Stochastic variational inequalities with jumps

This work is devoted to the study of a stochastic variational inequality with a Wiener–Poisson driving term. Existence and uniqueness are proven for Lipschitz coefficients and under general conditions for the unbounded term. One of the main tools used in order to obtain the existence result is a penalization method involving Moreau–Yosida regularization.     

Extrapolation-based implicit-explicit general linear methods

For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a new extrapolation-based approach to construct practical IMEX GLM pairs of high order. We look for methods with large absolute stability region, assuming that the implicit part of the method is A- or L-stable. We provide examples of IMEX GLMs with optimal stability properties. Their application to a two dimensional test problem confirms the theoretical findings.     

Invariant Measure Associated with a Generalized Countable Iterated Function System

Generalized countable iterated function systems (GCIFS) are an extension of countable iterated function systems by considering contractions from X × X into X instead of contractions on the compact metric space X into itself. For a GCIFS endowed with a system of probabilities we associate an invariant and normalized Borel measure whose support is just the attractor of the respective GCIFS, extending the classical Hutchinson’s construction.     

Overconvergent modular sheaves and modular forms for GL 2/F

Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ?, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.     

The synthesis of Leishmania major phosphoglycan fragments

The triglycosyl monophosphate 1, heptaglycosyl triphosphates 2 and 3, and octaglycosyl triphosphate 4, which are fragments of the phosphoglycan part of Leishmania major lipo- and proteo-phosphoglycans have been prepared using di- and tri-saccharide H-phosphonates for construction of the phosphodiester bridges.     

Performance-based design of permeation test cells for reliable evaluation of chemical protective materials

The test cell constitutes the core functionality of a permeation testing system. Accuracy of an experimental methodology depends on the ability of the test cell to efficiently deliver the challenge agents to the test material, collect all the transported permeate compounds from the test material and transfer those analytes to the online detector. Common test cell designs used in the US and internationally form the basis of their respective testing procedures. However, widespread usage does not necessarily equate to defensible assurance of analytical reliability. Consequently, chemical protective materials characterized with these cells may provide inadequate protection to users whose health and safety depend on barrier garments such as gloves and suits. Permeation test data, including those acquired in our laboratory, have emphasized the significance of test cell design on the accuracy of permeation measurements. This paper describes the key considerations necessary to ensure analytical reliability for a test cell, illustrates quantitative improvements demonstrated by existing prototypes and, finally, proposes a design which further advances the technology of permeation testing.     

Ferroelectricity and structure of BaTiO3 grown on YBa 2Cu3O_{7 - \delta } thin films

We have investigated the crystal structure and the ferroelectric properties of BaTiO₃ thin films with YBa₂Cu₃O as the bottom and Au as the top electrode. Epitaxial heterostructures of YBa₂Cu₃O and BaTiO₃ were prepared by dc and rf sputtering, respectively. The crystal structure of the films was characterised by X-ray diffraction. The ferroelectric behaviour of the BaTiO₃ films was confirmed by hysteresis loop measurements using a Sawyer Tower circuit. We obtain a coercive field of 30 kV/cm and a remanent polarisation of 1.25 μC/cm². At sub-switching fields the capacitance of the films obeys a relation analogous to the Rayleigh law. This behaviour indicates an interaction of domain walls with randomly distributed pinning centres. At a field of 5 MV/m we calculate a 3% contribution of the irreversible domain wall motion to the total dielectric constant. Received 24 June 1999 and Received in final form 27 August 1999     

Super-Instantons, Perfect Actions, Finite-Size Scaling, and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the 2DO(N) models. The continuum limit is taken either in an infinitevolume or in a box whose size is a fixed fraction of the infinite-volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be O(1) and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the socalled super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called “perfect actions”. It also shows that David’s recent claim that superinstanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.     

Characterization of electrical charge separation at the interface of two aqueous solutions in the presence of concentration gradients and cation/anion mobility ratio asymmetry

Physical consequences of ionic diffusion processes play a major role on the outcome of electrophysiology experiments due to both their contribution to the ionic transmembrane transport and phenomena taking place at the measuring instruments interface. As most of the time heterogenities in biological media with respect to ionic diffusion constants are disregarded, we intended to look upon the general case of ionic diffusion at the interface of two liquids on which gradients of these diffusion constants no longer can be neglected. We developed a theoretical model for the diffusion potential which emerges at an aqueous interface under gradients of concentration and diffusion constants. The experimental validation of our model was achieved through potential difference measurements of the diffusion potential between two solutions containing sodium chloride (NaCl) and glycerine solutions of various concentrations. Within the studied domain of the electrical charge mobility ratio, we noticed that experimental results are in agreement with the theoretically inferred diffusion potential values. This demonstrates that the resulting relationship for the diffusion potential inferred from our model could be applied for other cases, as well. When the ionic solutions contains an indefinite quantity of glycerine or an unknown substance able to modify diffusion constants of sodium and chloride, it was shown that through measurements of the diffusion potential one can infer the unknown concentration of glycerine and the modified ionic mobility ratio. This, in turn, builds up the foundation for a novel yet simple and efficient analitycal sensing device for quantitative determination in the field.