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We verify that cDFT is able to semiquantitatively reproduce the phase diagram in all cases. We also show that for these problems computationally cheap Gaussian approximations are nearly as good as full minimization based on finite differences.This work sets the exact equations for the quasiclassical response function and susceptibility of a Brownian particle immersed in a bath of quantum harmonic oscillators driven by nonlinear harmonic potentials. A delta force perturbation gives rise to a response whose susceptibility is the combination of a linear term, owner of the harmonic oscillator, plus a nonlinear one involving an integral equation. It is provided a recursion method to find its solutions based on functional equations in the Banach space. The ODE for the response function is a highly nonlinear damped nonautonomous Duffing equation for which the aforementioned method is used to get its solution.Motivated by the one-drop-filling (ODF) method for the industrial manufacturing of liquid crystal displays, we analyze the pressure-driven flow of a nematic in a channel with dissipative weak planar anchoring at the boundaries of the channel. We obtain quasisteady asymptotic solutions for the director angle and the velocity in the limit of small Leslie angle, in which case the key parameters are the Ericksen number and the anchoring strength parameter. In the limit of large Ericksen number, the solution for the director angle has narrow reorientational boundary layers and a narrow reorientational internal layer separated by two outer regions in which the director is aligned at the positive Leslie angle in the lower half of the channel and the negative Leslie angle in the upper half of the channel. On the other hand, in the limit of small Ericksen number, the solution for the director angle is dominated by splay elastic effects with viscous effects appearing at first order. As the Ericksen number varies, there is a continuous transition between these asymptotic behaviors, and in fact the two asymptotic solutions capture the behavior rather well for all values of the Ericksen number. The steady-state value of the director angle at the boundaries and the timescale of the evolution toward this steady-state value in the asymptotic limits of large and small Ericksen number are determined. In particular, using estimated parameter values for the ODF method, it is found that the boundary director rotation timescale is substantially shorter than the timescale of the ODF method, suggesting that there is sufficient time for significant transient flow-driven distortion of the nematic molecules at the substrates from their required orientation to occur.The atomistic simulation of materials growing in the layer-by-layer mode by the pulsed-laser deposition is a significant challenge mainly due to the short timescales in which the fastest processes on the surface occur together with long periods between pulses. We present a kinetic Monte Carlo algorithm which overcomes the scaling problem by approximation of fast diffusion and by neglecting complex chemical processes. The atomic diffusion is modeled as a two-dimensional gas of material units on each layer. The model is based on a few elementary processes-the condensation of units on the surface, their dissolution back to the gas, and interlayer transport, which can be influenced by the Ehrlich-Schwoebel barrier. With these simplifications, the computational time of the algorithm scales only linearly with the size of the substrate while describing physically relevant growth kinetics. We demonstrate that the simplified model is suitable for simulations of layered growth of thin films in the range from quasicontinuous deposition to low-frequency cases. The model is successfully implemented to provide an alternative explanation of the time evolution of layer coverages by interlayer transport after pulses of deposition experimentally observed during perovskite growth [G. Eres et al., Phys. Rev. B 84, 195467 (2011)PRBMDO1098-012110.1103/PhysRevB.84.195467].We numerically study interaction of a very intense (I∼10^17 to 5×10^19W/cm^2) femtosecond obliquely incident p-polarized laser pulse with a steep-gradient (L∼λ) plasma, i.e., within the conditions typical for modern experiments. It is shown that the hybrid stimulated Raman scattering-two-plasmon decay instability develops near the quarter-critical density surface and plays the dominant role for the plasma waves' excitation and energy absorption. The plasmons are excited as two wave packets confined near this surface with very wide ≈ω_0/c spatial spectra along its normal. selleckchem Hence, phase-matching conditions for the 3/2 harmonic generation are fulfilled immediately and include the mechanism coming from the high harmonics of plasma waves. This mechanism has been proved experimentally by observing an additional 3/2 harmonic beam.The complex Ginzburg-Landau (CGL) equation, an envelope model relevant in the description of several natural phenomena like binary-fluid convection and second-order phase transitions, and the Lugiato-Lefever (LL) equation, describing the dynamics of optical fields in pumped lossy cavities, can be viewed as nonintegrable generalizations of the nonlinear Schrödinger (NLS) equation, including diffusion, linear and nonlinear loss or gain terms, and external forcing. In this paper we treat the nonintegrable terms of both equations as small perturbations of the integrable focusing NLS equation, and we study the Cauchy problem of the CGL and LL equations corresponding to periodic initial perturbations of the unstable NLS background solution, in the simplest case of a single unstable mode. Using the approach developed in a recent paper by the authors with P. G. Grinevich [Phys. Rev. E 101, 032204 (2020)10.1103/PhysRevE.101.032204], based on the finite gap method and the theory of perturbations of soliton PDEs, we construct the proper analytic models describing quantitatively how the solution evolves, after a suitable transient, into a Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence of anomalous waves (AWs) described by slowly varying lower dimensional patterns (attractors) in the (x,t) plane, characterized by Δx=L/2 or Δx=0 in the case in which loss or gain, respectively, effects prevail, where Δx is the x-shift of the position of the AW during the recurrence and L is the period. We also obtain, in the CGL case, the analytic condition for which loss and gain exactly balance, stabilizing the ideal FPUT recurrence of periodic NLS AWs; such a stabilization is not possible in the LL case due to the external forcing. These processes are described, to leading order, in terms of elementary functions of the initial data in the CGL case, and in terms of elementary and special functions of the initial data in the LL case.
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