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2020-05-11
Manipulating 1-dimensinal skyrmion motion by external magnetic field gradient
We have investigated an analytic formula of the 1-dimensional magnetic skyrmion dynamics under external magnetic field gradient. We find excellent agreement between the analytical model and micromagnetic simulation results for various magnetic parameters such as the magnetic field gradient, Gilbert damping constant. We also observe much faster velocity of the chiral domain wall (DW) motion. The chiral DW is exist with smaller interfacial Dzyaloshinskii-Moriya interaction energy density cases. These results provide to develop efficient control of skyrmion for spintronic devices.
2005.05011v1
2020-06-28
Physical pendulum model: Fractional differential equation and memory effects
A detailed analysis of three pendular motion models is presented. Inertial effects, self-oscillation, and memory, together with non-constant moment of inertia, hysteresis and negative damping are shown to be required for the comprehensive description of the free pendulum oscillatory regime. The effects of very high initial amplitudes, friction in the roller bearing axle, drag, and pendulum geometry are also analysed and discussed. The model that consists of a fractional differential equation provides both the best explanation of, and the best fits to, experimental high resolution and long-time data gathered from standard action-camera videos.
2006.15665v3
2020-08-01
Equilibration of the chiral asymmetry due to finite electron mass in electron-positron plasma
We calculate the rate of collisional decay of the axial charge in an ultrarelativistic electron-positron plasma, also known as the chirality flipping rate. We find that contrary to the existing estimates, the chirality flipping rate appears already in the first order in the fine-structure constant $\alpha$ and is therefore orders of magnitude greater than previously believed. The main channels for the rapid relaxation of the axial charge are the collinear emission of a weakly damped photon and the Compton scattering. The latter contributes to the $\mathcal{O}(\alpha)$ result because of the infrared divergence in its cross section, which is regularized on the soft scale $\sim eT$ due to the thermal corrections. Our results are important for the description of the early Universe processes (such as leptogenesis or magnetogenesis) that affect differently left- and right-chiral fermions of the Standard Model, as discussed in more details in the companion Letter.
2008.00360v2
2020-08-12
Effective Field Theory for Quasicrystals and Phasons Dynamics
We build an effective field theory (EFT) for quasicrystals -- aperiodic incommensurate lattice structures -- at finite temperature, entirely based on symmetry arguments and a well-define action principle. By means of Schwinger-Keldysh techniques, we derive the full dissipative dynamics of the system and we recover the experimentally observed diffusion-to-propagation crossover of the phason mode. From a symmetry point of view, the diffusive nature of the phason at long wavelengths is due to the fact that the internal translations, or phason shifts, are symmetries of the system with no associated Noether currents. The latter feature is compatible with the EFT description only because of the presence of dissipation (finite temperature) and the lack of periodic order. Finally, we comment on the similarities with certain homogeneous holographic models and we formally derive the universal relation between the pinning frequency of the phonons and the damping and diffusion constant of the phason.
2008.05339v2
2020-08-18
Research on rolling friction's dependence on ball bearings' radius
There are two alternative historical laws of rolling resistance formulated by French scientist Coulomb and Dupuit. It has been decided to verify experimentally again, which of these laws describes freely rolling ball bearings on a hard surface better. An inducement to carrying out the measurements was the idea of the constant thickness of roadbed, which is consistent with Dupuit's theory. Measurements have been done using the damped oscillations in the pendulum bearings. Results have shown better consistency with the Coulomb's theory with small, but measurable deviations. These deviations were successfully explained by the so called "Cobblestones model". Parameters designated by this model have been successfully verified by the surface roughness's profile measurement. An additional theoretical aspect of this work is distinguishing two types of rolling friction force: dynamical and kinematical in an analogy to two types of specific heat capacity in the thermodynamics of gases.
2008.08127v1
2020-08-28
Finding Small and Large k-Clique Instances on a Quantum Computer
Algorithms for triangle-finding, the smallest nontrivial instance of the k-clique problem, have been proposed for quantum computers. Still, those algorithms assume the use of fixed access time quantum RAM (QRAM). We present a practical gate-based approach to both the triangle-finding problem and its NP-hard k-clique generalization. We examine both constant factors for near-term implementation on a Noisy Intermediate Scale Quantum computer (NISQ) device, and the scaling of the problem to evaluate long-term use of quantum computers. We compare the time complexity and circuit practicality of the theoretical approach and actual implementation. We propose and apply two different strategies to the k-clique problem, examining the circuit size of Qiskit implementations. We analyze our implementations by simulating triangle finding with various error models, observing the effect on damping the amplitude of the correct answer, and compare to execution on six real IBMQ machines. Finally, we estimate the date when the methods proposed can run effectively on an actual device based on IBM's quantum volume exponential growth forecast and the results of our error analysis.
2008.12525v1
2020-09-02
Frustrated bearings
In a bearing state, touching spheres (disks in two dimensions) roll on each other without slip. Here we frustrate a system of touching spheres by imposing two different bearing states on opposite sides and search for the configurations of lowest energy dissipation. If the dissipation between contacts of spheres is viscous (with random damping constants), the angular momentum continuously changes from one bearing state to the other. For Coulomb friction (with random friction coefficients) in two dimensions, a sharp line separates the two bearing states and we show that this line corresponds to the minimum cut. Astonishingly however, in three dimensions, intermediate bearing domains, that are not synchronized with either side, are energetically more favorable than the minimum-cut surface. Instead of a sharp cut, the steady state displays a fragmented structure. This novel type of state of minimum dissipation is characterized by a spanning network of slipless contacts that reaches every sphere. Such a situation becomes possible because in three dimensions bearing states have four degrees of freedom.
2009.01295v1
2020-09-04
Scalar Perturbations of a Single-Horizon Regular Black Hole
We investigate the massless scalar field perturbations, including the quasinormal mode spectrum and the ringdown waveform, of a regular black hole spacetime that was derived via the Loop Quantum Gravity inspired polymer quantization of spherical $4$D black holes. In contrast to most, if not all, of the other regular black holes considered in the literature, the resulting nonsingular spacetime has a single bifurcative horizon and hence no mass inflation. In the interior, the areal radius decreases to a minimum given by the Polymerization constant, $k$, and then re-expands into a Kantowski-Sachs universe. We find indications that this black hole model is stable against small scalar perturbations. We also show that an increase in the magnitude of $k$ will decrease the height of the QNM potential and gives oscillations with lower frequency and less damping.
2009.02367v2
2020-09-22
Quasinormal modes of dirty black holes in the two-loop renormalizable effective gravity
We consider gravitational quasinormal modes of the static and spherically-symmetric dirty black holes in the effective theory of gravity which is renormalizable at the two-loop level. It is demonstrated that using the WKB-Pad\'e summation proposed in \cite{jaOp} one can achieve sufficient accuracy to calculate corrections to the complex frequencies of the quasinormal modes caused by the Goroff-Sagnotti curvature terms. It is shown that the Goroff-Sagnotti correction (with our choice of the sign of the coupling constant) increases damping of the fundamental modes (except for the lowest fundamental mode) and decreases their frequencies. We argue that the methods adopted in this paper can be used in the analysis of the influence of the higher-order curvature terms upon the quasinormal modes and in a number of related problems that require high accuracy.
2009.10793v1
2020-10-04
On the interaction problem between a compressible viscous fluid and a nonlinear thermoelastic plate
In this paper we study the interaction problem between a nonlinear thermoelastic plate and a compressible viscous fluid with the adiabatic constant $\gamma>12/7$. The existence of a weak solution for this problem is obtained by constructing a time-continuous operator splitting scheme that decouples the fluid and the structure. The fluid sub-problem is given on a fixed reference domain in the arbitrary Lagrangian-Eulerian (ALE) formulation, and the continuity equation is damped on this domain as well. This allows the majority of the analysis to be performed on the fixed reference domain, while the convergence of the approximate pressure is obtained on the physical domain.
2010.01639v1
2020-10-08
On the cost of Bayesian posterior mean strategy for log-concave models
In this paper, we investigate the problem of computing Bayesian estimators using Langevin Monte-Carlo type approximation. The novelty of this paper is to consider together the statistical and numerical counterparts (in a general log-concave setting). More precisely, we address the following question: given $n$ observations in $\mathbb{R}^q$ distributed under an unknown probability $\mathbb{P}_{\theta^\star}$ with $\theta^\star \in \mathbb{R}^d$ , what is the optimal numerical strategy and its cost for the approximation of $\theta^\star$ with the Bayesian posterior mean? To answer this question, we establish some quantitative statistical bounds related to the underlying Poincar\'e constant of the model and establish new results about the numerical approximation of Gibbs measures by Cesaro averages of Euler schemes of (over-damped) Langevin diffusions. These last results include in particular some quantitative controls in the weakly convex case based on new bounds on the solution of the related Poisson equation of the diffusion.
2010.06420v2
2020-10-28
Tunable plasmon modes in doped AA-stacked bilayer graphene
We study plasmon modes in doped AA-stacked bilayer graphene (BLG) within the nearest-neighbor tight-binding and the random phase approximation. We obtain closed analytical expressions for the polarizability function which are used to obtain the low-energy dispersion relations of and the numerical results for both acoustic and optical plasmon modes. Our result reveal the potential of AA-stacked BLG to be used as a tunable plasmonic device. In particular we find that the long-wavelength acoustic plasmon disperse as $\omega_{+}\approx\sqrt{max(|\mu|,t_{1})q}$ with a phase space which shrinks and vanishes as the chemical potential approaches the interlayer hopping energy, preventing the existence of long-lived acoustic plasmon. Furthermore, we show that AA-stacked BLG support coherent optical plasmon only when the condition $(1+\frac{g_{\sigma}g_{v}e^{2}t_{1}d}{\kappa v_{F}^{2}}\frac{|\mu|}{t_{1}})^{1/2}<\frac{|\mu|}{t_{1}}$ is satisfied, specially indicating Landau damping of the optical plasmon in undoped AA-staked BLG even at long-wavelength limit. We also find that the optical plasmon mode disperses as $\omega_{-}\approx \Delta+Cq^{2}$ with constants that can be tuned by tuning the chemical potential.
2010.14999v3
2020-11-04
EAdam Optimizer: How $ε$ Impact Adam
Many adaptive optimization methods have been proposed and used in deep learning, in which Adam is regarded as the default algorithm and widely used in many deep learning frameworks. Recently, many variants of Adam, such as Adabound, RAdam and Adabelief, have been proposed and show better performance than Adam. However, these variants mainly focus on changing the stepsize by making differences on the gradient or the square of it. Motivated by the fact that suitable damping is important for the success of powerful second-order optimizers, we discuss the impact of the constant $\epsilon$ for Adam in this paper. Surprisingly, we can obtain better performance than Adam simply changing the position of $\epsilon$. Based on this finding, we propose a new variant of Adam called EAdam, which doesn't need extra hyper-parameters or computational costs. We also discuss the relationships and differences between our method and Adam. Finally, we conduct extensive experiments on various popular tasks and models. Experimental results show that our method can bring significant improvement compared with Adam. Our code is available at https://github.com/yuanwei2019/EAdam-optimizer.
2011.02150v1
2020-11-16
Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell
We perform Hamiltonian reduction of a model in which 2+1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of $ADS^2$ -- both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of $ADS^2$ momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.
2011.07971v2
2020-11-23
Energy decay rates of solutions to a viscoelastic wave equation with variable exponents and weak damping
The goal of the present paper is to study the asymptotic behavior of solutions for the viscoelastic wave equation with variable exponents \[ u_{tt}-\Delta u+\int_0^tg(t-s)\Delta u(s)ds+a|u_t|^{m(x)-2}u_t=b|u|^{p(x)-2}u\] under initial-boundary condition, where the exponents $p(x)$ and $m(x)$ are given functions, and $a,~b>0$ are constants. More precisely, under the condition $g'(t)\le -\xi(t)g(t)$, here $\xi(t):\mathbb{R}^+\to\mathbb{R}^+$ is a non-increasing differential function with $\xi(0)>0,~\int_0^\infty\xi(s)ds=+\infty$, general decay results are derived. In addition, when $g$ decays polynomially, the exponential and polynomial decay rates are obtained as well, respectively. This work generalizes and improves earlier results in the literature.
2011.11185v1
2020-11-27
Eigenvalue-corrected Natural Gradient Based on a New Approximation
Using second-order optimization methods for training deep neural networks (DNNs) has attracted many researchers. A recently proposed method, Eigenvalue-corrected Kronecker Factorization (EKFAC) (George et al., 2018), proposes an interpretation of viewing natural gradient update as a diagonal method, and corrects the inaccurate re-scaling factor in the Kronecker-factored eigenbasis. Gao et al. (2020) considers a new approximation to the natural gradient, which approximates the Fisher information matrix (FIM) to a constant multiplied by the Kronecker product of two matrices and keeps the trace equal before and after the approximation. In this work, we combine the ideas of these two methods and propose Trace-restricted Eigenvalue-corrected Kronecker Factorization (TEKFAC). The proposed method not only corrects the inexact re-scaling factor under the Kronecker-factored eigenbasis, but also considers the new approximation method and the effective damping technique proposed in Gao et al. (2020). We also discuss the differences and relationships among the Kronecker-factored approximations. Empirically, our method outperforms SGD with momentum, Adam, EKFAC and TKFAC on several DNNs.
2011.13609v1
2020-12-12
Stabilized explicit Adams-type methods
In this work we present explicit Adams-type multistep methods with extended stability interval, which are analogous to the stabilized Chebyshev Runge--Kutta methods. It is proved that for any $k\geq 1$ there exists an explicit $k$-step Adams-type method of order one with stability interval of length $2k$. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In general case to construct a $k$-step method of order $p$ it is necessary to solve a constrained optimization problem in which the objective function and $p$ constraints are second degree polynomials in $k$ variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.
2012.06767v1
2020-12-18
Quantum friction in the Hydrodynamic Model
We study the phenomenon of quantum friction in a system consisting of a polarizable atom moving at a constant speed parallel to a metallic plate. The metal is described using a charged hydrodynamic model for the electrons. This model featuring long-range interactions is appropriate for a clean metal in a temperature range where scattering due to Coulomb interactions dominates over the scattering of electron by impurities. We find that a quantum friction force between the atom and the metal surface exists even in the absence of intrinsic damping in the metal, but that it only starts once the velocity of the atom exceeds the effective speed of sound in the metal. We argue that this condition can be fulfilled most easily in metals with nearly empty or nearly filled bands. We make quantitative predictions for the friction force to the second and fourth order in the atomic polarizability, and show that the threshold behavior persists to all orders of the perturbation theory.
2012.10204v1
2020-12-20
A new model with solitary waves: solution, stability and quasinormal modes
We construct solitary wave solutions in a $1+1$ dimensional massless scalar ($\phi$) field theory with a specially chosen potential $V(\phi)$. The equation governing perturbations about this solitary wave has an effective potential which is a simple harmonic well over a region, and a constant beyond. This feature allows us to ensure the stability of the solitary wave through the existence of bound states in the well, which can be found by semi-analytical methods. A further check on stability is performed through our search for quasi-normal modes (QNM) which are defined for purely outgoing boundary conditions. The time-domain profiles of the perturbations and the parametric variation of the QNM values are presented and discussed in some detail. Expectedly, a damped oscillatory temporal behaviour (ringdown) of the fluctuations is clearly seen through our analysis of the quasi-normal modes.
2012.10967v2
2020-12-29
Strongly modulated ultrafast demagnetization and magnetization precession dynamics in ferrimagnetic Gdx(CoFe)1-x alloys via 3d-4f intersublattice exchange coupling
Manipulation of the intersublattice interaction strengh (JRE-TM) in rare earth (RE)-transition metal (TM) alloys is a key issue to understand how efficiently the laser-induced angular momentum transfers from 3d to 4f spins and to have a better control of the ultrafast spin dynamics. In this work, the relationships between laser-induced demagnetization process and the intersublattice 3d-4f interaction for the GdCoFe alloys were systematically studied. The ultrafast two-stage demagnetization process could change into a one-stage mode as the angular momentum transferring channel between 3d and 4f spins is switched off, which could be modulated by JRE-TM. Furthermore, both the effective g-factor and damping constant deduced by the subsequently laser-induced magnetization precession process diverge at the angular momentum compensation point based on the ferromagnetic resonance method with the LLG equations. The results provide an alternative way to efficiently manipulate the ultrafast demagnetization time for practical applications.
2012.14620v1
2021-02-01
Contour Dynamics for One-Dimensional Vlasov-Poisson Plasma with the Periodic Boundary
We revisit the contour dynamics (CD) simulation method which is applicable to large deformation of distribution function in the Vlasov-Poisson plasma with the periodic boundary, where contours of distribution function are traced without using spatial grids. Novelty of this study lies in application of CD to the one-dimensional Vlasov-Poisson plasma with the periodic boundary condition. A major difficulty in application of the periodic boundary is how to deal with contours when they cross the boundaries. It has been overcome by virtue of a periodic Green's function, which effectively introduces the periodic boundary condition without cutting nor reallocating the contours. The simulation results are confirmed by comparing with an analytical solution for the piece-wise constant distribution function in the linear regime and a linear analysis of the Landau damping. Also, particle trapping by Langmuir wave is successfully reproduced in the nonlinear regime.
2102.00866v1
2021-02-01
Strong coupling of Fe-Co alloy with ultralow damping to superconducting co-planar waveguide resonators
We report on the strong coupling between a metallic ferromagnetic Fe75Co25 thin film patterned element and a range of superconducting Nb half-wavelength co-planar waveguide (CPW) resonators. By varying the volume of the ferromagnet we demonstrate that the coupling rate scales linearly with the square root of the number of spins and achieve a coupling rate over 700 MHz, approaching the ultrastrong coupling regime. Experiments varying the center conductor width while maintaining constant magnetic volume verify that decreasing the center conductor width increases coupling and cooperativity. Our results show that the frequency dependence of the coupling rate is linear with the fundamental and higher order odd harmonics of the CPW, but with differing efficiencies. The results show promise for scaling planar superconducting resonator/magnetic hybrid systems to smaller dimensions.
2102.01129v1
2021-02-15
Magnetodynamic properties of dipole-coupled 1D magnonic crystals
Magnonic crystals are magnetic metamaterials, that provide a promising way to manipulate magnetodynamic properties by controlling the geometry of the patterned structures. Here, we study the magnetodynamic properties of 1D magnonic crystals consisting of parallel NiFe strips with different strip widths and separations. The strips couple via dipole-dipole interactions. As an alternative to experiments and/or micromagnetic simulations, we investigate the accuracy of a simple macrospin model. For the case of simple strips, a model with a single free parameter to account for an overestimation of the out-of-plane demagnetization of the magnonic lattice is described. By adjusting this parameter a good fit with experimental as well as micromagnetic results is obtained. Moreover, the Gilbert damping is found independent of the lattice constant however the inhomogeneous linewidth broadening found to increase with decreasing stripe separation.
2102.07712v2
2021-03-11
The Debye Length and the Running Coupling of QCD: a Potential and Phenomenological Approach
In this paper, one uses a damped potential to present a description of the running coupling constant of QCD in the confinement phase. Based on a phenomenological perspective for the Debye screening length, one compares the running coupling obtained here with both the Brodsky-de T\'eramond-Deur and the Richardson approaches. The results seem to indicate the model introduced here corroborate the Richardson approach. Moreover, the Debye screening mass in the confinement phase depends on a small parameter, which tends to vanish in the non-confinement phase of QCD.
2103.06642v2
2021-03-16
Adapted gauge to small mass ratio binary black hole evolutions
We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $(\alpha_0,\beta_0)$, and use them as initial values for their evolutions. We also use a position and black hole mass dependent damping term, $\eta[\vec{x}_1(t),\vec{x}_2(t),m_1,m_2]$, in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a 7:1 mass ratio, and then use 15:1 and 32:1 binaries for a convergence study. Finally, we apply our new gauge to a 64:1 binary and a 128:1 binary to well cover the comparable and small mass ratio regimes.
2103.09326v1
2021-03-24
"Second-Order Primal'' + "First-Order Dual'' Dynamical Systems with Time Scaling for Linear Equality Constrained Convex Optimization Problems
Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical system with constant viscous damping and time scaling for the linear equality constrained convex optimization problem, which consists of a second-order ODE for the primal variable and a first-order ODE for the dual variable. When the scaling satisfies certain conditions, we prove its convergence property without assuming strong convexity. Even the convergence rate can become exponential when the scaling grows exponentially. We also show that the obtained convergence property of the dynamical system is preserved under a small perturbation.
2103.12931v3
2021-04-15
Evolution of Anti-de Sitter black holes in Einstein-Maxwell-dilaton theory
We study the nonlinear evolution of the spherical symmetric black holes under a small neutral scalar field perturbation in Einstein-Maxwell-dilaton theory with coupling function $f(\phi)=e^{-b\phi}$ in asymptotic anti-de Sitter spacetime. The non-minimal coupling between scalar and Maxwell fields allows the transmission of the energy from the Maxwell field to the scalar field, but also behaves as a repulsive force for the scalar. The scalar field oscillates with damping amplitude and converges to a final value by a power law. The irreducible mass of the black hole increases abruptly at initial times and then saturates to the final value exponentially. The saturating rate is twice the decaying rate of the dominant mode of the scalar. The effects of the black hole charge, the cosmological constant and the coupling parameter on the evolution are studied in detail. When the initial configuration is a naked singularity spacetime with a large charge to mass ratio, a horizon will form soon and hide the singularity.
2104.07281v1
2021-04-23
Well-posedness of a nonlinear shallow water model for an oscillating water column with time-dependent air pressure
We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow water equations in the presence of this device is reformulated as a transmission problem related to the interaction between waves and a fixed partially-immersed structure. By imposing the conservation of the total fluid-OWC energy in the non-damped scenario, we are able to derive a transmission condition that involves a time-dependent air pressure inside the chamber of the device, instead of a constant atmospheric pressure as in \cite{bocchihevergara2021}. We then show that the transmission problem can be reduced to a quasilinear hyperbolic initial boundary value problem with a semi-linear boundary condition determined by an ODE depending on the trace of the solution to the PDE at the boundary. Local well-posedness for general problems of this type is established via an iterative scheme by using linear estimates for the PDE and nonlinear estimates for the ODE.
2104.11570v3
2021-04-27
Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation
We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Green's function of the corresponding linear equation of arbitrary order $N$ is shown to be a sum of generalised hypergeometric functions. For suitably damped initial conditions we plot the time dependence of the Cauchy problem over a range of $N$ values. For $N=1$, we introduce a spatial forcing term. Using connections between the associated second order linear Schr\"{o}dinger and Fokker-Planck equations, we give closed form expressions for the corresponding Green's functions of the sinked Bessel process with constant drift. We then apply the Green's function to give time dependent profiles for the corresponding forced Burgers Cauchy problem.
2104.12976v1
2021-05-16
Time-dependent conformal transformations and the propagator for quadratic systems
The method proposed by Inomata and his collaborators allows us to transform a damped Caldiroli-Kanai oscillator with time-dependent frequency to one with constant frequency and no friction by redefining the time variable, obtained by solving a Ermakov-Milne-Pinney equation. Their mapping ``Eisenhart-Duval'' lifts as a conformal transformation between two appropriate Bargmann spaces. The quantum propagator is calculated also by bringing the quadratic system to free form by another time-dependent Bargmann-conformal transformation which generalizes the one introduced before by Niederer and is related to the mapping proposed by Arnold. Our approach allows us to extend the Maslov phase correction to arbitrary time-dependent frequency. The method is illustrated by the Mathieu profile.
2105.07374v4
2021-06-21
Universal many-body diffusion from momentum dephasing
The open dynamics of quantum many-body systems involve not only the exchange of energy, but also of other conserved quantities, such as momentum. This leads to additional decoherence, which may have a profound impact in the dynamics. Motivated by this, we consider a many-body system subject to total momentum dephasing and show that under very general conditions this leads to a diffusive component in the dynamics of any local density, even far from equilibrium. Such component will usually have an intricate interplay with the unitary dynamics. To illustrate this, we consider the case of a superfluid and show that momentum dephasing introduces a damping in the sound-wave dispersion relation, similar to that predicted by the Navier-Stokes equation for ordinary fluids. Finally, we also study the effects of dephasing in linear response, and show that it leads to a universal additive contribution to the diffusion constant, which can be obtained from a Kubo formula.
2106.10984v1
2021-06-23
The MGT-Fourier model in the supercritical case
We address the energy transfer in the differential system $$ \begin{cases} u_{ttt}+\alpha u_{tt} - \beta \Delta u_t - \gamma \Delta u = -\eta \Delta \theta \\ \theta_t - \kappa \Delta \theta =\eta \Delta u_{tt}+ \alpha\eta \Delta u_t \end{cases} $$ made by a Moore-Gibson-Thompson equation in the supercritical regime, hence antidissipative, coupled with the classical heat equation. The asymptotic properties of the related solution semigroup depend on the strength of the coupling, ruling the competition between the Fourier damping and the MGT antidamping. Exponential stability will be shown always to occur, provided that the coupling constant is sufficiently large with respect to the other structural parameters. A fact of general interest will be also discussed, namely, the impossibility of attaining the optimal exponential decay rate of a given dissipative system via energy estimates.
2106.12402v2
2021-07-07
Amplification of light scattering in arrays of nanoholes by plasmonic absorption-induced transparency
Absorption induced transparency is an optical phenomenon that occurs in metallic arrays of nanoholes when materials featuring narrow lines in their absorption spectra are deposited on top of it. First reported in the visible range, using dye lasers as cover materials, it has been described as transmission peaks unexpectedly close to the absorption energies of the dye laser. In this work, amplification of light is demonstrated in the active regime of absorption induced transparency. Amplification of stimulated emission can be achieved when the dye laser behaves as a gain material. Intense illumination can modify the dielectric constant of the gain material, which in turn, changes the propagation properties of the plasmonic modes excited in the hole arrays, providing both less damping to light and further feedback, enhancing the stimulated emission process.
2107.03135v1
2021-08-26
The Anomalous Transport of Tracers in Active Baths
We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects that alter fluctuations and lead to superdiffusion and friction that grows with time when the tracer is dragged at a constant speed. In the singular limit of a completely symmetric tracer, we recover normal diffusion and finite friction. Furthermore, for small symmetric tracers, the active contribution to the friction becomes negative: active particles enhance motion rather than oppose it. These results show that, in low-dimensional systems, the motion of a passive tracer in an active bath cannot be modeled as a persistent random walker with a finite correlation time.
2108.11970v3
2021-09-23
Constraining Time Dependent Dark Matter Signals from the Sun
Dark matter (DM) particles captured by the Sun can produce high energy electrons outside the Sun through annihilating into meta-stable mediators. The corresponding cosmic-ray electron signals observed by the space-based experiments will be time dependent due to the orbital motion of the space-based detectors. The shape of this time dependence is predictable given the orbital information of the detectors. Since the high-energy CR electron (with energy E>100 GeV) fluxes are expected to be constant in time, non-observation of such time variation can be used to place upper limits on the DM annihilation cross section. We analyze the time dependence of dark matter cosmic-ray signals in three space-based experiments: AMS-02, DAMPE and CALET. Under the assumption that no time dependent signal is observed, we derive the 95% C.L. exclusion limits on the signal strength from the current data. We map our limits onto the parameter space of the dark photon model and find that the constraints are comparable with that derived from the supernova SN1987A.
2109.11662v3
2021-11-01
Magnon-driven dynamics of frustrated skyrmion in synthetic antiferromagnets: Effect of skyrmion precession
A theoretical study on the interplay of frustrated skyrmion and magnons is useful for revealing new physics and future experiments design. In this work, we investigated the magnon-driven dynamics of frustrated skyrmion in synthetic antiferromagnets, focusing on the effect of skyrmion precession. It is theoretically revealed that the scattering cross section of the injected magnons depends on the skyrmion precession, which in turn effectively modulates the skyrmion Hall motion. Specifically, the Hall angle decreases as the precession speed increases, which is also verified by the atomistic micromagnetic simulations. Moreover, the precession speed and the Hall angle of the frustrated skyrmion depending on the magnon intensity and damping constant are simulated, demonstrating the effective suppression of the Hall motion by the skyrmion precession. This work provides a comprehensive understanding of the magnon-skyrmion scattering in frustrated magnets, benefiting future spintronic and magnonic applications.
2111.00738v1
2021-11-01
Safe Online Gain Optimization for Variable Impedance Control
Smooth behaviors are preferable for many contact-rich manipulation tasks. Impedance control arises as an effective way to regulate robot movements by mimicking a mass-spring-damping system. Consequently, the robot behavior can be determined by the impedance gains. However, tuning the impedance gains for different tasks is tricky, especially for unstructured environments. Moreover, online adapting the optimal gains to meet the time-varying performance index is even more challenging. In this paper, we present Safe Online Gain Optimization for Variable Impedance Control (Safe OnGO-VIC). By reformulating the dynamics of impedance control as a control-affine system, in which the impedance gains are the inputs, we provide a novel perspective to understand variable impedance control. Additionally, we innovatively formulate an optimization problem with online collected force information to obtain the optimal impedance gains in real-time. Safety constraints are also embedded in the proposed framework to avoid unwanted collisions. We experimentally validated the proposed algorithm on three manipulation tasks. Comparison results with a constant gain baseline and an adaptive control method prove that the proposed algorithm is effective and generalizable to different scenarios.
2111.01258v1
2021-11-15
Extremely confined gap plasmon modes: when nonlocality matters
Historically, the field of plasmonics has been relying on the framework of classical electrodynamics, with the local-response approximation of material response being applied even when dealing with nanoscale metallic structures. However, when approaching the atomic-scale confinement of the electromagnetic radiation, mesoscopic effects are anticipated to become observable, e.g., those associated with the nonlocal electrodynamic surface response of the electron gas. We investigate nonlocal effects in propagating gap surface plasmon modes in ultrathin metal--dielectric--metal planar waveguides, exploiting monocrystalline gold flakes separated by atomic-layer-deposited aluminum oxide. We use scanning near-field optical microscopy to directly access the near-field of such confined gap plasmon modes and measure their dispersion relation (via their complex-valued propagation constants). We compare our experimental findings with the predictions of the generalized nonlocal optical response theory to unveil signatures of nonlocal damping, which becomes appreciable for smaller dielectric gaps.
2111.07561v1
2021-11-16
Flow around topological defects in active nematic films
We study the active flow around isolated defects and the self-propulsion velocity of $+1/2$ defects in an active nematic film with both viscous dissipation (with viscosity $\eta$) and frictional damping $\Gamma$ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length $\ell_d=\sqrt{\eta/\Gamma}$ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the vortical flows around the defect is controlled by the system size $R$. In the presence of friction that leads to a finite value of $\ell_d$, the vorticity field decays to zero on the lengthscales larger than $\ell_d$. We show that the self-propulsion velocity of $+1/2$ defects grows with $R$ in small systems where $R<\ell_d$, while in the infinite system limit or when $R\gg \ell_d$, it approaches a constant value determined by $\ell_d$.
2111.08537v2
2021-12-01
Axial perturbations of hairy Gauss-Bonnet black holes with massive self-interacting scalar field
We study the axial quasinormal modes of hairy black holes in Gauss-Bonnet gravity with massive self-interacting scalar field. Two coupling functions of the scalar field to the Gauss-Bonnet invariant are adopted with one of them leading to black hole scalarization. The axial perturbations are studied via time evolution of the perturbation equation, and the effect of the scalar field mass and the self-interaction constant on the oscillation frequency and damping time is examined. We study as well the effect of nonzero scalar field potential on the critical point at which the perturbation equation loses hyperbolicity in the case of black hole scalarization. The results show that the non-zero scalar field potential extends the range of parameters where such loss of hyperbolicity is observed thus shrinking the region of stable black hole existence. This will have an important effect on the nonlinear dynamical simulation studies in massive scalar Gauss-Bonnet gravity.
2112.00703v1
2021-12-20
Adversarially Robust Stability Certificates can be Sample-Efficient
Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust control, we consider additive and Lipschitz bounded adversaries that perturb the system dynamics. We show that under suitable assumptions of incremental stability on the underlying system, the statistical cost of learning an adversarial stability certificate is equivalent, up to constant factors, to that of learning a nominal stability certificate. Our results hinge on novel bounds for the Rademacher complexity of the resulting adversarial loss class, which may be of independent interest. To the best of our knowledge, this is the first characterization of sample-complexity bounds when performing adversarial learning over data generated by a dynamical system. We further provide a practical algorithm for approximating the adversarial training algorithm, and validate our findings on a damped pendulum example.
2112.10690v1
2022-02-10
Amplifying spin waves along Néel domain wall by spin-orbit torque
Traveling spin waves in magnonic waveguides undergo severe attenuation, which tends to result in a finite propagation length of spin waves, even in magnetic materials with the accessible lowest damping constant, heavily restricting the development of magnonic devices. Compared with the spin waves in traditional waveguides, propagating spin waves along strip domain wall are expected to exhibit enhanced transmission. Here, we demonstrate, theoretically and through micromagnetic simulations, that spin-orbit torque associated with a ferromagnet/heavy metal bilayer can efficiently control the attenuation of spin waves along a N\'eel-type strip domain wall, despite the complexity in the ground-state magnetization configuration. The direction of the electric current applied to the heavy-metal layer determines whether these spin waves are amplified or further attenuated otherwise. Remarkably, our simulations reveal that the effective current densities required to efficiently tune the decay of such spin waves are just ~10^10 Am-2, roughly an order smaller than those required in conventional spin waveguides. Our results will enrich the toolset for magnonic technologies.
2202.05181v1
2022-03-06
Elongated Skyrmion as Spin Torque Nano-Oscillator and Magnonic Waveguide
Spin torque nano-oscillator has been extensively studied both theoretically and experimentally in recent decades due to its potential applications in future microwave communication technology and neuromorphic computing. In this work, we present a skyrmion-based spin torque nano-oscillator driven by a spatially uniform direct current, where the skyrmion is confined by two pinning sites. Different from other skyrmion-based oscillators that arise from the circular motion or the breathing mode of a skyrmion, the steady-state oscillatory motions are produced by the periodic deformation of an elongated skyrmion. Through micromagnetic simulations, we find that the oscillation frequency depends on the driving current, the damping constant as well as the characteristics of pinning sites. This nonlinear response to direct current turns out to be universal and can also appear in the case of antiskyrmions, skyrmioniums and domain walls. Furthermore, the elongated skyrmion possesses a rectangle-like domain wall, which could also serve as a magnonic waveguide. Utilizing the propagation of spin waves in this waveguide, we propose a device design of logic gate and demonstrate its performance.
2203.02969v2
2022-03-11
Absence of Walker breakdown in the dynamics of chiral Neel domain walls driven by in-plane strain gradients
We investigate theoretically the motion of chiral N\'eel domain walls in perpendicularly magnetized systems driven by in-plane strain gradients. We show that such strain drives domain walls efficiently towards increasing tensile (compressive) strain for positive (negative) magnetostrictive materials. During their motion a local damping torque that opposes the precessional torque due to the strain gradient arises. This torque prevents the onset of turbulent dynamics, and steady domain wall motion with constant velocity is asymptotically reached for any arbitrary large strain gradient. Withal, velocities in the range of 500 m/s can be obtained using voltage-induced strain under realistic conditions.
2203.05826v1
2022-06-28
Origin of the spontaneous oscillations in a simplified coagulation-fragmentation system driven by a source
We consider a system of aggregated clusters of particles, subjected to coagulation and fragmentation processes with mass dependent rates. Each monomer particle can aggregate with larger clusters, and each cluster can fragment into individual monomers with a rate directly proportional to the aggregation rate. The dynamics of the cluster densities is governed by a set of Smoluchowski equations, and we consider the addition of a source of monomers at constant rate. The whole dynamics can be reduced to solving a unique non-linear differential equation which displays self-oscillations in a specific range of parameters, and for a number of distinct clusters in the system large enough. This collective phenomenon is due to the presence of a fluctuating damping coefficient and is closely related to the Li\'enard self-oscillation mechanism observed in a more general class of physical systems such as the van der Pol oscillator.
2206.13884v1
2022-06-29
Strongly coupled quantum Otto cycle with single qubit bath
We discuss a model of a closed quantum evolution of two-qubits where the joint Hamiltonian is so chosen that one of the qubits acts as a bath and thermalize the other qubit which is acting as the system. The corresponding exact master equation for the system is derived. Interestingly, for a specific choice of parameters the master equation takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients, representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite bath including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for heat engine regime (refrigerator regime) for different modifications of the joint Hamiltonian.
2206.14751v1
2022-07-24
Revisiting the central limit theorems for the SGD-type methods
We revisited the central limit theorem (CLT) for stochastic gradient descent (SGD) type methods, including the vanilla SGD, momentum SGD and Nesterov accelerated SGD methods with constant or vanishing damping parameters. By taking advantage of Lyapunov function technique and $L^p$ bound estimates, we established the CLT under more general conditions on learning rates for broader classes of SGD methods compared with previous results. The CLT for the time average was also investigated, and we found that it held in the linear case, while it was not generally true in nonlinear situation. Numerical tests were also carried out to verify our theoretical analysis.
2207.11755v3
2022-08-09
Parameter Estimation in Ill-conditioned Low-inertia Power Systems
This paper examines model parameter estimation in dynamic power systems whose governing electro-mechanical equations are ill-conditioned or singular. This ill-conditioning is because of converter-interfaced power systems generators' zero or small inertia contribution. Consequently, the overall system inertia decreases, resulting in low-inertia power systems. We show that the standard state-space model based on least squares or subspace estimators fails to exist for these models. We overcome this challenge by considering a least-squares estimator directly on the coupled swing-equation model but not on its transformed first-order state-space form. We specifically focus on estimating inertia (mechanical and virtual) and damping constants, although our method is general enough for estimating other parameters. Our theoretical analysis highlights the role of network topology on the parameter estimates of an individual generator. For generators with greater connectivity, estimation of the associated parameters is more susceptible to variations in other generator states. Furthermore, we numerically show that estimating the parameters by ignoring their ill-conditioning aspects yields highly unreliable results.
2208.04471v1
2022-08-09
Driven particle dispersion in narrow disordered racetracks
We study the disorder-induced deterministic dispersion of particles uniformly driven in an array of narrow tracks. For different toy models with quenched disorder we obtain exact analytical expressions for the steady-state mean velocity $v$ and the dispersion constant $D$ for any driving force $f$ above a putative depinning threshold. For short-range correlated pinning forces we find that at large drives $D\sim 1/v$ for random-field type of disorder while $D \sim 1/v^3$ for the random-bond type. We show numerically that these results are robust: the same scaling holds for models of massive damped particles, soft particles, particles in quasi-one dimensional or two dimensional tracks, and for a model of a magnetic domain wall with two degrees of freedom driven either by electrical current or magnetic field. Crossover and finite temperature effects are discussed. The universal features we identify may be relevant for describing the fluctuating dynamics of stable localized objects such solitons, superconducting vortices, magnetic domain walls and skyrmions, and colloids driven in quasi one-dimensional track arrays. In particular, the drive dependence of $D$ appears as a sensitive tool for characterizing and assessing the nature of disorder in the host materials.
2208.05031v2
2022-09-19
Stationary states of an active Brownian particle in a harmonic trap
We study the stationary states of an over-damped active Brownian particle (ABP) in a harmonic trap in two dimensions, via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with a certain velocity, whose magnitude is constant, but its direction is subject to Brownian rotation. In the limit where translational diffusion is negligible, the stationary distribution of the particle's position shows a transition between two different shapes, one with maximum and the other with minimum density at the centre, as the trap stiffness is increased. We show that this non-intuitive behaviour is captured by the relevant Fokker-Planck equation, which, under minimal assumptions, predicts a continuous ``phase transition" between the two different shapes. As the translational diffusion coefficient is increased, both these distributions converge into the equilibrium, Boltzmann form. Our simulations support the analytical predictions, and also show that the probability distribution of the orientation angle of the self-propulsion velocity undergoes a transition from unimodal to bimodal forms in this limit. We also extend our simulations to a three dimensional trap, and find similar behaviour.
2209.09184v2
2022-09-25
The Design of Observational Longitudinal Studies
This paper considers the design of observational longitudinal studies with a continuous response and a binary time-invariant exposure, where, typically, the exposure is unbalanced, the mean response in the two groups differs at baseline and the measurement times might not be the same for all participants. We consider group differences that are constant and those that increase linearly with time. We study power, number of study participants (N) and number of repeated measures (r), and provide formulas for each quantity when the other two are fixed, for compound symmetry, damped exponential and random intercepts and slopes covariances. When both N and r can be chosen by the investigator, we study the optimal combination for maximizing power subject to a cost constraint and minimizing cost for fixed power. Intuitive parameterizations are used for all quantities. All calculations are implemented in freely available software.
2209.12129v1
2022-10-09
How general is the strong cosmic censorship bound for quasinormal modes?
Hod's proposal claims that the least damped quasinormal mode of a black hole must have the imaginary part smaller than half of the surface gravity at the event horizon. The Strong Cosmic Censorship in General Relativity implies that this bound must be even weaker: half of the surface gravity at the Cauchy horizon. The appealing question is whether these bounds are limited by the Einstein theory only? Here we will present numerical evidence that once the black hole size is much smaller than then the radius of the cosmological horizon, both the Hod's proposal and the strong cosmic censorship bound for quasinormal modes are satisfied for general spherically symmetric black holes in an arbitrary metric theory of gravity. The low-lying quasinormal frequencies have the universal behavior in this regime and do not depend on the near-horizon geometry, but only on the asymptotic parameters: the value of the cosmological constant and black hole mass.
2210.04314v2
2022-12-12
Solving the Teukolsky equation with physics-informed neural networks
We use physics-informed neural networks (PINNs) to compute the first quasi-normal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the \texttt{PyTorch} framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasi-normal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved.
2212.06103v2
2023-01-27
Thermal curvature perturbations in thermal inflation
We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature $T_c$, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for $T>T_c$. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below $T_c$, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.
2301.11666v1
2023-02-20
Adiabatic computing for optimal thermodynamic efficiency of information processing
Landauer's principle makes a strong connection between information theory and thermodynamics by stating that erasing a one-bit memory at temperature $T_0$ requires an average energy larger than $W_{LB}=k_BT_0 \ln2$, with $k_B$ Boltzmann's constant. This tiny limit has been saturated in model experiments using quasi-static processes. For faster operations, an overhead proportional to the processing speed and to the memory damping appears. In this article, we show that underdamped systems are a winning strategy to reduce this extra energetic cost. We prove both experimentally and theoretically that, in the limit of vanishing dissipation mechanisms in the memory, the physical system is thermally insulated from its environment during fast erasures, i.e. fast protocols are adiabatic as no heat is exchanged with the bath. Using a fast optimal erasure protocol we also show that these adiabatic processes produce a maximum adiabatic temperature $T_a=2T_0$, and that Landauer's bound for fast erasures in underdamped systems becomes the adiabatic bound: $W_a = k_B T_0$.
2302.09957v2
2023-03-12
Can gravitational vacuum condensate stars be a dark energy source?
Gravitational vacuum condensate stars, also known as gravastars, have been proposed as an alternative to black holes. Their interior contains a perfect fluid with an equation of state akin to that of a cosmological constant. For this reason, they have recently been considered as a possible astrophysical source of dark energy. In this work we argue that gravitational vacuum condensate stars cannot be the source of dark energy and highlight that a direct coupling of their mass to the dynamics of the Universe would lead to an additional velocity dependent acceleration, damping their motion with respect to the cosmological frame. We briefly discuss the potential impact of this additional acceleration in the context of a recent proposal that the observed mass growth of compact objects at the core of elliptical galaxies might result from such a cosmological coupling.
2303.06630v1
2023-03-23
A Computational Study of Cluster Dynamics in Structural Lubricity: Role of Cluster Rotation
We present a computational study of sliding between gold clusters and a highly oriented pyrolytic graphite substrate, a material system that exhibits ultra-low friction due to structural lubricity. By means of molecular dynamics, it is found that clusters may undergo spontaneous rotations during manipulation as a result of elastic instability, leading to attenuated friction due to enhanced interfacial incommensurability. In the case of a free cluster, shear stresses exhibit a non-monotonic dependency on the strength of the tip-cluster interaction, whereby rigid clusters experience nearly constant shear stresses. Finally, it is shown that the suppression of the translational degrees of freedom of a cluster's outermost-layer can partially annihilate out-of-plane phonon vibrations, which leads to a reduction of energy dissipation that is in compliance with Stokesian damping. It is projected that the physical insight attained by the study presented here will result in enhanced control and interpretation of manipulation experiments at structurally lubric contacts.
2303.13707v1
2023-04-12
Using Demand Response to Improve Power System Small-Signal Stability
With the increase of uncertain and intermittent renewable energy supply on the grid, the power system has become more vulnerable to instability. In this paper, we develop a demand response strategy to improve power system small-signal stability. We pose the problem as an optimization problem wherein the total demand-responsive load is held constant at each time instance but shifted between different buses to improve small-signal stability, which is measured by small-signal stability metrics that are functions of subsets of the system's eigenvalues, such as the smallest damping ratio. To solve the problem, we use iterative linear programming and generalized eigenvalue sensitivities. We demonstrate the approach via a case study that uses the IEEE 14-bus system. Our results show that shifting the load between buses, can improve a small-signal stability margin. We explore the use of models of different fidelity and find that it is important to include models of the automatic voltage regulators and power system stabilizers. In addition, we show that load shifting can achieve similar improvements to generation shifting and better improvement than simply tuning power system stabilizers.
2304.05573v2
2023-04-19
Memory-induced oscillations of a driven particle in a dissipative correlated medium
The overdamped dynamics of a particle is in general affected by its interaction with the surrounding medium, especially out of equilibrium, and when the latter develops spatial and temporal correlations. Here we consider the case in which the medium is modeled by a scalar Gaussian field with relaxational dynamics, and the particle is dragged at constant velocity through the medium by a moving harmonic trap. This mimics the setting of an active microrheology experiment conducted in a near-critical medium. When the particle is displaced from its average position in the nonequilibrium steady state, its subsequent relaxation is shown to feature damped oscillations. This is similar to what has been recently predicted and observed in viscoelastic fluids, but differs from what happens in the absence of driving or for an overdamped Markovian dynamics, in which cases oscillations cannot occur. We characterize these oscillating modes in terms of the parameters of the underlying mesoscopic model for the particle and the medium, confirming our analytical predictions via numerical simulations.
2304.09684v2
2023-05-03
Solving irreducible stochastic mean-payoff games and entropy games by relative Krasnoselskii-Mann iteration
We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying irreducibility conditions. We show in particular that an $\epsilon$-approximation of the value of an irreducible concurrent stochastic game can be computed in a number of iterations in $O(|\log\epsilon|)$ where the constant in the $O(\cdot)$ is explicit, depending on the smallest non-zero transition probabilities. This should be compared with a bound in $O(|\epsilon|^{-1}|\log(\epsilon)|)$ obtained by Chatterjee and Ibsen-Jensen (ICALP 2014) for the same class of games, and to a $O(|\epsilon|^{-1})$ bound by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We also establish parameterized complexity bounds for entropy games, a class of matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn and Kozyakin. We derive these results by methods of variational analysis, establishing contraction properties of the relative Krasnoselskii-Mann iteration with respect to Hilbert's semi-norm.
2305.02458v1
2023-05-14
Adiabatic manipulation of a system interacting with a spin-bath
Stimulated Raman Adiabatic Passage, a very efficient technique for manipulating a quantum system based on the adiabatic theorem, is analyzed in the case where the manipulated physical system is interacting with a spin bath. Exploitation of the rotating wave approximation allows for the identification of a constant of motion which simplifies both the analytical and the numerical treatment, which allows for evaluating the total unitary evolution of system and bath. The efficiency of the population transfer process is investigated in several regimes, including the weak and strong coupling with the environment and the off-resonance. The formation of appropriate Zeno subspaces explains the lowering of the efficiency in the strong damping regime.
2305.08209v3
2023-06-08
Energy Efficient Skyrmion based Oscillator on Thermocoupled Nanotrack
The magnetic skyrmion-based spin transfer nano-oscillators (STNO) are the potential candidates for next-generation microwave signal generator and has gained popularity due to their performance, integrability and compatibility with existing CMOS technology. However, these devices suffer from the Joule heating problem that neglects their non-volatility advantage in spintronic devices. Therefore, it is necessary to investigate the alternative driving mechanisms for the development of energy-efficient skyrmion based nano-oscillators. In this paper, a skyrmion-based nano-oscillator has been designed that utilizes thermal power to drive skyrmion on a thermocoupled nanotrack. The thermocoupled nanotrack is designed in such a way that both the upper and lower nanotracks have different values of damping constants and a temperature difference is maintained between the extreme ends, in order to create a temperature gradient in the two nanotracks. By employing this technique, skyrmion is able to exhibit the periodic motion on the nanotrack with the maximum achievable frequency of 2.5GHz without any external stimuli. Moreover, the proposed device offers low thermal energy consumption of 0.84fJ/oscillation. Hence, this work provides the pathway for the development of energy-efficient future spintronic devices.
2306.05164v1
2023-08-31
Apply Non-Hermitian Physics to Realize Ultra-High-Quality Factors of Optically Trapped Particles
Optical trapping and binding systems are non-Hermitian. On one hand, the optical force is non-Hermitian and may pump energy into the trapped particle when the non-Hermiticity is sufficiently large. On the other hand, the ambient damping constitutes a loss to the particle. Here, we show that in a low-friction environment, the interplay between the energy pumped-in by light and the ambient dissipation can give rise to either instability or a periodic vibration characterized by a finite quality factor (Q-factor). Through a comprehensive exploration, we analyze the influence of various parameters on the non-Hermitian force field. Our investigation reveals several strategies for enhancing the non-Hermitian force field, such as augmenting particle radius and refractive index, utilizing triangular lattice optical clusters, and reducing lattice constants.
2308.16502v1
2023-09-06
BV solutions to a hyperbolic system of balance laws with logistic growth
We study BV solutions for a $2\times2$ system of hyperbolic balance laws. We show that when initial data have small total variation on $(-\infty,\infty)$ and small amplitude, and decay sufficiently fast to a constant equilibrium state as $|x|\rightarrow\infty$, a Cauchy problem (with generic data) has a unique admissible BV solution defined globally in time. Here the solution is admissible in the sense that its shock waves satisfy the Lax entropy condition. We also study asymptotic behavior of solutions. In particular, we obtain a time decay rate for the total variation of the solution, and a convergence rate of the solution to its time asymptotic solution. Our system is a modification of a Keller-Segel type chemotaxis model. Its flux function possesses new features when comparing to the well-known model of Euler equations with damping. This may help to shed light on how to extend the study to a general system of hyperbolic balance laws in the future.
2309.03129v1
2023-10-09
Anomaly and Brownian fluid particle in Navier-Stokes turbulence
We investigate the Navier-Stokes turbulence driven by a stochastic random Gaussian force. Using a field-theoretic approach, we uncover an anomaly that brings hidden structure to the theory. The anomaly is generated by a non-self-adjoint operator of the Jacobian and it follows the symmetries of the stochastic Navier-Stokes equation. We calculate the anomaly and demonstrate that by forcing the anomaly to vanish, the velocity field is constrained and a monopole-type object with a constant charge is formed. When the viscosity is zero, the anomaly can be interpreted as the Brownian damping coefficient of a random fluid particle. We provide the Brownian particle equation and its solution in the presence of a pump and viscosity. Our results suggest that the anomaly is an inherent feature of stochastic turbulence and must be taken into account in all stochastic turbulence calculations. This constitutes an additional law for the original set of stochastic Navier-Stokes equations.
2310.06007v3
2023-11-02
A Novel Adaptive Inertia Strategy in Large-Scale Electric Power Grids
The increasing penetration of new renewable sources of energy in today's power grids is accompanied by a decrease in available electromechanical inertia. This leads to a reduced dynamical stability. To counterbalance this effect, virtual synchronous generators have been proposed to emulate conventional generators and provide inertia to power systems. The high flexibility of these devices makes it possible to control the synthetic inertia they provide and to have them operate even more efficiently than the electromechanical inertia they replace. Here, we propose a novel control scheme for virtual synchronous generators, where the amount of inertia provided is large at short times - thereby absorbing local faults and disturbances as efficiently as conventional generators - but decreases over a tunable time interval to prevent long-time coherent oscillations from setting in. This new model is used to investigate the effect of adaptive inertia on large-scale power grids. Our model outperforms conventional constant inertia in all scenarios and for all performance measures considered. We show how an optimized geographical distribution of adaptive inertia devices not only effectively absorbs local faults, but also significantly improves the damping of inter-area oscillations.
2311.01350v1
2023-11-19
Two-step BEC coming from a temperature dependent energy gap
We report the effects on the thermodynamic properties of a 3D Bose gas caused by a temperature dependent energy gap $\Delta (T)$ at the lower edge of the energy spectrum of the particles constituting the Bose gas which behaves like an ideal Bose gas when the gap is removed. Explicit formulae are given for the critical temperature, the condensate fraction, the internal energy and the isochoric specific heat, which are calculated for three different gaps that abruptly go to zero at temperature $T_B$, as well as for the damped counterparts whose drop to zero we have smoothed. In particular, for the undamped BCS (Bardeen, Cooper and Schrieffer) gap it is observed that the Bose-Einstein condensation (BEC) critical temperature $T_c$ is equal to that of the ideal Bose gas $T_0$, for all $T_B \leq T_0$; surprisingly, the condensate fraction presents two different filling rates of the ground state at $T_c = T_0$ and at $T_B < T_0$; while the specific heat shows a finite jump at $T_c$ as well as a divergence at $T_B$. Three-dimensional infinite Bose gas results are recovered when the temperature independent gap is either a constant or equal to zero.
2311.11447v1
2024-02-08
Numerical solution of the Newtonian plane Couette flow with linear dynamic wall slip
An efficient numerical approach based on weighted average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed plate, and the motion is triggered by the motion of the other plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion.
2402.05736v1
2024-02-09
Local exact controllability to the trajectories of the convective Brinkman-Forchheimer equations
In this article, we discuss the local exact controllability to trajectories of the following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) defined in a bounded domain $\Omega \subset\mathbb{R}^d$ ($d=2,3$) with smooth boundary: \begin{align*} \frac{\partial\boldsymbol{u}}{\partial t}-\mu \Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{2}\boldsymbol{u}+\nabla p=\boldsymbol{f}+\boldsymbol{\vartheta}, \ \ \ \nabla\cdot\boldsymbol{u}=0, \end{align*} where the control $\boldsymbol{\vartheta}$ is distributed in a subdomain $\omega \subset \Omega$, and the parameters $\alpha,\beta,\mu>0$ are constants. We first present global Carleman estimates and observability inequality for the adjoint problem of a linearized version of CBF equations by using a global Carleman estimate for the Stokes system. This allows us to obtain its null controllability at any time $T>0$. We then use the inverse mapping theorem to deduce local results concerning the exact controllability to the trajectories of CBF equations.
2402.06335v1
2024-03-15
Beam Dynamics Framework Incorporating Acceleration to Define the Minimum Aperture in Two Focusing Schemes for Proton Radiotherapy Linac
In this paper, a self-consistent transverse beam dynamics framework is demonstrated, that incorporates acceleration into the transverse beam dynamics studies for a proton linac machine. Two focusing schemes are developed and discussed; the FODO-like scheme, and the minimum aperture scheme. The FODO-like scheme is a simple scheme, requiring only one quadrupole per cavity. The scheme is analytically solved to minimise the beam size at the cavity entrance/exit and ensures a constant beam size along the lattice, with respect to adiabatic damping due to longitudinally accelerating rf cavities. The minimum aperture scheme describes the regime that matches the beam ellipse to the acceptance ellipse of a cavity, allowing for the smallest possible aperture, for a given cavity length. A simple approximation of an rf cavity map is determined to allow changes in particle energy along a lattice, and acceleration is assumed only in the longitudinal direction.
2403.10212v1
2024-03-19
Unraveling the dynamics of magnetization in topological insulator-ferromagnet heterostructures via spin-orbit torque
Spin-orbit coupling stands as a pivotal determinant in the realm of condensed matter physics. In recent, its profound influence on spin dynamics opens up a captivating arena with promising applications. Notably, the topological insulator-ferromagnet heterostructure has been recognized for inducing spin dynamics through applied current, driven by spin-orbit torque. Building upon recent observations revealing spin flip signals within this heterostructure, our study elucidates the conditions governing spin flips by studying the magnetization dynamics. We establish that the interplay between spin-anisotropy and spin-orbit torque plays a crucial role in shaping the physics of magnetization dynamics within the heterostructure. Furthermore, we categorize various modes of magnetization dynamics, constructing a comprehensive phase diagram across distinct energy scales, damping constants, and applied frequencies. This research not only offers insights into controlling spin direction but also charts a new pathway to the practical application of spin-orbit coupled systems.
2403.12701v1
2024-03-25
Detection of spin pumping free of rectification and thermal artefacts in molecular-based ferromagnetic insulator V[TCNE]x~2
The molecular-based ferrimagnetic insulator V(TCNE)x has gained recent interest for efficient spin-wave excitation due to its low Gilbert damping ratio a=4E-5, and narrow ferromagnetic resonance linewidth f=1Oe. Here we report a clean spin pumping signal detected on V(TCNE)x/metal bilayer structures, free from spin rectification or thermal artifacts. On-chip coupling of microwave power is achieved via a coplanar waveguide to measure the in-plane angle-dependence of the inverse spin-Hall effect under ferromagnetic resonance conditions with respect to a constant external magnetic field. A signature of pure spin current from V(TCNE)x is observed in both platinum and permalloy metal layers, demonstrating the utility of V(TCNE)x for magnon spintronics studies in molecule/solid-state heterostructures.
2403.16429v2
2024-03-28
Quantum asymptotic amplitude for quantum oscillatory systems from the Koopman operator viewpoint
We have recently proposed a fully quantum-mechanical definition of the asymptotic phase for quantum nonlinear oscillators, which is also applicable in the strong quantum regime [Kato and Nakao 2022 Chaos 32 063133]. In this study, we propose a definition of the quantum asymptotic amplitude for quantum oscillatory systems, which extends naturally the definition of the asymptotic amplitude for classical nonlinear oscillators on the basis of the Koopman operator theory. We introduce the asymptotic amplitude for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the largest non-zero real eigenvalue. Using examples of the quantum van der Pol oscillator with the quantum Kerr effect, exhibiting quantum limit-cycle oscillations, and the quantum van der Pol model with the quantum squeezing and degenerate parametric oscillator with nonlinear damping, exhibiting quantum noise-induced oscillations, we illustrate that the proposed quantum asymptotic amplitude appropriately yields isostable amplitude values that decay exponentially with a constant rate.
2403.19297v1
2024-04-05
Stability Analysis of Adaptive Model Predictive Control Using the Circle and Tsypkin Criteria
Absolute stability is a technique for analyzing the stability of Lur'e systems, which arise in diverse applications, such as oscillators with nonlinear damping or nonlinear stiffness. A special class of Lur'e systems consists of self-excited systems (SES), in which bounded oscillations arise from constant inputs. In many cases, SES can be stabilized by linear controllers, which motivates the present work, where the goal is to evaluate the effectiveness of adaptive model predictive control for Lur'e systems. In particular, the present paper considers predictive cost adaptive control (PCAC), which is equivalent to a linear, time-variant (LTV) controller. A closed-loop Lur'e system comprised of the positive feedback interconnection of the Lur'e system and the PCAC-based controller can thus be derived at each step. In this work, the circle and Tsypkin criteria are used to evaluate the absolute stability of the closed-loop Lur'e system, where the adaptive controller is viewed as instantaneously linear time-invariant. When the controller converges, the absolute stability criteria guarantee global asymptotic stability of the asymptotic closed-loop dynamics.
2404.04170v1
1999-08-16
Thermal Equilibrium Curves and Turbulent Mixing in Keplerian Accretion Disks
We consider vertical heat transport in Keplerian accretion disks, including the effects of radiation, convection, and turbulent mixing driven by the Balbus-Hawley instability, in astronomical systems ranging from dwarf novae (DNe), and soft X-ray transients (SXTs), to active galactic nuclei (AGN). We propose a modified, anisotropic form of mixing-length theory, which includes radiative and turbulent damping. We also include turbulent heat transport, which acts everywhere within disks, regardless of whether or not they are stably stratified, and can move entropy in either direction. We have generated a series of vertical structure models and thermal equilibrium curves using the scaling law for the viscosity parameter $\alpha$ suggested by the exponential decay of the X-ray luminosity in SXTs. We have also included equilibrium curves for DNe using an $\alpha$ which is constant down to a small magnetic Reynolds number ($\sim 10^4$). Our models indicate that weak convection is usually eliminated by turbulent radial mixing. The substitution of turbulent heat transport for convection is more important on the unstable branches of thermal equilibrium S-curves when $\alpha$ is larger. The low temperature turnover points $\Sigma_{max}$ on the equilibrium S-curves are significantly reduced by turbulent mixing in DNe and SXT disks. However, in AGN disks the standard mixing-length theory for convection is still a useful approximation when we use the scaling law for $\alpha$, since these disks are very thin at the relevant radii. In accordance with previous work, we find that constant $\alpha$ models give almost vertical S-curves in the $\Sigma-T$ plane and consequently imply very slow, possibly oscillating, cooling waves.
9908166v1
2005-01-10
On variations in the fine-structure constant and stellar pollution of quasar absorption systems
At redshifts z_abs < 2, quasar absorption-line constraints on space-time variations in the fine-structure constant, alpha, rely on the comparison of MgII and FeII transition wavelengths. One potentially important uncertainty is the relative abundance of Mg isotopes in the absorbers which, if different from solar, can cause spurious shifts in the measured wavelengths and, therefore, alpha. Here we explore chemical evolution models with enhanced populations of intermediate-mass (IM) stars which, in their asymptotic giant branch (AGB) phase, are thought to be the dominant factories for heavy Mg isotopes at the low metallicities typical of quasar absorption systems. By design, these models partially explain recent Keck/HIRES evidence for a smaller alpha in z_abs < 2 absorption clouds than on Earth. However, such models also over-produce N, violating observed abundance trends in high-z_abs damped Lyman-alpha systems (DLAs). Our results do not support the recent claim of Ashenfelter, Mathews & Olive (2004b) that similar models of IM-enhanced initial mass functions (IMFs) may simultaneously explain the HIRES varying-alpha data and DLA N abundances. We explore the effect of the IM-enhanced model on Si, Al and P abundances, finding it to be much-less pronounced than for N. We also show that the 13C/12C ratio, as measured in absorption systems, could constitute a future diagnostic of non-standard models of the high-redshift IMF.
0501168v2
1994-04-11
Nonlinear Viscous Vortex Motion in Two-Dimensional Josephson-Junction Arrays
When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity, $\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.
9404022v1
2002-09-20
Onset of Convection in a Very Compressible Fluid : The Transient Toward Steady State
We analyze the time profile $\Delta T(t)$ of the temperature difference, measured across a very compressible supercritical $^3$He fluid layer in its convective state. The experiments were done along the critical isochore in a Rayleigh-B\'{e}nard cell after starting the vertical constant heat flow $q$. For $q$ sufficiently well above that needed for the convection onset, the transient $\Delta T(t)$ for a given $\epsilon\equiv(T-T_c)/T_c$, with $T_c$ = 3.318K, shows a damped oscillatory profile with period $t_{osc}$ modulating a smooth base profile. The smooth profile forms the exponential tail of the transient which tends to the steady-state $\Delta T(\infty)$ with a time constant $\tau_{tail}$. The scaled times $t_{osc}/t_D$ and $\tau_{tail}/t_D$ from all the data could be collapsed onto two curves as a function of the Rayleigh number over $\sim$ 3.5 decades. Here $t_D$ is the characteristic thermal diffusion time. Furthermore comparisons are made between measurements of a third characteristic time $t_m$ between the first peak and the first minimum in the $\Delta T(t)$ profile and its estimation by Onuki et al. Also comparisons are made between the observed oscillations and the 2D simulations by Onuki et al. and by Amiroudine and Zappoli. For $\epsilon < 9\times 10^{-3}$ the experiments show a crossover to a different transient regime. This new regime, which we briefly describe, is not understood at present.
0209495v1
2004-10-14
Cold Strongly Coupled Atoms Make a Near-perfect Liquid
Feshbach resonances of trapped ultracold alkali atoms allow to vary the atomic scattering length a. At very large values of a the system enters an universal strongly coupled regime in which its properties--the ground state energy, pressure {\it etc.}--become independent of a. We discuss transport properties of such systems. In particular, the universality arguments imply that the shear viscosity of ultracold Fermi atoms at the Feschbach resonance is proportional to the particle number density n, and the Plank constant \hbar \eta=\hbar n \alpha_\eta, where \alpha_\eta is a universal constant. Using Heisenberg uncertainty principle and Einstein's relation between diffusion and viscosity we argue that the viscosity has the lower bound given by \alpha_{\eta} \leq (6\pi)^{-1}. We relate the damping of low-frequency density oscillations of ultracold optically trapped ^{6}Li atoms to viscosity and find that the value of the coefficient \alpha_\eta is about 0.3. We also show that such a small viscosity can not be explained by kinetic theory based on binary scattering. We conclude that the system of ultracold atoms near the Feshbach resonance is a near-ideal liquid.
0410067v2
2004-09-24
Oscillator model for dissipative QED in an inhomogeneous dielectric
The Ullersma model for the damped harmonic oscillator is coupled to the quantised electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalised by performing a normal-mode expansion. The commutation relations of the diagonalising operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantised electric field is completely determined by the sources of the reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices.
0409161v1
2007-07-30
Extended Quintessence with non-minimally coupled phantom scalar field
We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane $(\psi, \psi')$. We formulate simple conditions on the value of coupling constant $\xi$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. It is also investigated the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.
0707.4471v2
2009-07-14
Nonlinear Schrödinger Equation with Spatio-Temporal Perturbations
We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger Equation (NLSE) with the following perturbations: non-parametric spatio-temporal driving of the form $f(x,t) = a \exp[i K(t) x]$, damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a Collective-Coordinate-Theory which yields a set of ODEs for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force $f(x)$. The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of $f(x)$. In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum $P(t)$ and soliton velocity $V(t)$: This is a parameter representation of a curve $P(V)$ which is visited by the soliton while time evolves. Our conjecture is that the soliton becomes unstable, if this curve has a branch with negative slope. This conjecture is fully confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the soliton lives longer, the shorter the branch with negative slope is.
0907.2438v2
2012-09-11
Macroscopic quantum tunneling of two coupled particles in the presence of a transverse magnetic field
Two coupled particles of identical masses but opposite charges, with a constant transverse external magnetic field and an external potential, interacting with a bath of harmonic oscillators are studied. We show that the problem cannot be mapped to a one-dimensional problem like the one in Ref. \cite{pa}, it strictly remains two-dimensional. We calculate the effective action both for the case of linear coupling to the bath and without a linear coupling using imaginary time path integral at finite temperature. At zero temperature we use Leggett's prescription to derive the effective action. In the limit of zero magnetic field we recover a two dimensional version of the result derived in Ref. \cite{em1} for the case of two identical particles. We find that in the limit of strong dissipation, the effective action reduces to a two dimensional version of the Caldeira-Leggett form in terms of the reduced mass and the magnetic field. The case of Ohmic dissipation with the motion of the two particles damped by the Ohmic frictional constant $\eta$ is studied in detail.
1209.2307v4
2013-08-28
On the evolution of the momentarily static radiation free data in the Apostolatos - Thorne cylindrical shell model
We study the evolution of the "Momentarily Static and Radiation Free" (MSRF) initial data for the Apostolatos - Thorne cylindrical shell model. We analyze the relation between the parameters characterizing the MSRF data those for the corresponding final static configuration, and show that there is a priori no conflict for any choice of initial MSRF data, in contrast with some recent results of Nakao, Ida and Kurita. We also consider the problem in the linear approximation, and show that the evolution is stable in all cases. We find that the approach to the final state is very slow, with an inverse logarithmic dependence on time at fixed radius. To complement these results we introduce a numerical computation procedure that allows us to visualize the explicit form of the evolution of the shell and of the gravitational field up to large times. The results are in agreement with the qualitative behaviour conjectured by Apostolatos and Thorne, with an initial damped oscillatory stage, but with oscillations about a position that approaches slowly that of the static final state, as indicated by our analysis. We also include an Appendix, where we prove the existence of solutions of the cylindrical wave equation with vanishing initial value for $r > R_0$, ($R_0 > 0$ some finite constant), that approach a constant value for large times. This result is crucial for the proof of compatibility of arbitrary MSRF initial data and a final static configuration for the system.
1308.6296v1
2014-01-17
Co2FeAl Heusler thin films grown on Si and MgO substrates: annealing temperature effect
10 nm and 50 nm Co$_{2}$FeAl (CFA) thin films have been deposited on MgO(001) and Si(001) substrates by magnetron sputtering and annealed at different temperatures. X-rays diffraction revealed polycrystalline or epitaxial growth (according to the relation CFA(001)[110]//MgO(001)[100] epitaxial relation), respectively for CFA films grown on a Si and on a MgO substrate. For these later, the chemical order varies from the A2 phase to the B2 phase when increasing the annealing temperature (Ta) while only the A2 disorder type has been observed for CFA grown on Si. Microstrip ferromagnetic resonance (MS-FMR) measurements revealed that the in-plane anisotropy results from the superposition of a uniaxial and of a fourfold symmetry term for CFA grown on MgO substrates. This fourfold anisotropy, which disappears completely for samples grown on Si, is in accord with the crystal structure of the samples. The fourfold anisotropy field decreases when increasing Ta while the uniaxial anisotropy field is nearly unaffected by Ta within the investigated range. The MS-FMR data also allow for concluding that the gyromagnetic factor remains constant and that the exchange stiffness constant increases with $T_{a}$. Finally, the FMR linewidth decreases when increasing Ta, due to the enhancement of the chemical order. We derive a very low intrinsic damping parameter (1.3*10^-3 and 1.1*10^-3 for films of 50 nm thickness annealed at 615 {\deg}C grown on MgO and on Si, respectively).
1401.4397v1
2014-02-04
Complete Tidal Evolution of Pluto-Charon
Both Pluto and its satellite Charon have rotation rates synchronous with their orbital mean motion. This is the theoretical end point of tidal evolution where transfer of angular momentum has ceased. Here we follow Pluto's tidal evolution from an initial state having the current total angular momentum of the system but with Charon in an eccentric orbit with semimajor axis $a \approx 4R_P$ (where $R_P$ is the radius of Pluto), consistent with its impact origin. Two tidal models are used, where the tidal dissipation function $Q \propto$ 1/frequency and $Q=$ constant, where details of the evolution are strongly model dependent. The inclusion of the gravitational harmonic coefficient $C_{22}$ of both bodies in the analysis allows smooth, self consistent evolution to the dual synchronous state, whereas its omission frustrates successful evolution in some cases. The zonal harmonic $J_2$ can also be included, but does not cause a significant effect on the overall evolution. The ratio of dissipation in Charon to that in Pluto controls the behavior of the orbital eccentricity, where a judicious choice leads to a nearly constant eccentricity until the final approach to dual synchronous rotation. The tidal models are complete in the sense that every nuance of tidal evolution is realized while conserving total angular momentum - including temporary capture into spin-orbit resonances as Charon's spin decreases and damped librations about the same.
1402.0625v1
2014-05-22
Tagged particle diffusion in one-dimensional systems with Hamiltonian dynamics - II
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal distribution. The correlation functions are studied in finite systems, and their forms examined at short and long times. Various one-dimensional systems are studied. Results of numerical simulations for the Fermi-Pasta-Ulam chain are qualitatively similar to results for the harmonic chain, and agree unexpectedly well with a simple description in terms of linearized equations for damped fluctuating sound waves. Simulation results for the alternate mass hard particle gas reveal that - in contradiction to our earlier results [1] with smaller system sizes - the diffusion constant slowly converges to a constant value, in a manner consistent with mode coupling theories. Our simulations also show that the behaviour of the Lennard-Jones gas depends on its density. At low densities, it behaves like a hard-particle gas, and at high densities like an anharmonic chain. In all the systems studied, the tagged particle was found to show normal diffusion asymptotically, with convergence times depending on the system under study. Finite size effects show up at time scales larger than sound traversal times, their nature being system-specific.
1405.5718v2
2014-09-01
Nitric Oxide as stress inducer and synchronizer of p53 dynamics
We study how the temporal behaviours of p53 and MDM2 are affected by stress inducing bioactive molecules NO (Nitric Oxide) in the p53-MDM2-NO regulatory network. We also study synchronization among a group of identical stress systems arranged in a three dimensional array with nearest neighbour diffusive coupling. The role of NO and effect of noise are investigated. In the single system study, we have found three distinct types of temporal behaviour of p53, namely, oscillation death, damped oscillation and sustain oscillation, depending on the amount of stress induced by the NO concentration, indicating how p53 responds to the incoming stress. The correlation among the coupled systems increases as the value of coupling constant (\epsilon) is increased (\gamma increases) and becomes constant after certain value of \epsilon. The permutation entropy spectra H(\epsilon) for p53 and MDM2 as a function of \epsilon are found to be different due to direct and indirect interaction of NO with the respective proteins. \gamma versus \epsilon for p53 and MDM2 are found to be similar in deterministic approach, but different in stochastic approach and the separation between \gamma of the respective proteins as a function of \epsilon decreases as system size increases. The role of NO is found to be twofold: stress induced by it is prominent at small and large values of \epsilon but synchrony inducing by it dominates in moderate range of \epsilon. Excess stress induce apoptosis to the system.
1409.0528v1
2015-10-15
Markov Chain Analysis of Cumulative Step-size Adaptation on a Linear Constrained Problem
This paper analyzes a (1, $\lambda$)-Evolution Strategy, a randomized comparison-based adaptive search algorithm, optimizing a linear function with a linear constraint. The algorithm uses resampling to handle the constraint. Two cases are investigated: first the case where the step-size is constant, and second the case where the step-size is adapted using cumulative step-size adaptation. We exhibit for each case a Markov chain describing the behaviour of the algorithm. Stability of the chain implies, by applying a law of large numbers, either convergence or divergence of the algorithm. Divergence is the desired behaviour. In the constant step-size case, we show stability of the Markov chain and prove the divergence of the algorithm. In the cumulative step-size adaptation case, we prove stability of the Markov chain in the simplified case where the cumulation parameter equals 1, and discuss steps to obtain similar results for the full (default) algorithm where the cumulation parameter is smaller than 1. The stability of the Markov chain allows us to deduce geometric divergence or convergence , depending on the dimension, constraint angle, population size and damping parameter, at a rate that we estimate. Our results complement previous studies where stability was assumed.
1510.04409v1
2016-02-02
Planck constraints on scalar-tensor cosmology and the variation of the gravitational constant
Cosmological constraints on the scalar-tensor theory of gravity by analyzing the angular power spectrum data of the cosmic microwave background (CMB) obtained from the Planck 2015 results are presented. We consider the harmonic attractor model, in which the scalar field has a harmonic potential with curvature ($\beta$) in the Einstein frame and the theory relaxes toward the Einstein gravity with time. Analyzing the {\it TT}, {\it EE}, {\it TE} and lensing CMB data from Planck by the Markov chain Monte Carlo method, we find that the present-day deviation from the Einstein gravity (${\alpha_0}^2$) is constrained as ${\alpha_0}^2<2.5\times10^{-4-4.5\beta^2}\ (95.45\% {\rm\ C.L.})$ and ${\alpha_0}^2<6.3\times10^{-4-4.5\beta^2}\ (99.99\%\ {\rm C.L.})$ for $0<\beta<0.4$. The time variation of the effective gravitational constant between the recombination and the present epochs is constrained as $G_{\rm rec}/G_0<1.0056\ (95.45\% {\rm\ C.L.})$ and $G_{\rm rec}/G_0<1.0115\ (99.99 \%{\rm\ C.L.})$. We also find that the constraints are little affected by extending to nonflat cosmological models because the diffusion damping effect revealed by Planck breaks the degeneracy of the projection effect.
1602.00809v2
2016-05-06
Eisenhart lifts and symmetries of time-dependent systems
Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in $n+2$ dimensions, equipped with its covariantly constant null Killing vector field. Reparametrization of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schr\"odinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaitre and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.
1605.01932v2
2016-05-24
Coherent magneto-elastic oscillations in superfluid magnetars
We study the effect of superfluidity on torsional oscillations of highly magnetised neutron stars (magnetars) with a microphysical equation of state by means of two-dimensional, magnetohydrodynamical- elastic simulations. The superfluid properties of the neutrons in the neutron star core are treated in a parametric way in which we effectively decouple part of the core matter from the oscillations. Our simulations confirm the existence of two groups of oscillations, namely continuum oscillations that are confined to the neutron star core and are of Alfv\'enic character, and global oscillations with constant phase and that are of mixed magneto-elastic type. The latter might explain the quasi-periodic oscillations observed in magnetar giant flares, since they do not suffer from the additional damping mechanism due to phase mixing, contrary to what happens for continuum oscillations. However, we cannot prove rigorously that the coherent oscillations with constant phase are normal modes. Moreover, we find no crustal shear modes for the magnetic field strengths typical for magnetars.We provide fits to our numerical simulations that give the oscillation frequencies as functions of magnetic field strength and proton fraction in the core.
1605.07638v1
2016-06-28
Negative stiffness and modulated states in active nematics
We examine the dynamics of a compressible active nematic liquid crystal on a frictional substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal dynamical model for the nematic order parameter, with elastic constants renormalized by activity. The renormalized elastic constants can become negative at large activity, leading to the selection of spatially inhomogeneous patterns via a mechanism analogous to that responsible for modulated phases arising at an equilibrium Lifshitz point. Tuning activity and the degree of nematic order in the passive system, we obtain a linear stability phase diagram that exhibits a nonequilibrium tricritical point where ordered, modulated and disordered phases meet. Numerical solution of the nonlinear equations yields a succession of spatial structures of increasing complexity with increasing activity, including kink walls and active turbulence, as observed in experiments on microtubule bundles confined at an oil-water interface. Our work provides a minimal model for an overdamped active nematic that reproduces all the nonequilibrium structures seen in simulations of the full active nematic hydrodynamics and provides a framework for understanding some of the mechanisms for selection of the nonequilibrium patterns in the language of equilibrium critical phenomena.
1606.08786v2
2017-03-11
Magnonic crystals - prospective structures for shaping spin waves in nanoscale
We have investigated theoretically band structure of spin waves in magnonic crystals with periodicity in one-(1D), two- (2D) and three-dimensions (3D). We have solved Landau-Lifshitz equation with the use of plane wave method, finite element method in frequency domain and micromagnetic simulations in time domain to find the dynamics of spin waves and spectrum of their eigenmodes. The spin wave spectra were calculated in linear approximation. In this paper we show usefulness of these methods in calculations of various types of spin waves. We demonstrate the surface character of the Damon-Eshbach spin wave in 1D magnonic crystals and change of its surface localization with the band number and wavenumber in the first Brillouin zone. The surface property of the spin wave excitation is further exploited by covering plate of the magnonic crystal with conductor. The band structure in 2D magnonic crystals is complex due to additional spatial inhomogeneity introduced by the demagnetizing field. This modifies spin wave dispersion, makes the band structure of magnonic crystals strongly dependent on shape of the inclusions and type of the lattice. The inhomogeneity of the internal magnetic field becomes unimportant for magnonic crystals with small lattice constant, where exchange interactions dominate. For 3D magnonic crystals, characterized by small lattice constant, wide magnonic band gap is found. We show that the spatial distribution of different materials in magnonic crystals can be explored for tailored effective damping of spin waves.
1703.04012v1
2018-02-17
Superconductivity induced by flexural modes in non $σ_{\rm h}$-symmetric Dirac-like two-dimensional materials: A theoretical study for silicene and germanene
In two-dimensional crystals that lack symmetry under reflections on the horizontal plane of the lattice (non-$\sigma_{\rm h}$-symmetric), electrons can couple to flexural modes (ZA phonons) at first order. We show that in materials of this type that also exhibit a Dirac-like electron dispersion, the strong coupling can result in electron pairing mediated by these phonons, as long as the flexural modes are not damped or suppressed by additional interactions with a supporting substrate or gate insulator. We consider several models: The weak-coupling limit, which is applicable only in the case of gapped and parabolic materials, like stanene and HfSe$_{2}$, thanks to the weak coupling; the full gap-equation, solved using the constant-gap approximation and considering statically screened interactions; its extensions to energy-dependent gap and to dynamic screening. We argue that in the case of silicene and germanene superconductivity mediated by this process can exhibit a critical temperature of a few degrees K, or even a few tens of degrees K when accounting for the effect of a high-dielectric-constant environment. We conclude that the electron/flexural-modes coupling should be included in studies of possible superconductivity in non-$\sigma_{\rm h}$-symmetric two-dimensional crystals, even if alternative forms of coupling are considered.
1802.06272v1
2019-04-29
A nonlinear subgrid-scale model for large-eddy simulations of rotating turbulent flows
Rotating turbulent flows form a challenging test case for large-eddy simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS) model for such flows. The proposed SGS model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rate-of-strain and rate-of-rotation tensors. The two corresponding model coefficients are a function of the vortex stretching magnitude. Therefore, the model is consistent with many physical and mathematical properties of the Navier-Stokes equations and turbulent stresses, and is easy to implement. We determine the two model constants using a nondynamic procedure that takes into account the interaction between the model terms. Using detailed direct numerical simulations (DNSs) and LESs of rotating decaying turbulence and spanwise-rotating plane-channel flow, we reveal that the two model terms respectively account for dissipation and backscatter of energy, and that the nonlinear term improves predictions of the Reynolds stress anisotropy near solid walls. We also show that the new SGS model provides good predictions of rotating decaying turbulence and leads to outstanding predictions of spanwise-rotating plane-channel flow over a large range of rotation rates for both fine and coarse grid resolutions. Moreover, the new nonlinear model performs as well as the dynamic Smagorinsky and scaled anisotropic minimum-dissipation models in LESs of rotating decaying turbulence and outperforms these models in LESs of spanwise-rotating plane-channel flow, without requiring (dynamic) adaptation or near-wall damping of the model constants.
1904.12748v1
2020-04-03
Probing modified gravity theories and cosmology using gravitational-waves and associated electromagnetic counterparts
The direct detection of gravitational waves by the LIGO-Virgo collaboration has opened a new window with which to measure cosmological parameters such as the Hubble constant $H_0$, and also probe general relativity on large scales. In this paper we present a new phenomenological approach, together with its inferencial implementation, for measuring deviations from general relativity (GR) on cosmological scales concurrently with a determination of $H_0$. We consider gravitational waves (GWs) propagating in an expanding homogeneous and isotropic background, but with a modified friction term and dispersion relation relative to that of GR. We find that a single binary neutron star GW detection will poorly constrain the GW friction term. However, a joint analysis including the GW phase and GW-GRB detection delay could improve constraints on some GW dispersion relations provided the delay is measured with millisecond precision. We also show that, for massive gravity, by combining 100 binary neutron stars detections with observed electromagnetic counterparts and hosting galaxy identification, we will be able to constrain the Hubble constant, the GW damping term and the GW dispersion relation with 2\%, 15\% and 2 \% accuracy, respectively. We emphasise that these three parameters should be measured together in order avoid biases. Finally we apply the method to GW170817, and demonstrate that for all the GW dispersions relations we consider, including massive gravity, the GW must be emitted $\sim$ 1.74s before the Gamma-ray burst (GRB). Furthermore, at the GW merger peak frequency, we show that the fractional difference between the GW group velocity and $c$ is $\lesssim 10^{-17}$.
2004.01632v2
2021-08-18
Velocity auto correlation function of a confined Brownian particle
Motivated by the simple models of molecular motor obeying a linear force-velocity relation, we have studied the stochastic dynamics of a Brownian particle in the presence of a linear velocity dependent force, $f_s(1-\frac{v}{v_0})$ where $f_{s}$ is a constant. The position and velocity auto correlation functions in different situations of the dynamics are calculated exactly. We observed that the velocity auto correlation function shows an exponentially decaying behaviour with time and saturates to a constant value in the time asymptotic limit, for a fixed $f_s$. It attains saturation faster with increase in the $f_{s}$ value. When the particle is confined in a harmonic well, the spectral density exhibits a symmetric behaviour and the corresponding velocity auto correlation function shows a damped oscillatory behaviour before decaying to zero in the long time limit. With viscous coefficient, a non-systematic variation of the velocity auto correlation function is observed. Further, in the presence of a sinusoidal driving force, the correlation in velocities increases with increase in the amplitude of driving in the transient regime. For the particle confined in a harmonic well, the correlation corresponding to the shift relative to the average position is basically the thermal contribution to the total position correlation. Moreover, in the athermal regime, the total correlation is entirely due to the velocity dependent force.
2108.07922v1
2021-12-21
Fast long-wavelength exchange spin waves in partially-compensated Ga:YIG
Spin waves in yttrium iron garnet (YIG) nano-structures attract increasing attention from the perspective of novel magnon-based data processing applications. For short wavelengths needed in small-scale devices, the group velocity is directly proportional to the spin-wave exchange stiffness constant $\lambda_\mathrm{ex}$. Using wave vector resolved Brillouin Light Scattering (BLS) spectroscopy, we directly measure $\lambda_\mathrm{ex}$ in Ga-substituted YIG thin films and show that it is about three times larger than for pure YIG. Consequently, the spin-wave group velocity overcomes the one in pure YIG for wavenumbers $k > 4$ rad/$\mu$m, and the ratio between the velocities reaches a constant value of around 3.4 for all $k > 20$ rad/$\mu$m. As revealed by vibrating-sample magnetometry (VSM) and ferromagnetic resonance (FMR) spectroscopy, Ga:YIG films with thicknesses down to 59 nm have a low Gilbert damping ($\alpha < 10^{-3}$), a decreased saturation magnetization $\mu_0 M_\mathrm{S}~\approx~20~$mT and a pronounced out-of-plane uniaxial anisotropy of about $\mu_0 H_{\textrm{u1}} \approx 95 $ mT which leads to an out-of-plane easy axis. Thus, Ga:YIG opens access to fast and isotropic spin-wave transport for all wavelengths in nano-scale systems independently of dipolar effects.
2112.11348v1
2022-04-11
Forecast and backcast of the solar cycles
Solar cycle is modeled as a forced and damped harmonic oscillator and the amplitudes, frequencies, phases and decay factors of such a harmonic oscillator are estimated by non-linear fitting the equation of sinusoidal and transient parts to the sunspot and irradiance (proxy for the sunspot) data for the years 1700-2008. We find that:(i) amplitude and frequency (or period of $\sim$11 yr) of the sinusoidal part remain constant for all the solar cycles; (ii) the amplitude of the transient part is phase locked with the phase of the sinusoidal part; (iii) for all the cycles, the period and decay factor (that is much less than 1) of the transient part remain approximately constant. The constancy of the amplitudes and the frequencies of the sinusoidal part and a very small decay factor from the transient part suggests that the solar activity cycle mainly consists of a persistent oscillatory part that might be compatible with long-period ($\sim$22 yr) Alfven oscillations. For all the cycles, with the estimated physical parameters (amplitudes, phases and periods) and, by an autoregressive model, we forecast (especially for coming solar cycle 25) and backcast (to check whether Maunder minimum type solar activity exists or not) the solar cycles. We find that amplitude of coming solar cycle 25 is almost same as the amplitude of the previous solar cycle 24. We also find that sun might not have experienced a deep Maunder minimum (MM) type of activity during 1645-1700 AD corroborating some of the paleoclimatic inferences and, MM type of activity will not be imminent in near future, until at least 200 years.
2204.04818v1