We study the evolution of cooperation in public goods games on the square lattice, focusing on the effects that are brought about by different sizes of groups where individuals collect their payoffs and search for potential strategy donors. We find that increasing the group size does not necessarily lead to mean-field behavior, as is traditionally observed for games governed by pairwise interactions, but rather that public cooperation may be additionally promoted by means of enhanced spatial reciprocity that sets in for very large groups. Our results highlight that the promotion of cooperation due to spatial interactions is not rooted solely in having restricted connections among players, but also in individuals having the opportunity to collect payoffs separately from their direct opponents. Moreover, in large groups the presence of a small number of defectors is bearable, which makes the mixed-phase region expand with increasing group size. Having a chance of exploiting distant players, however, offers defectors a different way to break the phalanx of cooperators and even to resurrect from small numbers to eventually completely invade the population.

A periodic segregation in a binary granular mixture of alumina and copper spheres has been found when the mixture is subjected to vertical vibrations, in which a stable percolation process has been experimentally studied. Measurements reveal that the percolation time of alumina particles through a permeable layer of copper particles increases linearly as the number of alumina particles increases. While the percolation current of alumina particles proves to be independent of the number of alumina particles, it shows a monotonically decreasing relationship with the number of copper particles in the mixture. Finally, we briefly discuss possible candidates to affect the percolation current.

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line that contains dynamical correlations that change irregularly under parameter variation. Capturing these correlations by incorporating higher-order terms, all schemes converge to the analytically exact result. Two of these methods are based on expanding the Taylor-Green-Kubo formula for diffusion, while the third method approximates Markov partitions and transition matrices by using a slight variation of the escape rate theory of chaotic diffusion. We check the practicability of the different methods by working them out analytically and numerically for a simple one-dimensional map, study their convergence, and critically discuss their usefulness in identifying a possible fractal instability of parameter-dependent diffusion, in the case of dynamics where exact results for the diffusion coefficient are not available.

The Gaussian model of discontinuous percolation, recently introduced by Araújo and Herrmann [Phys. Rev. Lett. 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple cubic lattice, in the thermodynamic limit we report a finite jump of the order parameter $J=0.415\pm 0.005$. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension $d_A=2.5\pm 0.2$. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with a finite number of clusters at the threshold.

We investigate the instabilities of a linear damped oscillator due to fluctuations of the damping parameter. The fluctuations are driven either by Gaussian white noise or Poisson white noise (white shot noise). We consider three notions of stability. The first two are the well-known notions of stability in the mean and stability in the mean square. We introduce the concept of thermodynamic stability, corresponding to a nonpositive rate of energy dissipation at all times. We derive analytical results for the various instability thresholds, confirm the validity of our approach for white shot noise by numerical simulations, and obtain the unexpected result that mean-square and thermodynamic stability coincide for the two types of white noise.

We show how attractive interactions dramatically influence emulsion rheology. Unlike the repulsive case, attractive emulsions below random close packing, ${\phi }_{\text{RCP}}$, can form soft gel-like elastic solids. However, above ${\phi }_{\text{RCP}}$, attractive and repulsive emulsions have similar elasticities. Such compressed attractive emulsions undergo an additional shear-driven relaxation process during yielding. Our results suggest that attractive emulsions begin to yield at weak points through the breakage of bonds, and, above ${\phi }_{\text{RCP}}$, also undergo droplet configurational rearrangements.

The structure of the system consisting of a grafted self-avoiding polymer chain attracted to the surface layer of a flat wall at a distance away by a short-ranged force is investigated. A first-order transition is determined between the coil state at a low attraction energy and the bridge state at a high attraction energy. The transition properties of the system are obtained by a Monte Carlo simulation, which uses the inverse density of states as the transition weight and is reweighted back to a canonical ensemble. The determination of the density of states follows a revised Wang-Landau procedure in which the center-of-mass distance from the grafted site is used as the variable. Scaling arguments are also given for the observed numerical results.

Freeze-dried perdeuterated sperm whale myoglobin was kept in a water-saturated atmosphere in order to obtain a hydration degree of 335 ${}^1$H${}_2$O molecules per one myoglobin molecule. Incoherent neutron scattering was performed at the neutron spectrometer TOFTOF at the FRM II in an angular range of $q$ from 0.6 to 1.8 Å${}^{-1}$ and a temperature range from 4 to 297 K. We used neutrons with a wavelength of λ $\alpha E$ 6 Å and an energy resolution of about 65 μeV corresponding to motions faster than 10 ps. At temperatures above 225 K, broad lines appear in the spectra caused by quasielastic scattering. For an explanation of these lines, we assumed that there are only two types of protons, those that are part of the hydration water (72$\%$) and those that belong to the protein (28$\%$). The protons of the hydration water were analyzed with the diffusion model of Singwi and Sjölander [Phys. Rev. 119, 863 (1960)]. In this model, a water molecule stays for a time ${\tau }_0$ in a bound state performing oscillatory motions. Thereafter, the molecule performs free diffusion for the time ${\tau }_1$ in a nonbound state followed again by the oscillatory motions for ${\tau }_0$ and so forth. We used the general formulation with no simplifications as ${\tau }_0\gg {\tau }_1$ or ${\tau }_1\gg {\tau }_0$. At room temperature, we obtained ${\tau }_0$ $\alpha E$ 104 ps and ${\tau }_1$ $\alpha E$ 37 ps. For the protein bound hydrogen, the dynamics is described by a Brownian oscillator where the protons perform overdamped motions in limited space.

Effects of the attractive and repulsive parts of hydrophobic interactions on $\alpha$ helices and $\beta$ sheets in small peptides are investigated using a simple atomic potential. Typically, a physical spatial range of attraction tends to favor $\beta$ sheets, but $\alpha$ helices would be favored if the attractive range were more extended. We also found that desolvation barriers favor $\beta$ sheets in collapsed conformations of polyalanine, polyvaline, polyleucine, and three fragments of amyloid peptides tested in this study. Our results provide insight into the multifaceted role of hydrophobicity in secondary structure formation, including the $\alpha$ to $\beta$ transitions in certain amyloid peptides.

Many technological networks can experience random and/or systematic failures in their components. More destructive situations can happen if the components have limited capacity, where the failure in one of them might lead to a cascade of failures in other components, and consequently break down the structure of the network. In this paper, the tolerance of cascaded failures was investigated in weighted networks. Three weighting strategies were considered including the betweenness centrality of the edges, the product of the degrees of the end nodes, and the product of their betweenness centralities. Then, the effect of the cascaded attack was investigated by considering the local weighted flow redistribution rule. The capacity of the edges was considered to be proportional to their initial weight distribution. The size of the survived part of the attacked network was determined in model networks as well as in a number of real-world networks including the power grid, the internet in the level of autonomous system, the railway network of Europe, and the United States airports network. We found that the networks in which the weight of each edge is the multiplication of the betweenness centrality of the end nodes had the best robustness against cascaded failures. In other words, the case where the load of the links is considered to be the product of the betweenness centrality of the end nodes is favored for the robustness of the network against cascaded failures.

Understanding the synchronization process of self-propelled objects is of great interest in science and technology. We propose a synchronization model for a self-propelled objects system in which we restrict the maximal angle change of each object to ${\theta }_R$. At each time step, each object moves and changes its direction according to the average direction of all of its neighbors (including itself). If the angle change is greater than a cutoff angle ${\theta }_R$, the change is replaced by ${\theta }_R$. We find that (i) counterintuitively, the synchronization improves significantly when ${\theta }_R$ decreases, (ii) there exists a critical restricted angle ${\theta }_{Rc}$ at which the synchronization order parameter changes from a large value to a small value, and (iii) for each noise amplitude $\eta$, the synchronization as a function of ${\theta }_R$ shows a maximum value, indicating the existence of an optimal ${\theta }_R$ that yields the best synchronization for every $\eta$.

We present a quantitative theory of the nonlinear dynamics and surfatron resonant acceleration of charged particles in the presence of random fluctuations of magnetic field. We demonstrate that the surfatron mechanism of acceleration is sufficiently stable versus the influence of fluctuations and particle accelerate even in the presence of a random noise. We estimate the maximum energy which particles could gain in the course of the surfatron acceleration.

We show, using covariant Lyapunov vectors, that the tangent space of spatially extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled “physical” modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying “spurious” modes. The decoupling of the physical and spurious subspaces is defined by the absence of tangencies between them and found to take place generally; we find evidence in partial differential equations in one and two spatial dimensions and even in lattices of coupled maps or oscillators. We conjecture that the physical modes may constitute a local linear description of the inertial manifold at any point in the global attractor.

The crater formation due to the impact of a water droplet onto a granular bed has been experimentally investigated. Three parameters were tuned: the impact velocity, the size of the droplet, and the size of the grains. The aim is to determine the influence of the kinetic energy on the droplet pattern. The shape of the crater depends on the kinetic energy at the moment the droplet starts to impact the bed. The spreading and recession of the liquid during the impact were carefully analyzed from the dynamical point of view, using image analysis of high-speed video recordings. The different observed regimes are characterized by the balance between the impregnation time of the water by the granular bed by the water and the capillary time responsible for the recession of the drop.

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Péclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

Interesting wake effects are found in simulations of dust grains in supersonically flowing plasma. A Mach cone is formed at an angle to the flow determined by the ratio of flow to Bohm speed. The latter is well approximated by ${[k(T_e+\gamma T_i)/m_i]}^{1/2}$ with $\gamma =3$. For ion temperatures significantly lower than the electron temperature, a second (inner) cone forms due to flow convergence. An “ion vacuum” and stagnation point occur downstream. These latter effects cannot be described by conventional (cold-ion) gas dynamics. Critically, none of the cones observed are shocks but are more akin to weak discontinuities.

Branching is an essential element of streamer discharge dynamics. We review the current state of theoretical understanding and recall that branching requires a finite perturbation. We argue that, in current laboratory experiments in ambient or artificial air, these perturbations can only be inherited from the initial state, or they can be due to intrinsic electron-density fluctuations owing to the discreteness of electrons. We incorporate these electron-density fluctuations into fully three-dimensional simulations of a positive streamer in air at standard temperature and pressure. We derive a quantitative estimate for the ratio of branching length to streamer diameter that agrees within a factor of 2 with experimental measurements. As branching without this noise would occur considerably later, if at all, we conclude that the intrinsic stochastic particle noise triggers branching of positive streamers in air at atmospheric pressure.

Numerous schemes have been proposed to incorporate a bulk forcing term into the lattice Boltzmann equation. In this paper we present a simple and straightforward comparative analysis of five popular schemes [Shan and Chen, Phys. Rev. E 47, 1815 (1993); Phys Rev Lett. 81, 1618 (1998); He et al., Phys. Rev. E 57, R13 (1998); Guo et al., Phys. Rev. E 65, 046308 (2002); Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)] in which their differences and similarities are identified. From the analysis we classify the schemes into two groups; the behaviors of the schemes in each group are proven to be identical up to second order. Numerical test simulating the two-dimensional unsteady Taylor-Green vortex flow problem demonstrate that all five schemes are of comparable accuracy for single-phase flow. However, for two-phase flow the situation is different, which is demonstrated by incorporating these schemes into different Shan-Chen-type multiphase models. The forcing scheme in the original Shan-Chen (SC) multiphase model turns out to be inaccurate in terms of the resulting surface tension for different density ratios and relaxation times. In the numerical tests, a typical equation of state and interparticle interactions including next-nearest neighbors were incorporated into the SC model. Our results confirm that the surface-tension values obtained from the original SC lattice Boltzmann method (LBM) simulation depend on the value of the relaxation time $\tau$. For $\tau <0.7\Delta t$, the surface tension agree well with the analytical solutions. However, when $\tau >0.7\Delta t$, the surface tension turns out to be systematically larger than the analytical one, exceeding it by more than a factor of 2 for $\tau =2\Delta t$. In contrast, with the application of the scheme proposed by He et al., the SC LBM produces very accurate surface tensions independent of the value of $\tau$. We also found that the densities of the coexisting liquid and gas can be adjusted to match those at thermodynamic equilibrium if the particle interaction term includes next-nearest-neighbor contributions. The obtained results will be useful for further studies of two-phase flow with high density ratios using the SC LBM approach.

Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the ${\chi }^2$ hypersurface, depending on a set of parameters $\left\{P_i\right\}$. This is usually done using the Levenberg-Marquardt algorithm. The main drawback of this algorithm is that despite its fast convergence, it can get stuck if the parameters are not initialized close to the final solution. We propose a modification of the Metropolis algorithm introducing a parameter step tuning that optimizes the sampling of parameter space. The ability of the parameter tuning algorithm together with simulated annealing to find the global ${\chi }^2$ hypersurface minimum, jumping across ${\chi }^2\left\{P_i\right\}$ barriers when necessary, is demonstrated with synthetic functions and with real data.

In this Comment we reveal the falsehood of the claim that the lattice Bhatnagar-Gross-Krook (BGK) model “is capable of modeling shear-driven, pressure-driven, and mixed shear-pressure-driven rarified [sic] flows and heat transfer up to $\text{Kn}=1$ in the transitional regime” made in a recent paper [Ghazanfarian and Abbassi, Phys. Rev. E 82, 026307 (2010)]. In particular, we demonstrate that the so-called “Knudsen effects” described are merely numerical artifacts of the lattice BGK model and they are unphysical. Specifically, we show that the erroneous results for the pressure-driven flow in a microchannel imply the false and unphysical condition that $6\sigma \text{Kn}<-1$, where $\text{Kn}$ is the Knudsen number $\sigma =(2-{\sigma }_v)/{\sigma }_v$ and ${\sigma }_v\in (0,1]$ is the tangential momentum accommodation coefficient. We also show explicitly that the defects of the lattice BGK model can be completely removed by using the multiple-relaxation-time collision model.