We investigate the critical behavior of the random-bond $\pm J$ Ising model on a square lattice at the multicritical Nishimori point in the $T\text{−}p$ phase diagram, where $T$ is the temperature and $p$ is the disorder parameter ($p=1$ corresponds to the pure Ising model). We perform a finite-size scaling analysis of high-statistics Monte Carlo simulations along the Nishimori line defined by $2p-1=\text{tanh}\left(1/T\right)$, along which the multicritical point lies. The multicritical Nishimori point is located at $p^{\ast }=0.89081\left(7\right)$, $T^{\ast }=0.9528\left(4\right)$, and the renormalization-group dimensions of the operators that control the multicritical behavior are $y_1=0.655\left(15\right)$ and $y_2=0.250\left(2\right)$; they correspond to the thermal exponent $\nu \equiv 1/y_2=4.00\left(3\right)$ and to the crossover exponent $\varphi \equiv y_1/y_2=2.62\left(6\right)$.

The exclusion process in which particles may jump any distance $l\ge 1$ with the probability that decays as $l^{-\left(1+\sigma \right)}$ is studied from the coarse-grained equation for density profile in the limit when the lattice spacing goes to zero. For $1<\sigma <2$, the usual diffusion term of this equation is replaced by the fractional one, which affects dynamical-scaling properties of the late-time approach to the stationary state. When applied to an open system with totally asymmetric hopping, this approach gives two results: First, it accounts for the $\sigma$-dependent exponent that characterizes the algebraic decay of a density profile in the maximum-current phase for $1<\sigma <2$, and second, it shows that in this region of $\sigma$ the exponent is of the mean-field type.

Numerical simulations of two-dimensional stationary dense granular flows are performed. We check that the system obeys the $h_{stop}$ phenomenology. Focusing on the spatial correlations of the instantaneous velocity fluctuations of the grains, we give evidence of the existence of correlated motion over several grain diameters in the bulk of the flow. Investigating the role of contact friction and restitution, we show that the associated typical length scale $\lambda$ is essentially independent of the grain properties. Moreover, we show that $\lambda$ is not controlled by the packing compacity. However, in agreement with previous experimental work, we observe that the correlation length decreases with the shear rate. Computing the flows inertia number $I$, we show a first-order dependence of $\lambda$ on $I$.

As a generic model system of an asymmetric binary-fluid mixture, hexadecane dissolved in carbon dioxide is considered, using a coarse-grained bead-spring model for the short polymer, and a simple spherical particle with Lennard-Jones interactions for the carbon dioxide molecules. In previous work, it has been shown that this model reproduces the real phase diagram reasonably well, and also the initial stages of spinodal decomposition in the bulk following a sudden expansion of the system could be studied. Using the parallelized simulation package ESPResSo on a multiprocessor supercomputer, phase separation of thin fluid films confined between parallel walls that are repulsive for both types of molecules are simulated in a rather large system ($1356\times 1356\times 67.8{\text{Å}}^3$, corresponding to about 3.2-million atoms). Following the sudden system expansion, a complicated interplay between phase separation in the directions perpendicular and parallel to the walls is found: In the early stages the hexadecane molecules accumulate mostly in the center of the slit pore, but as the coarsening of the structure in the parallel direction proceeds, the inhomogeneity in the perpendicular direction gets much reduced. Studying then the structure factors and correlation functions at fixed distances from the wall, the densities are essentially not conserved at these distances, and hence the behavior differs strongly from spinodal decomposition in the bulk. Some of the characteristic lengths show a nonmonotonic variation with time, and simple coarsening described by power-law growth is only observed if the domain sizes are much larger than the film thickness.

In this work, we study the cooperative adsorption of fluids in a heterogeneous pore, in which the pore walls are composed of homogeneous substrates with chemical groups (CGs) decorating them. The adsorption caused by the homogeneous substrates alone and that by CGs do not add up to the overall adsorption, indicating the existence of a cooperative effect. The cooperative effect is the source of cooperative adsorption, and is characterized in this work by the ratio of the overall adsorption to the sum of adsorption by the substrate only and that by CGs. It is found that the cooperative adsorption does not depend monotonically on the substrate or the CGs. Two different origins of the cooperative adsorption play different roles depending on which one dominates the overall adsorption. Our simulations reveal that, when the homogeneous substrate dominates the overall adsorption, weakening of the attractive fluid-substrate interaction or alternatively strengthening of the fluid-CGs interaction leads to a stronger cooperative effect and enhances the cooperative adsorption. However, when CGs dominate the overall adsorption, weakening of the attractive fluid-CG interaction or strengthening the fluid-substrate interaction results in strong cooperative adsorption. In order to investigate the effects of the distribution of CGs on cooperative adsorption, a design-test method is generalized and used in this work. Simulation results show that the overall adsorption can be significantly affected by the CG distribution.

We analyze the influence of a thin polymer layer with lateral side groups on the anchoring of a nematic liquid crystal. We show that the effective anisotropic part of the anchoring energy depends on the coupling of the nematic with the polymer side groups, as well as on the coupling of the polymer side groups with the surface. The relaxation time for the nematic orientation induced by an external field is evaluated by considering the surface dissipation connected to the relative motion of the nematic director with respect to the polymer side groups.

We consider two-dimensional dispersions of droplets of isotropic phase in a liquid with an $\mathit{XY}$-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a single droplet and a pair of droplets are calculated and a universal droplet-droplet pair potential is obtained. The interaction of dispersed droplets via the ordered phase is attractive at large distances and repulsive at short distances, which results in a well defined preferred separation for two droplets and topological stabilization of the emulsion. This interaction also drives self-assembly into chains. Preferred separations and energy barriers to coalescence are calculated, and the effects of thermal fluctuations and film thickness are discussed.

The adult vasculature is comprised of three distinct compartments: the arteries, which carry blood away from the heart and display a divergent flow pattern; the capillaries, where oxygen and nutrient delivery from blood to tissues, as well as metabolic waste removal, occurs; and the veins, which carry blood back to the heart and are characterized by a convergent flow pattern. These compartments are organized in series as regard to flow, which proceeds from the upstream arteries to the downstream veins through the capillaries. However, the spatial organization is more complex, as veins may often be found paralleling the arteries. The factors that control the morphogenesis of this hierarchically branched vascular network are not well characterized. Here, we explain how arteries exert a morphological control on the venous pattern. Indeed, during vertebrate development, the following transition may be observed in the spatial organization of the vascular system: veins first develop in series with the arteries, the arterial and venous territories being clearly distinct in space (cis-cis configuration). But after some time, new veins grow parallel to the existing arteries, and the arterial and venous territories become overlapped, with extensive and complex intercalation and interdigitation. Using physical arguments, backed up by experimental evidence (biological data from the literature and in situ optical and mechanical measurements of the chick embryo yolk-sac and midbrain developing vasculatures), we explain how such a transition is possible and why it may be expected with generality, as organisms grow. The origin of this transition lies in the remodeling of the capillary tissue in the vicinity of the growing arteries. This remodeling lays down a prepattern for further venous growth, parallel to the existing arterial pattern. Accounting for the influence of tissue growth, we show that this prepatterned path becomes favored as the body extends. As a consequence, a second flow route with veins paralleling the arteries (cis-trans configuration) emerges when the tissue extends. Between the cis-cis and cis-trans configurations, all configurations are in principle possible, and self-organization of the vessels contributes to determining their exact pattern. However, the global aspect depends on the size at which the growth stops and on the growth rate.

Recently, by analyzing the measurement data of Nikuradze [NACA Tech. Memo No. 1292 (1950)], it has been proposed [N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)] that the friction factor, $f$, of rough-pipe flow obeys a scaling law in the turbulent regime. Here, we provide a phenomenological scaling argument to explain this law and demonstrate how intermittency modifies the scaling form, thereby relating $f$ to the intermittency exponent, $\eta$. By statistically analyzing the measurement data of $f$, we infer a satisfactory estimate for $\eta$ $(\approx 0.02)$, the inclusion of which is shown to improve the data-collapse curve. This provides empirical evidence for intermittency other than the direct measurement of velocity fluctuations.

Spiral wave propagation in oscillatory media with a disk-shaped inhomogeneity is examined. Depending on the properties of the medium as well as the inhomogeneity (different frequencies in two regions), distinct spiral waves including sinklike spirals and dense-sparse spirals, are able to emerge. We find that, unlike the previously found outward group velocity for spiral waves (normal spirals or antispirals), the direction of the velocity of the sinklike spiral wave points inward. A qualitative analysis of the possible mechanism underlying their formation is discussed, considering the inhomogeneity as a wave sink or source. Numerical simulations performed on other typical reaction-diffusion models confirm this analysis and suggest that our findings are robust and could be observed in experiments.

A combination of reverse Monte Carlo (RMC) and computational homology is examined as a useful approach in connecting scattering experiments to mathematics for 3D morphology modeling. We develop a different method of morphology modeling from multiple two-dimensional (2D) scattering patterns of structure functions by RMC technique using coarse-grained particles. We perform RMC analysis for multiple 2D scattering patterns of the configuration generated from the surface equation of double gyroid morphology. Homology analysis enables us to classify complex three-dimensional morphologies by incorporating topologically invariant quantities, the so-called Betti numbers. It is demonstrated that RMC analysis reconstructs the DG morphology from multiple 2D scattering patterns.

In two recent papers, a detailed study has been presented of the out-of-equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this paper, we extend the treatment of the early time phase during which strong nonlinear correlations first develop, prior to the onset of “self-similar” scaling in the two-point correlation function. We establish more directly, using appropriate modifications of the numerical integration, that the development of these correlations can be well described by an approximation of the evolution in two phases: a first perturbative phase in which particle displacements are small compared to the lattice spacing, and a subsequent phase in which particles interact only with their nearest neighbors. For the range of initial amplitudes considered, we show that the first phase can be well approximated as a transformation of the perturbed lattice configuration into a Poisson distribution at the relevant scales. This appears to explain the universality of the spatial dependence of the asymptotic nonlinear clustering observed from both shuffled lattice and Poisson initial conditions.

The properties of contact matrices ($C$ matrices) needed for native proteins to be the lowest-energy conformations are considered in relation to a contact energy matrix ($E$ matrix). The total conformational energy is assumed to consist of pairwise interaction energies between atoms or residues, each of which is expressed as a product of a conformation-dependent function (an element of the $C$ matrix) and a sequence-dependent energy parameter (an element of the $E$ matrix). Such pairwise interactions in proteins force native $C$ matrices to be in a relationship as if the interactions are a Go-like potential [N. Go, Annu. Rev. Biophys. Bioeng. 12, 183 (1983)] for the native $C$ matrix, because the lowest bound of the total energy function is equal to the total energy of the native conformation interacting in a Go-like pairwise potential. This relationship between $C$ and $E$ matrices corresponds to (a) a parallel relationship between the eigenvectors of the $C$ and $E$ matrices and a linear relationship between their eigenvalues and (b) a parallel relationship between a contact number vector and the principal eigenvectors of the $C$ and $E$ matrices, where the $E$ matrix is expanded in a series of eigenspaces with an additional constant term. The additional constant term in the spectral expansion of the $E$ matrix is indicated by the lowest bound of the total energy function to correspond to a threshold of contact energy that approximately separates native contacts from non-native ones. Inner products between the principal eigenvector of the $C$ matrix, that of the $E$ matrix, and a contact number vector have been examined for 182 proteins, each of which is a representative from each family of the SCOP database [Murzin et al., J. Mol. Biol. 247, 536 (1995)], and the results indicate the parallel tendencies between those vectors. A statistical contact potential [S. Miyazawa and R. L. Jernigan, Proteins 34, 49 (1999); S. Miyazawa and R. L. Jernigan, Proteins50, 35 (2003)] estimated from protein crystal structures was used to evaluate pairwise residue-residue interactions in the proteins. In addition, the spectral representation of $C$ and $E$ matrices reveals that pairwise residue-residue interactions, which depend only on the types of interacting amino acids, but not on other residues in a protein, are insufficient and other interactions including residue connectivities and steric hindrance are needed to make native structures unique lowest-energy conformations.

When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate $h$, the interplay between creation and annihilation of excitable waves leads to an average activity $F$. It has recently been suggested that in the low-stimulus regime $\left(h\sim 0\right)$ the response function $F\left(h\right)$ of hypercubic deterministic systems behaves as a power law, $F\sim h^m$. Moreover, the response exponent $m$ has been predicted to depend only on the dimensionality $d$ of the lattice, $m=1/\left(1+d\right)$ [T. Ohta and T. Yoshimura, Physica D 205, 189 (2005)]. In order to test this prediction, we study the response function of excitable lattices modeled by either coupled Morris-Lecar equations or Greenberg-Hastings cellular automata. We show that the prediction is verified in our model systems for $d=1$, 2, and 3, provided that a minimum set of conditions is satisfied. Under these conditions, the dynamic range—which measures the range of stimulus intensities that can be coded by the network activity—increases with the dimensionality $d$ of the network. The power law scenario breaks down, however, if the system can exhibit self-sustained activity (spiral waves). In this case, we recover a scenario that is common to probabilistic excitable media: as a function of the conductance coupling $G$ among the excitable elements, the dynamic range is maximized precisely at the critical value $G_c$ above which self-sustained activity becomes stable. We discuss the implications of these results in the context of neural coding.

An investigation of the dynamo instability close to the threshold produced by an $ABC$ forced flow is presented. We focus on the on-off intermittency behavior of the dynamo and the countereffect of the Lorentz force in the nonlinear stage of the dynamo. The Lorentz force drastically alters the statistics of the turbulent fluctuations of the flow and reduces their amplitude. As a result, much longer bursts (on phases) are observed than is expected based on the amplitude of the fluctuations in the kinematic regime of the dynamo. For large Reynolds numbers, the duration time of the on phase follows a power law distribution, while for smaller Reynolds numbers the Lorentz force completely kills the noise and the system transits from a chaotic state into a laminar time periodic flow. The behavior of the on-off intermittency as the Reynolds number is increased is also examined. The connections with dynamo experiments and theoretical modeling are discussed.

Experiment demonstrates the first direct transformation of a tungsten wire core to the plasma state by Joule heating during nanosecond electrical explosion in vacuum. Energy of $\sim 130\text{eV}/\text{atom}$ was deposited into the $12\mu \text{m}$ $W$ wire coated by $2\mu \text{m}$ polyimide during the first $\sim 10\text{ns}$. All the metal rapidly transformed to highly ionized plasma, while the surrounding polyimide coating remained primarily in a gaseous state. This coating totally suppressed corona formation. The expansion velocity of the wire was $\sim 12-18\text{km}/\text{s}$, the average wire ionization at 50 ns reached $\sim 67\%$ with corresponding LTE temperature of $\sim 1.2\text{eV}$. Explosion of bare $W$ wire demonstrated earlier termination of the wire core heating due to shunting corona generation. Magnetohydrodynamic (MHD) simulation reproduces the main features of coated and uncoated $W$ wire explosion.

Excitation of electromagnetic fields in a cavity is studied in the time domain. A signal, which excites the fields, stands in Maxwell’s equations as the electric current density given by an integrable function of coordinates and time. The problem is solved within the framework of the evolutionary approach to electromagnetics. The modal field expansions with time-dependent modal amplitudes are derived. Exact solutions for the amplitudes are obtained as the convolution integrals with time as a variable of integration, where the signal function stands as a parameter of the integrands. Two examples of the signal functions having a beginning in time are considered: (a) a surge modeled by the double-exponential function of time and (b) a sinusoid oscillating with an arbitrary frequency.

We show by resolving single-particle dynamics as a function of contact number that dynamical heterogeneity in depletion colloidal gels must have more than one structural origin. Although the magnitude of dynamical heterogeneity of weak gels with cluster structure and strong gels with string structure is similar, the dependence of particle localization on contact number differs significantly in each. The observed transition between contact number dependent and independent dynamics for the weak and strong gels is abrupt. The results suggest that spatially heterogeneous dynamics cannot be a complete explanation of the dynamical heterogeneity of colloidal gels.

The low-lying spectrum of the three-dimensional Ising model is investigated numerically; we made use of an equivalence between the excitation gap and the reciprocal correlation length. In the broken-symmetry phase, the magnetic excitations are attractive, forming a bound state with an excitation gap $m_2$ $\left(<2m_1\right)$ ($m_1$: elementary excitation gap). It is expected that the ratio $m_2/m_1$ is a universal constant in the vicinity of the critical point. In order to estimate $m_2/m_1$, we perform a numerical diagonalization for finite clusters with $N\le 15$ spins. In order to reduce the finite-size errors, we incorporated the extended (next-nearest-neighbor and four-spin) interactions. As a result, we estimate the mass-gap ratio as $m_2/m_1=1.84\left(3\right)$.