In a coarsening system, persistent sites are defined as those that remain in the same phase throughout the time interval in question. It has been well-established that the total number of such sites decays with time rather slowly, as a power-law. We study the spatial distribution of persistent sites, and the time evolution of this distribution in various models of coarsening. It is shown that under certain conditions, the set of persistent sites forms a fractal structure in space. Analytic predictions for the fractal dimension and other aspects of the distribution are verified in numerical simulations.

A one-dimensional Ising model is coupled to two heat baths, such that the spins at even lattice sites have a temperature T_e and the spins at odd sites a temperature T_o. The spin dynamics is a generalization of the Glauber dynamics with a uniform temperature and can be described by a master equation. Because of the driving heat fluxes in the case of two temperatures the spin chain is in a non-equilibrium stationary state. We approach the stationary distribution of the master equation analytically with a perturbation theory in the temperature difference where the first two orders of perturbation theory are evaluated. In each order spin couplings arise in the stationary distribution. We also calculate the entropy production in the non-equilibrium stationary state via two different methods and compare the results.

Biological cells contain nanoscale machineries that exhibit a unique combination of high efficiency, high adaptibility to changing environmental conditions, and high reliability. Recent progress in obtaining atomic resolution structures provide an opportunity for an atomic level explanation of cellular machineries and the underlying physical mechanisms. A prime example in this regard is the apparatus with which purple bacteria harvest the light of the sun. It consists of up to five different type of proteins containing several hundred pigments that are organized in a highly symmetrical architecture. Through quantum physical calculations, we elucidate the mechanisms and pathways for excitation energy transfer underlying the light harvesting and photoprotective functions of the photosynthetic apparatus. The close interplay of biological functionality with quantum physical processes in this apparatus allow an illuminating demonstration of the fact that properties of living beings ultimately rely on and are determined by the laws of physics.

We discuss two nonequilibrium models whose steady state is an unusual phase separated state, characterised by strong fluctuations. The models are a fluctuating rough surface in 2+1 dimensions, and a set of hard-core particles sliding on it under gravity. The surface is characterised by dynamical exponent z and roughness exponent chi (0 < chi < 1). When the surface is rough (e.g., KPZ surface) the models show coarsening behaviour, with a characteristic length scale diverging as L(t) ~ t^(1/z), leading to a phase separated steady state. In this state, the particles cluster together over macroscopic length scales, wheras the rough surface forms valleys and hills which are infinitely broad. The steady state two-point correlator in both models scales with system size and the scaling function has a cusp near the origin. For Gaussian surfaces, we show exactly that the cusp exponent is simply the roughness exponent chi. The order parameter exhibits strong fluctuations, and the width of the distribution remains finite in the thermodynamic limit. These features make the steady state very different from conventional ordered states. We extend the study to the Edwards-Wilkinson surface which is only logarithmically rough. In this case, corrections to scaling are observed, and phase separation is marginal.

Biochemical networks are formed by thousands of simultaneous chemical reactions which display nonlinear kinetics. The complexity of such networks makes it near impossible to reason about them without a mathematical framework. Computer models can be developed using classical dynamics, the most popular way of simulating biochemical networks. I will present the software Gepasi, a framework for simulation of biochemical networks, and discuss the various methods it employs to process simulations and nonlinear optimization, which is required to construct models from observed data.

Molecular wires have interesting physical properties that make them good candidates for the next generation of electronic devices. I will discuss in this talk the possibility that, under certain conditions, electronic transport in molecular wires can be chaotic. Chaos is due to the formation of electric domains and domain walls in the wire when sequential resonant tunneling occurs between adjacent units of the wire. A similar phenomenon has been predicted and demonstrated for solid-state superlattices. However, unlike in superlattices, the electric domains in this case are distributed across the entire length of the wire. The difference between the two cases is due to the different spatial distribution of the electric field.

Magnetism, like gravity, is a phenomenon whose effects are readily recognized and, at the same time, profoundly difficult to explain. One way that one can probe the interactions that give rise to magnetic order in solids is to prepare families of compounds that are related to each other, but that vary, in a systematic way, a physical property such as the spacing in the unit cell. Establishing what effect the modification has on the bulk magnetic properties gives us insight into the mechanism of magnetic coupling. Carrying out this strategy using molecules as building blocks, rather than atoms, exploits the strength of chemical synthesis: it is possible to tune the size, shape and electronic properties of a molecule is a way that is impossible for a single atom. Carrying this plan out by preparing charge-transfer (CT) salts presents an additional very important advantage: ease of preparation. It has been shown that it is possible to prepare, in a few steps from commercially available starting materials, large numbers of structurally characterized, magnetically interesting, compounds by this route. Many candidate building block acceptors for realizing this goal have been identified from an examination of the Diels-Alder reaction, polyolefin and molecular metals literature where electron poor olefins and quinones have been featured.

We investigate the chaotic properties of passive advection in closed hydrodynamical flows. Considering a model of the Gulf Stream and simple Hamiltonian maps, we show that leaking the closed Hamiltonian dynamics by cutting out a region of the flow provides a simple method for visualizing the foliation of the system. We found that the structures of the unstable manifolds are comparable with structures traced out by chemical or biological processes in closed systems. With the help of the Kantz-Grassberger relation between dimension, escape rate and the average Lyapunov exponent, we study how the dimension depends on the leak. By measuring the escape rate as a function of the leak, we find a nontrivial shape dependence, which disappears, if random maps are considered. We thus conlude that the escape rate and the dimension of the advection process in chaotic (but nonturbulent) flows depends on the area of the leak only.

A parallel algorithm is represented by three important items: (a) initial data distribution, (b) communication schedule, and (c) local computational tasks. Depending on the constraints imposed on these three factors, different problems arise which might require distinct approaches to handle them. In this talk, we will discuss the issues involved in determining and designing optimal and/or efficient parallel numerical algorithms based on problem classification of these three criteria.

In non-equilibrium phase transitions, the question of universality is still far from being as well understood as its equilibrium counterpart. Simple models, where exact results could be found, are therefore particularly welcome. Following this idea we will introduce a reaction-diffusion process in which reactions only take place on a single site. Although extremely simple, this model exhibits a non-trivial phase transition into an absorbing state even in one dimension. Moreover, we will see that several pieces of analytical evidence support the idea that the exclusion constraint between particles may change the universality class of the transition. Up to now, we have failed finding a simple argument which could explain this surprising and counter-intuitive result.

Convection in a fluid layer heated from below (Rayleigh-Benard convection) provides many examples of complex pattern formation and is a model for transition to turbulence in hydrodynamical systems. Our objective is to predict the stability of different convection patterns. Beyond the onset of convection in a cell of moderate aspect ratio we found straight and bent rolls as stable patterns. By increasing the Rayleigh number, we studied the generation of defects, their dynamics of climbing and gliding, the existence of stable targets and spirals as well as the occurrence of core instabilities. We have also considered the effect of rotation in a cell of small aspect ratio. We studied the dynamics associated with transitions between states with adjacent azimuthal wave numbers far from onset. In certain regimes a novel burst-like state is identified and described.