Computation of functions and their derivatives in Content

Scientific software for investigation of dynamical systems usually allows the user to specify systems in the form of functions in some language. There are several problems related to this: how to compute derivatives of these functions (since numerical algorithms need to compute first and higher order derivatives) and how to convert these functions and their derivatives to a machine suitable form. The key issues are minimal effort required from the user to manipulate functions and high efficiency in calculations that extensively compute functions and their derivatives. This work presents some solutions to these problems which are incorporated in CONTENT, a new program for bifurcation analisys of dynamical systems. Derivatives are built during a three-stage process by means of transforming C source given by the user for right-hand sides into a C++ program which constructs another C program for computing derivatives. A special C++ class with overloaded operators and functions is used to produce this C program during the execution of the C++ program. A description of a dynamical system (i.e., functions and their derivatives) is compiled and linked as a dynamic library during a CONTENT session. This does not require linking with the rest of software. Dynamic libraries for different systems are created, loaded, and functions in them are accessed without necessity to quit CONTENT

The magnetic field influence on magnetostructural phase transition in Ni2.19Mn0.81Ga

Magnetic properties of a polycrystalline alloy Ni$_{2.19}$Mn$_{0.81}$Ga, which undergoes a first-order magnetostructural phase transition from cubic paramagnetic to tetragonal ferromagnetic phase, are studied. Hysteretic behavior of isothermal magnetization $M(H)$ has been observed in a temperature interval of the magnetostructural transition in magnetic fields from 20 to 100 kOe. Temperature dependencies of magnetization $M$, measured in magnetic fields $H = 400$ and 60 kOe, indicate that the temperature of the magnetostructural transition increases with increasing magnetic field.Comment: Presented at the Second Moscow International Symposium on Magnetism (Moscow-2002

Continuation of stationary solutions to evolution problems in CONTENT

A numerical algorithm for continuation of stationary solutions to nonlinear evolution problems representable in the form begin{array{ll u_t=F(u_{xx,u_{x,u,x,alpha),& 0 < x < 1, f^{0(u_x,u,alpha)=0,& x=0, f^{1(u_x,u,alpha)=0,& x=1, end{array is described as implemented in {sc content. Here F:{Bbb R^n times {Bbb R^n times {Bbb R^n times {Bbb R^m to {Bbb R^n and f^{0,1:{Bbb R^n times {Bbb R^n times {Bbb R^m to {Bbb R^n are sufficiently smooth nonlinear functions. The algorithm is based on the second-order finite-difference approximation with an adaptive non-uniform mesh selection. Special methods for efficient solution of linear systems appearing in the continuation are presented. Several examples are given

Research into the special features of the ultrasonic strengthening of turbomachine components

22.00; Translated from Russian (Izv. Vyssh. Uchebn. Zaved., Chern. Metall. 1987 (9) p. 68-71)Available from British Library Document Supply Centre- DSC:9022.06(BISI-Trans--26448)T / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo