Theory and simulations are used to study collisionless relaxation of a gravitational $N$-body system. It is shown that when the initial one-particle distribution function satisfies the virial condition—potential energy is minus twice the kinetic energy—the system quickly relaxes to a metastable state described quantitatively by the Lynden-Bell distribution with a cutoff. If the initial distribution function does not meet the virial requirement, the system undergoes violent oscillations, resulting in a partial evaporation of mass. The leftover particles phase-separate into a core-halo structure. The theory presented allows us to quantitatively predict the amount and the distribution of mass left in the central core, without any adjustable parameters. On a longer time scale ${\tau }_G\sim N$, collisionless relaxation leads to a gravothermal collapse.

A modified floor field model is proposed to simulate pedestrian evacuation in rooms with internal obstacles and multiple exits. The modifications lie in developing a method to calculate the static floor field for every lattice site, which is determined by the most feasible distance to an exit, and employing a logit-based discrete choice principle to govern the exit selection. Simulation results show that the evacuation time is sensitive to the exit position and some model parameters. For pedestrians unfamiliar with the exit location, additional doors may not be necessary and can cause a negative effect on evacuation time. It is also found that unfamiliarity with the room’s inner configuration and blindly following others will lead to an increase of the evacuation time.

We show through polarized light scattering experiments the spatially inhomogeneous orientational dynamics for shear-thinning wormlike micellar gels (cetyltrimethylammonium $\text{tosylate}+\text{sodium}$ $\text{chloride}+{\mathrm{H}}_2\mathrm{O}$) en route to rheochaos. For shear rates in the plateau of the flow curve, we see alternating bright and dark birefringent stripes stacked along the vorticity. The orientational order in adjacent bands is predominantly oriented at $+45°$ and $-45°$ to the flow $\left(\mathbf{v}\right)$ in the $(\mathbf{v},\mathbf{\nabla }\mathbf{v})$ plane, respectively. We have made an attempt to correlate the observed orientational ordering in terms of the two-dimensional Taylor-like velocity rolls in a gradient banding fluid. The bands show spatial motion along the vorticity, and the orientation dynamics of the interface delineating adjacent bands completely correlates with the temporal dynamics of the stress. Furthermore, the observed spatial dynamics of the interfaces of the rolls depends crucially on the gap width of the Couette cell.

The quasistatic contact-line dissipation model is applied to the dynamics of relaxation of periodically perturbed contact lines in the Wilhelmy plate geometry where a solid plate is withdrawn vertically at constant velocity from a bath of liquid. The resulting motion of the three-dimensional liquid meniscus is solved rigorously by numerical simulation. A detailed comparison is performed with the recent experimental results of Delon et al. [J. Fluid Mech. 604, 55 (2008)] and with their hydrodynamic approach. The described approach exhibits a better agreement with the experiments than the mentioned hydrodynamic approach. The influence of nonlinearity on the contact-line relaxation dynamics is analyzed. The deviation from the behavior predicted within the contact-line elasticity model is discussed.

We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing network models that perfectly match the structure of some real scale-free networks, such as the Internet. We obtain an analytic solution, supported by extensive simulations, for the degree distribution in superlinearly growing networks with arbitrary average degree, and confirm that in the true thermodynamic limit these networks are indeed degenerate, i.e., almost all nodes have low degrees. We then show that superlinear growth has vast preasymptotic regimes whose depths depend both on the average degree in the network and on how superlinear the preference kernel is. We demonstrate that a superlinearly growing network model can reproduce, in its preasymptotic regime, the structure of a real network, if the model captures some sufficiently strong structural constraints—rich-club connectivity, for example. These findings suggest that real scale-free networks of finite size may exist in pre-asymptotic regimes of network evolution processes that lead to degenerate network formations in the thermodynamic limit.

After a failure or attack the structure of a complex network changes due to node removal. Here, we show that the degree distribution of the distorted network, under any node disturbances, can be easily computed through a simple formula. Based on this expression, we derive a general condition for the stability of noncorrelated finite complex networks under any arbitrary attack. We apply this formalism to derive an expression for the percolation threshold $f_c$ under a general attack of the form $f_k\sim k^{\gamma }$, where $f_k$ stands for the probability of a node of degree $k$ of being removed during the attack. We show that $f_c$ of a finite network of size $N$ exhibits an additive correction which scales as $N^{-1}$ with respect to the classical result for infinite networks.

We determine the conditions for the occurrence of Turing instabilities in activator-inhibitor systems, where one component undergoes subdiffusion and the other normal diffusion. If the subdiffusing species has a nonlinear death rate, then coupling between the nonlinear kinetics and the memory effects of the non-Markovian transport process advances the Turing instability if the inhibitor subdiffuses and delays the Turing instability if the activator subdiffuses. We apply the results of our analysis to the Schnakenberg model, the Gray-Scott model, the Oregonator model of the Belousov-Zhabotinsky reaction, and the Lengyel-Epstein model of the chlorine dioxide–iodine–malonic acid reaction.

The effect of coupling strength inhomogeneity on the synchronization of identical oscillators is investigated. Through simulations and analysis of phase-reduced models, it is shown that the mean value of coupling function and the degree of inhomogeneity in the total of coupling strength to the each oscillator cooperate to stabilize incoherent states. Under some circumstances, there can be bistability between coherent and incoherent states. Various cases of coupled Morris-Lecar oscillators are studied as examples of our results.

Collective Thomson scattering with extreme ultraviolet light or x rays is shown to allow for a robust measurement of the free electron density in dense plasmas. Collective excitations like plasmons appear as maxima in the scattering signal. Their frequency position can directly be related to the free electron density. The range of applicability of the standard Gross-Bohm dispersion relation and of an improved dispersion relation in comparison to calculations based on the dielectric function in random phase approximation is investigated. More important, this well-established treatment of Thomson scattering on free electrons is generalized in the Born-Mermin approximation by including collisions. We show that, in the transition region from collective to noncollective scattering, the consideration of collisions is important.

A segregation criterion based on the inelastic Enskog kinetic equation is derived to show the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the different parameters of the system. In contrast to previous theoretical attempts, the approach is not limited to the near-elastic case, takes into account the influence of both thermal gradients and gravity, and applies for moderate densities. The form of the phase diagrams for the BNE-RBNE transition depends sensitively on the value of gravity relative to the thermal gradient, so that it is possible to switch between both states for given values of the mass and size ratios, the coefficients of restitution, and the solid volume fraction. In particular, the influence of collisional dissipation on segregation becomes more important when the thermal gradient dominates over gravity than in the opposite limit. The present analysis extends previous results derived in the dilute limit case and is consistent with the findings of some recent experimental results.

A generalized Lotka-Volterra model for a pair of interacting populations of predators and prey is studied. The model accounts for the prey’s interspecies competition and therefore is asymptotically stable, whereas its oscillatory behavior is induced by temporal variations in environmental conditions simulated by those in the prey’s reproduction rate. Two models of the variations are considered, each of them combining randomness with “hidden” periodicity. The stationary joint probability density function (PDF) of the number of predators and prey is calculated numerically by the path integration (PI) method based on the use of characteristic functions and the fast Fourier transform. The numerical results match those for the asymptotic case of white-noise variations for which an analytical solution is available. Several examples are studied, with calculations of important characteristics of oscillations, for example the expected rate of up-crossings given the level of the predator number. The calculated PDFs may be of predominantly random (unimodal) or predominantly periodic nature (bimodal). Thus, the PI method has been demonstrated to be a powerful tool for studies of the dynamics of predator-prey pairs. The method captures the random oscillations as observed in nature, taking into account potential periodicity in the environmental conditions.

We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging $l$ pairs of communities $(l>1)$ at each iteration prevents premature condensation into few large communities. Here, an empirical formula is presented for the choice of the step width $l$ that generates partitions with (close to) optimal modularity for 17 real-world and 1100 computer-generated networks. Furthermore, an in-depth analysis of the communities of two real-world networks (the metabolic network of the bacterium E. coli and the graph of coappearing words in the titles of papers coauthored by Martin Karplus) provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity, but also according to objective criteria. In other words, the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions.

We focus on the differences among the analytical optimization of traffic flow on a road network, modeled by a fluid-dynamic approach, and a dynamic random one. In particular, two real urban networks are analyzed: Re di Roma Square, in Rome, and Via Parmenide crossing, in Salerno. With such two examples, it is possible to show that dynamic random algorithms are not the right choice for the improvement of traffic conditions.

A lossy data compression scheme for uniformly biased Boolean messages is investigated via statistical mechanics techniques. We utilize a treelike committee machine (committee tree) and a treelike parity machine (parity tree) whose transfer functions are nonmonotonic. The scheme performance at the infinite code length limit is analyzed using the replica method. Both committee and parity treelike networks are shown to saturate the Shannon bound. The Almeida-Thouless stability of the replica symmetric solution is analyzed, and the tuning of the nonmonotonic transfer function is also discussed.

The Vicsek model (VM) [T. Vicsek et al., Phys. Rev. Lett. 75, 1226 (1995)], for the description of the collective behavior of self-driven individuals, assumes that each of them adopts the average direction of movement of its neighbors, perturbed by an external noise. A second-order transition between a state of ordered collective displacement (low-noise limit) and a disordered regime (high-noise limit) was found early on. However, this scenario has recently been challenged by Grégory and Chaté [G. Grégory and H. Chaté, Phys. Rev. Lett. 92, 025702 (2004)] who claim that the transition of the VM may be of first order. By performing extensive simulations of the VM, which are analyzed by means of both finite-size scaling methods and a dynamic scaling approach, we unambiguously demonstrate the critical nature of the transition. Furthermore, the complete set of critical exponents of the VM, in $d=2$ dimensions, is determined. By means of independent methods—i.e., stationary and dynamic measurements—we provide two tests showing that the standard hyperscaling relationship $d\nu -2\beta =\gamma$ holds, where $\beta$, $\nu$, and $\gamma$ are the order parameter, correlation length, and “susceptibility” critical exponents, respectively. Furthermore, we established that at criticality, the correlation length grows according to $\xi \sim t^{1∕z}$, with $z\simeq 1.27\left(3\right)$, independently of the degree of order of the initial configuration, in marked contrast with the behavior of the $XY$ model.

A simple three-state lattice model that incorporates two states for locally ordered and disordered forms of liquid water in addition to empty cells is introduced. The model is isomorphic to the Blume-Emery-Griffith model. The locally ordered $\left(O\right)$ and disordered $\left(D\right)$ forms of water are treated as two components, and we assume that the density of the $D$ component is larger. The density of the sample is determined by the fraction of cells occupied by the $O$ and $D$ forms of water. Due to the larger density of the $D$ state, the strength of the van der Waals (vdW) interactions increases in the direction $O\text{−}O<O\text{−}D<D\text{−}D$. On the other hand, the H-bond interactions are assumed only for the $O\text{−}O$ pairs. For the vdW and H-bond interaction parameters and the density ratio of the close-packed and ice forms of water compatible with experimentally known values, we find liquid-vapor and liquid-liquid transitions and the corresponding critical points in good agreement with other approaches. Water anomalies are correctly predicted within the mean-field approximation on a qualitative level.

When a chiral isotropic elastomer is brought to the low-temperature cholesteric phase, the nematic degree of freedom tends to order and form a helix. Due to the nematoelastic coupling, this also leads to elastic deformation of the polymer network that is locally coaxial with the nematic order. However, the helical structure of nematic order is incompatible with the energetically preferred elastic deformation. The system is therefore frustrated and appropriate compromise has to be achieved between the nematic ordering and the elastic deformation. For a strongly chiral elastomer whose pitch is much smaller than the system size, this problem has been studied by Pelcovits and Meyer, as well as by Warner. In this work, we study the isotropic-cholesteric transition in the weak-chirality limit, where the pitch is comparable to or much larger than system size. We compare two possible solutions: a helical state as well as a double-twist state. We find that the double-twist state very efficiently minimizes both the elastic free energy and the chiral nematic free energy. On the other hand, the pitch of the helical state is strongly affected by the nematoelastic coupling. As a result, this state is not efficient in minimizing the chiral nematic free energy.

The strength of a bonded interface is considered for the case in which bonding is the result of clusters of discrete bonds distributed along the interface. Assumptions appropriate for the case of adhesion of biological cells to an extracellular matrix are introduced as a basis for the discussion. It is observed that those individual bonds nearest to the edges of a cluster are necessarily subjected to disproportionately large forces in transmitting loads across the interface, in analogy with well-known behavior in elastic crack mechanics. Adopting Bell’s model for the kinetics of bond response under force, a stochastic model leading to a dependence of interface strength on cluster size is developed and analyzed. On the basis of this model, it is demonstrated that there is an optimum cluster size for maximum strength. This size arises from the competition between the nonuniform force distribution among bonds, which tends to promote smaller clusters, and stochastic response allowing bond reformation, which tends to promote larger clusters. The model results have been confirmed by means of direct Monte Carlo simulations. This analysis may be relevant to the observation that mature focal adhesion zones in cell bonding are found to have a relatively uniform size.

A key ingredient for continued expansion of nanotechnologies is the ability to create perfectly ordered arrays on a small scale with both site and size control. Self-assembly—i.e., the spontaneous formation of nanostructures—is a highly promising alternative to traditional fabrication methods. However, efforts to obtain perfect long-range order via self-assembly have been frustrated in practice as ensuing patterns contain defects. We use an idea based on the fundamental physics of pattern formation to introduce a strategy to consistently obtain perfect patterns.

Semiconductor lasers with optical feedback have chaotically pulsating output behavior. When two similar chaotic lasers are optically coupled, they can become synchronized in their optical fluctuations. Here we show that the synchronization is not only in the amplitude and in the timing of the pulses but that the short pulses are also phase coherent with each other. This is true even when the lasers are separated by distances much larger than their coherence length.