We study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation, with an initial condition that is a compact perturbation of a step function. A well-known result of Bramson states that, in the reference frame moving as 2t− (3/2) log t+x∞, the solution of the equation converges as t→ +∞ to a translate of the traveling wave corresponding to the minimal speed c∗ = 2...

Time evolution of a passive scalar is considered in a turbulent homogeneous incompressible Gaussian flow. The turbulent nature of the flow results in non-smooth coefficients in the corresponding evolution equation. A strong, in the probabilistic sense, solution of the equation is constructed using Wiener Chaos expansion, and the properties of the solution are studied. Among the results obtained...

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type o...

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness solutions for equation. Then, it is presented that first components their depend continuously on terminal values. Finally, give probabilistic interpretation viscosity nonlocal quasi-linear parabolic variational inequalities.

Probabilistic-based methods have been used for designing noise tolerant circuits recently. In these methods, however, there is not any reliability mechanism that is essential for nanometer digital VLSI circuits. In this paper, we propose a novel method for designing reliable probabilistic-based logic gates. The advantage of the proposed method in comparison with previous probabilistic-based met...

Sakarya province can be significantly affected by earthquakes on the North Anatolian Fault. Earthquake hazard includes some uncertainties. catalog data is needed for probabilistic earthquake calculations. In addition to current information, existing attenuation relationships, including characteristics region, should developed or their suitability checked. For this purpose, an analysis was carri...