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Articles **1** - **5** of ** 5**

## Full-Text Articles in Physics

Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

#### Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

*Physics*

We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.

Prediction Of The Stochastic Behavior Of Nonlinear Systems By Deterministic Models As A Classical Time-Passage Probabilistic Problem, L. M. Ivanov, A. D. Kirwan Jr., O. V. Melnichenko

#### Prediction Of The Stochastic Behavior Of Nonlinear Systems By Deterministic Models As A Classical Time-Passage Probabilistic Problem, L. M. Ivanov, A. D. Kirwan Jr., O. V. Melnichenko

*CCPO Publications*

Assuming that the behaviour of a nonlinear stochastic system can be described by a Markovian diffusion approximation and that the evolution equations can be reduced to a system of ordinary differential equations, a method for the calculation of prediction time is developed. In this approach, the prediction time depends upon the accuracy of prediction, the intensity of turbulence, the accuracy of the initial conditions, the physics contained in the mathematical model, the measurement errors, and the number of prediction variables. A numerical application to zonal channel flow illustrates the theory. Some possible generalizations of the theory are also discussed.

Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff

#### Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff

*All HMC Faculty Publications and Research*

We study the advection of a passive scalar by a vortex couple in the small-diffusion (i.e. large Péclet number, *Pe*) limit. The presence of weak diffusion enhances mixing within the couple and allows the gradual escape of the scalar from the couple into the surrounding flow. An averaging technique is applied to obtain an averaged diffusion equation for the concentration inside the dipole which agrees with earlier results of Rhines & Young for large times. At the outer edge of the dipole, a diffusive boundary layer of width *O*(*Pe*^{−½}) forms; asymptotic matching to the interior of the dipole yields effective boundary conditions for the averaged diffusion equation. The analysis predicts that first the scalar is homogenized along the streamlines ...

Multigrid Acceleration Of Time-Dependent Solutions Of Navier-Stokes Equations, Sarafa Oladele Ibraheem

#### Multigrid Acceleration Of Time-Dependent Solutions Of Navier-Stokes Equations, Sarafa Oladele Ibraheem

*Mechanical & Aerospace Engineering Theses & Dissertations*

Recent progress in Computational Fluid Dynamics is encouraging scientists to look at fine details of flow physics of problems in which natural unsteady phenomena have hitherto been neglected. The acceleration methods that have proven very successful in steady state computations can be explored for time dependent computations. In this work, an efficient multigrid methods is developed to solve the time-dependent Euler and Navier-Stokes equations. The Beam-Warming ADI method is used as the base algorithm for time stepping calculations. Application of the developed algorithm proved very efficient in selected steady and unsteady test problems. For instance, the inherent unsteadiness present in ...

Hexagons And Squares In A Passive Nonlinear Optical System, John Geddes, R.A. Indik, J.V. Moloney, Willie Firth

#### Hexagons And Squares In A Passive Nonlinear Optical System, John Geddes, R.A. Indik, J.V. Moloney, Willie Firth

*John B. Geddes*

Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern. We observe hexagonal patterns in a self-focusing medium, and squares in a self-defocusing one, in good agreement with analysis based on symmetry and asymptotic expansions.