In implicit large-eddy simulation (ILES), energy-containing large scales are resolved, and physics capturing numerics are used to spatially filter out unresolved scales and to implicitly model subgrid scale effects. From an applied perspective, it is highly desirable to estimate a characteristic Reynolds number (Re)—and therefore a relevant effective viscosity—so that the impact of resolution on predicted flow quantities and their macroscopic convergence can usefully be characterized. We argue in favor of obtaining robust Re estimates away from the smallest scales of the simulated flow—where numerically controlled dissipation takes place and propose a theoretical basis and framework to determine such measures. ILES examples include forced turbulence as a steady flow case, the Taylor-Green vortex to address transition and decaying turbulence, and simulations of a laser-driven reshock experiment illustrating a fairly complex turbulence problem of current practical interest.

We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in nonstationary diffusive lattice gases. We identify two universality classes of these fluctuations, which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of effective fluid, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the symmetric simple exclusion process, where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld [J. Stat. Phys. 137, 978 (2009)] and yields the optimal path of the system. For models of the hyperbolic class, the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.

The dynamics of surface gravity water waves can be described by the self-defocusing nonlinear Schrödinger equation. Recent observations of black solitons on the surface of water confirmed its validity for finite, below critical depth. The black soliton is a limiting case of a family of gray soliton solutions with finite amplitude depressions. Here, we report observations of gray solitons in water waves, thus, complementing our previous observations of black solitons.

In this work, we explore the nature of ion-channel-like conductance fluctuations across a reconstituted phospholipid bilayer due to insertion of ∼100 nm sized, streptavidin-linked magnetite nanoparticles under static magnetic fields (SMFs). For a fixed bias voltage, the frequency of current bursts increases with the application of SMFs. Apart from a closed conductance state $G_0$ (≤14 pS), we identify four major conductance states, with the lowest conductance level ($G_1$) being ∼126 pS. The number of channel events at $G_1$ is found to be nearly doubled (as compared to $G_0$) at a magnetic field of 70 G. The higher-order open states (e.g., 3$G_1$, 5$G_1$) are generally observable at larger values of biasing voltage and magnetic field. When the SMF of 145 G is applied, the multiconductance states are resolved distinctly and are assigned to the simultaneous opening and closing of several independent states. The origin of the current bursts is due to the instantaneous mechanical actuation of streptavidin-linked MNP chains across the phospholipid bilayer. The voltage-controlled, magnetogated ion channels are promising for diagnoses and therapeutic applications of excitable membranes and other biological systems.

We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.

The self-assembly of spherical magnets (magnetic balls) is addressed theoretically. Minimal energy structures are obtained by optimization procedures as well as Monte Carlo computer simulations. Three typical shapes are obtained depending on the number of constitutive magnets $N$. In the regime of small $N$, chains are stable as dimers or trimers (i.e., $N\le 3$), then rings become stable for ($4\le N\le 13$) where dipole vectors adopt a vortexlike arrangement. A major finding concerns the stacking of rings as soon as $N$ is large enough ($N\ge 14$). The number of stacked rings is found to increase as $N^{2/3}$, leading to a tubular structure at large $N$. All the relevant predicted shapes are experimentally reproduced by manipulating millimetric magnets.

We study the evolution of cooperation in the evolutionary spatial prisoner's dilemma game (PDG) and snowdrift game (SG), within which a fraction $\alpha$ of the payoffs of each player gained from direct game interactions is shared equally by the immediate neighbors. The magnitude of the parameter $\alpha$ therefore characterizes the degree of the relatedness among the neighboring players. By means of extensive Monte Carlo simulations as well as an extended mean-field approximation method, we trace the frequency of cooperation in the stationary state. We find that plugging into relatedness can significantly promote the evolution of cooperation in the context of both studied games. Unexpectedly, cooperation can be more readily established in the spatial PDG than that in the spatial SG, given that the degree of relatedness and the cost-to-benefit ratio of mutual cooperation are properly formulated. The relevance of our model with the stakeholder theory is also briefly discussed.

Molecular dynamic simulations were employed to study a waterlike model confined between hydrophobic and hydrophilic plates. The phase behavior of this system is obtained for different distances between the plates and particle-plate potentials. For both hydrophobic and hydrophilic walls, there are the formation of layers. Crystallization occurs at lower temperature at the contact layer than at the middle layer. In addition, the melting temperature decreases as the plates become more hydrophobic. Similarly, the temperatures of maximum density and extremum diffusivity decrease with hydrophobicity.

This paper presents a panoramic macroscopic outlook of rank distributions. We establish a general framework for the analysis of rank distributions, which classifies them into five macroscopic “socioeconomic” states: monarchy, oligarchy-feudalism, criticality, socialism-capitalism, and communism. Oligarchy-feudalism is shown to be characterized by discrete macroscopic rank distributions, and socialism-capitalism is shown to be characterized by continuous macroscopic size distributions. Criticality is a transition state between oligarchy-feudalism and socialism-capitalism, which can manifest allometric scaling with multifractal spectra. Monarchy and communism are extreme forms of oligarchy-feudalism and socialism-capitalism, respectively, in which the intrinsic randomness vanishes. The general framework is applied to three different models of rank distributions—top-down, bottom-up, and global—and unveils each model's macroscopic universality and versatility. The global model yields a macroscopic classification of the generalized Zipf law, an omnipresent form of rank distributions observed across the sciences. An amalgamation of the three models establishes a universal rank-distribution explanation for the macroscopic emergence of a prevalent class of continuous size distributions, ones governed by unimodal densities with both Pareto and inverse-Pareto power-law tails.

Liquid crystal layers sandwiched between a reference plate and a photosensitive substrate were investigated. We focused on the reverse geometry, where the cell was illuminated by a laser beam from the reference side. In planar cells both static and dynamic instabilities occurred, depending on the angle between the laser polarization and the director orientation on the reference plate. In cells where the molecules were aligned along the normal of the reference plate, a dynamic pattern was observed at all angles of polarization. A simple model based on a photoinduced surface torque accounts for the findings. Light scattering studies revealed some basic properties of the instabilities.

The dynamics of structural relaxation in a model polymer glass subject to spatially homogeneous, time-periodic shear deformation is investigated using molecular dynamics simulations. We study a coarse-grained bead-spring model of short polymer chains below the glass transition temperature. It is found that at small strain amplitudes, the segmental dynamics is nearly reversible over about ${10}^4$ cycles, while at strain amplitudes above a few percent, polymer chains become fully relaxed after a hundred cycles. At the critical strain amplitude, the transition from slow to fast relaxation dynamics is associated with the largest number of dynamically correlated monomers as indicated by the peak value of the dynamical susceptibility. The analysis of individual monomer trajectories showed that mobile monomers tend to assist their neighbors to become mobile and aggregate into relatively compact transient clusters.

The ability to design a transport network such that commodities are brought from suppliers to consumers in a steady, optimal, and stable way is of great importance for distribution systems nowadays. In this work, by using the circuit laws of Kirchhoff and Ohm, we provide the exact capacities of the edges that an optimal supply-demand network should have to operate stably under perturbations, i.e., without overloading. The perturbations we consider are the evolution of the connecting topology, the decentralization of hub sources or sinks, and the intermittence of supplier and consumer characteristics. We analyze these conditions and the impact of our results, both on the current United Kingdom power-grid structure and on numerically generated evolving archetypal network topologies.

Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.

We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree $k$ is proportional to $k^{\alpha }$, where $\alpha$ is a tuning parameter. We study both numerically and analytically three types of characteristic times, namely (i) the time the walker needs to come back to the starting node, (ii) the time it takes to visit a given node for the first time, and (iii) the time it takes to visit all the nodes of the network. We consider a large data set of real-world networks and we show that the value of $\alpha$ which minimizes the three characteristic times differs from the value ${\alpha }_{\min }=-1$ analytically found for uncorrelated networks in the mean-field approximation. In addition to this, we found that assortative networks have preferentially a value of ${\alpha }_{\min }$ in the range $[-1,-0.5]$, while disassortative networks have ${\alpha }_{\min }$ in the range $[-0.5,0]$. We derive an analytical relation between the degree correlation exponent $\nu$ and the optimal bias value ${\alpha }_{\min }$, which works well for real-world assortative networks. When only local information is available, degree-biased random walks can guarantee smaller characteristic times than the classical unbiased random walks by means of an appropriate tuning of the motion bias.

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

We investigate the onset of time-periodic oscillations for a system of two identical delay-coupled excitable (nonoscillatory) units. We first analyze these solutions by using asymptotic methods. The oscillations are described as relaxation oscillations exhibiting successive slow and fast changes. The analysis highlights the determinant role of the delay during the fast transition layers. We then study experimentally a system of two coupled electronic circuits that is modeled mathematically by the same delay differential equations. We obtain quantitative agreements between analytical and experimental bifurcation diagrams.

The structure and dynamics of fully developed turbulent flows responding to aeolian dune fields are studied using large-eddy simulation with an immersed boundary method. An aspect of particular importance in these flows is the downwind migration of coherent motions associated with Kelvin-Helmholtz instabilities that originate at the dune crests. These instabilities are responsible for enhanced downward transport of high-momentum fluid via the so-called turbulent sweep mechanism. However, the presence of such structures and their role in determining the bulk characteristics of fully developed dune field sublayer aerodynamics have received relatively limited attention. Moreover, many existing studies address mostly symmetric or mildly asymmetric dune forms. The White Sands National Monument is a field of aeolian gypsum sand dunes located in the Tularosa Basin in southern New Mexico. Aeolian processes at the site result in a complex, anisotropic dune field. In the dune field sublayer, the flow statistics resemble a mixing layer: At approximately the dune crest height, vertical profiles of streamwise velocity exhibit an inflection and turbulent Reynolds stresses are maximum; below this, the streamwise and vertical velocity fluctuations are positively and negatively skewed, respectively. We evaluate the spatial structure of Kelvin-Helmholtz instabilities present in the dune field sublayer (shear length $L_s$ and vortex spacing ${\Lambda }_x$) and show that ${\Lambda }_x=m_{\mathrm{dune}}{L}_s$, where $m_{\mathrm{dune}}\approx 7.2$ in the different sections considered (for turbulent mixing layers, $7<m<10$ [M. M. Rogers and R. D. Moser, Phys. Fluids A 6, 903 (1994)]).

The dynamical behavior of almost neutrally buoyant finite-size rigid fibers or rods in turbulent channel flow is studied by direct numerical simulations. The time evolution of the fiber orientation and translational and rotational motions in a statistically steady channel flow is obtained for three different fiber lengths. The turbulent flow is modeled by an entropy lattice Boltzmann method, and the interaction between fibers and carrier fluid is modeled through an external boundary force method. Direct contact and lubrication force models for fiber-fiber interactions and fiber-wall interaction are taken into account to allow for a full four-way interaction. The density ratio is chosen to mimic cellulose fibers in water. It is shown that the finite size leads to fiber-turbulence interactions that are significantly different from earlier reported results for pointlike particles (e.g., elongated ellipsoids smaller than the Kolmogorov scale). An effect that becomes increasingly accentuated with fiber length is an accumulation in high-speed regions near the wall, resulting in a mean fiber velocity that is higher than the mean fluid velocity. The simulation results indicate that the finite-size fibers tend to stay in the high-speed streaks due to collisions with the wall. In the central region of the channel, long fibers tend to align in the spanwise direction. Closer to the wall the long fibers instead tend to toward to a rotation in the shear plane, while very close to the wall they become predominantly aligned in the streamwise direction.

The electromagnetic fields of charges moving along the boundary of a “wire metamaterial” perpendicularly to the wires are investigated. The metamaterial under consideration represents a volume-periodic structure of thin parallel wires located in a square lattice. This structure is described by an effective permittivity tensor and exhibits both spatial and frequency dispersion. It is shown that the charge generates nondivergent radiation, as in the case of an infinite metamaterial. However, unlike the infinite-metamaterial case, the radiation concentrates near a certain plane (not line) behind the charge, and it is asymmetric with respect to this plane. An algorithm for calculating the wave fields of finite-length bunches is developed, and some typical numerical results are given. They demonstrate that the structure under consideration can be applied to determine the size and form of such bunches. The stopping and deflection forces acting on the charge are also calculated.

Network reciprocity is one mechanism for adding social viscosity, which leads to cooperative equilibrium in 2 × 2 prisoner's dilemma games. Previous studies have shown that cooperation can be enhanced by using a skewed, rather than a random, selection of partners for either strategy adaptation or the gaming process. Here we show that combining both processes for selecting a gaming partner and an adaptation partner further enhances cooperation, provided that an appropriate selection rule and parameters are adopted. We also show that this combined model significantly enhances cooperation by reducing the degree of activity in the underlying network; we measure the degree of activity with a quantity called effective degree. More precisely, during the initial evolutionary stage in which the global cooperation fraction declines because initially allocated cooperators becoming defectors, the model shows that weak cooperative clusters perish and only a few strong cooperative clusters survive. This finding is the most important key to attaining significant network reciprocity.