Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis.

Very efficient generation of monoenergetic, about $1\mathrm{MeV}$, electrons from underdense plasma with its electron density close to the critical, when irradiated by an intense femtosecond laser pulse, is found via two dimensional particle-in-cell simulation. The stimulated Raman scattering of a laser pulse with frequency $\omega ⩽2{\omega }_{\mathrm{pl}\max }$ gives rise to a giant electromagnetic vortex. In contrast to electron acceleration by the well-known laser pulse wake, injected plasma electrons are accelerated up to vortex ponderomotive potential forming a quite monoenergetic distribution. A relatively high charge of such an electron source makes very efficient generation of soft $\gamma$ rays with $h\omega >300\mathrm{keV}$.

We show here that the mosquito cannot only give rise to a higher water-supporting force than the water strider if the ratio of the water-supporting force to the body weight of the insect itself is compared, but also can safely take off or land on the water surface, and also can attach on any solid surface like the fly. We found that the mosquito’s legs are covered by numerous scales consisting of the uniform microscale longitudinal ridges (nanoscale thickness and microscale spacing between) and nanoscale cross ribs (nanoscale thickness and spacing between). Such special delicate microstructure and/or nanostructure on the leg surface give a water contact angle of $\sim 153°$ and give a surprising high water-supporting ability. It was found that the water-supporting force of a single leg of the mosquito is about 23 times the body weight of the mosquito, compared with a water strider’s leg giving a water-supporting force of about 15 times the body weight of the insect.

We reformulate the cavity approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our formulation, which allows for the treatment of multivalued variables, a further generalization to factor graphs with arbitrary order of interaction factors is explicitly carried out, and a message passing algorithm that implements the first order correction to the Bethe approximation is described. Furthermore, we investigate an implementation of the CA for pairwise interactions. In all cases considered we could confirm that $\mathrm{CA}\left[k\right]$ with increasing $k$ provides a sequence of approximations of markedly increasing precision. Furthermore, in some cases we could also confirm the general expectation that the approximation of order $k$, whose computational complexity is $O\left(N^{k+1}\right)$ has an error that scales as $1∕N^{k+1}$ with the size of the system. We discuss the relation between this approach and some recent developments in the field.

The invaded cluster approach is extended to the two-dimensional Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the two-dimensional parameter space spanned by temperature and the chemical potential of the vacancies. The tricritical point is identified as a simultaneous onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of the “geometrical disorder cluster.” The location of the tricritical point and the concentration of vacancies for $q=1,2,3$ are found to be in good agreement with the best known results. Scaling properties of the percolating scaling cluster and related critical exponents are also presented.

The formation of three-dimensional prismatic cracks in the drying process of starch-water mixtures is investigated numerically. We assume that the mixture is an elastic porous medium which possesses a stress field and a water content field. The evolution of both fields is represented by a spring network and a phenomenological model with the water potential, respectively. We find that the water content distribution has a propagating front which is not explained by a simple diffusion process. The prismatic structure of cracks driven by the water content field is observed. The depth dependence and the coarsening process of the columnar structure are also studied. The particle diameter dependence of the scale of the columns and the effect of the crack networks on the dynamics of the water content field are also discussed.

The influence of variability on the response of a net of bistable FitzHugh-Nagumo elements to a weak signal is investigated. The response of the net undergoes a resonancelike behavior due to additive variability. For an intermediate strength of additive variability the external signal is optimally enhanced in the output of the net (diversity-induced resonance). Furthermore, we show that additive noise strongly influences the diversity-induced resonance. Afterwards the interplay of additive and multiplicative variability on the response of the net is investigated. Starting with asymmetric bistable elements the enhancement of the signal is not very pronounced in the presence of additive variability. Via symmetry restoration by multiplicative variability the resonance is further enhanced. We call this phenomenon doubly diversity-induced resonance, because the interplay of both, additive and multiplicative variability, is essential to achieve the optimal enhancement of the signal. The restoration of symmetry can be explained by a systematic effect of the multiplicative variability, which changes the thresholds for the transitions between the two stable fixed points. We investigate the response to variability for globally and diffusively coupled networks and in dependency on the coupling strength.

We simulate turbulence in a plane Couette geometry by a spectral method intermediate between full resolution and the complete elimination of small modes common in large eddy simulations. The wave number grid is sparse in spanwise and downstream direction, with a total number of modes proportional to ${\mathrm{Re}}^{3∕4}\ln \mathrm{Re}$. At a Reynolds number of 2000 we could suppress more than 80% of the modes and still obtain a fairly accurate resolution of the boundary layer structures and friction factors. For a wide range of resolutions, the mean velocities are described by logarithmic profiles, with von Karman constant near a value of 0.4.

Slow, nonequilibrium dynamics during delayed sedimentation in a colloidal depletion gel was studied by x-ray photon correlation spectroscopy. The intermediate scattering functions change during the process from stretched to compressed exponential decays, indicating a jamming transition toward full aging. A complex aging behavior follows this process; it is proposed that large-scale network deformations trigger an unjamming, leading to the final collapse of the gel.

We study typical case properties of the 1-in-3 satisfiability problem, the Boolean satisfaction problem, where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 satisfiability and exact 3-cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region and develop a one-step replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.

Electric double layer in porous media is studied with direct numerical simulations of the Nernst-Planck-Poisson equation. The time evolution of the charging process of the electric double-layer along a straight pore is first studied, and confirm that the time evolution obeys a power law of the exponent 1/2. We find that the diffusion constant increases effectively by the effect of the width of the pore. Next it is found that the time evolution of the charging process in fractal porous media obeys a power law, and the exponent $\alpha$ is related to the fracton dimension. Finally, we propose a coupled map lattice model for the creation of pore structures by gas activation processes, and perform numerical simulation of the charging dynamics of the electric double layer.

Recent investigations have demonstrated that the short-time fluctuations in a supercooled liquid can be used as predictors of the long-time dynamic propensity (that is, the regions of the sample with enhanced tendency to be mobile within time scales on the order of the $\alpha$-relaxation time). This could mean that the long-time dynamics (the actual mobility of the particles at such long times) would be implicit in the short-time dynamics or else, that the long-time dynamic propensity [as defined in A. Widmer-Cooper and P. Harrowell, Phys. Rev. Lett. 96, 185701 (2006)], while providing a measure of the degree of jamming of the local structure, would only be sensitive to the short time behavior. The first scenario is in clear disagreement with our recent finding that the influence of the local structure on dynamics (as determined by the propensity for motion) is only local in time, fading out at times close to the metabasin lifetime, much before the $\alpha$-relaxation time. Thus, in this work we show that the short-time fluctuations in supercooled liquids do in fact represent precursors to the dynamics at intermediate times commensurate with the metabasin lifetime (being thus able to predict the regions of the sample that will present high propensity for motion at such stage) but that the dynamical behavior at later times of the $\alpha$ relaxation is unpredictable, in agreement with a metabasin random walk scenario.

Translocation of amphiphilic polymers (random and block copolymers), consisting of hydrophilic and hydrophobic monomers, threading a pore is studied by using a three-dimensional dynamic Monte Carlo simulation. We find that there is a “translocation-insertion” threshold in the fraction of hydrophobic monomers on an amphiphilic polymer. The translocation time is given by simple scaling laws and increases with increasing the fraction of hydrophobic monomers.

We develop a generalized theory of the site-specific DNA-protein interactions, which includes both the static as well as the dynamical factors influencing the one-dimensional diffusion of the nonspecifically bound protein molecule which is in the process of searching for the specific site on the DNA lattice. We argue that the chemically driven condensation of the DNA molecule introduces a static distribution in the one-dimensional phenomenological diffusion coefficient associated with the protein molecule and the conformational dynamics of the DNA introduces temporal fluctuations in the one-dimensional diffusion coefficient over the static distribution. We further derive the generalized inequality conditions and the scaling laws which are required to enhance the three-dimensional diffusion controlled site-specific association rate to an arbitrary order. Our model predicts that when the degree of condensation of the DNA molecule under consideration is very high, then the probability distribution associated with the stationary state one-dimensional diffusion coefficient variable as well as the stationary state one-dimensional diffusion length variable will be a flat one. Further analysis reveals that to achieve a site-specific association rate which is higher than that of the three-dimensional diffusion controlled rate, the one-dimensional diffusion length associated with the dynamics of the nonspecifically bound protein molecule on the DNA lattice should fall in certain critical ranges. Comparison of our theoretical results with the recent experimental observations reveals that when the DNA molecule is under a stretched condition, then the static distribution of the one-dimensional diffusion coefficient associated with the dynamics of the protein molecule on the DNA lattice is a Gaussian and therefore the fluctuations in the one-dimensional diffusion coefficient generated by the dynamical factors are confined in a harmonic type potential.

We present an approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks, such as the average degree of the nearest neighbors, the clustering coefficient, the “betweenness,” the distance between two nodes, and the diameter of a network. All these measures are well established for unweighted networks but have hitherto proven difficult to define for weighted networks. Our approach is based on the translation of a weighted network into an ensemble of edges. Further introducing this approach we demonstrate its advantages by applying the clustering coefficient constructed in this way to two real-world weighted networks.

We study wave propagation, interaction, and transmission across the boundary between two chemical media in a model of an oscillatory reaction-diffusion medium subjected to local periodic forcing. The forced waves can be either outwardly (OP) or inwardly propagating (IP), depending on the dispersion of the medium. Competition among forced waves, spontaneous spiral waves, and bulk oscillations is studied for both cases. We demonstrate development of a negatively refracted wave train when forced waves traverse the boundary between the OP medium and the IP medium.

We present an experimental study of the fingering patterns in a Hele-Shaw cell occurring when a gel-like material forms at the interface between aqueous solutions of a cationic surfactant (cetyltrimethylammonium bromide) and an organic salt (salicylic acid), two solutions known to form a highly elastic wormlike micellar fluid when mixed homogeneously. A variety of fingering instabilities are observed, depending on the velocity of the front (the injection rate), and on which fluid is injected into which. We have found a regime of nonconfined stationary or wavy fingers for which width selection seems to occur without the presence of bounding walls, unlike the Saffman-Taylor experiment. Qualitatively, some of our observations share common mechanisms with instabilities of cooling lava flows or growing biofilms.

We numerically study the distribution $P\left(f\right)$ of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling to resolve the asymptotic decay of $P\left(f\right)$ for large $f$, and determine $P\left(f\right)$ down to values of order ${10}^{-45}$ for ordered and disordered systems in two (2D) and three dimensions (3D). Our findings unambiguously show that, in the ensemble approach, the force distributions decay much faster than exponentially: $P\left(f\right)\sim \exp (-c{f}^{\alpha })$, with $\alpha \approx 2.0$ for 2D systems, and $\alpha \approx 1.7$ for 3D systems.

The quadratic contact process is formulated as an adsorption-desorption model on a two-dimensional square lattice. It involves random adsorption at empty sites and correlated desorption requiring diagonally adjacent pairs of empty neighbors. We assess the model behavior utilizing kinetic Monte Carlo simulations. One finds generic two-phase coexistence between a low-coverage active steady state and a completely covered or “poisoned” absorbing steady state; i.e., both states are stable over a finite range of adsorption rates or “pressures.” This behavior is in marked contrast to that for equilibrium phase separation. For spatially homogeneous systems, we provide a comprehensive characterization of the kinetics of relaxation to the steady states. We analyze rapid poisoning for higher pressures above an effective spinodal point terminating a metastable active state, nucleation-mediated poisoning in the metastable region, the dynamics of poisoned droplets within the two-phase coexistence region, and behavior reminiscent of bootstrap percolation dynamics for lower pressures. For spatially inhomogeneous systems, we analyze the propagation of planar interfaces between active and absorbing states, fully characterizing an orientation dependence which underlies the generic two-phase coexistence.