On the quasi-chemical theory of solutions

The classical canonical partition function for a one-dimensional, two-component system is examined for the case of nearest-neighbor interactions. The quasi-chemical model of solid solutions is found to be a natural consequence of the definition of the partition function when one replaces the normal configurational energy with a configurational free energy. Consequently, the quasi-chemical theory may be viewed as a consequence of the definition of the partition function and not as merely a physically pleasing model.     

Hohenberg–Kohn theorems in the presence of magnetic field

In this article, we examine Hohenberg–Kohn theorems for Current Density Functional Theory, that is, generalizations of the classical Hohenberg–Kohn theorem that includes both electric and magnetic fields. In the Vignale and Rasolt formulation (Vignale and Rasolt, Phys. Rev. Lett. 1987, 59, 2360), which uses the paramagnetic current density, we address the issue of degenerate ground states and prove that the ensemble‐representable particle and paramagnetic current density determine the degenerate ground states. For the formulation that uses the total current density, we note that the proof suggested by Diener (Diener, J. Phys.: Condens. Matter. 1991, 3, 9417) is unfortunately not correct. Furthermore, we give a proof that the magnetic field and the ensemble‐representable particle density determine the scalar and vector potentials up to a gauge transformation. This generalizes the result of Grayce and Harris (Grayce and Harris, Phys. Rev. A 1994, 50, 3089) to the case of degenerate ground states. We moreover prove the existence of a positive wavefunction that is the ground state of infinitely many different Hamiltonians. © 2014 Wiley Periodicals, Inc.     

Symmetry calculation for molecules and transition states

The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three‐dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label‐stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules. © 2014 Wiley Periodicals, Inc.     

Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule

In this paper, we use the theory of degeneracy graphs recently developed by Gal et al. to introduce a graph for studying the adjacency of almost complementary feasible bases, some of which may be degenerate, which are of interest in the context of the linear complementarity problem. We study the structure of this graph with particular reference to the possibility of cycling and various anticycling rules in the Lemke complementary pivoting algorithm. We consider the transition node pivot rule introduced by Geue and show that this rule helps in avoiding cycling in the Lemke complementary pivoting algorithm under a suitable assumption.     

A note on paper “Implicit and explicit secular equations for Rayleigh waves in two-dimensional anisotropic media”

The paper is devoted to correcting structure of the representation for Rayleigh waves at non-semisimple degeneracy of the fundamental matrix. The incorrect representation was given in a paper “Implicit and explicit secular equations for Rayleigh waves in two-dimensional anisotropic media” by Cerv and Plesek (2013) .     

Surface tension of superfluid helium

Summary We present here the calculation of the expression for the surface tension depression by taking into consideration the finite size of the molecular superfluid helium. The agreement between the experimental results (J. R. Eckardt, D. O. Edwards, S. Y. Shen and F. M. Gasparini:Phys. Rev. B,16, 1944 (1977)) and the theoretical results is much better than previously published (K. R. Atkins:Can. J. Phys.,31, 1165 (1953)).     

Paired-phonon analysis of impurities in bose fluids

Summary The paired-phonon analysis for boson mixtures is employed in conjunction with the hypernetted-chain approximation to study the ground-state properties of an impurity embedded in liquid⁴He. Chemical potentials, volume coefficients and other thermodynamic quantities as well as some of the most interesting optimal correlation functions are calculated for various impurities interacting with the⁴He background atoms via Lennard-Jones potentials of differing strength. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Determination of the Molecular Arrangement in Liquid Crystals by Polarization of Fluorescence

Polarized luminescence intensity reading and the polarized absorbance spectra of 4-diethyl-amino-4′-nitrostilbene “impurity” in the n-butyl-p/p-hexyloxyphenyloxycarbonyl/-phenyl-carbonate liquid crystal were measured. Degrees of orientational order, S₁ and S₂, of the nematic liquid were calculated from relative values of the absorbance and luminescence intensity components. A function, which describes the angular molecular distribution with respect to a preferred direction in the liquid crystal, is plotted.     

Quantum mechanical Hamiltonians with large ground-state degeneracy

Nonrelativistic Hamiltonians with large, even infinite, ground-state degeneracy are studied by connecting the degeneracy to the property of a Dirac operator. We then identify a special class of Hamiltonians, for which the full space of degenerate ground states in any spatial dimension can be exhibited explicitly. The two-dimensional version of the latter coincides with the Pauli Hamiltonian, and recently-discussed models leading to higher-dimensional Landau levels are obtained as special cases of the higher-dimensional version of this Hamiltonian. But, in our framework, it is only the asymptotic behavior of the background ‘potential’ that matters for the ground-state degeneracy. We work out in detail the ground states of the three-dimensional model in the presence of a uniform magnetic field and such potential. In the latter case one can see degenerate stacking of all 2d Landau levels along the magnetic field axis.     

Global classical solutions to a kind of quasilinear hyperbolic systems in several space variables

For a kind of quasilinear hyperbolic systems in several space variables whose coefficient matrices commute each other, by means of normalized coordinates, formulas of wave decomposition and pointwise decay estimates, the global existence of classical solution to the Cauchy problem for small and decaying initial data is obtained, under hypotheses of weak linear degeneracy and weakly strict hyperbolicity.