The modulation of low-energy proton distributions by propagating interplanetary shock waves - A numerical simulation
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Thermonuclear reactions occurring in supernova shock wave propagating through stellar envelope
An investigation of sonic-boom overpressures in water has been conducted by gun-launching small cone-cylinder models over water. Flights were conducted at Mach numbers of 2.7 and 5.7, in air, corresponding to Mach numbers of 0.6 and 1.3, respectively, in water. Shadowgraph pictures and underwater pressure measurements indicate that for horizontal flights at Mach numbers below Mach 4.4 in air (i.e., subsonic relative to the speed of sound in water) the resulting underwater disturbance is an acoustic wave whose peak pressure attenuates rapidly with water depth. In contrast, at supersonic Mach numbers, relative to water, the incident shock wave at the surface is transmitted into the water as a propagating shock wave and the peak pressure associated with it does not attenuate with water depth.
The main objective of this study is to quantitatively investigate the ignition and shock sensitivity of NASA Standard Detonator (NSD) and the shock wave propagation of a linear shaped charge (LSC) after being shocked by NSD flyer plate. This combined explosive train was modeled as a coupled Arbitrary Lagrangian-Eulerian (ALE) model with LS-DYNA hydro code. An ignition-and-growth (I&G) reactive model based on unreacted and reacted Jones-Wilkins-Lee (JWL) equations of state was used to simulate the shock initiation. Various NSD-to-LSC stand-off distances were analyzed to calculate the shock initiation (or failure to initiate) and detonation wave propagation along the shaped charge. Simulation results were verified by experimental data which included VISAR tests for NSD flyer plate velocity measurement and an aluminum target severance test for LSC performance verification. Parameters used for the analysis were obtained from various published data or by using CHEETAH thermo-chemical code.
A review is presented of observations of suprathermal particles in the interplanetary medium along with new data on low energy particles from experiments aboard the ISEE spacecraft. Energy spectra of protons in the near earth atmosphere are plotted in the rest frame of the solar wind noting that at energies above 10 to the 9th eV, the galactic cosmic ray electron component has an unattenuated access into the heliosphere. Solar transient events such as flares accelerate and release energetic particles into the interplanetary medium; flare particle fluxes generate shock waves propagating past 1 AU following the event. It is concluded that the energy spectra for shock wave accelerations show a characteristic shape in accordance with the power law with a rapid steepening at high energies.
Invariant finite amplitude spherical shock wave propagation in medium with inversely radial density
Recent developments in the field of numerical simulation models for the study of shock wave propagation in the corona are presented. These models are based on gasdynamic (GD) and ideal (that is, dissipationless, except at shocks) magnetohydrodynamic (MHD) theories. The characteristics and physical interpretations of the results derived from these models are discussed in some detail. The most significant physical results obtained to date are provided by the two-dimensional non-planar, time-dependent, MHD numerical simulation model. In this model, the non-linear interaction among the three essential MHD waves, i.e., fast-, slow-, and Alfven waves are demonstrated. Finally, the physical relevance of these numerical simulation models in relation to observed solar activity is presented.
A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.
Sonic boom and explosion shock wave propagation over long distances through turbulence modeled by sound speed fluctuation, including acoustic scattering effect
When the Mach number of a supernova shock wave, propagating through the hot interstellar gas, is less than the critical value 2.76, the interaction of the shock with an interstellar cloud produces a reflected pressure pulse that propagates away from the cloud as an acoustic wave. A preliminary analysis indicates that about 4% of the energy of an exploding supernova shell is converted into such waves. When the postshock gas temperature exceeds 2 x 10 to the 6th K, waves as short as 6 pc are damped in less than a wavelength, returning the energy to the hot gas. Longer waves, especially at late stages, are less strongly damped, and are superposed in the hot gas to create a fluctuating magnetoacoustic field, with typical periods of about 100,000 years. In the warm neutral clouds at temperatures of about 8000 K these waves are rapidly damped by plasma slip (ambipolar diffusion), providing a heat source that may account for the temperatures of these clouds.
Observations and theoretical models of interplanetary shock waves are reviewed, with emphasis on the large-scale characteristics of the associated solar wind disturbances and on the relationship of these disturbances to solar activity. The sum of observational knowledge indicates that shock waves propagate through the solar wind along a broad, roughly spherical front, ahead of plasma and magnetic field ejected from solar flares. Typically, the shock front reaches 1 AU about two days after its flare origin, and is of intermediate strength. Not all large flares produce observable interplanetary shock waves; the best indicator of shock production appears to be the generation of both type 2 and type 4 radio bursts by a flare. Theoretical models of shock propagation in the solar wind can account for the typically observed shock strength, transit time, and shape.
In 1968, a series of 0.5-ton and 100-ton TNT explosion experiments were conducted in granitic rock near Cedar City, Utah, as part of a basic research program on cratering and shock wave propagation. Of special interest was the formation of an important type of shock metamorphic feature, shatter cones. A description is presented of the first reported occurrence of shatter cones in high explosion trials. A background to shatter cone studies is presented and attention is given to the test program, geology and physical properties of the test medium, the observed cratering, and the formational pressures for shatter cones. The high explosion trials conducted demonstrate beyond any doubt, that shatter cones can be formed by shock wave processes during cratering and that average formational pressures in these crystalline rocks are in the 20-60 kb range.
This paper presents the recent updates the author has made to PCBoom sonic boom propagation code on its computational efficiency, predictive capability, and file operations. The updated version has recently been released and has a Burgers’ equation solver, which is computationally more efficient than that in the older version by 2 to 3 orders of magnitude. The updated version also enhances the accuracy of the sonic boom propagation prediction by accounting for the full wind effects on the shock wave propagation. Predictions from the updated PCBoom are compared with predictions from the older version and with data from flight tests. Other upgrades and changes that have been made in the latest version include support for Unix-like operating systems, bug fixes, and generation of new types of output files that allow for better manipulation of PCBoom-generated data.
Mathematical model of shock wave propagation in target subjected to hypervelocity projectile impact
Digital computer solution for propagation of a spherical shock wave in aluminum
The dynamic fragmentation in impacts into solids is examined using a physical model for the formation and growth of cracks in rocks. The physical model is then inserted into a numerical model (hydrocode) of stress wave propagation and interaction, from which the outcome of a given impact event can be computed. The hydrocode model predicts fragment sizes due to impact in terms of shock waves propagating in a homogeneous elastic medium containing a distribution of crack nucleation centers known as Weibull flaws.
Utilizing many years of observation from deep space and near-earth spacecraft a theoretical understanding has evolved on how ions and electrons are accelerated in interplanetary shock waves. This understanding is now being applied to solar flare-induced shock waves propagating through the solar atmosphere. Such solar flare phenomena as gamma-ray line and neutron emissions, interplanetary energetic electron and ion events, and Type II and moving Type IV radio bursts appear understandable in terms of particle acceleration in shock waves.
The first measurements of the structure of wind speed, electron density, and electron density fluctuations are reported for a shock wave propagating through the acceleration region of the solar wind. Radio scattering observations, consisting of spectral broadening, mean phase and amplitude scintillations, were made on August 18, 1979, 13.1 solar radii east of the sun near the ecliptic plane, using the 2.3 and 8.4 GHz radio signals of Voyager 1. The results show a shock wave speed of about 3,500 km/sec; which, when compared with average transit time speed to 1 AU, shows that substantial deceleration took place with outward propagation from the sun. This result is consistent with a blast wave.