Pattern of Reaction Diffusion Front in Laminar Flows

Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. The effect of advective flow on the autocatalytic reaction between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is analyzed experimentally and numerically using lattice BGK simulations. We do observe the existence of solitary waves with concentration profiles exhibiting a cusp and we delineate the eikonal and mixing regimes recently predicted.Comment: 4 pages, 3 figures. This paper report on experiments and simulations in different geometries which test the theory of Boyd Edwards on flow advection of chemical reaction front which just appears in PRL (PRL Vol 89,104501, sept2002

Bounding biomass in the Fisher equation

The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.Comment: 32 Pages, 13 Figure

Superfast front propagation in reactive systems with anomalous diffusion

We study a reaction diffusion system where we consider a non-gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with tails approaching to zero faster than a power law, the usual qualitative behaviours of the standard reaction diffusion system, i.e., exponential tails for the reacting field and a constant front speed, are recovered. On the contrary if the process has power law tails, also the reacting field shows power law tail and the front speed increases exponentially with time. The comparison with other reaction-transport systems which exhibit anomalous diffusion shows that, not only the presence of anomalous diffusion, but also the detailed mechanism, is relevant for the front propagation.Comment: 4 pages and 4 figure

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin

Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are Hamilton-Jacobi equations with convex ($L^1$ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $\bar H$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed $s_T$. An important problem in turbulent combustion theory is to study properties of $s_T$, in particular how $s_T$ depends on the flow amplitude $A$. In this paper, we will study the behavior of $\bar H=\bar H(A,d)$ as $A\to +\infty$ at any fixed diffusion constant $d > 0$. For the cellular flow, we show that $$\bar H(A,d)\leq O(\sqrt {\mathrm {log}A}) \quad \text{for all $d>0$}.$$ Compared with the inviscid G-equation ($d=0$), the diffusion dramatically slows down the front propagation. For the shear flow, the limit \nit $\lim_{A\to +\infty}{\bar H(A,d)\over A} = \lambda (d) >0$ where $\lambda (d)$ is strictly decreasing in $d$, and has zero derivative at $d=0$. The linear growth law is also valid for $s_T$ of the curvature dependent G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square root of log growt

On the folding and deployment of tape springs: a large displacements and large rotations rod model with highly flexible thin-walled cross-section

International audienceIn the framework of deployable structures, we focus on the modeling of tape springs, i.e. rod-like elastic bodies with thin-walled cross-section which develop localized folds due to a flattening of the cross-section. A rod model with highly deformable cross-section and few kinematics parameters is derived from a complete shell model, for large displacements, large rotations and dynamics. The simplicity of the model is achieved by introducing an elastica kinematics to describe the changes in the cross-section shape. This model is able to handle the formation of localized folds which can move along the rod line, merge or split, allowing to simulate complex scenarios of folding and deployment

Microsomal prostaglandin E synthase-2 is not essential for in vivo prostaglandin E2 biosynthesis

Prostaglandin E2 (PGE2) plays an important role in the normal physiology of many organ systems. Increased levels of this lipid mediator are associated with many disease states, and it potently regulates inflammatory responses. Three enzymes capable of in vitro synthesis of PGE2 from the cyclooxygenase metabolite PGH2 have been described. Here, we examine the contribution of one of these enzymes to PGE2 production, mPges-2, which encodes microsomal prostaglandin synthase-2 (mPGES-2), by generating mice homozygous for the null allele of this gene. Loss of mPges-2 expression did not result in a measurable decrease in PGE2 levels in any tissue or cell type examined from healthy mice. Taken together, analysis of the mPGES-2 deficient mouse lines does not substantiate the contention that mPGES-2 is a PGE2 synthase

The smectic order of wrinkles

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales. This insight allows better understanding of the wrinkling patterns seen in such systems, with which we explain pattern breaking into domains, the properties of domain walls and wrinkle undulation. We compare our predictions with numerical simulations and with experimental observations

Thermal fracture as a framework for quasi-static crack propagation

We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using only the principle of local symmetry and the Griffith criterion. We then argue that the calculations of the stress intensity factors can be combined with the standard crack propagation criteria to obtain the evolution equation for the crack tip within any loading configuration. The theoretical results of the thermal crack problem agree with the numerical simulations we performed using a phase field model. Moreover, it turns out that the phase-field model allows to clarify the nature of the transition between straight and oscillatory cracks which is shown to be supercritical.Comment: 19 pages, 8 figure

Genomes of the Most Dangerous Epidemic Bacteria Have a Virulence Repertoire Characterized by Fewer Genes but More Toxin-Antitoxin Modules

We conducted a comparative genomic study based on a neutral approach to identify genome specificities associated with the virulence capacity of pathogenic bacteria. We also determined whether virulence is dictated by rules, or if it is the result of individual evolutionary histories. We systematically compared the genomes of the 12 most dangerous pandemic bacteria for humans ("bad bugs") to their closest non-epidemic related species ("controls").We found several significantly different features in the "bad bugs", one of which was a smaller genome that likely resulted from a degraded recombination and repair system. The 10 Cluster of Orthologous Group (COG) functional categories revealed a significantly smaller number of genes in the "bad bugs", which lacked mostly transcription, signal transduction mechanisms, cell motility, energy production and conversion, and metabolic and regulatory functions. A few genes were identified as virulence factors, including secretion system proteins. Five "bad bugs" showed a greater number of poly (A) tails compared to the controls, whereas an elevated number of poly (A) tails was found to be strongly correlated to a low GC% content. The "bad bugs" had fewer tandem repeat sequences compared to controls. Moreover, the results obtained from a principal component analysis (PCA) showed that the "bad bugs" had surprisingly more toxin-antitoxin modules than did the controls.We conclude that pathogenic capacity is not the result of "virulence factors" but is the outcome of a virulent gene repertoire resulting from reduced genome repertoires. Toxin-antitoxin systems could participate in the virulence repertoire, but they may have developed independently of selfish evolution