Kink Localization under Asymmetric Double-Well Potential

We study diffuse phase interfaces under asymmetric double-well potential energies with degenerate minima and demonstrate that the limiting sharp profile, for small interface energy cost, on a finite space interval is in general not symmetric and its position depends exclusively on the second derivatives of the potential energy at the two minima (phases). We discuss an application of the general result to porous media in the regime of solid-fluid segregation under an applied pressure and describe the interface between a fluid-rich and a fluid-poor phase. Asymmetric double-well potential energies are also relevant in a very different field of physics as that of Brownian motors. An intriguing analogy between our result and the direction of the dc soliton current in asymmetric substrate driven Brownian motors is pointed out

Moving boundary approximation for curved streamer ionization fronts: Solvability analysis

The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner/outer matching ahead of the front has to be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a constant conductivity approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.Comment: 22 pages, 6 figure

Effects of pumping on entomopathogenic nematodes and temperature increase within a spray system

Exposure to hydrodynamic stresses and increased temperature during hydraulic agitation within a spray system could cause permanent damage to biological pesticides during spray application. Damage to a benchmark biopesticide, entomopathogenic nematodes (EPNs), was measured after a single passage through three different pump types (centrifugal, diaphragm, and roller) at operating pressures up to 828 kPa. No mechanical damage to the EPNs due to passage through the pumps was observed. Separate tests evaluated the effect of pump recirculation on temperature increase of water within a laboratory spray system (56.8-L spray tank) and a conventional-scale spray system (1136-L spray tank). A constant volume of water (45.4 L) was recirculated through each pump at 15.1 L/min within the laboratory spray system. After 2 h, the temperature increase for the centrifugal pump was 33.6 degrees C, and for the diaphragm and roller pumps was 8.5 degrees C and 11.2 degrees C, respectively. The centrifugal pump was also evaluated within the conventional spray system, under both a constant (757 L) and reducing volume scenario, resulting in an average temperature increase of 3.2 degrees C and 6.5 degrees C, respectively, during the 3-h test period. When comparing the number of recirculations for each test, the rate of temperature increase was the same for the conventional spray, system (for both the constant and reducing volume scenarios), while for the laboratory spray system the temperature increased at a greater rate, suggesting that the volume capacity of the spray tank is the primary factor influencing the temperature increase. Results from this study indicate that thermal influences during pump recirculation could be more detrimental to EPNs than mechanical stress. Results show that extensive recirculation of the tank mix can cause considerable increases in the liquid temperature. Diaphragm and roller pumps (low-capacity pumps) are better suited for use with biopesticides compared to the centrifugal pump, which was found to contribute significant heat to the spray system

Travelling waves in a tissue interaction model for skin pattern formation

Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation

In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the hamiltonian system $u_{xx} + f(u) = 0$ and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure

Kink Arrays and Solitary Structures in Optically Biased Phase Transition

An interphase boundary may be immobilized due to nonlinear diffractional interactions in a feedback optical device. This effect reminds of the Turing mechanism, with the optical field playing the role of a diffusive inhibitor. Two examples of pattern formation are considered in detail: arrays of kinks in 1d, and solitary spots in 2d. In both cases, a large number of equilibrium solutions is possible due to the oscillatory character of diffractional interaction.Comment: RevTeX 13 pages, 3 PS-figure

The Speed of Fronts of the Reaction Diffusion Equation

We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f > 0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.Comment: 7 pages Revtex, 1 figure not include

Dynamical mechanism of atrial fibrillation: a topological approach

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead this complexity is maintained as a dynamical balance between wave coalescence -- a unique, previously unidentified, topological process that increases the number of wavelets -- and wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure

Drift- or Fluctuation-Induced Ordering and Self-Organization in Driven Many-Particle Systems

According to empirical observations, some pattern formation phenomena in driven many-particle systems are more pronounced in the presence of a certain noise level. We investigate this phenomenon of fluctuation-driven ordering with a cellular automaton model of interactive motion in space and find an optimal noise strength, while order breaks down at high(er) fluctuation levels. Additionally, we discuss the phenomenon of noise- and drift-induced self-organization in systems that would show disorder in the absence of fluctuations. In the future, related studies may have applications to the control of many-particle systems such as the efficient separation of particles. The rather general formulation of our model in the spirit of game theory may allow to shed some light on several different kinds of noise-induced ordering phenomena observed in physical, chemical, biological, and socio-economic systems (e.g., attractive and repulsive agglomeration, or segregation).Comment: For related work see http://www.helbing.or