Discrete breathers that arise in doped alkali halides lead us to study two properties of these localized excitations. First, we note a bifurcation phenomenon, which we dub torus doubling, in which resonant coupling in the nonlinear modes induces a period doubling of the phase space structure. Second, we find that although two-frequency breather excitations are not in principle localized (because of phonon resonances), in practice they can survive ${10}^9$ times the characteristic time scale and give rise to marked physical phenomena, including the one that brought us to this study, the anomalous decay of luminescence.

We study numerically the tortuosity-porosity relation in a microscopic model of a porous medium arranged as a collection of freely overlapping squares. It is demonstrated that the finite-size, slow relaxation and discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity $\left(T\right)$ and porosity $\left(\varphi \right)$ given by $T-1\propto \ln \varphi$, that was found by others experimentally in granule packings and sediments. This relation can be also written as $T-1\propto RS∕\varphi$ with $R$ and $S$ denoting the hydraulic radius of granules and the specific surface area, respectively. Applicability of these relations appears to be restricted to porous systems of randomly distributed obstacles of equal shape and size.

We present results of statistical analysis of solar wind turbulence using an approach based on the theory of Markov processes. It is shown that the Chapman-Kolmogorov equation is approximately satisfied for the turbulent cascade. We evaluate the first two Kramers-Moyal coefficients from experimental data and show that the solution of the resulting Fokker-Planck equation agrees well with experimental probability distributions. Our analysis provides evidence that the transfer of fluctuations from large to smaller eddies must be independent of the dynamics on large scales and in particular it must be independent of the driving mechanisms for solar wind turbulence. Our results also suggest the presence of a local transfer mechanism for magnetic field fluctuations in solar wind turbulence.

We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under the action of direct ac forces is shown.

A time-going-backward quasidynamics method is developed for global optimization of cluster structures, and its merits are examined by a simple classical mechanics model, indicating that the probability for the system to jump over high potential barriers by this method is much higher than that by common annealing methods. The method is then used to investigate the isomers of a Lennard-Jones cluster containing 38 atoms and the ${\mathrm{C}}_{60}$ cluster with the Brenner potential, and can easily give the most stable structures, which are difficult to obtain by common annealing methods. In addition, for small carbon clusters ${\mathrm{C}}_n$ $(n=21–30)$, most of the potential energies optimized by this method are much lower than those obtained by a genetic algorithm.

Using theoretical arguments, we prove the numerically well-known fact that the eigenvalues of all localized stationary solutions of the cubic-quintic $(2+1)$-dimensional nonlinear Schrödinger equation exhibit an upper cutoff value. The existence of the cutoff is inferred using Gagliardo-Nirenberg and Hölder inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schrödinger equation behave similarly to those of the cubic nonlinear Schrödinger equation.

A direct observation of the photochemical switching between colloidal crystals with different lattice constants in a liquid-crystal (LC) emulsion is reported. Glycerol droplets introduced in a nematic liquid crystal form two-dimensional hexagonal colloidal crystal at the nematic-air interface with a lattice constant depending on the surface tension ${\sigma }_{\mathit{LCA}}$. We dope an azobenzene derivative into the LC emulsion to modulate the colloidal structures by using cis-trans photoisomerization of the doped dye. The photoisomerization changes ${\sigma }_{\mathit{LCA}}$ and the lattice constant of colloidal crystals with a relaxation time $T\sim 10\mathrm{s}$. A simple theoretical description, which qualitatively agrees with experimental results, has been proposed. Possible applications in infrared range photonic crystals are discussed. The number of different kinds of dyes $N$ set the number of different possible photonic crystals as $2^N$, which may be transformed one into another by corresponding $2N$ light beams inducing cis-trans photoisomerization of the doped dyes.

We study the statistical mechanics of a closed random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. Scaling analysis yields a unified description of such swollen manifolds, according to which the mean volume gradually increases with particle number, following a single scaling law. This is markedly different from the swelling under fixed pressure difference, where certain models exhibit criticality. We thereby indicate when the swelling due to encapsulated particles is thermodynamically inequivalent to that caused by fixed pressure. The general predictions are supported by Monte Carlo simulations of two particle-encapsulating model systems: a two-dimensional self-avoiding ring and a three-dimensional self-avoiding fluid vesicle. In the former the particle-induced swelling is thermodynamically equivalent to the pressure-induced one, whereas in the latter it is not.

We investigate the cooperation dynamics attributed to the interplay between the evolution of individual strategies and evolution of individual partnerships. We focus on the effect of reputation on an individual’s partner-switching process. We assume that individuals can either change their strategies by imitating their partners or adjust their partnerships based on local information about reputations. We manipulate the partner switching in two ways; that is, individuals can switch from the lowest reputation partners, either to their partners’ partners who have the highest reputation (i.e., ordering in partnership) or to others randomly chosen from the entire population (i.e., randomness in partnership). We show that when individuals are able to alter their behavioral strategies and their social interaction partnerships on the basis of reputation, cooperation can prevail. We find that the larger temptation to defect and the denser the partner network, the more frequently individuals need to shift their partnerships in order for cooperation to thrive. Furthermore, an increasing tendency of switching to partners’ partners is more likely to lead to a higher level of cooperation. We show that when reputation is absent in such partner-switching processes, cooperation is much less favored than that of the reputation involved. Moreover, we investigate the effect of discounting an individual’s reputation on the evolution of cooperation. Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships.

Nacre causes the shining beauty of pearl due to its remarkable layered structure, which is also strong. We reconsider a simplified layered model of nacre proposed previously [Okumura and de Gennes, Eur. Phys. J. E 4, 121 (2001)] and obtain an analytical solution to a fundamental crack problem. The result asserts that the fracture toughness is enhanced due to a large displacement around the crack tip (even if the crack-tip stress is not reduced). The derivation offers ideas for solving a number of boundary problems for partial differential equations important in many fields.

The existence of a finite threshold, the yield stress, for the onset of plastic yielding is a universal feature of plasticity. This jamming-unjamming transition is naturally accounted for by the dynamics of a bistable internal state field. We show, within the athermal shear transformation zone theory of amorphous plasticity, that the transition is accompanied by the propagation of plastic fronts. We further show that the mean-field theory cannot select the velocity of these fronts, and go beyond the mean-field description to include fluctuations and correlations effects, resulting in additional nonlocal terms in the equations. Finally, we demonstrate that these terms, with an associated intrinsic length scale, provide a velocity selection mechanism for the plastic fronts.

We propose a model to represent the motility of social elements. The model is completely deterministic, possesses a small number of parameters, and exhibits a series of properties that are reminiscent of the behavior of comunities in social-ecological competition; these are (i) similar individuals attract each other; (ii) individuals can form stable groups; (iii) a group of similar individuals breaks into subgroups if it reaches a critical size; (iv) interaction between groups can modify the distribution of the elements as a result of fusion, fission, or pursuit; (v) individuals can change their internal state by interaction with their neighbors. The simplicity of the model and its richness of emergent behaviors, such as, for example, pursuit between groups, make it a useful toy model to explore a diversity of situations by changing the rule by which the internal state of individuals is modified by the interactions with the environment.

A comparative definition for community in networks is proposed, and the corresponding detecting algorithm is given. A community is defined as a set of nodes, which satisfies the requirement that each node’s degree inside the community should not be smaller than the node’s degree toward any other community. In the algorithm, the attractive force of a community to a node is defined as the connections between them. Then employing an attractive-force-based self-organizing process, without any extra parameter, the best communities can be detected. Several artificial and real-world networks, including the Zachary karate club, college football, and large scientific collaboration networks, are analyzed. The algorithm works well in detecting communities, and it also gives a nice description of network division and group formation.

We consider the effect of laser beam shaping on proton acceleration in the interaction of a tightly focused pulse with ultrathin double-layer solid targets in the regime of directed Coulomb explosion. In this regime, the heavy ions of the front layer are forced by the laser to expand predominantly in the direction of the pulse propagation, forming a moving longitudinal charge separation electric field, thus increasing the effectiveness of acceleration of second-layer protons. The utilization of beam shaping, namely, the use of flat-top beams, leads to more efficient proton acceleration due to the increase of the longitudinal field.

We show that, for a test ion moving in a collisionless single-species electron plasma, exact analytical solutions can be obtained for certain anisotropic velocity distributions of the electron plasma. By comparing the analytical formula with the numerical results calculated for the more realistic Maxwellian plasma, we demonstrate that plasmas with three different velocity distributions behave similarly for ions moving with velocity smaller than the velocity spread of the electrons. Furthermore, we show that the response of the electron density to a rest ion decays exponentially with distance, provided the anisotropic velocity distribution exhibits elliptical symmetry.

We present exact analytic solutions for discrete breathers in essentially nonlinear oscillatory chains, belonging to both of the most common universality classes (Klein-Gordon and Fermi-Pasta-Ulam). The exact solutions can be obtained due to use of vibroimpact potentials, combining extreme nonlinearity with the possibility of description in terms of a forced linear model under conditions of self-consistency. A crossover between the cases of high and low energies can be studied directly. The solutions obtained may be used as a high-energy limit for models with other realistic potentials, as well as benchmarks for the testing of approximate approaches in the theory of discrete breathers.

A free material surface which supports surface diffusion becomes unstable when put under external nonhydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite-time cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.

We derive the thermodynamic curvature of a two-dimensional ideal anyon gas of particles obeying fractional statistics. The statistical interactions of anyon gas can be attractive or repulsive. For attractive statistical interactions, thermodynamic curvature is positive and for repulsive statistical interactions, it is negative, which indicates a more stable anyon gas. There is a special case between the two where the thermodynamic curvature is zero. Small deviations from the classical limit will also be explored.

A critical dilute $\mathrm{O}\left(n\right)$ model on the kagome lattice is investigated analytically and numerically. We employ a number of exact equivalences which, in a few steps, link the critical $\mathrm{O}\left(n\right)$ spin model on the kagome lattice to the exactly solvable critical $q$-state Potts model on the honeycomb lattice with $q={(n+1)}^2$. The intermediate steps involve the random-cluster model on the honeycomb lattice and a fully packed loop model with loop weight $n^{\prime }=\sqrt{q}$ and a dilute loop model with loop weight $n$, both on the kagome lattice. This mapping enables the determination of a branch of critical points of the dilute $\mathrm{O}\left(n\right)$ model, as well as some of its critical properties. These properties differ from those of the generic $\mathrm{O}\left(n\right)$ critical points. For $n=0$, our model reproduces the known universal properties of the $\theta$ point describing the collapse of a polymer. For $n\ne 0$ it displays a line of multicritical points, with the same universal behavior as a branch of critical points that was found earlier in a dilute $\mathrm{O}\left(n\right)$ model on the square lattice. These findings are supported by a finite-size-scaling analysis in combination with transfer-matrix calculations.

We study the passage (translocation) of a self-avoiding polymer through a membrane pore in two dimensions. In particular, we numerically measure the probability distribution $Q\left(T\right)$ of the translocation time $T$, and the distribution $P(s,t)$ of the translocation coordinate $s$ at various times $t$. When scaled with the mean translocation time $⟨T⟩$, $Q\left(T\right)$ becomes independent of polymer length, and decays exponentially for large $T$. The probability $P(s,t)$ is well described by a Gaussian at short times, with a variance of $s$ that grows subdiffusively as $t^{\alpha }$ with $\alpha \approx 0.8$. For times exceeding $⟨T⟩$, $P(s,t)$ of the polymers that have not yet finished their translocation has a nontrivial stable shape.