Browsing Department of Mathematics by Author "Greenspan, Donald"

Now showing items 1-20 of 100

    • Absolute Minimization by Supercomputer Computation 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1987)
      **Please note that the full text is embargoed** ABSTRACT: Numerical methodology is developed for approximating the absolute minimum of a function or a functional. Only simplistic numerical techniques are introduced and ...

    • Accurate Quasi-Quantum Mechanical Numerical Methodology 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of MathematicsDepartment of Mathematics, 1990-10)
      **Please note that the full text is embargoed** ABSTRACT: A quasi-quantum mechanical method in which energy is determined by quantum mechanics and motion by Newtonian mechanics is studied by combining it with numerical ...

    • An Analysis of Stress Wave Propagation in Slender Bars Using a Discrete Particle Approach 

      Greenspan, Donald; Reeves, W. R. (University of Texas at ArlingtonDepartment of Mathematics, 1980-12)
      **Please note that the full text is embargoed** ABSTRACT: In this paper, a discrete particle approach is developed for the quantitative analysis of stress wave propagation in metal bars. Though linear forces are emphasized, ...

    • Analytical and Numerical Studies on the States of Ions and Atoms 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1985)
      **Please note that the full text is embargoed** ABSTRACT: A speculative model is described which refines and extends the method of Bohr to various atoms and ions which have four or fewer electrons. The results for ground, ...

    • Arbitrary Order, Hamiltonian Conserving Numerical Solutions of Calogero and Toda Systems 

      Greenspan, Donald; Marciniak, Andrzej (University of Texas at ArlingtonDepartment of Mathematics, 1990)
      **Please note that the full text is embargoed** ABSTRACT: For Calogero and Toda dynamical equations two numerical methods of arbitrary high order, conserving the Hamiltonian are developed. The methods consist of modifications ...

    • An Arithmetic Computer Approach to Gas Dynamical Modeling 

      Greenspan, Donald; Wadia, Aspi Rustom (University of Texas at ArlingtonDepartment of Mathematics, 1979-01)
      **Please note that the full text is embargoed** ABSTRACT: Unsteady, two dimensional internal and external flows are analyzed using an arithmetic n-body formulation. A Lagrangian approach is used to study the internal shock ...

    • A Classical Molecular Approach to Computer Simulation of Biological Sorting 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1980-05)
      **Please note that the full text is embargoed** ABSTRACT: Steinberg's theory of sorting is modified by replacing the free energy minimization principle with dynamical equations of a molecular nature. Correct cellular sorting ...

    • Classical, Computer Studies of One-Electron and Two-Electron Atoms and Ions 

      Greenspan, Donald (University of Texas of ArlingtonDepartment of Mathematics, 1991-06)
      **Please note that the full text is embargoed** ABSTRACT: A geometrical, computer-oriented method is utilized to generate circular orbits of electrons in one-electron and two-electron atoms and ions. The radii of these ...

    • Completely Conservative and Covariant Numerical Methodology for N-Body Problems With Distance-Dependent Potentials 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1992-01)
      **Please note that the full text is embargoed** ABSTRACT: We consider a general class of N-body problems for arbitrary, distance-dependent potentials. Completely conservative, covariant numerical methodology is established ...

    • Computer Experiments for Molecular Motions and Chemical Bonding 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1995-12)
      **Please note that the full text is embargoed** ABSTRACT: It is shown how to simulate first the ground state molecule H. The correct bond length, period, and electron cloud result. The method is then extended to ground ...

    • Computer Files for Drop Formation 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1987)
      **Please note that the full text is embargoed**

    • Computer Modelling of a Dynamical Water Molecule 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1995)
      **Please note that the full text is embargoed** ABSTRACT: A model of a ground state water molecule is formulated dynamically and studied by computer simulations. The enigmatic 104.5° bond angle is approximated by introducing ...

    • Computer Simulation of a Dynamical Model of the Water Molecule 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1982-07)
      **Please note that the full text is embargoed** ABSTRACT: A new computer-orlented theory for molecular dynamics is applied to modeling the water molecule. The dynamical equations are derived from molecular stability ...

    • Computer Studies in Particle Modeling of Fluid Phenomena 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1984-02)
      **Please note that the full text is embargoed** ABSTRACT: A new, numerical approach is developed for modeling fluid phenomena. Unlike the continuum and statistical mechanics approaches, it uses relatively small sets of ...

    • Computer Studies of a Semiclassical Model of the Water Molecule 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1993)
      **Please note that the full text is embargoed** ABSTRACT: A semiclassical model of the water molecule is formulated in ground state as an eleven-body problem. The stiff system of dynamical, nonlinear, ordinary differential ...

    • Computer Studies of the Classical Oxygen Molecule 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1980-03)
      **Please note that the full text is embargoed** ABSTRACT: A classical, simplistic model of the molecular dynamics of 02 is developed for interactions which are not readily amenable to quantum mechanical analysis. ...

    • Computer Study of a Semiclassical Model of the Dynamical Water Molecule 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1993-03)
      **Please note that the full text is embargoed** ABSTRACT: A semiclassical model of the water molecule is formulated as an eleven-body problem. The stiff system of differential equations is run for two billion time steps ...

    • Computer-Oriented, n-Body Modelling of Minimal Surfaces 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1982-12)
      **Please note that the full text is embargoed** ABSTRACT: In this paper a new approach to the modeling of minimal surfaces is described and applied. Rather than use a continuous model, we develop a discrete n-body model ...

    • Conservative Difference Formulations of Calogero and Toda Hamiltonian Systems 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1988)
      **Please note that the full text is embargoed** ABSTRACT: Calogero and Toda Hamiltonian systems are reformulated using only differences. The formulations prove to have the same fundamental invariants as the continuous ...

    • Conservative Motion of a Discrete, Nonsymmetric, Hexahedral Gyroscope 

      Greenspan, Donald (University of Texas at ArlingtonDepartment of Mathematics, 1997)
      **Please note that the full text is embargoed** ABSTRACT: Gyroscopic motion is simulated by applying a molecular dynamics formulation to a rigid hexahedron. The conservative dynamical differential equations are solved ...