•Scaled Brownian motion.•Superstatistics.•Grey Brownian motion.•Diffusing diffusivity.•Anomalous diffusion.
Nowadays, the number of physical systems that have reported non-Gaussian diffusion ...emergence in systems whose diffusivity fluctuates is increasing. These systems may present non-Gaussian diffusion associated with a mean square displacement of trace-particles that may be normal or anomalous. To include anomalous diffusion, recent research has investigated superstatistics of scaled Brownian motion (SBM) to describe diffusion in biological matter. In this paper, we propose two diffusion models for SBM with random diffusivity governed by a stochastic equation. Based on a thorough analysis of simulations of stochastic modeling, we have shown the main remarkable features of each model. The first model generalizes the grey Brownian motion for SBM; this model is suitable to describe systems whose diffusion is ever non-Gaussian. The second model generalizes the minimal diffusing diffusivity model and is suitable to describe systems which present crossover from non-Gaussian to standard Gaussian processes. These results imply rich classes of the Non-Gaussian diffusion processes that may admit normal and anomalous diffusion as well as the crossover between them.
Brownian motion of particles affects many branches of science. We report on the Brownian motion of micrometer-sized beads of glass held in air by an optical tweezer, over a wide range of pressures, ...and we measured the instantaneous velocity of a Brownian particle. Our results provide direct verification of the energy equipartition theorem for a Brownian particle. For short times, the ballistic regime of Brownian motion was observed, in contrast to the usual diffusive regime. We discuss the applications of these methods toward cooling the center-of-mass motion of a bead in vacuum to the quantum ground motional state.
In this article, we construct two families of processes, from a unique Lévy process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the ...two independent Gaussian processes. As applications of this result, we obtain families of processes that converge in law towards fractional Brownian motion, sub-fractional Brownian motion and bifractional Brownian motion, respectively.
In this study, two dimensional mixed convective MHD stagnation point flow of Casson fluid past an infinite plate in porous medium is considered. Effects of thermophoresis, Brownian motion, non-linear ...thermal radiation, heat generation and chemical reaction are considered. The governing differential equations are modified using similarity transformation. System of ODE is solved using HAM. Effects of different vital parameters on velocity, temperature and concentration profiles are shown graphically. The numerical values of the velocity, temperature and concentration gradient are also obtained in tabular form. It is illustrated that, mixed convection parameter λ, buoyancy force parameter N, non-linear thermal radiation parameter Nr and heat generation parameter H tends to improve motion of the fluid throughout the flow field. It is also seen that, heat and mass transfer process improve with Brownian motion Nb and thermophoresis parameter Nt. Brownian motion and thermophoresis parameters have negative impacts on temperature gradient.
We study the rheology of silicate melts containing platinum-group element (PGE) particles. They exhibit a shear-thinning behaviour, an intense aggregation tendency, and an anomalously high apparent ...viscosity in the low shear rate limit, even at very low particle volume fraction. Using a compilation of published experimental data, we analyse these effects in three steps. Firstly, we observe that the viscosities of these suspensions are much higher than those of natural silicate crystal-bearing melts for low shear rate regimes. Secondly, we demonstrate that the viscosities at low shear rate limit cannot be estimated by classical rheological models but rather may be understood as the result of particle aggregation, trapping dead fluid, and thereby increasing the effective particle volume fraction. Finally, we scale the critical shear rates for shear-thinning using a Peclet number analysis-invoking a competition between random thermal particle motion and hydrodynamic shearing motion-and, using an empirical extension, we additionally account for the particle-particle interaction energetics. We propose a framework in which the rheology of this family of particle-bearing melts can be predicted, and demonstrate that at low Peclet numbers, PGE-bearing particle aggregation is driven by interparticle forces and Brownian motion.
This paper concerns the stabilisation problem of a class of multi-weights stochastic complex networks driven by G-Brownian motion (G-MSN) via aperiodically intermittent adaptive control. It is worth ...noting that the intermittent control we consider is aperiodic and adaptive and it is used to stabilise G-MSN for the first time. Because of the particularity of G-expectation, the usual Halanay-type differential inequality for intermittent control problem are not applicable. A new inequality for dealing with the dynamic properties of G-MSN with intermittent control is established, based on which the stability problem is analysed by virtue of Lyapunov method and graph theory. Then, sufficient criteria are derived to guarantee the exponential stability in mean square, which are less conservative. Subsequently, a multi-weights stochastic oscillators system driven by G-Brownian motion is investigated as an application of the main results, and a numerical example is also presented to show the validity of the control strategy.
Active Brownian particles Romanczuk, P.; Bär, M.; Ebeling, W. ...
The European physical journal. ST, Special topics,
03/2012, Letnik:
202, Številka:
1
Journal Article
Recenzirano
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis ...on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.
This paper proposed a new class of stochastic cellular neural networks (SCNNs) with distributed time delays. It is driven by time‐varying Brownian motion. By constructing the Lyapunov functions with ...a more concise form and using the time‐varying Itô formula, combining some inequality techniques, this paper proved the almost surely exponential stability and the
p$$ p $$‐th moment exponential stability of the solution of the SCNNs. The numerical example verifies the theoretical results of this paper.
Heat transfer studying in channels is crucial for transport of the fluids in the oil and gas industry. In this study, numerical approach is applied to analyze the thermal behavior of alumina ...nanofluid in a duct. Brownian motion impact has been included for predicting nanofluid properties. Neural Network was employed to estimate the heat transfer rate. Numerical data has been obtained via Runge–Kutta method. Our outputs display that GMDH achieved an operative method for an efficient recognition of trends in data. Impact of expansion ratio, nanoparticle concentration, power law index and Reynolds number on Nu was also studied. Our findings reveal that heat transfer intensifies by rise of nanoparticle concentration while it has a reducing trend with rise of expansion ratio.
•Application of Neural Network for prediction of heat transfer is studied.•Al2O3-water has been used as working fluid.•KKL model is employed to estimate thermal conductivity and viscosity of nanofluid.•Nusselt number intensifies by increasing power law index.
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