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The aim of this Letter is to examine and identify longitudinal resistive wall wake potential behaviours of medium‐β long bunches and ultra‐relativistic short bunches using different beam and pipe properties for particle accelerator applications. The lack of detailed analysis in current literature for the chosen set of parameters ignites this work. Since computations of wake potentials for the considered beam parameters by particle‐in‐cell codes are extremely difficult the author uses an analytical approach. Numerical integrations are evaluated for large domains with fine discretisations. The author observes that conductivity of beam pipe has a larger impact on medium‐β long bunches, variation of beam velocity effects wakes of short bunches more significantly, beam radii changes may have a contribution to instability for low energy short bunches. Interesting numerical results are presented and their physical explanations are discussed in this Letter. [ABSTRACT FROM AUTHOR]

We construct an efficient quadrature method for the integration of the Galerkin weak form over general 3D polyhedral elements based on the radial integration method (RIM). The basic idea of the proposed method is to convert the polyhedral domain integrals to contour plane integrals of the element by utilizing the RIM which can be used for accurate evaluation of various complicated domain integrals. The quadrature construction scheme for irregular polyhedral elements involves the treatment of the nonpolynomial shape functions as well as the arbitrary geometry shape of the elements. In this approach, the volume integrals for polyhedral elements with triangular or quadrilateral faces are evaluated by transforming them into face integrals using RIM. For those polyhedral elements with irregular polygons, RIM is again used to convert the face integrals into line integrals. As a result, the volume integration of Galerkin weak form over the polyhedral elements can be easily carried out by a number of line integrals along the edges of the polyhedron. Some benchmark numerical examples including the patch tests are utilized to demonstrate the accuracy and convenience of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Numerical integration formulas in n-dimensional Euclidean space of degree three are discussed. In this paper, for the product regions a method is presented to construct numerical integration formulas of degree three with 2n real points and positive weights. The presented problem is a little different from those dealt with by other authors. All the corresponding one-dimensional integrals can be different from each other and they are also nonsymmetrical. In this paper an n-dimensional numerical integration problem is turned into n one-dimensional moment problems, which simplifies the construction process. Some explicit numerical formulas are given. Furthermore, a more generalized numerical integration problem is considered, which will shed light on the final solution to the third degree numerical integration problem. [Copyright &y& Elsevier]

An interesting connection exists between convex functions and uniformly continuous functions. This linkage leads to some interesting functional inequalities over the open interval which works well in quadrature rules and means. In this paper, we establish two new theorem which connect the Hermite–Hadamard type functions. [Copyright &y& Elsevier]

The origin of Centaurs is one of the most interesting problems of Solarsystem science, and it has not yet been solved. To shed light onthis problem one can investigate Centaurs' past and future orbitalevolution. In this paper we discuss the results of Chiron's orbitalevolution modeling. It was the first discovered Centaur and is thebrightest one. Numerical integration was produced for 1 Myrforward and backward from the present time. A program based on theEverhart single sequence method for integrating orbits was used. [ABSTRACT FROM AUTHOR]

The present paper is a brief report of how, along the lines of a previous paper, the implementation of the program KEPLER1, for the numerical integration of the perturbations of the Kepler problem, has been carried out. [ABSTRACT FROM AUTHOR]

Here two types of optimal V-cycle multigrid algorithms are presented for Wilson nonconforming finite element. [ABSTRACT FROM AUTHOR]