Construction of modular branching functions from Bethe's equations in the 3-state Potts chain

We use the single-particle excitation energies and the completeness rules of the 3-state antiferromagnetic Potts chain, which have been obtained from Bethe's equation, to compute the modular invariant partition function. This provides a fermionic construction for the branching functions of theD ₄ representation ofZ ₄ parafermions which complements the bosonic constructions. It is found that there are oscillations in some of the correlations and a new connection with the field theory of the Lee-Yang edge is presented.     

Significance of Updating Schemes in Computational Models: Dynamics of Neutral Networks

A Hopfield neural network was constructed with relevance to protein dynamics. The dynamics of this network was analyzed by determining the distribution of first passage times between memories and its dependence on temperature. The distribution depended on the updating scheme. This illustrates the importance of choosing an updating scheme that leads to physically meaningful results in computational models of dynamic processes, such as in neural networks or molecular dynamics.     

Crack growth in single crystals of α-iron (3 wt.% Si)

Experimental and theoretical investigations by the method of acoustic emission and atomistic simulations by a molecular dynamics technique show that brittle-ductile transition in α-iron is very sensitive to loading rate and that the character of acoustic emission is different when different processes operate at the crack tip. A self-similar concept for comparison of experimental and atomistic results is proposed for fracture tensile tests. The work was supported by the Grant Agencies GA CR and GA AS in Prague under the contracts No. 106/93/1110 and No. A 2076701, respectively, and also by an EC-Project Copernicus ERB-CIPA-CT94-0223.     

Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow

We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.     

Reaching the Unreachable: Technology and the Semantics of Asymptotes

This work is part of a larger attempt to explore the nature of symbolic understanding involving graphic technology. This study describes learning advanced mathematics that occurs through constructing qualitative reasoning methods using graphic technology. Data was gathered from a precalculus class who, for a few weeks, investigated and explored asymptotic behavior of rational functions. The analysis is based on observations of group discussions and written works. Learning about asymptotes using software which serves as tool box for numerical evaluation and graphic representation amplifies epistemological complexities related to the infinity concept. Using the software to watch examples of rational functions, generated by symbolic and graphic operations between polynomial functions, enabled students to leave their own traces on the formalization of asymptotes – on its definition, its symbolic structure, and its computational procedures. The discrepancy between technology as a support for visual perception but a tool that cannot support theconception of approaching infinities, makes the study of asymptotes an intriguing domain for investigating what is being manipulated with software and how.This revised version was published online in September 2005 with corrections to the Cover Date.     

Membrane position of ibuprofen agrees with suggested access path entrance to cytochrome P450 2C9 active site

Cytochrome P450 2C9 (CYP2C9) is a membrane-anchored human microsomal protein involved in the drug metabolism in liver. CYP2C9 consists of an N-terminal transmembrane anchor and a catalytic cytoplasmic domain. While the structure of the catalytic domain is well-known from X-ray experiments, the complete structure and its incorporation into the membrane remains unsolved. We constructed an atomistic model of complete CYP2C9 in a dioleoylphosphatidylcholine membrane and evolved it by molecular dynamics simulations in explicit water on a 100+ ns time-scale. The model agrees well with known experimental data about membrane positioning of cytochromes P450. The entry to the substrate access channel is proposed to be facing the membrane interior while the exit of the product egress channel is situated above the interface pointing toward the water phase. The positions of openings of the substrate access and product egress channels correspond to free energy minima of CYP2C9 substrate ibuprofen and its metabolite in the membrane, respectively.     

Molecular mass dependence of adsorbed amount and hydrodynamic thickness of polyelectrolyte layers

Highly charged polyelectrolytes adsorbed on oppositely charged colloidal particles are investigated by electrophoresis and dynamic light scattering. The dependence of the adsorbed amount and of the hydrodynamic layer thickness on the molecular mass and the salt level is analyzed. The adsorbed amount increases with increasing salt level and decreases with increasing molecular mass. The hydrodynamic layer thickness is independent of the molecular mass at low salt levels, but increases with the molecular mass as a power law with an exponent 0.10 ± 0.01 at high salt. The same behavior was observed for different polyelectrolytes and substrates and therefore is suspected to be generic. Due to semi-quantitative agreement with computer simulations carried out by Kong and Muthukumar in 1998, the observed behavior is interpreted with conformational changes of single adsorbed polyelectrolyte chains.