Boltzmann Model for Viscoelastic Particles: Asymptotic Behavior,Pointwise Lower Bounds and Regularity

We investigate the long-time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state with explicit rate of convergence towards it. Exponential lower pointwise bounds and propagation of regularity are also studied. These results can be seen as a generalization of several classical results holding for the pseudo-Maxwellian and constant normal restitution models.     

Adsorption properties of silica-based sorbents containing phosphonic acid residues

Isotherms are measured for nitrogen, n-hexane, triethylamine, and water vapor adsorption on silicas of different origins, the surface layers of which contain functional groups of the ??Si(CH₂)₂P(O)(OH)₂ composition, namely, ethylene- and phenylene-bridged polysilsesquioxane xerogels produced by the sol-gel method, silica microspheres synthesized from tetraethoxysilane in the presence of [CH₃(CH₂)₁₇N(CH₃)₃]Br as a template by spray-drying method, and SBA-15 mesoporous silica produced based on tetraethoxysilane using Pluronic 123 as a template. It is shown that all of the samples possess high specific surface areas, while the types of adsorption isotherms and the accessibility of active acidic sites for adsorption interactions with electron-donor molecules depend on the structures of pores and surface layers, which are governed by the methods of synthesis and postsynthesis sample treatment.     

Modelling multiple-simultaneous impact problems with a nonlinear smooth approach: pool/billiard application

Nonlinear Dynamics - Smooth approaches are able to model reasonably well contact/impact events between two bodies, showing some peculiarities when dealing with certain geometries and arising...     

Diels-Alder reactivity of 4-aryl-1-phthalimido-2-siloxy-1,3-butadienes

The reaction of (1Z,3E) and (1E,3E) 4-aryl-1-phthalimido-2-trialkylsiloxy-1,3-butadienes with maleimides and quinones has been studied. The observed exo-stereospecifity can be attributed to the simultaneous presence of the phthalimido and aryl groups, which produce strong hindrance during the endo approach.     

Study of clusters of interest for liquid ionic alloys

Calculations are reported of the total energies and related quantities of sequences of small clusters of the form A_m Pb_n, where A is an alkali atom, n <6 and m < 9. The object of this study is to shed light on the stoichiometry and the possible formation of complexes in A-Pb liquid alloys. The calculations are performed using empty core pseudopotentials and the spherical average approximation for the cluster. The results are insensitive to the choice of alkali atom apart from a smooth trend with the progression from Li to Cs. The calculated total energies suggest that clusters with compositions A₄Pb and A₄Pb₄ are very stable against a change in the number of Pb or A atoms and support the possibility of these clusters forming in the liquid alloys. This stability arises from an electronic shell-closing effect.     

Integrable Deformations of Algebraic Curves

We present a general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations. We emphasize the use of several types of dynamical variables: branches, power sums, and potentials.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 94–101, July, 2005.     

New synthesis of arcyriaflavin-A via silyl enol ether-mediated and Fischer indolisations

A new synthesis of the natural product arcyriaflavin-A is described. It was brought about through Diels-Alder cycloaddition and two indolisations based on silyl enol ether nucleophilic attack and Fischer processes.