No abstract

An average Reynolds equation for predicting the effects of deterministic periodic roughness, taking Jakobsson, Floberg, and Olsson mass flow preserving cavitation model into account, is introduced based upon the double scale analysis approach. This average Reynolds equation can be used both for a microscopic interasperity cavitation and a macroscopic one. The validity of such a model is verified by numerical experiments both for one-dimensional and two-dimensional roughness patterns.

Abstract. This paper deals with the weak formulation of a free (moving) boundary problem arising in theoretical glaciology. Considering shallow ice sheet ow w e present the mathematical analysis and the numerical resolution of the second order, nonlinear, degenerate parabolic equation modelling, in the isothermal case, the ice sheet non-newtoniandynamics. An obstacle problem is then deduced and analysed. The existence of a free boundary generated by the support of the solution is proved and its location and evolution are qualitatively described by using a comparison principle and an energy method. Then the solutions are numerically computed with a method of characteristics and a duality algorithm to cope with the resulting variational inequalities. The weak framework we introduce and its analysis (both qualitative a n d n umerical) are not restricted to the simple physics of the ice sheet model we consider nor to the model dimension. They can be applied succesfully to more realistic and sophisticated models related to other geophysical settings.

In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of the computations on multicore devices such as graphics processing units (GPUs). Our approach consists of a novel method of stratification which appears to be crucial for large scale parallelization.

No abstract

In this work, we study connections between dynamic behavior and network parameters, for self-regulatory networks. To that aim, a method to compute the regions in the space of parameters that sustain bimodal or binary protein distributions has been developed. Such regions are indicative of stochastic dynamics manifested either as transitions between absence and presence of protein or between two positive protein levels. The method is based on the continuous approximation of the chemical master equation, unlike other approaches that make use of a deterministic description, which as will be shown can be misleading. We find that bimodal behavior is a ubiquitous phenomenon in cooperative gene expression networks under positive feedback. It appears for any range of transcription and translation rate constants whenever leakage remains below a critical threshold. Above such a threshold, the region in the parameters space which sustains bimodality persists, although restricted to low transcription and high translation rate constants. Remarkably, such a threshold is independent of the transcription or translation rates or the proportion of an active or inactive promoter and depends only on the level of cooperativity. The proposed method can be employed to identify bimodal or binary distributions leading to stochastic dynamics with specific switching properties, by searching inside the parameter regions that sustain such behavior.

This work presents a new methodology, based on the maximum entropy method, to obtain bubble characteristics in fluidized beds. The probability distributions (PDF) of bubble pierced length and velocity are obtained applying the maximum entropy principle to experimental measurements. In addition, the bubble diameter distribution has been inferred from experimental pierced length measurements. This method is applied to characterize bubbles in fluidized beds for the first time and the most general bubble geometry, a truncated spheroid, is considered. The distance between probes, s, which is the minimum pierced length that is possible to measure accurately using intrusive probes, has been introduced as a constraint in the derivation of the size distribution equation. The maximum entropy method is applied to experimental measurements of bubble characteristics carried out using optical and pressure probes in a three-dimensional fluidized bed of Geldart B particles. Results on bubble size obtained from pressure and optical probes are very similar, although optical probes provide more local information and can be used at any position in the bed. The maximum entropy principle has been found to be a simple method that offers many advantages over other methods applied before for size distribution modeling in fluidized beds.

No abstract