Diffusion in a locally stationary random environment

This paper deals with homogenization of diffusion processes in a locally stationary random environment. Roughly speaking, such an environment possesses two evolution scales: both a fast microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims at giving a macroscopic approximation that takes into account the microscopic heterogeneities.     

Renormalization of Critical Gaussian Multiplicative Chaos and KPZ Relation

Gaussian Multiplicative Chaos is a way to produce a measure on \({\mathbb{R}^d}\) (or subdomain of \({\mathbb{R}^d}\) ) of the form \({e^{\gamma X(x)} dx}\) , where X is a log-correlated Gaussian field and \({\gamma \in [0, \sqrt{2d})}\) is a fixed constant. A renormalization procedure is needed to make this precise, since X oscillates between ?∞ and ∞ and is not a function in the usual sense. This procedure yields the zero measure when \({\gamma = \sqrt{2d}}\) . Two methods have been proposed to produce a non-trivial measure when \({\gamma = \sqrt{2d}}\) . The first involves taking a derivative at \({\gamma = \sqrt{2d}}\) (and was studied in an earlier paper by the current authors), while the second involves a modified renormalization scheme. We show here that the two constructions are equivalent and use this fact to deduce several quantitative properties of the random measure. In particular, we complete the study of the moments of the derivative multiplicative chaos, which allows us to establish the KPZ formula at criticality. The case of two-dimensional (massless or massive) Gaussian free fields is also covered.     

A determination of antioxidant efficiencies using ESR and computational methods

Using Transition-State Theory, experimental rate constants, determined over a range of temperatures, for reactions of Vitamin E type antioxidants are analysed in terms of their enthalpies and entropies of activation. It is further shown that computational methods may be employed to calculate enthalpies and entropies, and hence Gibbs free energies, for the overall reactions. Within the linear free energy relationship (LFER) assumption, that the Gibbs free energy of activation is proportional to the overall Gibbs free energy change for the reaction, it is possible to rationalise, and even to predict, the relative contributions of enthalpy and entropy for reactions of interest, involving potential antioxidants. A method is devised, involving a competitive reaction between *CH3 radicals and both the spin-trap PBN and the antioxidant, which enables the relatively rapid determination of a relative ordering of activities for a series of potential antioxidant compounds, and also of their rate constants for scavenging *CH3 radicals (relative to the rate constant for addition of *CH3 to PBN).     

Headgroup effect on silane structures at buried polymer/silane and polymer/polymer interfaces and their relations to adhesion

Sum frequency generation (SFG) vibrational spectroscopy was used to study the effect of silane headgroups on the molecular interactions that occur between poly(ethylene terephthalate) (PET) and various epoxy silanes at the PET/silane and PET/silicone interfaces. Three different silanes were investigated: (3-glycidoxypropyl) trimethoxysilane (γ-GPS), (3-glycidoxypropyl) methyl-dimethoxysilane (γ-GPMS), and (3-glycidoxypropyl) dimethyl-methoxysilane (γ-GPDMS). These silanes share the same backbone and epoxy end group but have different headgroups. SFG was used to examine the interfaces between PET and each of these silanes, as well as silanes mixed with methylvinylsiloxanol (MVS). We also examined the interfaces between PET and uncured or cured silicone with silanes or silane-MVS mixtures. Silanes with different headgroups were found to exhibit a variety of methoxy group interfacial segregation and ordering behaviors at various interfaces. The effect of MVS was also dependent upon silane headgroup choice, and the interfacial molecular structures of silane methoxy headgroups were found to differ at PET/silane and PET/silicone interfaces. Epoxy silanes have been widely used as adhesion promoters for polymer adhesives; therefore, the molecular structures probed using SFG were correlated to adhesion testing results to understand the molecular mechanisms of silicone-polymer adhesion. Our results demonstrated that silane methoxy headgroups play important roles in adhesion at the PET/silicone interfaces. The presence of MVS can change interfacial methoxy segregation and ordering, leading to different adhesion strengths.     

Polyakov’s formulation of $2d$ bosonic string theory

Publications mathématiques de l'IHÉS -     

Fracture mechanics of multiple load path structure

The strain energy approach to linear elastic fracture mechanics is combined with a ‘virtual work’ technique for general structural analysis in order to provide a means of predicting the crack propagation behaviour in a multiple load path structure. Progressive failure in one member may lead to significant changes in the relative stiffness of the load paths, and consequent re-distribution of loads within the structure. A simple example is presented, to illustrate the general approach.     

High-brightness terawatt KrF* (248 nm) system

19 W/cm² range with improved shot-to-shot energy stability. This system gives a resulting brightness of ∼3.3×10²¹ W cm^-2 sr^-1. Received: 5 November 1996/Revised version: 29 November 1996     

Vibrational relaxation in SnCl4

The vibrational relaxation in liquid SnCl₄ was determined as a function of temperature. Comparison of theory and experiment leads to the conclusion of a simultaneous relaxation of three internal modes.