Computers in Physics
Computers in Physics was published from 1987 until the end of 1998. At the beginning of 1999 CIP was merged with IEEE Computational Science & Engineering to create the bimonthly magazine: Computing in Science and Engineering. Computing in Science and Engineering is a joint publication of the American Institute of Physics and IEEE Computer Society.
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New approach for simulating chain conformations in dense polymers using fully populated lattice models
View Description Hide DescriptionA twodimensional implementation of a new computational approach for the simulation of the microscopic chain conformations in dense linear polymers is presented. The macromolecular chains are represented as selfavoiding and mutually avoiding random walks on a fully populated lattice corresponding to the amorphous regions of a lamellar semicrystalline morphology. In this approach, information is generated based on a transfer matrix approach in terms of the permutations of the vertical and the horizontal bonds in the lattice rows. The data are then subsequently corrected to eliminate contributions from unwanted microscopic states containing closed loop (ring) chain structures. It is shown that the linear chain conformational entropy can be estimated from first principles by an efficient accounting of all the feasible microstates. In addition, statistical information on the chain conformations can also be obtained. The chain statistics presented here are compared with the predictions of ideal or nearly ideal random walks (Gambler’s ruin models) from the literature where little or no excluded volume effects are taken into account. It is shown that the chain connectivity influences the chain statistics significantly. © 1998 American Institute of Physics.
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Explicit sixthorder Bessel and Neumann fitted method for the numerical solution of the Schrödinger equation
View Description Hide DescriptionAn explicit sixthalgebraicorder method for the numerical solution of the Schrödinger equation for a neutral particle is developed. The new formula considered contains free parameters that are defined in order to integrate the spherical Bessel and Neumann functions exactly. Based on the new method and a method of Simos we obtained a variablestep algorithm. The results produced, based on the numerical solution of the radial Schrödinger equation, indicate that this new approach is more efficient than other wellknown ones. © 1998 American Institute of Physics.
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New formula for 9j symbols and their direct calculation
View Description Hide DescriptionAn algebraic expression for 9 symbols in the form of a summation of the products of binomial coefficients is obtained. An algorithm is also devised to calculate these binomial coefficients recursively. This avoids the evaluation of factorials of integers, which is the main source of overflow in calculation of coupling coefficients for large angular momenta. Thus, the new formula permits accurate calculation of 9 symbols. In addition, it has higher symmetry and involves only a twofold summation. Therefore, a direct approach for accurate and efficient calculation of 9 symbols for very large angular momenta is thereby established. © 1998 American Institute of Physics.
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A tensorial approach to computational continuum mechanics using objectoriented techniques
View Description Hide DescriptionIn this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuummechanics codes: this is achieved by making the toplevel syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Objectorientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computationalfluiddynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.
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Mathematica package for analysis and control of chaos in nonlinear systems
View Description Hide DescriptionIn this article a symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented. We start by presenting the main properties of chaos and describing some commands with which to obtain qualitative and quantitative measures of chaos, such as the bifurcation diagram and the Lyapunov exponents, respectively. Then we analyze the problem of chaos control and suppression, illustrating the different methodologies proposed in the literature by means of two representative algorithms (linear feedback control and suppression by perturbing the system variables). A novel analytical treatment of these algorithms using the symbolic capabilities of Mathematica is also presented. Well known one and twodimensional maps (the logistic and Hénon maps) and flows (the Duffing and Rössler systems) are used throughout the article to illustrate the concepts and algorithms. © 1998 American Institute of Physics.
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Agency: AIP Publishing
Agency: AIP Publishing