Anisotropic Shock Research Articles

Non-local adaptive structure tensors: Application to anisotropic diffusion and shock filtering

Structure tensors are used in several PDE-based methods to estimate information on the local structure in the image, such as edge orientation. They have become a common tool in many image processing applications. To integrate the local data information, the structure tensor is based on a local regularization of a tensorial product. In this paper, we propose a new regularization model based on the non-local properties of the tensor product. The resulting non-local structure tensor is effective in the restitution of the non homogeneity of the local orientation of the structures. It is particularly efficient in texture regions where patches repeat non locally. The new tensor regularization also offers the advantage of automatically adapting the smoothing parameter to the local structures of the tensor product. Finally, we explain how this new adaptive structure tensor can be plugged into two PDEs: an anisotropic diffusion and a shock filter. Comparisons with other tensor regularization methods and other PDEs demonstrate the clear advantage of using the non-local structure tensor.

Frontiers in the Constitutive Modeling of Anisotropic Shock Waves

Studies of anisotropic materials and the discovery of various novel and unexpected phenomena under shock loading has contributed significantly to our understanding of the behavior of condensed matter. The variety of experimental studies for isotropic materials displays systematic patterns, giving basic insights into the underlying physics of anisotropic shock wave modeling. There are many similarities and significant differences in the phenomena observed for isotropic and anisotropic materials under shock-wave loading. Despite this, the anisotropic constitutive equations must represent mathematical and physical generalization of the conventional constitutive equations for isotropic material and reduce to the conventional constitutive equations in the limit of isotropy. This article presents the current state of the art in the constitutive modeling of this fascinating field.

An equation of state of a carbon-fibre epoxy composite under shock loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [A.A. Lukyanov, Int. J. Plasticity 24, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Grüneisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity Us A and particle velocity up was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the Us A-up relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship Us A-up over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of c0 A (the intercept of the Us A-up curve) that is in the range between first and second generalised anisotropic bulk speed of sound [A.A. Lukyanov, Eur. Phys. J. B 64, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HSLs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.

Reactive Molecular Dynamics of Hypervelocity Collisions of PETN Molecules

Born-Oppenheimer direct dynamics classical trajectory simulations of bimolecular collisions of PETN molecules have been performed to investigate the fundamental mechanisms of hypervelocity chemistry relevant to initiating reactions immediately behind the shock wavefront in energetic molecular crystals. The solid-state environment specifies the initial orientations of colliding molecules. The threshold velocities for initiating chemistry for a variety of crystallographic orientations were correlated with available experimental data on anisotropic shock sensitivity of PETN. Collisions normal to the planes (001) and (110) were found to be most sensitive with threshold velocities on the order of characteristic particle velocities in detonating PETN. The production of NO2 is the dominant reaction pathway in most of the reactive cases. The simulations show that the reactive chemistry, driven by dynamics rather than temperature during hypervelocity collisions, can occur at a very short time scale (10(-13) s) under highly nonequilibrium conditions.

Density Functional Theory Calculations of Solid Nitromethane under Hydrostatic and Uniaxial Compressions with Empirical van der Waals Correction

First-principles density functional theory calculations have been performed with and without an empirical van der Waals (vdW) correction to obtain constitutive relationships of solid nitromethane under hydrostatic and uniaxial compressions. The unit-cell parameters at zero pressure and the hydrostatic equation of state at 0 K are in reasonable agreement with experimental data using pure DFT, and the agreement is significantly improved with the inclusion of the vdW dispersion correction. Uniaxial compressions normal to the {100}, {010}, {001}, {110}, {101}, {011}, and {111} planes were performed, and a comparison of the principal stresses, changes in energy, and shear stresses for different compression directions clearly indicate anisotropic behavior of solid nitromethane upon compression. The calculated anisotropic constitutive relationships might help to link the anisotropic shock sensitivity and the underlying atomic-scale properties of solid nitromethane.

A Boltzmann-kinetical description of an MHD shock with arbitrary field inclination

Aims. We revisit the general problem of the anisotropic MHD shock for arbitrary magnetic field inclinations, where the jump conditions are underdetermined. To describe the transition region of the shock, we derive a variant of a kinetic Boltzmann-Vlasov equation previously used to describe the perpendicular shock in the absence of dissipative processes. Methods. We derive effective force terms, for the kinetic equation, that are based on the conservation of the Chew-Goldberger-Low (CGL) MHD invariants which appear in the standard model for anisotropic MHD. This approach is based on a generalisation of the well-known equivalence between the first CGL invariant and the integral over the magnetic moments of the underlying particles. Results. Assuming an arbitrary distribution function on the upstream side, we integrate the kinetic equation across the shock. This result allows us to establish further relations between the MHD velocity moments on both sides. Using this additional information, we close the anisotropic MHD jump conditions. In addition, the now unique solution of the jump conditions allows us to present explicit cuts through a representative Maxwellian distribution function on both sides of the shock. In the kinetic equation, one only requires two parameters that need to be derived from the classical jump conditions, the classical MHD compression ratio and an equivalent ratio for the magnetic field strengths.

コンピュータグラフィックス 非等方ショックフィルタによる迷路風スクラッチ画の生成

We introduce a non-photorealistic rendering technique for transforming an input photograph into a maze-like scratch image.Stripe patterns are generated on the input image with an anisotropic shock filter,and then the edges of the stripes are extracted and thickened.These thickened edges are overdrawn on the input image to produce a maze-like scratch image.Three-dimensional (3D) effects are then added to the maze-like image using bump mapping.The displacement of edges produces a pop-up effect on the maze-like scratch lines.

非等方ショックフィルタによる非写実的流れ模様の強調と生成

An anisotropic shock filter is presented for edge-preserving enhancement of flow patterns in images. The filter consists of an anisotropic smoothing filter and a shock filter. Edges in images are sharpened in the direction of the principal eigenvector of the structure tensors. The filter is suitable for enhancing and visualizing flow patterns in images. This characteristic of the filter is used for actively generating flow patterns in images, and this technique is applied to non-photorealistic rendering for transforming photographs into oil-painting-like images or crayon-scratch-like pictures.

Quasi–static studies of the deformation and failure of PBX 9501

This paper examines the influence of microstructure on the quasi–static failure of PBX 9501, a polymer–bonded explosive (PBX) manufactured for the Los Alamos National Laboratory in America. Optical microscopy has been used to examine qualitatively cracked and pristine material. Consequent on the manufacturing process, the explosive crystals display angular features and natural facets. In addition, considerable growth twinning, internal defects and voidage has been observed. These defects are found significantly to alter the failure path. In common with other PBXs, failure paths tend to run around the long straight edges of the explosive filler and avoid regions of fine filler and binder. Explosive crystals were found to fracture due either to cracks propagating from another region or internal defects. These observations are confirmed by the use of high–resolution moire interferometry. This sensitive optical technique allows the deformation of the sample to be measured up to and including the point of failure. By taking white–light micrographs that are in exact registration with the measured displacement maps, the influence of the underlying microstructure can be seen.

Jet and vortex flow induced by anisotropic blast wave: experimental and computational study

This paper discusses gas-dynamic aspects of intense explosions in uniform environments. In experiments, the energy of a laser is almost instantaneously released in a volume of air shaped as either a flattened or stretched cylinder generating a blast wave. Its shape evolves in time and ultimately becomes spherical. But momentum transferred to the air when the blast wave is strongly nonspherical is anisotropic. As a result, a subsonic jet and a vortex are induced and propagate along the symmetry axis or along the perpendicular plane, depending on the initial configuration of the blast wave. Simulations based on a free-Lagrangian method for a nonviscous gas are in good agreement with the experiments. Velocities, circulation, and positions of fluid particles found in computations give an insight into the causes and details of the flow. Two simultaneous and contrary processes take place – vorticity production by the anisotropic shock wave and baroclinical generation of vorticity at the boundary of the heated gas – which give rise to net circulation.

Color Snakes

A framework for object segmentation in vector-valued images is presented in this paper. The first scheme proposed is based on geometric active contours moving toward the objects to be detected in the vector-valued image. Object boundaries are obtained as geodesics or minimal weighted-distance curves, where the metric is given by a definition of edges in vector-valued data. The curve flow corresponding to the proposed active contours holds formal existence, uniqueness, stability, and correctness results. The scheme automatically handles changes in the deforming curve topology. The technique is applicable, for example, to color and texture images as well as multiscale representations. We then present an extension of these vector active contours, proposing a possible image flow for vector-valued image segmentation. The algorithm is based on moving each one of the image level sets according to the proposed vector active contours. This extension also shows the relation between active contours and a number of partial-differential-equations-based image processing algorithms as anisotropic diffusion and shock filters.

Filament disappearances and associated shocks of May 1979

In late May 1979 a shock was seen at each of two locations separated by about 90° in heliolongitude and at about the same time. A shock was detected near the Earth, and a shock was detected at Helios 1 when it was off the Sun's west limb. Some authors have considered that these shocks were part of the same event, which originated with a filament disappearance near 65°W. We discuss the observations which show that a large complex filament, extending from 20°W to 70°W, disappeared in several places, probably generating more than one shock. The shock detected near Earth was probably associated with a filament section which disappeared near the central meridian. If this is the case, then the interplanetary scintillation observations of this time period can be explained without invoking highly anisotropic shock propagation.

Classification of shock waves in a collisionless anisotropic plasma

Starting from the conservation equations and the conservation of the mean magnetic moment of the fluid element we derive shock jump conditions in theChew-Goldberger-Low approximation. We show that in a collisionless, anisotropic plasma shock waves can be classified in the same manner as in collision dominated magnetohydrodynamics being tangential, transverse and compressive, respectively, but in the last case one can distinguish two additional classes, namely pseudo-MHD and reverse-MHD shocks.