F. Schwabl

Scaling laws and simulation results for the self-organized critical forest-fire model.

We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer simulations in 1 to 8 dimensions. The simulations suggest a critical dimension

Theory of periodic ferromagnetic multilayers

d_c=6

Second harmonic light scattering in paraelectric perovskites

above which the critical exponents assume their mean--field values. Changing the lattice symmetry and allowing trees to be immune against fire, we show that the critical exponents are universal.

Phase transitions and soft modes in ferroelectric superlattices

Abstract We investigate the statics and dynamics of periodic multilayers consisting of two ferromagnetic materials. Our theory is based on a general Ginzburg-Landau functional for inhomogeneous systems and the appropriate equations of motion. We compute the transition temperature of the composite material, the temperature dependence of the magnetization and the magnon dispersion relation. The statics apply also to other multilayer systems such as ferroelectrics.

Soft modes in ferroelectric superlattices

Although one expects second harmonic generation to be absent in phases with inversion symmetry, second harmonic signals are observed in the paraelectric phase of several perovskite. We explain this frequency-doubled intensity and its temperature dependence by second harmonic scattering (SHS) due to static point defects inducing a local polarisation and dynamic fluctuations. The intensity and polarisation properties are calculated for both contributions.

Exact results for the one-dimensional self-organized critical forest-fire model.

A theory of periodic ferroelectric multilayers is presented. The multilayer system consists of two alternating ferroelectrics with different transition temperatures. The system is described by a Ginzburg-Landau functional with space-dependent coefficients. In particular, the authors consider the case of a ferroelectric phase transition of first order. Expressions for static properties such as transition temperature, supercooling temperature and polarisation profile are derived. Immediately below the transition temperature there are unpolarised domains within the stronger ferroelectric layers. Their existence is due to the possible phase coexistence of the ordered and disordered phases in the corresponding bulk material. In order to describe the soft-mode dynamics they use phenomenological equations of motion and study the spectrum of transverse optical modes. The lowest bands are almost dispersion-free and the corresponding modes are confined to those layers which have the lower bulk soft-mode frequency. Because the bulk soft modes of the two layers soften at different temperatures the localisation of the modes in one or the other layer depends upon the temperature. This temperature dependence of the mode form can be seen in the lineshape of the polarisation correlation function if the soft-mode damping of the two layers is different. Furthermore, interface modes are shown to exist. Their energy lies below the continuum, confined by the two bulk soft-mode frequencies. These modes result from the special form of the inhomogeneous polarisation profile in a superlattice in contrast to the Fuchs-Kliever interface modes, which have their origin in the long-range dipolar interaction. The number of these bound states depends on the temperature.

Forest-fire model with immune trees

Abstract A phenomenological theory of periodic ferroelectric multilayers, consisting of two alternating ferroelectrics with different transition temperatures, is presented. We consider the case of a ferroelectric phase transition of first order. Interface modes are shown to exist, resulting from the special form of the inhomogeneous polarization profile in the superlattice close below its first order phase transition temperature. The lineshape of the dynamical polarization correlation function has a characteristic temperature dependence, if the damping of the soft mode within each layer constituent is differently strong.

Elastically coupled molecular motors

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very close to the critical point, we calculate the probability that a string of [ital n] neighboring sites is occupied by a given configuration of trees. The critical exponent describing the size distribution of forest clusters is exactly [tau]=2 and does not change under certain changes of the model rules. Computer simulations confirm the analytic results.

Computer simulations of the forest-fire model

We present a generalization of the forest-fire model of P. Bak et al. by including the immunity g which is the probability that a tree is not ignited although one of its neighbors is burning. When g reaches a critical value gc(p), which depends on the tree growth rate p, the fire cannot survive any more, i.e. a continuous phase transition takes place from a steady state with fire to a steady state without fire. We present results of computer simulations and explain them by analytic calculations. The fire spreading at the phase transition represents a new type of percolation which is called “fluctuating site percolation”.

On the critical dynamics of ferromagnets

Abstract:We study the influence of filament elasticity on the motion of collective molecular motors. It is found that for a backbone flexibility exceeding a characteristic value (motor stiffness divided through the mean displacement between attached motors), the ability of motors to produce force reduces as compared to rigidly coupled motors, while the maximum velocity remains unchanged. The force-velocity-relation in two different analytic approximations is calculated and compared with Monte-Carlo simulations. Finally, we extend our model by introducing motors with a strain-dependent detachment rate. A remarkable crossover from the nearly hyperbolic shape of the Hill curve for stiff backbones to a linear force-velocity relation for very elastic backbones is found. With realistic model parameters we show that the backbone flexibility plays no role under physiological conditions in muscles, but it should be observable in certain in vitro assays.