We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e., one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat, are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains where noncatastrophic topological change induced by a small parameter variation becomes inevitable. A geometric mechanism depending on dimension and an associated conjecture depict why topological change is expected but not catastrophic, thus providing an explanation of how and why deterministic chaos persists in high dimensions.

The dynamical properties of double-stranded DNA are studied in the framework of the Peyrard-Bishop-Dauxois model using Langevin dynamics. Our simulations are analyzed in terms of two distribution functions describing localized separations (“bubbles”) of the double strand. The result that the bubble distributions are more sharply peaked at the active sites than thermodynamically obtained distributions is ascribed to the fact that the bubble lifetimes affect the distributions. Certain base-pair sequences are found to promote long-lived bubbles, and we argue that this is a result of length scale competition between the nonlinearity and disorder present in the system.

The ground state entropy density of the triangular Ising antiferromagnet is considered as a function of boundary conditions on domains for which the ground states do not admit a dimer covering. These domains admit a rich set of ground states that cannot be classified in the usual way in terms of nonintersecting strings. Various parametrized boundary conditions and domain shapes are identified that allow the ground state entropy density to be varied between zero and maximal degeneracy. The dependence of degeneracy on boundary spins and/or domain shape is interpreted in terms of strings that are not restricted to be nonintersecting.

When a binary mixture of granular materials, differing in shape or size, is poured into a quasi-two-dimensional silo, segregation of the mixture is observed. Depending on the size ratio $d_2∕d_1$ of the species, the mixture segregates completely or partially into the pure species. To study the partial-segregation effect we propose a theoretical model based on the work of Boutreux and de Gennes [J. Phys. I 6, 1295 (1996)] but we introduce more realistic collision functions. To compare the partial- and complete-segregation effects, we also discuss calculations for the complete-segregation model proposed by Makse [Phys. Rev. E 56, 7008 (1997)]. Our experiments confirm the analytical solutions for both types of segregation. We find that the transition from complete segregation to partial segregation appears as the size ratio of the species is decreased below a critical value, which is found to be $d_2∕d_1\simeq 1.4$ for our system. Our experimental and analytical studies predict the regime for applicability of both partial- and complete-segregation models in terms of the size ratio of the species and the respective model parameters.

Compact polymers are self-avoiding random walks that visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte Carlo algorithm that uniformly samples compact polymer configurations in an efficient manner, allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self-averaging in the long-chain limit and strictly less than 1. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure.

Infectious diseases and computer malwares spread among humans and computers through the network of contacts among them. These networks are characterized by wide connectivity fluctuations, connectivity correlations, and the small-world property. In a previous work [Phys. Rev. Lett. 96, 038702 (2006)] I have shown that the connectivity fluctuations together with the small-world property lead to a spreading law characterized by an initial power law growth with an exponent determined by the average node distance on the network. Here I extend these results to consider the influence of connectivity correlations which are generally observed in real networks. I show that assortative and disassortative connectivity correlations enhance and diminish, respectively, the range of validity of this spreading law. As a corollary I obtain the region of connectivity fluctuations and degree correlations characterized by the absence of an epidemic threshold. These results are relevant for the spreading of infectious diseases, rumors, and information among humans and the spreading of computer viruses, email worms, and hoaxes among computer users.

We report the observation of an exotic radiation (unconventional Smith-Purcell radiation) from a one-dimensional photonic crystal. The physical origin of the exotic radiation is direct excitation of the photonic bands by an ultrarelativistic electron beam. The spectrum of the exotic radiation follows photonic bands of a certain parity, in striking contrast to the conventional Smith-Purcell radiation, which shows solely a linear dispersion. Key ingredients for the observation are the facts that the electron beam is in an ultrarelativistic region and that the photonic crystal is finite. The origin of the radiation was identified by comparison of experimental and theoretical results.

Dissipative particle dynamics (DPD) is a mesoscopic method in which coarse graining is done at the molecular level to capture the physics at the meso level. In this paper, we present a DPD model for two-phase flows involving liquid and vapor phases. The model is based on mean-field theory. Phase segregation between the two phases is simulated by the choice of an equation of state with a van der Waals loop. Surface tension is modeled by a term that depends on higher-order density gradients and accounts for long-range attractive forces. To test the model, we present results from simulations of a liquid layer, several liquid cylinders of varying size to verify the Laplace’s law, small- and large-amplitude liquid cylinder oscillations and capillary waves. In all these cases we compare DPD results with results available from analytical solutions.

For a chain of homogeneous nonlinear oscillators starting from different initial phases, a certain amount of time is required for the system to evolve to complete phase synchronization. The effect of independent noise in such a system was investigated, and an optimal noise intensity was found that minimized the average synchronization time. Both threshold noise and connection noise show similar effects. The features of the phenomenon and the underlying mechanism are discussed through the analysis of a two-unit system and the numerical studies of chains up to $30\text{units}$ in length.

We present an analytic method for calculating spectral densities of empirical covariance matrices for correlated data. In this approach the data is represented as a rectangular random matrix whose columns correspond to sampled states of the system. The method is applicable to a class of random matrices with radial measures including those with heavy (power-law) tails in the probability distribution. As an example we apply it to a multivariate Student distribution.

Within the framework of Ericksen-Leslie continuum theory we analyze the influence of shear flow on the magnetic-field-induced Fréedericksz transition in nematic liquid crystal with rodlike molecules. We consider three basic orientational configurations of a nematic planar layer in the uniform magnetic field. Conditions of rigid director coupling on the boundaries of the layer and constant shear flow gradient inside the layer are used. We exhibit some flow aligning effects for nematic liquid crystals with various ratio of rotary viscosities and investigate how unequal elastic constants (elastic anisotropy) alter the magnetic Fréedericksz transition in sheared nematics. Our calculations predict that surface boundary effects in nematic films and magnetic field action lead to existence of stationary flow regimes in the so-called nonflow aligning nematics, otherwise, surface and magnetic forces extend the range of viscous coefficient values corresponding to the flow aligning regimes. We show that imposing of shear flow on the Fréedericksz transition leads to a threshold behavior or to a “smoothing” of the transition. It depends on the orientation of the nematic layer in magnetic field and magnitudes of rotary viscous coefficients.

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time.

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.

In a two-dimensional rectangular microwave cavity dressed with one pointlike scatterer, a semiclassical approach is used to analyze the spectrum in terms of periodic orbits and diffractive orbits. We show, both numerically and experimentally, how the latter can be accounted for in the so-called length spectrum, which is retrieved from two-point correlations of a finite-range frequency spectrum. Beyond its fundamental interest, this first experimental evidence of the role played by diffractive orbits in the spectrum of an actual cavity, can be the first step towards a technique to detect and track small defects in wave cavities.

We study the control of oscillations in a system of inhibitory coupled noisy excitable and oscillatory units. Using dynamical properties of inhibition, we find regimes when the oscillations can be suppressed but the information signal of a certain frequency can be transmitted through the system. The mechanism of this phenomenon is a resonant interplay of noise and the transmission signal provided by certain value of inhibitory coupling. Analyzing a system of three or four oscillators representing neural clusters, we show that this suppression can be effectively controlled by coupling and noise amplitudes.

Dissipative effects in electromagnetism on macroscopic scales are examined by coarse-graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are formulated within the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework, accounting also for inhomogeneous temperature.

We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions $d=4$, 5, and 6 to be ${\varphi }_{\mathit{MRJ}}\approx 0.46$, 0.31, and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling form ${\varphi }_{\mathit{MRJ}}=c_1∕2^d+\left(c_{2}d\right)∕2^d$, where $c_1=-2.72$ and $c_2=2.56$, which appears to be consistent with the high-dimensional asymptotic limit, albeit with different coefficients. Calculations of the pair correlation function $g_2\left(r\right)$ and structure factor $S\left(k\right)$ for these states show that short-range ordering appreciably decreases with increasing dimension, consistent with a recently proposed “decorrelation principle,” which, among other things, states that unconstrained correlations diminish as the dimension increases and vanish entirely in the limit $d\to \infty$. As in three dimensions (where ${\varphi }_{\mathit{MRJ}}\approx 0.64$), the packings show no signs of crystallization, are isostatic, and have a power-law divergence in $g_2\left(r\right)$ at contact with power-law exponent $\approx 0.4$. Across dimensions, the cumulative number of neighbors equals the kissing number of the conjectured densest packing close to where $g_2\left(r\right)$ has its first minimum. Additionally, we obtain estimates for the freezing and melting packing fractions for the equilibrium hard-sphere fluid-solid transition, ${\varphi }_F\approx 0.32$ and ${\varphi }_M\approx 0.39$, respectively, for $d=4$, and ${\varphi }_F\approx 0.20$ and ${\varphi }_M\approx 0.25$, respectively, for $d=5$. Although our results indicate the stable phase at high density is a crystalline solid, nucleation appears to be strongly suppressed with increasing dimension.

The transport processes in dilute neutral gases are studied by using the kinetic equation with a collision relaxation model that meets all conservation requirements. The kinetic equation is solved keeping the whole anisotropic part of the distribution function with the use of the continued fractions. The conservative laws of the collision operator are taken into account with the projection operator techniques. The generalized heat flux and stress tensor are calculated in the linear approximation, as functions of the lower moments, i.e., the density, the flow velocity and the temperature. The results obtained are valid for arbitrary collision frequency $\nu$ with the respect to $k{v}_t$ and the characteristic frequency $\omega$, where $k^{-1}$ is the characteristic length scale of the system and $v_t$ is the thermal velocity. The transport coefficients constitute accurate closure relations for the generalized hydrodynamic equations. An application to the dispersion and the attenuation of sound waves in the whole collisionality regime is presented. The results obtained are in very good agreement with the experimental data.