A simulation study is performed to investigate the dynamics of coupled Langmuir waves (LWs) and ion-acoustic waves (IAWs) in an unmagnetized plasma. The effects of dispersion due to charge separation and the density nonlinearity associated with the IAWs are considered to modify the properties of Langmuir solitons, as well as to model the dynamics of relatively large amplitude wave envelopes. It is found that the Langmuir wave electric field, indeed, increases by the effect of ion-wave nonlinearity (IWN). Use of a low-dimensional model, based on three Fourier modes, shows that a transition to temporal chaos is possible, when the length scale of the linearly excited modes is larger than that of the most unstable ones. The chaotic behaviors of the unstable modes are identified by the analysis of Lyapunov exponent spectra. The space-time evolution of the coupled LWs and IAWs shows that the IWN can cause the excitation of many unstable harmonic modes and can lead to strong IAW emission. This occurs when the initial wave field is relatively large or the length scale of IAWs is larger than the soliton characteristic size. Numerical simulation also reveals that many solitary patterns can be excited and generated through the modulational instability of unstable harmonic modes. As time goes on, these solitons are seen to appear in the spatially partial coherence state due to the free ion-acoustic radiation as well as in the state of spatiotemporal chaos due to collision and fusion in the stochastic motion. The latter results in the redistribution of initial wave energy into a few modes with small length scales, which may lead to the onset of Langmuir turbulence in laboratory as well as space plasmas.

We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence (DHIT) in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, $Z_R$, and the initial ratio of the rotational and translational temperatures, $T_{R0}/T_{L0}$, on the dynamics of various turbulence statistics including the kinetic energy $K\left(t\right)$, the dissipation rate $\epsilon \left(t\right)$, the energy spectrum $E\left(k,t\right)$, the root mean square of the velocity divergence ${\theta }^{\prime }\left(t\right)$, the skewness $S_u\left(t\right)$ and the flatness $F_u\left(t\right)$ of the velocity derivatives, and the probability distribution functions of the local Mach number Ma and the shocklet strength $\chi$. The larger the $Z_R$ is, the faster the compressibility decays after an initial time. Similarly, with a fixed $T_{L0}$, the higher the initial energy ratio $T_{R0}/T_{L0}$, the weaker is the compressibility in the flow. It is also observed that the effect of $T_{R0}/T_{L0}$ is strong in all times in the decay, while the effect of $Z_R$ is severe only in the later times passing through the stage with strong nonlinearity. We also observe that the multitemperature model does not affect the self-similarities obeyed by the probability distribution functions of Ma and $\chi$, which appear to be a robust feature of the compressible DHIT.

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses—also observed experimentally.

We show that the eigenvalue density of a product $X=X_1{X}_2\cdots X_M$ of $M$ independent $N\times N$ Gaussian random matrices in the limit $N\to \infty$ is rotationally symmetric in the complex plane and is given by a simple expression $\rho \left(z,\overline{z}\right)=\frac{1}{M\pi }{\sigma }^{-2/M}{\left|z\right|}^{-2+\left(2/M\right)}$ for $\left|z\right|\le \sigma$, and is zero for $\left|z\right|>\sigma$. The parameter $\sigma$ corresponds to the radius of the circular support and is related to the amplitude of the Gaussian fluctuations. This form of the eigenvalue density is highly universal. It is identical for products of Gaussian Hermitian, non-Hermitian, and real or complex random matrices. It does not change even if the matrices in the product are taken from different Gaussian ensembles. We present a self-contained derivation of this result using a planar diagrammatic technique. Additionally, we conjecture that this distribution also holds for any matrices whose elements are independent centered random variables with a finite variance or even more generally for matrices which fulfill Pastur-Lindeberg’s condition. We provide a numerical evidence supporting this conjecture.

We derive an integral expression for the plane-wave expansion of the time-varying (nonstationary) random field inside a mode-stirred reverberation chamber. It is shown that this expansion is a so-called oscillatory process, whose kernel can be expressed explicitly in closed form. The effect of nonstationarity is a modulation of the spectral density of the field on a time scale that is a function of the cavity relaxation time. It is also shown how the contribution by a nonzero initial value of the field can be incorporated into the expansion. The results are extended to a special class of second-order processes, relevant to the reception of a mode-stirred reverberation field by a device under test with a first-order (relaxation-type) frequency response.

In the present study we analyze some consequences that come from revised measures as the Wehrl entropy and the Fisher information for the problem of a particle in a magnetic field starting from a complete description of the Husimi function. We discuss in the most complete form (three dimensions) some results related to measures in contrast with the incomplete form (two dimensions) shown in previous contributions. Some limiting cases as high and low temperatures are discussed. From the present reasoning, it is suggested that the formulation in two dimensions is sufficient unto itself to explain the problem whenever the length of the cylindrical geometry of the system is large enough. Otherwise, it is not possible to work in all finite temperatures, a natural lower temperature bound emerges from the analysis when three dimensions are considered.

Flexible polymers such as long DNA, RNA molecules, and proteins, can pass through a narrow pore whose size is comparable to their molecular thickness. We highlight the richness and complexity involved in the dynamics of this unique mode of molecular transport, called translocation, actively driven by external forces. In particular, the process takes place in the condition far from equilibrium accompanying of large conformational distortion in line with the propagation of the tensile force along the chain backbone. A general framework is proposed, which captures such essential features, whereby can account for reported various experimental data from a unified viewpoint.

We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise. It is also competitive with the best currently available algorithms in terms of speed and size of solvable systems. We find that the computational demand often exhibits superlinear scaling $O\left(L^{1.3}\right)$ where $L$ is the number of edges in the system, and we have applied the algorithm to synthetic systems as large as $40\times {10}^6$ nodes and over $1\times {10}^9$ edges. A previous stumbling block encountered by popular community detection methods is the so-called “resolution limit.” Being a “local” measure of community structure, our Potts model is free from this resolution-limit effect, and it further remains a local measure on weighted and directed graphs. We also address the mitigation of resolution-limit effects for two other popular Potts models.

Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, we study a “biased rewiring model” where clustering is enhanced by means of a fugacity as in the Strauss (or “triangle”) model, but where the number of links attached to each node is strictly preserved. Similar models have been proposed previously in Milo et al. [Science 298, 824 (2002)]. Our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree $k>2$ we find a single first order transition. For all nonregular networks that we studied (including Erdös-Rényi, scale-free, and several real-world networks) multiple jumps resembling first order transitions appear. The jumps coincide with the sudden emergence of “cluster cores:” groups of highly interconnected nodes with higher than average degrees, where each edge participates in many triangles. Hence, clustering is not smoothly distributed throughout the network. Once formed, the cluster cores are difficult to remove, leading to strong hysteresis. To study the cluster cores visually, we introduce $q$ -clique adjacency plots. Cluster cores constitute robust communities that emerge spontaneously from the triangle generating process, rather than being put explicitly into the definition of the model. All the quantities we measured including the modularity, assortativity, clustering and number of four and five-cliques exhibit simultaneous jumps and are equivalent order parameters. Finally, we point out that cluster cores produce pitfalls when using the present (and similar) models as null models for strongly clustered networks, due to strong hysteresis which leads to broken ergodicity on realistic sampling time scales.

We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law with an exponent ${\tau }_a=1.5$. We derive a scaling relation ${\tau }_a=2\tau -1$ between the local cluster exponent ${\tau }_a$ and the global avalanche exponent $\tau$. For length scales longer than a crossover length proportional to the Larkin length, the aspect ratio of the local clusters scales with the roughness exponent of the line model. Our analysis provides an explanation for experimental results on planar crack avalanches in Plexiglas plates, but the results are applicable also to other systems with long-range interactions.

We study the synchronization of Kuramoto oscillators with all-to-all coupling in the presence of slow, noisy frequency adaptation. In this paper, we develop a model for oscillators, which adapt both their phases and frequencies. It is found that this model naturally reproduces some observed phenomena that are not qualitatively produced by the standard Kuramoto model, such as long waiting times before the synchronization of clapping audiences. By assuming a self-consistent steady state solution, we find three stability regimes for the coupling constant $k$, separated by critical points $k_1$ and $k_2$: (i) for $k<k_1$ only the stable incoherent state exists; (ii) for $k>k_2$, the incoherent state becomes unstable and only the synchronized state exists; and (iii) for $k_1<k<k_2$ both the incoherent and synchronized states are stable. In the bistable regime spontaneous transitions between the incoherent and synchronized states are observed for finite ensembles. These transitions are well described as a stochastic process on the order parameter $r$ undergoing fluctuations due to the system’s finite size, leading to the following conclusions: (a) in the bistable regime, the average waiting time of an $\text{incoherent}\to \text{coherent}$ transition can be predicted by using Kramer’s escape time formula and grows exponentially with the number of oscillators; (b) when the incoherent state is unstable $\left(k>k_2\right)$, the average waiting time grows logarithmically with the number of oscillators.

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross-diffusive terms, often neglected in the heuristic derivation of reaction-diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.

What is the average time a random walker takes to get from A to B on a fractal structure and how does this mean time scale with the size of the system and the distance between source and target? We take a nonprobabilistic approach toward this problem and show how the solution is readily obtained using an analysis of thermal vibrations on fractals. Invariance under scaling and continuity with respect to the spectral dimension are shown to be emergent properties of the solution obtained via vibrational analysis. Our result emphasizes the duality between diffusion and vibrations on fractal structures. Applications to biological systems are discussed.

Liquid-crystalline blue phases exhibit exceptional properties for applications in the display and sensor industry. However, in single component systems, they are stable only for very narrow temperature range between the isotropic and the chiral nematic phase, a feature that severely hinders their applicability. Systematic high-resolution calorimetric studies reveal that blue phase III is effectively stabilized in a wide temperature range by mixing surface-functionalized nanoparticles with chiral liquid crystals. This effect is present for two liquid crystals, yielding a robust method to stabilize blue phases, especially blue phase III. Theoretical arguments show that the aggregation of nanoparticles at disclination lines is responsible for the observed effects.

It was predicted recently that sufficiently complex knots on a linear wormlike chain can have a metastable size, preventing their spontaneous expansion. We tested this prediction via computer simulations for $7_1$ and ${10}_{151}$ knots. We calculated the equilibrium distributions of knot size $S$ for both knots. By using the umbrella sampling, we were able to obtain the distributions over a wide range of $S$ values. The distributions were converted into the dependencies of the free energy on the knot size. The obtained free energy profiles have no pronounced local minima, so there are no metastable knot sizes for these knots. We also performed Brownian dynamics simulation of $7_1$ knot relaxation that started from a very tight knot conformation. The simulation showed that knot expansion is a fast process compared to knot displacement along the chain contour by diffusion.

We present the numerical results for the dynamics of a single chain in steady shear flow. The chain is represented by a bead-spring model and the smoothed profile method is used to accurately account for the effects of thermal fluctuations and hydrodynamic interactions acting on beads due to host fluids. It was observed that the chain undergoes tumbling motions and that its dimensionless frequency $F=6\pi \eta {\sigma }^3\nu /k_{\text{B}}T$ depends only on the Peclet number Pe with a power law $F\propto {\text{Pe}}^{\alpha }$, where $k_{\text{B}}$ is the Boltzmann constant, $T$ is the temperature, and $\sigma$ is the diameter of the beads. The exponent $\alpha$ clearly changes from 2/3 to 1 around the critical Peclet number, ${\text{Pe}}_{\text{c}}$, indicating that the crossover reflects the competition of thermal fluctuation and shear flow. The presented numerical results agree well with our theoretical analysis based on Jeffrey’s work.

We investigate a weighted self-propelled agent system, wherein each agent’s direction is determined by its spatial neighbors’ directions with exponential weights according to the neighbor numbers. In order to describe the fact that some agents with more neighbors might have larger influence on its neighbors, we introduce a scaling exponent of the neighbor number between 0 and $\infty$. When the exponent is equal to 1, the convergence efficiency is enhanced in our simulation. Furthermore, as the exponent increases, i.e., the effect of weight becomes stronger, the network of agents becomes easier to achieve direction consensus.

The transition from integrability to nonintegrability for a set of two-dimensional Hamiltonian mappings exhibiting mixed phase space is considered. The phase space of such mappings show a large chaotic sea surrounding Kolmogorov-Arnold-Moser islands and limited by a set of invariant tori. The description of the phase transition is made by the use of scaling functions for average quantities of the mapping averaged along the chaotic sea. The critical exponents are obtained via extensive numerical simulations. Given the mappings considered are parametrized by an exponent $\gamma$ in one of the dynamical variables, the critical exponents that characterize the scaling functions are obtained for many different values of $\gamma$. Therefore classes of universality are defined.

Time delay is introduced in the coupling between a pair of electrochemical cells. As coupling parameters are varied, the anodic current in the two cells oscillate in synchrony in regimes of periodic as well as chaotic dynamics. When the time delay is varied a phase-flip transition is observed: the relative phase between the synchronized oscillations changes abruptly by $\pi$. This is accompanied by an experimentally measurable discontinuous change in the frequency of the synchronized oscillators.

We study the existence of multiple equilibrium states in a simple fluid network using Newtonian fluids and laminar flow. We demonstrate theoretically the presence of hysteresis and bistability, and we confirm these predictions in an experiment using two miscible fluids of different viscosity—sucrose solution and water. Possible applications include blood flow, microfluidics, and other network flows governed by similar principles.