Derivation and application of time step model in solidification process simulation

The heat transfer during the casting solidification process includes the heat radiation of the high temperature casting and the mold,the heat convection between the casting and the mold,and the heat conduction inside the casting and from the casting to the mold. In this paper,a formula of time step in simulation of solidification is derived,considering the heat radiation,convection and conduction based on the conservation of energy. The different heat transfer conditions between the conventional sand casting and the permanent mold casting are taken into account in this formula. The characteristics of heat transfer in the interior and surface of the casting are also considered. The numerical experiments show that this formula can avoid computational dispersion,and improve the computational efficiency by about 20% in the simulation of solidification process.

Derivative formulas and Poincaré inequality for Kohn-Laplacian type semigroups

As a generalization to the heat semigroup on the Heisenberg group, the diffusion semigroup generated by the subelliptic operator L :=1/2 sum from i=1 to m X_i^2 on R^(m+d):= R^m× R^d is investigated, where X_i(x, y) = sum (σki?xk) from k=1 to m+sum (((A_lx)_i?_(yl)) from t=1 to d,(x, y) ∈ R^(m+d), 1 ≤ i ≤ m for σ an invertible m × m-matrix and {A_l}_1 ≤ l ≤d some m × m-matrices such that the Hrmander condition holds.We first establish Bismut-type and Driver-type derivative formulas with applications on gradient estimates and the coupling/Liouville properties, which are new even for the heat semigroup on the Heisenberg group; then extend some recent results derived for the heat semigroup on the Heisenberg group.

Derivative Formula and Coupling Property for Linear SDEs Driven by Lévy Processes

In this paper we investigate an integration by parts formula for Lévy processes by using lower bound conditions of the corresponding Lévy measure. As applications, derivative formula and coupling property are derived for transition semigroups of linear SDEs driven by Lévy processes.

Efficient Computational Method for the Non-Probabilistic Reliability of Linear Structural Systems

The non-probabilistic reliability in higher dimensional situations cannot be calcu- lated efficiently using traditional methods, which either require a large amount of calculation or cause significant error. In this study, an efficient computational method is proposed for the cal- culation of non-probabilistic reliability based on the volume ratio theory, specificMly for linear structural systems. The common expression for non-probabilistic reliability is obtained through formula derivation with the amount of computation considerably reduced. The compatibility be- tween non-probabilistic and probabilistic safety measures is demonstrated through the Monte Carlo simulation. The high efficiency of the presented method is verified by several numerical examples.

Stochastic Volterra equations driven by fractional Brownian motion

This paper is devoted to study a class of stochastic Volterra equations driven by fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct application, we provide an alternative method to describe the regularities of the law of the solution. Secondly, by using the Malliavin calculus, the Bismut type derivative formula is established, which is then applied to the study of the gradient estimate and the strong Feller property. Finally, we establish the Talagrand type transportation cost inequalities for the law of the solution on the path space with respect to both the uniform metric and the L^2-metric.