We investigate the effect of randomness in both relationships and decisions on the evolution of cooperation. Simulation results show, in such randomness’ presence, the system evolves more frequently to a cooperative state than in its absence. Specifically, there is an optimal amount of randomness, which can induce the highest level of cooperation. The mechanism of randomness promoting cooperation resembles a resonancelike fashion, which could be of particular interest in evolutionary game dynamics in economic, biological, and social systems.

The statistics of burst avalanche sizes $n$ during failure processes in a fiber bundle follows a power law $D\left(n\right)\sim n^{-\xi }$ for large avalanches. The exponent $\xi$ depends upon how the avalanches are provoked. While it is known that when the load on the bundle is increased in a continuous manner the exponent takes the value $\xi =5∕2$, we show that when the external load is increased in discrete and not too small steps, the exponent value $\xi =3$ is relevant. Our analytic treatment applies to bundles with a general probability distribution of the breakdown thresholds for the individual fibers. The preasymptotic size distribution of avalanches is also considered.

We study an autonomous four-dimensional dynamical system used to model certain geophysical processes. This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents ${\lambda }_i$ that satisfy ${\lambda }_1+{\lambda }_2+{\lambda }_3<0$, so the Lyapunov dimension is $D_L=2+\mid {\lambda }_3\mid ∕{\lambda }_1<3$ in the range of coupling parameter values studied. As a result, it should be possible to find three-dimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into $R^3$ to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from $R^4$ to $R^3$. In one case the one-parameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes self-intersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other.

We use a microcavity laser to explore the properties of experimental coherent waves as an analogous study of the chaotic wave functions in quantum billiards. With the eigenstate expansion method, the experimental high-order chaotic coherent waves are well reconstructed. The reconstructed wave functions are employed to calculate the field and intensity correlations. It is found that the spreading of $k$-space (momentum space) distribution leads to not only wave localization in coordinate space but also enhancement of long-range correlations.

We study the band structures of one-dimensional (1D) photonic crystals (PCs) in the subwavelength limit. A “spatial-averaged single-negative” (SASN) gap whose edges correspond to zero (volume) averaged permittivity $(\overline{\epsilon }=0)$ and zero (volume) averaged permeability $(\overline{\mu }=0)$ will appear when metamaterial is included in the PC. Unlike the Bragg gap, the frequency range of the SASN gap is invariant to the geometrical scaling and insensitive to the incident angle and disorder. In the subwavelength limit, both the zero-$\overline{n}$ gap in the left-handed 1D PC and the zero-effective-phase gap in the single-negative 1D PC can be understood as SASN gaps. When the subwavelength condition is not fulfilled, the zero-$\overline{n}$ gap and zero-effective-phase gap begin to act differently.

We study the properties of junctions created by the crossing of $N$ identical branches of linear discrete networks. We reveal that for $N>2$ such a junction creates a topological defect and supports two types of spatially localized modes. We analyze the wave scattering by the junction defect and demonstrate nonzero reflection for any set of parameters. If the junction is nonlinear, it is possible to achieve the maximum transmission for any frequency by tuning the intensity of the scattering wave. In addition, near the maximum transmission the system shows the bistable behavior.

We study the aging properties, in particular the two-time autocorrelations, of the two-dimensional randomly diluted Ising ferromagnet below the critical temperature via Monte Carlo simulations. We find that the autocorrelation function displays additive aging $C(t,t_w)=C_{st}\left(t\right)+C_{ag}(t,t_w)$, where the stationary part $C_{st}$ decays algebraically. The aging part shows anomalous scaling $C_{ag}(t,t_w)=\mathcal{C}\left[h\right(t)∕h(t_w\left)\right]$, where $h\left(u\right)$ is a nonhomogeneous function excluding a $t∕t_w$ scaling.

Proposed is an alternative method for permutational sampling in quantum gases using the path integral formulation of statistical mechanics. It is shown that in principle we are able to use two operators which enable us to construct a Markov chain through a graph of the irreducible representation of the symmetric group. As an illustration of this method, a test calculation of four particles in a harmonic trap is performed.

The interaction of two oppositely highly charged surfaces in an electrolyte solution and the number of released counterions from the slit between the surfaces were studied in terms of the anisotropic hypernetted chain and nonlinear Poisson-Boltzmann theories. Liquid theory predictions of the attractive pressure and release of counterions between the plates are larger than those of the mean field approach at low and moderate concentration of added salt. Further, at high salt concentration there is an opposite relationship of the two theories in their numerical results for the attractive pressure for all surface separations. These deviations of the predicted equilibrium properties arise both from the charge density and the ion size correlation effects included in hypernetted chain theory.

Colloidal particles that are dissolved in a liquid can become charged by preferential adsorption or dissociation of surface molecules. The assumption of a constant surface charge density leads to a particle charge that is proportional to the square of the radius. Recent experiments however have shown that in a number of cases the charge is linearly proportional to its size. We present a simple model for the charging of colloidal particles leading to a linear relation between charge and size in the framework of the mean-field Poisson-Boltzmann theory. The model is based on preferential adsorption or dissociation of surface molecules, in combination with a large concentration of chargeable surface sites. The model also predicts a surface potential that is independent of the particle size. Numerical simulations show that this model is in good agreement with analytical approximations.

We report on the temperature dependence of the response time for the photochemical and thermal back relaxation processes observed in a material exhibiting a photostimulated, isothermal nematic-isotropic phase transition. It is found that the time required for the system to achieve the photostationary state as well as to recover the original state after photoirradiation with a uv beam is a smooth function of the absolute temperature of the sample, except in the vicinity of the transition. The duration of the recovery can be split into two parts: delay time and response time. Using a simple description based on the Maier-Saupe model, we show that the temperature dependence of the response time can be understood in terms of the order parameter excess between the equilibrium and photostimulated states.

We study the low-frequency, long-wavelength dynamics of liquid crystal elastomers, crosslinked in the smectic-$A$ phase, in their smectic-$A$, biaxial smectic and smectic-$C$ phases. Two different yet related formulations are employed. One formulation describes the pure hydrodynamics and does not explicitly involve the Frank director, which relaxes to its local equilibrium value in a nonhydrodynamic time. The other formulation explicitly treats the director and applies beyond the hydrodynamic limit. We compare the low-frequency, long-wavelength dynamics of smectic-$A$ elastomers to that of nematics and show that the two are closely related. For the biaxial smectic and the smectic-$C$ phases, we calculate sound velocities and the mode structure in certain symmetry directions. For the smectic-$C$ elastomers, in addition, we discuss in some detail their possible behavior in rheology experiments.

Rhythm generation mechanisms are very important for genetic network functions as well as for the design of synthetic genetic circuits. A significant attention to date has been focused on the synchronization of communicating genetic units, which results in the production of an unified rhythm. In contrast to this we address the question: what mechanisms of intercell communication can be responsible for multirhythmicity in globally coupled genetic units? Here, we show that an autoinducer intercell communication system that provides coupling between synthetic genetic oscillators will inherently lead to multirhythmicity and the appearance of several coexisting dynamical regimes, if the time evolution of the genetic network can be split in two well-separated time scales. We investigate in detail a variety of dynamical regimes in a genetic population and show the possibility for multiple element distributions between clusters, as well as the possibility of generating complex oscillations with different return times in one limit cycle.

This paper examines the dynamics of an ensemble of hysteresis-based genetic relaxation oscillators, focusing on the influence of noise and cell-to-cell coupling on the appearance of new dynamical regimes. In particular, we show that control of the coupling strength and noise can effectively change the dynamics of the system leading to behaviors such as clustering, synchronous and asynchronous oscillations, and suppression. Moreover, under certain conditions an optimal amount of noise can lead to increased order in the system. The results obtained are correlated with relevant biological processes that occur in living organisms.

The molecular mechanism of B-Z DNA transition remains elusive since the elucidation of the left-handed Z-DNA structure using atomic resolution crystallographic study. Numerous proposals for the molecular mechanism have been advanced, but none has provided a satisfactory explanation for the process. A nonlinear DNA model is proposed which enables one to derive various hypothesized molecular mechanisms, namely the Harvey model, Zang and Olson model, and the stretched intermediate model, by imposing certain constraints and conditions on the model. These constraints raise the need to reevaluate experimental investigations on B-Z DNA transition.

We investigated the use of the quantum Grover algorithm in the mass-spectrometry-based protein identification process. The approach coded the mass spectra on a quantum register and uses the Grover search algorithm for searching multiple solutions to find matches from a database. Measurement of the fidelity between the input and final states was used to quantify the similarity between the experimental and theoretical spectra. The optimal number of iteration is proven to be $\frac{\pi }{4}\sqrt{\frac{N}{k}}$, where $k$ refers to the number of marked states. We found that one iteration is sufficient for the search if we let more that 62% of the $N$ states be marked states. By measuring the fidelity after only one iteration of Grover search, we discovered that it resembles that of the correlation-based measurement used in the existing protein identification software. We concluded that the quantum Grover algorithm can be adapted for a correlation-based mass spectra database search, provided that decoherence can be kept to a minimum.

We present numerical evidence of fractional behavior in reactions for a prototype model of three-degree-of-freedom isomerization. The survival probability in the well exhibits two distinct ranges of time scales: one where it decreases with a power law, and the other where it decreases exponentially. Trajectories corresponding to power law decays exhibit $1∕f$ spectra and subdiffusion in action space, and those with exponential decays exhibit Lorentzian spectra and normal diffusion. The existence of these two types of behavior is explained on the basis of nonergodicity in the network of nonlinear resonances (Arnold web) in the well, and connection between the saddle and the Arnold web. Implications of the fractional dynamics are discussed in terms of Maxwell’s demon in molecules.

Understanding the fundamental properties of polymeric liquids remains a challenge in materials science and soft matter physics. Here, we present a simple and computationally efficient criterion for topological constraints, i.e., uncrossability of chains, in polymeric liquids using the dissipative particle dynamics (DPD) method. No new length scales or forces are added. To demonstrate that this approach really prevents chain crossings, we study a melt of linear homopolymers. We show that for short chains the model correctly reproduces Rouse-like dynamics whereas for longer chains the dynamics becomes reptational as the chain length is increased—something that is not attainable using standard DPD or other coarse-grained soft potential methods.

The synchronization threshold in the general form of a one-way coupled time-delayed system is discussed. Based on the Krasovskii-Lyapunov theory, the deduction process and the application range of the synchronization threshold are given. In addition, a misuse of the synchronization threshold is presented and is illustrated by an example.

Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system must satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe nonequilibrium phase coexistence, as illustrated on different models. We finally discuss the issue of the equalization of ITPs when two different systems are put into contact. This issue is closely related to the possibility of measuring the ITPs using a small auxiliary system, in the same way as temperature is measured with a thermometer, and points at one of the major difficulties of nonequilibrium statistical mechanics. In addition, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.