Semi-explicit methods for isospectral flows

In this paper we propose semi-explicit schemes based on Taylor methods for the solution of the isospectral equation L=[B,L] for d×d real matrices L, while reproducing the isospectrality of the exact equation. Although the theoretical solution may be symmetric, the proposed schemes usually do not retain symmetry of the underlying flow. We present techniques that allow us to decrease the breakdown in symmetry.     

Oil Plume Distribution in an Anisotropic Porous Medium

The saturation distribution—within an anisotropic aquifer—of a pollutant discharging from an underground source is modeled by a two-dimensional, nonlinear diffusion–convection equation. A closed form self-similar solution is obtained for the steady saturation distribution in the immiscible zone. The results may be used to rationalize field data collected for predicting locations of underground leakage sources in aquifers and to understand the influence of the anisotropic permeability’s parameters on the oil distribution in the porous medium. An erratum to this article can be found at     

Similarity solution to unconfined flow in an aquifer

In this study we refer to a non-steady state, one-dimensional unconfined flow in an aquifer described by the Boussinesq equation. A closed-form analytical solution is derived for a semi-infinite porous medium possessing a boundary condition of the power law type.     

Biorthogonal polynomials: Recent developments

An important application of biorthogonal polynomials is in the generation of polynomial transformations that map zeros in a predictable way. This requires the knowledge of the explicit form of the underlying biorthogonal polynomials.The most substantive set of parametrized Borel measures whose biorthogonal polynomials are known explicitly are theMöbius quotient functions (MQFs), whose moments are Möbius functions in the parameter. In this paper we describe recent work on the characterization of MQFs, following two distinct approaches. Firstly, by restricting the attention to specific families of Borel measures, of the kind that featured in [4], it is possible sometimes to identify all possible MQFs by identifying a functional relationship between weight functions for different values of the parameter. Secondly, provided that the coefficients in Möbius functions are smooth (in a well defined sense), it is possible to prove that the weight function obeys a differential relationship that, in specific cases, allows an explicit characterization of MQFs. In particular, if all such coefficients are polynomial, the MQFs form a subset of generalized hypergeometric functions.Dedicated to Syvert P. Nørsett on the occasion of his 50th birthdayThis paper has been written during the author's visit to California Institute of Technology, Pasadena.     

The existence of large commutator subgroups in factors and subgroups of non-nilpotent groups

We prove that any finite non-nilpotent group G must possess certain factors K / M with a large commutator subgroup, where M is nilpotent. These results are related to recent results by M. Herzog and the authors on large commutator subgroups.Received: 26 August 2004     

Theoretical evaluation of potential surfaces,equilibrium geometries and vibronic transition intensities of excimers: the pyrene crystal excimer

A general method for evaluation of equilibrium geometries and vibronic transition intensities of crystalline excimers is described. The method provides realistic potential surfaces which include, in addition to the α electron surfaces, also the repulsive hard core of the α electrons and the effect of the crystal potential. The method is applied to the study of the potential surfaces of the pyrene excimer, both in the crystal and in the gas phase. The method is also used for a direct evaluation of the vibronic structure of the excimer emission. The calculations reproduce the main experimentally observed properties including the structureless envelope of the emission band and the temperature dependence of its line width.     

Solvation free energies of molecules. The most stable anionic tautomers of uracil

Anionic states of nucleic acid bases are suspected to play a role in the radiation damage processes of DNA. Our recent studies suggested that the excess electron attachment to the nucleic acid bases can stabilize some rare tautomers, i.e. imine-enamine tautomers and other tautomers with a proton being transferred from nitrogen sites to carbon sites (with respect to the canonical tautomer). So far, these new anionic tautomers have been characterized by the gas-phase electronic structure calculations and photoelectron spectroscopy experiments. In the current contribution we explore the effect of water solvation on the stability of the new anionic tautomers of uracil. The accurate free energies of solvation are calculated in a two step approach. The major contribution was calculated using the classical free-energy perturbation adiabatic-charging approach, where it is assumed that the solvated molecule has the charge distribution given by the polarizable continuum model. In the second step the free energy of solvation is refined by taking into account the real, average solvent charge distribution. This is done using our accelerated QM/MM simulations, where the QM energy of the solute is calculated in the mean potential averaged over many MD steps. We found that in water solution three of the recently identified anionic tautomers are 6.5-3.6 kcal mol(-1) more stable than the anion of the canonical tautomer.     

One-dimensional model for water and aqueous solutions. II. Solvation of inert solutes in water

The two one-dimensional models introduced in Part I are used to study the thermodynamics of solvation of inert solutes in water. It is shown that the anomalously large Gibbs energy of solvation of inert solutes in water, on one hand, and the large negative entropy of solvation, on the other hand, arise from different molecular sources. While the primitive model can give rise to a large positive solvation Gibbs energy, it fails to show large negative entropy and enthalpy of solvation. It is remarkable that the primitive cluster model can show both the large positive Gibbs energy and enthalpy of solvation.