Symbolic Manipulation Techniques Research Articles

Van der Waals perturbation theory for fermion and boson ground-state matter.

Using computer algebraic symbolic manipulation techniques, we rearrange the ideal-gas-based low-density expansions for the ground-state energy of a many-fermion and a many-boson system interacting via arbitrary pair central forces, into a repulsive-core-fluid-based perturbation expansion. Applications through second order are reported for liquid $^{4}\mathrm{He}$ and liquid $^{3}\mathrm{He}$.

Dual lanczos transformation theory; exact continued fraction expression for resonant γ-ray absorption spectrum of a harmonically bound atom executing classical motion described by smoluchowski dynamics

Implementing the mathematical apparatus of dual Lanczos transformation theory with the aid of symbolic manipulation techniques, we construct a previously unknown exact continued fraction expression for the resonant γ-ray absorption spectrum of a harmonically bound atom with an excited nucleus possessing a single radiative lifetime and executing classical motion described by Smoluchowski dynamics.

The role of computerized symbolic manipulation in rotorcraft dynamics analysis

The potential role of symbolic manipulation programs in development and solution of the governing equations for rotorcraft dynamics problems is discussed and illustrated. Nonlinear equations of motion for a helicopter rotor blade represented by a rotating beam are developed making use of the computerized symbolic manipulation program MACSYMA. The use of computerized symbolic manipulation allows the analyst to concentrate on more meaningful tasks, such as establishment of physical assumptions, without being sidetracked by the tedioys and trivial details of the algebraic manipulations. Furthermore, the resulting equations can be produced, if necessary, in a format suitable for numerical solution. A perturbation-type solution for the resulting dynamical equations is shown to be possible with a combination of symbolic manipulation and standard numerical techniques. This should ultimately lead to a greater physical understanding of the behaviour of the solution than is possible with purely numerical techniques. The perturbation analysis of the flapping motion of a rigid rotor blade in forward flight is presented, for illustrative purposes, via computerized symbolic manipulation with a method that bypasses Floquet theory.

Symbolic manipulation techniques for plasma kinetic theory derivations

Much of the analysis of instabilities and wave propagation in warm plasmas involves perturbative solutions of the Vlasov or collisionless Boltzmann equation. In general, a dielectric tensor which describes the response of the plasma to perturbations must be derived. A typical derivation involves choosing an equilibrium distribution function which models some plasma of interest, calculating a perturbed distribution function by solving a partial differential equation (usually by the method of characteristics), calculating density and current moments of this perturbed distribution function, and using these quantities in Maxwell's equations. For many equilibrium models of physical interest, this process can be completely carried out analytically. However, even in simple cases, the procedure is tedious-involving hundreds or thousands of separate algebraic or calculus operations and is fraught with opportunity for error. It will be illustrated here how the symbolic manipulation language MACSYMA can be used to automate many of the steps involved in such derivations. By way of example, the classic problem of oscillations in a homogeneous, uniformly magnetized plasma will be considered.

A generalized scientific information system

Information which is used for computation by any investigator in a quantitative branch of science may be broadly classified as numerical and nonnumeric. In handbook, numeric information is typically given in the form of tables or graphs. Nonnumeric information corresponds to the physical laws that hold in that branch of science. The physical laws are given in the form of functions or expressions. The user selects, from the handbook, information appropriate to the problem and manipulates the information using suitable tools (e.g. numeric, algebraic, heuristic). The scientific Information System (SIS) is a terminal oriented system that allows users facilities to retrieve information in the form of data of formulae and manipulate it. In this way, SIS gives the facility of using a handbook and also permits the user to solve problems using numeric and symbolic manipulation techniques.

Automation of the nonrelativistic ϕ3 field theory in two spatial dimensions

Both symbol manipulation and numerical techniques are used to automate the calculations in a nonrelativistic ϕ 3 theory in two spatial dimensions. This work applies primarily to the n-loop expansion. The system performed an entire 3-loop calculation in a perturbative orderindependent fashion, that is, generated graphs and the corresponding algebraic expressions, located and manipulated divergent subgraphs, did Feynman parameterization and analytic integration of momentum variables, and did the modifications for the vertex case and the numerical integration of the Feynman parameterization integrals. Since the system is implemented in FORTRAN it can be used almost anywhere. It can be used to facilitate both research and instruction in physics.

An Improved Symbolic Manipulation Technique for the Simulation of Nonlinear Dynamic Systems With Mixed Time-Varying and Constant Terms

The time domain behavior of nonlinear dynamic systems often is obtained by numerical integration on the digital computer. These solutions are usually expensive and limit the scope of the dynamic study. The proposed improved technique results in a substantial increase in the computational efficiency by using automatic symbolic manipulation to generate explicit equations of motion algebraically prior to numerical integration. A model is presented which considers the effects of the presence of time-invariant and time-varying symbolic terms and of the sparsity of system elements to provide analytical guidelines for the use of this technique. A number of case studies including typical computational costs are presented.

A correlation between crystallographic computing and artificial intelligence research

Artificial intelligence research, as a part of computer science, has produced a variety of programs of experimental and applications interest: programs for scientific inference, chemical synthesis, planning robot control, extraction of meaning from English sentences, speech understanding, interpretation of visual images, and so on. The symbolic manipulation techniques used in artificial intelligence provide a framework for analyzing and coding the knowledge base of a problem independently of an algorithmic implementation. A possible application of artificial intelligence methodology to protein crystallography is described.

An improved symbolic manipulation technique for the simulation of nonlinear dynamic systems with mixed time-varying and constant terms

An improved symbolic manipulation technique for the simulation of nonlinear dynamic systems with mixed time-varying and constant terms

Application of Symbolic Manipulation to Time Domain Analysis of Nonlinear Dynamic Systems

The digital computer is often used to perform time domain dynamic analyses of non-linear systems. Such analyses are notoriously expensive. In many cases this expense is due to algebraic computation with the solution process. Presented is a solution approach, using modern automatic symbolic manipulation techniques, which will result in substantial computational savings for a wide class of problems. Included are guidelines based on fundamental mathematical analysis, to predict which problems will benefit from this simulation approach.