The Chang-Łoś-Suszko theorem in a topological setting

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.     

A cellular automaton technique for modelling of a binary dendritic growth with convection

A two-dimensional model for the simulation of a binary dendritic growth with convection has been developed in order to investigate the effects of convection on dendritic morphologies. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (s/l) interface. The dynamics of the interface controlled by temperature, solute diffusion and Gibbs–Thomson effects, is coupled with the continuum model for energy, solute and momentum transfer with liquid convection. The solid fraction is calculated by a governing equation, instead of some approximate methods such as lever rule method [A. Jacot, M. Rappaz, Acta Mater. 50 (2002) 1909–1926.] or interface velocity method [L. Nastac, Acta Mater. 47 (1999) 4253; L. Beltran-Sanchez, D.M. Stefanescu, Mat. and Mat. Trans. A 26 (2003) 367.]. For the dendritic growth without convection, mesh independency of simulation results is achieved. The simulated steady-state tip velocity are compared with the predicted values of LGK theory [Lipton, M.E. Glicksmanm, W. Kurz, Metall. Trans. 18(A) (1987) 341.] as a function of melt undercooling, which shows good agreement. The growth of dendrite arms in a forced convection has been investigated. It was found that the dendritic growth in the upstream direction was amplified, due to larger solute gradient in the liquid ahead of the s/l interface caused by melt convection. In the isothermal environment, the calculated results under very fine mesh are in good agreement with the Oseen–Ivanstov solution for the concentration-driven growth in a forced flow.     

Using the gradients of temperature and internal parameters in Continuum ThermodynamicsIntroduction des gradients de température et de paramètres internes en Thermodynamique des Milieux Continus

In this paper, the possibility of using the gradients of the temperature and of the internal parameters as additional state variables in Continuum Thermodynamics is considered. The expressions of the two principles are discussed and Clausius–Duhem inequality is derived under an appropriate statement of the internal entropy production. Several formulations are proposed and compared to existing results in the literature. To cite this article: P. Ireman, Q.S. Nguyen, C. R. Mecanique 332 (2004).     

On the Constituent Structure of a Classical Mixture

Thiw work is concerned with the formulation of constituent interactions and corresponding balance relations in classical mixture theory as based on a model for the (classical) constituent structure of such a mixture.     

Average Atom Model in Hot Plasmas

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Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

On the characterization of continuum structure functions

A continuum structure function is a non-decreasing mapping from the unit hypercube to the unit interval. Within the class of continuum structure functions, new axiomatic characterizations of the Natvig and the Barlow-Wu subclass are obtained.     

A structural and energetics analysis of the binding of a series of N-acetylneuraminic-acid-based inhibitors to influenza virus sialidase

Summary A molecular dynamics/energy-minimisation protocol has been used to analyse the structural and energetic effects of functional group substitution on the binding of a series of C4-modified 2-deoxy-2,3-didehydro-N-acetylneuraminic acid inhibitors to influenza virus sialidase. Based on the crystal structure of sialidase, a conformational searching protocol, incorporating multiple randomisation steps in a molecular dynamics simulation was used to generate a range of minimum-energy structures. The calculations were useful for predicting the number, location, and orientation of structural water molecules within protein-ligand complexes. Relative binding energies were calculated for the series of complexes using several empirical molecular modelling approaches. Energies were computed using molecular-mechanics-derived interactions as the sum of pairwise atomic nonbonded energies, and in a more rigorous manner including solvation effects as the change in total electrostatic energy of complexation, using a continuum-electrostatics (CE) approach. The CE approach exhibited the superior correlation with observed affinities. Both methods showed definite trends in observed and calculated binding affinities; in both cases inhibitors with a positively charged C4 substituent formed the tightest binding to the enzyme, as observed experimentally.This paper is based on a presentation given at the 14th Molecular Graphics and Modelling Society Conference, held in Cairns, Australia, August 27–September 1, 1995.Presently on a visiting postdoctoral fellowship in the Department of Biomolecular Structure, Glaxo Research & Development Ltd, Greenford, Middlesex UB6 OHE, U.K.     

Theoretical basis of the empirical reaction field approximations through continuum model

We derive from exact integral equations of classical electrostatics some approximate expressions of the interaction energy of a point charge distribution with a dielectric medium. We show how they can be used for computing the wave functions of solvated species imbedded in cavities formed by interlocking spheres in a polarizable continuum. We discuss the relation between these formulae and the ones proposed earlier on empirical basis and we especially emphasize the improvement that they bring out.