Showing papers on "Shock (mechanics) published in 2003"

Small-Scale Structure of the SN 1006 Shock with Chandra Observations

Abstract: The northeast shell of SN 1006 is the most probable acceleration site of high-energy electrons (up to ~100 TeV) with the Fermi acceleration mechanism at the shock front. We resolved nonthermal filaments from thermal emission in the shell with the excellent spatial resolution of Chandra. The thermal component is extended over ~100'' (about 1 pc at 1.8 kpc distance) in width, consistent with the shock width derived from the Sedov solution. The spectrum is fitted with a thin thermal plasma of kT = 0.24 keV in nonequilibrium ionization, typical for a young supernova remnant. The nonthermal filaments are likely thin sheets with scale widths of ~4'' (0.04 pc) and ~20'' (0.2 pc) upstream and downstream, respectively. The spectra of the filaments are fitted with a power-law function of index 2.1-2.3, with no significant variation from position to position. In a standard diffusive shock acceleration model, the extremely small scale length in the upstream region requires the magnetic field nearly perpendicular to the shock normal. The injection efficiency (η) from thermal to nonthermal electrons around the shock front is estimated to be ~1 × 10-3 under the assumption that the magnetic field in the upstream region is 10 μG. In the filaments, the energy densities of the magnetic field and nonthermal electrons are similar to each other, and both are slightly smaller than that of thermal electrons. These results suggest that the acceleration occurs in more compact regions with larger efficiency than suggested by previous studies.

Fine Structures of Shock of SN 1006 with the Chandra Observation

Abstract: The north east shell of SN 1006 is the most probable acceleration site of high energy electrons (up to ~ 100 TeV) with the Fermi acceleration mechanism at the shock front. We resolved non-thermal filaments from thermal emission in the shell with the excellent spatial resolution of Chandra. The thermal component is extended widely over about ~ 100 arcsec (about 1 pc at 1.8 kpc distance) in width, consistent with the shock width derived from the Sedov solution. The spectrum is fitted with a thin thermal plasma of kT = 0.24 keV in non-equilibrium ionization (NEI), typical for a young SNR. The non-thermal filaments are likely thin sheets with the scale widths of ~ 4 arcsec (0.04 pc) and ~ 20 arcsec (0.2 pc) at upstream and downstream, respectively. The spectra of the filaments are fitted with a power-law function of index 2.1--2.3, with no significant variation from position to position. In a standard diffusive shock acceleration (DSA) model, the extremely small scale length in upstream requires the magnetic field nearly perpendicular to the shock normal. The injection efficiency (eta) from thermal to non-thermal electrons around the shock front is estimated to be ~ 1e-3 under the assumption that the magnetic field in upstream is 10 micro G. In the filaments, the energy densities of the magnetic field and non-thermal electrons are similar to each other, and both are slightly smaller than that of thermal electrons. in the same order for each other. These results suggest that the acceleration occur in more compact region with larger efficiency than previous studies.

Smoothed particle hydrodynamics for numerical simulation of underwater explosion

Abstract: Underwater explosion arising from high explosive detonation consists of a complicated sequence of energetic processes. It is generally very difficult to simulate underwater explosion phenomena by using traditional grid-based numerical methods due to the inherent features such as large deformations, large inhomogeneities, moving interface and so on. In this paper, a meshless, Lagrangian particle method, smoothed particle hydrodynamics (SPH) is applied to simulate underwater explosion problems. As a free Lagrangian method, SPH can track the moving interface between the gas produced by the explosion and the surrounding water effectively. The meshless nature of SPH overcomes the difficulty resulted from large deformations. Some modifications are made in the SPH code to suit the needs of underwater explosion simulation in evolving the smoothing length, treating solid boundary and material interface. The work is mainly focused on the detonation of the high explosive, the interaction of the explosive gas with the surrounding water, and the propagation of the underwater shock. Comparisons of the numerical results for three examples with those from other sources are quite good. Major features of underwater explosion such as the magnitude and location of the underwater explosion shock can be well captured.

Direct Detection of a CME-Associated Shock in LASCO White Light Images

Abstract: The LASCO C2 and C3 coronagraphs recorded a unique coronal mass ejection on April 2, 1999. The event did not have the typical three-part CME structure and involved a small filament eruption without any visibile overlying streamer ejecta. The event exhibited an unusually clear signature of a wave propagating at the CME flanks. The speed and density of the CME front and flanks were consistent with the existence of a shock. To better establish the nature of the white light wave signature, we employed a simple MHD simulation using the LASCO measurements as constraints. Both the measurements and the simulation strongly suggest that the white light feature is the density enhancement from a fast-mode MHD shock. In addition, the LASCO images clearly show streamers being deflected when the shock impinges on them. It is the first direct imaging of this interaction.

Interpreting shock tube ignition data

Abstract: Chemical kinetic modelers make extensive use of shock tube ignition data in the development and validation of combustion reaction mechanisms. These data come from measurements using a range of diagnostics and a variety of shock tubes, fuels, and initial conditions. With the wide selection of data available, it is useful to realize that not all of the data are of the same type or quality, nor are all the data suitable for simple, direct comparison with the predictions of reaction mechanisms. We present here a discussion of some guidelines for the comparison of shock tube ignition time data with reaction mechanism modeling. Areas discussed include definitions of ignition time; ignition time correlations (with examples taken from recent n-heptane and isooctane measurements); shock tube constant-volume behavior; shock tube diameter and boundary layer effects; carrier gas and impurity effects; and future needs and challenges in shock tube research. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36:510–523, 2004

A method for tractable dynamical studies of single and double shock compression.

Abstract: A new multiscale simulation method is formulated for the study of shocked materials. The method combines molecular dynamics and the Euler equations for compressible flow. Treatment of the difficult problem of the spontaneous formation of multiple shock waves due to material instabilities is enabled with this approach. The method allows the molecular dynamics simulation of the system under dynamical shock conditions for orders of magnitude longer time periods than is possible using the popular nonequilibrium molecular dynamics approach. An example calculation is given for a model potential for silicon in which a computational speedup of 10(5) is demonstrated. Results of these simulations are consistent with the recent experimental observation of an anomalously large elastic precursor on the nanosecond time scale.

An experimental investigation of shock wave propagation in periodically layered composites

Abstract: In heterogeneous media, scattering due to interfaces/microstructure between dissimilar materials could play an important role in shock wave dissipation and dispersion. In this work, the influence of interface scattering on finite-amplitude shock waves was experimentally investigated by impacting flyer plates onto periodically layered polycarbonate/6061 aluminum, polycarbonate/304 stainless steel and polycarbonate/glass composites. Experimental results (obtained using velocity interferometer and stress gage) show that these periodically layered composites can support steady structured shock waves. Due to interface scattering, the effective shock viscosity increases with the increase of interface impedance mismatch, and decreases with the increase of interface density (interface area per unit volume) and loading amplitude. For the composites studied here, the strain rate within the shock front is roughly proportional to the square of the shock stress. This indicates that layered composites have much larger shock viscosity due to the interface/microstructure scattering in comparison with the increase of shock strain rate by the fourth power of the shock stress for homogeneous metals. Experimental results also show that due to the scattering effects, shock propagation in the layered composites is dramatically slowed down and the shock speed in composites can be lower than that either of its components.

Pointwise Green Function Bounds for Shock Profiles of Systems with Real Viscosity

Abstract: Following the pointwise semigroup approach of [ZH,MZ.1], we establish sharp pointwise Green function bounds and consequent linearized stability for viscous shock profiles of general hyperbolic-parabolic systems of conservation laws of dissipative type, under the necessary assumptions ([Z.1,Z.3,Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave; transversality of the connecting profile; and hyperbolic stability of the corresponding ideal shock of the associated inviscid system, with no additional assumptions on the structure or strength of the shock. These bounds are used in a companion paper [MZ.2] to establish nonlinear stability of small-amplitude Lax shocks of symmetrizable hyperbolic-parabolic systems.

Board level drop test and simulation of TFBGA packages for telecommunication applications

Abstract: Reliabilit!- perfonnance of IC packages during drop impact is critical, especially for handheld electronic products. Currently. thcrc is no detailed test standard in the industry to advise on the procedures for board level dmp test. nor there is any model Ilia1 providcs good correlation with experimental ineasiircinents of acceleration and impact life. In this paper; detailed drop tests and simulations are pcrfonned on TFBGA (Thin-profile Fine-pitch BGA) and VFBGA (Vey-thinprofile Fine-pitch BGA) packages at board level using testing procediires developed in-house. The packages are susceptible to solder joint failures, induced by a combination of PCB bending and iueclwnical shock during impact. The critical solder ball is obsewed to occur at the outennost comer solder .joint_ and fails along the solder and PCB pad interface. Various testing parameters are studied experimentally and analytically. to understand the effects of drop heightl drop oricntation, number of PCB mounting screws to fixture. position of component on board: PCB bending: solder material, and etc. Drop height, fclt thickness, and contact conditions are used to fine-tune the shape aud level of shock pulse required. Board level drop test can be better controlled. compared with system or product level test such as impact of mobile phone. which sometimes has rather unpredictable results due to higher complexity and variations in drop orientation. At tlie same time, dynamic simulation is perfonncd to compare with esperiniental results. The model established has close values of peak acceleration and impact duration as measured in actual drop test. The failure mode and critical solder ball location predicted by modeling correlate well with testing. For the first time, an accurate life prediction model is proposed for board level drop test to estiinatc the number of drops to failure for a package. For the correlation cases studied. the nminmm nonual peeling stresses of critical solder joints correlate well with the mean impact lives measured during the drop test. The uncertainty of impact life prediction is within M drops, for a typical test of 50 drops. With this new model, a failure-free state can be detennined, and drop test performance of new package design can be quantified. and fuliher enhanced through modeling. This quantitative approach is different from traditional qualitative modeling. as it provides both accurate relative and absolute impact life prediction. The relative performance of package may be different under board level drop test ,and thennal cycling test. Different design guidelines should be considered, depcnding on application and area of concern

Particle Transport in Tangled Magnetic Fields and Fermi Acceleration at Relativistic Shocks

Abstract: This Letter presents a new method of Monte Carlo simulations of test particle Fermi acceleration at relativistic shocks. The particle trajectories in tangled magnetic fields are integrated out exactly from entry to exit through the shock, and the conditional probability of return as a function of ingress and egress pitch angles is constructed by Monte Carlo iteration. These upstream and downstream probability laws are then used in conjunction with the energy gain formula at shock crossing to reproduce Fermi acceleration. For pure Kolmogorov magnetic turbulence upstream and downstream, the spectral index is found to evolve smoothly from s = 2.09 ± 0.02 for mildly relativistic shocks with Lorentz factor Γs = 2 to s 2.26 ± 0.04 in the ultrarelativistic limit Γs 1. The energy gain is ~Γ at first shock crossing, and ~2 in all subsequent cycles, as anticipated by Gallant & Achterberg. The acceleration timescale is found to be as short as a fraction of Larmor time when Γs 1.

Individual effects of stride length and frequency on shock attenuation during running

Abstract: MERCER, J. A., P. DEVITA, T. R. DERRICK, and B. T. BATES. Individual Effects of Stride Length and Frequency on Shock Attenuation during Running. Med. Sci. Sports Exerc., Vol. 35, No. 2, pp. 307–313, 2003. Shock attenuation during running is the process of absorbing impact energy due to the foot-grou

A unified treatment of the gamma-ray burst 021211 and its afterglow

Abstract: The gamma-ray burst (GRB) 021211 had a simple light curve, containing only one peak and the expected Poisson fluctuations. Such a burst may be attributed to an external shock, offering the best chance for a unified understanding of the gamma-ray burst and afterglow emissions. We analyse the properties of the prompt (burst) and delayed (afterglow) emissions of GRB 021211 within the fireball model. Consistency between the optical emission during the first 11 min (which, presumably, comes from the reverse shock heating of the ejecta) and the later afterglow emission (arising from the forward shock) requires that, at the onset of deceleration (∼2 s), the energy density in the magnetic field in the ejecta, expressed as a fraction of the equipartition value (e B ), is larger than in the forward shock at 11 min by a factor of approximately 10 3 . We find that synchrotron radiation from the forward shock can account for the gamma-ray emission of GRB 021211; to explain the observed GRB peak flux requires that, at 2 s, e B in the forward shock is larger by a factor 100 than at 11 min. These results suggest that the magnetic field in the reverse shock and early forward shock is a frozen-in field originating in the explosion and that most of the energy in the explosion was initially stored in the magnetic field. We can rule out the possibility that the ejecta from the burst for GRB 021211 contained more than 10 electron-positron pairs per proton.

The role of instability in gaseous detonation

Abstract: In detonation, the coupling between fluid dynamics and chemical energy release is critical. The reaction rate behind the shock front is extremely sensitive to temperature perturbations and, as a result, detonation waves in gases are always unstable. A broad spectrum of behavior has been reported for which no comprehensive theory has been developed. The problem is extremely challenging due to the nonlinearity of the chemistry-fluid mechanics coupling and extraordinary range of length and time scales exhibited in these flows. Past work has shown that the strength of the leading shock front oscillates and secondary shock waves propagate transversely to the main front. A key unresolved issue has emerged from the past 50 years of research on this problem: What is the precise nature of the flow within the reaction zone and how do the instabilities of the shock front influence the combustion mechanism? This issue has been examined through dynamic experimentation in two facilities. Key diagnostic tools include unique visualizations of superimposed shock and reaction fronts, as well as short but informative high-speed movies. We study a range of fuel-oxidizer systems, including hydrocarbons, and broadly categorize these mixtures by considering the hydrodynamic stability of the reaction zone. From these observations and calculations, we show that transverse shock waves do not essentially alter the classic detonation structure of Zeldovich-von Neumann-Doring (ZND) in weakly unstable detonations, there is one length scale in the instability, and the combustion mechanism is simply shock-induced chemical-thermal explosion behind a piecewise-smooth leading shock front. In contrast, we observe that highly unstable detonations have substantially different behavior involving large excursions in the lead shock strength, a rough leading shock front, and localized explosions within the reaction zone. The critical decay rate model of Eckett et al. (JFM 2000) is combined with experimental observations to show that one essential difference in highly unstable waves is that the shock and reaction front may decouple locally. It is not clear how the ZND model can be effectively applied in highly unstable waves. There is a spectrum of length scales and it may be possible that a type of "turbulent" combustion occurs. We consider how the coupling between chemistry and fluid dynamics can produce a large range of length scales and how possible combustion regimes within the front may be bounded.

Three-dimensional Dynamic Finite Element Analysis of Multiple Laser Shock Peening Processes

Abstract: Laser shock peening (LSP) is an innovative surface treatment technique successfully applied to improving fatigue performance of metallic materials. The fatigue strength and fatigue life of the laser peened material can be significantly improved by deep compressive residual stresses being introduced into the material. The compressive residual stress distribution along the depth of the material is attributed to a high amplitude stress wave induced by a high energy laser pulse. The present paper describes a finite element method for simulating the residual stress distribution in a metal alloy 35CD4 50 HRC steel in single and multiple LSP processes. The process used a three-dimensional dynamic finite element model impacted by a square laser spot. The predicted results for single LSP were well correlated with the available experimental data. Meanwhile, the effects of multiple LSP processes, pressure magnitude and duration, and laser spot sizes on the compressive stress field in the metal alloy were eva...

Particle acceleration and coronal mass ejection driven shocks: Shocks of arbitrary strength

Abstract: [1] There is substantial evidence suggesting that energetic particles observed in “gradual” solar energetic particle events are accelerated at shock waves driven out of the corona by coronal mass ejections (CMEs). We present a model of particle acceleration at interplanetary shock waves, assumed to be driven by CMEs, in which the upstream wave intensity, driven by the accelerated particles, is calculated self-consistently using the steady-state solution to the wave growth equation. This then allows for the self-consistent calculation of the momentum dependent spatial diffusion coefficient which ultimately governs both the acceleration and subsequent evolution of the energetic particles. The model is consequently applicable to shock waves of arbitrary strength, a significant improvement on previous models which were generally only valid for very strong shock waves. The model is able to calculate minimum and maximum particles energies as the shock propagates out into the solar wind and can determine time-dependent downstream spectra. The spectra of particles escaping into the relatively undisturbed upstream medium is also calculated and in future will be used as input to a detailed transport model to determine upstream spectra and intensity profiles. Although we do not compare the results with any individual observations, the model is able to reproduce some of the observed features of “gradual” SEP events. The self-consistent calculation of the upstream wave intensity will in future allow this model to be extended to consider the acceleration of particles of various charge states and masses.

Variation of cosmic ray injection across supernova shocks

Abstract: The injection rate of suprathermal protons into the diffusive shock acceleration process should vary strongly over the surface of supernova remnant shocks. These variations and the absolute value of the injection rate are investigated. In the simplest case, like for SN 1006, the shock can be approximated as spherical in a uniform large-scale magnetic field. The injection rate depends strongly on the shock obliquity and diminishes as the angle between the ambient field and the shock normal increases. Therefore efficient particle injection, which leads to conversion of a significant fraction of the kinetic energy at a shock surface element, arises only in relatively small regions near the "poles", reducing the overall CR production. The sizes of these regions depend strongly on the random background field and the Alfven wave turbulence generated due to the CR streaming instability. For the cases of SN 1006 and Tycho's SNR they correspond to about 20, and for Cas A to between 10 and 20 percent of the entire shock surface. In a first approximation, the CR production rate, calculated under the assumption of spherical symmetry, has therefore to be renormalized by this factor, while the shock as such remains roughly spherical.

Variation of cosmic ray injection across supernova shocks

Abstract: The injection rate of suprathermal protons into the diffusive shock acceleration process should vary strongly over the surface of supernova remnant shocks. These variations and the absolute value of the injection rate are investigated. In the simplest case, like for SN 1006, the shock can be approximated as being spherical in a uniform large-scale magnetic field. The injection rate depends strongly on the shock obliquity and diminishes as the angle between the ambient field and the shock normal increases. Therefore efficient particle injection, which leads to conversion of a significant fraction of the kinetic energy at a shock surface element, arises only in relatively small regions near the "poles", reducing the overall CR production. The sizes of these regions depend strongly on the random background field and the Alfven wave turbulence generated due to CR streaming instability. For the cases of SN 1006 and Tycho's SNR they correspond to about 20, and for Cas A to between 10 and 20 percent of the entire shock surface. In first approximation, the CR production rate, calculated under the assumption of spherical symmetry, has therefore to be renormalized by this factor, while the shock as such remains roughly spherical.

The properties and causes of rippling in quasi-perpendicular collisionless shock fronts

Abstract: . The overall structure of quasi-perpendicular, high Mach number collisionless shocks is controlled to a large extent by ion reflection at the shock ramp. Departure from a strictly one-dimensional structure is indicated by simulation results showing that the surface of such shocks is rippled, with variations in the density and all field components. We present a detailed analysis of these shock ripples, using results from a two-dimensional hybrid (particle ions, electron fluid) simulation. The process that generates the ripples is poorly understood, because the large gradients at the shock ramp make it difficult to identify instabilities. Our analysis reveals new features of the shock ripples, which suggest the presence of a surface wave mode dominating the shock normal magnetic field component of the ripples, as well as whistler waves excited by reflected ions. Key words. Space plasma physics (numerical simulation studies; shock waves; waves and instabilities)

Shock front nonstationarity of supercritical perpendicular shocks

Abstract: [1] The shock front nonstationarity of perpendicular shocks in super-critical regime is analyzed by examining the coupling between “incoming” and “reflected” ion populations. For a given set of parameters including the upstream Mach number (MA) and the fraction α of reflected to incoming ions, a self-consistent, time-stationary solution of the coupling between ion streams and the electromagnetic field is sought for. If such a solution is found, the shock is stationary; otherwise, the shock is nonstationary, leading to a self-reforming shock front often observed in full particle simulations of quasi-perpendicular shocks. A parametric study of this numerical model allows us to define a critical αcrit between stationary and nonstationary regimes. The shock can be nonstationary even for relatively low MA(2–5). For a moderate MA(5–10), the critical value αcrit is about 15 to 20%. For very high MA (>10), αcrit saturates around 20%. Moreover, present full simulations show that self-reformation of the shock front occurs for relatively low βi and disappears for high βi, where βi is the ratio of upstream ion plasma to magnetic field pressures. Results issued from the present theoretical model are found to be in good agreement with full particle simulations for low βi case; this agreement holds as long as the motion of reflected ions is coherent enough (narrow ion ring) to be described by a single population in the model. The present model reveals to be “at variance” with full particle simulations results for the high βi case. Present results are also compared with previous hybrid simulations.

Observation of shock transverse waves in elastic media.

Abstract: We report the first experimental observation of a shock transverse wave propagating in an elastic medium. This observation was possible because the propagation medium, a soft solid, allows one to reach a very high Mach number. In this extreme configuration, the shock formation is observed over a distance of less than a few wavelengths, thanks to a prototype of an ultrafast scanner (that acquires 5000 frames per second). A comparison of these new experimental data with theoretical predictions, based on a modified Burger's equation, shows good agreement.

Shock Shells in Coulomb Explosions of Nanoclusters

Abstract: We predict that Coulomb explosion of a nanoscale cluster, which is ionized by high-intensity laser radiation and has a naturally occurring spatial density profile, will invariably produce shock waves. In most typical situations, two shocks, a leading and a trailing one, form a shock shell that eventually encompasses the entire cluster. Being the first example of shock waves on the nanometer scale, this phenomenon promises interesting effects and applications, including high-rate nuclear reactions inside each individual cluster.

Shock-Vortex Interactions at High Mach Numbers

Abstract: We perform a computational study of the interaction of a planar shock wave with a cylindrical vortex. We use a particularly robust High Resolution Shock Capturing scheme, Marquina's scheme, to obtain high quality, high resolution numerical simulations of the interaction. In the case of a very-strong shock/vortex encounter, we observe a severe reorganization of the flow field in the downstream region, which seems to be due mainly to the strength of the shock. The numerical data is analyzed to study the driving mechanisms for the production of vorticity in the interaction.

Shock response of tantalum: Lateral stress and shear strength through the front

Abstract: Lateral stresses generated by shock loading in tantalum have been determined using manganin stress gauges. These have been used in combination with the measured longitudinal impact stresses to determine the shear strength behind the shock. Results show that with an increase in impact stress, the shear strength in tantalum also increases. Analysis shows that during shock loading the lateral stress in tantalum increases behind the shock front. Since the longitudinal stress is nominally constant until arrival of the release, this implies that the shear strength is reducing behind the shock front. The shock-wave response of tantalum is discussed in the context of a previous weak-shock wave-profile analysis of tantalum, and in terms of the defect generation and storage response of pure face-centered- versus body-centered-cubic metals.