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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