Related papers: Generalized Bagley-Torvik Equation and Fractional …
We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…
Nonergodic Brownian motion is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding either a vanishing or a divergent zero-frequency friction strength, the non-Markovian Browninan dynamics exhibits…
Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the…
The fractional Brownian motion of index $0 < H < 1$, H-FBM, with d-dimensional time is considered on an expanding set TG, where G is a bounded convex domain that contains 0 at its boundary. The main result: if 0 is a point of smoothness of…
In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…
We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
We revisit the question of quantum dynamics of electrons on the off-diagonal Fibonacci tight-binding model. We find that typical dynamical quantities, such as the probability of an electron to remain in its original position as a function…
Rotation damping and alignment are discussed as prerequisites for polarization power. An expression is derived from first principles, for the damping time of the rotation of a particle in a magnetic field, under the Faraday braking torque,…
We study the behavior of skyrmions in thin films under the action of stochastic torques arising from thermal fluctuations. We find that the Brownian motion of skyrmions is described by a stochastic Thiele's equation and its corresponding…
Acoustic fields effect steady transport of suspended particles by rectifying the inertia of primary oscillations. We develop a fully analytic theory that relates this steady particle motion to incident oscillatory (acoustic) flow and the…
In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time…
We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact…
The focus of our study in this paper is on the active dynamics and a fractional generalized Langevin equation with a memory kernel K(t). The Fokker-Planck equation is obtained by deriving it from a second-order differential equation. The…
We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles are described by a Langevin equation with Rayleigh-Helmholtz…
We study small vibrations of a string with time-dependent length $\ell(t)$ and boundary damping. The vibrations are described by a 1-d wave equation in an interval with one moving endpoint at a speed $\ell'(t)$ slower than the speed of…
We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…
We present a treatise on solving the Takagi-Taupin equations in the case of a strain field with an additional, spatially slowly varying component (owing to \emph{e.g.}~heat expansion or angular compression). We show that the presence of…