The Propagation of Shock Waves in a Stellar Model with Continuous Density Distribution.

1951 ◽  
Vol 113 ◽  
pp. 496 ◽  
Author(s):  
Pierre A. Carrus ◽  
Phyllis A. Fox ◽  
Felix Haas ◽  
Zdenek Kopal
Keyword(s):  
Shock Waves ◽  
Density Distribution ◽  
Stellar Model ◽  
Continuous Density

scholarly journals Thin Layer Approximation in 3-D

1997 ◽  
Vol 166 ◽  
pp. 137-140
Author(s):  
G.S. Bisnovatyi-Kogan ◽  
S.A. Silich
Keyword(s):  
Shock Waves ◽  
Thin Layer ◽  
Density Distribution ◽  
Interstellar Matter ◽  
Thin Layer Approximation

AbstractEquations are derived which describe the propagation of strong shocks in the interstellar matter, without any restrictions for symmetry, in a thin layer approximation (2.5 dimensions). Using these equations permits to calculate the propagation of shock waves from nonsymmetric supernovae explosions in a medium with arbitrary density distribution and the formation of superbubbles in galaxies.

Towards Nonlinear Multimaterial Topology Optimization Using Unsupervised Machine Learning and Metamodel-Based Optimization

2015 ◽  
Author(s):  
Kai Liu ◽  
Andrés Tovar ◽  
Emily Nutwell ◽  
Duane Detwiler
Keyword(s):  
Machine Learning ◽  
Topology Optimization ◽  
Density Distribution ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Kriging Interpolation ◽  
Unsupervised Machine Learning ◽  
Continuous Density ◽  
Structural Problems ◽  
Synthesis Strategy

This work introduces a multimaterial density-based topology optimization method suitable for nonlinear structural problems. The proposed method consists of three stages: continuous density distribution, clustering, and metamodel-based optimization. The initial continuous density distribution is generated following a synthesis strategy without penalization, e.g., the hybrid cellular automaton (HCA) method. In the clustering stage, unsupervised machine learning (e.g., K-means clustering) is used to optimally classify the continuous density distribution into a finite number of clusters based on their similarity. Finally, a metamodel (e.g., Kriging interpolation) is generated and iteratively updated following a global optimization algorithm (e.g., genetic algorithms) to ultimately converge to an optimal material distribution. The proposed methodology is demonstrated with the design of multimaterial stiff (minimum compliance) structures, compliant mechanisms, and a thin-walled S-rail structure for crashworthiness.

Determining integral density distribution in the mach reflection of shock waves

2017 ◽  
Vol 43 (5) ◽  
pp. 473-476 ◽  
Author(s):  
A. M. Shevchenko ◽  
M. P. Golubev ◽  
A. A. Pavlov ◽  
Al. A. Pavlov ◽  
D. V. Khotyanovsky ◽  
...  
Keyword(s):  
Shock Waves ◽  
Density Distribution ◽  
Mach Reflection ◽  
Integral Density

scholarly journals Towards a Smoothed Particle Hydrodynamics Algorithm for Shocks Through Layered Materials

2013 ◽  
Author(s):  
Iason Zisis ◽  
Bas van der Linden ◽  
Christina Giannopapa
Keyword(s):  
Shock Waves ◽  
Density Distribution ◽  
Smoothed Particle Hydrodynamics ◽  
Shock Loading ◽  
Numerical Technique ◽  
Layered Materials ◽  
Functionally Graded ◽  
Particle Hydrodynamics ◽  
Graded Material ◽  
Smoothed Particle

Hypervelocity impacts (HVIs) are collisions at velocities greater than the target object’s speed of sound. Such impacts produce pressure waves that generate sharp and sudden changes in the density of the materials. These are propagated as shock waves. Previous computational research has given insight into this shock loading for the case of homogeneous materials. Shock-wave propagation through materials with discontinuous density distribution has not been considered in depth yet. Smoothed Particle Hydrodynamics (SPH) is a numerical technique, which has been extensively used for the simulation of HVIs. It is especially suitable for this purpose as it describes both the solid and fluid-like behavior effectively as well as the violent breakup of the material under impact. In previous studies on SPH, impact loading of composite materials was modeled by homogenization of the material, or under assumption of being a so-called functionally graded material (FGM). Both these models neglect the reflection-transmission effects on the interface between materials of different density. In this paper the shock loading of layered materials is studied. A modification to the standard SPH method is developed and tested, that incorporates materials with purely discontinuous density distribution. The developed method’s performance at simple shock loading cases is investigated; reflection-transmission patterns of shock-waves through layered materials are discussed, along with a parametric study of the governing parameters.

A Sequence of E-Type Composite Analytical Solutions of the Lane-Emden Equation

1982 ◽  
Vol 4 (4) ◽  
pp. 376-378 ◽  
Author(s):  
J.O. Murphy
Keyword(s):  
Density Distribution ◽  
Analytical Solutions ◽  
Surface Density ◽  
Radial Distance ◽  
Stellar Model ◽  
The Other ◽  
Uniform Density ◽  
Density Condition ◽  
Emden Equation ◽  
Type Composite

The polytropic stellar model with index n = 0 has a uniform density distribution throughout, and consequently its physical radius is essentially arbitrary because the surface density condition, ϱ = 0, is never satisfied. This surface anomaly, which is not associated with the other polytopic models for 0 < n ≤ 5, could be a constraining factor in certain astrophysical applications involving the n = 0 polytrope. For example, in some circumstances it may be appropriate to utilize the simple physical formulation of the model but on the other hand inappropriate to disregard any zero boundary requirements for the surface density. A sequence of new E-type (as defined below) composite analytical solutions to the Lane-Emden equation, based on the indices 0 and 1, has been developed which eliminates this physical indetermination. The associated polytropic models can be classified as essentially uniform density models. Specifically, they have a large central uniform density n = 0 zone matched, in a physically consistent way, to a small outer n = 1 zone which has a steep density gradient giving ϱ = 0, along with T = 0 and P = 0, at the radial distance corresponding to the first zero of the composite solution.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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.

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