Since the experimental observation of antiwaves in reaction-diffusion (RD) systems, the discrepancy between the theoretical prediction and the experimental observation on the transition from inwardly rotating chemical waves to normal waves remains an unsolved problem. Theoretical predictions using both RD model and complex Ginzberg-Landau equation indicate that there exists a trend in which wave vector approaches to zero in the transition process, while disordered plane waves near the onset were observed in experiment. This discrepancy motivated us to conduct a systematic research to investigate the transition. Using chlorite-iodide-malonic acid reaction as model system and with a thorough parameter scanning, we found clear trend that the wave vector decreased near the transition point, where wavelength diverged. This observation is consistent with the theoretical predictions. However, disordered plane waves appeared in the region near the onset. Comparing the experimental results with the results from numerical simulation, we found that spatial inhomogeneity of the diffusion coefficient was the main cause of the disordered plane waves.

Slip boundary conditions for the velocity field impact on the spectral properties of the advection-diffusion operator describing transport of passive particles in laminar parallel flows. By considering the Hermitian operator (referred to as the weighted Laplacian), describing the interplay between axial convection and cross-sectional diffusion of a scalar field, we show that the spectral watershed between slip and no-slip boundary conditions is a qualitatively different scaling behavior of the mean of the normalized eigenfunctions of the weighted Laplacian. The occurrence of slip conditions also influences the scaling of the density of states as regards both the leading and the subleading term in the Weyl’s expansion.

Expanded-ensemble Monte Carlo method with Wang-Landau algorithm was used for calculations of the ratio of partition functions for classes of permutations in the problem of several interacting quantum particles (fermions) in an external field. Simulations for systems consisting of 2 up to 7 interacting particles in harmonic or Coulombic field were performed. The presented approach allows one to carry out calculations for low enough temperatures that makes it possible to extract data for the ground-state energy and low-temperature thermodynamics.

We conduct an investigation into the dispersive post-shock oscillations in an entropic lattice-Boltzmann method (ELBM), in particular the entropic lattice-Bhatnagar-Gross-Krook (ELBGK) scheme. Simulations on the one-dimensional shock tube show no benefit in terms of regularization from using ELBGK over the standard LBGK. We also conduct an experiment investigating equipping the LBGK method with median filtering (a local method) at a single point per tim e step. Here we observe that significant regularization of a systemic problem can be achieved with a local method of correction.

The normal phase diffusion problem in magnetic resonance imaging (MRI) is treated by means of the Langevin equation for the phase variable using only the properties of the characteristic function of Gaussian random variables. The calculation may be simply extended to anomalous diffusion using a fractional generalization of the Langevin equation proposed by Lutz [E. Lutz, Phys. Rev. E 64, 051106 (2001)] pertaining to the fractional Brownian motion of a free particle coupled to a fractal heat bath. The results compare favorably with diffusion-weighted experiments acquired in human neuronal tissue using a 3 T MRI scanner.

Particles floating on the surface of a turbulent incompressible fluid accumulate along string-like structures, while leaving large regions of the flow domain empty. This is reflected experimentally by a very peaked probability distribution function of $c_r$, the coarse-grained particle concentration at scale $r$, around $c_r=0$, with a power-law decay over two decades of $c_r$, $\Pi \left(c_r\right)\propto c_r^{-{\beta }_r}$. The positive exponent ${\beta }_r$ decreases with scale in the inertial range and stays approximately constant in the dissipative range, thus, indicating a qualitative difference between the dissipative and the inertial ranges of scales, also visible in the first moment of $c_r$.

Absolute spectral emissivities for Doppler broadened ${\text{H}}_{\alpha }$ profiles are measured and compared with predictions of energetic hydrogen ion, atom, and molecule behavior in low-current electrical discharges in ${\text{H}}_2$ at very high electric field $E$ to gas density $N$ ratios $E/N$ and low values of $Nd$, where $d$ is the parallel-plate electrode separation. These observations reflect the energy and angular distributions for the excited atoms and quantitatively test features of multiple-scattering kinetic models in weakly ionized hydrogen in the presence of an electric field that are not tested by the spatial distributions of ${\text{H}}_{\alpha }$ emission. Absolute spectral intensities agree well with predictions. Asymmetries in Doppler profiles observed parallel to the electric field at $4\le E/N\le 20\text{kTd}$ result primarily from excitation by fast H atoms directed toward the cathode and diffusely reflected from the cathode. $\left(1\text{Td}={10}^{-21}\text{V}{\text{m}}^2\right)$ The effects of reflection of hydrogen particles and of changes with cathode material are modeled accurately without adjustable parameters. Maximum measured wavelength shifts result from acceleration of ${\text{H}}^{+}$ ions and charge transfer to fast H atoms. The Doppler profiles are consistent with models of reactions among ${\text{H}}^{+}$, ${\text{H}}_2^{+}$, ${\text{H}}_3^{+}$, H, and ${\text{H}}_2$ leading to fast H atoms and then fast excited $\text{H}\left(n=3\right)$ atoms.

Based on fully kinetic model using drift-Maxwellian distributions and taking into account the transverse electrostatic field (TEF), it is shown that the current-filamentation instability (CFI) grows unexpectedly with the plasma temperature. The growth is attributed to the decreasing of the TEF as the plasma becomes hot. In the low-temperature plasma regime where the TEF is strong, it is identified that the TEF can dominate over the thermal pressure in suppressing the CFI. Since the TEF originates from the temperature difference between the beam and the plasma, the plasma temperature plays a significant role for the development of the CFI and the quasistatic magnetic fields in a hot-beam warm-plasma system. Particle-in-cell simulations verify the above results.

The classical problem of radiation emitted by an accelerated charge in the relativistic case is considered. Only accelerations which occur in a short time interval are taken into account. We first discuss the one dimensional trajectories, for later extending the analysis to the two-dimensional case by means of a first-order approximation. We find an expression for the allowed radiated frequencies and we discuss the inconvenience of the concept of formation time of radiation. The results allow us to treat the case of successive collisions, in order to study the behavior of the interference terms.

A combination of two molecular simulation algorithms has been used to determine the solid-liquid coexistence of the Weeks-Chandler-Andersen (WCA) fluid from low temperatures up to very high temperatures. Values are reported for the coexistence pressure, temperature, energy, enthalpy change, and densities of both the liquid and solid phases. At very high temperatures, the coexistence pressure approaches the same 12th-power soft-sphere asymptote as the 12–6 Lennard-Jones potential. However, in contrast to the Lennard-Jones potential, which shows a discontinuity of pressure at low temperatures, the coexistence pressure of the WCA potential approaches the zero-temperature limit. Empirical relationships are determined to accurately reproduce the coexistence pressure and both solid and liquid phase densities from near zero temperature to very high temperatures. The simulation data are used to improve the accuracy of a WCA equation of state. The validity of common melting and freezing rules is tested.

We introduce a method for estimating the wettability of rock/oil/brine systems using noninvasive in situ nuclear magnetic relaxation dispersion. This technique scans over a large range of applied magnetic fields and yields unique information about the extent to which a fluid is dynamically correlated with a solid rock surface. Unlike conventional transverse relaxation studies, this approach is a direct probe of the dynamical surface affinity of fluids. To quantify these features we introduce a microscopic dynamical surface affinity index which measures the dynamical correlation (i.e., the microscopic wettability) between the diffusive fluid and the fixed paramagnetic relaxation sources at the pore surfaces. We apply this method to carbonate reservoir rocks which are known to hold about two thirds of the world’s oil reserves. Although this nondestructive method concerns here an application to rocks, it could be generalized as an in situ liquid/surface affinity indicator for any multimodal porous medium including porous biological media.

In recent years, there has been a growing interest in studying the role of costly punishment in promoting altruistic behaviors among selfish individuals. Rejections in ultimatum bargaining as a metaphor exemplify costly punishment, where the division of a sum of resources proposed by one side may be rejected by the other side, and both sides get nothing. Under a setting of the network of contacts among players, we find that the largest Laplacian eigenvalue of the network determines the critical division of players’ proposals, below which pure punishers who never accept any offers will emerge as a phase transition in the system. The critical division of offers that predicts the emergence of costly punishment is termed as the selfishness tolerance of a network within evolutionary ultimatum game, and extensive numerical simulations on the data of the science collaboration network, and computer-generated small-world/scale-free networks support the analytical findings.

We empirically study the market impact of trading orders. We are specifically interested in large trading orders that are executed incrementally, which we call hidden orders. These are statistically reconstructed based on information about market member codes using data from the Spanish Stock Market and the London Stock Exchange. We find that market impact is strongly concave, approximately increasing as the square root of order size. Furthermore, as a given order is executed, the impact grows in time according to a power law; after the order is finished, it reverts to a level of about 0.5–0.7 of its value at its peak. We observe that hidden orders are executed at a rate that more or less matches trading in the overall market, except for small deviations at the beginning and end of the order.

We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem’s linear limit, we identify the system’s eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in detail. We observe that the nonlinearity leads to a frequency dependence in the amplitude of the oscillations, a static mutual displacement of the parts of the chain separated by a defect, and for chains with two defects that are not in contact, it induces symmetry-breaking bifurcations.

We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper [Phys. Rev. Lett. 97, 230602 (2006)], our algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of superhops, one particle at a time. By partitioning the simulation space into nonoverlapping protecting domains each containing only one or two particles, the algorithm factorizes the $N$-body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective domains is enabled through the use of time-dependent Green’s functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte Carlo model exactly. Extensive numerical examples demonstrate that for an important class of diffusion-reaction models the algorithm is efficient at low particle densities, where other existing algorithms slow down severely.

A modified delayed feedback control algorithm with the improved global properties is proposed. The modification is based on the ergodic features of chaotic systems. We do not perturb the system until its state approaches a desired unstable periodic orbit and then we activate the delayed feedback control force. To evaluate the closeness of the system state to the target orbit, a special algorithm is devised. For continuous-time systems, it can be implemented by means of a simple low-pass filter. An additional low-pass filter can be used for selection of the particular orbit from several unstable orbits of the same period.

The inference of causal interaction structures in multivariate systems enables a deeper understanding of the investigated network. Analyzing nonlinear systems using partial directed coherence requires high model orders of the underlying vector-autoregressive process. We present a method to overcome the drawbacks caused by the high model orders. We calculate the corresponding statistics and provide a significance level. The performance is illustrated by means of model systems and in an application to neurological data.

We calculate the temperature-dependent condensate density ${\rho }^0\left(T\right)$ of interacting bosons in three dimensions using the functional renormalization group (FRG). From the numerical solution of suitably truncated FRG flow equations for the irreducible vertices we obtain ${\rho }^0\left(T\right)$ for arbitrary temperatures. We carefully extrapolate our numerical results to the critical point and determine the order parameter exponent $\beta \approx 0.32$ in reasonable agreement with the expected value 0.345 associated with the $XY$-universality class. We also calculate the condensate density in two dimensions at zero temperature using a truncation of the FRG flow equations based on the derivative expansion including cubic and quartic terms in the expansion of the effective potential in powers of the density. As compared with the widely used quadratic approximation for the effective potential, the coupling constants associated with the cubic and quartic terms lead to small corrections of the condensate density.

This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed provided all these superpositions have the same fixed energy. Such a condition is not equivalent to the conventional microcanonical condition because the latter limits the participating eigenstates to a very narrow energy window. The statistics is obtained analytically for both the entire system and its small subsystem. In a significant departure from the Boltzmann-Gibbs statistics, the average occupation numbers of quantum states exhibit in the present case weak algebraic dependence on energy. In the macroscopic limit, this dependence is routinely accompanied by the condensation into the lowest-energy quantum state. This work contains initial numerical tests of the above statistics for finite systems and also reports the following numerical finding: when the basis states of large but finite random matrix Hamiltonians are expanded in terms of eigenstates, the participation of eigenstates in such an expansion obeys the newly obtained statistics. The above statistics might be observable in small quantum systems, but for the macroscopic systems, it rather re-enforces doubts about self-sufficiency of nonrelativistic quantum mechanics for justifying the Boltzmann-Gibbs equilibrium.

We show that for the Boolean model of random composite media one can, from a single image of a system at any particle fraction, define a set of parameters which allows one to accurately reconstruct the medium for all other phase fractions. The morphological characterization is based on a family of measures known in integral geometry which provides powerful formulas for the Boolean model. The percolation thresholds of either phase are obtained with good accuracy. From the reconstructions one can subsequently predict property curves for the material across all phase fractions from the single three-dimensional image. We illustrate this for transport and mechanical properties of complex Boolean systems and for experimental sandstone samples.