Variational bounds on the energy dissipation rate in body-forced shear flow

A new variational problem for upper bounds on the rate of energy dissipation in body-forced shear flows is formulated by including a balance parameter in the derivation from the Navier-Stokes equations. The resulting min-max problem is investigated computationally, producing new estimates that quantitatively improve previously obtained rigorous bounds. The results are compared with data from direct numerical simulations.Comment: 15 pages, 7 figure

Exponentially growing solutions in homogeneous Rayleigh-Benard convection

It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full non-linear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.Comment: 4 pages, 3 figures, to be published in Phys. Rev. E - rapid communication

Phase space dynamics of overdamped quantum systems

The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation of Fokker-Planck type valid from high down to very low temperatures. The effect of quantum fluctuations is discussed and the accuracy of these findings is tested against exact data for a harmonic system.Comment: 7 pages, 2 figures, to appear in Euro. Phys. Let

An Evaluation of Computational Fluid Dynamics for Spillway Modelling

Computational Fluid Dynamics (CFD) is used extensively by engineers to model and analyse complex issues related hydraulic design, planning studies for future generating stations, civil maintenance, supply efficiency, and dam safety. The integrity of computed values from CFD models is of considerable economic importance in the design, upgrading and maintenance of hydroelectric generating stations. CFD models have the ability to predict many characteristics flow over a spillway and Manitoba Hydro has had good agreement with physical model results in the past. However, date there has not been a review that brings all the available information together for a comprehensive assessment. The objective of this research is to build upon previous investigations on the use of CFD modelling, by focusing specifically on the ability to accurately model spillways using CFD. This paper discusses three-dimensional numerical modelling of several different spillway configurations using the CFD software Flow-3D and compares the predicted rating curves, pressures, and water surface elevations to corresponding physical model experimental values. The numerical model results were generally in agreement with physical model data, however, the relative differences in discharges were found to have a P/Hd dependency. The accuracy for a given model resolution and associated computational time required was also considered

Superconducting Fluxon Pumps and Lenses

We study stochastic transport of fluxons in superconductors by alternating current (AC) rectification. Our simulated system provides a fluxon pump, "lens", or fluxon "rectifier" because the applied electrical AC is transformed into a net DC motion of fluxons. Thermal fluctuations and the asymmetry of the ratchet channel walls induce this "diode" effect, which can have important applications in devices, like SQUID magnetometers, and for fluxon optics, including convex and concave fluxon lenses. Certain features are unique to this novel two-dimensional (2D) geometric pump, and different from the previously studied 1D ratchets.Comment: Phys. Rev. Lett. 83, in press (1999); 4 pages, 5 .gif figures; figures also available at http://www-personal.engin.umich.edu/~nori/ratche

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation

Coherent State path-integral simulation of many particle systems

The coherent state path integral formulation of certain many particle systems allows for their non perturbative study by the techniques of lattice field theory. In this paper we exploit this strategy by simulating the explicit example of the diffusion controlled reaction $A+A\to 0$. Our results are consistent with some renormalization group-based predictions thus clarifying the continuum limit of the action of the problem.Comment: 20 pages, 4 figures. Minor corrections. Acknowledgement and reference correcte