Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures

We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the morphology of the interface. We find evidence for the formation of a structure which moves along with the growth site. The time average of the structure, which is defined with respect to the active spot of growth, defines an activity-centered pattern. Extensive Monte Carlo simulations show that the pattern has a tail which decays slowly, as a power law. To understand this sort of pattern formation, we write down an approximate integral equation involving the local interface dynamics and long-ranged jumps of the growth spot. We clarify the nature of the approximation by considering a model for which the integral equation is exactly derivable from an extended master equation. Improvements to the equation are considered by adding a second coupled equation which provides a self-consistent description. The pattern, which defines a one-point correlation function, is shown to have a strong effect on ordinary space-fixed two-point correlation functions. Finally we present evidence that this sort of pattern formation is not confined to the interface problem, but is generic to situations in which the activity at succesive time steps is correlated, as for instance in several other extremal models. We present numerical results for activity-centered patterns in the Bak-Sneppen model of evolution and the Zaitsev model of low-temperature creep.Comment: RevTeX, 18 pages, 19 eps-figures, To appear in Phys. Rev.

Dynamics of Wetting Fronts in Porous Media

We propose a new phenomenological approach for describing the dynamics of wetting front propagation in porous media. Unlike traditional models, the proposed approach is based on dynamic nature of the relation between capillary pressure and medium saturation. We choose a modified phase-field model of solidification as a particular case of such dynamic relation. We show that in the traveling wave regime the results obtained from our approach reproduce those derived from the standard model of flow in porous media. In more general case, the proposed approach reveals the dependence of front dynamics upon the flow regime.Comment: 4 pages, 2 figures, revte

Preferential Paths of Air-water Two-phase Flow in Porous Structures with Special Consideration of Channel Thickness Effects.

Accurate understanding and predicting the flow paths of immiscible two-phase flow in rocky porous structures are of critical importance for the evaluation of oil or gas recovery and prediction of rock slides caused by gas-liquid flow. A 2D phase field model was established for compressible air-water two-phase flow in heterogenous porous structures. The dynamic characteristics of air-water two-phase interface and preferential paths in porous structures were simulated. The factors affecting the path selection of two-phase flow in porous structures were analyzed. Transparent physical models of complex porous structures were prepared using 3D printing technology. Tracer dye was used to visually observe the flow characteristics and path selection in air-water two-phase displacement experiments. The experimental observations agree with the numerical results used to validate the accuracy of phase field model. The effects of channel thickness on the air-water two-phase flow behavior and paths in porous structures were also analyzed. The results indicate that thick channels can induce secondary air flow paths due to the increase in flow resistance; consequently, the flow distribution is different from that in narrow channels. This study provides a new reference for quantitatively analyzing multi-phase flow and predicting the preferential paths of immiscible fluids in porous structures

Upregulation of the cell-cycle regulator RGC-32 in Epstein-Barr virus-immortalized cells

Epstein-Barr virus (EBV) is implicated in the pathogenesis of multiple human tumours of lymphoid and epithelial origin. The virus infects and immortalizes B cells establishing a persistent latent infection characterized by varying patterns of EBV latent gene expression (latency 0, I, II and III). The CDK1 activator, Response Gene to Complement-32 (RGC-32, C13ORF15), is overexpressed in colon, breast and ovarian cancer tissues and we have detected selective high-level RGC-32 protein expression in EBV-immortalized latency III cells. Significantly, we show that overexpression of RGC-32 in B cells is sufficient to disrupt G2 cell-cycle arrest consistent with activation of CDK1, implicating RGC-32 in the EBV transformation process. Surprisingly, RGC-32 mRNA is expressed at high levels in latency I Burkitt's lymphoma (BL) cells and in some EBV-negative BL cell-lines, although RGC-32 protein expression is not detectable. We show that RGC-32 mRNA expression is elevated in latency I cells due to transcriptional activation by high levels of the differentially expressed RUNX1c transcription factor. We found that proteosomal degradation or blocked cytoplasmic export of the RGC-32 message were not responsible for the lack of RGC-32 protein expression in latency I cells. Significantly, analysis of the ribosomal association of the RGC-32 mRNA in latency I and latency III cells revealed that RGC-32 transcripts were associated with multiple ribosomes in both cell-types implicating post-initiation translational repression mechanisms in the block to RGC-32 protein production in latency I cells. In summary, our results are the first to demonstrate RGC-32 protein upregulation in cells transformed by a human tumour virus and to identify post-initiation translational mechanisms as an expression control point for this key cell-cycle regulator

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids

Gas injection in a liquid saturated porous medium. Influence of pressurization effects and liquid films

We study numerically and experimentally the displacement of a liquid by a gas in a two-dimensional model porous medium. In contrast with previous pore-network studies on drainage in porous media, the gas compressibility is fully taken account. The influence of the gas injection rate on the displacement pattern, breakthrough time and the evolution of the pressure in the gas phase due in part to gas compressibility are investigated. A good agreement is found between the simulations and the experiments as regards the invasion patterns. The agreement is also good on the drainage kinetics when the dynamic liquid films are taken into account

Avalanche Dynamics in Evolution, Growth, and Depinning Models

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and evolution is presented. Specifically, we include the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models into a unified treatment encompassing a large class of far from equilibrium processes. The formation of fractal structures, the appearance of $1/f$ noise, diffusion with anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be related to the same underlying avalanche dynamics. This dynamics can be represented as a fractal in $d$ spatial plus one temporal dimension. We develop a scaling theory that relates many of the critical exponents in this broad category of extremal models, representing different universality classes, to two basic exponents characterizing the fractal attractor. The exact equations and the derived set of scaling relations are consistent with numerical simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the manuscript supplied on reques

Distributions of epistasis in microbes fit predictions from a fitness landscape model.

How do the fitness effects of several mutations combine? Despite its simplicity, this question is central to the understanding of multilocus evolution. Epistasis (the interaction between alleles at different loci), especially epistasis for fitness traits such as reproduction and survival, influences evolutionary predictions "almost whenever multilocus genetics matters". Yet very few models have sought to predict epistasis, and none has been empirically tested. Here we show that the distribution of epistasis can be predicted from the distribution of single mutation effects, based on a simple fitness landscape model. We show that this prediction closely matches the empirical measures of epistasis that have been obtained for Escherichia coli and the RNA virus vesicular stomatitis virus. Our results suggest that a simple fitness landscape model may be sufficient to quantitatively capture the complex nature of gene interactions. This model may offer a simple and widely applicable alternative to complex metabolic network models, in particular for making evolutionary predictions