Asymptotic equivalence between the hydrodynamic and kinetic stages for the Lorentz model

The asymptotic equivalence between the kinetic and hydrodynamic evolutions for the Lorentz model in a semi-infinite medium with a perfectly reflecting boundary is proved in a Hilbert space formalism.     

On stable potentials

Examples are given of one- and two-dimensional stable potentials which cannot be decomposed into the sum of a non-negative function and a continuous stable potential.     

Using optimal control theory to identify network structures that foster synchrony

Network structures are known to influence a population’s propensity to synchronize. Previous attempts to identify synchrony promoting structures have focused on homogeneous populations. We use optimal control theory to construct networks that allow heterogeneous populations to maintain high levels of synchrony, explore the relationship between population heterogeneity and the structure of the optimal networks, and identify salient optimal network features that may enhance synchrony. In particular, we identify a new parameter, the average strength of neighbors, that may foster synchrony and observe that repulsion, in addition to attraction, can foster synchrony.     

Non‐Lipschitzian control algorithms: application to a nanofriction model

Recently we proposed a new feedback control algorithm for quantities describing global features of non‐linear dynamical systems. The performance of the algorithm, which is based on the concepts of non‐Lipschitzian dynamics and global targeting, has been successfully demonstrated for systems confined to one spatial dimension and for a specific targeted global quantity, namely the velocity of the centre of mass. In this paper we extend the scope of the non‐Lipschitzian control scheme to multi‐dimensional systems and different targeted quantities. We illustrate the efficiency of the non‐Lipschitzian feedback w.r.t. the ordinary (Lipschitzian) feedback, as well as the robustness and accuracy of the algorithm in a broad variety of control scenarios on the 2‐d Frenkel‐Kontorova model for nanofriction. Published in 2005 by John Wiley & Sons, Ltd.     

Optimal control of a reflection boundary coefficient in an acoustic wave equation

We seek to optimally control a reflection boundary coefficient for an acoustic wave equation. The goal-quantified by an objective functional- is to drive the solution close to a target by adjusting this coefficient, which acts as a control. The problem is solved by finding the optimal control, which minimizes the objective functional. Then the optimal control is used as a an approximation for an inverse “ identification” problem.     

Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a Theta(+) pentaquark, while the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis, we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a Theta(+). Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.     

On the spectral decompositions of the linear transport operator with periodic boundary conditions

It is shown that the linear transport operator for a slab with periodic boundary conditions, or for infinite medium, can be analyzed within the Friedrichs' model of perturbation for non-selfadjoint operators. This leads to rephrasing Case's generalized eigenfunction expansion in terms of Hilbert space operators only.