Dynamical real-space renormalization group calculations with a highly connected clustering scheme on disordered networks.

We have defined a type of clustering scheme preserving the connectivity of the nodes in a network, ignored by the conventional Migdal-Kadanoff bond moving process. In high dimensions, our clustering scheme performs better for correlation length and dynamical critical exponents than the conventional Migdal-Kadanoff bond moving scheme. In two and three dimensions we find the dynamical critical exponents for the kinetic Ising model to be z=2.13 and z=2.09 , respectively, at the pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behavior of randomly bond diluted lattices in d=2 and 3 in the light of this transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law and Poissonian degree distributions.

Statistics of a hydrophobic chain near a hydrophobic boundary.

We study the behavior of a hydrophobic chain near a hydrophobic boundary in two dimensions, adapting the decorated lattice model of Berkema and Widom (G.T. Barkema, B. Widom, J. Chem. Phys. 113, 2349 (2000)) to obtain effective, temperature-dependent intrachain and chain-boundary interactions. We use these interactions to construct two model Hamiltonians. The resulting partition functions may be integrated numerically. Our results compare favorably with preliminary Monte Carlo computations, using the same effective interactions. At relatively low temperatures and at high temperatures, we find that the chain is randomly configured in the ambient water, and detached from the wall, whereas at intermediate temperatures it adsorbs onto the wall in a stretched or partially folded state, again depending upon the temperature, and the energy of solvation.

Slow regions percolate near glass transition.

A nanosecond scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as it nears the glass transition. The scaling behaviour is in the same universality class as percolation. The exponents gamma and beta are found to be 1.7 +/- 0.1 and 0.41 +/- 0.01 in agreement with the best percolation results in three dimensions.

Strategies for the evolution of sex.

We find that the hypothesis made by Jan, Stauffer, and Moseley [Theory Biosci. 119, 166 (2000)] for the evolution of sex, namely, a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multistable regime. On the other hand, in the limit of extremely slow drive, another transition takes place to a different steady state distribution, with fewer deleterious mutations within the population.

Evolutionary route to diploidy and sex.

By using a bit-string model of evolution, we find a successful route to diploidy and sex in simple organisms. Allowing the sexually reproducing diploid individuals to also perform mitosis, as they do in a haploid-diploid cycle, leads to the complete takeover of the population by sexual diploids. This mechanism is so robust that even the accidental conversion and pairing of only two diploids give rise to a sexual population.

Delocalization transition of a rough adsorption-reaction interface

We introduce a kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-affine interface with Kardar-Parisi-Zhang-like scaling behavior undergoes a delocalization transition with critical exponents that fall into a different universality class. As the critical point is approached, the interface becomes a multivalued, multiply connected self-similar fractal set. The scaling behavior and critical exponents of the relevant correlation functions are determined from Monte Carlo simulations and scaling arguments.

Glassy dynamics of protein folding.

A coarse-grained model of a random polypeptide chain, with only discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues is shown to display stretched exponential relaxation under Metropolis dynamics at low temperatures with the exponent beta approximately 1/4, in agreement with the best experimental results. The time dependent correlation functions for fluctuations about the native state, computed in the Gaussian approximation for real proteins, have also been found to have the same functional form. Our results indicate that the energy landscape exhibits universal features over a very large range of energies and is relatively independent of the specific dynamics.

Dynamics of pinned interfaces with inertia.

We introduce velocity dependent pinning into two models which are known to be in the universality class of the directed percolation depinning (DPD) model. The effective internal force acting on any point of the interface is enchanced by a factor f at that point of the interface which has last moved. This causes the effective roughness exponent to cross over continuously from the DPD value of 0.63, to unity in the non-dissipative limit of f-->infinity, while the growth exponent tends to 3/4. DPD scaling is recovered for length scales above a persistence length which grows with the enchancement factor as f(psi), with a new exponent psi approximately equal to 1.3.