On weak spreadability of distributed-parameter systems and its achievement via linear--quadratic control techniques

In this paper, the concept of weak spreadability is introduced.It constitutes an extension of the idea developed by El Jai& Kassara. In the case of linear distributed systems weconsider quadratic control techniques with a conveniently penalizedcriterion which makes the system weakly spreadable. The approachis outlined for a convection—diffusion system, and theresults of a numerical study are also included to illustratethe main features of the considered problem.     

Formulation,Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems

In this paper, we present a unified treatment and analysis of a dynamic traffic network model with elastic demands formulated and studied as a projected dynamical system. We propose a travel route choice adjustment process that satisfies the projected dynamical system. Under certain conditions, stability and asymptotical stability of the equilibrium patterns are then derived. Finally, two discrete-time algorithms, the Euler method and the Heun method, are proposed for the computation of the solutions, and convergence results established. The convergence results depend crucially on stability analysis. The performance of the algorithms is then illustrated on several transportation networks.     

On the spectra of finite-dimensional quadratic Bose operators

A complete study of the spectrum of a finite-dimensional Bose operator is carried out in the paper. The cases in which the spectrum is discrete or continuous are studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 835–854, June, 1997. Translated by A. M. Chebotarev     

Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

Comparison of Thermodynamic Characteristics of a Potential Well under Quantum and Classical Approaches

The conjecture according to which the mean energy of an equilibrium system in quantum theory exceeds the mean energy of the corresponding classical system is considered. It is rigorously proved that the conjecture holds for the potential well. The estimates for the mean energy of the potential well at high and low temperatures are of special interest.     

Shell model interaction between proton holes and between proton holes and neutron particles around 208Pb

An effective residual interaction between particles and holes for shell model calculations around ²⁰⁸Pb, derived from the interaction between free nucleons, is compared with the measured properties of proton-hole neutron states in ²⁰⁸Tl and the interaction between proton holes is adjusted to newly measured level energies in ²⁰⁶Hg. These interaction elements are particularly relevant for neutron-rich nuclei. The adjustment of two mixing elements reproduces the known γ-decay data in ²⁰⁸Tl. Received: 2 April 2002 / Accepted: 2 May 2002     

Polling systems in heavy traffic: Exhaustiveness of service policies

We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is excellent for practical heavy-traffic scenarios. This revised version was published online in June 2006 with corrections to the Cover Date.     

Balance constraints reduction of large-scale linear programming problems

This paper describes a method and the corresponding algorithms for simplification of large-scale linear programming models. It consists of the elimination of the balance constraints (i.e. constraints with zero RHS term). The idea is to apply some linear transformations to the original problem in order to nullify the balance constraints. These transformations are able to simultaneously eliminate more balance rows. The core of this contribution is the introduction of the reduction matrix and the associated theorems on the equivalent linear programs (original and reduced). The numerical experiments with this method of simplification proved this approach to be beneficial for a large class of LP problems.This research work was done while the first author was at Duisburg University, Mess-, Steuer und Regelungstechnik, Germany, under the greatly appreciated financial assistance given by the Alexander-von-Humboldt Foundation.     

A COMPLETE METRIC OF POSITIVE CURVATURE ON R~n AND EXISTENCE OF CLOSED GEODESICS

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Universality in some classical Coulomb systems of restricted dimension

Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond–1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.Laboratoire associé au Centre National de la Recherche Scientifique-URA D0063.