In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuat...

In this paper we introduce an improvement in the path planning algorithm for the humanoid soccer playing robot which uses Ferguson splines and PSO (Particle Swarm Optimization). The objective of the algorithm is to find a path through other playing robots to the ball, which should be as short as possible and also safe enough. Ferguson splines create preliminary paths using random generated para...

We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where all the particles are different (APD). The equilibrium properties of this APD system were studied in our earlier work [L. S. Shagolsem et al., J. Chem. Phys. 142, 051104 (2015).]. We use molecular dynamics simulations to investigate the statistical properties of particle trajectories i...

Scaling limits of continuous-time random walks are used in physics to model anomalous diffusion in which particles spread at a different rate than the classical Brownian motion. In this paper, we characterize the scaling limit of the average of multiple particles, independently moving as a continuous-time random walk. The limit is taken by increasing the number of particles and scaling from mic...

We investigate the dynamics of a particle moving randomly along a disordered heteropolymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between the enhanced diffusion and the quenched disorder. The dispersion speed exhibits universal behavior independent of the folding statistics. On the other hand it i...

We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1 − p. When an active particle hits a sleeping particle, the latter becomes active. Phase transit...

We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1 − p. When an active particle hits a sleeping particle, the latter becomes active. Phase transit...

MEMS (Micro Electro Mechanical System) gyroscopes have been widely applied to various fields, but MEMS gyroscope random drift has nonlinear and non-stationary characteristics. It has attracted much attention to model and compensate the random drift because it can improve the precision of inertial devices. This paper has proposed to use wavelet filtering to reduce noise in the original data of M...

We study properties of multiple random walks on a graph under variousassumptions of interaction between the particles.To give precise results, we make our analysis for random regular graphs.The cover time of a random walk on a random r-regular graph was studiedin [6], where it was shown with high probability (whp), that for r ≥ 3 thecover time is asymptotic to θrn lnn, where...