Binary collisions between charged particles in an external magnetic field are considered within a classical second-order perturbation theory, i.e., up to contributions which are quadratic in the binary interaction, starting from the unperturbed helical motion of the particles. The calculations are done with the help of an improved binary collisions treatment which is valid for any strength of the magnetic field, where the second-order energy and velocity transfers are represented in Fourier space for arbitrary interaction potentials. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and nonsingular at the origin, and which involves as limiting cases the Debye (i.e., screened) and Coulomb potential. Two distinct cases are considered in detail: (i) the collision of two identical (e.g., electron-electron) particles, and (ii) the collision between a magnetized electron and a uniformly moving heavy ion. The energy transfer involves all harmonics of the electron cyclotron motion. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte Carlo calculations which also allows to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the nonperturbative numerical classical trajectory Monte Carlo results agree excellently with the predictions of the perturbative treatment.

We investigate the hydrodynamic response of plasma gradients during the interaction with ultraintense energetic laser pulses using kinetic particle simulations. Energetic laser pulses are capable of compressing preformed plasma gradients over short times, while accelerating low-density plasma backward. As light is absorbed on a steepened interface, hot-electron temperature and coupling efficiency drop below the ponderomotive scaling and we are left with an absorption mechanism that strongly relies on the electrostatic potential caused by low-density preformed plasma. We describe this process, discuss properties of the resulting electron spectra and identify the parameter regime where strong compression occurs. Finally, we discuss implications for fast ignition and other applications.

Under the generalized coherent-potential approximation, we established a “quasimode” theory to study the effective-medium properties of electromagnetic metamaterials. With this theory, we calculate the self-energy, density of states (DOS), and mean-free paths for optical modes traveling inside a metamaterial, and then determine the effective permittivity and permeability of the metamaterial by maximizing the DOS function. Compared with the traditional methods for calculating effective-medium parameters, the present approach could provide quantitative judgments on how meaningful are the obtained effective-medium parameters. As illustrations, we employed the theory to study the effective-medium properties of several examples including finite metallic wires and split ring resonators.

The telegraph equation combines features of both the diffusion and wave equations and has many applications to heat propagation, transport in disordered media, and elsewhere. We describe a quantum lattice gas algorithm (QLGA) for this partial differential equation with one spatial dimension. This algorithm generalizes one previously known for the diffusion equation. We present an analysis of the algorithm and accompanying simulation results. The QLGA is suitable for simulation on combined classical-quantum computers.

We report on the capillary rise of water in three-dimensional networks of hydrophilic silica pores with 3.5 nm and 5 nm mean radii, respectively (porous Vycor monoliths). We find classical square root of time Lucas-Washburn laws for the imbibition dynamics over the entire capillary rise times of up to 16 h investigated. Provided we assume two preadsorbed strongly bound layers of water molecules resting at the silica walls, which corresponds to a negative velocity slip length of $-0.5\text{nm}$ for water flow in silica nanopores, we can describe the filling process by a retained fluidity and capillarity of water in the pore center. This anticipated partitioning in two dynamic components reflects the structural-thermodynamic partitioning in strongly silica bound water layers and capillary condensed water in the pore center which is documented by sorption isotherm measurements.

We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a variant of the central limit theorem which is especially suited to models whose partition function is explicitly known. In particular, we provide a theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.

We present a numerical study of the zero-temperature response of the Gaussian random-field Ising model to a slowly varying external field, allowing the system to be trapped in microscopic configurations that are not fully metastable. This modification of the standard single-spin-flip dynamics results in an increase in dissipation (hysteresis) somewhat similar to that observed with a finite driving rate. We then study the distribution of avalanches along the hysteresis loop and perform a finite-size scaling analysis that shows good evidence that the critical exponents associated to the disorder-induced phase transition are not modified.

We investigate using a discrete element method the kinetic properties of a system composed of a bilayer of granular spheres submitted to a vertical vibration. For moderate dimensionless acceleration, no mixing between layers is observed and the horizontal velocity distributions of the top-layer particles with are quasi-Gaussian. The robustness of this phenomenon is examined for a variety of physical parameters (acceleration of the bottom plate, mass ratio, layer coverage, etc.). A microscopic analysis of the simulation dynamics leads to a simple picture of the underlying mechanisms.

We show that the rate of site-specific association of a protein molecule of interest with the DNA chain can be $\sim {10}^2$ times higher than that of the three-dimensional diffusion-controlled collision rate limit $\sim {10}^8{\text{mol}}^{-1}{\text{s}}^{-1}$ only when the protein molecule of interest searches for its specific site on the DNA chain in a reduced dimensional space with a dimensionality $d_r$ of $d_r<1$. Upon considering the concurrent dynamics of the linear DNA chain that is embedded in a $d$-dimensional space along with the one-dimensional diffusion dynamics of the nonspecifically bound protein molecule on the DNA chain, we derive the generalized scaling law $\epsilon \sim 2^{3\left(2-d\right)+3}$, where $\epsilon$ is the number of times by which the rate of site-specific association of the protein molecule with the DNA chain can be enhanced over the three-dimensional diffusion-controlled collision rate limit and $d$ is the dimensionality of the reduced search space. Using the analogy between the self-intersection loop length in the theory of random walks and the ring-closure events in the theory of site specific interactions of a protein molecule with the DNA chain, we further show that the extent of packaging and volume compression of the genomic DNA inside the living cell is designed in such a way that the efficiency of the protein molecule in the process of searching for its specific site on the genomic DNA is a maximum. Our simulation results suggest that the volume compression factor $\theta$ which is the ratio between the total volume of the living cell and the volume occupied by the DNA chain along with all the other bound protein molecules should be such that $\theta \ge 100$ for an efficient site specific interaction of a protein molecule of interest with the linear DNA chain that is embedded in a three-dimensional space. Our theoretical and simulation results agree well with the E. coli cellular system.

The Lyapunov exponents for Anderson localization are studied in a one-dimensional disordered system. A random Gaussian potential with the power-law decay $\sim 1/{\left|x\right|}^q$ of the correlation function is considered. The exponential growth of the moments of the eigenfunctions and their derivative is obtained. Positive Lyapunov exponents, which determine the asymptotic growth rate, are found.

Traffic flow is a function of many natural, environmental, and human factors. Not only that weather and road condition can vary, but drivers’ decisions and policies also can affect the flow. Here we analyze the effect of distribution of desired speeds. We show that a broader distribution can reduce the flow efficiency and increase congestions. Since different drivers react differently to changes in weather or road conditions, such a change leads to a change in desired speed distribution as well. As a result, nonintuitive changes in traffic flow may occur. Besides providing insight and analyzing the underlying mechanism of a collective phenomenon, this example sheds light on a fundamental aspect of computational modeling. Although “mean-field” models that deal with average values only and ignore variability are simpler and easier to analyze, they can very easily turn into oversimplifications and miss relevant qualitative phenomena.

When a drop (or gas bubble) is placed in a strong viscous flow (e.g., a shear flow), it develops very sharp tips at its ends. Sharp tips are also formed when a viscous fluid is withdrawn from the neighborhood of its interface with the ambient air or with another fluid (selective withdrawal). However, it is observed frequently that there exists a critical flow strength above which the drop transitions toward a “jetting state” in which a jet comes out from the tip. In this paper, we look numerically for stationary drop shapes, both globally and close to the tip, which we study with very high resolution. To this end we use a boundary integral method to solve the axisymmetric flow equations for arbitrary viscosity ratios in the inertialess (Stokes) limit. Stationary states are solved for using Newton’s method. This permits us to find both stable and unstable steady states and to investigate the nature of the jetting transition. The critical parameters for this transition are in reasonable agreement with slender-body theory. Excellent agreement is found with our earlier experiments in the selective withdrawal geometry [S. Courrech du Pont and J. Eggers, Phys. Rev. Lett. 96, 034501 (2006)], for which the viscosity of the phase inside the tip is negligible. We describe a scale invariance of the experimental interface profiles away from the tip. Then we investigate the highly curved tip region not considered previously with comparable precision. We find that the shape near the tip is universal, i.e., independent of the outer flow and of the geometry of the system (drop or selective withdrawal). While the tip curvature becomes extremely large, it always remains finite if surface tension is present.

We revisit the radial viscous fingering problem in a Hele-Shaw cell, and consider the action of viscous stresses originated from velocity gradients normal to the fluid-fluid interface. The evolution of the interface during linear and weakly nonlinear stages is described analytically through a mode-coupling approach. We find that the introduction of normal stresses influences the stability and the ultimate morphology of the emerging patterns. Although at early stages normal stresses tend to stabilize the interface, they act to favor the development of tip-splitting phenomena at the weakly nonlinear regime. We have also verified that finger competition events are only significantly affected by normal stresses for circumstances involving the development of a large number of interfacial fingers.

Two problems exist in the current studies on the application of the lattice Boltzmann method (LBM) to rarefied gas dynamics. First, most studies so far are applications of two-dimensional models. The numbers of velocity particles are small. Consequently, the boundary-condition methods of these studies are not directly applicable to a multispeed finite-difference lattice Boltzmann method (FDLBM) that has many velocity particles. Second, the LBM and FDLBM share their origins with the Boltzmann equation. Therefore, the results of LBM and FDLBM studies should be verified by the results of the continuous Boltzmann equation. In my review to date on the LBM studies, it appears that such verifications were seldom done. In this study, velocity slip and temperature jump simulations in the slip-flow regime were conducted using a three-dimensional FDLBM model. The results were compared with preceding theoretical studies based on the continuous Boltzmann equation. The results agreed with the theory with errors of a few percent. To further improve the accuracy of the FDLBM, it seems necessary to increase the number of velocity particles.

We study the thermoacoustic wave propagation and reflection near the liquid-gas critical point. Specifically, we perform a numerical investigation of the acoustic responses in a near-critical fluid to thermal perturbations based on the same setup of a recent ultrasensitive interferometry measurement in ${\text{CO}}_2$ [Y. Miura et al., Phys. Rev. E 74, 010101(R) (2006)]. The numerical results agree well with the experimental data. Different features regarding the reflection pattern of thermoacoustic waves near the critical point under pulse perturbations are revealed by the proper inclusion of the critically diverging bulk viscosity.

We study the relaxation of a single colloidal sphere which is periodically driven between two nonequilibrium steady states. Experimentally, this is achieved by driving the particle along a toroidal trap imposed by scanned optical tweezers. We find that the relaxation time after which the probability distributions have been relaxed is identical to the decay of the velocity autocorrelation function measured in a steady state. In quantitative agreement with theoretical calculations the relaxation time strongly increases when driving the system further away from thermal equilibrium.

We consider diffusion-controlled evolution of the $A$-particle island – $B$-particle island system in a semi-infinite medium at propagation of the sharp annihilation front $A+B\to 0$. We show that depending on the initial particle number ratio, the system demonstrates three asymptotic regimes: self-accelerating collapse of one of the islands, synchronous power-law relaxation of both islands, and exponential death of one of the islands at a constant velocity of front propagation. We find asymptotic scaling laws of evolution in these regimes and reveal the limits of their applicability for the cases of mean field and fluctuation fronts.

We investigate the condensation phenomena of conserved-mass aggregation (CA) with mass-dependent diffusion rate on scale-free networks (SFNs). In the model, the mass $m$ of a node isotropically diffuses to one of directly linked nodes with rate $D\left(m\right)=m^{-\alpha }$, where $\alpha >0$. With rate $\omega$, unit mass is chipped from the mass and also isotropically diffuses. It was shown that no condensation phase transitions occur on regular lattices. However, on SFNs with degree distribution $P\left(k\right)\sim k^{-\gamma }$, we show from mean-field approximation that the model exhibits various types of condensation phenomena according to $\alpha$ and $\gamma$. There exists crossover ${\alpha }_c=\left(\gamma -2\right)/\left(\gamma -1\right)$ over which a system undergoes the same type of the condensation as that of zero-range process with jumping rate $p\left(m\right)=m^{\delta }$ regardless of $\gamma \left(>2\right)$. We find $\delta =1-\alpha$ for ${\alpha }_c\le \alpha <1$ and $\delta =0$ for $\alpha \ge 1$. For $\alpha <{\alpha }_c$, however, the diffusion of masses cannot be ignored and so a system exhibits different behavior according to the network structure, i.e., $\gamma$. For $\gamma >3$, a system exhibits the behavior on regular lattice. For $\gamma \le 3$, the condensation always occurs for any density with non-power-law background mass distribution. We also numerically confirm the mean-field predictions. Therefore, the network structure leads to the various condensation phenomena of the CA model unlike on regular lattices.

A nonlinear streamwise traveling-wave solution is obtained by homotopy for square duct flow. For a particular symmetry of the perturbations, this wave comes into existence at about ${\text{Re}}_b=600$ (based on half-duct width and bulk speed) for a streamwise wave number $\alpha =0.85$. The resulting four-vortex mean flow resembles the transitional flow structures observed in previous simulations.