory governed by unknown
forces, our Neural New-Physics Detector (NNPhD) aims to detect new physics by
decomposing the force field into conservative and non-conservative components,
which are represented by a Lagrangian Neural Network (LNN) and a universal
approximator network (UAN), respectively, trained to minimize the force
recovery error plus a constant $\lambda$ times the magnitude of the predicted
non-conservative force. We show that a phase transition occurs at $\lambda$=1,
universally for arbitrary forces. We demonstrate that NNPhD successfully
discovers new physics in toy numerical experiments, rediscovering friction
(1493) from a damped double pendulum, Neptune from Uranus' orbit (1846) and
gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD
coupled with an integrator outperforms previous methods for predicting the
future of a damped double pendulum. | 2106.00026v2 |
2021-07-29 | $n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability | We consider position-dependent mass (PDM) Lagrangians/Hamiltonians in their
standard textbook form, where the long-standing \emph{gain-loss balance}
between the kinetic and potential energies is kept intact to allow conservation
of total energy (i.e., $L=T-V$, $H=T+V$, and $dH/dt=dE/dt=0$). Under such
standard settings, we discuss and report on $n$-dimensional PDM damped harmonic
oscillators (DHO). We use some $n$-dimensional point canonical transformation
to facilitate the linearizability of their $n$-PDM dynamical equations into
some $n$-linear DHOs' dynamical equations for constant mass setting.
Consequently, the well know exact solutions for the linear DHOs are mapped,
with ease, onto the exact solutions for PDM DHOs. A set of one-dimensional and
a set of $n$-dimensional PDM-DHO illustrative examples are reported along with
their phase-space trajectories. | 2107.14617v1 |
2022-07-17 | Locational Aspect of Fast Frequency Reserves in Low-Inertia Systems -- Control Performance Analysis | This paper evaluates the frequency performance of an AC system when primary
frequency response is provided by inverter-based resources located at
remote-areas. Due to potentially larger wave propagation constants over longer
lines, fast active power response from inverter based resources may have a
negative impact on the system frequency response. Within this context, this
paper presents a control performance analysis is presented in order to identify
limitations for improving the frequency stability when inverter-based resources
in remote locations use local frequency measurements. Our results suggest that
there exists a trafeoff between disturbance rejection and stability robustness
when allocating primary frequency control. In particular, fast frequency
control can have a negative impact on the damping ratio of poorly damped
electromechanical modes. | 2207.08188v1 |
2022-08-17 | Linking fluctuation and dissipation in spatially extended out-of-equilibrium systems | For systems in equilibrium at a temperature $T$, thermal noise and energy
damping are related to $T$ through the fluctuation-dissipation theorem (FDT).
We study here an extension of the FDT to an out of equilibrium steady state: a
microcantilever subject to a constant heat flux. The resulting thermal profile
in this spatially extended system interplays with the local energy dissipation
field to prescribe the amplitude of mechanical fluctuations. Using three
samples with different damping profiles (localized or distributed), we probe
this approach and experimentally demonstrate the link between fluctuations and
dissipation. The thermal noise can therefore be predicted a priori from the
measurement of the dissipation as a function of the maximum temperature of the
micro-oscillator. | 2208.08356v2 |
2022-09-07 | Classical correlations for Generic States are Fragile under Decoherence | Quantum correlations typically decrease with increasing noise, although
classical correlators (CCors) may rise for a particular class of states with
noise. To analyse the behavior of classical correlation (CC) in the presence of
local noise, we scrutinize the set of classical correlators, axiomatic CC
measures like classical discord, and local work for Haar uniformly generated
states. Like quantum correlation measures, we illustrate that when noise levels
rise, the average value of the CC measures for noisy output states obtained
from random input states decreases for most of the channels. We also
demonstrate a connection between the CCors of the noise-affected multipartite
states that are produced and the CCors of the initial states that exhibit
exponential, polynomial, and constant behavior as the noise level changes.
Moreover, based on CCors of the generalised N-qubit W state as input, we
determine a method to discriminate between the quantum channels, namely phase
damping, depolarizing, and amplitude damping channels. We also relate
classical, quantum, and total correlation measures that exhibit a comparable
reaction to decoherence for generic states. | 2209.03334v1 |
2022-10-19 | Global well-posedness of the partially damped 2D MHD equations via a direct normal mode method for the anisotropic linear operator | We prove the global well-posedness of the 2D incompressible non-resistive MHD
equations with a velocity damping term near the non-zero constant background
magnetic field. To this end, we newly design a normal mode method of
effectively leveraging the anisotropy of the linear propagator that encodes
both the partially dissipative nature of the non-resistive MHD system and the
stabilizing mechanism of the underlying magnetic field. Isolating new key
quantities and estimating them with themselves in an entangling way via the
eigenvalue analysis based on Duhamel's formulation, we establish the global
well-posedness for any initial data $(v_0,B_0)$ that is sufficiently small in a
space rougher than $H^{4}\cap L^1$. This improves the recent work in SIAM J.
Math. Anal. 47, 2630-2656 (2015) where the similar result was obtained provided
that $(v_0,B_0)$ was small enough in a space strictly embedded in $H^{20}\cap
W^{6,1}$. | 2210.10283v1 |
2022-11-07 | On Vacuum Free Boundary Problem of the Spherically Symmetric Euler Equations with Damping and Solid Core | In this paper, the global existence of smooth solution and the long-time
asymptotic stability of the equilibrium to vacuum free boundary problem of the
spherically symmetric Euler equations with damping and solid core have been
obtained for arbitrary finite positive gas constant $A$ in the state equation
$p=A \rho^\gamma$ with $p$ being the pressure and $\rho$ the density, provided
that $\gamma>4/3,$ initial perturbation is small and the radius of the
equilibrium $R$ is suitably larger than the radius of the solid core $r_0$.
Moreover, we obtain the pointwise convergence from the smooth solution to the
equilibrium in a surprisingly exponential time-decay rate. The proof is mainly
based on weighted energy method in Lagrangian coordinate. | 2211.03347v2 |
2022-11-16 | Endemic Oscillations for SARS-CoV-2 Omicron -- A SIRS model analysis | The SIRS model with constant vaccination and immunity waning rates is well
known to show a transition from a disease-free to an endemic equilibrium as the
basic reproduction number $r_0$ is raised above threshold. It is shown that
this model maps to Hethcote's classic endemic model originally published in
1973. In this way one obtains unifying formulas for a whole class of models
showing endemic bifurcation. In particular, if the vaccination rate is smaller
than the recovery rate and $r_- < r_0 < r_+$ for certain upper and lower bounds
$r_\pm$, then trajectories spiral into the endemic equilibrium via damped
infection waves. Latest data of the SARS-CoV-2 Omicron variant suggest that
according to this simplified model continuous vaccination programs will not be
capable to escape the oscillating endemic phase. However, in view of the strong
damping factors predicted by the model, in reality these oscillations will
certainly be overruled by time-dependent contact behaviors. | 2211.09005v2 |
2022-12-21 | Global existence and Blow-up for the 1D damped compressible Euler equations with time and space dependent perturbation | In this paper, we consider the 1D Euler equation with time and space
dependent damping term $-a(t,x)v$. It has long been known that when $a(t,x)$ is
a positive constant or $0$, the solution exists globally in time or blows up in
finite time, respectively. We prove that those results are invariant with
respect to time and space dependent perturbations. We suppose that the
coefficient $a$ satisfies the following condition $$ |a(t,x)- \mu_0| \leq
a_1(t) + a_2 (x), $$ where $\mu_0 \geq 0$ and $a_1$ and $a_2$ are integrable
functions with $t$ and $x$. Under this condition, we show the global existence
and the blow-up with small initial data, when $\mu_0 >0$ and $\mu=0$
respectively. | 2212.11072v2 |
2023-02-13 | A damped elastodynamics system under the global injectivity condition: Local wellposedness in $L^p$-spaces | The purpose of this paper is to model mathematically mechanical aspects of
cardiac tissues. The latter constitute an elastic domain whose total volume
remains constant. The time deformation of the heart tissue is modeled with the
elastodynamics equations dealing with the displacement field as main unknown.
These equations are coupled with a pressure whose variations characterize the
heart beat. This pressure variable corresponds to a Lagrange multiplier
associated with the so-called global injectivity condition. We derive the
corresponding coupled system with nonhomogeneous boundary conditions where the
pressure variable appears. For mathematical convenience a damping term is
added, and for a given class of strain energies we prove the existence of
local-in-time solutions in the context of the $L^p$-parabolic maximal
regularity. | 2302.06327v2 |
2024-02-29 | Quantum coherence and entanglement under the influence of decoherence | In this work, we delve into the dynamic traits of the relative entropy of
quantum coherence (REQC) as the quantum system interacts with the different
noisy channels, drawing comparisons with entanglement (concurrence). The
research results demonstrate the broader prevalence and stronger robustness of
the REQC as opposed to concurrence. It's worth noting that the bit flip channel
cannot uphold a constant nonzero frozen the REQC, besides, the concurrence
follows a pattern of temporary reduction to zero, followed by recovery after a
certain time span. More importantly, the REQC maintains its presence
consistently until reaching a critical threshold, whereas concurrence
experiences completely attenuation to zero under the influence of phase damping
and amplitude damping channels. | 2402.19055v1 |
2003-01-31 | Ultraviolet spectroscopy of narrow coronal mass ejections | We present Ultraviolet Coronagraph Spectrometer (UVCS) observations of 5
narrow coronal mass ejections (CMEs) that were among 15 narrow CMEs originally
selected by Gilbert et al. (2001). Two events (1999 March 27, April 15) were
"structured", i.e. in white light data they exhibited well defined interior
features, and three (1999 May 9, May 21, June 3) were "unstructured", i.e.
appeared featureless. In UVCS data the events were seen as 4-13 deg wide
enhancements of the strongest coronal lines HI Ly-alpha and OVI (1032,1037 A).
We derived electron densities for several of the events from the Large Angle
Spectrometric Coronagraph (LASCO) C2 white light observations. They are
comparable to or smaller than densities inferred for other CMEs. We modeled the
observable properties of examples of the structured (1999 April 15) and
unstructured (1999 May 9) narrow CMEs at different heights in the corona
between 1.5 and 2 R(Sun). The derived electron temperatures, densities and
outflow speeds are similar for those two types of ejections. They were compared
with properties of polar coronal jets and other CMEs. We discuss different
scenarios of narrow CME formation either as a jet formed by reconnection onto
open field lines or CME ejected by expansion of closed field structures.
Overall, we conclude that the existing observations do not definitively place
the narrow CMEs into the jet or the CME picture, but the acceleration of the
1999 April 15 event resembles acceleration seen in many CMEs, rather than
constant speeds or deceleration observed in jets. | 0301649v1 |
2005-06-02 | Enhanced algorithms for Local Search | Let G=(V,E) be a finite graph, and f:V->N be any function. The Local Search
problem consists in finding a local minimum of the function f on G, that is a
vertex v such that f(v) is not larger than the value of f on the neighbors of v
in G. In this note, we first prove a separation theorem slightly stronger than
the one of Gilbert, Hutchinson and Tarjan for graphs of constant genus. This
result allows us to enhance a previously known deterministic algorithm for
Local Search with query complexity O(\log n)\cdot d+O(\sqrt{g})\cdot\sqrt{n},
so that we obtain a deterministic query complexity of
d+O(\sqrt{g})\cdot\sqrt{n}, where n is the size of G, d is its maximum degree,
and $g$ is its genus. We also give a quantum version of our algorithm, whose
query complexity is of O(\sqrt{d})+O(\sqrt[4]{g})\cdot\sqrt[4]{n}\log\log n.
Our deterministic and quantum algorithms have query complexities respectively
smaller than the generic algorithms of Aldous and of Aaronson for large classes
of graphs, including graphs of bounded genus and planar graphs. Independently
from this work, Zhang has recently given a quantum algorithm which finds a
local minimum on the planar grid over \{1,...,\sqrt{n}\}^2 using
O(\sqrt[4]{n}(\log\log n)^2) queries. Our quantum algorithm can be viewed as a
strongly generalized, and slightly enhanced version of this algorithm. | 0506019v1 |
2007-09-27 | Predictions of the causal entropic principle for environmental conditions of the universe | The causal entropic principle has been proposed as a superior alternative to
the anthropic principle for understanding the magnitude of the cosmological
constant. In this approach, the probability to create observers is assumed to
be proportional to the entropy production \Delta S in a maximal causally
connected region -- the causal diamond. We improve on the original treatment by
better quantifying the entropy production due to stars, using an analytic model
for the star formation history which accurately accounts for changes in
cosmological parameters. We calculate the dependence of \Delta S on the density
contrast Q=\delta\rho/\rho, and find that our universe is much closer to the
most probable value of Q than in the usual anthropic approach and that
probabilities are relatively weakly dependent on this amplitude. In addition,
we make first estimates of the dependence of \Delta S on the baryon fraction
and overall matter abundance. Finally, we also explore the possibility that
decays of dark matter, suggested by various observed gamma ray excesses, might
produce a comparable amount of entropy to stars. | 0709.4443v2 |
2009-03-16 | The Transit Light Curve Project. XII. Six Transits of the Exoplanet XO-2b | We present photometry of six transits of the exoplanet XO-2b. By combining
the light-curve analysis with theoretical isochrones to determine the stellar
properties, we find the planetary radius to be 0.996 +0.031/-0.018 rjup and the
planetary mass to be 0.565 +/- 0.054 mjup. These results are consistent with
those reported previously, and are also consistent with theoretical models for
gas giant planets. The mid-transit times are accurate to within 1 min and are
consistent with a constant period. However, the period we derive differs by 2.5
sigma from the previously published period. More data are needed to tell
whether the period is actually variable (as it would be in the presence of an
additional body) or if the timing errors have been underestimated. | 0903.2687v1 |
2010-10-23 | Closure method for spatially averaged dynamics of particle chains | We study the closure problem for continuum balance equations that model
mesoscale dynamics of large ODE systems. The underlying microscale model
consists of classical Newton equations of particle dynamics. As a mesoscale
model we use the balance equations for spatial averages obtained earlier by a
number of authors: Murdoch and Bedeaux, Hardy, Noll and others. The momentum
balance equation contains a flux (stress), which is given by an exact function
of particle positions and velocities. We propose a method for approximating
this function by a sequence of operators applied to average density and
momentum. The resulting approximate mesoscopic models are systems in closed
form. The closed from property allows one to work directly with the mesoscale
equaitons without the need to calculate underlying particle trajectories, which
is useful for modeling and simulation of large particle systems. The proposed
closure method utilizes the theory of ill-posed problems, in particular
iterative regularization methods for solving first order linear integral
equations. The closed from approximations are obtained in two steps. First, we
use Landweber regularization to (approximately) reconstruct the interpolants of
relevant microscale quantitites from the average density and momentum. Second,
these reconstructions are substituted into the exact formulas for stress. The
developed general theory is then applied to non-linear oscillator chains. We
conduct a detailed study of the simplest zero-order approximation, and show
numerically that it works well as long as fluctuations of velocity are nearly
constant. | 1010.4832v1 |
2013-05-17 | Spectral gap for stochastic energy exchange model with nonuniformly positive rate function | We give a lower bound on the spectral gap for a class of stochastic energy
exchange models. In 2011, Grigo et al. introduced the model and showed that,
for a class of stochastic energy exchange models with a uniformly positive rate
function, the spectral gap of an $N$-component system is bounded from below by
a function of order $N^{-2}$. In this paper, we consider the case where the
rate function is not uniformly positive. For this case, the spectral gap
depends not only on $N$ but also on the averaged energy $\mathcal{E}$, which is
the conserved quantity under the dynamics. Under some assumption, we obtain a
lower bound of the spectral gap which is of order $C(\mathcal{E})N^{-2}$ where
$C(\mathcal{E})$ is a positive constant depending on $\mathcal {E}$. As a
corollary of the result, a lower bound of the spectral gap for the mesoscopic
energy exchange process of billiard lattice studied by Gaspard and Gilbert [J.
Stat. Mech. Theory Exp. 2008 (2008) p11021, J. Stat. Mech. Theory Exp. 2009
(2009) p08020] and the stick process studied by Feng et al. [Stochastic
Process. Appl. 66 (1997) 147-182] are obtained. | 1305.4066v3 |
2015-03-16 | Dynamics of Current and Field Driven Domain Wall Motion under the Influence of Transverse Magnetic Field | The dynamics of transverse Neel domain wall in a ferromagnetic nanostrip in
the presence of driving field, current and transverse magnetic field is
investigated by the Landau-Lifshitz-Gilbert(LLG) equation with the adiabatic
and non-adiabatic spin-transfer torques both analytically and numerically. The
analytical expressions for the velocity, width, excitation angle and
displacement for the domain wall are obtained by using small angle
approximation along with Walkers trial function. The results show that the
initial velocity of the domain wall can be controlled by the adiabatic
spin-transfer torque and the saturated velocity can be controlled by the
non-adiabatic spin-transfer torque and driving field. The large increase in the
saturated velocity of the domain wall driven by current and field due to the
transverse magnetic field is identified through the presence of driving field.
There is no impact in the saturated velocity of the domain wall driven by
current from the transverse magnetic field. For the domain wall driven by the
current in the presence of the transverse magnetic field, the saturated
velocity remains constant. The transverse magnetic field along with current and
driving field is more advantageous that the transverse magnetic field along
with current for increasing the saturated velocity of the domain wall. The
numerical results showed that the saturated velocity is increased by the
transverse magnetic field with the irrespective of the directions of the
driving field and current further it is higher and lower when the directions of
driving field and current are antiparallel and parallel respectively. The
obtained analytical solutions are closely coincided with the computed numerical
results. | 1503.04560v2 |
2015-03-25 | Rigorous numerical study of strong microwave photon-magnon coupling in all-dielectric magnetic multilayers | We demonstrate theoretically a strong local enhancement of the intensity of
the in-plane microwave magnetic field in multilayered structures made from a
magneto-insulating yttrium iron garnet (YIG) layer sandwiched between two
non-magnetic layers with a high dielectric constant matching that of YIG. The
enhancement is predicted for the excitation regime when the microwave magnetic
field is induced inside the multilayer by the transducer of a stripline
Broadband Ferromagnetic Resonance (BFMR) setup. By means of a rigorous
numerical solution of the Landau-Lifshitz-Gilbert equation consistently with
the Maxwell's equations, we investigate the magnetisation dynamics in the
multilayer. We reveal a strong photon-magnon coupling, which manifests itself
as anti-crossing of the ferromagnetic resonance (FMR) magnon mode supported by
the YIG layer and the electromagnetic resonance mode supported by the whole
multilayered structure. The frequency of the magnon mode depends on the
external static magnetic field, which in our case is applied tangentially to
the multilayer in the direction perpendicular to the microwave magnetic field
induced by the stripline of the BFMR setup. The frequency of the
electromagnetic mode is independent of the static magnetic field. Consequently,
the predicted photon-magnon coupling is sensitive to the applied magnetic field
and thus can be used in magnetically tuneable metamaterials based on
simultaneously negative permittivity and permeability achievable thanks to the
YIG layer. We also suggest that the predicted photon-magnon coupling may find
applications in microwave quantum information systems. | 1503.07282v1 |
2015-11-11 | Magnetization switching by current and microwaves | We propose a theoretical model of magnetization switching in a ferromagnetic
multilayer by both electric current and microwaves. The electric current gives
a spin transfer torque on the magnetization, while the microwaves induce a
precession of the magnetization around the initial state. Based on numerical
simulation of the Landau-Lifshitz-Gilbert (LLG) equation, it is found that the
switching current is significantly reduced compared with the switching caused
solely by the spin transfer torque when the microwave frequency is in a certain
range. We develop a theory of switching from the LLG equation averaged over a
constant energy curve. It was found that the switching current should be
classified into four regions, depending on the values of the microwave
frequency. Based on the analysis, we derive an analytical formula of the
optimized frequency minimizing the switching current, which is smaller than the
ferromagnetic resonance frequency. We also derive an analytical formula of the
minimized switching current. Both the optimized frequency and the minimized
switching current decrease with increasing the amplitude of the microwave
field. The results will be useful to achieve high thermal stability and low
switching current in spin torque systems simultaneously. | 1511.03366v2 |
2016-09-16 | Convex separation from convex optimization for large-scale problems | We present a scheme, based on Gilbert's algorithm for quadratic minimization
[SIAM J. Contrl., vol. 4, pp. 61-80, 1966], to prove separation between a point
and an arbitrary convex set $S\subset\mathbb{R}^{n}$ via calls to an oracle
able to perform linear optimizations over $S$. Compared to other methods, our
scheme has almost negligible memory requirements and the number of calls to the
optimization oracle does not depend on the dimensionality $n$ of the underlying
space. We study the speed of convergence of the scheme under different promises
on the shape of the set $S$ and/or the location of the point, validating the
accuracy of our theoretical bounds with numerical examples. Finally, we present
some applications of the scheme in quantum information theory. There we find
that our algorithm out-performs existing linear programming methods for certain
large scale problems, allowing us to certify nonlocality in bipartite scenarios
with upto $42$ measurement settings. We apply the algorithm to upper bound the
visibility of two-qubit Werner states, hence improving known lower bounds on
Grothendieck's constant $K_G(3)$. Similarly, we compute new upper bounds on the
visibility of GHZ states and on the steerability limit of Werner states for a
fixed number of measurement settings. | 1609.05011v2 |
2017-08-16 | Magneto Acoustic Spin Hall Oscillators | This paper introduces a novel oscillator that combines the tunability of spin
Hall-driven nano oscillators with the high quality factor (Q) of high overtone
bulk acoustic wave resonators (HBAR), integrating both reference and tunable
oscillators on the same chip with CMOS. In such magneto acoustic spin Hall
(MASH) oscillators, voltage oscillations across the magnetic tunnel junction
(MTJ) that arise from a spin-orbit torque (SOT) are shaped by the transmission
response of the HBAR that acts as a multiple peak-bandpass filter and a delay
element due to its large time constant, providing delayed feedback. The
filtered voltage oscillations can be fed back to the MTJ via a) strain, b)
current, or c) magnetic field. We develop a SPICE-based circuit model by
combining experimentally benchmarked models including the stochastic
Landau-Lifshitz-Gilbert (sLLG) equation for magnetization dynamics and the
Butterworth Van Dyke (BVD) circuit for the HBAR. Using the self-consistent
model, we project up to $\sim$ 50X enhancement in the oscillator linewidth with
Q reaching up to 52825 at 3 GHz, while preserving the tunability by locking the
STNO to the nearest high Q peak of the HBAR. We expect that our results will
inspire MEMS-based solutions to spintronic devices by combining attractive
features of both fields for a variety of applications. | 1708.04735v2 |
2018-04-19 | Equilibrium magnetization of a quasispherical cluster of single-domain particles | Equilibrium magnetization curve of a rigid finite-size spherical cluster of
single-domain particles is investigated both numerically and analytically. The
spatial distribution of particles within the cluster is random. Dipole-dipole
interactions between particles are taken into account. The particles are
monodisperse. It is shown, using the stochastic Landau-Lifshitz-Gilbert
equation that the magnetization of such clusters is generally lower than
predicted by the classical Langevin model. In a broad range of dipolar coupling
parameters and particle volume fractions, the cluster magnetization in the weak
field limit can be successfully described by the modified mean-field theory,
which was originally proposed for the description of concentrated ferrofluids.
In moderate and strong fields, the theory overestimates the cluster
magnetization. However, predictions of the theory can be improved by adjusting
the corresponding mean-field parameter. If magnetic anisotropy of particles is
additionally taken into account and if the distribution of the particles' easy
axes is random and uniform, then the cluster equilibrium response is even
weaker. The decrease of the magnetization with increasing anisotropy constant
is more pronounced at large applied fields. The phenomenological generalization
of the modified mean-field theory, that correctly describes this effect for
small coupling parameters, is proposed. | 1804.07196v2 |
2018-06-24 | Nanoscopic time crystal obtained by nonergodic spin dynamics | We study the far-from-equilibrium properties of quenched magnetic nanoscopic
classical spin systems. In particular, we focus on the interplay between
lattice vibrations and magnetic frustrations induced by surface effects typical
of an antiferromagnet. We use a combination of Monte Carlo simulations and
explore the dynamical behaviours by solving the stochastic
Landau-Lifshitz-Gilbert equation at finite temperature. The Monte Carlo
approach treats both the ionic degrees of freedom and spin variables on the
same footing, via an extended Lennard-Jones Hamiltonian with a spin-lattice
coupling. The zero temperature phase diagram of the finite size nanoscopic
systems with respect to the range of the Heisenberg interaction and the
Lennard-Jones coupling constant shows two main structures with non-trivial
magnetisation triggered by antiferromagnetism: a simple cubic and a
body-centred cubic. At non zero temperature, the competition between spins and
the ionic vibrations considerably affects the magnetization of the system.
Exploring the dynamics reveals a non-trivial structural induced behaviour in
the spin relaxation with a concomitant memory of the initially applied
ferromagnetic quench. We report the observation of a non-trivial dynamical
scenario, obtained after a ferromagnetic magnetic quench at low temperature.
Furthermore, we observe long-lived non-thermal states which could open new
avenues for nano-technology. | 1806.09130v4 |
2018-07-19 | Magnetization nutation induced by surface effects in nanomagnets | We investigate the magnetization dynamics of ferromagnetic nanoparticles in
the atomistic approach taking account of surface anisotropy and the spin
misalignment it causes. We demonstrate that such inhomogeneous spin
configurations induce nutation in the dynamics of the particle's magnetization.
More precisely, in addition to the ordinary precessional motion with frequency
$f_{p}\sim10\,{\rm GHz}$, we find that the dynamics of the net magnetic moment
exhibits two more resonance peaks with frequencies $f_{c}$ and $f_{n}$ which
are higher than the frequency $f_{p} : f_{c}=4\times f_{p}\sim40\,{\rm GHz}$ is
related with the oscillations of the particle's magnetic moment between the
minima of the effective potential induced by weak surface anisotropy. On the
other hand, the much higher frequency $f_{n}\sim1\,{\rm THz}$ is attributed to
the magnetization fluctuations at the atomic level driven by exchange
interaction. We have compared our results on nutation induced by surface
effects with those rendered by the macroscopic approach based on the
Landau-Lifshitz-Gilbert equation augmented by an inertial term (proportional to
the second-order time derivative of the macroscopic moment) with a
phenomenological coefficient. The good agreement between the two models have
allowed us to estimate the latter coefficient in terms of the atomistic
parameters such as the surface anisotropy constant. We have thus proposed a new
origin for the magnetization nutations as being induced by surface effects and
have interpreted the corresponding resonance peaks and their frequencies. | 1807.07392v1 |
2008-11-21 | Geodesic dynamo chaotic flows and non-Anosov maps in twisted magnetic flux tubes | Recently Tang and Boozer [{\textbf{Phys. Plasmas (2000)}}], have investigated
the anisotropies in magnetic field dynamo evolution, from local Lyapunov
exponents, giving rise to a metric tensor, in the Alfven twist in magnetic flux
tubes (MFTs). Thiffeault and Boozer [\textbf{Chaos}(2001)] have investigated
the how the vanishing of Riemann curvature constrained the Lyapunov exponential
stretching of chaotic flows. In this paper, Tang-Boozer-Thiffeault differential
geometric framework is used to investigate effects of twisted magnetic flux
tube filled with helical chaotic flows on the Riemann curvature tensor. When
Frenet torsion is positive, the Riemann curvature is unstable, while the
negative torsion induces an stability when time $t\to{\infty}$. This enhances
the dynamo action inside the MFTs. The Riemann metric, depends on the radial
random flows along the poloidal and toroidal directions. The Anosov flows has
been applied by Arnold, Zeldovich, Ruzmaikin and Sokoloff [\textbf{JETP
(1982)}] to build a uniformly stretched dynamo flow solution, based on Arnold's
Cat Map. It is easy to show that when the random radial flow vanishes, the
magnetic field vanishes, since the exponential Lyapunov stretches vanishes.
This is an example of the application of the Vishik's anti-fast dynamo theorem
in the magnetic flux tubes. Geodesic flows of both Arnold and twisted MFT
dynamos are investigated. It is shown that a constant random radial flow can be
obtained from the geodesic equation. Throughout the paper one assumes, the
reasonable plasma astrophysical hypothesis of the weak torsion. Pseudo-Anosov
dynamo flows and maps have also been addressed by Gilbert [\textbf{Proc Roy Soc
A London (1993)} | 0811.3630v1 |
2017-03-22 | Magnetization induced dynamics of a Josephson junction coupled to a nanomagnet | We study the superconducting current of a Josephson junction (JJ) coupled to
an external nanomagnet driven by a time dependent magnetic field both without
and in the presence of an external AC drive. We provide an analytic, albeit
perturbative, solution for the Landau-Lifshitz (LL) equations governing the
coupled JJ-nanomagnet system in the presence of a magnetic field with arbitrary
time-dependence oriented along the easy axis of the nanomagnet's magnetization
and in the limit of weak dimensionless coupling $\epsilon_0$ between the JJ and
the nanomagnet. We show the existence of Shapiro-like steps in the I-V
characteristics of the JJ subjected to a voltage bias for a constant or
periodically varying magnetic field and explore the effect of rotation of the
magnetic field and the presence of an external AC drive on these steps. We
support our analytic results with exact numerical solution of the LL equations.
We also extend our results to dissipative nanomagnets by providing a
perturbative solution to the Landau-Lifshitz-Gilbert (LLG) equations for weak
dissipation. We study the fate of magnetization-induced Shapiro steps in the
presence of dissipation both from our analytical results and via numerical
solution of the coupled LLG equations. We discuss experiments which can test
our theory. | 1703.07717v3 |
2021-04-05 | When Can Liquid Democracy Unveil the Truth? | In this paper, we investigate the so-called ODP-problem that has been
formulated by Caragiannis and Micha [10]. Here, we are in a setting with two
election alternatives out of which one is assumed to be correct. In ODP, the
goal is to organise the delegations in the social network in order to maximize
the probability that the correct alternative, referred to as ground truth, is
elected. While the problem is known to be computationally hard, we strengthen
existing hardness results by providing a novel strong approximation hardness
result: For any positive constant $C$, we prove that, unless $P=NP$, there is
no polynomial-time algorithm for ODP that achieves an approximation guarantee
of $\alpha \ge (\ln n)^{-C}$, where $n$ is the number of voters. The reduction
designed for this result uses poorly connected social networks in which some
voters suffer from misinformation. Interestingly, under some hypothesis on
either the accuracies of voters or the connectivity of the network, we obtain a
polynomial-time $1/2$-approximation algorithm. This observation proves formally
that the connectivity of the social network is a key feature for the efficiency
of the liquid democracy paradigm. Lastly, we run extensive simulations and
observe that simple algorithms (working either in a centralized or
decentralized way) outperform direct democracy on a large class of instances.
Overall, our contributions yield new insights on the question in which
situations liquid democracy can be beneficial. | 2104.01828v1 |
2021-05-18 | Magnetic flux structuring of the quiet Sun internetwork. Center-to-limb analysis of solar-cycle variations | It is now well established that the quiet Sun contains in total more magnetic
flux than active regions and represents an important reservoir of magnetic
energy. But the nature and evolution of these fields remain largely unknown.
We investigate the solar-cycle and center-to-limb variations of magnetic-flux
structures at small scales in internetwork regions of the quiet Sun.
We used Hinode SOT/SP data from the irradiance program between 2008 and 2016.
Maps of the magnetic-flux density are derived from the center-of gravity method
applied to the FeI 630.15 nm and FeI 630.25 nm lines. To correct the maps from
the instrumental smearing, we applied a deconvolution method based on a
principal component analysis of the line profiles and on a Richardson-Lucy
deconvolution of their coefficients. We then performed a spectral analysis of
the spatial fluctuations of the magnetic-flux density in 10'' x 10''
internetwork regions spanning a wide range of latitudes.
At low and mid latitudes the power spectra do not vary significantly with the
solar cycle. However at solar maximum for one scan in the activity belt showing
an enhanced network, a marginal increase in the power of the magnetic
fluctuations is observed at granular and larger scales in the internetwork. At
high latitudes, we observe variations at granular and larger scales where the
power decreases at solar maximum. At all the latitudes the power of the
magnetic fluctuations at scales smaller than 0.5''remain constant throughout
the solar cycle.
Our results favor a small-scale dynamo that operates in the internetwork, but
they show that the global dynamo also contributes to the internetwork fields. | 2105.08657v1 |
2019-03-14 | Low Field-size, Rate-Optimal Streaming Codes for Channels With Burst and Random Erasures | In this paper, we design erasure-correcting codes for channels with burst and
random erasures, when a strict decoding delay constraint is in place. We
consider the sliding-window-based packet erasure model proposed by Badr et al.,
where any time-window of width $w$ contains either up to $a$ random erasures or
an erasure burst of length at most $b$. One needs to recover any erased packet,
where erasures are as per the channel model, with a strict decoding delay
deadline of $\tau$ time slots. Presently existing rate-optimal constructions in
the literature require, in general, a field-size which grows exponential in
$\tau$, for a constant $\frac{a}{\tau}$. In this work, we present a new
rate-optimal code construction covering all channel and delay parameters, which
requires an $O(\tau^2)$ field-size. As a special case, when $(b-a)=1$, we have
a field-size linear in $\tau$. We also present three other constructions having
linear field-size, under certain constraints on channel and decoding delay
parameters. As a corollary, we obtain low field-size, rate-optimal
convolutional codes for any given column distance and column span. Simulations
indicate that the newly proposed streaming code constructions offer lower
packet-loss probabilities compared to existing schemes, for selected instances
of Gilbert-Elliott and Fritchman channels. | 1903.06210v1 |
2019-05-16 | Ultralow-loss domain wall motion driven by magnetocrystalline anisotropy gradient in antiferromagnetic nanowire | Searching for new methods controlling antiferromagnetic (AFM) domain wall is
one of the most important issues for AFM spintronic device operation. In this
work, we study theoretically the domain wall motion of an AFM nanowire, driven
by the axial anisotropy gradient generated by external electric field, allowing
the electro control of AFM domain wall motion in the merit of ultra-low energy
loss. The domain wall velocity depending on the anisotropy gradient magnitude
and intrinsic material properties is simulated based on the
Landau-Lifshitz-Gilbert equation and also deduced using the energy dissipation
theorem. It is found that the domain wall moves at a nearly constant velocity
for small gradient, and accelerates for large gradient due to the enlarged
domain wall width. The domain wall mobility is independent of lattice dimension
and types of domain wall, while it is enhanced by the Dzyaloshinskii-Moriya
interaction. In addition, the physical mechanism for much faster AFM wall
dynamics than ferromagnetic wall dynamics is qualitatively explained. This work
unveils a promising strategy for controlling the AFM domain walls, benefiting
to future AFM spintronic applications. | 1905.06695v2 |
2020-01-06 | Highly efficient spin orbit torque in Pt/Co/Ir multilayers with antiferromagnetic interlayer exchange coupling | We have studied the spin orbit torque (SOT) in Pt/Co/Ir multilayers with 3
repeats of the unit structure. As the system exhibits oscillatory interlayer
exchange coupling (IEC) with varying Ir layer thickness, we compare the SOT of
films when the Co layers are coupled ferromagnetically and
antiferromagnetically. SOT is evaluated using current induced shift of the
anomalous Hall resistance hysteresis loops. A relatively thick Pt layer,
serving as a seed layer to the multilayer, is used to generate spin current via
the spin Hall effect. In the absence of antiferromagnetic coupling, the SOT is
constant against the applied current density and the corresponding spin torque
efficiency (i.e. the effective spin Hall angle) is $\sim$0.09, in agreement
with previous reports. In contrast, for films with antiferromagnetic coupling,
the SOT increases with the applied current density and eventually saturates.
The SOT at saturation is a factor of $\sim$15 larger than that without the
antiferromagnetic coupling. The spin torque efficiency is $\sim$5 times larger
if we assume the net total magnetization is reduced by a factor of 3 due to the
antiferromagnetic coupling. Model calculations based on the Landau Lifshitz
Gilbert equation show that the presence of antiferromagnetic coupling can
increase the SOT but the degree of enhancement is limited, in this case, to a
factor of 1.2-1.4. We thus consider there are other sources of SOT, possibly at
the interfaces, which may account for the highly efficient SOT in the
uncompensated synthetic anti-ferromagnet (SAF) multilayers. | 2001.01454v1 |
2021-08-27 | Distributed Control and Optimization of DC Microgrids: A Port-Hamiltonian Approach | This article proposes a distributed secondary control scheme that drives a dc
microgrid to an equilibrium point where the generators share optimal currents,
and their voltages have a weighted average of nominal value. The scheme does
not rely on the electric system topology nor its specifications; it guarantees
plug-and-play design and functionality of the generators. First, the
incremental model of the microgrid system with constant impedance, current, and
power devices is shown to admit a port-Hamiltonian (pH) representation, and its
passive output is determined. The economic dispatch problem is then solved by
the Lagrange multipliers method; the Karush-Kuhn-Tucker conditions and weighted
average formation of voltages are then formulated as the control objectives. We
propose a control scheme that is based on the Control by Interconnection design
philosophy, where the consensus-based controller is viewed as a virtual pH
system to be interconnected with the physical one. We prove the regional
asymptotic stability of the closed-loop system using Lyapunov and LaSalle
theorems. Equilibrium analysis is also conducted based on the concepts of graph
theory and economic dispatch. Finally, the effectiveness of the presented
scheme for different case studies is validated with a test microgrid system,
simulated in both MATLAB/Simulink and OPAL-RT environments. | 2108.12341v1 |
2021-10-23 | Bootstrap percolation in random geometric graphs | Following Bradonji\'c and Saniee, we study a model of bootstrap percolation
on the Gilbert random geometric graph on the $2$-dimensional torus. In this
model, the expected number of vertices of the graph is $n$, and the expected
degree of a vertex is $a\log n$ for some fixed $a>1$. Each vertex is added with
probability $p$ to a set $A_0$ of initially infected vertices. Vertices
subsequently become infected if they have at least $ \theta a \log n $ infected
neighbours. Here $p, \theta \in [0,1]$ are taken to be fixed constants.
We show that if $\theta < (1+p)/2$, then a sufficiently large local outbreak
leads with high probability to the infection spreading globally, with all but
$o(n)$ vertices eventually becoming infected. On the other hand, for $ \theta >
(1+p)/2$, even if one adversarially infects every vertex inside a ball of
radius $O(\sqrt{\log n} )$, with high probability the infection will spread to
only $o(n)$ vertices beyond those that were initially infected.
In addition we give some bounds on the $(a, p, \theta)$ regions ensuring the
emergence of large local outbreaks or the existence of islands of vertices that
never become infected. We also give a complete picture of the (surprisingly
complex) behaviour of the analogous $1$-dimensional bootstrap percolation model
on the circle. Finally we raise a number of problems, and in particular make a
conjecture on an `almost no percolation or almost full percolation' dichotomy
which may be of independent interest. | 2110.12166v1 |
2022-01-30 | OverChain: Building a robust overlay with a blockchain | Blockchains use peer-to-peer networks for disseminating information among
peers, but these networks currently do not have any provable guarantees for
desirable properties such as Byzantine fault tolerance, good connectivity and
small diameter. This is not just a theoretical problem, as recent works have
exploited unsafe peer connection policies and weak network synchronization to
mount partitioning attacks on Bitcoin. Cryptocurrency blockchains are safety
critical systems, so we need principled algorithms to maintain their networks.
Our key insight is that we can leverage the blockchain itself to share
information among the peers, and thus simplify the network maintenance process.
Given that the peers have restricted computational resources, and at most a
constant fraction of them are Byzantine, we provide communication-efficient
protocols to maintain a hypercubic network for blockchains, where peers can
join and leave over time. Interestingly, we discover that our design can
\emph{recover} from substantial adversarial failures. Moreover, these
properties hold despite significant churn.
A key contribution is a secure mechanism for joining the network that uses
the blockchain to help new peers to contact existing peers. Furthermore, by
examining how peers join the network, i.e., the "bootstrapping service," we
give a lower bound showing that (within log factors) our network tolerates the
maximum churn rate possible. In fact, we can give a lower bound on churn for
any fully distributed service that requires connectivity. | 2201.12809v1 |
2022-07-24 | Contention Resolution for Coded Radio Networks | Randomized backoff protocols, such as exponential backoff, are a powerful
tool for managing access to a shared resource, often a wireless communication
channel (e.g., [1]). For a wireless device to transmit successfully, it uses a
backoff protocol to ensure exclusive access to the channel. Modern radios,
however, do not need exclusive access to the channel to communicate; in
particular, they have the ability to receive useful information even when more
than one device transmits at the same time. These capabilities have now been
exploited for many years by systems that rely on interference cancellation,
physical layer network coding and analog network coding to improve efficiency.
For example, Zigzag decoding [56] demonstrated how a base station can decode
messages sent by multiple devices simultaneously.
In this paper, we address the following question: Can we design a backoff
protocol that is better than exponential backoff when exclusive channel access
is not required. We define the Coded Radio Network Model, which generalizes
traditional radio network models (e.g., [30]). We then introduce the Decodable
Backoff Algorithm, a randomized backoff protocol that achieves an optimal
throughput of $1-o(1)$. (Throughput $1$ is optimal, as simultaneous reception
does not increase the channel capacity.) The algorithm breaks the constant
throughput lower bound for traditional radio networks [47-49], showing the
power of these new hardware capabilities. | 2207.11824v1 |
2022-09-15 | Almost Ramanujan Expanders from Arbitrary Expanders via Operator Amplification | We give an efficient algorithm that transforms any bounded degree expander
graph into another that achieves almost optimal (namely, near-quadratic, $d
\leq 1/\lambda^{2+o(1)}$) trade-off between (any desired) spectral expansion
$\lambda$ and degree $d$. Furthermore, the algorithm is local: every vertex can
compute its new neighbors as a subset of its original neighborhood of radius
$O(\log(1/\lambda))$. The optimal quadratic trade-off is known as the Ramanujan
bound, so our construction gives almost Ramanujan expanders from arbitrary
expanders.
The locality of the transformation preserves structural properties of the
original graph, and thus has many consequences. Applied to Cayley graphs, our
transformation shows that any expanding finite group has almost Ramanujan
expanding generators. Similarly, one can obtain almost optimal explicit
constructions of quantum expanders, dimension expanders, monotone expanders,
etc., from existing (suboptimal) constructions of such objects. Another
consequence is a "derandomized" random walk on the original (suboptimal)
expander with almost optimal convergence rate. Our transformation also applies
when the degree is not bounded or the expansion is not constant.
We obtain our results by a generalization of Ta-Shma's technique in his
breakthrough paper [STOC 2017], used to obtain explicit almost optimal binary
codes. Specifically, our spectral amplification extends Ta-Shma's analysis of
bias amplification from scalars to matrices of arbitrary dimension in a very
natural way. Curiously, while Ta-Shma's explicit bias amplification
derandomizes a well-known probabilistic argument (underlying the
Gilbert--Varshamov bound), there seems to be no known probabilistic (or other
existential) way of achieving our explicit ("high-dimensional") spectral
amplification. | 2209.07024v1 |
2023-08-25 | Thermal effect on microwave pulse driven magnetization switching of Stoner particle | Recently it has been demonstrated that the cosine chirp microwave pulse
(CCMP) is capable of achieving fast and energy-efficient magnetization-reversal
of a nanoparticle with zero-Temperature. However, we investigate the finite
temperature, $T$ effect on the CCMP-driven magnetization reversal using the
framework of the stochastic Landau Lifshitz Gilbert equation. At finite
Temperature, we obtain the CCMP-driven fast and energy-efficient reversal and
hence estimate the maximal temperature, $T_{max}$ at which the magnetization
reversal is valid. $T_{max}$ increases with increasing the nanoparticle
cross-sectional area/shape anisotropy up to a certain value, and afterward
$T_{max}$ decreases with the further increment of nanoparticle cross-sectional
area/shape anisotropy. This is because of demagnetization/shape anisotropy
field opposes the magnetocrystalline anisotropy, i.e., reduces the energy
barrier which separates the two stable states. For smaller cross-sectional
area/shape anisotropy, the controlling parameters of CCMP show decreasing trend
with temperature. We also find that with the increment easy-plane
shape-anisotropy, the required initial frequency of CCMP significantly reduces.
For the larger volume of nanoparticles, the parameters of CCMP remains constant
for a wide range of temperature which are desired for the device application.
Therefore, The above findings might be useful to realize the CCMP-driven fast
and energy-efficient magnetization reversal in realistic conditions. | 2308.13124v1 |
2023-10-13 | Midpoint geometric integrators for inertial magnetization dynamics | We consider the numerical solution of the inertial version of
Landau-Lifshitz-Gilbert equation (iLLG), which describes high-frequency
nutation on top of magnetization precession due to angular momentum relaxation.
The iLLG equation defines a higher-order nonlinear dynamical system with very
different nature compared to the classical LLG equation, requiring twice as
many degrees of freedom for space-time discretization. It exhibits essential
conservation properties, namely magnetization amplitude preservation,
magnetization projection conservation, and a balance equation for generalized
free energy, leading to a Lyapunov structure (i.e. the free energy is a
decreasing function of time) when the external magnetic field is constant in
time. We propose two second-order numerical schemes for integrating the iLLG
dynamics over time, both based on implicit midpoint rule. The first scheme
unconditionally preserves all the conservation properties, making it the
preferred choice for simulating inertial magnetization dynamics. However, it
implies doubling the number of unknowns, necessitating significant changes in
numerical micromagnetic codes and increasing computational costs especially for
spatially inhomogeneous dynamics simulations. To address this issue, we present
a second time-stepping method that retains the same computational cost as the
implicit midpoint rule for classical LLG dynamics while unconditionally
preserving magnetization amplitude and projection. Special quasi-Newton
techniques are developed for solving the nonlinear system of equations required
at each time step due to the implicit nature of both time-steppings. The
numerical schemes are validated on analytical solution for macrospin terahertz
frequency response and the effectiveness of the second scheme is demonstrated
with full micromagnetic simulation of inertial spin waves propagation in a
magnetic thin-film. | 2310.09043v1 |
2023-10-28 | Einstein-de Haas torque as a discrete spectroscopic probe allows nanomechanical measurement of a magnetic resonance | The Einstein-de Haas (EdH) effect is a fundamental, mechanical consequence of
any temporal change of magnetism in an object. EdH torque results from
conserving the object's total angular momentum: the angular momenta of all the
specimen's magnetic moments, together with its mechanical angular momentum.
Although the EdH effect is usually small and difficult to observe, it increases
in magnitude with detection frequency. We explore the frequency-dependence of
EdH torque for a thin film permalloy microstructure by employing a ladder of
flexural beam modes (with five distinct resonance frequencies spanning from 3
to 208 MHz) within a nanocavity optomechanical torque sensor via magnetic
hysteresis curves measured at mechanical resonances. At low DC fields the
gyrotropic resonance of a magnetic vortex spin texture overlaps the 208 MHz
mechanical mode. The massive EdH mechanical torques arising from this
co-resonance yield a fingerprint of vortex core pinning and depinning in the
sample. The experimental results are discussed in relation to mechanical
torques predicted from both macrospin (at high DC magnetic field) and
finite-difference solutions to the Landau-Lifshitz-Gilbert (LLG) equation. A
global fit of the LLG solutions to the frequency-dependent data reveals a
statistically significant discrepancy between the experimentally observed and
simulated torque phase behaviours at spin texture transitions that can be
reduced through the addition of a time constant to the conversion between
magnetic cross-product torque and mechanical torque, constrained by experiment
to be in the range of 0.5 - 4 ns. | 2310.18546v2 |
2024-01-11 | Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers | We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature
regime, where thermal fluctuations are modeled by a random magnetic field whose
variance is proportional to the temperature. By rescaling the temperature
proportionally to the computational cell size $\Delta x$ ($T \to T\,\Delta
x/a_{\text{eff}}$, where $a_{\text{eff}}$ is the lattice constant) [M. B. Hahn,
J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures $T_{\text{C}}$
that are in line with the experimental values for cobalt, iron and nickel. For
finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie
temperature varies with the smallest size $d$ of the system. We show that the
difference between the computed finite-size $T_{\text{C}}$ and the bulk
$T_{\text{C}}$ follows a power-law of the type: $(\xi_0/d)^\lambda$, where
$\xi_0$ is the correlation length at zero temperature, and $\lambda$ is a
critical exponent. We obtain values of $\xi_0$ in the nanometer range, also in
accordance with other simulations and experiments. The computed critical
exponent is close to $\lambda=2$ for all considered materials and geometries.
This is the expected result for a mean-field approach, but slightly larger than
the values observed experimentally. | 2401.05722v1 |
2014-02-21 | How to Scale Exponential Backoff | Randomized exponential backoff is a widely deployed technique for
coordinating access to a shared resource. A good backoff protocol should,
arguably, satisfy three natural properties: (i) it should provide constant
throughput, wasting as little time as possible; (ii) it should require few
failed access attempts, minimizing the amount of wasted effort; and (iii) it
should be robust, continuing to work efficiently even if some of the access
attempts fail for spurious reasons. Unfortunately, exponential backoff has some
well-known limitations in two of these areas: it provides poor (sub-constant)
throughput (in the worst case), and is not robust (to resource acquisition
failures).
The goal of this paper is to "fix" exponential backoff by making it scalable,
particularly focusing on the case where processes arrive in an on-line,
worst-case fashion. We present a relatively simple backoff
protocol~Re-Backoff~that has, at its heart, a version of exponential backoff.
It guarantees expected constant throughput with dynamic process arrivals and
requires only an expected polylogarithmic number of access attempts per
process.
Re-Backoff is also robust to periods where the shared resource is unavailable
for a period of time. If it is unavailable for $D$ time slots, Re-Backoff
provides the following guarantees. When the number of packets is a finite $n$,
the average expected number of access attempts for successfully sending a
packet is $O(\log^2( n + D))$. In the infinite case, the average expected
number of access attempts for successfully sending a packet is $O( \log^2(\eta)
+ \log^2(D) )$ where $\eta$ is the maximum number of processes that are ever in
the system concurrently. | 1402.5207v4 |
2003-07-01 | Highly damped quasinormal modes of Kerr black holes | Motivated by recent suggestions that highly damped black hole quasinormal
modes (QNM's) may provide a link between classical general relativity and
quantum gravity, we present an extensive computation of highly damped QNM's of
Kerr black holes. We do not limit our attention to gravitational modes, thus
filling some gaps in the existing literature. The frequency of gravitational
modes with l=m=2 tends to \omega_R=2 \Omega, \Omega being the angular velocity
of the black hole horizon. If Hod's conjecture is valid, this asymptotic
behaviour is related to reversible black hole transformations. Other highly
damped modes with m>0 that we computed do not show a similar behaviour. The
real part of modes with l=2 and m<0 seems to asymptotically approach a constant
value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of
a. For any perturbing field, trajectories in the complex plane of QNM's with
m=0 show a spiralling behaviour, similar to the one observed for
Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the
asymptotic separation in the imaginary part of consecutive modes with m>0 is
given by 2\pi T_H (T_H being the black hole temperature). We conjecture that
for all values of l and m>0 there is an infinity of modes tending to the
critical frequency for superradiance (\omega_R=m) in the extremal limit.
Finally, we study in some detail modes branching off the so--called
``algebraically special frequency'' of Schwarzschild black holes. For the first
time we find numerically that QNM multiplets emerge from the algebraically
special Schwarzschild modes, confirming a recent speculation. | 0307013v2 |
2019-10-15 | Adversarial Examples for Models of Code | Neural models of code have shown impressive results when performing tasks
such as predicting method names and identifying certain kinds of bugs. We show
that these models are vulnerable to adversarial examples, and introduce a novel
approach for attacking trained models of code using adversarial examples. The
main idea of our approach is to force a given trained model to make an
incorrect prediction, as specified by the adversary, by introducing small
perturbations that do not change the program's semantics, thereby creating an
adversarial example. To find such perturbations, we present a new technique for
Discrete Adversarial Manipulation of Programs (DAMP). DAMP works by deriving
the desired prediction with respect to the model's inputs, while holding the
model weights constant, and following the gradients to slightly modify the
input code. We show that our DAMP attack is effective across three neural
architectures: code2vec, GGNN, and GNN-FiLM, in both Java and C#. Our
evaluations demonstrate that DAMP has up to 89% success rate in changing a
prediction to the adversary's choice (a targeted attack) and a success rate of
up to 94% in changing a given prediction to any incorrect prediction (a
non-targeted attack). To defend a model against such attacks, we empirically
examine a variety of possible defenses and discuss their trade-offs. We show
that some of these defenses can dramatically drop the success rate of the
attacker, with a minor penalty of 2% relative degradation in accuracy when they
are not performing under attack. Our code, data, and trained models are
available at https://github.com/tech-srl/adversarial-examples . | 1910.07517v5 |
2020-02-14 | Testing Physical Models for Cosmic Ray Transport Coefficients on Galactic Scales: Self-Confinement and Extrinsic Turbulence at GeV Energies | The microphysics of ~GeV cosmic ray (CR) transport on galactic scales remain
deeply uncertain, with almost all studies adopting simple prescriptions (e.g.
constant-diffusivity). We explore different physically-motivated, anisotropic,
dynamical CR transport scalings in high-resolution cosmological FIRE
simulations of dwarf and ~$L_{\ast}$ galaxies where scattering rates vary with
local plasma properties motivated by extrinsic turbulence (ET) or
self-confinement (SC) scenarios, with varying assumptions about e.g. turbulent
power spectra on un-resolved scales, Alfven-wave damping, etc. We
self-consistently predict observables including $\gamma$-rays ($L_{\gamma}$),
grammage, residence times, and CR energy densities to constrain the models. We
demonstrate many non-linear dynamical effects (not captured in simpler models)
tend to enhance confinement. For example, in multi-phase media, even allowing
arbitrary fast transport in neutral gas does not substantially reduce CR
residence times (or $L_{\gamma}$), as transport is rate-limited by the ionized
WIM and 'inner CGM' gaseous halo ($10^{4}-10^{6}$ K gas within 10-30 kpc), and
$L_{\gamma}$ can be dominated by trapping in small 'patches.' Most physical ET
models contribute negligible scattering of ~1-10 GeV CRs, but it is crucial to
account for anisotropy and damping (especially of fast modes) or else
scattering rates would violate observations. We show that the most
widely-assumed scalings for SC models produce excessive confinement by factors
>100 in the WIM and inner CGM, where turbulent and Landau damping dominate.
This suggests either a breakdown of quasi-linear theory used to derive the CR
transport parameters in SC, or that other novel damping mechanisms dominate in
intermediate-density ionized gas. | 2002.06211v2 |
2021-06-11 | Dynamics and Nonmonotonic Drag for Individually Driven Skyrmions | We examine the motion of an individual skyrmion driven through an assembly of
other skyrmions by a constant or increasing force in the absence of quenched
disorder. The skyrmion behavior is determined by the ratio of the damping and
Magnus terms, as expressed in terms of the intrinsic skyrmion Hall angle. For a
fixed driving force in the damping dominated regime, the effective viscosity
decreases monotonically with increasing skyrmion density, similar to what is
observed in overdamped systems where it becomes difficult for the driven
particle to traverse the surrounding medium at high densities. In contrast, in
the Magnus dominated regime the velocity dependence on the density is
nonmonotonic, and there is a regime in which the skyrmion moves faster with
increasing density, as well as a pronounced speed-up effect in which a skyrmion
traveling through a dense medium moves more rapidly than it would at low
densities or in the single particle limit. At higher densities, the effective
damping increases and the velocity decreases. The velocity-force curves in the
Magnus-dominated regime show marked differences from those in the
damping-dominated regimes. Under an increasing drive we find that there is a
threshold force for skyrmion motion which increases with density. Additionally,
the skyrmion Hall angle is drive dependent, starting near zero at the threshold
for motion and increasing with increasing drive before reaching a saturation
value, similar to the behavior found for skyrmions driven over quenched
disorder. We map dynamic phase diagrams showing the threshold for motion,
nonlinear flow, speed-up, and saturation regimes. We also find that in some
cases, increasing the density can reduce the skyrmion Hall angle while
producing a velocity boost, which could be valuable for applications. | 2106.06093v1 |
2022-03-28 | Composite Anderson acceleration method with dynamic window-sizes and optimized damping | In this paper, we propose and analyze a set of fully non-stationary Anderson
acceleration algorithms with dynamic window sizes and optimized damping.
Although Anderson acceleration (AA) has been used for decades to speed up
nonlinear solvers in many applications, most authors are simply using and
analyzing the stationary version of Anderson acceleration (sAA) with fixed
window size and a constant damping factor. The behavior and potential of the
non-stationary version of Anderson acceleration methods remain an open
question. Since most efficient linear solvers use composable algorithmic
components. Similar ideas can be used for AA to solve nonlinear systems. Thus
in the present work, to develop non-stationary Anderson acceleration
algorithms, we first propose two systematic ways to dynamically alternate the
window size $m$ by composition. One simple way to package sAA(m) with sAA(n) in
each iteration is applying sAA(m) and sAA(n) separately and then average their
results. It is an additive composite combination. The other more important way
is the multiplicative composite combination, which means we apply sAA(m) in the
outer loop and apply sAA(n) in the inner loop. By doing this, significant gains
can be achieved. Secondly, to make AA to be a fully non-stationary algorithm,
we need to combine these strategies with our recent work on the non-stationary
Anderson acceleration algorithm with optimized damping (AAoptD), which is
another important direction of producing non-stationary AA and nice performance
gains have been observed. Moreover, we also investigate the rate of convergence
of these non-stationary AA methods under suitable assumptions. Finally, our
numerical results show that some of these proposed non-stationary Anderson
acceleration algorithms converge faster than the stationary sAA method and they
may significantly reduce the storage and time to find the solution in many
cases. | 2203.14627v1 |
2017-05-01 | A note on the initial conditions within the effective field theory approach of cosmic acceleration | By using the effective field theory approach, we investigate the role of
initial condition for the dark energy or modified gravity models. In details,
we consider the constant and linear parametrization of the effective Newton
constant models. Firstly, under the adiabatic assumption, the correction from
the extra scalar degree of freedom in the beyond $\Lambda$CDM model is found to
be negligible. The dominant ingredient in this setup is the primordial
curvature perturbation originated from inflation mechanism, and the energy
budget of the matter components is not very crucial. Secondly, the
iso-curvature perturbation sourced by the extra scalar field is studied. For
the constant and linear model of the effective Newton constant, there is no
such kind of scalar mode exist. For the quadratic model, there is a non-trivial
one. However, the amplitude of the scalar field is damped away very fast on all
scales. Consequently, it could not support a reasonable structure formation.
Finally, we study the importance of the setup of the scalar field starting
time. By setting different turn-on time, namely $a=10^{-2} $ and $a=10^{-7} $,
we compare the cosmic microwave background radiation temperature, lensing
deflection angle auto-correlation function as well as the matter power spectrum
in the constant and linear model. We find there is an order of
$\mathcal{O}(1\%)$ difference in the observable spectra for constant model,
while for the linear model, it is smaller than $\mathcal{O}(0.1\%)$. | 1705.00502v1 |
2000-05-29 | Entropy Production in a Persistent Random Walk | We consider a one-dimensional persisent random walk viewed as a deterministic
process with a form of time reversal symmetry. Particle reservoirs placed at
both ends of the system induce a density current which drives the system out of
equilibrium. The phase space distribution is singular in the stationary state
and has a cumulative form expressed in terms of generalized Takagi functions.
The entropy production rate is computed using the coarse-graining formalism of
Gaspard, Gilbert and Dorfman. In the continuum limit, we show that the value of
the entropy production rate is independent of the coarse-graining and agrees
with the phenomenological entropy production rate of irreversible
thermodynamics. | 0005063v1 |
2012-12-13 | A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations | We propose a $\theta$-linear scheme for the numerical solution of the
quasi-static Maxwell-Landau-Lifshitz-Gilbert (MLLG) equations. Despite the
strong nonlinearity of the Landau-Lifshitz-Gilbert equation, the proposed
method results in a linear system at each time step. We prove that as the time
and space steps tend to zero (with no further conditions when
$\theta\in(1/2,1]$), the finite element solutions converge weakly to a weak
solution of the MLLG equations. Numerical results are presented to show the
applicability of the method. | 1212.3369v1 |
2013-09-28 | Global Well-Posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey space | We establish the global well-posedness of the Landau-Lifshitz-Gilbert
equation in $\mathbb R^n$ for any initial data ${\bf m}_0\in H^1_*(\mathbb
R^n,\mathbb S^2)$ whose gradient belongs to the Morrey space $M^{2,2}(\mathbb
R^n)$ with small norm $\displaystyle\|\nabla {\bf m}_0\|_{M^{2,2}(\mathbb
R^n)}$. The method is based on priori estimates of a dissipative Schr\"odinger
equation of Ginzburg-Landau types obtained from the Landau-Lifshitz-Gilbert
equation by the moving frame technique. | 1309.7426v1 |
2016-10-26 | Iterated Gilbert Mosaics and Poisson Tropical Plane Curves | We propose an iterated version of the Gilbert model, which results in a
sequence of random mosaics of the plane. We prove that under appropriate
scaling, this sequence of mosaics converges to that obtained by a classical
Poisson line process with explicit cylindrical measure. Our model arises from
considerations on tropical plane curves, which are zeros of random tropical
polynomials in two variables. In particular, the iterated Gilbert model
convergence allows one to derive a scaling limit for Poisson tropical plane
curves. Our work raises a number of open questions at the intersection of
stochastic and tropical geometry. | 1610.08533v1 |
2017-05-29 | Strong solvability of regularized stochastic Landau-Lifshitz-Gilbert equation | We examine a stochastic Landau-Lifshitz-Gilbert equation based on an exchange
energy functional containing second-order derivatives of the unknown field.
Such regularizations are featured in advanced micromagnetic models recently
introduced in connection with nanoscale topological solitons. We show that, in
contrast to the classical stochastic Landau-Lifshitz-Gilbert equation based on
the Dirichlet energy alone, the regularized equation is solvable in the
stochastically strong sense. As a consequence it preserves the topology of the
initial data, almost surely. | 1705.10184v1 |
2021-04-03 | Improving the Gilbert-Varshamov Bound by Graph Spectral Method | We improve Gilbert-Varshamov bound by graph spectral method. Gilbert graph
$G_{q,n,d}$ is a graph with all vectors in $\mathbb{F}_q^n$ as vertices where
two vertices are adjacent if their Hamming distance is less than $d$. In this
paper, we calculate the eigenvalues and eigenvectors of $G_{q,n,d}$ using the
properties of Cayley graph. The improved bound is associated with the minimum
eigenvalue of the graph. Finally we give an algorithm to calculate the bound
and linear codes which satisfy the bound. | 2104.01403v3 |
2001-12-20 | What is the manifestation of a "quasar" at z > 10^{10} ? | The process of forming an image of a cosmological point source (CPS) in
condition of high optical depth is considered accounting for all types of
interactions. It is shown that the energy conservation law causes the size of
this image which is keeping constant over all redshifts of the CPSs. This
effect must be taken into account for the consideration of the angular power
spectrum of the CMBR. In particular, distant point sources and small scale
fluctuations which were damping before recombination will contribute their
energy in the region of angular scale \theta_0 \approx 20'. | 0112493v1 |
1994-12-17 | The Crucial Formula for Determination of the Occurrence of the Non-Chaotic States in the rf-biased Nonlinear Oscillators | The crucial formulas to determine the non-chaotic states in the rf-biased
nonlinear oscillators are derived from the numerical experiments. The nature of
these formulas, which depends on symmetrical properties of the potential well,
in terms of the driven-frequency as a function of the damping constant k is
investigated. All these ones provide crucial guide posts to check which kinds
of solutions (simple or complicated) can be tailored in the dissipative
rf-biased nonlinear oscillators, respectively. | 9412011v1 |
1995-03-17 | Motion of heavy particles coupled to fermionic and bosonic environments in one dimension | Making use of a simple unitary transformation we change the hamiltonian of a
particle coupled to an one dimensional gas of bosons or fermions to a new form
from which the many body degrees of freedom can be easily traced out. The
effective dynamics of the particle allows us to compute its damping constant in
terms of the reflection coefficient of the interaction potential and the
occupation number of the environmental particles. We apply our results to a
delta repulsive potential. | 9503089v2 |
2001-03-31 | Stability of nonlinear stationary waves in composite superconductors | The thermomagnetic instability of the critical state in superconductors is
analysed with account of the dissipation and dispersion. The possibility is
demonstrated of the existance of a nonlinear shok wave describing the final
stage of the instability evolution in a superconductor. The structures possess
a finite-amplitude and propagate at a constant velocity. The apperance of these
structures is qualititively described and the wave propagation velocity is
estimated. The problem of nonlinear wave stability with respect to small
thermal and electromagnetic perturbations. It is shown that only damped
perturbations correspond to space-limited solutions. | 0104007v1 |
2002-03-06 | Deterministic ratchets: route to diffusive transport | The rectification efficiency of an underdamped ratchet operated in the
adiabatic regime increases according to a scaling current-amplitude curve as
the damping constant approaches a critical threshold; below threshold the
rectified signal becomes extremely irregular and eventually its time average
drops to zero. Periodic (locked) and diffusive (fully chaotic) trajectories
coexist on fine tuning the amplitude of the input signal. The transition from
regular to chaotic transport in noiseless ratchets is studied numerically. | 0203129v1 |
2002-03-06 | Stokes' Drift of linear Defects | A linear defect, viz. an elastic string, diffusing on a planar substrate
traversed by a travelling wave experiences a drag known as Stokes' drift. In
the limit of an infinitely long string, such a mechanism is shown to be
characterized by a sharp threshold that depends on the wave parameters, the
string damping constant and the substrate temperature. Moreover, the onset of
the Stokes' drift is signaled by an excess diffusion of the string center of
mass, while the dispersion of the drifting string around its center of mass may
grow anomalous. | 0203131v1 |
2002-05-17 | Long-Ranged Correlations in Sheared Fluids | The presence of long-ranged correlations in a fluid undergoing uniform shear
flow is investigated. An exact relation between the density autocorrelation
function and the density-mometum correlation function implies that the former
must decay more rapidly than $1/r$, in contrast to predictions of simple mode
coupling theory. Analytic and numerical evaluation of a non-perturbative
mode-coupling model confirms a crossover from $1/r$ behavior at ''small'' $r$
to a stronger asymptotic power-law decay. The characteristic length scale is
$\ell \approx \sqrt{\lambda_{0}/a}$ where $% \lambda_{0}$ is the sound damping
constant and $a$ is the shear rate. | 0205366v1 |
2002-12-12 | Disorder-induced rounding of certain quantum phase transitions | We study the influence of quenched disorder on quantum phase transitions in
systems with over-damped dynamics. For Ising order parameter symmetry disorder
destroys the sharp phase transition by rounding because a static order
parameter can develop on rare spatial regions. This leads to an exponential
dependence of the order parameter on the coupling constant. At finite
temperatures the static order on the rare regions is destroyed. This restores
the phase transition and leads to a double-exponential relation between
critical temperature and coupling strength. We discuss the behavior based on
Lifshitz-tail arguments and illustrate the results by simulations of a model
system. | 0212305v1 |
2002-12-13 | Scaling behavior of a nonlinear oscillator with additive noise, white and colored | We study analytically and numerically the problem of a nonlinear mechanical
oscillator with additive noise in the absence of damping. We show that the
amplitude, the velocity and the energy of the oscillator grow algebraically
with time. For Gaussian white noise, an analytical expression for the
probability distribution function of the energy is obtained in the long-time
limit. In the case of colored, Ornstein-Uhlenbeck noise, a self-consistent
calculation leads to (different) anomalous diffusion exponents. Dimensional
analysis yields the qualitative behavior of the prefactors (generalized
diffusion constants) as a function of the correlation time. | 0212330v1 |
2003-06-13 | Scaling of the magnetic response in doped antiferromagnets | A theory of the anomalous $\omega/T$ scaling of the dynamic magnetic response
in cuprates at low doping is presented. It is based on the memory function
representation of the dynamical spin suceptibility in a doped antiferromagnet
where the damping of the collective mode is constant and large, whereas the
equal-time spin correlations saturate at low $T$. Exact diagonalization results
within the t-J model are shown to support assumptions. Consequences, both for
the scaling function and the normalization amplitude, are well in agreement
with neutron scattering results. | 0306366v2 |
2004-01-28 | Microscopic mechanisms of magnetization reversal | Two principal scenarios of magnetization reversal are considered. In the
first scenario all spins perform coherent motion and an excess of magnetic
energy directly goes to a nonmagnetic thermal bath. A general dynamic equation
is derived which includes a tensor damping term similar to the
Bloch-Bloembergen form but the magnetization magnitude remains constant for any
deviation from equilibrium. In the second reversal scenario, the absolute value
of the averaged sample magnetization is decreased by a rapid excitation of
nonlinear spin-wave resonances by uniform magnetization precession. We have
developed an analytic k-space micromagnetic approach that describes this entire
reversal process in an ultra-thin soft ferromagnetic film for up to 90^{o}
deviation from equilibrium. Conditions for the occurrence of the two scenarios
are discussed. | 0401590v1 |
2006-06-07 | Ferromagnetic relaxation by magnon-induced currents | A theory for calculating spin wave relaxation times based on the
magnon-electron interaction is developed. The theory incorporates a thin film
geometry and is valid for a large range of magnon frequencies and wave vectors.
For high conductivity metals such as permalloy, the wave vector dependent
damping constant approaches values as high as 0.2, showing the large magnitude
of the effect, and can dominate experimentally observed relaxation. | 0606197v1 |
1999-12-01 | Brane-world cosmology | A simple model of the brane-world cosmology has been proposed, which is
characterized by four parameters, the bulk cosmological constant, the spatial
curvature of the universe, the radiation strength arising from bulk space-time
and the breaking parameter of $Z_2$-symmetry. The bulk space-time is assumed to
be locally static five-dimensional analogue of the Schwarzschild-anti-de Sitter
space-time, and then the location of three-brane is determined by metric
junction. The resulting Friedmann equation recovers standard cosmology, and a
new term arises if the assumption $Z_2$-symmetry is dropped, which behaves as
cosmological term in the early universe, next turns to negative curvature term,
and finally damps rapidly. | 9912002v1 |
2003-01-05 | On non-Riemannian geometry of superfluids | The Gross-Pitaevski (GP) equation describing helium superfluids is extended
to non-Riemannian spacetime background where torsion is shown to induce the
splitting in the potential energy of the flow. A cylindrically symmetric
solution for Minkowski background with constant torsion is obtained which shows
that torsion induces a damping on the superfluid flow velocity. The Sagnac
phase shift is computed from the superfluid flow velocity obtained from the
solution of GP equations. | 0301013v1 |
2003-04-28 | Sphaleron relaxation temperatures | The transition of sphaleron processes from non-equilibrium to thermal
equilibrium in the early Universe is examined in detail. The relations between
the damping rates and frequencies of the weak and QCD sphaleron degeneracy
parameters are determined in general form and the respective relaxation
temperatures are calculated in specific scenarios. It is pointed out that the
gauge coupling constants running with energy produces strong and weak sphaleron
rates closer to each other at very high temperatures and makes them larger in
supersymmetric models than in the standard model case. | 0304263v4 |
2006-08-10 | Effects of Cosmic Strings on Free Streaming | We study the effect of free streaming in a universe with cosmic strings with
time-varying tension as well as with constant tension. Although current
cosmological observations suggest that fluctuation seeded by cosmic strings
cannot be the primary source of cosmic density fluctuation, some contributions
from them are still allowed. Since cosmic strings actively produce isocurvature
fluctuation, the damping of small scale structure via free streaming by dark
matter particles with large velocity dispersion at the epoch of
radiation-matter equality is less efficient than that in models with
conventional adiabatic fluctuation. We discuss its implications to the
constraints on the properties of particles such as massive neutrinos and warm
dark matter. | 0608115v1 |
2006-10-26 | QCD traveling waves beyond leading logarithms | We derive the asymptotic traveling-wave solutions of the nonlinear
1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in
momentum-space, with 1-loop running coupling constant and equipped with the
Balitsky-Kovchegov-Kuraev-Lipatov kernel at next-to-leading logarithmic
accuracy, conveniently regularized by different resummation schemes. Traveling
waves allow to define "universality classes" of asymptotic solutions, i.e.
independent of initial conditions and of the nonlinear damping. A dependence on
the resummation scheme remains, which is analyzed in terms of geometric scaling
properties. | 0610354v3 |
1999-12-20 | $Λ$-symmetry and background independence of noncommutative gauge theory on $\mathbb R^n$ | Background independence of noncommutative Yang-Mills theory on $\mathbb R^n$
is discussed. The quantity $\theta \hat F \theta - \theta$ is found to be
background dependent at subleading order, and it becomes background independent
only when the ordinary gauge field strength $F$ is constant. It is shown that,
at small values of $B$, the noncommutative Dirac-Born-Infeld action possesses
$\Lambda$-symmetry at least to subleading order in $\theta$ if $F$ damps fast
enough at infinity. | 9912174v2 |
1998-10-18 | Simulation and analysis of electron cyclotron resonance discharges | We describe in detail the method for Particle-in cell/Monte-Carlo simulation
of electron cyclotron resonance (ECR) discharges. In the simulation, electric
and magnetic fields are obtained by solving Maxwell equations, and electrons
and ions are accelerated by solving equations of motion. We consider two
different cases: (i) propagation of electromagnetic wave in the presence of a
constant external magnetic field; (ii) propagation of electromagnetic wave in
the presence of a linearly decreasing magnetic field which corresponds to a
realistic ECR discharge. The simulation results indicate that at the resonance
layer, the electrons are heated by the electromagnetic wave, and the incoming
wave amplitude is pronouncedly damped, with the wave hardly propagating through
the ECR layer. | 9810033v1 |
2003-08-30 | Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian | We show that the ground state of the well-known pseudo-stationary states for
the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state,
which has the minimum allowed uncertainty $\Delta q \Delta p = \hbar
\sigma_0/2$, where $\sigma_0 (\geq 1)$ is a constant depending on the damping
factor and natural frequency. The most general symmetric Gaussian states are
obtained as the one-parameter squeezed states of the pseudo-stationary ground
state. It is further shown that the coherent states of the pseudo-stationary
ground state constitute another class of the generalized minimum uncertainty
states. | 0309003v1 |
2004-03-31 | Quantum and Thermal Corrections to a Classically Chaotic Dissipative System | The effects of quantum and thermal corrections on the dynamics of a damped
nonlinearly kicked harmonic oscillator are studied. This is done via the
Quantum Langevin Equation formalism working on a truncated moment expansion of
the density matrix of the system. We find that the type of bifurcations present
in the system change upon quantization and that chaotic behavior appears for
values of the nonlinear parameter that are far below the chaotic threshold for
the classical model. Upon increase of temperature or Planck's constant,
bifurcation points and chaotic thresholds are shifted towards lower values of
the nonlinear parameter. There is also an anomalous reverse behavior for low
values of the cutoff frequency. | 0404001v1 |
2005-06-22 | A degenerate three-level laser with a parametric amplifier | The aim of this paper is to study the squeezing and statistical properties of
the light produced by a degenerate three-level laser whose cavity contains a
degenerate parametric amplifier. In this quantum optical system the top and
bottom levels of the three-level atoms injected into the laser cavity are
coupled by the pump mode emerging from the parametric amplifier. For a linear
gain coefficient of 100 and for a cavity damping constant of 0.8, the maximum
intracavity squeezing is found at steady state and at threshold to be 93%. | 0506178v3 |
2007-08-21 | Dimer diffusion in a washboard potential | The transport of a dimer, consisting of two Brownian particles bounded by a
harmonic potential, moving on a periodic substrate is investigated both
numerically and analytically. The mobility and diffusion of the dimer center of
mass present distinct properties when compared with those of a monomer under
the same transport conditions. Both the average current and the diffusion
coefficient are found to be complicated non-monotonic functions of the driving
force. The influence of dimer equilibrium length, coupling strength and damping
constant on the dimer transport properties are also examined in detail. | 0708.2858v2 |
2007-09-13 | Spin polarization in biased Rashba-Dresselhaus two-dimensional electron systems | Based on spin-charge coupled drift-diffusion equations, which are derived
from kinetic equations for the spin-density matrix in a rigorous manner, the
electric-field-induced nonequilibrium spin polarization is treated for a
two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit
coupling. Most emphasis is put on the consideration of the field-mediated spin
dynamics for a model with equal Rashba and Dresselhaus coupling constants, in
which the spin relaxation is strongly suppressed. Weakly damped
electric-field-induced spin excitations are identified, which remind of
space-charge waves in crystals. | 0709.2054v1 |
2007-12-31 | Quantum mechanics of the closed collapsing Universe | Two approaches to quantization of Freedman's closed Universe are compared. In
the first approach, the Shrodinger's norm of the wave function of Universe is
used, and in the second approach, the Klein-Gordon's norm is used. The second
one allows building the quasi-Heisenberg operators as functions of time and
finding their average values. It is shown that the average value of the
Universe scale factor oscillates with damping and approaches to some constant
value at the end of the Universe evolution. | 0801.0212v1 |
2008-04-08 | Quantum Cosmology and Tachyons | We discuss the relevance of the classical and quantum rolling tachyons
inflation in the frame of the standard, p-adic and adelic minisuperspace
quantum cosmology. The field theory of tachyon matter proposed by Sen in a
zero-dimensional version suggested by Kar leads to a model of a particle moving
in a constant external field with quadratic damping. We calculate the exact
quantum propagator of the model, as well as, the vacuum states and conditions
necessary to construct an adelic generalization. | 0804.1328v1 |
2008-04-24 | Confined gravitational waves for chiral matter with heat | The GR wave self-heating of geodesic massive bodies with constant
thermo-gravimechanical energies increases the brightness-to-charge ratio along
spiral radial transitions in the energy-to-energy gravitation. Paired confined
gravitons locally warm accelerated matter that suggests the thermodynamical
origin of electromagnetic outbursts with oscillating Wien's displacements.
Damping of orbital periods by chiral GR waves is more efficient for neutron
stars around giant companions than for binary pulsars. | 0804.3820v3 |
2008-05-08 | Dislocations in cubic crystals described by discrete models | Discrete models of dislocations in cubic crystal lattices having one or two
atoms per unit cell are proposed. These models have the standard linear
anisotropic elasticity as their continuum limit and their main ingredients are
the elastic stiffness constants of the material and a dimensionless periodic
function that restores the translation invariance of the crystal and influences
the dislocation size. For these models, conservative and damped equations of
motion are proposed. In the latter case, the entropy production and
thermodynamic forces are calculated and fluctuation terms obeying the
fluctuation-dissipation theorem are added. Numerical simulations illustrate
static perfect screw and 60$^\circ$ dislocations for GaAs and Si. | 0805.1221v1 |
2008-07-21 | The Analysis of Rotated Vector Field for the Pendulum | The pendulum, in the presence of linear dissipation and a constant torque, is
a non-integrable, nonlinear differential equation. In this paper, using the
idea of rotated vector fields, derives the relation between the applied force
$\beta$ and the periodic solution, and a conclusion that the critical value of
$\beta$ is a fixed one in the over damping situation. These results are of
practical significance in the study of charge-density waves in physics. | 0807.3288v2 |
2008-08-01 | Electric-field driven long-lived spin excitations on a cylindrical surface with spin-orbit interaction | Based on quantum-kinetic equations, coupled spin-charge drift-diffusion
equations are derived for a two-dimensional electron gas on a cylindrical
surface. Besides the Rashba and Dresselhaus spin-orbit interaction, the elastic
scattering on impurities, and a constant electric field are taken into account.
From the solution of the drift-diffusion equations, a long-lived spin
excitation is identified for spins coupled to the Rashba term on a cylinder
with a given radius. The electric-field driven weakly damped spin waves are
manifest in the components of the magnetization and have the potential for
non-ballistic spin-device applications. | 0808.0069v1 |
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