Related papers: On Fractional Annealing Process
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
Jamming is a common feature of out of equilibrium systems showing slow relaxation dynamics. Here we review our efforts in understanding jamming in granular materials using experiments and computer simulations. We first obtain an estimation…
An experimental arrangement and a set of experiments are developed to generate empirical evidence of the effect of noise on a rotating, macro-scale cantilever structure. The experiment is a controlled representation of a rotating machinery…
Most avalanching systems in nature should involve diffusive processes as well which can change the behavior of such systems and should be taken into account. We examine the effects of diffusion on the model of a dissipative bi-directional…
We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.
We study the dynamics of thermalization resulting from a time-dependent noise in a Quantum Ising Chain subject to a sudden quench of the transverse magnetic field. For weak noise the dynamics shows a pre-thermalized state at intermediate…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a…
We investigate a problem of the necessary and sufficient conditions for appearance of the 1/f fluctuations in the simple systems affected by the external random perturbations, i.e. the power spectral density of the flux of particles moving…
Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level…
Sintering is a widespread manufacturing process, accounting for a significant portion of global energy expenditure. However, controlling this process has been mostly a trial-and-error process, being costly in both time and money. The recent…
We investigate the thermodynamics of model systems exhibiting two-scale fractal spectra. In particular, we present both analytical and numerical studies on the temperature dependence of the vibrational and electronic specific heats. For…
In this paper, we consider the exact fractional variation for the temporal process of the solution to the fractional stochastic heat equation on $\mathbb{R}$ driven by a space-time white noise, and as an application we give the estimate of…
We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value $b$, we provide the limiting distribution for the amount of time that the workload process…
We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system…
Local magnetic moments in disordered sytems can be described in terms of annealed magnetic disorder, in addition to the underlying quenched disorder. It is shown that for noninteracting electron systems at zero temperature, the annealed…
We investigate the time dependent thermal relaxation of a two-dimensional electron system in the fractional quantum Hall regime where ballistic phonons are used to heat up the system to a non-equilibrium temperature. The thermal relaxation…
Zero temperature states of matter are holographically described by a spacetime with an asymptotic electric flux. This flux can be sourced either by explicit charged matter fields in the bulk, by an extremal black hole horizon, or by a…
We investigate the effect of annealed disorder on the mechanical properties and plasticity of a modeled amorphous solid by introducing a small fraction of heavy impurities into the material which resembles real experimental systems. The…
Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly…