Vol. 3, No 3, 1999 < Volumes
(ISSN 1428-6394)

Contents:

  • P.Syty, The J-matrix Method: Numerical Computations | abstract
  • P.Maponi, An Inverse Medium Problem for the Heat Equation | abstract
  • J.Bosko and W.Sadowski, Molecular Dynamics Study of Temperature-induced Structural Changes in YBa2Cu3O7 Crystal | abstract
  • R.Laskowski and M.Chybicki, The Influence of Low Density Behaviour of State Equation on Lattice Inverted Pair Potential for Lead | abstract
  • D.R.Ripoll, A.Liwo, C.Czaplewski and H.A.Scheraga, The ECEPP Package for Conformational Analysis of Polypeptides | abstract
  • B.Pliszka and S.Oldziej, Molecular Dynamic Simulations of Large RNA Molecules: The Yeast tRNA | abstract
  • H.Kudela, Application of the Votex-In-Cell Method for the Simulation of Two-Dimensional Viscous Flow | abstract

From the History of Science and Technology in Ancient Gdansk:

  • A.Januszajtis, Fortifications of Old Gdansk

Abstracts:

h P.Syty, The J-matrix Method: Numerical Computations

Numerical calculations of scattering phase shifts have been done using J-matrix method (both non-relativistic and relativistic versions). Results of computations for some simple potentials are described and discussed in this paper. In particularly, it has been shown, that successive numerical approximations converge to results obtained using an analytical formula.

 

h P.Maponi, An Inverse Medium Problem for the Heat Equation

In the article we consider the two-dimensional heat equation in a circular domain where the thermal diffusivity is a piecewise constant function in the radial directon and is a constant function in the angular direction. In particular we consider the problem of computation of a perturbation in this stratified medium having some information/knowledge about the temperature on the boundary of the domain due to heat flux applied to the same boundary. A linearized version of this inverse problem is considered and a linear integral equation is used for the numerical solution of the inverse problem. Some numerical examples are reported.

 

h J.Bosko and W.Sadowski, Molecular Dynamics Study of Temperature-induced Structural Changes in YBa2Cu3O7 Crystal

The structure of YBa2Cu3O7 crystal has been studied with the aid of molecular-dynamics (MD) technique. A two-body model potentials proposed by Zhang and Catlow have been used in MD simulations performed in wide range of temperature. The temperature-induced orthorhombic-to-tetragonal phase transition is observed. The distruction of the arrangement of atoms in the CuO chains due to diffusion of oxygen atoms is observed. The diffusion coefficients are calculated, and their variation as a function of temperature is analysed. The activation energy is estimated.

 

h R.Laskowski and M.Chybicki, The Influence of Low Density Behaviour of State Equation on Lattice Inverted Pair Potential for Lead

A pair potential for lead (Pb) is extracted from the ab-initio energy-volume data using the lattice inversion procedure of Carlsson and co-workers [Phil. Mag. 41 (1980), p. 241]. Because of a limited accuracy of the ab-initio techniques, we extrapolate the energy-volume data for low-density systems with suitable analytical tail functions. We discuss the dependence of the molecular dynamics (MD) simulation structural results and the elastic modules on the choice of the cohesive energy tail function. The MD-simulated radial distribution functions (RDFs), obtained for several energy tails, in several temperatures are discussed.

 

h D.R.Ripoll, A.Liwo, C.Czaplewski and H.A.Scheraga, The ECEPP Package for Conformational Analysis of Polypeptides

We present here the ECEPPAK (developed in the laboratory of prof. H.A. Scheraga, Cornell University) and ANALYZE packages for the conformational search of polypeptides that is based on the ECEPP/3 force field. The functions of the program include energy calculation and minimization and global conformational search using the Electrostatically Driven Monte Carlo (EDMC) method. The search can be constrained using experimental information e.g., the distance constraints from NMR measurements. The sister program, ANALYZE, allows the user to classify the conformations by means of cluster analysis and fit the statistical weights of the conformations to best fit the experimental observables. The package is extensively parallelized, which allows the user to carry out the conformational search even of comparatively large polypeptides in real time.

 

h B.Pliszka and S.Oldziej, Molecular Dynamic Simulations of Large RNA Molecules: The Yeast tRNA

Molecular dynamics trajectories (700 ps) of the solvated and neutralized 75-residue yeast tRNAPhe were generated using the AMBER 5.0 molecular dynamics software package. The cut-off scheme was used to treat electrostatic interactions; consequently, all long-range interactions beyond 12 angstroms were neglected. The equilibration procedure and conditions during simulations led to a dynamically stable model of the tRNA molecule. During the simulations all base-base interactions (which determine the secondary and the tertiary structure of the molecule) were well preserved. Consequently, the global shape of the molecule was preserved well and the RMS deviation calculated between the starting x-ray structure and the final structure after 700 ps of simulations was 3.25 angstroms. The biggest deviation is observed in the region of the anticodon hairpin loop; this high mobility is associated with the presence of a very unusual Y-base and a binding site of a magnesium ion in this region.

 

h H.Kudela, Application of the Votex-In-Cell Method for the Simulation of Two-Dimensional Viscous Flow

In the paper the vortex in cell method for the simulation of the viscous flow in a complex geometry was described. Vorticity field is approximated by the collection of the particles that carries the circulation. The local velocity of a particle was obtained by the solution of the Poisson equation for the stream function by the grid method and then interpolation of velocity from the grid nodes to the vortex particle position. The Poisson equation for the stream function was solved by fast elliptic solvers. To be able to solve the Poisson equation in a region with a complex geometry, the capacitance matrix technique was used. The viscosity of the fluid was taken in a stochastic manner. A suitable stochastic differential equation was solved by the Huen method. The non-slip condition on the wall was realized by the generation of the vorticity. The program was tested by solving several flows in the channels with a different geometry and at a different Reynolds number. Here we present the testing results concerning the flow in a channel with sudden symmetric expansion, for the flow in channel with backward step, and the flow over building systems.

 

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