Modern methods of direct numerical simulations of transfer processes in random media

The paper considers the methods of direct numerical investigation of the behaviour of dynamical systems of explosive type under the influence of random noise. Dynamical systems are described by a system of nonstationary ordinary differential equations (ODE). The dynamics of the system, taking into account random noise, is described by a system of stochastic ordinary differential equations (SODE). The paper provides an overview of modern algorithms based on modifications of Runge – Kutta integration methods. The features of the analysis of weak and strong convergence of the SODE integration methods are described. Methods for generating random noise with complex temporal structure (color noise) are described. The method of numerical solution of the system of SODE is used to generate random color noise. Examples of the study of the influence of random noise on biological and mechanical systems of explosive type are presented. It is shown that random noises acting on such systems qualitatively change the character of their behaviour.

Mach Fronts in Random Media with Fractal and Hurst Effects

An investigation of transient second sound phenomena due to moving heat sources on planar random media is conducted. The spatial material randomness of the relaxation time is modeled by Cauchy or Dagum random fields allowing for decoupling of fractal and Hurst effects. The Maxwell–Cattaneo model is solved by a second-order central differencing. The resulting stochastic fluctuations of Mach wedges are examined and compared to unperturbed Mach wedges resulting from the heat source traveling in a homogeneous domain. All the examined cases are illustrated by simulation movies linked to this paper.

Enhancement of Radar Detection Accuracy Using H-Beam Wave Polarization in Random Media

This work addresses the range in which the accuracy of object identification is enhanced regardless of radar parameters. We compute the radar cross-section (RCS) of conducting objects in free space and random media. We use beam wave incidence and postulate its coherency with a finite width around an object located in the far field. Accordingly, we examine the impact of radar parameters on the RCS, where these parameters include the incident angle, target size and complexity, medium fluctuation intensity and the beam size of the incident waves. H-wave polarization is assumed for the waves’ incidence.

Unfairness of Random Access with Collision Avoidance in Industrial Internet of Things Networks

This paper is focused on the analysis of unfairness of random media access in Local Operating Networks (LON), which is one of the commercial platforms of the Industrial Internet of Things (IIoT). The unfairness in accessing the LON channel is introduced by a collision avoidance mechanism in the predictive p-persistent CSMA protocol adopted at the media access control layer. The study on the bandwidth share in predictive p-persistent CSMA calls for the analysis of multiple memoryless backoff. In this paper, it is shown that the channel access in LON systems is unfair in the short term for medium traffic load conditions, and in the long term for heavy loaded networks. Furthermore, it is explained that the average bandwidth allocated to a particular node is determined implicitly by the load scenario, while an actual node bandwidth fluctuates in time according to stochastic dynamics of the predictive p-persistent CSMA. Next, it is formally proven that the average bandwidth available to a node is a linear function of its backoff state and does not depend on backoff states of the other stations. Finally, it is demonstrated that possibly unfair bandwidth share in LON networks determined implicitly by load scenario is stable because, with lowering a fraction of actual network bandwidth accessible by a given station, the probability to decrease it in the future also drops.