Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Publication Year
- Publication Type
Articles 31 - 60 of 196
Full-Text Articles in Mathematics
Studies In Rapid Kinetic Reactions By Quasi-Quantum Mechanical, Conservative Methodology, Donald Greenspan
Studies In Rapid Kinetic Reactions By Quasi-Quantum Mechanical, Conservative Methodology, Donald Greenspan
Mathematics Technical Papers - Archive
Simulations are made of prototype, ground state, rapid kinetic reactions for A+BC, in which B, and C are hydrogen atoms and BC is a hydrogen molecule. We study cases in which B and C first unbind, and then A, B, and C undergo complex, three-body, oscillatory behavior in accordance with the Morse potential. It is shown that, in every case, one of A, or C is ejected and the remaining two atoms form an H2 bond with precisely correct ground state energy, frequency, and bond length. Pico second trajectories are described and discussed. The numerical method employed conserves the system's …
A Method For Approximating The Solution Set Of A System Of Convex Inequalities By Polytopes, Yair Censor, Dan Butnariu
A Method For Approximating The Solution Set Of A System Of Convex Inequalities By Polytopes, Yair Censor, Dan Butnariu
Mathematics Technical Papers - Archive
In this note a method for computing approximations by polytopes of the solution set [see pdf for notation] of a system of convex inequalities is presented. It is shown that such approximations can be determined by an algorithm which converges in finitely many steps when the solution set of the given system of inequalities is bounded. In this case, the algorithm generates "inner" and "outer' approximations having the Hausdorff distance to each other (and to the set [see pdf for notation]) not greater than an a priori fixed [see pdf for notation] and having their extremal points in [see pdf …
Generalized Gradient Methods For Solving Locally Lipschitz Feasibility Problems, Dan Butnariu
Generalized Gradient Methods For Solving Locally Lipschitz Feasibility Problems, Dan Butnariu
Mathematics Technical Papers - Archive
In this paper we study the behavior of a class of iterative algorithms for solving feasibility problems, that is finite systems of inequalities [see pdf for notation], where each [see pdf for notation] is a locally Lipschitz functional on a Hilbert space X. We show that, under quite mild conditions, the algorithms studied in this note, if converge, then they approximate a solution of the feasibility given problem, provided that the feasibility problem is consistent. We prove several convergence criteria showing that, when the envelope of the functionals [see pdf for notation], is sufficiently "regular", then the algorithms converge. The …
Accurate Quasi-Quantum Mechanical Numerical Methodology, Donald Greenspan
Accurate Quasi-Quantum Mechanical Numerical Methodology, Donald Greenspan
Mathematics Technical Papers - Archive
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 methodology which conserves energy exactly at each time step. Application is made to the study of the diameter and vibrational frequency of the ground state H2 molecule. The numerical results agree exactly with experimental and quantum mechanical results.
Supercomputer Simulation Of The Modes Of Colliding Microdrops Of Water, Larry F. Heath, Donald Greenspan
Supercomputer Simulation Of The Modes Of Colliding Microdrops Of Water, Larry F. Heath, Donald Greenspan
Mathematics Technical Papers - Archive
No abstract provided.
On The Error In Quasi-Quantum Mechanical Calculations, Donald Greenspan
On The Error In Quasi-Quantum Mechanical Calculations, Donald Greenspan
Mathematics Technical Papers - Archive
A numerical simulation of the vibration of a ground state H2 molecule is made from a quasi-quantum mechanical point of view, that is, energy has been determined by quantum mechanics and trajectories determined by Newtonian mechanics. The numerical method used is implicit and conserves the energy exactly at each time step. A variety of CRAY X-MP/SE14 calculations are described and discussed. Comparisons are made with correct oscillation and diameter values.
A Particle Model Of Ground State H2, Donald Greenspan
A Particle Model Of Ground State H2, Donald Greenspan
Mathematics Technical Papers - Archive
A particle model is developed for the ground state H2 molecule. Interparticle forces are formulated which are noncoulombic, but nearly coulombic. The vibration is simulated by a numerical method which conserves the molecule's energy exactly. Numerical examples are described and discussed.
Energy Conserving Numerical Solutions Of Simplified Turbulence Equations, Donald Greenspan, Andrzej Marciniak
Energy Conserving Numerical Solutions Of Simplified Turbulence Equations, Donald Greenspan, Andrzej Marciniak
Mathematics Technical Papers - Archive
The purpose of this paper is to develop some numerical methods for solving non-Hamiltonian nonintegrable simplified turbulence equations which conserve the energy. We present two kinds of conservative methods for solving these equations: a second order method which uses simple differences, and an arbitrary high order method based on a modification of conventional polynomial extrapolation.
Quasimolecular Simulation Of Pendent Water Drops, Donald Greenspan
Quasimolecular Simulation Of Pendent Water Drops, Donald Greenspan
Mathematics Technical Papers - Archive
Pendent water drops are simulated by molecular aggregates, called quasimolecules. The quasimolecules interact in accordance with classical molecular type formulas. Supercomputer examples are described and discussed for both stationary and for falling drops.
Supercomputer, Simulation Of Liquid Drop Formation, Fall, And Collision, Donald Greenspan
Supercomputer, Simulation Of Liquid Drop Formation, Fall, And Collision, Donald Greenspan
Mathematics Technical Papers - Archive
A generic molecular type model of liquid drops is developed and studied. Drop formation, fall, and collision are simulated on a CRAY X-MP/24 and associated modes of oscillation are described. Methods for application to particular fluids with known Lennard-Jones parameters are given.
Particle Simulation Of Biological Sorting On A Supercomputer, Donald Greenspan
Particle Simulation Of Biological Sorting On A Supercomputer, Donald Greenspan
Mathematics Technical Papers - Archive
Cell sorting, or, self reorganization, is modelled by means of particles which obey classical molecular dynamical equations. A system of N second order, nonlinear, ordinary differential equations results when the number of particles is N. Applications and examples are described and discussed, with N > 1000, for both double layer and triple layer self reorganization.
Covariant Computation In Special Relativistic Dynamics, Donald Greenspan
Covariant Computation In Special Relativistic Dynamics, Donald Greenspan
Mathematics Technical Papers - Archive
The motion of a particle in a special relativistic framework is studied numerically. Difference equations which are covariant are developed first. It is then shown how computations can be done in both the lab and rocket frames so that the numerical results are related by the Lorentz transformation. Finally, assuming the usual force formula for harmonic oscillation, it is shown that the dynamical equation is necessarily nonlinear and trajectories are studied numerically for various initial data.
Conservative Difference Formulations Of Calogero And Toda Hamiltonian Systems, Donald Greenspan
Conservative Difference Formulations Of Calogero And Toda Hamiltonian Systems, Donald Greenspan
Mathematics Technical Papers - Archive
Calogero and Toda Hamiltonian systems are reformulated using only differences. The formulations prove to have the same fundamental invariants as the continuous systems and, in addition, are readily implementable on modern digital computers.
Absolute Minimization By Supercomputer Computation, Donald Greenspan
Absolute Minimization By Supercomputer Computation, Donald Greenspan
Mathematics Technical Papers - Archive
Numerical methodology is developed for approximating the absolute minimum of a function or a functional. Only simplistic numerical techniques are introduced and explored. CRAY X—MP/24 computer examples are described and discussed.
Programs For Vortex Street Generation, Donald Greenspan
Programs For Vortex Street Generation, Donald Greenspan
Mathematics Technical Papers - Archive
No abstract provided.
Computer Files For Drop Formation, Donald Greenspan
Computer Files For Drop Formation, Donald Greenspan
Mathematics Technical Papers - Archive
No abstract provided.
Cray X-Mp/24 Fortran Programs For Capillarity, Donald Greenspan
Cray X-Mp/24 Fortran Programs For Capillarity, Donald Greenspan
Mathematics Technical Papers - Archive
This technical report contains the FORTRAN programs used in generating capillary action. They are provided so that the computations described elsewhere can be reproduced by the interested reader. Without this availability, computer calculations and experiments could not be duplicated exactly, and related results and conclusions might be suspect.
Zeros Of Bouligand-Nagumo Fields, Flow-Invariance And The Bouwer Fixed Point Theorem, Nicolae H. Pavel
Zeros Of Bouligand-Nagumo Fields, Flow-Invariance And The Bouwer Fixed Point Theorem, Nicolae H. Pavel
Mathematics Technical Papers - Archive
Mainly, in this paper we prove that if D is a convex compact of Rn, then the Brouwer fixed point property of D is equivalent to the fact that every Bouligand-Nagums vector field on D, has a zero in D. Using a version of this result on a normed space, as well as the Day [9] and Dugundji [10] theorems, we give a new proof to the fact that in every infinite dimensional Banach space X, there exists a continuous function from the closed unit ball B (of X) into B, without fixed points in B. We also show that …
Supercomputer Simulation Of Sessile And Pendent Drops, Donald Greenspan
Supercomputer Simulation Of Sessile And Pendent Drops, Donald Greenspan
Mathematics Technical Papers - Archive
A intermolecular approach is developed for the modeling of sessile and pendent drops. Fundamental mechanisms of drop formation are formulated in terms of gravity and classical intermolecular type forces. CRAY X-MP/24 computer examples illustrate standing and falling drops, free surface motions, and convergence to equilibrium. The role of temperature in drop configuration modeling is shown to be significant.
Semiclassical Modeling Of The States And Spectra Of Para Hellium Singlets, Donald Greenspan
Semiclassical Modeling Of The States And Spectra Of Para Hellium Singlets, Donald Greenspan
Mathematics Technical Papers - Archive
It is commonly believed that the excited states of helium are solutions of the Schroedinger equation for helium. We show first that this is, in general, false by demonstrating that the Principal spectral series derived from quantum mechanical energy states for para helium singlets are incorrect, independently of computational accuracy. Accurate energy states and spectra are then deduced from a proposed semiclassical extension of the Bohr approach to hydrogen, but modified so that most of the usual criticisms are not valid. The elated computer methodology is simple and economical, with no computation requiring more than one second on a Dec …
A New Algorithm For Unstable Three Terms Recurrence Relations, S. Sivasundaram, D. Trigiante
A New Algorithm For Unstable Three Terms Recurrence Relations, S. Sivasundaram, D. Trigiante
Mathematics Technical Papers - Archive
A modified version of Miller's and Olver's algorithm based on the "double sweep" method is presented. It is very stable in both directions and automatically controls the maximum number of steps to be used.
Multivalued Maps And Multivalued Differential Equations, K. Deimling
Multivalued Maps And Multivalued Differential Equations, K. Deimling
Mathematics Technical Papers - Archive
Everybody meets multivalued maps very early in his mathematical education, as inverses of maps which are not one-to-one, but in elementary lectures the multivalued aspect is usually suppressed by means of elementary tricks or restrictions which make sense for practical purposes; think of [see pdf for notation] which has the inverse[see pdf for notation], from [see pdf for notation] (the subsets of R); or think of a linear operator [see pdf for notation] with kernel [see pdf for notation]; in which case one uses the trick to consider [see pdf for notation], defined by [see pdf for notation] which is …
Hydrogenic Formulas For Excited States Of The Atoms Through Carbon, Donald Greenspan
Hydrogenic Formulas For Excited States Of The Atoms Through Carbon, Donald Greenspan
Mathematics Technical Papers - Archive
One of the beautiful consequences of Bohr's simplistic theory for hydrogen was a single formula for the excited states of the atom. Since this formula can be stated in terms of the constants of the hydrogen atom, it is called a hydrogenic formula. In this paper, analogous formulas are developed for the atoms through carbon.
Elliptic Regularization For A Class Of Strongly Nonlinear Degenerate Eigenvalue Problems On Orlicz-Sobolev Spaces. I: The Ode Case, Pierre A. Vuillermot
Elliptic Regularization For A Class Of Strongly Nonlinear Degenerate Eigenvalue Problems On Orlicz-Sobolev Spaces. I: The Ode Case, Pierre A. Vuillermot
Mathematics Technical Papers - Archive
This paper is devoted to proving sharp Holder-Lipschitz regularity estimates for the eigensolutione to a class of degenerate Sturm-Liouville eigenvalue problems with polynomial and exponential nonlinearities. The general method of proof represents as blending of a suitable regularization procedure along with a new method of auxiliary solutions, which we develop in detail. it allows one to exhibit a phenomenon of screening to regularity due to degeneracy and a new phenomenon of breakdown of regularity at short distances: while all of the eigensolutions are Lipschitz-continuous functions of their argument, their first derivatives exhibit a transition from Lipschitz-continuity to Hoder-continuity when the …
Nonexistence Of Spatially Localized Free Vibrations For A Class Of Nonlinear Wave Equations, Pierre A. Vuillermot
Nonexistence Of Spatially Localized Free Vibrations For A Class Of Nonlinear Wave Equations, Pierre A. Vuillermot
Mathematics Technical Papers - Archive
We prove the nonexistence of free vibrations of arbitrary period with polynomially decreasing profiles for a large class of nonlinear wave equations in one space dimension. Our class of admissible models includes examples of non integrable wave equations with certain polynomial nonlinearities, as well as examples of completely integrable ones with exponential nonlinearities related to Mikhailov's equations. Our result thus proves a particular case of a conjecture first formulated by Eleonskii, Kulagin, Novozhilova and Silin, and dispels some confusion regarding the relationship between the existence of so-called breather-solutions and the complete integrability of the wave equation. Our class of admissible …
The Energy States Of Helium Via Bohr-Einstein Determinism, Donald Greenspan
The Energy States Of Helium Via Bohr-Einstein Determinism, Donald Greenspan
Mathematics Technical Papers - Archive
Correct ground, ionization, singly excited and doubly (excited energy states are deduced deterministically by a direct extension of Bohr's method for hydrogen. The theory incorporates a classical interpretation of electron pairing and requires computer methodology to solve the resulting mathematical equations.
Sample Solutions Of Stochastic Ordinary Differential Equations, K. Waling
Sample Solutions Of Stochastic Ordinary Differential Equations, K. Waling
Mathematics Technical Papers - Archive
Motivated by the stochastic differential equation[see pdf for notation] in [see pdf for notation] we prove a measurable dependence on parameters theorem for ODEs in case f is only continuous in [see pdf for notation] is done by means of a known result about measurable selections of multivalued maps. Afterwards we discuss consequences for stochastic ODEs.
An Elementary Algebraic Method For Approximating Average Radii Of First And Secong Ring Electrons, Donald Greenspan
An Elementary Algebraic Method For Approximating Average Radii Of First And Secong Ring Electrons, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper, experimental ionization energies are used to determine algebraic equations whose solutions approximate relativistic quantum mechanical estimates of average atomic radii. These algebraic equations are nonlinear and are solved on a digital computer by Newton's method. Pairing is an essential element in the formulation.
Sample Solutions Of Stochastic Boundary Value Problems, V. Lakshmikantham, G. S. Ladde, K. Deimling
Sample Solutions Of Stochastic Boundary Value Problems, V. Lakshmikantham, G. S. Ladde, K. Deimling
Mathematics Technical Papers - Archive
We prove existence theorems for nonlinear stochastic Sturmiouville problems which improve results from [4]. In the simplest case this is done by means of a known result about measurable selections of multivalued maps and a new fixed point theorem for stochastic nonlinear operators which is more realistic than existing ones.
Existence And Regularity Theory For Isoperimetric Variational Problems On Orlicz-Sobolev Spaces: A Review, Pierre A. Vuillermot
Existence And Regularity Theory For Isoperimetric Variational Problems On Orlicz-Sobolev Spaces: A Review, Pierre A. Vuillermot
Mathematics Technical Papers - Archive
In this review article, we outline and discuss our most recent results regarding the existence and the regularity theory for a class of strongly nonlinear eigenvalue problems on Orlicz-Sobolev spaces, with a glance at other contemporary attempts to understand the structure of some strongly nonlinear variational boundary-value problems defined on certain nonreflexive Banach spaces. The class of eigenvalue problems recently investigated can best be defined as follows. With [see pdf for notation] be an open bounded domain with closure -6 and smooth [see pdf for notation] boundary asp; let [see pdf for notation] be a family of [see pdf for …