A prey-predator system with intelligent pursuit and evasion is studied by means of computer simulations. It is found that the model exhibits a coexistence state between prey and predators. In this state and depending on the parameters, the system may evolve toward two different regimes, characterized by the behavior of the prey-predator population. Whitin the oscillatory (fixed point) regime the specie's density changes periodically (remains constant), respectively. The transition between such regimes is rationalized in terms of a dynamic percolation process.

Quarks and gluons have never been detected as free particles despite the fact that they are undoubtedly constituents of hadrons. This fact has led to the confinement hypothesis. In this talk three prerequisites of a possible confinement mechanism in Landau gauge will be discussed. Two of them are found in and related to each other by the infrared behavior of QCD Green's functions. Contrary to the previously wide-spread believe that the gluon propagator is highly infrared-singular several recent non-perturbative calculations leave no doubt that it is suppressed in the infrared. On the other hand, the propagator of the Faddeev-Popov ghosts turns out to be enhanced in the infrared signaling the fulfillment of the Kugo-Ojima confinement criterion. QCD vertex functions are shown to be also infrared-singular. Finally, the present knowledge on the infrared behavior of the quark propagator is presented.

Plane Couette flow of a liquid occurs between two parallel plates which are rectilinearly sheared. In the viscous regime, laminar flow dominates and a linear velocity profile is obtained as a function of the plate separation. But in the turbulent zone, the velocity flow near the boundary layer is seen to vary as a logarithmic function of the plate separation. In the process, an universal number (the von Karman's constant), has been calculated and this is compared with available experimental results.

The universality classes for dynamic critical behavior near second-order equilibrium phase transitions are well-understood. This talk will address the question what happens when the detailed-balance conditions are violated for "model H" describing the critical dynamics near liquid-gas transitions (phase separation of binary liquids), with a conserved scalar order parameter density coupled to a conserved non-critical (transverse) current. It is demonstrated that isotropic non-equilibrium perturbations do not affect the asymptotic behavior, i.e., detailed balance and the equilibrium critical exponents are restored. If detailed balance is violated through the introduction of anisotropic noise strengths, however, this is clearly not the case, and the properties of the ensuing effective model are as yet not fully understood.

The dissipation of energy upon collisions of macroscopic particles or grains is one of the key features of granular media. Energy can be dissipated, i.e. be removed from the translational motion, by several emechanisms including plasic deformation, viscoelastic behvior, or excitation of vibrations. Here, the latter mechanism is investigated and a method to go beyond the famous calculation of quasistatic contact by Hertz and its extension by Rayleigh is developed. The method is applied numerically to the collision of spheres. It is found that energy
dissipation by excitation of vibrations plays a small but noticeable role for equal spheres and becomes more important if the spheres differ in size.

I will discuss the properties of discrete one-dimensional systems with ferromagnetic interactions that decay like the square of the distance between the particles. It is little known that these systems, despite their great simplicity, are believed to exhibit very  interesting critical behavior. By means of a combination of renormalization-group arguments and precise numerical calculations,  it is demonstrated that the phase transition is actually the analog of the famous Kosterlitz-Thouless transition in two-dimensional  systems.

The problem of persisting random events is a very natural question in the theory of random processes but very few examples have been solved by mathematicians. As a matter of fact it is a very difficult problem although the question of persistance is very simple.    After reminding the audience of some basic knowledge about random processes used in statistical physics I will try, in this talk, to show how persistence problems are of interest to physicists (links with scaling laws, new types of exponents...). I will then illustrate this with a few examples of solved and unsolved problems, and if I have time, will end with my small contribution to that field.

Foams (such as soap froth and emulsions) have unique rheological properties that can support finite stress like a solid but yield and flow under large stress like a fluid. This solid to fluid transition depends sensitively on foams' structures but the mechanism is not yet understood. I will present a theoretical derivation of foams' energy minima based on the geometrical and topological structures. The results enable us to define a mesoscopic stress and strain, thus lead to the possibility of developing a constitutive stress-strain relationship for foams. I will compare the theory with ferrofluid foam and soap foam experiments and computer simulations. Interestingly this study also sheds light into the classic isoperimetric problem in mathematics.

Coupled map lattices are determinstic model systems that display a high-dimensional chaotic dynamics. In these systems local chaotic units, i.e. chaotic maps like the logistic map, are iterated and coupled to its nearest neighbors on the lattice. The resulting dynamics shows a very rich ergodic behavior with different regimes. In this talk I will discuss a special system on a one-dimensional lattice for which one can derive a stochastic dynamics on a coarse-grained level. In particular, there is a close connection of this coupled map lattice to the Glauber dynamics of the Ising model.

Random walks under the influence of an additional dynamical feedback-coupling is analyzed anayltically and numerically. The feedback introduced via a generalized master equation is controlled by a memory term of strength λ the explicit form of which is motivated by arguments of the mode-coupling theory. For a negative memory term, λ < 0, we find superdiffusive behavior whereas a positive memory term leads to localization. The numerical simulations are in agreement with renormalization group results. Applications to supercooled liquids as well as the relation to weather observations and to the financial market are discussed shortly.

We study the dynamics of rigid spheres embedded in viscoelastic media and address two questions of importance to microrheology. First we calculate the complete response to an external force of a single bead in a homogeneous elastic network viscously coupled to an incompressible fluid. From this response function we find the frequency range where the standard assumptions of microrheology are valid. Second we study fluctuations when embedded spheres perturb the media around them and show that mutual fluctuations of two separated spheres provide a more accurate determination of the complex shear modulus than do the fluctuations of a single sphere.

We will start with general introduction to probabilistic cellular automata (PCA). Then some of the problems concerning PCA will be translated into problems of equilibrium statistical mechanics (ESM) on sample space (histories) of PCA. Ideas and techniques developed in the context of ESM, real space renormalization group and cluster expansion, in particular, will be applied to analyze behavior of a class of low noise dissipative PCA (low noise PCA give rise to low-temperature ESM systems).

We study the interplay between inertia, dissipation and external driving on the dynamics of Heisenberg spins. In the absence of external driving, the spin system approaches equilibrium by the joint action of dissipation and inertia. Following a quench from the disordered to a broken symmetry phase, the spins evolve slowly producing self-similar patterns over large length scales. This gives rise to universal features in the dynamics. Inertia plays a significant role in determining these universal properties when the dynamics preserves the total magnetisation. Introduction of an external current drives the system away from equilibrium resulting in a rich non-equilibrium phase diagram of final states. For the Heisenberg spins subject to an anisotropic current the non-equilibrium phases include a high-temperature paramagnetic phase, a new critical phase induced by the driving, and a spatio-temporal chaotic phase. The latter may be `controlled' by an anisotropic potential, giving rise to stable steady states with broken chiral symmetry.

I will first provide an introduction to the nature of the Liesegang phenomenon, and briefly describe the ways theorists have attempted to account for it throughout the XXth century. I will then focus on a more recent scenario based on spinodal decomposition, highlighting its advantages, and review some recent numerical results obtained in this framework.