By using the $q$-Gaussian distribution derived by the maximum entropy method for spatially correlated $N$-unit nonextensive systems, we have calculated the generalized Fisher information matrix of $g_{{\theta }_n{\theta }_m}$ for $\left({\theta }_1,{\theta }_2,{\theta }_3\right)=\left({\mu }_q,{\sigma }_q^2,s\right)$, where ${\mu }_q$, ${\sigma }_q^2$, and $s$ denote the mean, variance, and degree of spatial correlation, respectively, for a given entropic index $q$. It has been shown from the Cramér-Rao theorem that (1) an accuracy of an unbiased estimate of ${\mu }_q$ is improved (degraded) by a negative (positive) correlation $s$, (2) that of ${\sigma }_q^2$ is worsen with increasing $s$, and (3) that of $s$ is much improved for $s\simeq -1/\left(N-1\right)$ or $s\simeq 1.0$ though it is worst at $s=\left(N-2\right)/2\left(N-1\right)$. Our calculation provides a clear insight to the long-standing controversy whether the spatial correlation is beneficial or detrimental to decoding in neuronal ensembles. We discuss also a calculation of the $q$-Gaussian distribution applying the superstatistics to the Langevin model subjected to spatially correlated inputs.

The critical behavior of the Ising model with nonconserved dynamics and an external driving field mimicking a shear profile is analyzed by studying its dynamical evolution in the short-time regime. Starting from high-temperature disordered configurations (fully disordered configurations, FDC), the critical temperature $T_c$ is determined when the order parameter, defined as the absolute value of the transversal spin profile, exhibits a power-law behavior with an exponent that is a combination of some of the critical exponents of the transition. For each value of the shear field magnitude, labeled as $\dot{\gamma }$, $T_c$ has been estimated and two stages have been found: (1) a growing stage at low values of $\dot{\gamma }$, where $T_c\sim {\dot{\gamma }}^{\psi }$ and $\psi =0.52\left(3\right)$, and (2) a saturation regime at large $\dot{\gamma }$. The same values of $T_c\left(\dot{\gamma }\right)$ were found studying the dynamical evolution from the ground-state configuration with all spins pointing in the same direction. By combining the exponents of the corresponding power laws obtained from each initial configuration, the set of critical exponents was calculated. These values, at large external field magnitude, define a critical behavior different from that of the Ising model and of other driven lattice gases.

We study pulse propagation in one-dimensional chains of spherical granules decorated with small grains placed between large granules. The effect of the small granules can be captured by replacing the decorated chains by undecorated chains of large granules of appropriately renormalized mass and effective interaction between the large granules. This allows us to obtain simple analytic expressions for the pulse propagation properties using a generalization of the binary collision approximation introduced in our earlier work [Phys. Rev. E 80, 031303 (2009); Phys. Rev. E 69, 037601 (2004)].

Self-consistent field theory is applied to model the structure and stability of polyelectrolyte complex micelles with incorporated protein (molten globule) molecules in the core. The electrostatic interactions that drive the micelle formation are mimicked by nearest-neighbor interactions using Flory-Huggins $\chi$ parameters. The strong qualitative comparison with experimental data proves that the Flory-Huggins approach is reasonable. The free energy of insertion of a proteinlike molecule into the micelle is nonmonotonic: there is (i) a small repulsion when the protein is inside the corona; the height of the insertion barrier is determined by the local osmotic pressure and the elastic deformation of the core, (ii) a local minimum occurs when the protein molecule is at the core-corona interface; the depth (a few $k_{B}T$’s) is related to the interfacial tension at the core-corona interface and (iii) a steep repulsion (several $k_{B}T$) when part of the protein molecule is dragged into the core. Hence, the protein molecules reside preferentially at the core-corona interface and the absorption as well as the release of the protein molecules has annealed rather than quenched characteristics. Upon an increase of the ionic strength it is possible to reach a critical micellization ionic (CMI) strength. With increasing ionic strength the aggregation numbers decrease strongly and only few proteins remain associated with the micelles near the CMI.

In biological systems, expression dynamics that can provide fitted phenotype patterns with respect to a specific function have evolved through mutations. This has been observed in the evolution of proteins for realizing folding dynamics through which a target structure is shaped. We study this evolutionary process by introducing a statistical-mechanical model of interacting spins, where a configuration of spins and their interactions $\mathit{J}$ represent a phenotype and genotype, respectively. The phenotype dynamics are given by a stochastic process with temperature $T_S$ under a Hamiltonian with $\mathit{J}$. The evolution of $\mathit{J}$ is also stochastic with temperature $T_J$ and follows mutations introduced into $\mathit{J}$ and selection based on a fitness defined for a configuration of a given set of target spins. Below a certain temperature $T_S^{c2}$, the interactions $\mathit{J}$ that achieve the target pattern evolve, whereas another phase transition is observed at $T_S^{c1}<T_S^{c2}$. At low temperatures $T_S<T_S^{c1}$, the Hamiltonian exhibits a spin-glass-like phase, where the dynamics toward the target pattern require long time steps, and the fitness often decreases drastically as a result of a single mutation to $\mathit{J}$. In the intermediate-temperature region, the dynamics to shape the target pattern proceed rapidly and are robust to mutations of $\mathit{J}$. The interactions in this region have no frustration around the target pattern and results in funnel-type dynamics. We propose that the ubiquity of funnel-type dynamics, as observed in protein folding, is a consequence of evolution subjected to thermal noise beyond a certain level; this also leads to mutational robustness of the fitness.

The spatial distribution of most species in nature is nonuniform. We have shown recently [B. Houchmandzadeh, Phys. Rev. Lett. 101, 078103 (2008)] on an experimental ecological community of amoeba that the most basic facts of life—birth and death—are enough to cause considerable aggregation which cannot be smoothened by random movements of the organisms. This clustering, termed neutral and always present, is independent of external causes and social interaction. We develop here the theoretical groundwork of this phenomenon by explicitly computing the pair-correlation function and the variance to mean ratio of the above neutral model and its comparison to numerical simulations.

The rhythmic motion of membrane pore behavior under nonequilibrium conditions was studied. Application of the surfactant triton X-100 (TX-100) caused lipid vesicles to exhibit two types of shrinking dynamics with pore generation, which depended on both the size of the vesicles and the concentration of added TX-100. Small vesicles and the addition of a low concentration of TX-100 resulted in rhythmic-pore dynamics, where a transient pore was generated within a vesicle in a repetitive manner. In contrast, large vesicles and a high concentration of TX-100 led to continuous-pore dynamics, where the vesicle maintained an open pore during the shrinking process. In the rhythmic-pore membrane, long-cycle oscillation was observed with large vesicles and a low concentration TX-100. The period of one cycle decreased with a decrease in the vesicle size and an increase in the TX-100 concentration. We discuss the mechanism of these trends by considering the elastic free energy of the membrane.

We present an analytical model for unstable interfaces with surface tension in fluids of arbitrary viscosity. Linear and nonlinear asymptotic solutions are obtained for growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities. In Rayleigh-Taylor instability, both surface tension and viscosity decrease the asymptotic bubble velocity. For Richtmyer-Meshkov instability, the analysis of the model suggests a dependence of the decaying rate of the bubble velocity on the relative importance of viscosity and surface tension. Results of numerical simulations are also given, and comparisons of the solutions of the model with numerical results are in good agreement.

In this paper, we discuss the eigenspectra of networks with community structure. It is shown that in many cases, the spectrum of eigenvalues of the adjacency matrix of a network with community structure gives a clear indication of the number of communities in the network. In particular, for a network with $N$ nodes and $N_c$ communities, there will typically be $N_c$ eigenvalues that are significantly larger than the magnitudes of all the other $\left(N-N_c\right)$ eigenvalues. We discuss this property as well as its use and limitations for determining $N_c$.

Chemical reactions involving radical-ion pairs are ubiquitous in biology, since not only are they at the basis of the photosynthetic reaction chain, but are also assumed to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments with magnetic-sensitive radical-ion-pair reactions provided strong evidence for the radical-ion-pair magnetoreception mechanism, verifying the expected magnetic sensitivities and chemical product yield changes. It is here shown that the theoretical description of radical-ion-pair reactions used since the 70s cannot explain the observed data, because it is based on phenomenological equations masking quantum coherence effects. The fundamental density-matrix equation derived here from basic quantum measurement theory considerations naturally incorporates the quantum Zeno effect and readily explains recent experimental observations on low- and high magnetic-field radical-ion-pair reactions.

Extensive (asymptotic) spatiotemporal chaos is comprised of statistically similar subsystems that interact only weakly. A systematic study of transient spatiotemporal chaos reveals extensive system behavior in all three reaction-diffusion networks for various boundary conditions. The Lyapunov dimension, the sum of positive Lyapunov exponents, and the logarithm of the transient lifetime grow linearly with the system size. The unstable manifold of the chaotic saddle has nearly the same dimension as the saddle itself, and the stable manifold is nearly space filling.

We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization characterized as an ergodic chaotic dynamical state with a Gibbs distribution over the modes. Our results show that the fraction of thermalizing modes is finite and grows with the nonlinearity strength.

We report the generation of a dynamic labyrinthine pattern in an active alcohol film. A dynamic labyrinthine pattern is formed along the contact line of air/pentanol/aqueous three phases. The contact line shows a clear time-dependent change with regard to both perimeter and area of a domain. An autocorrelation analysis of time development of the dynamics of the perimeter and area revealed a strong geometric correlation between neighboring patterns. The pattern showed autoregressive behavior. The behavior of the dynamic pattern is strikingly different from those of stationary labyrinthine patterns. The essential aspects of the observed dynamic pattern are reproduced by a diffusion-controlled geometric model.

We present the application of short-pulse laser-driven hard x rays $\left(>40\text{keV}\right)$ for the direct density measurement of iron compressed by a laser-driven shock. By using an on-shot calibration of the spectral absorption, we are able to obtain line densities with 5%–10% precision, although the x-ray source is not monochromatic. We also discuss possibilities for increasing the precision, which would be an improvement for equation of state measurements.

We develop a framework for the multiple scattering of a polarized wave. We consider particles with spin propagating in a medium filled with scatterers. We write the amplitudes of each spin eigenstate in a local mobile frame. One of the axes is in the direction of propagation of the particle. We use this representation to define a directional Green’s operator of the homogeneous medium and also to write the spin-dependent scattering amplitudes. We show that this representation reveals a Berry phase. We establish a generalized Green-Dyson equation for the multiple-scattering problem in this framework. We show that the generalized Green-Dyson equation can be solved by linear algebra if one uses a representation of the rotations based on Wigner $D$ matrices. The properties of light scattering are retrieved if we use spin 1 particles. Our theory allows to take into account several kinds of anisotropies such as circular or linear dichroism and birefringence, Faraday effects, and Mie scattering within the same formalism. Several anisotropies can be present at the same time.

Spectral clustering uses the global information embedded in eigenvectors of an inter-item similarity matrix to correctly identify clusters of irregular shape, an ability lacking in commonly used approaches such as $k$–means and agglomerative clustering. However, traditional spectral clustering partitions items into hard clusters, and the ability to instead generate fuzzy item assignments would be advantageous for the growing class of domains in which cluster overlap and uncertainty are important. Korenblum and Shalloway [Phys. Rev. E 67, 056704 (2003)] extended spectral clustering to fuzzy clustering by introducing the principle of uncertainty minimization. However, this posed a challenging nonconvex global optimization problem that they solved by a brute-force technique unlikely to scale to data sets having more than $O\left({10}^2\right)$ items. Here we develop a method for solving the minimization problem, which can handle data sets at least two orders of magnitude larger. In doing so, we elucidate the underlying structure of uncertainty minimization using multiple geometric representations. This enables us to show how fuzzy spectral clustering using uncertainty minimization is related to and generalizes clustering motivated by perturbative analysis of almost-block-diagonal matrices. Uncertainty minimization can be applied to a wide variety of existing hard spectral clustering approaches, thus transforming them to fuzzy methods.

Parallel tempering, also known as replica exchange Monte Carlo, is studied in the context of two simple free-energy landscapes. The first is a double-well potential defined by two macrostates separated by a barrier. The second is a “golf course” potential defined by microstates having two possible energies with exponentially more high-energy states than low-energy states. The equilibration time for replica exchange is analyzed for both systems. For the double-well system, parallel tempering with a number of replicas that scales as the square root of the barrier height yields exponential speedup of the equilibration time. On the other hand, replica exchange yields only marginal speedup for the golf course system. For the double-well system, the free-energy difference between the two wells has a large effect on the equilibration time. Nearly degenerate wells equilibrate much more slowly than strongly asymmetric wells. It is proposed that this difference in equilibration time may lead to a bias in measuring overlaps in spin glasses. These examples illustrate the strengths and weaknesses of replica exchange and may serve as a guide for understanding and improving the method in various applications.

In nanowire growth, kinetic processes at the growth interface can play an important role in governing wire compositions, morphologies, and growth rates. Molecular-dynamics simulations have been undertaken to probe such processes in a system featuring a solid-liquid interface shape characterized by a facet bounded by rough orientations. Simulated growth rates display a dependence on nanowire diameter consistent with a size-dependent barrier for facet nucleation. A theory for the interface mobility is developed, establishing a source for size-dependent growth rates that is an intrinsic feature of systems possessing growth interfaces with faceted and rough orientations.

A method of numerical calculation of the fourth virial coefficients of the mixture of additive hard spheres is proposed. The results are compared with an exact analytical formula for the fourth partial virial coefficient $B_4^{\left[1\right]}$ (i.e., three spheres of diameters ${\sigma }_1$ and one sphere of diameter ${\sigma }_2$) and a semiempirical expression for $B_4^{\left[2\right]}$ (i.e., two spheres of each kind). It is shown that the first formula is nonanalytic and the implication to the equations of state for hard-sphere mixtures is discussed.

The gradient method for the study of irreversible phase transitions in far-from-equilibrium lattice systems is proposed and successfully applied to both the archetypical case of the Ziff-Gulari-Barshad model [R. M. Ziff et al., Phys. Rev. Lett. 56, 2553 (1986)] and a forest-fire cellular automaton. By setting a gradient of the control parameter along one axis of the lattice, one can simultaneously treat both the active and the inactive phases of the system. In this way different interfaces are defined whose study allows us to find the active-inactive phase transition (both of first and second order), as well as the description of the active phase as composed of two further phases: the percolating and the nonpercolating ones. The average location and the width of the interfaces obey standard scaling behavior that is essentially governed by the roughness exponent $\alpha =1/\left(1+\nu \right)$, where $\nu$ is the suitable correlation length exponent.