Error bounds for the solution to the algebraic equations in Runge-Kutta methods

In the implementation of implicit Runge-Kutta methods inaccuracies are introduced due to the solution of the implicit equations. It is shown that these errors can be bounded independently of the stiffness of the differential equation considered if a certain condition is satisfied. This condition is also sufficient for the existence and uniqueness of a solution to the algebraic equations. TheBSI-andBS-stability properties of several classes of implicit methods are established.     

相对论性核碰撞中φ介子增强

用强子和弦级联模型LUCIAE系统地研究了相对论性p+p和Pb+Pb碰撞中φ介子产生.在模型框架内实验测得的158AGeV/cPb+Pb碰撞中φ介子产额相对于同能量p+p碰撞的增强现象,依赖于弦发射胶子的集体效应和奇异夸克压低约化两机制,在一定程度内能得到解释.     

Two-dimensional random walk description of fluid flow in the presence of a wall: The origin of stick versus slip boundary conditions in the continuum limit

It is shown how a fairly simple random walk on a lattice provides insight into the nature of hydrodynamic boundary conditions. In a flow parallel to the boundary, collisions of up and downward moving particles induce lateral bulk diffusion. At the wall the model accounts essentially for 1) specular reflection, 2) diffuse reflection and 3) trapping at the surface. The steady state is solved exactly. In the continuum limit the case of stick versus slip boundary conditions is explained in its relation to the interplay of bulk and boundary processes.     

On the functional integral representation of general continuous markov processes

The unambiguous continuous functional integral representation of general diffusion processes will be derived by means of a transformation invariant Fourier series analysis of the alternate paths between specified endpoints. Previous results from Stratonovich, Horsthemke and Bach, and Graham will be confirmed, while deeper insight is gained into the limit of continuity in functional integration.