Biomedical subjects
Publications and source records attributed to Olaf Stenull.
We present a theory for the low-frequency, long-wavelength dynamics of soft smectic-C elastomers with locked-in smectic layers. Our theory, which goes beyond pure hydrodynamics, predicts a dynamic soft elasticity of these elastomers and allows us to calculate the storage and loss moduli relevant for rheology experiments as well as the mode structure.
Smectic-C elastomers can be prepared by cross-linking, e.g., liquid crystal polymers, in the smectic-A phase followed by a cooling through the smectic-A to smectic-C phase transition. This transition from D(infinityh) to C(2h) symmetry spontaneously breaks rotational symmetry in the smectic plane as does the transition from a smectic-A to a biaxial smectic phase with D(2h) symmetry. We study these transitions and the emergent elasticity of the smectic-C and biaxial phases in three related models and show that these phases exhibit soft elasticity analogous to that of nematic elastomers.
The renowned general epidemic process describes the stochastic evolution of a population of individuals which are either susceptible, infected, or dead. A second order phase transition belonging to the universality class of dynamic isotropic percolation lies between the endemic and pandemic behavior of the process. We generalize the general epidemic process by introducing a fourth kind of individuals, viz., individuals which are weakened by the process but not yet infected. This weakening gives rise to a mechanism that introduces a global instability in the spreading of the process and therefore opens the possibility of a discontinuous transition in addition to the usual continuous percolation transition. The tricritical point separating the lines of first and second order transitions constitutes an independent universality class, namely, the universality class of tricritical dynamic isotropic percolation. Using renormalized field theory we work out a detailed scaling description of this universality class. We calculate the scaling exponents in an epsilon expansion below the upper critical dimension d(c) =5 for various observables describing tricritical percolation clusters and their spreading properties. In a remarkable contrast to the usual percolation transition, the exponents beta and beta(') governing the two order parameters, viz., the mean density and the percolation probability, turn out to be different at the tricritical point. In addition to the scaling exponents we calculate for all our static and dynamic observables logarithmic corrections to the mean-field scaling behavior at d(c) =5.
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles specifying the directions of the spins) at the percolation threshold. Each of the cumulants has its own independent critical exponent, i.e., there are infinitely many critical exponents involved in the problem. Working out the connection to the random resistor network, we determine these multifractal exponents to two-loop order. Depending on the specifics of the Hamiltonian of each individual model, the amplitudes of the higher cumulants can vanish and in this case, effectively, only some of the multifractal exponents are required.
We study the low-frequency, long-wavelength dynamics of soft and semisoft nematic elastomers using two different but related dynamic theories. Our first formulation describes the pure hydrodynamic behavior of nematic elastomers in which the nematic director has relaxed to its equilibrium value in the presence of strain. We find that the sound-mode structure for soft elastomers is identical to that of columnar liquid crystals. Our second formulation generalizes the derivation of the equations of nematohydrodynamics by Forster et al. to nematic elastomers. It treats the director explicitly and describes slow modes beyond the hydrodynamic limit.
Uniaxial elastomers are characterized by five elastic constants. If their elastic modulus C5 describing the energy of shear strains in planes containing the anisotropy axis vanishes, they are said to be soft. In spatial dimensions d less than or equal to 3, soft elastomers exhibit anomalous elasticity with certain length-scale-dependent bending moduli that diverge and shear moduli that vanish at large length scales. Using renormalized field theory at d=3 and to first order in epsilon=3-d, we calculate critical exponents and other properties characterizing the anomalous elasticity of two soft systems: (i) nematic elastomers in which softness is a manifestation of a Goldstone mode induced by the spontaneous symmetry breaking associated with a transition from an isotropic state to a nematic state, and (ii) a particular version of what we call a critically soft elastomer in which C(5)=0 corresponds to a critical point terminating the stability regime of a uniaxial elastomer with C5>0.
We investigate corrections to scaling induced by irrelevant operators in randomly diluted systems near the percolation threshold. The specific systems that we consider are the random resistor network and a class of continuous spin systems, such as the x-y model. We focus on a family of least irrelevant operators and determine the corrections to scaling that originate from this family. Our field theoretic analysis carefully takes into account that irrelevant operators mix under renormalization. It turns out that long standing results on corrections to scaling are respectively incorrect (random resistor networks) or incomplete (continuous spin systems).
We study directed percolation at the upper critical transverse dimension d=4, where critical fluctuations induce logarithmic corrections to the leading (mean-field) behavior. Viewing directed percolation as a kinetic process, we address the following properties of directed percolation clusters: the mass (the number of active sites or particles), the radius of gyration, and the survival probability. Using renormalized dynamical field theory, we determine the leading and the next to leading logarithmic corrections for these quantities. In addition, we calculate the logarithmic corrections to the equation of state that describes the stationary homogeneous particle density in the presence of a homogeneous particle source.
Based on the field theoretic formulation of the general epidemic process, we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine these corrections for some of the most interesting time dependent observables in dynamic percolation at the critical point up to and including the next to leading correction. For clusters emanating from a local seed at the origin, we calculate the number of active sites, the radius of gyration, as well as the survival probability.
We study the critical behavior of various geometrical and transport properties of percolation in six dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up to and including the next-to-leading order correction. Our study comprehends the percolation correlation function, i.e., the probability that two given points are connected, and some of the fractal masses describing percolation clusters. To be specific, we calculate the mass of the backbone, the red bonds, and the shortest path. Moreover, we study key transport properties of percolation as represented by the random resistor network. We investigate the average two-point resistance as well as the entire family of multifractal moments of the current distribution.
We investigate diamagnetic fluctuations in percolating granular superconductors. Granular superconductors are known to have a rich phase diagram including normal, superconducting, and spin-glass phases. Focusing on the normal-superconducting and the normal-spin-glass transition at low temperatures, we study the diamagnetic susceptibility chi((1)) and the mean square fluctuations of the total magnetic moment chi((2)) of large clusters. Our work is based on a random Josephson network model that we analyze with the powerful methods of renormalized field theory. We investigate the structural properties of the Feynman diagrams contributing to the renormalization of chi((1)) and chi((2)). This allows us to determine the critical behavior of chi((1)) and chi((2)) to arbitrary order in perturbation theory.
The prisoner's dilemma has become the leading paradigm to explain the evolution of cooperation among selfish individuals. Here, we present an adaptive strategy that implements new mechanisms to process information about past encounters. The history of moves is summarized in an internal state which then determines the subsequent move. This enables the strategy to adjust its decisions to the character of the current opponent and to adapt the most promising strategic behavior. For this reason, we call such strategies Adaptor. Through evolutionary simulations, we demonstrate that the concept of Adaptor leads to strategic patterns that are (a) highly cooperative when playing against kin, (b) stable in a sense that goes far beyond the concept of evolutionary stability, (c) robust to environmental changes, i.e. variations of the parameter values and finally (d) superior in performance to the most prominent strategies in the literature.
Recently it has been shown analytically that electric currents in a random-diode network are distributed in a multifractal manner [O. Stenull and H. K. Janssen, Europhys. Lett. 55, 691 (2001)]. In the present paper we investigate the multifractal properties of a random diode network at the critical point by numerical simulations. We analyze the currents running on a directed percolation cluster and confirm the field-theoretic predictions for the scaling behavior of moments of the current distribution. It is pointed out that a random diode network is a particularly good candidate for a possible experimental realization of directed percolation.
Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the nonpercolating and the directed percolating phase. Building on first principles such as symmetries and relevance we derive a field theoretic Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of the current distribution that are governed by a family of critical exponents [psi(l)]. We calculate the family [psi(l)] to two-loop order in a diagrammatic perturbation calculation augmented by renormalization group methods.