In terms of the reduced potential energy barrier ζ = ΔuTS/kT, the rate coefficients for chemical reactions are usually expressed as proportional to e-ζ. The coupling between vibrational modes of the medium to the reaction coordinate leads to a proportionality of the regularized gamma function of Euler Q(a,ζ) = Γ(a,ζ)/Γ(a), with a being the number of modes coupled to the reaction coordinate. In ...

Height coordinate ocean models commonly represent topography as a ‘‘staircase’’ of discontinuous steps that are fitted to the model grid. Here the ramifications of an alternative approach are studied in which ‘‘shaved cells’’ are used to represent irregular topography. The problem is formulated using the finite-volume method and care is taken to ensure that the discrete forms have appropriate c...

In this paper, we address the problem of how to seamlessly and without repetition artifacts or visible projective distortion cover the surface of a polygonally-defined model with a texture pattern derived from an acquired 2D image such that the dominant orientation of the pattern will everywhere follow the surface shape in an aesthetically pleasing way. Specifically, we propose an efficient, au...

The Grad–Shafranov plasma equilibrium equation was originally solved analytically in toroidal geometry, which fitted the geometric shape of first Tokamaks. poloidal surface Tokamak has evolved over years from a circular to D-shaped ellipse. natural geometry that describes such is prolate elliptical one, i.e., cap-cyclide coordinate system. When written this can be terms general Heun function. I...

This paper is about the study of B-FQI, an Approximated Value Iteration (AVI) algorithm that exploits a boosting procedure to estimate the action-value function in reinforcement learning problems. B-FQI is an iterative off-line algorithm that, given a dataset of transitions, builds an approximation of the optimal action-value function by summing the approximations of the Bellman residuals acros...

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted can exactly integrate (except round-off errors) the common test: y?=?w2y. local truncation error method derived, we show that order convergence maintained. stability analysis addressed, demonstrate absolutely ...