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     

A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems

We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique.     

Letter: Models of Relativistic Particle with Curvature and Torsion Revisited

Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and explicitly determined using the Lancret program. The moduli subspaces of closed solitons in the three sphere are also determined.     

An isochore versal deformation theorem

We introduce a cohomological approach to isochore deformation problems. We use this formulation in order to prove an isochore versal deformation theorem for holomorphic function germs.     

Effect of the reaction state on the polymerization of p-xylenesulfonium salts

1,4-Phenylenebis(methylene) sulfonium salts were polymerized under different conditions to yield p-xylylene sulfonium salt polyelectrolytes in a broad range of molecular weights. The aqueous reaction mixture formed a reversible gel at initial monomer concentrations higher than 1.0M, but at lower concentrations it remained as an emulsion until reaction completion. The effect of reaction time on intrinsic viscosities and polymer yields for both the emulsion and the gel state is discussed. The higher yields obtained when the reaction was carried out in the presence of a water-immiscible organic solvent were apparently due to the effect of this solvent on increasing the concentration of the reactive intermediate that led to the polyelectrolyte. Both the addition of an organic solvent and the variation of the initial monomer concentrations allowed some control over the molecular weight of the polyelectrolyte formed.     

Associative and segregative phase separations of poly(N-tert-butylacrylamide)/poly(acrylic acid) mixtures. Effect of solvent

Poly(N-tert-butylacrylamide) (PNtBAm) and poly(acrylic acid) (PAA) form interpolymer complexes in 1- and 2-propanol, blend in ethanol, whereas a segregative phase separation is observed when using methanol as solvent as shown by Fourier transform infrared (FTIR) spectrometry and elemental analysis studies. The composition of PNtBAm/PAA complexes has been determined. Thermal studies demonstrated that all complexes show unique glass transition temperatures, higher than those of the polymer components. Complexation of PAA with PNtBAm results in an improvement of its thermal stability. Solvent effects and specific interactions in the system PNtBAm/PAA have been studied by FTIR, revealing that differences in the polymer–solvent interactions are a decisive factor governing complex formation in solution.     

Analytic geometry and semi-classical analysis

We study deformation theory for quantum integrable systems and prove several theorems concerning the Gevrey convergence and the unicity of perturbative expansions. à V.I. Arnold pour ses 70 ans     

Partial linearization for noninvertible mappings

A Hartman-Grobman result for noninvertible mappings is proved. It is assumed that the spectrum of the linearized mapping contains zero but is disjoint from the complex unit circle. In the infinite-dimensional case, additional spectral conditions are assumed. These additional conditions are satisfied if the linearized mapping is completely continuous. The proof combines Hartman'sC ¹ linearization method for contractive mappings [10] with our previous result [1] on linearization of the expanding part.The paper was written while the second author was an Alexander-von-Humboldt Research Fellow in the Mathematical Institute of the University of Augsburg, Germany.