Cellular automaton for bacterial towers

A simulation approach to the stochastic growth of bacterial towers is presented, in which a non-uniform and finite nutrient supply essentially determines the emerging structure through elementary chemotaxis. The method is based on cellular automata and we use simple, microscopic, local rules for bacterial division in nutrient-rich surroundings. Stochastic nutrient diffusion, while not crucial to the dynamics of the total population, is influential in determining the porosity of the bacterial tower and the roughness of its surface. As the bacteria run out of food, we observe an exponentially rapid saturation to a carrying capacity distribution, similar in many respects to that found in a recently proposed phenomenological hierarchical population model, which uses heuristic parameters and macroscopic rules. Complementary to that phenomenological model, the simulation aims at giving more microscopic insight into the possible mechanisms for one of the recently much studied bacterial morphotypes, known as "towering biofilm", observed experimentally using confocal laser microscopy. A simulation suggesting a mechanism for biofilm resistance to antibiotics is also shown

Hierarchical population model with a carrying capacity distribution

A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, $B$, and of death, $D$, determine the carrying capacity $K$. Due to the randomness the population depends strongly on position, $x$, and there is a distribution of carrying capacities, $\Pi (K)$. This distribution has self-similar character owing to the imposed hierarchy. The most probable carrying capacity and its probability are studied as a function of $B$ and $D$. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to random local bactericidal agent (antibiotic spray). A gradual overall temperature change away from optimal growth conditions, for instance, reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.Comment: 25 pages, 11 (9+2) figure

Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry

In the framework of mean-field theory the equation for the order-parameter profile in a spherically-symmetric geometry at the bulk critical point reduces to an Emden-Fowler problem. We obtain analytic solutions for the surface universality class of extraordinary transitions in $d=4$ for a spherical shell, which may serve as a starting point for a pertubative calculation. It is demonstrated that the solution correctly reproduces the Fisher-de Gennes effect in the limit of the parallel-plate geometry.Comment: (to be published in Z. Phys. B), 7 pages, 1 figure, uuencoded postscript file, 8-9

Ising model for distribution networks

An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters

Charging Effects and Quantum Crossover in Granular Superconductors

The effects of the charging energy in the superconducting transition of granular materials or Josephson junction arrays is investigated using a pseudospin one model. Within a mean-field renormalization-group approach, we obtain the phase diagram as a function of temperature and charging energy. In contrast to early treatments, we find no sign of a reentrant transition in agreement with more recent studies. A crossover line is identified in the non-superconducting side of the phase diagram and along which we expect to observe anomalies in the transport and thermodynamic properties. We also study a charge ordering phase, which can appear for large nearest neighbor Coulomb interaction, and show that it leads to first-order transitions at low temperatures. We argue that, in the presence of charge ordering, a non monotonic behavior with decreasing temperature is possible with a maximum in the resistance just before entering the superconducting phase.Comment: 15 pages plus 4 fig. appended, Revtex, INPE/LAS-00

From nonwetting to prewetting: the asymptotic behavior of 4He drops on alkali substrates

We investigate the spreading of 4He droplets on alkali surfaces at zero temperature, within the frame of Finite Range Density Functional theory. The equilibrium configurations of several 4He_N clusters and their asymptotic trend with increasing particle number N, which can be traced to the wetting behavior of the quantum fluid, are examined for nanoscopic droplets. We discuss the size effects, inferring that the asymptotic properties of large droplets correspond to those of the prewetting film

Shapes, contact angles, and line tensions of droplets on cylinders

Using an interface displacement model we calculate the shapes of nanometer-size liquid droplets on homogeneous cylindrical surfaces. We determine effective contact angles and line tensions, the latter defined as excess free energies per unit length associated with the two contact lines at the ends of the droplet. The dependences of these quantities on the cylinder radius and on the volume of the droplets are analyzed.Comment: 26 pages, RevTeX, 10 Figure