Influence of high-order dispersion on self-focusing. II. Numerical investigation

The self-focusing described by the nonlinear Schrödinger equation with a higher-order derivative term is investigated numerically. We demonstrate that, depending on the sign before this term, it may lead in the final stage either to defocusing or to a steady homogeneous wave beam. In both cases the transition to the final state is shown to be oscillatory.     

Resonance fluorescence spectrum of a three-level atom. II. Numerical results

Numerical computations are presented for the excitation spectra arising from the interaction between a three-level atom in the cascade configuration and a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered when the laser field is at resonance with the equally spaced levels of the atom as well as a function of the detunings. The physical process of optical amplification occurs without population inversion and it is more pronounced when the laser field is detuned than when it is at resonance. The shapes of the spectral lines for a number of side-bands are of the absorption-amplification type rather than that of the absorption one. In the presence of detunings as well as in the cooperative two-photon cascade process, the resulting spectra are far more complicated than those occuring at resonance. Results of numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically.     

Numerical modelling of unsteady heating and melting of the anode by electric arc. Part 2. Numerical characteristics of the anode weldpool

Numerical computations of the electric-arc heating and anode melting were carried out within the framework of the two-dimensional unsteady mathematical model. The influence of the viscous interaction ??plasma-melt??, surface tension forces, electromagnetic forces, and gravitational convection on the formation of the hydrodynamics of the anode melt was considered.     

Diffraction from modulated structures. V. Numerical calculations of diffuse intensity

Numerical calculations of the intensityI(h)/M ²,I(h)/M as well as the interference functions(h)/M and(h) in the vicinity of (200) and (800) matrix reciprocal lattice points for both the periodic and quasiperiodic (monodisperse and polydisperse) models of modulated structures are presented.     

Model stellar atmospheres—I. Numerical techniques

We present a series of new numerical techniques and novel uses of existing techniques to solve the model stellar atmosphere problem. The techniques are applied to the fully linearized LTE problem and procedures for generalizing to the non-LTE problem are indicated.We also show that the usual angle quanrature schemes, particularly the n = 3 double Gauss scheme, can introduce significant errors in the calculation of the mean intensity. Alternative schemes are presented that substantially improve on this.     

Time-domain simulation of damped impacted plates. II. Numerical model and results

A time-domain model for the flexural vibrations of damped plates was presented in a companion paper [Part I, J. Acoust. Soc. Am. 109, 1422-1432 (2001)]. In this paper (Part II), the damped-plate model is extended to impact excitation, using Hertz's law of contact, and is solved numerically in order to synthesize sounds. The numerical method is based on the use of a finite-difference scheme of second order in time and fourth order in space. As a consequence of the damping terms, the stability and dispersion properties of this scheme are modified, compared to the undamped case. The numerical model is used for the time-domain simulation of vibrations and sounds produced by impact on isotropic and orthotropic plates made of various materials (aluminum, glass, carbon fiber and wood). The efficiency of the method is validated by comparisons with analytical and experimental data. The sounds produced show a high degree of similarity with real sounds and allow a clear recognition of each constitutive material of the plate without ambiguity.     

A model of modulated diffusion. II. Numerical results on statistical properties

We investigate numerically the statistical properties of a model of modulated diffusion for which we have already computed analytically the diffusion coefficientD. Our model is constructed by adding a deterministic or random noise to the frequency of an integrable isochronous system. We consider in particular the central limit theorem and the invariance principle and we show that they follow wheneverD is positive and for any magnitude of the noise; we also investigate the asymptotic distribution in a case whenD=0.     

Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part II. Numerical methods

The scaling exponent and the scaling function for the 1D single-species coagulation model (A+AA) are shown to be universal, i.e., they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties of the concentration: Monte Carlo simulations and extrapolations of exact finite-lattice data. These methods are tested in a case where analytical results are available. To obtain reliable results from finite-size extrapolations, numerical data for lattices up to ten sites are sufficient.     

Numerical simulation of ion-acoustic turbulence in the B. B. Kadomtsev model

The present report is devoted to the discussion of the properties of two equations relatively long ago proposed by B. B. Kadomtsev for the nonlinear theory of ion-acoustic plasma turbulence and some results of their solutions. We concern with these equations as objects of mathematical physics, focusing attention to both the approach to their study and arising numerical results.     

Numerical Models of the Vertical Turbulent Exchange in Stably Stratified Water Body: II. Results of Numerical Experiments

On the basis of the developed models [1], numerical modeling of the problem on penetration of a turbulent layer of mixed liquid in linearly stratified medium under constant shear stress is performed. The calculation results are in satisfactory agreement with the known experimental data and show a significant effect of anisotropy of the flow on its main characteristics.     

Plastic Strain Localization in Polycrystalline Titanium. Numerical Simulation

Russian Physics Journal - The paper presents numerical simulation of polycrystalline titanium deformation in terms of the crystal plasticity theory. Based on the experimental data, a...     

Numerical simulations of pulsating detonations: II. Piston initiated detonations

Extremely long time, high-resolution one-dimensional numerical simulations are performed in order to investigate the evolution of pulsating detonations initiated and driven by a constant velocity piston, or equivalently by shock reflection from a stationary wall. The results are compared and contrasted to previous simulations where the calculations are initiated by placing a steady detonation on the numerical grid. The motion of the piston eventually produces a highly overdriven detonation propagating into the quiescent fuel. The detonation subsequently decays in a quasi-steady manner towards the steady state corresponding to the given piston speed. For cases where the steady state is one-dimensionally unstable, the shock pressure begins to oscillate with a growing amplitude once the detonation speed drops below a stability boundary. However, the overdrive is still being degraded by a rarefaction which overtakes the front, but on a time-scale which is very long compared with both the reaction time and the period of oscillation. As the overdrive decreases, the detonation becomes more unstable as it propagates and the nature (e.g. period and amplitude) of the oscillations change with time. If the steady detonation is very unstable then the oscillations evolve in time from limit cycle to period doubled oscillations and finally to irregular oscillations. The ultimate nature of the oscillations asymptotically approaches that of the saturated nonlinear behaviour as found from calculations initiated by the steady state. However, the nonlinear stability of the steady detonation investigated in previous calculations represents only the very late time (O(10⁵) characteristic reaction times) behaviour of the piston problem.     

Analysis and synthesis of varactor frequency doublers. Part. 2. Numerical modeling and experimental investigations

Problems connected with optimization of frequency doubling regimes at high levels of pumping power are discussed. Both design and engineering methods of improving the energy characteristics of the devices are considered. Results of calculations are compared with field experiments carried out in the frequency range 200‒220 GHz.     

Infinite Compressibility States in the Hierarchical Reference Theory of Fluids. II. Numerical Evidence

Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility _T we now turn to the available numerical evidence to elucidate the character of the partial differential equation: Of the three scenarios identified previously, only the assumption of the equations turning stiff when building up the divergence of _T allows for a satisfactory interpretation of the data. In addition to the asymptotic regime where the arguments of part I directly apply, a similar mechanism is identified that gives rise to transient stiffness at intermediate cutoff for low enough temperature. Heuristic arguments point to a connection between the form of the Fourier transform of the perturbational part of the interaction potential and the cutoff where finite difference approximations of the differential equation cease to be applicable, and they highlight the rather special standing of the hard-core Yukawa potential as regards the severity of the computational difficulties.     

Solution of the Ornstein-Zernike equation for a softcore Yukawa fluid. II. Numerical results

Numerical calculations are reported for the simplest case of the soft-core Yukawa fluid introduced in an earlier paper. Attention is given to the thermodynamic behavior, the correlation functions, and the interparticle potentials found by inverting the structural information using Percus-Yevick and hypernetted chain integration equation approximations.Supported by ARGC grant No. B7715646R.