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G. Sh. Tsitsiashvili

Publications and source records attributed to G. Sh. Tsitsiashvili.

3 recordsLinked to original sources
arXiv2018

Probability of detection of an extraneous mobile object by autonomous unmanned underwater vehicles as a solution of the Buffon problem

Underwater robotics addresses the problem of object detection apparatus. Offers a probabilistic formulation of the problem, which uses the reduction of the detection task to a classical task of Buffon. This formulation arises naturally in the formulation of the problem in the coordinate system associated with the apparatus. It is shown that the problem allows analysis in the presence of an asymptotic parameter, determined by the ratio of the local scan size of the apparatus to the global size of the problem under consideration.

cs.RO↗
arXiv2003

Anomalous Diffusion with Periodical Initial Conditions on Interval with Reflecting Edges

Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and etc. In this model a coordinate of a particle has stable distribution (not normal one). As a result a density of its distribution function satisfies an analog of diffusion equation in which second derivative by coordinate is replaced by partial derivative. In this paper the anomalous diffusion with periodic initial conditions on an interval with reflecting edges is considered. Such problem is important for example in technical mechanics for an analysis of fuel mixing in straight flow engine too. As A.A. Borovkov suggested special probability methods are developed to analyze such a diffusion.

math.PR↗