We report an experimental observation suggesting plasma channel formation by focusing a relativistic laser pulse into a long-scale-length preformed plasma. The channel direction coincides with the laser axis. Laser light transmittance measurement indicates laser channeling into the high-density plasma with relativistic self-focusing. A three-dimensional particle-in-cell simulation reproduces the plasma channel and reveals that the collimated hot-electron beam is generated along the laser axis in the laser channeling. These findings hold the promising possibility of fast heating a dense fuel plasma with a relativistic laser pulse.

We study the distribution of domain areas, areas enclosed by domain boundaries (“hulls”), and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial conditions. We show that the number of hulls per unit area, $n_h(A,t)dA$, with enclosed area in the interval $(A,A+dA)$, is described, for a disordered initial condition, by the scaling function $n_h(A,t)=2c_h∕{(A+{\lambda }_{h}t)}^2$, where $c_h=1∕8\pi \sqrt{3}\approx 0.023$ is a universal constant and ${\lambda }_h$ is a material parameter. For a critical initial condition, the same form is obtained, with the same ${\lambda }_h$ but with $c_h$ replaced by $c_h∕2$. For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form $n_d(A,t)=2c_d{\left({\lambda }_{d}t\right)}^{{\tau }^{\prime }-2}∕{(A+{\lambda }_{d}t)}^{{\tau }^{\prime }}$, where $c_d$ and ${\lambda }_d$ are numerically very close to $c_h$ and ${\lambda }_h$, respectively, and ${\tau }^{\prime }=187∕91\approx 2.055$. For critical initial conditions, one replaces $c_d$ by $c_d∕2$ and the exponent is $\tau =379∕187\approx 2.027$. These results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins. These predictions are supported by extensive numerical simulations. We also study numerically the geometric properties of the boundaries and areas.

In a well-dispersed nanofluid with strong cluster-fluid attraction, thermal conduction paths can arise through percolating amorphouslike interfacial structures. This results in a thermal conductivity enhancement beyond the Maxwell limit of $3\varphi$, with $\varphi$ being the nanoparticle volume fraction. Our findings from nonequilibrium molecular dynamics simulations, which are amenable to experimental verification, can provide a theoretical basis for the development of future nanofluids.

Methods to search for periodic orbits are usually implemented with the Newton-Raphson type algorithms that extract the orbits as fixed points. When used to find periodic orbits in flows, however, many such approaches have focused on using mappings defined on the Poincaré surfaces of section, neglecting components perpendicular to the surface of section. We propose a Newton-Raphson based method for Hamiltonian flows that incorporates these perpendicular components by using the full monodromy matrix. We investigated and found that inclusion of these components is crucial to yield an efficient process for converging upon periodic orbits in high dimensional flows. Numerical examples with as many as nine degrees of freedom are provided to demonstrate the effectiveness of our method.

The energetics of the stochastic process has shown the balance of energy on the mesoscopic level. The heat and the energy defined there are, however, generally different from their macroscopic counterpart. We show that this discrepancy can be removed by adding to these quantities the reversible heat associated with the mesoscopic free energy.

The clustering and nucleation of ions in aqueous solutions results from a competition between ion hydration and association. Molecular dynamics simulations of aqueous NaCl solutions are used to investigate ion clustering with a force field adjusted to reproduce experimental properties of the pure NaCl crystal and melt, and of concentrated solutions. The simulation results point to strong sensitivity of the nucleation mechanism to small changes in the force field. We report the numerical evidence for rapid crystal nucleation near saturation or under supercritical conditions.

Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, i.e., by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor $S^{-1}\left(k\right)$ predicted by a “one-loop” approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of an UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to $S^{-1}\left(k\right)$ is shown to be the sum of (i) a $k$-independent contribution that arises from a renormalization of the effective $\chi$ parameter, (ii) a $k$-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to $k^2$ that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a $k$-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.

Chaotic itinerancy is a universal dynamical concept that describes itinerant motion among many different ordered states through chaotic transition in dynamical systems. Unlike the expectation of the prevalence of chaotic itinerancy in high-dimensional systems, we identify chaotic itinerant behavior from a relatively simple ecological system, which consists only of two coupled consumer-resource pairs. The system exhibits chaotic bursting activity, in which the explosion and the shrinkage of the population alternate indefinitely, while the explosion of one pair co-occurs with the shrinkage of the other pair. We analyze successfully the bursting activity in the framework of chaotic itinerancy, and find that large duration times of bursts tend to cluster in time, allowing the effective burst prognosis. We also investigate the control schemes on the bursting activity, and demonstrate that invoking the competitive rise of the consumer in one pair can even elongate the burst of the other pair rather than shorten it.

The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and derive the corresponding scaling properties in the critical region. For scale-free networks with the degree distribution $P\left(k\right)\sim k^{-\gamma }$ at large $k$, we found that the finite-size exponent $\overline{\nu }$ takes on the value 5/2 when $\gamma >5$, the same as in the globally coupled Kuramoto model. For highly heterogeneous networks $\left(3<\gamma <5\right)$, $\overline{\nu }$ and the order parameter exponent $\beta$ depend on $\gamma$. The analytical expressions for these exponents obtained from the mean-field theory are shown to be in excellent agreement with data from extensive numerical simulations.

We propose here a model to simulate the process of opinion formation, which accounts for the mutual affinity between interacting agents. Opinion and affinity evolve self-consistently, manifesting a highly nontrivial interplay. A continuous transition is found between single and multiple opinion states. Fractal dimension and signature of critical behavior are also reported. A rich phenomenology is presented and discussed with reference to corresponding psychological implications.

We study a large-scale instability in a sheared nonhelical turbulence that causes generation of large-scale vorticity. Three types of the background large-scale flows are considered, i.e., the Couette and Poiseuille flows in a small-scale homogeneous turbulence, and the “log-linear” velocity shear in an inhomogeneous turbulence. It is known that laminar plane Couette flow and antisymmetric mode of laminar plane Poiseuille flow are stable with respect to small perturbations for any Reynolds numbers. We demonstrate that in a small-scale turbulence under certain conditions the large-scale Couette and Poiseuille flows are unstable due to the large-scale instability. This instability causes formation of large-scale vortical structures stretched along the mean sheared velocity. The growth rate of the large-scale instability for the “log-linear” velocity shear is much larger than that for the Couette and Poiseuille background flows. We have found a turbulent analogue of the Tollmien-Schlichting waves in a small-scale sheared turbulence. A mechanism of excitation of turbulent Tollmien-Schlichting waves is associated with a combined effect of the turbulent Reynolds stress-induced generation of perturbations of the mean vorticity and the background sheared motions. These waves can be excited even in a plane Couette flow imposed on a small-scale turbulence when perturbations of mean velocity depend on three spatial coordinates. The energy of these waves is supplied by the small-scale sheared turbulence.

We investigate the interplay between substrate roughness and surrounding gas pressure in controlling the dynamics of splashing when a liquid drop hits a dry solid surface. We associate two distinct forms of splashing with each of these control parameters: Prompt splashing is due to surface roughness and corona splashing is due to instabilities produced by the surrounding gas. The size distribution of ejected droplets reveals the length scales of the underlying droplet-creation process in both cases.

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

This is the first paper of a series of three, in which we report on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. The influence of various assembling processes on packing microstructures is investigated. It is accurately checked that frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, higher solid fractions corresponding to more ordered configurations with traces of crystallization. Specific properties directly related to isostaticity of the force-carrying structure in the rigid limit are discussed. With frictional grains, different preparation procedures result in quite different inner structures that cannot be classified by the sole density. If partly or completely lubricated they will assemble like frictionless ones, approaching the RCP solid fraction ${\Phi }_{\mathrm{RCP}}\simeq 0.639$ with a high coordination number: $z^{*}\simeq 6$ on the force-carrying backbone. If compressed with a realistic coefficient of friction $\mu =0.3$ packings stabilize in a loose state with $\Phi \simeq 0.593$ and $z^{*}\simeq 4.5$. And, more surprisingly, an idealized “vibration” procedure, which maintains an agitated, collisional regime up to high densities results in equally small values of $z^{*}$ while $\Phi$ is close to the maximum value ${\Phi }_{\mathrm{RCP}}$. Low coordination packings have a large proportion $(>10\%)$ of rattlers—grains carrying no force—the effect of which should be accounted for on studying position correlations, and also contain a small proportion of localized “floppy modes” associated with divalent grains. Low-pressure states of frictional packings retain a finite level of force indeterminacy even when assembled with the slowest compression rates simulated, except in the case when the friction coefficient tends to infinity. Different microstructures are characterized in terms of near neighbor correlations on various scales, and some comparisons with available laboratory data are reported, although values of contact coordination numbers apparently remain experimentally inaccessible.

This is the second paper of a series of three investigating, by numerical means, the geometric and mechanical properties of spherical bead packings under isotropic stresses. We study the effects of varying the applied pressure $P$ (from 1 or $10\mathrm{kPa}$ up to $100\mathrm{MPa}$ in the case of glass beads) on several types of configurations assembled by different procedures, as reported in the preceding paper [I. Agnolin and J.-N. Roux, Phys. Rev. E 76, 061302 (2007)]. As functions of $P$, we monitor changes in solid fraction $\Phi$, coordination number $z$, proportion of rattlers (grains carrying no force) $x_0$, the distribution of normal forces, the level of friction mobilization, and the distribution of near neighbor distances. Assuming that the contact law does not involve material plasticity or damage, $\Phi$ is found to vary very nearly reversibly with $P$ in an isotropic compression cycle, but all other quantities, due to the frictional hysteresis of contact forces, change irreversibly. In particular, initial low $P$ states with high coordination numbers lose many contacts in a compression cycle and end up with values of $z$ and $x_0$ close to those of the most poorly coordinated initial configurations. Proportional load variations which do not entail notable configuration changes can therefore nevertheless significantly affect contact networks of granular packings in quasistatic conditions.

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures, as described in the first companion paper, and then subjected to a varying confining pressure, as reported in the second companion paper, are investigated. In addition to the pressure, which determines the stiffness of contacts because of Hertz’s law, elastic moduli are chiefly sensitive to the coordination number $z$, which should not be regarded as a function of the packing density. Comparisons of numerical and experimental results for glass beads in the $10\mathrm{kPa}–10\mathrm{MPa}$ pressure range reveal similar differences between dry samples prepared in a dense state by vibrations and lubricated packings, so that the greater stiffness of the latter, in spite of their lower density, can be attributed to a larger coordination number. Effective medium type approaches, or Voigt and Reuss bounds, provide good estimates of bulk modulus $B$, which can be accurately bracketed, but badly fail for shear modulus $G$, especially in low $z$ configurations under low pressure. This is due to the different response of tenuous, fragile networks to changes in load direction, as compared to load intensity. In poorly coordinated packings, the shear modulus, normalized by the average contact stiffness, tends to vary proportionally to the degree of force indeterminacy per unit volume, even though this quantity does not vanish in the rigid limit. The elastic range extends to small strain intervals and compares well with experimental observations on sands. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.

Time-domain perturbation theory of photon diffusion up to third order was evaluated for its accuracy in deducing optical properties of breast tumors using simulated and physical phantoms and by analyzing 141 projection mammograms of 87 patients with histology-validated tumors that had been recorded by scanning time-domain optical mammography. The slightly compressed breast was modeled as (partially) homogeneous diffusely scattering infinite slab containing a scattering and absorbing spherical heterogeneity representing the tumor. Photon flux densities were calculated from densities of transmitted photons, assuming extended boundary conditions. Explicit formulas are provided for second-order changes in transmitted photon density due to the presence of absorbers or scatterers. The results on phantoms obtained by perturbation theory carried up to third order were compared with measured temporal point spread functions, with numerical finite-element method (FEM) simulations of transmitted photon flux density, with results obtained from the diffraction of diffuse photon density waves, and from Padé approximants. The breakdown of first-, second-, and third-order perturbation theory is discussed for absorbers and a general expression was derived for the convergence of the Born series in this case. Taking tumor optical properties derived by the diffraction model as reference we conclude that estimates of tumor absorption coefficients by perturbation theory agree with reference values within $\pm 25\%$ in only 65% (first order), 66% (second order), and 77% (third order) of all mammograms analyzed. In the remaining cases tumor absorption is generally underestimated due to the breakdown of perturbation theory. On average the empirical Padé approximants yield tumor absorption coefficients similar to third-order perturbation theory, yet at noticeable lower computational efforts.

Owing to the superhydrophobicity of their legs, such creatures as water striders and fisher spiders can stand effortlessly, walk and jump quickly on water. Directed toward understanding their superior repellency ability, we consider hydrophobic thin rods of several representative cross sections pressing a water surface. First, the shape function of the meniscus surrounding a circular rod is solved analytically, and thereby the maximal buoyant force is derived as a function of the Young’s contact angle and the rod radius. Then we discuss the critical conditions for a rod to sink into water, including the maximal volume condition and the meniscus-contact condition. Furthermore, we study the sinking conditions and the maximal buoyant forces of hydrophobic long rods with elliptical, triangular, or hexagonal cross-section shapes. The theoretical solutions are quantitatively consistent with existing experimental and numerical results. Finally, the optimized structures of water strider legs are analyzed to elucidate why they can achieve a very big buoyant force on water.

We simulated the diffusion process into oil-saturated porous media using the modified diffusion-limited aggregation and the lattice Boltzmann method algorithms. The results were matched to visual experiments for cocurrent (two sides of the model open to flow) and countercurrent (only one side of the model open to flow) diffusion for horizontally and vertically positioned samples. The model saturated with oil was exposed to pentane in order for a miscible interaction to take place. These experiments mimic the transfer between the rock matrix and fracture during gas or liquid solvent injection for enhanced oil recovery, underground waste disposal, groundwater contamination, and $\mathrm{C}{\mathrm{O}}_2$ sequestration in naturally fractured reservoirs. Finger development at the early stages of the process was controlled by oil viscosity and the interaction type dictated by the boundary conditions. The convective transport driven by the buoyancy that was experimentally observed on vertically oriented samples and transfer driven by diffusion on the horizontal ones were captured in the LBM simulation of the process.