M-lump and interactive solutions to a (3 $${+}$$ + 1)-dimensional nonlinear system

Nonlinear Dynamics - This paper aims at computing M-lump solutions for the $$(3+1)$$ -dimensional nonlinear evolution equation. These solutions in all directions decline to an identical state...     

Analytical modeling of synthetic fiber ropes. Part II: A linear elastic model for 1 + 6 fibrous structures

In part I of this study it was shown that, to model synthetic fiber ropes, two scale transition models can be used in sequence. The first model (continuum model) has been presented in the part I and the present paper examines the behavior of a fibrous structure consisting of 6 helicoidal strands around a central core (1 + 6 structure). An analytical model will be presented which enables the global elastic behavior of such a cable under tension–torsion loading to be predicted. In this model, first, the core and the strands are described as Kirchhoff–Love beams and then the traction–torsion coupling behavior is taken into account for both of them. By modeling the contact conditions between the strands and the core, with certain assumptions, it is possible to describe the behavior of the cable section as a function of the degrees of freedom of the core. The behavior of the cable can thus be deduced from the tension–torsion coupling behavior of its constituents. Tensile tests have been performed on the core, the strands and then on a full scale 205 ton failure load cable. Finally, predicted stiffness from the analytical models is compared to the test results.     

Simulations of hot, dense iron plasma opacity at 89 eV and comparison with experiment

Predictions of hot, dense iron plasma opacity at 89 eV photon energy are compared with experimental determinations from the transmission of laser-heated iron to extreme ultra-violet (EUV) laser radiation. The EUV laser was pumped using six beams of an Nd-Yag laser in a refraction compensating geometry, while another beam irradiated a tamped solid iron target with an intensity of 10¹⁴ W cm⁻². The Ehybrid hydrodynamic and atomic physics code was used to predict temperatures, densities and ionisation throughout the evolving iron plasma. The iron opacities were deduced taking into account free–free, bound–free and bound–bound absorption. Bound–bound absorption was considered using atomic data generated by the Opacity Project. Reasonable overall agreement between theory and experiment was obtained for the iron layer transmission. The simulations indicated the dominance of bound–bound absorption throughout most regions of the iron plasma, but also the potential importance of photoionisation from core levels where energetically possible.     

Rational solutions for a combined (3 + 1)-dimensional generalized BKP equation

Nonlinear Dynamics - In this paper, we focus on the rational solutions for a combined (3 + 1)-dimensional generalized BKP equation. By using the symbolic computation with Maple,...     

A simplified quasi‐two‐dimensional model for gain optimization in carbon dioxide gasdynamic lasers (GDL)

In this paper a simplified quasi‐two‐dimensional model for small signal gain optimization in gasdynamic laser is introduced. In order to obtain a homogeneous medium with maximum optical gain in the active medium, by nozzle shape formation, the shock occurrence position is controlled and is postponed to some point behind the laser active medium. Then the method of calculus of variation is used to find the supersonic part of the nozzle of a gasdynamic laser with maximum gain in the active medium. The interesting result is that the supersonic part of such a nozzle consists of a wedge as the accelerating part of the nozzle, a smooth surface for the uniformization, and finally a channel for the relaxation of the medium. (The middle section is characterized as the geometrical locus of points whose characteristic curves are concurrent at a certain point.) It is also shown that, overlooking a minor difference in the gain, the nozzle can be chosen to be a shock free one with the ultimate optical uniformity. Copyright © 2002 John Wiley & Sons, Ltd.     

Comment on “A note on generalized radial mesh generation for plasma electronic structure”

In a recent note, B.G. Wilson and V. Sonnad [1] proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert’s function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h[α] using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we propose a direct proof of that equation.     

MODEL OF POLYMORPHIC TRANSFORMATION IN A SHOCK WAVE. 2. SILICA

Journal of Applied Mechanics and Technical Physics - A model linking the shock-inducedd polymorphic transformation of a crystalline material with a change in its elastic energy is presented. The...     

A mode III crack in a piezoelectric semiconductor of crystals with 6 mm symmetry

A finite mode III crack in a piezoelectric semiconductor of 6 mm crystals is analyzed. Fourier transform is employed to reduce the mixed boundary value problem to a pair of dual-integral equations. Numerical solution of these equations yields coupled electromechanical fields, the intensity factor and the energy release rate near the crack tip. Numerical results are presented graphically to show the fracture behavior which is affected by the semiconduction.     

Some laws for precipitation of aerosols on a charged collector in the reynolds number range 10–100

Experimental data are presented on the efficiency of electrostatic precipitation of aqueous aerosol particles on a strongly charged sphere in the medium Reynolds number range (Re = 10–100). The asymptotic solutions for the problem are presented, and typical errors allowable in interpreting this type of experiment are discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 190–193, May–June, 1976.     

A cryomechanics technique to measure dissipated energies of 10 nJ

A new cryomechanics measurement technique has been developed to measure fracture-induced dissipated energies as small as 10 nJ (10×10⁻⁹ J) at temperatures near 4.2 K. The technique, with much less stringent instrumentation requirements than those used for measurement of ∼10 nJ energies, was applied to an induced fracture experiment where dissipation energies were of the order of ∼100 μJ. Fracture of 0.5-mm diameter pencil leads of two different hardnesses gave rise to measured energies of 65 ∼ 110 μJ. A two-dimensional finite-element analysis was used to interpret the experimental measurements. Based on the analysis, approximately 50 μJ of 65 ∼ 110 μJ measured is estimated to be the dissipated energy associated with crack formation and propagation.     

HYDRODYNAMIC DAMPING OF A CYLINDER AT β≈10

This paper describes delicate, but large-scale, experiments aimed at measuring the hydrodynamic damping of a circular cylinder oscillating in still water and transversely in a current. Attention is concentrated on the regime of very small Keulegan–Carpenter numbers, in which the drag coefficient is inversely proportional to the Keulegan–Carpenter number. Measurements in still water at β=650 000 and 1250 000 point to drag coefficients about twice those appropriate to two-dimensional laminar flow, in common with earlier measurements at β≈10⁵. In the presence of a slowly varying transverse current (generated by placing the cylinder at the node of standing waves of long period), the damping increased with the reduced velocity of the ambient flow at a rate that increased with the Reynolds number.     

Spectroscopic observations of Fermi-degenerate aluminum compressed and heated to four times solid density and 20 eV

Shock waves generated by temporally shaped laser ablation compressed and heated Al to ρ = 11 ± 5 g/cm³ and 20 ± 2 eV. The inferred density and temperature demonstrate that highly compressed, Fermi-degenerate plasma can be created by tuning the temporal pulse shape of the laser drive intensity. The density and temperature of these plastic-tamped Al plasmas in the warm dense matter regime were diagnosed using the Stark-broadened, Al 1s–2p absorption spectral line shapes. These observations represent the forefront of opacity measurements for warm dense matter and are important for high energy density physics and inertial confinement fusion.     

A review of new wire arrays with open and closed magnetic configurations at the 1.6 MA Zebra generator for radiative properties and opacity effects

The studies emphasize investigation of plasma formation, implosion, and radiation features as a function of two load configurations: compact multi-planar and cylindrical wire arrays. Experiments with different Z-pinch loads were performed on 1.6 MA, 100 ns, Zebra generator at University of Nevada, Reno. The multi-planar wire arrays (PWAs) were studied in open and closed configurations with Al, Cu, brass, Mo and W wires. In the open magnetic configurations (single, double, triple PWAs) magnetic fields are present inside the arrays from the beginning of discharge, while in closed configurations (prism-like PWA) the global magnetic field is excluded inside before plasma flow occurs. The new prism-like PWA allows high flexibility in control of implosion dynamics and precursor formation. The spectral modeling, magneto-hydrodynamic (MHD) and wire ablation dynamic model (WADM) codes were used to describe the plasma evolution and plasma parameters. Experimentally observed electron temperature and density in multiple bright spots reached 1.4 keV and 5 × 10²¹ cm^?3, respectively. Two types of bright spots were observed. With peak currents up to 1.3 MA opacity effects became more pronounced and led to a limiting of the X-ray yields from compact cylindrical arrays. Despite different magnetic energy to plasma coupling mechanisms early in the implosion a comparison of compact double PWA and cylindrical WA results indicates that during the stagnation stage the same plasma heating mechanism may occur. The double PWA was found to be the best radiator tested at University scale 1 MA generator. It is characterized by a combination of larger yield and power, mm-scale size, and provides the possibility of radiation pulse shaping. Further, the newer configuration, the double PWA with skewed wires, was tested and showed the possibility of a more effective X-ray generation.     

A theory for freezing of electron processes in lowtemperature plasma jets

The question of finding the asymptotic values of the relative election concentrations obtained when the gas temperature and pressure along the streamliner are reduced naturally arises in a number of problems in ionized-gas dynamics. An example of such a problem is that of the flow of a low-temperature plasma in a divergent nozzle. In this case, the velocities of all elementary processes approach zero in proportion to distance from the critical section of the nozzle, due to the marked temperature and pressure drops in the nozzle. Hence, it follows that the relative electron concentration must approach some constant value, which is called the frozen concentration. The study of these processes is of great importance as applied to rocket-engine nozzles [1] and magnetohydrodynamic equipment.     

A collisional-radiative code for computing air plasma in high enthalpy flow

A time-dependent collisional-radiative model for air plasma has been developed to study the effects of nonequilibrium atomic and molecular processes on population densities in a weakly ionized high enthalpy flow. This model consists of 15 species: e^-,N, N⁺,N²⁺,O, O⁺,O²⁺,O^-,N₂,N₂⁺,NO, NO⁺,O₂,O₂⁺{{\rm e}^{-},{\rm N, N}^{+},{\rm N}^{2+},{\rm O, O}^{+},{\rm O}^{2+},{\rm O}^{-},{\rm N}_{2},{{\rm N}_{2}}^{+},{\rm NO, NO}^{+},{\rm O}_{2},{{\rm O}_{2}}^{+}}, and O₂^-{{{\rm O}_{2}}^{-}} with their major electronic excited states. Many elementary processes are considered in the number density range of 10¹²/cm³ ≤ N ≤ 10¹⁹/cm³ and the temperature range of 300 K ≤ T ≤ 40,000 K. We then compare our results with an existing collisional-radiative code to validate our model. Additionally, the unsteady nature of pulsively heated air plasma is investigated. When the ionization relaxation time is of the same order as the time scale of a heating pulse, the effects of unsteady ionization are important for estimating air plasma states. From parametric computations, we determine the appropriate conditions for the collisional-radiative steady state, local thermodynamic equilibrium, and corona equilibrium models in that density and temperature range.     

A ballistic compressor-based experiment for the visualization of liquid propellant jet combustion above 100 MPa

 This paper describes the components and operation of an experimental setup for the visualization of liquid propellant (LP) jet combustion at pressures above 100 MPa. The apparatus consists of an in-line ballistic compressor and LP injector. The ballistic compressor, based on a modified 76 mm gun, provides high-pressure (ca. 55 MPa) clear hot gas for the jet ignition. A piston (projectile) is fired toward a test chamber beyond the barrel’s end, and its rebound is arrested in a transition section that seals the test chamber to the barrel. The LP jet is injected once the piston is restrained, and combustion of the jet further elevates the pressure. At a preset pressure, a disc in the piston ruptures and the combustion gas vents sonically into the barrel. If a monopropellant is used, the jet injection-combustion process then resembles liquid rocket combustion but at very high pressures (ca. 140 MPa). This paper discusses the ballistics of the compression and compares experimental results to those predicted by a numerical model of the apparatus. Experimentally, a pressure of 70 MPa was achieved upon a 12.5 volumetric compression factor by firing a 10 kg piston into 1.04 MPa argon using a charge of 75 g of small-grain M1 propellant. Received: 16 December 1996/Accepted: 15 July 1997