Least-squares fitting applied to nuclear mass formulas. Solution by the Gauss–Seidel method

In this paper, a numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear system which is solved by iterations according to the Gauss–Seidel scheme. The steps of the algorithm are given in detail. In practice, the method is very simple to implement and is able to treat large data in a very fast way. In fact, although this method has been illustrated here by specific examples, it can be applied without difficulty to any experimental or statistical data of the same type, i.e. those leading to linear system characterized by symmetric and positive-definite matrices.

Coupling Friction with Visual Appearance

We present a novel meso-scale model for computing anisotropic and asymmetric friction for contacts in rigid body simulations that is based on surface facet orientations. The main idea behind our approach is to compute a direction dependent friction coefficient that is determined by an object's roughness. Specifically, where the friction is dependent on asperity interlocking, but at a scale where surface roughness is also a visual characteristic of the surface. A GPU rendering pipeline is employed to rasterize surfaces using a shallow depth orthographic projection at each contact point in order to sample facet normal information from both surfaces, which we then combine to produce direction dependent friction coefficients that can be directly used in typical LCP contact solvers, such as the projected Gauss-Seidel method. We demonstrate our approach with a variety of rough textures, where the roughness is both visible in the rendering and in the motion produced by the physical simulation.

Algorithm for simulating the self-starting of a group of asynchronous electric motors with a short-circulated rotor

PURPOSE. To consider the problems of modeling the processes of run-out, self-starting of a group of asynchronous electric motors (AM) in case of short-term power outages (NEC) and voltage drops in external short circuits (SC), convenient for programming and practical use. To establish the integral reaction of the AM group during self-start to the disturbing effect, taking into account their characteristics and duration to establish the permissible limit values of the NEC. To develop an algorithm for the transient process of self-starting of the AM group when using matrix and vector data representation when solving the basic equation of the rotor motion and its computer implementation. METHODS. When solving the problem, the following methods were used: successive approximations when solving the basic electromechanical equation, taking into account electromagnetic transient processes; Gauss-Seidel method with accelerating the convergence of the iterative process when solving the equations of the parameters of the regime; method of nodal stresses. The algorithm is implemented in VBA and tested in Matlab Simulink. RESULTS. The article describes the relevance of the topic, considers a model of AM according to catalog data, an algorithm for self-starting a group of an AM with NEC and external short circuits, taking into account electromagnetic transient processes, which has high accuracy and is convenient for practical use. CONCLUSION. The use of asynchronous motor catalogs makes it possible not to carry out laborious preliminary calculations of the parameters of asynchronous motors. The application of the Gauss-Seidel method with acceleration of convergence provides a decrease in the number of iterations. Taking into account electromagnetic transients and the effect of displacement of the rotor current allows you to evaluate the mutual influence of motors and increase the accuracy of calculations. The use of the method of nodal voltages makes it possible to determine the residual voltage on the busbar section with AM, if at the first moment the motors are switched on to short circuit. The implementation of the algorithm in the VBA environment is convenient for practical use.

Algorithm for simulating the self-starting of a group of asynchronous electric motors with a short-circulated rotor

PURPOSE. To consider the problems of modeling the processes of run-out, self-starting of a group of asynchronous electric motors (AM) in case of short-term power outages (NEC) and voltage drops in external short circuits (SC), convenient for programming and practical use. To establish the integral reaction of the AM group during self-start to the disturbing effect, taking into account their characteristics and duration to establish the permissible limit values of the NEC. To develop an algorithm for the transient process of self-starting of the AM group when using matrix and vector data representation when solving the basic equation of the rotor motion and its computer implementation. METHODS. When solving the problem, the following methods were used: successive approximations when solving the basic electromechanical equation, taking into account electromagnetic transient processes; Gauss-Seidel method with accelerating the convergence of the iterative process when solving the equations of the parameters of the regime; method of nodal stresses. The algorithm is implemented in VBA and tested in Matlab Simulink. RESULTS. The article describes the relevance of the topic, considers a model of AM according to catalog data, an algorithm for self-starting a group of an AM with NEC and external short circuits, taking into account electromagnetic transient processes, which has high accuracy and is convenient for practical use. CONCLUSION. The use of asynchronous motor catalogs makes it possible not to carry out laborious preliminary calculations of the parameters of asynchronous motors. The application of the Gauss-Seidel method with acceleration of convergence provides a decrease in the number of iterations. Taking into account electromagnetic transients and the effect of displacement of the rotor current allows you to evaluate the mutual influence of motors and increase the accuracy of calculations. The use of the method of nodal voltages makes it possible to determine the residual voltage on the busbar section with AM, if at the first moment the motors are switched on to short circuit. The implementation of the algorithm in the VBA environment is convenient for practical use.

Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices

This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.