Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Multiple solutions of unrestricted Hartree-Fock equations: The SNH+ radical as an example

A case of appearance of multiple unrestricted Hartree-Fock (UHF) solutions in the SNH⁺ (²A') radical is reported. This kind of solution does not arise from different electron configurations or symmetry breaking effects and seem to be exclusive of the UHF method. Three solutions are found and studied on the basis of wave function stability tests and several conclusions about their origin are given.     

Experimental and theoretical study of the structures and binding energies of eugenol (H2O)n, n=0-2

Eugenol (4-Allyl-2-methoxyphenol), a phenol-derivative with an intramolecular -OH ...OCH(3) hydrogen bond (H bond), has been studied in a supersonic expansion using a number of complementary laser spectroscopic techniques. The mass-resolved excitation spectrum of eugenol and its water complexes are reported for the first time. The most intense set of bands on the resonantly enhanced multiphoton ionization (REMPI) spectrum of eugenol originate in a conformer whose S(1)<--S(0) transition is at 35 202 cm(-1) and the ionization threshold at (I(0)<--S(0)) 62 544+/-150 cm(-1) (7.755+/-0.019 eV). In addition, two low intensity features redshifted with respect to the 0(0) (0) transition have been identified as due to a second, less stable conformer. Ab initio calculations show that the potential energy landscape depicts at least three minima associated with one folded and two extended conformers, one of which is the most stable. Clusters of eugenol/water were prepared in a supersonic expansion by seeding eugenol and water in noble gas He and examined by two-color REMPI (R2PI) and IR-UV double resonance spectroscopies. Only one single isomer was observed for both 1:1 and 1:2 complexes, in contrast with the several stable conformers provided by the computations. The dissociation energies of the 1:1 and 1:2 complexes have been determined by the fragmentation threshold method and the results compared with those from ab initio calculations conducted at the B3LYP and MP2 levels with a variety of basis sets.     

Bifurcations of non-smooth systems

Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.     

An approach for solving competitive location problems with variable demand using multicore systems

A planar competitive location and design problem with variable demand is considered. The assumption that the demand may vary depending on the conditions of the market makes the problem more realistic, but it also increases its complexity, and therefore, the computational effort needed to solve it. In this paper, a modification of a heuristic recently proposed to cope with the problem is presented, which allows, on the one hand, to obtain the same solutions as the original heuristic more quickly and, on the other hand, to handle larger size problems. Furthermore, a parallel version of the algorithm, suitable for being run in most of today’s personal computers, has also been proposed. The parallel algorithm has been implemented using the OpenMP library and the results show an ideal efficiency up to at least eight processors (the largest number of available processing elements). The effectiveness of the parallel algorithm has also been measured. From the computational results, it can be inferred that the proposed parallelization is robust.