Social behavior of bacteria: from physics to complex organization

I describe how bacteria develop complex colonial patterns by utilizing intricate communication capabilities, such as quorum sensing, chemotactic signaling and exchange of genetic information (plasmids) Bacteria do not store genetically all the information required for generating the patterns for all possible environments. Instead, additional information is cooperatively generated as required for the colonial organization to proceed. Each bacterium is, by itself, a biotic autonomous system with its own internal cellular informatics capabilities (storage, processing and assessments of information). These afford the cell certain plasticity to select its response to biochemical messages it receives, including self-alteration and broadcasting messages to initiate alterations in other bacteria. Hence, new features can collectively emerge during self-organization from the intra-cellular level to the whole colony. Collectively bacteria store information, perform decision make decisions (e.g. to sporulate) and even learn from past experience (e.g. exposure to antibiotics)-features we begin to associate with bacterial social behavior and even rudimentary intelligence. I also take Schrdinger’s’ “feeding on negative entropy” criteria further and propose that, in addition organisms have to extract latent information embedded in the environment. By latent information we refer to the non-arbitrary spatio-temporal patterns of regularities and variations that characterize the environmental dynamics. In other words, bacteria must be able to sense the environment and perform internal information processing for thriving on latent information embedded in the complexity of their environment. I then propose that by acting together, bacteria can perform this most elementary cognitive function more efficiently as can be illustrated by their cooperative behavior.     

Transport of self-propelling bacteria in micro-channel flow

Understanding the collective motion of self-propelling organisms in confined geometries, such as that of narrow channels, is of great theoretical and practical importance. By means of numerical simulations we study the motion of model bacteria in 2D channels under different flow conditions: fluid at rest, steady and unsteady flow. We find aggregation of bacteria near channel walls and, in the presence of external flow, also upstream swimming, which turns out to be a very robust result. Detailed analysis of bacterial velocity and orientation fields allows us to quantify the phenomenon by varying cell density, channel width and fluid velocity. The tumbling mechanism turns out to have strong influence on velocity profiles and particle flow, resulting in a net upstream flow in the case of non-tumbling organisms. Finally we demonstrate that upstream flow can be enhanced by a suitable choice of an unsteady flow pattern.     

a-Ge/Au双层膜分形过程的计算机模拟

从实验观察结果出发,提出与传统扩散控制聚集(DLA)模型不同的分形生长模型,用Monte-Carlo方法模拟了具有不同界面结构的a-Ge/Au双层膜在晶化过程的分形行为,得到了和实验结果相符合的分形结构。结果表明:在a-Ge/Au双层膜的退火过程中,由非晶晶化潜热形成的局域温度场在分形过程中起主要作用;密集分枝结构的出现是由粒子扩散的局域性引起的;模拟结果还表明DLA形态的分形结构也可以在粒子扩散距离相对短的条件下获得。 关键词：     

Modeling of spatiotemporal patterns in bacterial colonies

A diffusion-reaction model for the growth of bacterial colonies is presented. The often observed cooperative behavior developed by bacteria which increases their motility in adverse growth conditions is here introduced as a nonlinear diffusion term. The presence of this mechanism depends on a response which can present hysteresis. By changing only the concentrations of agar and initial nutrient, numerical integration of the proposed model reproduces the different patterns shown by Bacillus subtilis OG-01.     

Simulations of complex fluids by mixed lattice Boltzmann—finite difference methods

We present the numerical results of simulations of complex fluids under shear flow. We employ a mixed approach which combines the lattice Boltzmann method for solving the Navier–Stokes equation and a finite difference scheme for the convection–diffusion equation. The evolution in time of shear banding phenomenon is studied. This is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow.     

Population dynamics advected by chaotic flows: A discrete-time map approach

A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where fluid particles are advected by a two-dimensional symplectic map possibly yielding Lagrangian chaos. Each fluid particle carries concentrations of active substances which evolve according to its own reaction dynamics. This evolution is also modeled in terms of maps. Motivated by the question, of relevance in marine ecology, of how a localized distribution of nutrients or preys affects the spatial structure of predators transported by a fluid flow, we study a specific model in which the population dynamics is given by a logistic map with space-dependent coefficient, and advection is given by the standard map. Fractal and random patterns in the Eulerian spatial concentration of predators are obtained under different conditions. Exploiting the analogies of this coupled-map (advection plus reaction) system with a random map, some features of these patterns are discussed. (c) 2001 American Institute of Physics.     

Influence of atomic defect generation on the propagation of elastic waves in laser-excited solid layers

The mechanical behavior of solid layers subjected to laser irradiation is investigated by a dynamical model that is based on coupled evolution equations for the elastic displacement of the medium and lattice defect-density fields. The evolution of defect-density is governed by the (i) generation of defects by irradiation, (ii) their diffusion and recombination and (iii) diffusion induced by strain field. The strain field associated with lattice dilatation due to atomic defects is shown to couple with deformation fields of the layer. Frequency equations corresponding to the symmetric and anti-symmetric modes of vibration of the layer are obtained. It is found that coupling between diffusion and strain fields cause dispersion of the general waveform. Explicit expressions are defined for the wave velocity, and the attenuation (amplification) coefficients which characterize these waves.     

Lateral diffusion of the topological charge density in stochastic optical fields

Stochastic (i.e. random and quasi-random) optical fields may contain distributions of optical vortices that are represented by non-uniform topological charge densities. Numerical simulations are used to investigate the evolution under free-space propagation of topological charge densities that are inhomogeneous along one dimension. It is shown that this evolution is described by a diffusion process that has a diffusion parameter which depends on the propagation distance.     

Observation of molecular migration in porous media using 2D exchange spectroscopy in the inhomogeneous magnetic field

We present a new method for observing fluid diffusion in a porous medium. The method employs 2D exchange spectroscopy for molecules diffusing in the presence of local magnetic field inhomogeneities, in our case distilled water in various sized glass bead packs. Our experiment involves an acquisition and evolution time domain with the two Fourier domains corresponding to the spectral distribution of local fields. We show that exchange in the internal magnetic field can be seen in a 2D spectrum with a characteristic time on the order of that required to diffuse 0.15 sphere diameters with similar behavior found for computer simulations. The method is potentially useful for studying the internal migrations in more complicated systems such as sandstones or other porous media.     

Localization of nonlocal theories

We show that a certain class of nonlocal scalar models, with a kinetic operator inspired by string field theory, is equivalent to a system which is local in the coordinates but nonlocal in an auxiliary evolution variable. This system admits both Lagrangian and Hamiltonian formulations, and its Cauchy problem and quantization are well-defined. We classify exact nonperturbative solutions of the localized model which can be found via the diffusion equation governing the fields.     

Mechanism of branching in negative ionization fronts

When a strong electric field is applied to nonconducting matter, narrow channels of plasma called streamers may form. Branchlike patterns of streamers have been observed in anode directed discharges. We explain a mechanism for branching as the result of a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. The dispersion relation for transversal perturbation of a planar negative front is obtained analytically when the ratio D between the electron diffusion coefficient and the intensity of the externally imposed electric field is small. We estimate the spacing lambda between streamers and deduce a scaling law lambda approximately D(1/3).     

The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

This paper studies a reaction–diffusion–chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.     

Diffusion of colloidal particles in swimming suspensions

Previously, we have proposed to analyse the hydrodynamic interactions in a suspension of swimmers with respect to an effective hydrodynamic diffusion coefficient, which only considers the fluctuating motion caused by the stirring of the fluid. In this work, we study the diffusion of colloidal particles immersed in a bath of swimmers. To accurately resolve the many-body hydrodynamic interactions responsible for this diffusion, we use a direct numerical simulation scheme based on the smooth profile method. We consider a squirmer model for the self-propelled swimmers, as it accurately reproduces the flow field generated by real microorganisms, such as bacteria or spermatozoa. We show that the diffusion coefficients of the colloids are comparable with the effective diffusion coefficients of the swimmers, provided that the concentration of swimmers is high enough. At low concentrations, the difference in the way colloids and swimmers react to the flow leads to a reduction in the diffusion coefficient of the colloids. This is clearly seen in the appearance of a negative-correlation region for the velocity-correlation function of the colloids, which does not exist for the swimmers.     

Dendritic flux avalanches and nonlocal electrodynamics in thin superconducting films

We report a mechanism of nonisothermal dendritic flux penetration in superconducting films. Our numerical and analytical analysis of coupled nonlinear Maxwell and thermal diffusion equations shows that dendritic flux pattern formation results from spontaneous branching of propagating flux filaments due to nonlocal magnetic flux diffusion and positive feedback between flux motion and Joule heating. The branching is triggered by a thermomagnetic edge instability, which causes stratification of the critical state. The resulting distribution of thermomagnetic microavalanches is not universal, because it depends on a spatial distribution of defects. Our results are in good agreement with experiments on Nb films.     

Shocks and finite-time singularities in Hele-Shaw flow

Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that this ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating into the viscous fluid. The graph of shocks grows and branches. Velocity and pressure have finite discontinuities across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive weak solution in algebro-geometrical terms as an evolution of the Krichever-Boutroux complex curve. We study in detail the most generic (2, 3)-cusp singularity, which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.     

Lattice Boltzmann Model for Free Surface Flow for Modeling Foaming

We present a 2D- and 3D-lattice Boltzmann model for the treatment of free surface flows including gas diffusion. Interface advection and related boundary conditions are based on the idea of the lattice Boltzmann equation. The fluid dynamic boundary conditions are approximated by using the mass and momentum fluxes across the interface, which do not require explicit calculation of gradients. A similar procedure is applied to fulfill the diffusion boundary condition. Simple verification tests demonstrate the correctness of the algorithms. 2D- and 3D-foam evolution examples demonstrate the potential of the method.     

Diffusion processes with singular drift fields

A class of stochastic differential equations with highly singular drift fields is considered. Using a purely probabilistic approach, we can show the unattainability of the nodal set. Moreover, a global existence and uniqueness theorem for diffusion processes with singular drift fields is established. The finite action condition of Carlen and Zheng can be modified. We relate our results to the diffusions which describe the time evolution of quantum systems in stochastic mechanics.     

Natural convection in porous annular domains: Mimetic scheme and family of steady states

Natural convection of the incompressible fluid in the porous media based on the Darcy hypothesis (Lapwood convection) gives an intriguing branching off of one-parameter family of steady patterns. This scenario may be suppressed in computations when governing equations are approximated by schemes which do not preserve the cosymmetry property. We consider the problem for the annular porous domain in polar coordinates and derive a mimetic finite-difference scheme. This scheme allows to compute the family of convective regimes accurately and to detect the instabilities on some parts of the family.     

Large scale structure in Bekenstein's theory of relativistic modified Newtonian dynamics

A relativistic theory of modified gravity has been recently proposed by Bekenstein. The tensor field in Einstein's theory of gravity is replaced by a scalar, a vector, and a tensor field which interact in such a way to give modified Newtonian dynamics (MOND) in the weak-field nonrelativistic limit. We study the evolution of the Universe in such a theory, identifying its key properties and comparing it with the standard cosmology obtained in Einstein gravity. The evolution of the scalar field is akin to that of tracker quintessence fields. We expand the theory to linear order to find the evolution of perturbations on large scales. The impact on galaxy distributions and the cosmic microwave background is calculated in detail. We show that it may be possible to reproduce observations of the cosmic microwave background and galaxy distributions with Bekenstein's theory of MOND.