Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws

We present some new convergence results for a discrete velocities BGK approximation to an initial boundary value problem for a single hyperbolic conservation law. In this paper we show stability and convergence toward a unique entropy solution in the general framework without any restriction either on the data of the limit problem or on the set of velocity of the BGK model.

     

Zero entropy, non-integrable geodesic flows and a non-commutative rotation vector

Let be a -step nilpotent Lie algebra; we say is non-integrable if, for a generic pair of points , the isotropy algebras do not commute: . Theorem: If is a simply-connected -step nilpotent Lie group, is non-integrable, is a cocompact subgroup, and is a left-invariant Riemannian metric, then the geodesic flow of on is neither Liouville nor non-commutatively integrable with first integrals. The proof uses a generalization of the rotation vector pioneered by Benardete and Mitchell.

     

Letter: Adiabatic Decaying Vacuum Model for the Universe

We study a model that the entropy per particle in the universe is constant. The sources for the entropy are the particle creation and a decaying term. We find exact solutions for the Einstein field equations and show the compatibility of the model with respect to the age and the acceleration of the universe.     

On the Fine Structure of Stationary Measures in Systems Which Contract-on-Average

Suppose {f ₁,...,f _m } is a set of Lipschitz maps of ^d . We form the iterated function system (IFS) by independently choosing the maps so that the map f _i is chosen with probability p _i ( ^m _i=1 p _i =1). We assume that the IFS contracts on average. We give an upper bound for the upper Hausdorff dimension of the invariant measure induced on ^d and as a corollary show that the measure will be singular if the modulus of the entropy _i p _i log p _i is less than d times the modulus of the Lyapunov exponent of the system. Using a version of Shannon's Theorem for random walks on semigroups we improve this estimate and show that it is actually attainable for certain cases of affine mappings of .     

A Finite Partition in a Dynamical System with Entropy Depending on the Size

A finite partition X in a C*-dynamical system has the Alicki–Fannes entropy depending on the size of X so that the dynamical entropy is . Examples are given as Cuntz's canonical endomorphism, the inner automorphism Adu on the crossed product of a quantum spin chain by the shift, and the free shift.     

Calorimetric Behaviour of Anhydrous β-Cyclodextrin at Very Low Temperature

Heat capacities of anhydrous -cyclodextrin were measured between 10 K to 300 K using an adiabatic low-temperature calorimeter. Two distinct types of thermal behaviour were observed in the temperature range 50–130 K, depending on the way the sample was cooled. In the absence of hydration water molecules, we assumed that the two types of thermal behaviour could be attributed to freezing in more or less ordered states of the hydroxyl groups engaged in the intramolecular interglucose flip-flop-type interactions.     

Quantum dynamics of a system of coupled nonlinear oscillators: Spectral and information entropy‐based analysis

The quantum dynamics of the evolution of a system of a few coupled nonlinear oscillators is studied. The spectral entropy and the quantal information entropy, as well as their correlation functions, are computed and used to identify distinctive phases of the evolution. The two entropy functions lead to similar conclusions. It appears that adiabatic switching of the nonlinear interaction does not affect the nature of the short time dynamics but affects the dynamics over intermediate time scales. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Factors influencing enantiomeric recognition of primary alkylammonium salts by pyridino-18-crown-6 type ligands

Equilibrium constant (K), enthalpy change (H), and entropy change (S) values were determined for the interactions of a series of chiral pyridino-18-crown-6 type ligands with enantiomers of several primary alkylammonium salts in various solvents. Good enantiomeric recognition in terms of logK was observed in many systems with logK values greater than 0.4. The extent of enantiomeric recognition and the stabilities of the chiral crown ether-ammonium salt complexes were found to depend on the rigidity of the macrocyclic frame of the ligand, the type and arrangement of the donor atoms on the ligand, the bulkiness of the substituents on the ligand's chiral centers, the location of the chiral centers on the ligand, and the solvent. The effects of these factors on the extent of enantiomeric recognition and on the stabilities of the complexes were examined for the systems studied.     

Enthalpy-entropy compensation of micellization of ethoxylated nonyl-phenols

The thermodynamics of micellization of non-ionic surfactants (ethoxylated nonyl-phenols with different chain length) was studied as a function of ethoxy group number, electrolyte concentration and type, and concentration of short-chain alcohols at different temperature. On the basis of the thermodynamic data the enthalpy/entropy correlation and the H/S compensation temperature were calculated to characterize the solvent-solute and solute-solute interaction. The experimental results have definitely proved that a well-defined correlation exists for all investigated systems and the compensation temperature is independent of the ethoxy group number and the presence of alcohols. The inorganic electrolytes, however, decrease theT _c compared to both alcohol-free and alcohol-containing systems, indicating the change in the mechanism of the micellization process. The new theoretical results significantly contribute to confirmation of the earlier conclusion concerning the stability and the structure of non-ionic surfactant solutions.