Theory of Shock-Wave Ionization upon High-Velocity Impact of Micrometeorites

1974 ◽  
Vol 29 (6) ◽  
pp. 870-879 ◽  
Author(s):  
S. Drapatz ◽  
K. W. Michel
Keyword(s):  
Shock Wave ◽  
Particle Density ◽  
Analytical Form ◽  
High Impact ◽  
Surface Ionization ◽  
High Velocity Impact ◽  
Laboratory Measurements ◽  
Isentropic Expansion ◽  
Rate Processes ◽  
Simple Analytical Form

The relevant processes in shock wave ionization of a solid Fe micrometeorite impinging on a W target are analyzed. The internal energy behind the shock wave in shown to depend on impact velocity w, target and meteorite density in a simple analytical form. For low impact velocities (w<7 km sec-1) the ions generated by the shock are mostly due to surface ionization. For high impact velocities [w>20 km sec-1) the number of ions can satisfactorily be explained by isentropic expansion of the shocked material to a particle density of n ≈ 1020 cm-3 whereupon the rate processes in the expanding ion cloudlet govern the residual ionization. In velocity regions where laboratory measurements can be carried out, the agreement between theory and experiment confirms the assumptions made.

scholarly journals A Simple Free Energy for the Isotropic-Nematic Phase Transition of Rods

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Remco Tuinier
Keyword(s):  
Free Energy ◽  
Nematic Phase ◽  
Analytical Form ◽  
Orientation Distribution ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Aspect Ratios ◽  
Wide Range ◽  
Hard Rods ◽  
Simple Analytical Form

A free energy expression is proposed that describes the isotropic-nematic binodal concentrations of hard rods. A simple analytical form for this free energy was yet only available using a Gaussian trial function for the orientation distribution function (ODF), leading, however, to a significant deviation of the predicted binodals. The new free energy proposed here is based upon a rationalized correction to the orientational and packing entropies when using the Gaussian ODF. In combination with Parsons-Lee theory or scaled particle theory, it enables describing the isotropic-nematic phase coexistence concentrations of rods accurately using the simple Gaussian ODF for a wide range of aspect ratios.

scholarly journals Shock wave and fracture propagation in water ice by high velocity impact

2000 ◽  
Vol 27 (3) ◽  
pp. 305-308 ◽  
Author(s):  
Masahiko Arakawa ◽  
Kei Shirai ◽  
Manabu Kato
Keyword(s):  
Shock Wave ◽  
High Velocity ◽  
Fracture Propagation ◽  
High Velocity Impact ◽  
Velocity Impact ◽  
Water Ice

Neutral eigensolutions of the stability equation for stratified shear flow

1969 ◽  
Vol 36 (4) ◽  
pp. 673-683 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Differential Equation ◽  
Shear Flow ◽  
Analytical Form ◽  
Analytic Solutions ◽  
Stability Equation ◽  
Hypergeometric Differential Equation ◽  
Stratified Shear Flow ◽  
Parallel Shear Flow ◽  
The Stability ◽  
Simple Analytical Form

Many of the known analytic solutions of the equation for neutral disturbances to a stably stratified, inviscid, parallel shear flow are shown to belong to a wider family of solutions when a transformation to the hypergeometric differential equation is possible. Two particular cases in which the transformation can be made are examined in some detail and the solutions are expressed in a simple analytical form. A number of novel solutions are presented as examples.

Cratering and Shock Wave Phenomena in Steel Plates at High Impact Speeds

1960 ◽  
Vol 31 (3) ◽  
pp. 472-473 ◽  
Author(s):  
Earle B. Mayfield ◽  
James W. Rogers
Keyword(s):  
Shock Wave ◽  
High Impact ◽  
Steel Plates ◽  
Wave Phenomena

On the transient Leveque's problem with an application in electrochemistry

1981 ◽  
Vol 46 (13) ◽  
pp. 3209-3220 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Mass Transfer ◽  
Shear Flow ◽  
Analytical Form ◽  
Step Change ◽  
Electrochemical Potential ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Efficient Data ◽  
Current Densities ◽  
Simple Analytical Form

The electrochemically induced unsteady mass transfer to a uniform shear flow from a local wall electrode subjected to a step change in electrochemical potential is studied. Due to neglecting the streamwise diffusion, the problem has two solutions which however differ only insignificantly. The resulting transient characteristics of current densities have a simple analytical form suitable for an efficient data treatment.

Further Properties of the Wave Charts

1962 ◽  
Vol 66 (624) ◽  
pp. 789-792 ◽  
Author(s):  
W. A. Woods
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Wave Speed ◽  
Pressure Waves ◽  
Perfect Gas ◽  
Expansion Waves ◽  
Isentropic Expansion ◽  
Constant State ◽  
Mach Numbers ◽  
Straight Lines

In a previous paper charts were given which related the flow Mach numbers on either side of a wave to a dimensionless wave speed. Charts were given for shock waves, isentropic expansion waves and isentropic non-steep pressure waves in a perfect gas. In this note it is shown that the lines of constant state ratio plotted on the charts constitute families of straight lines; this fact is particularly important in the case of the shock wave chart. The wave domains are also established and compared diagrammatically.

Active earth thrust by backfills subject to a line surcharge

2005 ◽  
Vol 42 (5) ◽  
pp. 1255-1263 ◽  
Author(s):  
Venanzio R Greco
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Lateral Pressure ◽  
Analytical Form ◽  
Active State ◽  
Active Condition ◽  
Simple Analytical Form

The current analytical solution for the thrust computation when a line of vertical surcharge acts on the backfill behind a wall assumes the soils to be simultaneously elastic, for calculating part of the thrust, and in the active state of failure, for calculating the remaining part of the thrust. This paper gives a coherent analytical solution based on Coulomb's approach. The position of the active thrust is also given in a simple analytical form and compared with the approximate solution of Terzaghi.Key words: active earth force, cantilever walls, lateral pressure, active condition.

scholarly journals The magnetic properties of bismuth, III. Further measurements on the de Haas-van Alphen effect

1939 ◽  
Vol 170 (942) ◽  
pp. 341-364 ◽  
Keyword(s):  
Low Temperatures ◽  
Detailed Comparison ◽  
Analytical Form ◽  
Inhomogeneous Field ◽  
Cubic Lattice ◽  
Low Field ◽  
Faraday Method ◽  
The Magnetic Field ◽  
Simple Analytical Form ◽  
Field Strengths

As was'first shown by de Haas and van Alphen (1932), the susceptibility of bismuth single crystals at low temperatures depends in a peculiar periodic fashion on the magnetic field, and later this effect was studied in greater detail by Shoenberg and Zaki Uddin (1936), especially as regards the influence of temperature and impurities. The general features of the effect were found to agree qualitatively with Peierls’ theory (Peierls 1933), but since this theory was for a cubic lattice it could take no account of the directional features of the effect, and no detailed comparison could be made between the theory and the experiments. Since then, however, the theory has been developed by taking into account the actual crystal symmetry of bismuth (Blackman 1938; Landau 1938), and Landau has shown that the theory assumes a relatively simple analytical form at low field strengths, thus making desirable measurements at fields rather lower than those used in the previous experiments. With the ordinary Faraday method, it is not easy to make accurate susceptibility measurements at field strengths below about 4000 gauss, and this indeed was roughly the lowest field used in the previous work, but an even more serious disadvantage of this method is that it necessarily involves the crystal being in an inhomogeneous field, with the result that the measured susceptibility is always an average over an appreciable range of fields.

Propagation of electromagnetic waves in inhomogeneous plasmas

1994 ◽  
Vol 52 (3) ◽  
pp. 443-456 ◽  
Author(s):  
E. Busatti ◽  
A. Ciucci ◽  
M. De Rosa ◽  
V. Palleschi ◽  
S. Rastelli ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Inhomogeneous Plasma ◽  
Analytical Form ◽  
Reflection And Transmission Coefficients ◽  
Physical Parameters ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Simple Analytical Form

The reflection and transmission coefficients for an electromagnetic beam propagating in an inhomogeneous plasma are calculated analytically using the Magnus approximation in different physical configurations. The theoretical predictions for such coefficients are expressed in simple analytical form, and are compared with the exact results obtained by numerical solution of the wave propagation equations, using the Berreman 4 × 4 matrix method. It is shown that the theoretical approach is able to reproduce the correct results for reflection and transmission coefficients over a wide range of physical parameters. The accuracy of the theoretical analysis, at different orders of approximation, is also discussed.

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