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Articles 91 - 120 of 343
Full-Text Articles in Mathematics
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 Colliding Microdrops Of Water, Donald Greenspan
Supercomputer Simulation Of Colliding Microdrops Of Water, Donald Greenspan
Mathematics Technical Papers - Archive
Microdrop collisions are important in fast kinetic, microwave, nucleation, and rainstorm studies. In this Paper a molecular model of colliding microdrops of water is simulated on a CRAY X-MP/24. A least squares fit of the force field allows relatively large time steps in the numerical procedure. Rotating "raindrop" modes, "dumbell" modes, and oscillatory oblateness modes are demonstrated, as are nonadhesive soft and hard collisions.
The Compensatory Bargaining Set Of A Cooperative N-Person Game With Side Payments, Irinel C. Dragan
The Compensatory Bargaining Set Of A Cooperative N-Person Game With Side Payments, Irinel C. Dragan
Mathematics Technical Papers - Archive
The bargaining sets have been introduced as solution concepts for cooperative n-person games with side payments by R. J. Aumann and M. Maschler (1964). A further study on the relationships between various concepts of solution for such games is due to R. J. Aumann and J. Dreze (1975). The Aumann/Maschler definition of a bargaining set relies upon a stability principle imposed to the payoffs in this set: an admissible payoff belongs to a bargaining set if for every objection against this payoff there is a counter objection. Two modification of the stability principle have been discussed in earlier papers of …
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.
Dynamics Of Large Eddies In Turbulent Channel Flows, F. R. Payne, S. K. Hong
Dynamics Of Large Eddies In Turbulent Channel Flows, F. R. Payne, S. K. Hong
Mathematics Technical Papers - Archive
A turbulence model that describes dynamics of large, characteristic eddies in inhomogeneous flows is proposed; two closure parameters are initially undetermined. To determine the optimum values of these parameters, the present model is applied to channel flows at two Reynolds numbers. The nature of the closure parameters and their effects upon predicted Reynolds stresses and other turbulence structural quantities are examined and optimum values are suggested. It is demonstrated that the current Large-Eddy Interaction Model not only predicts Reynolds stresses reasonably but also presents an opportunity to illuminate typical characteristic motions of large-scale turbulence and the phenomenological aspects of engineering …
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.
Programs And Data Sets For Quasimolecular Modeling Of Cavity Flow, Donald Greenspan
Programs And Data Sets For Quasimolecular Modeling Of Cavity Flow, 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.
Programs And Data Sets For Quasimolecular Modeling Of Vortices, Donald Greenspan
Programs And Data Sets For Quasimolecular Modeling Of Vortices, Donald Greenspan
Mathematics Technical Papers - Archive
No abstract provided.
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.
Rapid Computation Of The Energy States Of Two-Electron Atoms And Ions With An Explicit Formula For The Excited States Of Helium, Donald Greenspan
Rapid Computation Of The Energy States Of Two-Electron Atoms And Ions With An Explicit Formula For The Excited States Of Helium, Donald Greenspan
Mathematics Technical Papers - Archive
A new computational approach is developed for the energy states of two electron atoms and ions. The theory incorporates a classical interpretation of electron pairing and requires Only simple numerical methodology for its implementation. Accurate computer results are described and discussed. These results lead directly to an explicit formula for the excited states of helium. Also, extension to the hydrogen molecule [see pdf for notation] is indicated.
An Asymptotic Result In Forced Oscillations Of Pendulum-Type Equations, R. Kannan, R. Ortega
An Asymptotic Result In Forced Oscillations Of Pendulum-Type Equations, R. Kannan, R. Ortega
Mathematics Technical Papers - Archive
The forced pendulum-type equation is given by [see pdf for notation] where [see pdf for notation] is continuous and T-periodic and p(t) is[see pdf for notation] -periodic. When g(x) = a sin x, a > 0, we obtain the classical pendulum equation. The question of existence of [see pdf for notation] periodic solution of (1.1) for a given p(t) has been studied recently in [1], [3], [5] (cf. [4] for an extensive bibliography). Throughout this paper we denote by [see pdf for notation] the average of [see pdf for notation]. Some of the existence literature obtains sufficient conditions on the magnitudes …
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 …
Efficient Nonlinear Parameter Estimation For Exponential Type, Least Square Approximation, Donald Greenspan
Efficient Nonlinear Parameter Estimation For Exponential Type, Least Square Approximation, Donald Greenspan
Mathematics Technical Papers - Archive
A computer algorithm is described for fitting data sets by least squares to the functions [see pdf for notation]. A non matrix form of Newton's method is utilized which is economical, easily implementable, and exceptionally fast. Computer examples are described and discussed.
Remarks On Bellman's Structural Identifiability, Jerome Eisenfeld
Remarks On Bellman's Structural Identifiability, Jerome Eisenfeld
Mathematics Technical Papers - Archive
This paper remarks on unidentifiable compartmental systems. Emphasis is placed on detecting properties of the system directly from the compartmental diagram without resort to complicated analysis. New concepts are introduced. One is separability, a condition in which two or more parameters enter the identification equations only as a certain combination thereby preventing their identification. Concepts from linear algebra such as span, basis, and dimension are adopted to "parameter spaces". A necessary and sufficient condition for interval identification is presented.
Rapid Approximation Of The Energy States Of Three-Electron Systems, Donald Greenspan
Rapid Approximation Of The Energy States Of Three-Electron Systems, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper, we show how to approximate rapidly the energy states of systems with one electron in the second ring. Using known energy states and average radii of two-electron systems in ground state, the Method requires only the computer solution of a single nonlinear equation in one unknown. This can always be accomplished by Newton's method when applied with a correct initial guess. Computational results for [see pdf for notation] are compared with available quantum mechanical estimates.
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.
Rapid Computation Of The Energy States Of Two-Electron Systems, Donald Greenspan
Rapid Computation Of The Energy States Of Two-Electron Systems, Donald Greenspan
Mathematics Technical Papers - Archive
A new deterministic approach to modelling atoms and molecules is developed which uses static and dynamic numerical methods. The estimate for the ground state energy of [see pdf for notation] is closer to the experimental estimate than is the quantum mechanical result. for the hydrogen molecule ion, the result obtained is entirely comparable to that from quantum mechanics. For various atomic calculations, the results deviate from experimental results by less than one half of one percent. The theory incorporates a classical interpretation of electron pairing from a superstring point of view. The approach leads to a new, explicit formula for …
Analytical And Numerical Studies On The States Of Ions And Atoms, Donald Greenspan
Analytical And Numerical Studies On The States Of Ions And Atoms, Donald Greenspan
Mathematics Technical Papers - Archive
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, single, and multiple excited states are of unexpectedly high accuracy for so simplistic an approach.
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 …
Particle Simulation Of Spiral Galaxy Evolution, Donald Greenspan
Particle Simulation Of Spiral Galaxy Evolution, Donald Greenspan
Mathematics Technical Papers - Archive
Spiral galaxies are modelled as n-body systems by means of long range and molecular-type short range forces. A relatively massive, elliptic, type core is sit into rotational motion in a less dense, tidal prone medium. Pressure waves result along whose leading edges there is increased luminosity, which develops in a spiral pattern.
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 …