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Extension to the Cases of Two Dimensional and Spherically Symmetric Flows of Two Particular Solutions to the Equations of Motion Governing Unsteady Flow in a Gas

Description: "The author previously discovered two interesting particular solutions to the equations of motion describing unsteady flow in a gas confined solely to a one-dimensional duct. These solutions are now extended to cover the more noteworthy cases of central symmetry in two and three dimensions" (p. 1).
Date: June 1952
Creator: Pozzi, Lorenzo
Partner: UNT Libraries Government Documents Department

On the Analysis of Linear and Nonlinear Dynamical Systems From Transient-Response Data

Description: Note presenting a general theory of the so-called equations of motion methods for the analysis of linear dynamical systems. When viewed from this general vantage point, all of the linear methods can be extended in a straightforward manner to apply to the analysis of nonlinear systems.
Date: December 1954
Creator: Shinbrot, Marvin
Partner: UNT Libraries Government Documents Department

Sixth-Order Lie Group Integrators

Description: In this paper we present the coefficients of several 6th order symplectic integrator of the type developed by R. Ruth. To get these results we fully exploit the connection with Lie groups. This integrator, as well as all the explicit integrators of Ruth, may be used in any equation where some sort of Lie bracket is preserved. In fact, if the Lie operator governing the equation of motion is separable into two solvable parts, the Ruth integrators can be used.
Date: March 1, 1990
Creator: Forest, E.
Partner: UNT Libraries Government Documents Department

Towards a string formulation of vortex dynamics

Description: We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom.
Date: January 1, 1998
Creator: Inst.], Elsebeth Schroeder & Toernkvist, Ola
Partner: UNT Libraries Government Documents Department

Semiclassical (SC) Description of Electronically Non-AdiabaticDynamics via the Initial Value Representation (IVR)

Description: The initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the Meyer-Miller/Stock-Thoss description of electronic degrees of freedom in order to treat electronically non-adiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wavefunction), but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SC-IVR framework. For example, in the traditional Ehrenfest model (a mixed quantum-classical approach) the nuclear motion emerges from a non-adiabatic encounter on an average potential energy surface (a weighted average according to the population in the various electronic states), while the SC-IVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forward-backward versions of SC-IVR theory (FB-IVR) are presented to illustrate this behavior. An even more approximate version of the SC-IVR, the linearized approximation (LSC-IVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSC-IVR is also not able to describe the correct correlation between nuclear and electronic dynamics.
Date: June 22, 2007
Creator: Ananth, V.; Venkataraman, C. & Miller, W.H.
Partner: UNT Libraries Government Documents Department

Real time correlation function in a single phase spaceintegral--beyond the linearized semiclassical initial valuerepresentation

Description: It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the 2nd order WD based on 'Winger trajectories', and the full Donoso-Martens dynamics (full DMD) and the 2nd order DMD based on 'Donoso-Martens trajectories'--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of these four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (non-linear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.
Date: July 10, 2007
Creator: Liu, Jian & Miller, William H.
Partner: UNT Libraries Government Documents Department

Spherical Wave Propagation in a Nonlinear Elastic Medium

Description: Nonlinear propagation of spherical waves generated by a point-pressure source is considered for the cases of monochromatic and impulse primary waveforms. The nonlinear five-constant elastic theory advanced by Murnaghan is used where general equations of motion are put in the form of vector operators, which are independent of the coordinate system choice. The ratio of the nonlinear field component to the primary wave in the far field is proportional to ln(r) where r is a propagation distance. Near-field components of the primary field do not contribute to the far field of nonlinear component.
Date: July 1, 2009
Creator: Korneev, Valeri A.
Partner: UNT Libraries Government Documents Department

Wheel rolling constraints and slip in mobile robots

Description: It is widely accepted that dead reckoning based on the rolling with no slip condition on wheels is not a reliable method to ascertain the position and orientation of a mobile robot for any reasonable distance. We establish that wheel slip is inevitable under the dynamic model of motion using classical results on the accessibility and controllability in nonlinear control theory and an analytical model of rolling of two linearly elastic bodies.
Date: March 1, 1997
Creator: Shekhar, S.
Partner: UNT Libraries Government Documents Department

Particle motion in the stable region near the edge of a linear sum resonance stopband

Description: This paper studies the particle motion when the tune is in the stable region close to the edge of linear sum resonance stopband. Results are found for the tune and the beta functions. Results are also found for the two solutions of the equations of motion. The results found are shown to be also valid for small accelerators where the large accelerator approximation may not be used.
Date: July 1, 1997
Creator: Parzen, G.
Partner: UNT Libraries Government Documents Department

Methods of beam cooling

Description: Diverse methods which are available for particle beam cooling are reviewed. They consist of some highly developed techniques such as radiation damping, electron cooling, stochastic cooling and the more recently developed, laser cooling. Methods which have been theoretically developed, but not yet achieved experimentally, are also reviewed. They consist of ionization cooling, laser cooling in three dimensions and stimulated radiation cooling.
Date: February 1, 1996
Creator: Sessler, A.M.
Partner: UNT Libraries Government Documents Department

Massively Parallel Direct Simulation of Multiphase Flow

Description: The authors understanding of multiphase physics and the associated predictive capability for multi-phase systems are severely limited by current continuum modeling methods and experimental approaches. This research will deliver an unprecedented modeling capability to directly simulate three-dimensional multi-phase systems at the particle-scale. The model solves the fully coupled equations of motion governing the fluid phase and the individual particles comprising the solid phase using a newly discovered, highly efficient coupled numerical method based on the discrete-element method and the Lattice-Boltzmann method. A massively parallel implementation will enable the solution of large, physically realistic systems.
Date: August 10, 2000
Partner: UNT Libraries Government Documents Department

Derivation of the coupled equations of motion for a circular ring rotating about an axis in the plane of the ring

Description: The coupled equations of motion for a circular ring or circular ring segment are developed for the case where the ring is rotating about an axis in its plane and subjected to an angular velocity as well as an angular acceleration. Coupling results from bending in and out of the plane of the ring as well as from extension and torsion of the ring. These equations are then applied to special cases to determine the coupled equations of motion for a ring, beam and cable rotating at a constant angular speed. Coupled equations of motion for a non-rotating circular ring or circular ring segment are developed for the cases of extensional motion and inextensional motion. These equations are subsequently linearized and uncoupled for extensional and inextensional motion in the plane of the ring as well as for uncoupled motion out of the plane of the ring. The critical angular speed for lateral dynamic instability is determined for a rotating circular shaft which supports several rotating circular ring segments.
Date: March 1, 1996
Creator: Benedetti, G.A.
Partner: UNT Libraries Government Documents Department

Bubble Dynamics in a Superheated Liquid

Description: This report presents an extensive literature survey on bubble dynamics. Growth of a single spherical bubble moving in a uniformly superheated liquid is considered. Equations of motion and energy are presented in the forms that take into consideration the interaction between the motion and the growth. The fourth-order Runge-Kutta method is used to obtain a simultaneous solution of equations of motion and growth rate, and the solution is compared with available experimental results. Results for liquid sodium are presented for a range of pressures and Jakob numbers.
Date: September 1977
Creator: Sha, William T. & Shah, V. L.
Partner: UNT Libraries Government Documents Department

The Satellite Code: A Numerical Satellite Integration Program for the IBM 704

Description: From Introduction: "This report is intended as a handbook for the users of the Satellite code which was developed as a general purpose satellite and space probe program. The components of acceleration, in a three-dimensional rectangular coordinate system, are integrated to produce the velocities and coordinates. These may be transformed into elliptical elements at each time step. The output, therefore, may resemble an integration in the coordinates as well as in the parameters."
Date: June 1959
Creator: Smith, Virginia S.; Bruijnes, Hans R. & Sherman, Nevin W.
Partner: UNT Libraries Government Documents Department

Effect of Product of Inertia on Lateral Stability

Description: Note presenting a theoretical investigation made to determine the effect of the product-of-inertia terms in the lateral equations of motion on the lateral-stability boundaries. The product of inertia results from the inclination of the principal longitudinal axis of the airplane to the flight path. The results indicated that the product-of-inertia terms should be included in the lateral equations of motion to determine the lateral stability of an airplane.
Date: March 1947
Creator: Sternfield, Leonard
Partner: UNT Libraries Government Documents Department

An Algebraic Approach to the Evolution of Emittances upon Crossing the Linear Coupling Difference Resonance

Description: One of the hallmarks of linear coupling is the resonant exchange of oscillation amplitude between the horizontal and vertical planes when the difference between the unperturbed tunes is close to an integer. The standard derivation of this phenomenon (known as the difference resonance) can be found, for example, in the classic papers of Guignard [1, 2]. One starts with an uncoupled lattice and adds a linear perturbation that couples the two planes. The equations of motion are expressed in hamiltonian form. As the difference between the unperturbed tunes approaches an integer, one finds that the perturbing terms in the hamiltonian can be divided into terms that oscillate slowly and ones that oscillate rapidly. The rapidly oscillating terms are discarded or transformed to higher order with an appropriate canonical transformation. The resulting approximate hamiltonian gives equations of motion that clearly exhibit the exchange of oscillation amplitude between the two planes. If, instead of the hamiltonian, one is given the four-by-four matrix for one turn around a synchrotron, then one has the complete solution for the turn-by-turn (TBT) motion. However, the conditions for the phenomenon of amplitude exchange are not obvious from a casual inspection of the matrix. These conditions and those that give rise to the related sum resonance are identified in this report. The identification is made using the well known formalism of Edwards and Teng [3, 4, 5] and, in particular, the normalized coupling matrix of Sagan and Rubin [6]. The formulae obtained are general in that no particular hamiltonian or coupling elements are assumed. The only assumptions are that the one-turn matrix is symplectic and that it has distinct eigenvalues on the unit circle in the complex plane. Having identified the conditions of the one-turn matrix that give rise to the resonances, we focus on the difference resonance ...
Date: September 1, 2008
Creator: Gardner,C.
Partner: UNT Libraries Government Documents Department

Phil Wallace and Theoretical Physics at McGill in the 1950's: A Personal Perspective

Description: In 1946 Philip (Phil) Russell Wallace joined the Mathematics Department of McGill University as an Associate Professor of Applied Mathematics, apparently because A. H. S. Gillson, Dean of Arts and Science, wanted theoretical physicists to be in the Mathematics Department. He came with the dream of creating a theoretical physics group at McGill. By the spring of 1949, Phil was authorized to recruit two junior faculty in Mathematics. He hired Theodore (Ted) F. Morris from U. Toronto, who joined in September 1949, and me, who came in January 1950. The group had begun. Phil Wallace was born in Toronto in 1915 and grew up there. He entered the University of Toronto in 1933, earned a B.A. in mathematics in 1937, a M.A. in 1938, and a Ph.D. in applied mathematics in 1940 under Leopold Infeld. His Ph.D. thesis in general relativity was entitled 'On the relativistic equations of motion in electromagnetic theory.' In 1940 World War II had engulfed Europe and was having its effect on Canada, but the US was still at peace. L. J. Synge, Head of the Applied Mathematics Department at Toronto, told Wallace that people such as he would be needed in war work, but things were not ready quite yet. Hold yourself ready. Phil took a two-year position as lecturer in mathematics at the University of Cincinnati (1940-42); in the fall of 1942 he became a lecturer in mathematics at M.I.T. It was from there that he was recruited by Synge to join the war effort from 1943 to 1946 at N.R.C.'s Montreal Laboratory, the genesis of the Canadian Atomic Energy Project. Phil has described those heady wartime years in these pages. Much of the effort of the theoretical physicists was on nuclear reactor theory and the properties of relevant materials, such as graphite, under ...
Date: November 18, 2010
Creator: Jackson, John David
Partner: UNT Libraries Government Documents Department

Nonstandard jump functions for radially symmetric shock waves

Description: Nonstandard analysis is applied to derive generalized jump functions for radially symmetric, one-dimensional, magnetogasdynamic shock waves. It is assumed that the shock wave jumps occur on infinitesimal intervals, and the jump functions for the physical parameters occur smoothly across these intervals. Locally integrable predistributions of the Heaviside function are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the physical parameters for two families of self-similar flows. It is shown that the microstructures for these families of radially symmetric, magnetogasdynamic shock waves coincide in a nonstandard sense for a specified density jump function
Date: October 1, 2008
Creator: Baty, Roy S.; Tucker, Don H. & Stanescu, Dan
Partner: UNT Libraries Government Documents Department

A preliminary study of molecular dynamics on reconfigurable computers

Description: In this paper we investigate the performance of platform FPGAs on a compute-intensive, floating-point-intensive supercomputing application, Molecular Dynamics (MD). MD is a popular simulation technique to track interacting particles through time by integrating their equations of motion. One part of the MD algorithm was implemented using the Fabric Generator (FG)[l I ] and mapped onto several reconfigurable logic arrays. FG is a Java-based toolset that greatly accelerates construction of the fabrics from an abstract technology independent representation. Our experiments used technology-independent IEEE 32-bit floating point operators so that the design could be easily re-targeted. Experiments were performed using both non-pipelined and pipelined floating point modules. We present results for the Altera Excalibur ARM System on a Programmable Chip (SoPC), the Altera Strath EPlS80, and the Xilinx Virtex-N Pro 2VP.50. The best results obtained were 5.69 GFlops at 8OMHz(Altera Strath EPlS80), and 4.47 GFlops at 82 MHz (Xilinx Virtex-II Pro 2VF50). Assuming a lOWpower budget, these results compare very favorably to a 4Gjlop/40Wprocessing/power rate for a modern Pentium, suggesting that reconfigurable logic can achieve high performance at low power on jloating-point-intensivea pplications.
Date: January 1, 2003
Creator: Wolinski, C. (Christophe); Trouw, F. R. (Frans R.) & Gokhale, M. (Maya)
Partner: UNT Libraries Government Documents Department

EMPHASIS/Nevada UTDEM user guide. Version 2.0.

Description: The Unstructured Time-Domain ElectroMagnetics (UTDEM) portion of the EMPHASIS suite solves Maxwell's equations using finite-element techniques on unstructured meshes. This document provides user-specific information to facilitate the use of the code for applications of interest. UTDEM is a general-purpose code for solving Maxwell's equations on arbitrary, unstructured tetrahedral meshes. The geometries and the meshes thereof are limited only by the patience of the user in meshing and by the available computing resources for the solution. UTDEM solves Maxwell's equations using finite-element method (FEM) techniques on tetrahedral elements using vector, edge-conforming basis functions. EMPHASIS/Nevada Unstructured Time-Domain ElectroMagnetic Particle-In-Cell (UTDEM PIC) is a superset of the capabilities found in UTDEM. It adds the capability to simulate systems in which the effects of free charge are important and need to be treated in a self-consistent manner. This is done by integrating the equations of motion for macroparticles (a macroparticle is an object that represents a large number of real physical particles, all with the same position and momentum) being accelerated by the electromagnetic forces upon the particle (Lorentz force). The motion of these particles results in a current, which is a source for the fields in Maxwell's equations.
Date: September 1, 2011
Creator: Turner, C. David; Seidel, David Bruce & Pasik, Michael Francis
Partner: UNT Libraries Government Documents Department

Ion bombardment in RF photoguns

Description: A linac-ring eRHIC design requires a high-intensity CW source of polarized electrons. An SRF gun is viable option that can deliver the required beam. Numerical simulations presented elsewhere have shown that ion bombardment can occur in an RF gun, possibly limiting lifetime of a NEA GaAs cathode. In this paper, we analytically solve the equations of motion of ions in an RF gun using the ponderomotive potential of the Rf field. We apply the method to the BNL 1/2-cell SRF photogun and demonstrate that a significant portion of ions produced in the gun can reach the cathode if no special precautions are taken. Also, the paper discusses possible mitigation techniques that can reduce the rate of ion bombardment.
Date: May 4, 2009
Creator: Pozdeyev,E.; Kayran, D. & Litvinenko, V. N.
Partner: UNT Libraries Government Documents Department

Effects of Transverse Coupling on Transverse Beam Size, Simulation and Measurements

Description: The equations of motion for particles in an accelerator lattice show that a larger physical aperture is required to hold a beam of constant invariant emittance if there is a transverse coupling of the tunes. The results of a tracking simulation of particle motion in the Fermilab accumulator ring are discussed, and results are shown from beam tests carried out in the accumulator to demonstrate this effect.
Date: January 1, 1992
Creator: Halling, Alfred Mike
Partner: UNT Libraries Government Documents Department

Study of Collective Beam Instabilities using a Correleation-moment Analysis

Description: A general formalism for treating simultaneously the transverse coupled bunch and transverse coupled mode instabilities is presented. In this approach, the equations of motion of a coupled multi-bunch beam are expanded to yield a system of equations involving correlation-moments of the transverse and longitudinal motions. After a proper truncation, the system of equations is closed and can be solved. This approach allows us to formulate within one framework several known instability mechanisms including the single bunch mode coupling instability, the coupled bunch instability, the mode coupling instability, and the coupled mode coupled bunch instability as particular cases.
Date: October 24, 2006
Creator: Heifets, S. A. & Chao, A. W.
Partner: UNT Libraries Government Documents Department

Orbit dynamics for unstable linear motion

Description: A treatment is given of the orbit dynamics for linear unstable motion that allows for the zeros in the beta function and makes no assumptions about the realness of the betatron and phase functions. The phase shift per turn is shown to be related to the beta function and the number of zeros the beta function goes through per turn. The solutions of the equations of motion are found in terms of the beta function.
Date: July 1997
Creator: Parzen, G.
Partner: UNT Libraries Government Documents Department