We measure the statistics of phase locking levels of coupled fiber lasers with fluctuating cavity lengths. We found that the measured distribution of the phase locking level of such coupled lasers can be described by the generalized extreme value distribution. For large number of lasers the distribution of the phase locking level can be approximated by a Gumbel distribution. We present a simple model, based on the spectral response of coupled lasers, and the calculated results are in good agreement with the experimental results.

Understanding synchronous and traveling-wave oscillations, particularly as they relate to transitions between different types of behavior, is a central problem in modeling biological systems. Here, we address this problem in the context of central pattern generators (CPGs). We use contraction theory to establish the global stability of a traveling-wave or synchronous oscillation, determined by the type of coupling. This opens the door to better design of coupling architectures to create the desired type of stable oscillations. We then use coupling that is both amplitude and phase dependent to create either globally stable synchronous or traveling-wave solutions. Using the CPG motor neuron network of a leech as an example, we show that while both traveling and synchronous oscillations can be achieved by several types of coupling, the transition between different types of behavior is dictated by a specific coupling architecture. In particular, it is only the “repulsive” but not the commonly used phase or rotational coupling that can explain the transition to high-frequency synchronous oscillations that have been observed in the heartbeat pattern generator of a leech. This shows that the overall dynamics of a CPG can be highly sensitive to the type of coupling used, even for coupling architectures that are widely believed to produce the same qualitative behavior.

An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected to orthogonal polynomials. We show that two different orthogonal polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to express the Doi-Peliti formalism explicitly.

We analyze the Kuramoto model generalized by explicit consideration of deterministically time-varying parameters. The oscillators' natural frequencies and/or couplings are influenced by external forces with constant or distributed strengths. A dynamics of the collective rhythms is observed, consisting of the external system superimposed on the autonomous one, a characteristic feature of many thermodynamically open systems. This deterministic, stable, continuously time-dependent, collective behavior is fully described, and the external impact to the original system is defined in both the adiabatic and the nonadiabatic limits.

This Rapid Communication presents a stochastic Wang tiling-based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite set of tiles assembled by a stochastic tiling algorithm, thereby allowing to accurately reproduce long-range orientation orders in a computationally efficient manner. Although the basic features of the method are demonstrated for a two-dimensional particulate suspension, the present framework is fully extensible to generic multidimensional media.

In microswimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of “pushers” and maximal disorder in suspensions of “pullers.” Nonlinear simulations show that hydrodynamic interactions can limit and modify chemotactically driven aggregation dynamics. In puller suspensions the dynamics form aggregates that are mutually repelling due to the nontrivial flows. In pusher suspensions chemotactic aggregation can lead to destabilizing flows that fragment the regions of aggregation.

We examine the critical behavior of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report [Ferreira et al., Phys. Rev. E 85, 010901(R) (2012)], which suggested that the critical behavior of the model differs from the expected directed percolation (DP) universality class. Surprisingly, only some of the critical exponents ($\beta$, $\alpha$, ${\nu }_{\perp }$, and $z$) take non-DP values while some others (${\beta }^{\prime }$, ${\nu }_{\left|\right|}$, and spreading-dynamics exponents $\Theta$, $\delta$, $z^{\prime }$) remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations $\beta =\alpha {\nu }_{\left|\right|}$, ${\beta }^{\prime }=\delta {\nu }_{\left|\right|}$, and the generalized hyperscaling relation $\Theta +\alpha +\delta =d/z$, where the dynamical exponent $z$ is, however, used instead of the spreading exponent $z^{\prime }$. Both in $d=1$ and $d=2$ versions of our model, the exponent $\beta$ most likely takes the mean-field value $\beta =1$, and we speculate that it might be due to the roulette-wheel selection, which is used to choose the site to supply a nutrient.

We present an alternative approach to the problem of interacting fluids, which we believe may provide important insights into microscopic mechanisms that lead to the occurrence of phase transitions. The approach exploits enumerative properties and combinatorial meaning of Bell polynomials. We derive the exact formula for the probability of a general system of $N$ particles at temperature $T$ to consist of $k$ weakly coupled clusters of various sizes. We also show that the grand potential of the system may be considered the exponential generating function for the number of internal states (thermodynamic probability) of these clusters. The microscopic interpretation of the grand potential is surprising, especially if one recalls that until now only the thermodynamic meaning of this free energy was known. We also derive an approximated expression for the density of states.

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

The problem of tiling or tessellating (i.e., completely filling) three-dimensional Euclidean space ${\mathbb{R}}^3$ with polyhedra has fascinated people for centuries and continues to intrigue mathematicians and scientists today. Tilings are of fundamental importance to the understanding of the underlying structures for a wide range of systems in the biological, chemical, and physical sciences. In this paper, we enumerate and investigate the most comprehensive set of tilings of ${\mathbb{R}}^3$ by any two regular polyhedra known to date. We find that among all of the Platonic solids, only the tetrahedron and octahedron can be combined to tile ${\mathbb{R}}^3$. For tilings composed of only congruent tetrahedra and congruent octahedra, there seem to be only four distinct ratios between the sides of the two polyhedra. These four canonical periodic tilings are, respectively, associated with certain packings of tetrahedra (octahedra) in which the holes are octahedra (tetrahedra). Moreover, we derive two families of an uncountably infinite number of periodic tilings of tetrahedra and octahedra that continuously connect the aforementioned four canonical tilings with one another, containing the previously reported Conway-Jiao-Torquato family of tilings [Conway et al., Proc. Natl. Acad. Sci. USA 108, 11009 (2011)] as a special case. For tilings containing infinite planar surfaces, nonperiodic arrangements can be easily generated by arbitrary relative sliding along these surfaces. We also find that there are three distinct canonical periodic tilings of ${\mathbb{R}}^3$ by congruent regular tetrahedra and congruent regular truncated tetrahedra associated with certain packings of tetrahedra (truncated tetrahedra) in which the holes are truncated tetrahedra (tetrahedra). Remarkably, we discover that most of the aforementioned periodic tilings can be obtained by “retessellating” the well-known tiling associated with the face-centered-cubic lattice, i.e., by combining the associated fundamental tiles (regular tetrahedra and octahedra) to form larger polyhedra.

We perform three-dimensional simulations of the impact of a granular jet for both frictional and frictionless grains. Small shear stress observed in the experiment [X. Cheng et al., Phys. Rev. Lett. 99, 188001 (2007)] is reproduced through our simulation. However, the fluid state after the impact is far from a perfect fluid, and thus the similarity between granular jets and quark gluon plasma is superficial because the observed viscosity is finite and its value is consistent with the prediction of the kinetic theory.

Yield loci of a granular material are derived in case of triaxial compression carried out at constant pressure. The theory is based upon a simple micromechanical model in which particles move according to an average, homogeneous deformation. We show how the presence of an inherent anisotropy in the aggregate (typical of laboratory samples due to depositional processes) produces a deviation of the yield loci in the stress space from the expected Mohr-Coulomb prediction. That is, when the compaction pressure in an anisotropic aggregate is increased, irreversibility associated with sliding between particles occurs and this will influence the yield function in the subsequent triaxial test. Numerical simulations support the theoretical result.

We consider a simplified coarse-grained model for colloid-polymer mixtures, in which polymers are represented as monoatomic molecules interacting by means of pair potentials. We use it to study polymer-colloid segregation in the presence of a quenched matrix of colloidal hard spheres. We fix the polymer-to-colloid size ratio to 0.8 and consider matrices such that the fraction $f$ of the volume that is not accessible to the colloids due to the matrix is equal to 40$\%$. As in the Asakura-Oosawa-Vrij (AOV) case, we find that binodal curves in the polymer and colloid volume-fraction plane have a small dependence on disorder. As for the position of the critical point, the behavior differs from that observed in the AOV case: While the critical colloid volume fraction is essentially the same in the bulk and in the presence of the matrix, the polymer volume fraction at criticality increases as $f$ increases. At variance with the AOV case, no capillary colloid condensation or evaporation is generically observed.

We consider a lattice polymer model of the two-tolerant type (i.e., a random walk allowed to visit lattice bonds at most twice), in which doubly visited bonds yield an attractive energy term (pairing energy). Such a model has been previously proposed as a rough, nonspecific description of the RNA folding mechanism. Indeed, the model predicts, besides the usual theta collapse, an extra transition to a low-temperature fully paired state. In the current work, we propose an extension of the model, in which a “micromolecular” chemical species can bind the polymer and locally forbid segment pairing. We investigate equilibrium thermodynamics in the grand-canonical picture, at the level of a Bethe approximation, which is, a refined mean-field technique, equivalent to the exact solution on a random-regular graph. The general trend we observe is that expected from the mechanism implemented in the model (increasing micromolecule concentration favors unfolding and lowers the transition temperature), but the resulting phase diagram turns out to be remarkably interesting and rich.

Probability density functions (PDF's) of the eigenvalues of the strain tensor of an incompressible isotropic turbulence in 3, 4, and 5 dimensions are computed by direct numerical simulation of Navier-Stokes equations. The PDF's of the smallest (negative) eigenvalue are found to be wider than those of the other ones in all dimensions and to be very insensitive to the dimension. In any dimension, the eigenvalues other than the lowest one increase as the lowest one decreases, so that they tend to be positive for the large magnitude of the lowest eigenvalue. In such a situation the flow comes in along a single direction and comes out in the other directions, which is consistent with the dynamics of the Burgers turbulence in $d$ dimensions. It is suggested that a driving motor of most intermittent turbulent structure is the compression along a single direction. For the velocity 2 form the conditional averages of the enstrophy and the total squared strain in three dimensions are computed as functions of the smallest eigenvalue and found to be monotonically increasing as the magnitude of the smallest eigenvalue increases. Also, it is found that PDF of the source term of the Poisson equation for the pressure is positively skewed but tends to be symmetric with increase of the spatial dimension. Dimension effects on the dynamics of the most compressible eigenvalue are argued.

High-resolution laser probing diagnostics at a wavelength of 266 nm allow observation of the internal structure and instabilities in dense stagnated $Z$ pinches, typically hidden by trailing material. The internal structure of the 1-MA $Z$ pinch includes strong kink and sausage instabilities, loops, flares, and disruptions. Mid- and small-scale density perturbations develop in the precursor and main pinch. The three-dimensional shape and dynamics of the wire-array $Z$ pinch are predetermined by the initial configuration of the wire array. Cylindrical, linear, and star wire-array $Z$ pinches present different sets of instabilities seeded to the pinch at the implosion stage. Prolonged implosion of trailing mass can enhance x-ray production in wire arrays. Fast plasma motion with a velocity >100 km/s was observed in the $Z$ pinch at stagnation with two-frame shadowgraphy. Development of instabilities in wire arrays is in agreement with three-dimensional magnetohydrodynamic simulations.

The paper presents an extended description of the amplified wire ablation dynamics model (WADM), which accounts in a single simulation for the processes of wire ablation and implosion of a wire array load of arbitrary geometry and wire material composition. To investigate the role of wire ablation effects, the implosions of cylindrical and planar wire array loads at the university based generators Cobra (Cornell University) and Zebra (University of Nevada, Reno) have been analyzed. The analysis of the experimental data shows that the wire mass ablation rate can be described as a function of the current through the wire and some coefficient defined by the wire material properties. The aluminum wires were found to ablate with the highest rate, while the copper ablation is the slowest one. The lower wire ablation rate results in a higher inward velocity of the ablated plasma, a higher rate of the energy coupling with the ablated plasma, and a more significant delay of implosion for a heavy load due to the ablation effects, which manifest the most in a cylindrical array configuration and almost vanish in a single-planar array configuration. The WADM is an efficient tool suited for wire array load design and optimization in wide parameter ranges, including the loads with specific properties needed for the inertial confinement fusion research and laboratory astrophysics experiments. The data output from the WADM simulation can be used to simplify the radiation magnetohydrodynamics modeling of the wire array plasma.

The growth of the two-dimensional single-mode Rayleigh-Taylor instability (RTI) at low Atwood number ($A=0.04$) is investigated using Direct Numerical Simulations. The main result of the paper is that, at long times and sufficiently high Reynolds numbers, the bubble acceleration becomes stationary, indicating mean quadratic growth. This is contrary to the general belief that single-mode Rayleigh-Taylor instability reaches a constant bubble velocity at long times. At unity Schmidt number, the development of the instability is strongly influenced by the perturbation Reynolds number, defined as ${\text{Re}}_p\equiv \lambda \sqrt{Ag\lambda /(1+A)}/\nu$. Thus, the instability undergoes different growth stages at low and high ${\text{Re}}_p$. A new stage, chaotic development, was found at sufficiently high ${\text{Re}}_p$ values, after the reacceleration stage. During the chaotic stage, the instability experiences seemingly random acceleration and deceleration phases, as a result of complex vortical motions, with strong dependence on the initial perturbation shape (i.e., wavelength, amplitude, and diffusion thickness). Nevertheless, our results show that the mean acceleration of the bubble front becomes constant at late times, with little influence from the initial shape of the interface. As ${\text{Re}}_p$ is lowered to small values, the later instability stages, chaotic development, reacceleration, potential flow growth, and even the exponential growth described by linear stability theory, are subsequently no longer reached. Therefore, the results suggest a minimum Reynolds number and a minimum development time necessary to achieve all stages of single-mode RTI development, requirements which were not satisfied in the previous studies of single-mode RTI.

The description of diffusion processes is possible in different frameworks such as random walks or Fokker-Planck or Langevin equations. Whereas for classical diffusion the equivalence of these methods is well established, in the case of anomalous diffusion it often remains an open problem. In this paper we aim to bring three approaches describing anomalous superdiffusive behavior to a common footing. While each method clearly has its advantages it is crucial to understand how those methods relate and complement each other. In particular, by using the method of subordination, we show how the Langevin equation can describe anomalous diffusion exhibited by Lévy-walk-type models and further show the equivalence of the random walk models and the generalized Kramers-Fokker-Planck equation. As a result a synergetic and complementary description of anomalous diffusion is obtained which provides a much more flexible tool for applications in real-world systems.