Nonlinear Growth Regimes Research Articles

Simulations of non-integer upconversion in resonant six-wave scattering

Resonant upconversion through a sixth order relativistic nonlinearity resulting in a unique resonance was recently proposed [Malkin and Fisch, Phys. Rev. E 108, 045208 (2023)]. The high order resonance is a unique non-integer multiple of a driving pump frequency resulting in a frequency upshift by a factor of ≈3.73. We demonstrate the presence, unique requirements, and growth of this mode numerically. Through tuning waves to high amplitude, in a mildly underdense plasma, the six-photon process may grow more than other non-resonant but lower order processes. The growth of the high frequency mode remains below the nonlinear growth regime. However, extending current numerical results to more strongly coupled resonances with longer pulse propagation distances suggests a pathway to significant upconversion.

Prolonged pattern coarsening in ion irradiated swinging Si substrates

Low energy ion beams are regarded as an effective means to spatio-temporally pattern a wide variety of surfaces that exhibit intriguing motifs. In this work, an unconventional technique of surface patterning has been demonstrated by studying the topographical evolution of a Si(100) surface in the presence of azimuthal sample swinging (Δϕ=20∘) under 500 eV Ar+irradiation with a polar incidence angle of 67°. A prolonged wavelength coarsening is also noticed for the swinging sample. Ripple anticoarsening is observed for static sample at high fluences. The linear and nonlinear growth regimes are found to bear a direct consequence of this unconventional geometry. Furthermore, two-dimensional slope distributions of the surface morphologies clearly indicate reduced asymmetries in the surface structures. The present geometry brings in an additional factor of differential exposure and redeposition effects in addition to the near-surface mass redistribution, the former being inconceivable in the static configuration. This study establishes the role of this unconventional yet simple method to precisely modify and control surface asymmetries and influence regime shifts.

Cross-code verification and sensitivity analysis to effectively model the electrothermal instability

This manuscript presents verification cases that are developed to study the electrothermal instability (ETI). Specific verification cases are included to ensure that the unit physics components necessary to model the ETI are accurate, providing a path for fluid-based codes to effectively simulate ETI in the linear and nonlinear growth regimes. Two software frameworks with different algorithmic approaches are compared for accuracy in their ability to simulate diffusion of a magnetic field, linear growth of the ETI, and a fully nonlinear ETI evolution. The nonlinear ETI simulations show early time agreement, with some differences emerging, as noted in the wavenumber spectrum, late into the nonlinear development of ETI. A sensitivity study explores the role of equation-of-state (EOS), vacuum density, and vacuum resistivity. EOS and vacuum resistivity are found to be the most critical factors in the modeling of nonlinear ETI development.

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

Influence of Binary Polymer Mixtures on the Nonlinear Growth Regimes of Polyelectrolyte Multilayer Films

We report on ellipsometric studies of the nonlinear growth regimes of electrostatically assembled polyelectrolyte multilayer films under in situ conditions. Poly(styrenesulfonate) (PSS) and poly(diallylmethylammonium) (PDADMA) with different molecular weights in 0.1 mol/L NaCl are used. Always, the linear growth is preceded by a parabolic growth regime. For films made from binary PDADMA mixtures, the compositions in the film and the adsorption solution are nearly identical. To explain these findings, a molecular model that describes the parabolic growth quantitatively is introduced. Neutron reflectivity of films prepared from PSS molecular weight above a threshold, >25 kDa, shows that its center of mass is vertically immobile, in both the parabolic and linear growth regimes. Below 25 kDa, the multilayer buildup starts with an exponential growth regime, and pronounced PSS interdiffusion is found with neutron reflectivity. The exponential buildup regime is extended on decrease of PSS molecular weight. For f...

Non-axisymmetric flows in a differential-disk rotating system

The non-axisymmetric structure of an unstable Stewartson shear layer generated via a differential rotation between flush disks and a cylindrical enclosure is investigated numerically using both three-dimensional direct numerical simulation and a quasi-two-dimensional model. Previous literature has only considered the depth-independent quasi-two-dimensional model due to its low computational cost. The three-dimensional model implemented here highlights the supercritical instability responsible for the polygonal deformation of the shear layer in the linear and nonlinear growth regimes and reveals that linear stability analysis is capable of accurately determining the preferred azimuthal wavenumber for flow conditions near the onset of instability. This agreement is lost for sufficiently forced flows where nonlinear effects encourage the coalescence of vortices towards lower-wavenumber structures. Time-dependent flows are found for large Reynolds numbers defined based on the Stewartson layer thickness and azimuthal velocity differential. However, this temporal behaviour is not solely characterized by Reynolds number but is rather a function of both the Rossby and Ekman numbers. At high Ekman and Rossby numbers, unsteady flow emerges through a small-scale azimuthal destabilization of the axial jets within the Stewartson layers; at low Ekman numbers, unsteady flow emerges through a modulation in the strength of one of the axial vortices rolled up by non-axisymmetric instability of the Stewartson layer.

Indirect-drive ablative Rayleigh-Taylor growth experiments on the Shenguang-II laser facility

In this research, a series of single-mode, indirect-drive, ablative Rayleigh-Taylor (RT) instability experiments performed on the Shenguang-II laser facility [X. T. He and W. Y. Zhang, Eur. Phys. J. D 44, 227 (2007)] using planar target is reported. The simulation results from the one-dimensional hydrocode for the planar foil trajectory experiment indicate that the energy flux at the hohlraum wall is obviously less than that at the laser entrance hole. Furthermore, the non-Planckian spectra of x-ray source can strikingly affect the dynamics of the foil flight and the perturbation growth. Clear images recorded by an x-ray framing camera for the RT growth initiated by small- and large-amplitude perturbations are obtained. The observed onset of harmonic generation and transition from linear to nonlinear growth regime is well predicted by two-dimensional hydrocode simulations.

Experimental validation of a Richtmyer–Meshkov scaling law over large density ratio and shock strength ranges

A universal scaling law for the Richtmyer–Meshkov instability is validated with experimental results covering a wide range of density ratios and shock strengths. These results include the first membraneless, gas-phase, interface experiments for A>0.5 and M>1.5. The shock-accelerated, sinusoidal interface experiments are conducted in a vertical shock tube with a large square cross section and cover the experimental parameter space: 0.29<A<0.95, 1.1<M<3, and 3.1×104<Re<1.4×107. Results provide growth-rate data for comparison with computational fluid dynamics simulation codes and verify the nondimensional time and amplitude parameters chosen for scaling are the correct ones. Correct scaling is obtained by including a growth-reduction factor that accounts for diffusion at the interface. Planar imaging techniques are used to diagnose the instability development for a nearly single-mode interface, and results are reported for eight scenarios (including three distinct gas pairs) that span the linear and nonlinear growth regimes. Images from the strongly shocked, high A experiments are the first to provide evidence of bubble-growth suppression due to shock proximity.

Rayleigh-Taylor Instability Experiments with Precise and Arbitrary Control of the Initial Interface Shape

In a Rayleigh-Taylor instability a dense fluid sits metastably atop a less dense fluid, a configuration that can be stabilized using a magnetic field gradient when one fluid is highly paramagnetic. On switching off the magnetic field, the instability occurs as the dense fluid falls under gravity. By affixing appropriately shaped magnetically permeable wires to the outside of the cell, one may impose arbitrarily chosen and well-controlled initial perturbations on the interface. This technique is used to examine both the linear and nonlinear growth regimes for which the perturbation amplitudes, growth rates, and nonlinear growth coefficients are obtained.

Simulation of growth dynamics in atomic layer deposition. Part III. Polycrystalline films from tetragonal crystallites

Materials with one- and two-dimensional crystal structures often form crystals with the shape of needles and platelets, respectively. This should be expected to have great influence on the properties of thin films grown from such materials, and the effect on texture and topography is shown in this paper by a series of simulations. The topic of this paper is the effect of different aspect ratios of crystals with tetragonal symmetry on the resulting thin films. However the major results should also apply to crystals of other types of symmetry having aspect ratios deviating from one. The growth dynamics in atomic layer deposition of polycrystalline thin films have been simulated for randomly oriented and randomly positioned crystallites. Crystalline seed objects adapting shapes of tetragonal boxes with aspect ratios from 0.1 (platelets) to 10 (needles) has been used as examples for growth of films from tetragonal crystals. The dependence of roughness, surface crystal density, and texture on the film thickness is shown. Topography and cross sections of simulated films with different aspect ratios are discussed. Non-linear growth regimes are consistently found in the initial stage of the film formation. A conversion from type-2 to type-1 substrate inhibited growth is observed as the aspect ratio deviates significantly from one.

Simulation of surface relief effect on ALD process

Using kinetic MC model simulation of ALD process is carried out. Influence of surface substrate relief and sticking center concentration on growth rate of ALD films at initial stages of growth are investigated. Relationship between growth rate and nucleus center concentration in a nonlinear regime is obtained. For increasing nucleation rate of ALD process combination of CVD and ALD processes in the first cycle is suggested. To increase ALD layers quality and reduce a nonlinear growth regime formation of loose rough surface layer on the substrate before deposition process is recommended.

Electro-optics of colloids coated with multilayers from strong polyelectrolytes:surface charge relaxation

The electrical properties and structure of polyelectrolyte multilayers prepared by layer-by-layer deposition of poly(sodium 4-styrenesulfonate) (PSS) and poly(diallyldimethylammonium chloride) (PDADMAC) on ellipsoidal β-ferric hydrous oxide particles are examined in situ using the electric light scattering method. In the initial nonlinear growth regime, the electro-optical effect is found to increase almost in the same manner as the thickness of the multilayer film. This reveals an increase in the multilayer surface charge due to the nonlinear increase in polyelectrolyte adsorption. Above five deposition cycles, the electro-optical effect reaches a plateau and the thickness increment per layer becomes constant, indicating regular film growth. Evidence is given that the concentration of small residual ions incorporated into the PSS/PDADMAC film is negligible. Polarization of counterions, bound near to the surface of the last-adsorbed polyion, is assumed to explain the relaxation of the electro-optical effect in the frequency range 10 3–10 5 Hz.

On the development of G�rtler vortices in wall jet flow

The development of Gortler vortices in wall jet flow over curved surfaces is considered in both the linear and nonlinear growth regimes. It is shown, using asymptotic methods based on the largeness of the wavenumber of the vortices, that this hydrodynamic instability is prone to occur more readily on concave rather than convex surfaces. It is found that after passing the position of neutral stability, the flow develops a surprising structure quite unlike that produced in the Blasius boundary-layer. Once the flow is into the unstable regime, the effect of increasing the Gortler number is to move the vortices away from the wall.