Stationary diffusion in the membrane systems with the ongoing reversible chemical reactions

The diffusion phenomena were analyzed using the phenomenological equations of the thermodynamics of irreversible processes. The diffusion coefficient was thought to be dependent on local concentrations and pressure, unlike it was done in the linear theories. The reversible chemical reactions were modeled as intermolecular interaction. The ideal and regular solutions and solutions, described by the Margules's and Sketchard–Hammer's equations, were investigated and analytical solutions were found.     

Low-Energy Collisions of Protonated Enantiopure Amino Acids with Chiral Target Gases

Here we report on the gas-phase interactions between protonated enantiopure amino acids (l- and d-enantiomers of Met, Phe, and Trp) and chiral target gases [(R)- and (S)-2-butanol, and (S)-1-phenylethanol] in 0.1–10.0 eV low-energy collisions. Two major processes are seen to occur over this collision energy regime, collision-induced dissociation and ion-molecule complex formation. Both processes were found to be independent of the stereo-chemical composition of the interacting ions and targets. These data shed light on the currently debated mechanisms of gas-phase chiral selectivity by demonstrating the inapplicability of the three-point model to these interactions, at least under single collision conditions.

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Graphical Abstract

     

Links between microscopic and macroscopic fluid mechanics

The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility.     

Gaussian Property of the Rings R(X) and R〈X〉

The content of a polynomial f over a commutative ring R is the ideal c(f) of R generated by the coefficients of f. A commutative ring R is said to be Gaussian if c(fg) = c(f)c(g) for every polynomials f and g in R[X]. A number of authors have formulated necessary and sufficient conditions for R(X) (respectively, R?X?) to be semihereditary, have weak global dimension at most one, be arithmetical, or be Prüfer. An open question raised by Glaz is to formulate necessary and sufficient conditions that R(X) (respectively, R?X?) have the Gaussian property. We give a necessary and sufficient condition for the rings R(X) and R?X? in terms of the ring R in case the square of the nilradical of R is zero.