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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas
Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L’vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of nonperturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that …
Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty
Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we discuss some interesting applications of Dirac's delta function in Statistics. We have tried to extend some of the existing results to the more than one variable case. While doing that, we particularly concentrate on the bivariate case.
Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas
Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. …
Quantum Phases For A Generalized Harmonic Oscillator, Paul Bracken
Quantum Phases For A Generalized Harmonic Oscillator, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.
A Fragment On Euler's Constant In Ramanujan's Lost Notebook, Bruce C. Berndt, Timothy Huber
A Fragment On Euler's Constant In Ramanujan's Lost Notebook, Bruce C. Berndt, Timothy Huber
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
A formula for Euler’s constant found in Ramanujan’s lost notebook and also in a problem he submitted to the Journal of the Indian Mathematical Society is proved and discussed.
An Action For A Classical String, The Equation Of Motion And Group Invariant Classical Solutions, Paul Bracken
An Action For A Classical String, The Equation Of Motion And Group Invariant Classical Solutions, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.