Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.     

Dynamic Formation of Hybrid Peptidic Capsules by Chiral Self‐Sorting and Self‐Assembly

Owing to their versatility and biocompatibility, peptide‐based self‐assembled structures constitute valuable targets for complex functional designs. It is now shown that artificial capsules based on β‐barrel binding motifs can be obtained by means of dynamic covalent chemistry (DCC) and self‐assembly. Short peptides (up to tetrapeptides) are reversibly attached to resorcinarene scaffolds. Peptidic capsules are thus selectively formed in either a heterochiral or a homochiral way by simultaneous and spontaneous processes, involving chiral sorting, tautomerization, diastereoselective induction of inherent chirality, and chiral self‐assembly. Self‐assembly is shown to direct the regioselectivity of reversible chemical reactions. It is also responsible for shifting the tautomeric equilibrium for one of the homochiral capsules. Two different tautomers (keto‐enamine hemisphere and enol‐imine hemisphere) are observed in this capsule, allowing the structure to adapt for self‐assembly.     

Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid

Two problems will be studied in this contribution. First, we analyse some phenomena which take place in a laminated solid and are caused by a fluctuation of time-dependent boundary tractions. Second, we investigate the transient effect of initial displacement fluctuations on the behaviour of a laminate. To solve the above problems we propose a new macroscopic 3D model for investigations of initial-boundary value problems in elastodynamics of a laminated medium.     

On the modelling of dynamic problems for plates with a periodic structure

Summary The subject of analysis is the bending of elastic plates exhibiting a nonhomogeneous periodic structure and/or a periodically variable thickness in a certain direction parallel to the plate's midplane. The fundamental modelling problem is how to obtain an effective 2D-model of a plate under consideration, i.e., a 2D-model represented by PDEs with constant coefficients. This problem for periodic plates has been solved independently in [5] and [10], using asymptotic homogenization. However, homogenization neglects dynamic phenomena related to the plate's rotational inertia and cannot be applied to the analysis of higher-order vibration frequences. The main aim of this contribution is to formulate a new non-asymptotic effective 2D-model of a periodic plate which is free from the mentioned drawbacks and describes the dynamic behaviour of plates having the thickness of the order of the period length. The proposed model is applied to the analysis of some vibration problems.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Polarisation control of light by light in a nonlinear polymer

Received: 11 December 1997/Revised version: 11 May 1998     

The large-amplitude motions in quasi-symmetric top molecules with internal C3v rotors: Interpretation of the low frequency Raman spectrum of disiloxane

The vibration-torsion-rotation Hamiltonian developed previously has been used to study the skeletal bending-torsion-rotation energy levels of disiloxane. The zeroth-order skeletal bending-torsion-rotation Hamiltonian for a molecule of this type is presented. The symmetry classification of the molecular wavefunctions and energy levels as well as infrared and Raman selection rules are considered. The energies of the skeletal bending-torsional-rotational states have been calculated and these results are used to interpret the low frequency Raman spectra of gaseous disiloxane-d₀ and disiloxane-d₆. It is shown that the treatment presented enables one to properly interpret these spectra. The results are compared to those obtained with other more approximate Hamiltonians.