Mahmoodbyskov7815

We show that a commonly accepted transparency threshold for a thin foil in a strong circularly polarized normally incident laser pulse needs a refinement. We present an analytical model that correctly accounts for laser absorption. The refined threshold is determined not solely by the laser amplitude, but by other parameters that are equally or even more important. Our predictions are in perfect agreement with particle-in-cell simulations. The refined criterion is crucial for configuring laser plasma experiments in the high-field domain. In addition, an opaque foil steepens the pulse front, which can be important for numerous applications.If a static perturbation is applied to a liquid crystal, then the director configuration changes to minimize the free energy. If a shear flow is applied to a liquid crystal, then one might ask Does the director configuration change to minimize any effective potential? To address that question, we derive the Leslie-Ericksen equations for dissipative dynamics and determine whether they can be expressed as relaxation toward a minimum. The answer may be yes or no, depending on the number of degrees of freedom. Using theory and simulations, we consider two specific examples, reverse tilt domains under simple shear flow and dowser configurations under plane Poiseuille flow, and we demonstrate that each example shows relaxation toward the minimum of an effective potential.We numerically estimate the leading asymptotic behavior of the length L_n of the longest increasing subsequence of random walks with step increments following Student's t-distribution with parameters in the range 1/2≤ν≤5. We find that the expected value E(L_n)∼n^θlnn, with θ decreasing from θ(ν=1/2)≈0.70 to θ(ν≥5/2)≈0.50. (1S,3R)-RSL3 For random walks with a distribution of step increments of finite variance (ν>2), this confirms previous observation of E(L_n)∼sqrt[n]lnn to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of E(L_n) for random walks with step increments of finite variance.We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean-field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain a simple field theory which describes the first deviations from this uncorrelated behavior in a ε=d_c-d expansion below the upper critical dimension d_c of the model. We apply it to calculate the correlations between (i) avalanche sizes (ii) avalanche dynamics in two successive avalanches, or more generally, in two avalanches separated by a uniform displacement W of the interface. For (i) we obtain the correlations of the total sizes, of the local sizes, and of the total sizes with given seeds (starting points). For (ii) we obtain the correlations of the velocities, of the durations, and of the avalanche shapes. In general we find that the avalanches are anticorrelated, the occurrence of a larger avalanche making more likely the occurrence of a smaller one, and vice versa. link2 Examining the universality of our results leads us to conjecture several exact scaling relations for the critical exponents that characterize the different distributions of correlations. The avalanche size predictions are confronted to numerical simulations for a d=1 interface with short range elasticity. They are also compared to our recent related work on static avalanches (shocks). Finally we show that the naive extrapolation of our result into the thermally activated creep regime at finite temperature predicts strong positive correlations between the forward motion events, as recently observed in numerical simulations.We present a full kinetic model of a hydrogel that undergoes phase separation during swelling and deswelling. link3 The model accounts for the interfacial energy of coexisting phases, finite strain of the polymer network, and solvent transport across free boundaries. For the geometry of an initially dry layer bonded to a rigid substrate, the model predicts that forcing solvent into the gel at a fixed rate can induce a volume phase transition, which gives rise to coexisting phases with different degrees of swelling, in systems where this cannot occur in the free-swelling case. While a nonzero shear modulus assists in the propagation of the transition front separating these phases in the driven-swelling case, increasing it beyond a critical threshold suppresses its formation. Quenching a swollen hydrogel induces spinodal decomposition, which produces several highly localized, highly swollen phases which coarsen and are then ejected from free boundary. The wealth of dynamic scenarios of this system is discussed using phase-plane analysis and numerical solutions in a one-dimensional setting.The effect of confinement on the behavior of liquid crystals is interesting from a fundamental and practical standpoint. In this work, we report Monte Carlo simulations of hard rods in an array of hard nanoposts, where the surface-to-surface separations between nanoposts are comparable to or less than the length of hard rods. This particular system shows promise as a means of generating large-scale organization of the nematic liquid by introducing an entropic external field set by the alignment of nanoposts. The simulations show that nematic ordering of hard rods is enhanced in the nanopost arrays compared with that in bulk, in the sense that the nematic order is significant even at low concentrations at which hard rods remain isotropic in bulk, and the enhancement becomes more significant as the passage width between two nearest nanoposts decreases. An analysis of local distribution of hard-rod orientations at low concentrations with weak nematic ordering reveals that hard rods are preferentially aligned along nanoposts in the narrowing regions between two curved surfaces of nearest nanoposts; hard rods are less ordered in the passages and in the centers of interpost spaces. It is concluded that at low concentrations the confinement in a dense array of nanoposts induces the localized nematic order first in the narrowing regions and, as the concentration further increases, the nematic order spreads over the whole region. The formation of a well-ordered phase at low concentrations of hard rods in a dense array of nanoposts can provide a new route to the low-concentration preparation of nematic liquid crystals that can be used as anisotropic dispersion media.In this paper, we describe the unification and extension of multiple kinematic theories on the advection of colloidal particles through periodic obstacle lattices of arbitrary geometry and infinitesimally small obstacle size. We focus specifically on the particle displacement lateral to the flow direction (termed "deterministic lateral displacement") and the particle-obstacle interaction frequency, and develop methods for describing these as a function of particle size and lattice parameters for arbitrary lattice geometries. We then demonstrate design algorithms for microfluidic devices consisting of chained obstacle lattices of this type that approximate any lateral displacement function of size to arbitrary accuracy with respect to multiple optimization metrics, prove their validity mathematically, and compare the generated results favorably to designs in the literature with respect to metrics such as accuracy, device size, and complexity.Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Einstein condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the 1↔2 interactions between the condensate and the excited atoms. The other two describe the 2↔2 and 1↔3 interactions between the excited atoms themselves.We report on the enhancement of the hydrodynamic damping of gravity waves at the surface of a fluid layer as they interact with a turbulent vortex flow in a sloshing experiment. Gravity surface waves are excited by oscillating horizontally a square container holding our working fluid (water). At the bottom of the container, four impellers in a quadrupole configuration generate a vortex array at moderate to high Reynolds number, which interact with the wave. We measure the surface fluctuations using different optical nonintrusive methods and the local velocity of the flow. In our experimental range, we show that as we increase the angular velocity of the impellers, the gravity wave amplitude decreases without changing the oscillation frequency or generating transverse modes. This wave dissipation enhancement is contrasted with the increase of the turbulent velocity fluctuations from particle image velocimetry measurements via a turbulent viscosity. To rationalize the damping enhancement a periodically forced shallow water model including viscous terms is presented, which is used to calculate the sloshing wave resonance curve. The enhanced viscous dissipation coefficient is found to scale linearly with the measured turbulent viscosity. Hence, the proposed scheme is a good candidate as an active surface gravity wave dampener via vortex flow reconfiguration.One-dimensional localized sequences of bound (coupled) traveling pulses, wave trains with a finite number of pulses, are described in a piecewise-linear reaction-diffusion system of the FitzHugh-Nagumo type with linear cross-diffusion terms of opposite signs. The simplest case of two bound pulses, the paired-pulse waves (pulse pairs), is solved analytically. The solutions contain oscillatory tails in the wave profiles so that the pulse pairs consist of a double-peak core and wavy edges. Several pulse pairs with different profile shapes and propagation speeds can appear for the same parameter values of the model when the cross diffusion is dominant. The more general case of many bound pulses, multipulse waves, is studied numerically. It is shown that, dependent on the values of the cross-diffusion coefficients, the multipulse waves upon collision can pass through one another with unchanged size and shape, exhibiting soliton behavior. Moreover, multipulse collisions with the system boundaries can generate a rich variety of wave transformations the transition from the multipulse waves to pulse-front waves and further to simple fronts or to annihilation as well the transition to solitary pulses or to multipulse waves with lower numbers of pulses. Analytical and numerical results for the pulse pairs agree well with each other.Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by the non-Markovian version of the Langevin equation that includes an arbitrary memory function. When averaged over cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterized by Gaussian velocity distributions. Accordingly, the data are described by a linear memory model which includes different random walk models that were previously used to account for various aspects of cell motility such as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memory function is extracted from the trajectory data without restrictions or assumptions, thus making our approach truly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayed single-exponential negative friction, which clearly distinguishes cell motion from the simple persistent random walk model and suggests a regulatory feedback mechanism that controls cell migration.