Studies of Bacterial Branching Growth using Reaction-Diffusion Models for Colonial Development

Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during colonial development. One method of modeling is the continuous, or coupled reaction-diffusion approach, in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields. In the context of branching growth, this idea has been pursued by a number of groups. We present an additional model which includes a lubrication fluid excreted by the bacteria. We also add fields of chemotactic agents to the other models. We then present a critique of this whole enterprise with focus on the models' potential for revealing new biological features.Comment: 1 latex file, 40 gif/jpeg files (compressed into tar-gzip). Physica A, in pres

Leaking method approach to surface transport in the Mediterranean Sea from a numerical ocean model

We use Lagrangian diagnostics (the leaking and the exchange methods) to characterize surface transport out of and between selected regions in the Western Mediterranean. Velocity fields are obtained from a numerical model. Residence times of water of Atlantic origin in the Algerian basin, with a strong seasonal dependence, are calculated. Exchange rates between these waters and the ones occupying the northern basin are also evaluated. At surface, northward transport is dominant, and involves filamental features and eddy structures that can be identified with the Algerian eddies. The impact on these results of the presence of small scale turbulent motions is evaluated by adding Lagrangian diffusion.Comment: 21 pages using the elsart style. Higher resolution figures available from http://www.imedea.uib.es/physdept/publications/showpaper_en.php?indice=119

Multi-Particle Diffusion Limited Aggregation

We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which initially consists of the origin. Non-aggregated particles move as continuous time simple random walks obeying the exclusion rule, whereas aggregated particles do not move. The aggregate grows by attaching particles to its surface whenever a particle attempts to jump onto it. This evolution is referred to as multi-particle diffusion limited aggregation. Our main result states that if on d>1 the initial density of particles is large enough, then with positive probability the aggregate has linearly growing arms, i.e. if F(t) denotes the point of the aggregate furthest away from the origin at time t>0, then there exists a constant c>0 so that |F(t)|>ct, for all t eventually. The key conceptual element of our analysis is the introduction and study of a new growth process. Consider a first passage percolation process, called type 1, starting from the origin. Whenever type 1 is about to occupy a new vertex, with positive probability, instead of doing it, it gives rise to another first passage percolation process, called type 2, which starts to spread from that vertex. Each vertex gets occupied only by the process that arrives to it first. This process may have three phases: an extinction phase, where type 1 gets eventually surrounded by type 2 clusters, a coexistence phase, where infinite clusters of both types emerge, and a strong survival phase, where type 1 produces an infinite cluster that successfully surrounds all type 2 clusters. Understanding the behavior of this process in its various phases is of mathematical interest on its own right. We establish the existence of a strong survival phase, and use this to show our main result.Comment: More thorough explanations in some steps of the proof

Spatio-selection in Expanding Bacterial Colonies

Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial colonies. Such sectors are spatially segregated sub-populations of mutants. The sectors can be seen both in disk-shaped colonies and in branching colonies. We study the sectors using two models we have used in the past to study bacterial colonies -- a continuous reaction-diffusion model with non-linear diffusion and a discrete ``Communicating Walkers'' model. We find that in expanding colonies, and especially in branching colonies, segregation processes are more likely than in a spatially static population. One such process is the establishment of stable sub- population having neutral mutation. Another example is the maintenance of wild-type population along side with sub-population of advantageous mutants. Understanding such processes in bacterial colonies is an important subject by itself, as well as a model system for similar processes in other spreading populations

Flux quantization effects in disordered normal metal rings and superconducting networks

The effects of the magnetic flux on the properties of disordered normal metal rings and bond or site diluted two-dimensional superconducting networks are investigated theoretically, with an emphasis on the quantum coherence of the electrons and the localization nature in the disordered systems. The conductance of disordered metal rings in magnetic field is obtained via the Landauer\u27s formula through calculations of the localization length L[subscript] c. The important role of the ensemble averaging and the self-averaging to obtain the half-flux-quantum h/2e conductance oscillation is demonstrated unambiguously in both rings of a strictly one-dimensional geometry and rings with a finite width. The amplitude of the localization length oscillation is found to follow a universal relation for all the numerical data: [delta](L[subscript] c/L) = [alpha](L[subscript] c/L)[superscript]2. L is the radius of the ring. The expected universal conductance fluctuations are observed for L[subscript] c/L ~ 1. For L[subscript] c \u3e L, much larger oscillation amplitudes are obtained. In the case of two-dimensional site or bond percolation superconducting networks, the nature of the eigenstates and the effects on the superconducting-to-normal phase boundary is examined by finite-size transfer matrix calculations within the mean-field Ginzburg-Landau theory of second order phase transitions. The fine structures of the T[subscript] c-H phase boundary are found to be washed out immediately when a small fraction of sites or bonds is removed. A rich structure for the mobility edge is obtained. The existence of two different phase boundaries, one for the first eigenstate and the other for the first mobility edge, may have important experimental consequences. ftn*DOE Report IS-T-1388. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy

Numerical Modeling Of Collision And Agglomeration Of Adhesive Particles In Turbulent Flows

Particle motion, clustering and agglomeration play an important role in natural phenomena and industrial processes. In classical computational fluid dynamics (CFD), there are three major methods which can be used to predict the flow field and consequently the behavior of particles in flow-fields: 1) direct numerical simulation (DNS) which is very expensive and time consuming, 2) large eddy simulation (LES) which resolves the large scale but not the small scale fluctuations, and 3) Reynolds-Averaged Navier-Stokes (RANS) which can only predict the mean flow. In order to make LES and RANS usable for studying the behavior of small suspended particles, we need to introduce small scale fluctuations to these models, since these small scales have a huge impact on the particle behavior. The first part of this dissertation both extends and critically examines a new method for the generation of small scale fluctuations for use with RANS simulations. This method, called the stochastic vortex structure (SVS) method, uses a series of randomly positioned and oriented vortex tubes to induce the small-scale fluctuating flow. We first use SVS in isotropic homogenous turbulence and validate the predicted flow characteristics and collision and agglomeration of particles from the SVS model with full DNS computations. The calculation speed for the induced velocity from the vortex structures is improved by about two orders of magnitude using a combination of the fast multiple method and a local Taylor series expansion. Next we turn to the problem of extension of the SVS method to more general turbulent flows. We propose an inverse method by which the initial vortex orientation can be specified to generate a specific anisotropic Reynolds stress field. The proposed method is validated for turbulence measures and colliding particle transport in comparison to DNS for turbulent jet flow. The second part of the dissertation uses DNS to examine in more detail two issues raised during developing the SVS model. The first issue concerns the effect of two-way coupling on the agglomeration of adhesive particles. The SVS model as developed to date does not account for the effect of particles on the flow-field (one-way coupling). We focused on examination of the local flow around agglomerates and the effect of agglomeration on modulation of the turbulence. The second issue examines the microphysics of turbulent agglomeration by examining breakup and collision of agglomerates in a shear flow. DNS results are reported both for one agglomerate in shear and for collision of two agglomerates, with a focus on the physics and role of the particle-induced flow field on the particle dynamics