Density-equicontinuity and Density-sensitivity

In this paper we introduce the notions of (Banach) density-equicontinuity and densitysensitivity. On the equicontinuity side, it is shown that a topological dynamical system is densityequicontinuous if and only if it is Banach density-equicontinuous. On the sensitivity side, we introduce the notion of density-sensitive tuple to characterize the multi-variant version of density-sensitivity. We further look into the relation of sequence entropy tuple and density-sensitive tuple both in measuretheoretical and topological setting, and it turns out that every sequence entropy tuple for some ergodic measure on an invertible dynamical system is density-sensitive for this measure; and every topological sequence entropy tuple in a dynamical system having an ergodic measure with full support is densitysensitive for this measure.     

Existence of a fundamental solution of partial differential equations associated to Asian options

We prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for the pricing problem relevant to path dependent options. We improve previous results in that we provide a closed form expression for the solution of the Cauchy problem under weak regularity assumptions on the coefficients of the differential operator. Our method is based on a limiting procedure, whose convergence relies on some barrier arguments and uniform a priori estimates recently discovered.     

Quantumness Measures for a System of Two Qubits Interacting with a Field in the Presence of the Time-Dependent Interaction and Kerr Medium

In this work, we introduce the standard Tavis-Cummings model to describe two-qubit system interacting with a single-mode field associated to power-law (PL) potentials. We explore the effect of the time-dependent interaction and the Kerr-like medium. We solve the Schrödinger equation to obtain the density operator that allows us to investigate the dynamical behaviour of some quantumness measures, such as von Neumann entropy, negativity and Mandel’s parameter. We provide how these entanglement measures depend on the system parameters, which paves the way towards better control of entanglement generation in two-qubit systems. We find that the enhancement and preservation of the atoms-field entanglement and atom-atom entanglement can be achieved by a proper choice of the initial parameters of the field in the absence and presence of the time-dependent interaction and Kerr medium. We examine the photons distribution of the field and determine the situations for which the field exhibits super-poissonian, poissonian or sub-poissonian distribution.     

Adsorption of 1-Monoglycerides at the Hexane/Water Interface: II. 1-Monolaurin

The interfacial tension of a hexane solution of 1-monolaurin against water was measured as a function of temperature and concentration under atmospheric pressure. The thermodynamic quantity changes associated with the adsorption of 1-monolaurin were evaluated and compared with those of the previously reported 1-monomyristin. The decrease of two carbon atoms in the hydrocarbon chain results in a slight expansion of the 1-monolaurin adsorbed film and in a slight decrease in entropy and energy changes compared with those of the 1-monomyristin system. The large negative value of the entropy change at a high concentration is related to the restricted orientation of the polar head group of 1-monolaurin at the hexane/water interface due to the strong interaction between the large hydrophilic group of 1-monolaurin and the water molecules, as in the 1-monomyristin system. The origin of the distinction in the entropy change behavior between the adsorption from the hexane phase and water phase was discussed. The usefulness of an easier calculation process for the partial molar entropy change is verified by comparison with the usual reliable value and with the entropy of adsorption.     

Chiral recognition by enantioselective liquid chromatography: Mechanisms and modern chiral stationary phases

An overview of the state-of-the-art in LC enantiomer separation is presented. This tutorial review is mainly focused on mechanisms of chiral recognition and enantiomer distinction of popular chiral selectors and corresponding chiral stationary phases including discussions of thermodynamics, additivity principle of binding increments, site-selective thermodynamics, extrathermodynamic approaches, methods employed for the investigation of dominating intermolecular interactions and complex structures such as spectroscopic methods (IR, NMR), X-ray diffraction and computational methods. Modern chiral stationary phases are discussed with particular focus on those that are commercially available and broadly used. It is attempted to provide the reader with vivid images of molecular recognition mechanisms of selected chiral selector–selectand pairs on basis of solid-state X-ray crystal structures and simulated computer models, respectively. Such snapshot images illustrated in this communication unfortunately cannot account for the molecular dynamics of the real world, but are supposed to be helpful for the understanding. The exploding number of papers about applications of various chiral stationary phases in numerous fields of enantiomer separations is not covered systematically.     

Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics

This paper is an introduction to the modelling of viscoelastic fluids,with an emphasis on micromacro(or multiscale) models.Some elements of mathematical and numerical analysis are provided.These notes closely follow the lectures delivered by the second author at the Chinese Academy of Science during the Workshop "Stress Tensor E?ects on Fluid Mechanics" in January 2010.     

The velocity of sound and compressibility in the melts of Hg-Te system

Liquid Hg-Te system has been investigated as a function of composition and temperature by measuring the velocity of sound. A minimum in the sound velocity as a function of temperature observed for Te persists up to 50 at.% Hg, of which the position increases rather steeply between 20 and 30 at.% Hg. This suggests that the molten HgTe and alloys in the Te-rich side undergo structural changes involving the change in coordination number with increasing temperature, and the crossover of the nature of the chemical bond from p-p to sp³ covalent bond takes place with changing composition. It is concluded that the structural change in liquid HgTe is due to intrinsic nature of bonding of HgTe as a compound. Received 2 September 1998 and Received in final form 16 March 1999     

On the Trend to Equilibrium for Some Dissipative Systems with Slowly Increasing a Priori Bounds

We prove convergence to equilibrium with explicit rates for various kinetic equations with relatively bad control of the distribution tails: in particular, Boltzmann-type equations with (smoothed) soft potentials. We compensate the lack of uniform-in-time estimates by the use of precise logarithmic Sobolev-type inequalities, and the assumption that the initial datum decays rapidly at large velocities. Our method not only gives explicit results on the times of convergence, but is also able to cover situations in which compactness arguments apparently do not apply (even mere convergence to equilibrium was an open problem for soft potentials).     

Viscous regularization of the full set of nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation‐Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here, we extend the theoretical grounds for the method and derive an entropy minimum principle for the full set of nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation‐hydrodynamic shock simulations. Radiative shock calculations using constant and temperature‐dependent opacities are compared against semi‐analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations. Copyright © 2017 John Wiley & Sons, Ltd.