scholarly journals Erratum: Shock formation in stellar perturbations and tidal shock waves in binaries

2011 ◽  
Vol 418 (2) ◽  
pp. 1408-1408
Author(s):  
Carsten Gundlach ◽  
Jeremiah W. Murphy
Keyword(s):  
Shock Waves ◽  
Shock Formation ◽  
Stellar Perturbations

Shock Waves in Mathematical Models of the Aorta

1970 ◽  
Vol 37 (1) ◽  
pp. 34-37 ◽  
Author(s):  
George Rudinger
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Shock Waves ◽  
Method Of Characteristics ◽  
Wave Form ◽  
Shock Formation ◽  
Rapid Flow ◽  
Latex Tube ◽  
Flow Changes ◽  
The Mathematical Model

If the nonlinear equations for nonsteady blood flow are solved by the method of characteristics, shock discontinuities may develop as a result of omitting from the mathematical model some aspect of the system that becomes significant at rapid flow changes. As an illustration, the flow from the heart into the aorta at the beginning of systole is analyzed. An equation is derived which yields shock formation distances between a few centimeters and several meters depending on the elastic properties of the aorta. Since knowledge of the actual wave form would be useful for computer programming, a few exploratory experiments were performed with an unrestrained latex tube. They indicated wave transitions extending over several tube diameters, but maximum steepening of the wave has not yet been achieved.

Structure and stability of shock waves in granular gases

2019 ◽  
Vol 873 ◽  
pp. 568-607 ◽  
Author(s):  
Nick Sirmas ◽  
Matei I. Radulescu
Keyword(s):  
Shock Waves ◽  
Molecular Dynamic ◽  
Travelling Wave ◽  
Granular Gases ◽  
Shock Formation ◽  
Molecular Dynamic Simulations ◽  
Dynamic Simulations ◽  
Relaxation Effects ◽  
Molecular Noise ◽  
Dynamics Simulations

Previous experiments have revealed that shock waves driven through dissipative media may become unstable, for example, in granular gases, and in molecular gases undergoing strong relaxation effects. The current paper addresses this problem of shock stability at the Euler and Navier–Stokes continuum levels in a system of disks (two-dimensional) undergoing activated inelastic collisions. The dynamics of shock formation and stability is found to be in very good agreement with earlier molecular dynamic simulations (Sirmas & Radulescu, Phys. Rev. E, vol. 91, 2015, 023003). It was found that the modelling of shock instability requires the introduction of molecular noise for its development and sustenance. This is confirmed in two stability problems. In the first, the evolution of shock formation dynamics is monitored without noise, with only initial noise and with continuous molecular noise. Only the latter reproduces the results of shock instability of molecular dynamics simulations. In the second problem, the steady travelling wave solution is obtained for the shock structure in the inviscid and viscous limits and its nonlinear stability is studied with and without molecular fluctuations, again showing that instability can be sustained only in the presence of fluctuations. The continuum results show that instability takes the form of a rippled front of a wavelength comparable with the relaxation thickness of the steady shock wave, at scales at which molecular fluctuations become important, in excellent agreement with the molecular dynamic simulations.

Ion reflection by shock waves and pulse generation by cross-field ion beams

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
Yukiharu Ohsawa
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Interstellar Medium ◽  
Spatial Scales ◽  
Ion Beams ◽  
Pulse Generation ◽  
The Other ◽  
Shock Formation ◽  
Density Control ◽  
Particle Simulations

Comparisons are made of two different particle simulations: one for the study of plasma-based accelerators (Gueroult & Fisch, Phys. Plasmas, vol. 23, 2016, 032113) and the other for the study of shock formation in the interstellar medium (Yamauchi & Ohsawa, Phys. Plasmas, vol. 14, 2007, 053110). In the former, shock waves used for plasma density control create ion beams by reflection. In the latter, a fast and dense beam of exploding ions penetrates a surrounding plasma. In both simulations, magnetic bumps are generated from the motion of ion beams perpendicular to a magnetic field. Despite the apparent differences of their purposes, configurations and spatial scales, the two simulations show strong similarities in the generation processes and effects of the bumps, suggesting that these are not rare plasma phenomena. The bump created by the exploding ions develops into backward and forward magnetosonic pulses.

scholarly journals Vectorial dispersive shock waves on an incoherent landscape

2020 ◽  
Vol 238 ◽  
pp. 11010
Author(s):  
Javier Nuño ◽  
Christophe Finot ◽  
Miro Erkintalo ◽  
Julien Fatome
Keyword(s):  
Shock Waves ◽  
Optical Fiber ◽  
Short Pulse ◽  
Shock Formation ◽  
Probe Wave ◽  
Partially Coherent ◽  
Diffusive Term ◽  
The Impact

We study the impact of temporal randomness on the formation of vectorial dispersive shock-waves that emerge due to the interaction of a partially coherent probe wave co-propagating together with an orthogonally polarized intense short pulse. Experiments carried out in a normally dispersive optical fiber demonstrate that the lack of coherence of the probe landscape acts as a strong diffusive term, which is able to hamper or inhibit the vectorial shock formation.

Propagation of weak shock waves in a non-ideal gas

2011 ◽  
Vol 1 (3) ◽  
Author(s):  
Lal. Singh ◽  
Dheerendra Singh ◽  
Subedar Ram
Keyword(s):  
Shock Waves ◽  
Gas Flow ◽  
Nonlinear Distortion ◽  
Mathematical Formulation ◽  
Weak Shock ◽  
Ideal Gas ◽  
Shock Formation ◽  
Coupled Transport ◽  
First Order ◽  
The Ideal

AbstractThis paper investigates the problem of propagation of planar and non-planar weak shock waves in a non-ideal medium. The mathematical formulation developed in this work leads to a closed system of coupled transport equations which efficiently describes the strength of a shock wave and the first order discontinuities induced behind it. The influence of the parameter of non-idealness and the non planar configuration of the wavefront on the nonlinear distortion, attenuation and shock formation of pulses, are discussed in detail. An analytical expression for the shock formation distance is obtained and a direct comparison between the ideal versus the non ideal gas flow is established. Also, the usual asymptotic decay laws for weak shock are recovered.

An improved perturbation theory for shock waves propagating through non-uniform regions

1960 ◽  
Vol 8 (2) ◽  
pp. 193-209 ◽  
Author(s):  
M. P. Friedman
Keyword(s):  
Shock Wave ◽  
Perturbation Theory ◽  
Shock Waves ◽  
Subsonic Flow ◽  
Shock Formation ◽  
Explicit Solutions ◽  
Flow Equations ◽  
Present Solution ◽  
Non Linear ◽  
Uniform Tube

This paper considers the problem of the propagation of a shock wave down a non-uniform tube. Linearized solutions to the problem (Chester 1954) do not hold when the velocity behind the shock is near or at the sonic speed. By retaining appropriate non-linear terms of the flow equations, a solution is obtained which holds for all conditions behind the shock, and reduces to the linearized solution for conditions away from sonic.The behaviour of supersonic or subsonic flow entering regions of expanding or contracting area changes is discussed. It is found that subsidiary shocks may be formed; these can be located and described using the present solution. Explicit solutions are given for the cases of supersonic or subsonic flow entering a region of linearly expanding or contracting area. The point of shock formation as well as the path of the subsidiary shock is obtained for the case in which the area contracts.

Investigation of shock-wave deformation history from recovered structure

1986 ◽  
Vol 44 ◽  
pp. 434-435
Author(s):  
M.A. Mogilevsky ◽  
L.S. Bushnev
Keyword(s):  
Shock Wave ◽  
Plastic Deformation ◽  
Dislocation Density ◽  
Shock Waves ◽  
Shock Front ◽  
Single Crystals ◽  
Residual Deformation ◽  
Deformation Structure ◽  
Deformation History ◽  
Deformation Velocity

Single crystals of Al were loaded by 15 to 40 GPa shock waves at 77 K with a pulse duration of 1.0 to 0.5 μs and a residual deformation of ∼1%. The analysis of deformation structure peculiarities allows the deformation history to be re-established.After a 20 to 40 GPa loading the dislocation density in the recovered samples was about 1010 cm-2. By measuring the thickness of the 40 GPa shock front in Al, a plastic deformation velocity of 1.07 x 108 s-1 is obtained, from where the moving dislocation density at the front is 7 x 1010 cm-2. A very small part of dislocations moves during the whole time of compression, i.e. a total dislocation density at the front must be in excess of this value by one or two orders. Consequently, due to extremely high stresses, at the front there exists a very unstable structure which is rearranged later with a noticeable decrease in dislocation density.

Sign in / Sign up

Export Citation Format

Share Document