Showing papers on "Shock (mechanics) published in 2001"

Nonlinear theory of diffusive acceleration of particles by shock waves

Abstract: Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data.

Particle acceleration by ultrarelativistic shocks: theory and simulations

Abstract: We consider the acceleration of charged particles near ultra-relativistic shocks, with Lorentz factor Gamma_s >> 1. We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultra-relativistic shocks is a power law, N(E) \propto E^{-s}, with a nearly universal value s \approx 2.2 - 2.3 for the slope of this power law. We confirm that the ultra-relativistic equivalent of Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle theta_c \approx 1/Gamma_s around the shock normal. We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount: Delta theta ~ 1/Gamma_s. This limits the energy change per shock crossing cycle to Delta E ~ E, except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor ~ Gamma_s^2 for those particles that are scattered back across the shock into the upstream region.

Particle acceleration by ultra-relativistic shocks: theory and simulations

Abstract: We consider the acceleration of charged particles near ultra-relativistic shocks, with Lorentz factor Gamma_s >> 1. We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultra-relativistic shocks is a power law, N(E) \propto E^{-s}, with a nearly universal value s \approx 2.2 - 2.3 for the slope of this power law. We confirm that the ultra-relativistic equivalent of Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle theta_c \approx 1/Gamma_s around the shock normal. We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount: Delta theta ~ 1/Gamma_s. This limits the energy change per shock crossing cycle to Delta E ~ E, except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor ~ Gamma_s^2 for those particles that are scattered back across the shock into the upstream region.

Conditions for shock revival by neutrino heating in core-collapse supernovae

Abstract: Energy deposition by neutrinos can rejuvenate the stalled bounce shock and can provide the energy for the supernova explosion of a massive star. This neutrino-heating mechanism, though investigated by numerical simulations and analytic studies, is not finally accepted or proven as the trigger of the explosion. Part of the problem is that different groups have obtained seemingly discrepant results, and the complexity of the hydrodynamic models often hampers a clear and simple interpretation of the results. This demands a deeper theoretical understanding of the requirements of a successful shock revival. A toy model is developed here for discussing the neutrino heating phase analytically. The neutron star atmosphere between the neutrinosphere and the supernova shock can well be considered to be in hydrostatic equilibrium, with a layer of net neutrino cooling below the gain radius and a layer of net neutrino heating above. Since the mass infall rate to the shock is in general different from the rate at which gas is advected into the neutron star, the mass in the gain layer varies with time. Moreover, the gain layer receives additional energy input by neutrinos emitted from the neutrinosphere and the cooling layer. Therefore the determination of the shock evolution requires a time-dependent treatment. To this end the hydrodynamical equations of continuity and energy are integrated over the volume of the gain layer to obtain conservation laws for the total mass and energy in this layer. The radius and velocity of the supernova shock can then be calculated from global properties of the gain layer as solutions of an initial value problem, which expresses the fact that the behavior of the shock is controlled by the cumulative effects of neutrino heating and mass accumulation in the gain layer. The described toy model produces steady-state accretion and mass outflow from the nascent neutron star as special cases. The approach is useful to illuminate the conditions that can lead to delayed explosions and in this sense supplements detailed numerical simulations. On grounds of the model developed here, a criterion is derived for the requirements of shock revival. It confirms the existence of a minimum neutrino luminosity that is needed for shock expansion, but also demonstrates the importance of a sufficiently large mass infall rate to the shock. If the neutrinospheric luminosity or accretion rate by the shock are too low, the shock is weakened because the gain layer loses more mass than is resupplied by inflow. On the other hand, very high infall rates damp the shock expansion and above some threshold, the development of positive total energy in the neutrino-heating layer is prevented. Time-dependent solutions for the evolution of the gain layer show that the total specific energy transferred to nucleons by neutrinos is limited by about 1052 erg (~5 MeV per nucleon). This excludes the possibility of very energetic explosions by the neutrino-heating mechanism, because the typical mass in the gain layer is about 0.1 and does not exceed a few tenths of a solar mass. The toy model also allows for a crude discussion of the global effects of convective energy transport in the neutrino-heating layer. Transfer of energy from the region of maximum heating to radii closer behind the shock mainly reduces the loss of energy by the inward flow of neutrino-heated matter through the gain radius.

Explosive dispersal of solid particles

Abstract: . The rapid dispersal of inert solid particles due to the detonation of a heterogeneous explosive, consisting of a packed bed of steel beads saturated with a liquid explosive, has been investigated experimentally and numerically. Detonation of the spherical charge generates a blast wave followed by a complex supersonic gas-solid flow in which, in some cases, the beads catch up to and penetrate the leading shock front. The interplay between the particle dynamics and the blast wave propagation was investigated experimentally as a function of the particle size (100–925 $\mu$ m) and charge diameter (8.9–21.2 cm) with flash X-ray radiography and blast wave instrumentation. The flow topology during the dispersal process ranges from a dense granular flow to a dilute gas-solid flow. Difficulties in the modeling of the high-speed gas-solid flow are discussed, and a heuristic model for the equation of state for the solid flow is developed. This model is incorporated into the Eulerian two-phase fluid model of Baer and Nunziato (1986) and simulations are carried out. The results of this investigation indicate that the crossing of the particles through the shock front strongly depends on the charge geometry, the charge size and the material density of the particles. Moreover, there exists a particle size limit below which the particles cannot penetrate the shock for the range of charge sizes considered. Above this limit, the distance required for the particles to overtake the shock is not very sensitive to the particle size but remains sensitive to the particle material density. Overall, excellent agreement was observed between the experimental and computational results.

Multidimensional Stability of Planar Viscous Shock Waves

Abstract: Physical and mathematical considerations warrant the inclusion of regularizing effects such as diffusion, dissipation, and/or relaxation in the study of stability of shock waves, particularly in MHD, combustion, and multiphase flow. Indeed, in this generality, the “ideal shock” approximation has relevance only in the long-wave limit, that is, in the large, but not in the small scale. Likewise, multidimensional effects are known both from experiment and from the study of the inviscid (hyperbolic) case to play a key role in determining stability. Yet, until very recently, there were no rigorous analyses for systems taking into account both effects simultaneously.

Numerical testing of the stability of viscous shock waves

Abstract: A new theoretical Evans function condition is used as the basis of a numerical test of viscous shock wave stability. Accuracy of the method is demonstrated through comparison against exact solutions, a convergence study, and evaluation of approximate error equations. Robustness is demonstrated by applying the method to waves for which no current analytic results apply (highly nonlinear waves from the cubic model and strong shocks from gas dynamics). An interesting aspect of the analysis is the need to incorporate features from the analytic Evans function theory for purposes of numerical stability. For example, we find it necessary, for numerical accuracy, to solve ODEs on the space of wedge products.

Experimental observations of flame acceleration and transition to detonation following shock-flame interaction

Abstract: Observations are presented from experiments where laminar flame bubbles were perturbed successively by incident and reflected shock waves. Significant flame acceleration was observed in many instances, with the flame closely coupled to the reflected shock wave. The coupled waves are interpreted using a generalized Hugoniot analysis. As the incident shock velocity increased, detonation emerged near the highly convolved reaction zone. Prior to detonation the external visual attributes of the combustion fronts appear identical to turbulent combustion. However, they cannot be due to classical isotropic turbulence. The overall conclusion is that the observed enhancement of combustion is driven by chemi-acoustic interactions and related gas-dynamic effects. An analysis of the prevailing thermodynamic states suggests that thermal auto-ignition chemistry could also play a significant role prior to the onset of detonation.

Shock absorbing midsole for an athletic shoe

Abstract: A midsole comprises a heel cup having a semi-rigid upper plate, a lower plate composed of a material that is softer than the upper plate, and at least one telescopic shock absorber between the upper and lower plates. The telescopic shock absorbers have one portion that collapses into a second portion when the shock absorber is loaded or compressed. On release of the load, the shock absorbers of the invention return only a controlled portion of the compressive load originally applied. A second embodiment has a translucent heel cup and shock absorbers and a lamp for illuminating the heel cup and shock absorbers.

Optimal protection from impact, shock and vibration

Abstract: Systems with Isolators and Problems from Optimizing Their Characteristics. Optimal Protection of Rectilinearly Moving Systems from an Instantaneous Impact. Optimal Protection of Rotating Objects from an Instantaneous Impact. Optimal Isolation for a Class of Disturbances. Optimization of Shock Isolators for an Object with Incompletely Prescribed Mass. Optimization of Vibration Isolation Systems. Optimal Damping of Transient Motion in Multi-Degree-of-Freedom Systems. Computational Methods for a Limiting Performance Analysis. Design of Optimal Shock Isolators. Is Optimal Shock Isolation Always Provided by a Constant Control Force?

Hip joint prostheses

Abstract: A joint prosthesis comprising at least a first and a second load carrying member, the first load carrying member being substantially more shock absorbing and resilient than the second load carrying member.

Numerical modeling of finite-amplitude sound beams: Shock formation in the near field of a cw plane piston source

Abstract: Two theoretical models and the corresponding numerical codes for the description of nonlinear acoustic beams radiated from intense cw sources in water are presented. In the first model, diffraction effects are included using the Rayleigh integral, whereas nonlinearity and thermoviscous absorption are accounted for in a quasi-plane approximation. The simulations are performed in the time domain using the code previously developed for single-pulse propagation in medium having arbitrary frequency-dependent absorption. The second model is based on the Khokhlov–Zabolotskaya–Kuznetsov equation, which, contrary to the first model, accounts for diffraction in the parabolic approximation. The simulations are performed in the frequency domain using a novel algorithm that has been developed. A variable number of harmonics, which follows the nonlinear broadening of the wave spectrum are employed in the algorithm to speed up calculations. In order to prove the validity and the accuracy of the two codes developed, the simulation of diffraction and nonlinear effects in the near field of an intense ultrasound circular piston source in water is performed. The results of modeling obtained by both codes are compared with each other and with known experimental data, and are found to be in a good agreement. Frequency-domain code is then used for detailed study of the strongly nonlinear regime of propagation, when shocks are developed in the waveform close to the source. It is demonstrated that diffraction plays a major role in shock formation. Development of two shocks in each cycle and their further collision is predicted. It is also shown that nonlinear propagation and shock formation result at some distance in the two times excess of peak positive pressure in comparison with the maximum value obtained in the case of linear propagation. The beam total power decay due to formation of shocks as a function of the propagation distance is compared with the intensity in a plane wave propagation without diffraction. It is shown that nonlinear energy decay starts earlier for the beam, but decreases slower over longer distances.

Shock Drift Acceleration of Electrons

Abstract: We review the theory of shock drift acceleration, developing the theory in detail for gyrophaseaveraged particles. It is shown howboth the upstream and downstream velocity spaces separate into different regions according to the interaction of the particles with the shock (reflection, transmission, head-on, overtaking). The effects of the cross-shock electric field and of the magnetic overshoot are discussed. The effectiveness of acceleration is estimated for Maxwellian and power law distributions. The condition for a beam instability to be generated by reflected particles is determined and found to be independent of the distribution function for isotropic inflowing electrons.

Mixed shock models

Abstract: Traditionally, shock models are of two kinds. The failure (of a system) is related either to the cumulative effect of a (large) number of shocks or it is caused by a shock which is larger than some critical level. The present paper is devoted to a mixed model, in which the system is supposed to break down either because of one (very) large shock, or as a result of many smaller ones.

Shock absorbing member capable of absorbing larger impact applied to electronic apparatus

Abstract: A shock absorbing body is interposed between an internal component such as a hard disk drive (HDD) and the inside surface of an enclosure for an electronic apparatus such as a notebook personal computer. The shock absorbing body includes a first receiving surface defined at one end of the shock absorbing body so as to receive the internal component. A second receiving surface is defined at the other end of the shock absorbing body so as to receive the inside surface of the enclosure. A constriction is formed in the shock absorbing body between the first and second receiving surfaces. When a larger impact is applied to the enclosure, the shock absorbing body is allowed to suffer from a fracture at the constriction. The energy of the impact is transformed into the energy of the fracture at the constriction. The impact energy is sufficiently consumed in this manner. The internal component can be protected from the larger impact.

Magnetic field fluctuations across the Earth’s bow shock

Abstract: . We present a statistical analysis of 132 dayside (LT 0700-1700) bow shock crossings of the AMPTE/IRM spacecraft. We perform a superposed epoch analysis of low frequency, magnetic power spectra some minutes up-stream and downstream of the bow shock. The events are devided into categories depending on the angle θBn between bow shock normal and interplanetary magnetic field, and on plasma-β. In the foreshock upstream of the quasi-parallel bow shock, the power of the magnetic fluctuations is roughly 1 order of magnitude larger (δB ~ 4 nT for frequencies 0.01–0.04 Hz) than upstream of the quasi-perpendicular shock. There is no significant difference in the magnetic power spectra upstream and downstream of the quasi-parallel bow shock; only at the shock itself, is the magnetic power enhanced by a factor of 4. This enhancement may be due to either an amplification of convecting upstream waves or to wave generation at the shock interface. On the contrary, downstream of the quasi-perpendicular shock, the magnetic wave activity is considerably higher than upstream. Down-stream of the quasi-perpendicular low-β bow shock, we find a dominance of the left-hand polarized component at frequencies just below the ion-cyclotron frequency, with amplitudes of about 3 nT. These waves are identified as ion-cyclotron waves, which grow in a low-β regime due to the proton temperature anisotropy. We find a strong correlation of this anisotropy with the intensity of the left-hand polarized component. Downstream of some nearly perpendicular (θBn ≈ 90°) high-β crossings, mirror waves are identified. However, there are also cases where the conditions for mirror modes are met downstream of the nearly perpendicular shock, but no mirror waves are observed. Key words. Interplanetary physics (plasma waves and turbulence) – Magnetospheric physics (magnetosheath; plasma waves and instabilities)

Broadband Observations and Modeling of the Shell-Type Supernova Remnant G347.3-0.5

Abstract: The supernova remnant G347.3–0.5 emits a featureless power-law in X-rays, thought to indicate shock-acceleration of electrons to high energies. We here produce a broadband spectrum of the bright NW limb of this source by combining radio observations from the Australia Telescope Compact Array (ATCA), X-ray observations from the Advanced Satellite for Cosmology and Astrophysics (ASCA), and TeV γ-ray observations from the CANGAROO imaging y Cerenkov telescope. We assume this emission is produced by an electron population generated by diffusive shock acceleration at the remnant forward shock. The nonlinear aspects of the particle acceleration force a connection between the widely different wavelength bands and between the electrons and the unseen ions, presumably accelerated simultaneously with the electrons. This allows us to infer the relativistic proton spectrum and estimate ambient parameters such as the supernova explosion energy, magnetic field, matter density in the emission region, and efficiency of the shock acceleration process. We find convincing evidence that the shock acceleration is efficient, placing> 25% of the shock kinetic energy flux into relativistic ions. Despite this high efficiency, the maximum electron and proton energies, while depending somewhat on assumptions for the compression of the magnetic field in the shock, are well below the observed ‘knee’ at ∼ 10 15 eV in the Galactic cosmic-ray spectrum. Subject headings: Supernova remnants — acceleration of particles — cosmic-rays — X-rays — radio — gamma-rays: ISM: individual (G347.3-0.5)

Densification of fused silica due to shock waves and its implications for 351 nm laser induced damage.

Abstract: High-power 351 nm (3ω) laser pulses can produce damaged areas in high quality fused silica optics. Recent experiments have shown the presence of a densified layer at the bottom of damage initiation craters. We have studied the propagation of shock waves through fused silica using large-scale atomistic simulations since such shocks are expected to accompany laser energy deposition. These simulations show that the shocks induce structural transformations in the material that persist long after the shock has dissipated. Values of densification and thickness of densified layer agree with experimental observations. Moreover, our simulations give an atomistic description of the structural changes in the material due to shock waves and their relation to Raman spectra measurements.

The location of low Mach number bow shocks at Earth

Abstract: On April 26 and 27 and May 10-12, 1999, unusually low solar wind densities produced unusually low Alfven Mach numbers that moved the Earth's bow shock far out past its normal location. The shocks observed by the Wind spacecraft corresponded to shock subsolar distances of 45 and 42 R E , respectively, on these days which are the most distant locations at which the shock has ever been seen. Shock observations by three other spacecraft on these days along with 34 previously reported distant shocks are used to compare with the predictions of different models. A recent MHD bow shock model of Cairns and Lyon [1995] predicts the observed locations quite well as does a modified gasdynamic model of Farris and Russell [1994] if a new Mach-number-dependent shape parameter is used. A third model of Verigin et al. [1997] also predicts a shock shape and is also quite good. Bow shock predictions are limited by uncertainties in measurements of the very low densities and uncertainties in the position and shape of the magnetopause. Asymmetries in the shock shape caused by the interplanetary magnetic field direction and not accounted for by models are another likely source of uncertainty. These uncertainties make it impossible to clearly favor one theoretical model over another.

Shock event error logging in a disk drive

Abstract: A disk drive with a shock event logger that records information about a shock event as determined by a shock detection system. The shock detection system analyzes signals that result from movement of part of the disk drive and determines if the movement is due to a shock. Information about the shock event is recorded by the shock event logger to a non-volatile memory. In one embodiment, the shock detection system is a position error signal processor that detects shocks based on deviation of a transducer from its reference position, or based on time elapsed during settling of the deviated transducer. In one embodiment, the shock event logger records information about the shock event sequentially. In another embodiment, the shock event logger records the shock event information in the form of a histogram. Logged shock event information improves the manner in which the disk drive is diagnosed and serviced.

Broad-band Observations and Modeling of the Shell-Type Supernova Remnant G347.3-0.5

Abstract: The supernova remnant G347.3--0.5 emits a featureless power-law in X-rays, thought to indicate shock-acceleration of electrons to high energies. We here produce a broad-band spectrum of the bright NW limb of this source by combining radio observations from the Australia Telescope Compact Array (ATCA), X-ray observations from the Advanced Satellite for Cosmology and Astrophysics (ASCA), and TeV gamma-ray observations from the CANGAROO imaging Cerenkov telescope. We assume this emission is produced by an electron population generated by diffusive shock acceleration at the remnant forward shock. The nonlinear aspects of the particle acceleration force a connection between the widely different wavelength bands and between the electrons and the unseen ions, presumably accelerated simultaneously with the electrons. This allows us to infer the relativistic proton spectrum and estimate ambient parameters such as the supernova explosion energy, magnetic field, matter density in the emission region, and efficiency of the shock acceleration process. We find convincing evidence that the shock acceleration is efficient, placing >25% of the shock kinetic energy flux into relativistic ions. Despite this high efficiency, the maximum electron and proton energies, while depending somewhat on assumptions for the compression of the magnetic field in the shock, are well below the observed `knee' at about 10^{15} eV in the Galactic cosmic-ray spectrum.

Observation of a Hydrodynamically Driven, Radiative Precursor Shock

Abstract: Observations of a radiative-precursor shock that evolves from a purely hydrodynamic system are presented. The radiative precursor is observed in low-density SiO2 aerogel foam using x-ray absorption spectroscopy. A plastic slab, shocked and accelerated by high-intensity laser irradiation, drives the shock which then produces the radiative precursor. The length and temperature profile of the radiative precursor are examined as the intensity of the laser is varied.

Shock absorbing member and bumper

Abstract: A shock absorbing member for a vehicle is designed to absorb the impact energy in a plastic deformation manner to absorb the axial compressive load. The shock absorbing member includes a hollow member whose cross-section is roughly constant and whose axis is adapted to extend forward and rearward of the vehicle. A flange is formed on the hollow member roughly along the axis of the hollow member and projects by an amount increasing gradually from one side toward the other side of the axis.

Shock wave propagation and dispersion in glow discharge plasmas

Abstract: Spark-generated shock waves were studied in glow discharges in argon and argon–nitrogen mixtures. Ultraviolet filtered Rayleigh scattering was used to measure radial profiles of gas temperature, and the laser schlieren method was used to measure shock arrival times and axial density gradients. Time accurate, inviscid, axisymmetric fluid dynamics computations were run and results compared with the experiments. Our simulation show that changes in shock structure and velocity in weakly ionized gases are explained by classical gas dynamics, with the critical role of thermal and multi-dimensional effects (transverse gradients, shock curvature, etc.). A direct proof of the thermal mechanism was obtained by pulsing the discharge. With a sub-millisecond delay between starting the discharge and shock launch, plasma parameters reach their steady-state values, but the temperature is still low, laser schlieren signals are virtually identical to those without the discharge, differing dramatically from the signals in discharges with fully established temperature profiles.