Search results for "brownian motion"
showing 10 items of 177 documents
Stochastic model of memristor based on the length of conductive region
2021
Abstract We propose a stochastic model of a voltage controlled bipolar memristive system, which includes the properties of widely used dynamic SPICE models and takes into account the fluctuations inherent in memristors. The proposed model is described by rather simple equations of Brownian diffusion, does not require significant computational resources for numerical modeling, and allows obtaining the exact analytical solutions in some cases. The noise-induced transient bimodality phenomenon, arising under resistive switching, was revealed and investigated theoretically and experimentally in a memristive system, by finding a quite good qualitatively agreement between theory and experiment. B…
The Itô Integral
2014
The Ito integral allows us to integrate stochastic processes with respect to the increments of a Brownian motion or a somewhat more general stochastic process. We develop the Ito integral first for Brownian motion and then for generalized diffusion processes (so called Ito processes). In the third section, we derive the celebrated Ito formula. This is the chain rule for the Ito integral that enables us to do explicit calculations with the Ito integral. In the fourth section, we use the Ito formula to obtain a stochastic solution of the classical Dirichlet problem. This in turn is used in the fifth section in order to show that like symmetric simple random walk, Brownian motion is recurrent …
Negative Interfacial Tension in Phase-Separated Active Brownian Particles.
2015
We study numerically a model for active suspensions of self-propelled repulsive particles, for which a stable phase separation into a dilute and a dense phase is observed. We exploit the fact that for nonsquare boxes a stable "slab" configuration is reached, in which interfaces align with the shorter box edge. Evaluating a recent proposal for an intensive active swimming pressure, we demonstrate that the excess stress within the interface separating both phases is negative. The occurrence of a negative tension together with stable phase separation is a genuine nonequilibrium effect that is rationalized in terms of a positive stiffness, the estimate of which agrees excellently with the numer…
Numerical simulation of resonant activation in a fluctuating metastable model system
1998
We study the escape time from a metastable overdamped model system in the presence of two noise sources: a white noise and a random telegraph noise. The random telegraph noise controls the height of the potential barrier of the metastable system while the white noise mimics the presence of a given temperature. We report on numerical simulations about: (i) the average residence time of the system in the metastable state; (ii) the probability density function (PDF) of the residence time at various values of the correlation time T c of the random telegraph noise. Resonant activation is observed in the dynamics of the investigated system. The PDF shows different shapes for different values of τ…
2D dynamical arrest transition in a mixed nanoparticle-phospholipid layer studied in real and momentum spaces
2015
AbstractWe investigate the interfacial dynamics of a 2D self-organized mixed layer made of silica nanoparticles interacting with phospholipid (DPPC) monolayers at the air/water interface. This system has biological relevance, allowing investigation of toxicological effects of nanoparticles on model membranes and lung surfactants. It might also provide bio-inspired technological solutions, exploiting the self-organization of DPPC to produce a non-trivial 2D structuration of nanoparticles. The characterization of interfacial dynamics yields information on the effects of NPs on the mechanical properties, important to improve performances of systems such as colloidosomes, foams, creams. For thi…
Coexistence of active Brownian disks: van der Waals theory and analytical results
2020
At thermal equilibrium, intensive quantities like temperature and pressure have to be uniform throughout the system, restricting inhomogeneous systems composed of different phases. The paradigmatic example is the coexistence of vapor and liquid, a state that can also be observed for active Brownian particles steadily driven away from equilibrium. Recently, a strategy has been proposed that allows to predict phase equilibria of active particles [Solon et al., Phys. Rev. E 97, 020602(R) (2018)2470-004510.1103/PhysRevE.97.020602]. Here we elaborate on this strategy and formulate it in the framework of a van der Waals theory for active disks. For a given equation of state, we derive the effecti…
Lévy flights in confining potentials.
2009
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are considered: those driven by Langevin equation with L\'{e}vy noise and those, named by us topological L\'{e}vy processes (occurring in systems with topological complexity like folded polymers or complex networks and generically in inhomogeneous media), whose Langevin representation is unknown and possibly nonexistent. Our major finding is that both above classes of processes stay in affinity and may share common stationary (eventually asymptotic) probability densit…
Exact simulation of diffusion first exit times: algorithm acceleration
2020
In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random variables might be either momentarily unavailable or too expensive in terms of computation time. It therefore needs to be replaced by an approximation procedure. As was previously the case, the ambitious exact simulation of exit times for diffusion processes was unreachable though it concerns many applications in different fields like mathematical finance, neuroscience or reliability. The usual way to describe exit times was to use discretization schemes, that are of course approxim…
A measurement-based trajectory model for drifted motions towards a target zone
2016
Trajectory models have numerous applications in the area of wiewlwss communications. The aim of this paper is to develop an empirical trajectory model for drifted motions. Recently, a highly flexible trajectory model based on the primitives of Brownian fields (TramBrown) was proposed by A. Borhani and M. Patzold. This paper provides an empirical proof for TramBrown using global positioning system (GPS) data collected from real life user traces drifting to a particular target point or a zone. The recorded location coordinates of the mobile user are processed to compute the total travelling length and the angle-of-motion (AOM) along the drifted trajectory. It is shown that the probability den…
Deuteron n.m.r. in relation to the glass transition in polymers
1985
Abstract 2H n.m.r. is introduced as a tool for investigating slow molecular motion in the glass transition region of amorphous polymers. In particular, we compare 2H spin alignment echo spectra of chain deuterated polystyrene with models for restricted rotational Brownian motion. Molecular motion in the polystyrene-toluene system has been investigated by analysing 2H n.m.r. of partially deuterated polystyrene and toluene, respectively. The diluent mobility in the mixed glass has been decomposed into ‘solid’ and ‘liquid’ components where the respective average correlation times differ by more than 5 decades.