We investigate the generation of ultrashort $K\alpha$ pulses from plasmas produced by intense femtosecond $p$-polarized laser pulses on Copper and Titanium targets. Particular attention is given to the interplay between the angle of incidence of the laser beam on the target and a controlled prepulse. It is observed experimentally that the $K\alpha$ yield can be optimized for correspondingly different prepulse and plasma scale-length conditions. For steep electron-density gradients, maximum yields can be achieved at larger angles. For somewhat expanded plasmas expected in the case of laser pulses with a relatively poor contrast, the $K\alpha$ yield can be enhanced by using a near-normal-incidence geometry. For a certain scale-length range (between 0.1 and 1 times a laser wavelength) the optimized yield is scale-length independent. Physically this situation arises because of the strong dependence of collisionless absorption mechanisms—in particular resonance absorption—on the angle of incidence and the plasma scale length, giving scope to optimize absorption and hence the $K\alpha$ yield. This qualitative description is supported by calculations based on the classical resonance absorption mechanism and by particle-in-cell simulations. Finally, the latter simulations also show that even for initially steep gradients, a rapid profile expansion occurs at oblique angles in which ions are pulled back toward the laser by hot electrons circulating at the front of the target. The corresponding enhancement in $K\alpha$ yield under these conditions seen in the present experiment represents strong evidence for this suprathermal shelf formation effect.

We investigate the optical trapping of a Rayleigh particle by a linearly or radially polarized Gaussian beam. The Mie theory is applied to obtain a full solution, with the incident beam being described by the mixed dipole model, which is beyond the paraxial approximation. We then obtain approximate analytical expressions for the optical force, equilibrium position, and trap stiffness for a Rayleigh particle. At equilibrium, the displacement for the particle from the focus scales like $a^3$ (where $a$ is the radius) for a transparent particle, owing to scattering, whereas for absorptive particles it scales like $C+D{a}^2$, owing to absorption. The trap stiffness is found to be proportional to $a^3$, in agreement with the recent experiment. The radially polarized beam is found to be superior to the linearly polarized beam in the Rayleigh regime in terms of its ability to trap. It is found that the larger the ratio of ${\epsilon }_r/{\epsilon }_i$, the closer the equilibrium to the focus, and thus higher stability.

A lattice Boltzmann model for two-dimensional wave equation is proposed by using the higher-order moment method. The higher-order moment method is based on the solution of a series of partial differential equations obtained by using multiscale technique and Chapman-Enskog expansion. In order to obtain the lattice Boltzmann model for the wave equation with higher-order accuracy of truncation errors, we removed the second-order dissipation term and the third-order dispersion term by employing the moments up to fourth order. The reversibility in time appears owing to the absence of the second-order dissipation term and the third-order dispersion term. As numerical examples, some classical examples, such as interference, diffraction, and wave passing through a convex lens, are simulated. The numerical results show that this model can be used to simulate wave propagation.

We propose a generic model to describe the mechanical response and failure of systems which undergo a series of stick-slip events when subjected to an external load. We model the system as a bundle of fibers, where single fibers can gradually increase their relaxed length with a stick-slip mechanism activated by the increasing load. We determine the constitutive equation of the system and show by analytical calculations that on the macroscale a plastic response emerges followed by a hardening or softening regime. Releasing the load, an irreversible permanent deformation occurs which depends on the properties of sliding events. For quenched and annealed disorder of the failure thresholds the same qualitative behavior is found, however, in the annealed case the plastic regime is more pronounced.

We analyze transport through conical channels that is driven by the difference in particle concentrations on the two sides of the membrane. Because of the detailed balance, fluxes of noninteracting particles through the same channel, inserted into the membrane in two opposite orientations, are equal. We show that this flux symmetry is broken by particle-particle interactions so that one of the orientations can be much more efficient for transport under the same external conditions. The results are obtained analytically using a one-dimensional diffusion model and confirmed by three-dimensional Brownian dynamics simulations.

Transport and diffusion of particles on modulated surfaces is a nonequilibrium problem which is receiving a great deal of attention due to its technological applications, but analytical calculations are scarce. In earlier work, we developed a perturbative approach to begin to provide an analytic platform for predictions about particle trajectories over such surfaces. In some temperature and forcing regimes, we successfully reproduced results for average particle velocities obtained from numerical simulations. In this paper, we extend the perturbation theory to the calculation of higher moments, in particular the diffusion tensor and the skewness. Numerical simulations are used to check the domain of validity of the perturbative approach.

We study through numerical simulations the dependence of the hydraulic permeability of granular materials on the particle shape and the grain size distribution. Several models of sand are constructed by simulating the settling under gravity of the grains; the friction coefficient is varied to construct packs of different porosity. The size distribution and shapes of the grains mimic real sands. Fluid flow is simulated in the resulting packs using a finite element method and the permeability of the packs is successfully compared with available experimental data. Packs of nonspherical particles are less permeable than sphere packs of the same porosity. Our results indicate that the details of grain shape and size distribution have only a small effect on the permeabilty of the systems studied.

We present experimental results on the equilibrium microstructure of a sedimented magnetorheological suspension, namely, an aqueous suspension of micron-sized superparamagnetic particles. We develop a study of the electrical interactions on the suspension by processing video-microscopy images of the sedimented particles. We calculate the pair distribution function, $g\left(r\right)$, which yields the electrostatic pair potential $u\left(r\right)$, showing an anomalous attractive interaction for distances on the order of twice the particle diameter, with characteristic parameters whose values show a dependence with the two-dimensional concentration of particles. The repulsive body of the potential is adjusted to a DLVO expression in order to calculate the Debye screening length and the effective surface charge density. Influence of confinement and variations on the Boltzmann sedimentation profile because of the electrostatic interactions appear to be essential for the interpretation of experimental results

In this paper, a multiscale approach spanning atomistic and mesoscopic regimes to model the rheology of suspensions that have strongly interacting particles in highly viscous solvents is presented. The model suspensions studied here have 65% sucrose solution—a Newtonian fluid with a viscosity of 170 cP at room temperature—as the solvent phase with ceramic particles of sizes on the order of a few $\mu \text{ms}$ as the dispersed (solute) phase. A multiscale approach is proposed to quantitatively account for the effect of the properties of constituent materials on the bulk rheology of the suspension apart from the effect of hydrodynamic factors. A dissipative particle dynamics-type particle-based approach is adopted to which material-specific, mesoscopic force fields developed using molecular dynamics are fed. Issues pertaining to the handling of the vast spectrum of time and length scales present and an appropriate Gallilean-invariant thermostat for solvent dynamics are addressed and resolved. Numerical calculations compare reasonably well to experimentally measured viscosities up to reasonably high Peclet numbers $\left(\sim {10}^4\right)$.

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type $A$ and one is of type $B$; the bonding interactions between each pair of spots have strengths ${ϵ}_{AA}$, ${ϵ}_{BB}$, and ${ϵ}_{AB}$. The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains $\left({ϵ}_{AA}\ne 0,{ϵ}_{AB}={ϵ}_{BB}=0\right)$, hyperbranched polymers $\left({ϵ}_{AB}\ne 0,{ϵ}_{AA}={ϵ}_{BB}=0\right)$, and dimers $\left({ϵ}_{BB}\ne 0,{ϵ}_{AA}={ϵ}_{AB}=0\right)$. These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains ($AA$ clusters connected by a few $AB$ or $BB$ bonds); of hyperbranched polymers ($AB$ clusters connected by $AA$ bonds); or of dimers ($BB$ clusters connected by $AA$ bonds). Interestingly, there is no critical point when ${ϵ}_{AA}$ vanishes despite the fact that $AA$ bonds alone cannot drive condensation.

Recently, it has been demonstrated [Magee et al., Phys. Rev. Lett. 96, 207802 (2006)] that isolated square-well homopolymers can spontaneously break chiral symmetry and “freeze” into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics combined with an optimized parallel tempering scheme to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of the polymer govern the details of the helix structure. The width of the square well (proportional to $\lambda$) is found to control the radius of the helix, which decreases with increasing well width until the polymer forms a coiled sphere for sufficiently large wells. The helices are found to be stable for only a “window” of molecular weights. If the polymer is too short, the helix will not form. If the polymer is too long, the helix is no longer the minimum energy structure, and other folded structures will form. The size of this window is governed by the chain stiffness, which in this model is a function of the ratio of the monomer size to the bond length. Outside this window, the polymer still freezes into a locked structure at low temperature; however, unless the chain is sufficiently stiff, this structure will not be unique and is similar to a glassy state.

We analyze the ferromagnetic Ising model on a scale-free tree; the growing random tree model with the linear attachment kernel $A_k=k+\alpha$. We derive an estimate of the divergent temperature $T_s$ below which the zero-field susceptibility of the system diverges. Our result shows that $T_s$ is related to $\alpha$ as $\text{tanh}\left(J/T_s\right)=\alpha /\left[2\left(\alpha +1\right)\right]$, where $J$ is the ferromagnetic interaction. An analysis of exactly solvable limit for the model and numerical calculation supports the validity of this estimate.

Supercooled liquids have been shown to be dynamically heterogeneous with different regions of the system presenting dynamics that vary from each other even by orders of magnitude. Computer simulations have confirmed such a picture by detecting that the mobile particles in model glass formers are not homogeneously distributed within the system but arranged in clusters. More recently, the dynamics of small systems has been characterized by demonstrating that their structural relaxation is not homogeneous in time, in the sense that it does not evolve gradually but it is signed by rapid bursts of mobility characterized by relative compact clusters of mobile particles. These events (which have been named $d$ clusters) are fast and sparse and trigger the transitions the system experiences between metabasins (MB) of its potential-energy surface. The MB residence times are much larger than the time scales of occurrence of the $d$ clusters, and it has been suggested that the events that occur within them scarcely contribute to the structural relaxation of the system. Thus, the picture of glassy relaxation that emerges would indicate that at any time a supercooled liquid may present different spatial regions, each one characterized by different structural relaxation times. In turn, each of such regions would not relax smoothly or gradually but by means of sporadic sharp relaxation events. Here, we assess for a model glass former the relative relevance of the MB exploration events and of the $d$ clusters both in small systems and within regions of large systems, to show that the structural relaxation at the region level is indeed extremely heterogeneous in time and utterly governed by the latter.

Strongly correlated amorphous solids are a class of glass formers whose interparticle potential admits an approximate inverse power-law form in a relevant range of interparticle distances. We study the steady-state plastic flow of such systems, first in the athermal quasistatic limit and second at finite temperatures and strain rates. In all cases we demonstrate the usefulness of scaling concepts to reduce the data to universal scaling functions where the scaling exponents are determined a priori from the interparticle potential. In particular we show that the steady plastic flow at finite temperatures with efficient heat extraction is uniquely characterized by two scaled variables; equivalently, the steady-state displays an equation of state that relates one scaled variable to the other two. We discuss the range of applicability of the scaling theory, and the connection to density scaling in supercooled liquid dynamics. We explain that the description of transient states calls for additional state variables whose identity is still far from obvious.

We report a computer simulation study of viscous fingering patterns in a lifting Hele-Shaw cell with grooves. Here circular or square grooves concentric to the plates are etched on the lower plate. Experiments show that the presence of such grooves affect formation of viscous fingers quite strongly. We report a simulated pressure map generated in such grooved cells, when the two plates are separated with a constant force and compare the patterns with experiments. Variation in the simulated patterns for different fluid viscosity and lifting force is also studied.

We introduce a model which integrates the complex Ginzburg-Landau equation in two dimensions (2Ds) with the linear-cubic-quintic combination of loss and gain terms, self-defocusing nonlinearity, and a periodic potential. In this system, stable 2D dissipative gap solitons (DGSs) are constructed, both fundamental and vortical ones. The soliton families belong to the first finite band gap of the system’s linear spectrum. The solutions are obtained in a numerical form and also by means of an analytical approximation, which combines the variational description of the shape of the fundamental and vortical solitons and the balance equation for their total power. The analytical results agree with numerical findings. The model may be implemented as a laser medium in a bulk self-defocusing optical waveguide equipped with a transverse 2D grating, the predicted DGSs representing spatial solitons in this setting.

The vertex cover problem is a prototypical hard combinatorial optimization problem. It was studied in recent years by physicists using the cavity method of statistical mechanics. In this paper, the stability of the finite-temperature replica-symmetric (RS) and the first-step replica-symmetry-broken (1RSB) cavity solutions of the vertex cover problem on random regular graphs of finite vertex degree $K$ are analyzed by population dynamics simulations. We found that (1) the lowest temperature for the RS solution to be stable, $T_{\text{RS}}\left(K\right)$, is not a monotonic function of $K$; (2) at relatively large connectivity $K$ and temperature $T$ slightly below the dynamic transition temperature $T_d\left(K\right)$, the 1RSB solutions with small but non-negative complexity values are stable, and (3) the dynamical transition temperature $T_d$ and Kauzmann temperature $T_K$ is equal to each other. Similar results are obtained on random Poissonian graphs.

The effects of cholesterol on membrane bending modulus $K_{\text{C}}$, membrane thickness $D_{\text{HH}}$, the partial and apparent areas of cholesterol and lipid, and the order parameter $S_{\text{xray}}$ are shown to depend upon the number of saturated hydrocarbon chains in the lipid molecules. Particularly striking is the result that up to 40% cholesterol does not increase the bending modulus $K_{\text{C}}$ of membranes composed of phosphatidylcholine lipids with two cis monounsaturated chains, although it does have the expected stiffening effect on membranes composed of lipids with two saturated chains. The $B$ fluctuational modulus in the smectic liquid crystal theory is obtained and used to discuss the interactions between bilayers. Our $K_{\text{C}}$ results motivate a theory of elastic moduli in the high cholesterol limit and they challenge the relevance of universality concepts. Although most of our results were obtained at $30°\text{C}$, additional data at other temperatures to allow consideration of a reduced temperature variable do not support universality for the effect of cholesterol on all lipid bilayers. If the concept of universality is to be valid, different numbers of saturated chains must be considered to create different universality classes. The above experimental results were obtained from analysis of x-ray scattering in the low angle and wide angle regions.

Cardiac alternans, a beat-to-beat alternation of cardiac electrical dynamics, and ventricular tachycardia, generally associated with a spiral wave of electrical activity, have been identified as frequent precursors of the life-threatening spatiotemporally chaotic electrical state of ventricular fibrillation (VF). Schemes for the elimination of alternans and the stabilization of spiral waves through the injection of weak external currents have been proposed as methods to prevent VF but have not performed at the level required for clinical implementation. In this paper we propose a control method based on linear-quadratic regulator (LQR) control. Unlike most previously proposed approaches, our method incorporates information from the underlying model to increase efficiency. We use a one-dimensional ringlike geometry, with a single control electrode, to compare the performance of our method with that of two other approaches, quasi-instantaneous suppression of unstable modes (QISUM) and time-delay autosynchronization (TDAS). We find that QISUM fails to suppress alternans due to conduction block. Although both TDAS and LQR succeed in suppressing alternans, LQR is able to suppress the alternans faster and using a much weaker control current. Our results highlight the benefits of a model-based control approach despite its inherent complexity compared with nonmodel-based control such as TDAS.