Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

Relaxation and overlap probability function in the spherical and mean spherical model

The problem of the equivalence of the spherical and mean spherical models, which has been thoroughly studied and understood in equilibrium, is considered anew from the dynamical point of view during the time evolution following a quench from above to below the critical temperature. It is found that there exists a crossover time $t^* \sim V^{2/d}$ such that for $t < t^*$ the two models are equivalent, while for $t > t^*$ macroscopic discrepancies arise. The relation between the off equilibrium response function and the structure of the equilibrium state, which usually holds for phase ordering systems, is found to hold for the spherical model but not for the mean spherical one. The latter model offers an explicit example of a system which is not stochastically stable.Comment: 11 pages, 1 figure, references corrected, to appear in Phys.Rev.

On the effect of different flux limiters on the performance of an engine gas exchange gas-dynamic model

[EN] A suitable tool for the design of intake and exhaust systems of internal combustion engines is provided by time domain non-linear finite volume models. These models, however, are affected by overshoots at discontinuities and numerical dispersion unless some flux limiter is used. In this paper, the effect of the most relevant of such flux limiters on a non-linear staggered-mesh finite-volume model is evaluated. Flux-Corrected-Transport (FCT) and Total Variation Diminishing (TVD) schemes, together with a Momentum Diffusion Term (MDT) are presented for such a model, and the performance of the resulting methods is checked in different problems representative of the influence of engine gas exchange flows on engine performance and intake and exhaust noise. First, two one-dimensional cases are considered: the shock-tube problem, and the propagation of a finite amplitude pressure pulse. Secondly, a simple but representative three-dimensional geometry is studied. From the results obtained, it can be concluded that, even if none of the methods is able to handle properly the three problems considered, the FCT method provides the best overall performance. (C) 2017 Elsevier Ltd. All rights reserved.M. Hernandez is partially supported through contract FPI-S2-2015-1064 of Programa de Apoyo para la Investigacion y Desarrollo (PAID) of Universitat Politecnica de Valencia.Torregrosa, AJ.; Broatch, A.; Arnau Martínez, FJ.; Hernández-Marco, M. (2017). On the effect of different flux limiters on the performance of an engine gas exchange gas-dynamic model. International Journal of Mechanical Sciences. 133:740-751. https://doi.org/10.1016/j.ijmecsci.2017.09.029S74075113

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

Stochastic combinatorial optimization with controllable risk aversion level

Due to their wide applicability and versatile modeling power, stochastic programming problems have received a lot of attention in many communities. In particular, there has been substantial recent interest in 2–stage stochastic combinatorial optimization problems. Two objectives have been considered in recent work: one sought to minimize the expected cost, and the other sought to minimize the worst–case cost. These two objectives represent two extremes in handling risk — the first trusts the average, and the second is obsessed with the worst case. In this paper, we interpolate between these two extremes by introducing an one–parameter family of functionals. These functionals arise naturally from a change of the underlying probability measure and incorporate an intuitive notion of risk. Although such a family has been used in mathematical finance [12] and stochastic programming [14] before, its use in the context of approximation algorithms seems new. We show that under standard assumptions, our risk–adjusted objective can be efficiently treated by the Sample Average Approximation (SAA) method [10]. In particular, our result generalizes a recent sampling theorem by Charikar et al. [2], and it shows that it is possible to incorporate some degree of robustness even when we are only allowed to access the underlying probability distribution in a black–box fashion. We also show that when combined with known techniques (e.g. [4, 15]), our result yields new approximation algorithms for many 2–stage stochastic combinatorial optimization problems under the risk–adjusted setting.

A fluid dynamic model for unsteady compressible flow in wall-flow diesel particulate filters

The use of particulate filters (DPF) in Diesel engines has become in recent years the standard technology for the control of soot aerosol emissions. Once emissions reduction through the management of filtration and regeneration aspects has reached its maturity, the effect of the system location on engine performance and acoustics are key topics to be addressed. In this paper, a fluid dynamic model for wall-flow monolith filters is described in which non-homentropic one-dimensional unsteady compressible flow is considered. The good agreement with experimental data confirms that the model is able to describe the mechanisms contributing to the pressure drop across the whole filter under steady and impulsive flow conditions. The approach of the flow governing equations provides a reliable evaluation of the contributions to the pressure drop with axial resolution in the description of the flow field properties. In addition, the frequency response predicted by the model confirms its ability to evaluate the dynamic response and acoustic potential of the DPF. © 2010 Elsevier Ltd.This work has been partially supported by the Spanish Ministerio de Ciencia e Innovacion through grant number DPI2010-20891-C02-02.Torregrosa Huguet, AJ.; Serrano Cruz, JR.; Arnau Martínez, FJ.; Piqueras Cabrera, P. (2011). A fluid dynamic model for unsteady compressible flow in wall-flow diesel particulate filters. Energy. 36(1):671-684. https://doi.org/10.1016/j.energy.2010.09.047S67168436