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1
Pope, M. H., and D. B. Melrose. "Diffusive Shock Acceleration by Multiple Shock Fronts with Differing Properties." Publications of the Astronomical Society of Australia 11, no. 2 (August 1994): 175–79. http://dx.doi.org/10.1017/s1323358000019858.
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AbstractThe effect of diffusive shock acceleration on a distribution of particles is explored for multiple shocks, taking into account adiabatic expansion between the shocks. Specifically, the spectral index is calculated numerically for two cases: a sequence of identical shocks, and a sequence of pairs of shocks with alternating shock strength. How these two cases evolve to the asymptotic limit is examined, and it is shown that the evolution of the paired-shock case can be described by a sequence of identical shocks with shock strength equal to the mean of the two.
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Kevlahan, N. K. R. "The propagation of weak shocks in non-uniform flows." Journal of Fluid Mechanics 327 (November 25, 1996): 161–97. http://dx.doi.org/10.1017/s0022112096008506.
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A new theory of the propagation of weak shocks into non-uniform, two-dimensional flows is introduced. The theory is based on a description of shock propagation in terms of a manifold equation together with compatibility conditions for shock strength and its normal derivatives behind the shock. This approach was developed by Ravindran & Prasad (1993) for shocks of arbitrary strength propagating into a medium at rest and is extended here to non-uniform media and restricted to moderately weak shocks. The theory is tested against known analytical solutions for cylindrical and plane shocks, and against a full direct numerical simulation (DNS) of a shock propagating into a sinusoidal shear flow. The test against DNS shows that the present theory accurately predicts the evolution of a moderately weak shock front, including the formation of shock-shocks due to shock focusing. The theory is then applied to the focusing of an initially parabolic shock, and to the propagation of an initially straight shock into a variety of simple flows (sinusoidal shear, vortex array, point-vortex array) exhibiting some fundamental properties of turbulent flows. A number of relations are deduced for the variation of shock quantities with initial shock strength MS0 and the Mach number of the flow ahead of the shock MU (e.g. separation of shock-shocks and maximum shock strength at a focus). It is found that shock-shocks are likely to form in turbulent flows with Mt/M1N > 0.14–0.25, where Mt is the average Mach number of the turbulence and M1N is the Mach number of the shock in a flow at rest. The shock moves up to 1.5% faster in a two-dimensional vortex array than in uniform flow.
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Garcia, S. L., N. L. Garcia, L. R. Oliveira, V. L. C. C. Rodrigues, and M. L. S. Mello. "Experimentally induced heat- and cold-shock tolerance in adult Panstrongylus megistus (Burmeister) (Hemiptera, Reduviidae)." Brazilian Journal of Biology 63, no. 3 (August 2003): 449–55. http://dx.doi.org/10.1590/s1519-69842003000300010.
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The survival rate of domestic male and female adult Panstrongylus megistus was studied after sequential heat and cold shocks in order to investigate shock tolerance compared to that previously reported for nymphs. Sequential shocks were such that a milder shock (0°C, 5°C, 35°C, or 40°C for 1 h) preceded a severe one (0°C or 40°C for 12 h), separated by intervals of 8, 18, 24, and 72 h at 28°C (control temperature). The preliminary thermal shock induced tolerance to the more severe one, although tolerance intensity depended on the initial shock temperature and the interval between treatments. Despite the observed tolerance, the survival rate for insects subjected to both shocks decreased when compared to that of individuals subjected to a single mild shock. When tolerance differed with sex, females showed greater values than males. In contrast to the response detected in nymphs, for which higher heat tolerance values were sustained for intervals of up to 24 h (preliminary shock, 35ºC) or even longer (preliminary shock, 40ºC) between sequential shocks, significant values were verified in adults only for shock intervals of up to 8 h (preliminary shock, 40ºC). While findings for nymphs exhibited considerable cold-shock tolerance under conditions in which preliminary shocks were given at 5ºC or 0ºC and the periods between shocks were up to 72 h long, the adults were shown to be capable of acquiring a substancial tolerance response to a more severe cold shock only when the preliminary shock was given at 0ºC and shock interval surpassed 18 h. It is assumed that the mechanisms involved in the cellular protection of P. megistus under sequential temperature shocks (heat shock protein action?) may loose effectiveness with insect development.
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Bai, Jianming, Yun Chen, Chun Yuan, and Xiaoling Yin. "Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/828979.
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This paper considers a more general shock model with insurance and financial risk background, in which the system is subject to two types of shocks called primary shocks and secondary shocks. Each primary shock causes a series of secondary shocks according to some cluster pattern. In reliability applications, a primary shock can represent an issue of insurance policies of an insurer company, and the secondary shocks then denote the relevant insurance claims generated by the policy. We focus on the local cumulative shock process where only a certain number of the most recent primary and secondary shocks are accumulated. This process is a very new topic in the available literature which is more flexible and realistic in modeling some more complex reliability situations such as bankrupt behavior of an insurance company. Based on the theory of infinite divisibility and stable distributions, we establish a central limit theorem for the local cumulative shock process and obtain the conditions for the process to converge to an infinitely divisible distribution or to anα-stable law. Also, by choosing the proper scale parameters, the process converges to a normal distribution.
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Watari, S., and T. Detman. "In situ local shock speed and transit shock speed." Annales Geophysicae 16, no. 4 (April 30, 1998): 370–75. http://dx.doi.org/10.1007/s00585-998-0370-9.
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Abstract. A useful index for estimating the transit speeds was derived by analyzing interplanetary shock observations. This index is the ratio of the in situ local shock speed and the transit speed; it is 0.6–0.9 for most observed shocks. The local shock speed and the transit speed calculated for the results of the magnetohydrodynamic simulation show good agreement with the observations. The relation expressed by the index is well explained by a simplified propagation model assuming a blast wave. For several shocks the ratio is approximately 1.2, implying that these shocks accelerated during propagation in slow-speed solar wind. This ratio is similar to that for the background solar wind acceleration.Keywords. Interplanetary physics (Flare and stream dynamics; Interplanetary shocks; Solar wind plasma)
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Wu, C. C., M. Dryer, and S. T. Wu. "Slow shock interactions in the heliosphere using an adaptive grid MHD model." Annales Geophysicae 23, no. 3 (March 30, 2005): 1013–23. http://dx.doi.org/10.5194/angeo-23-1013-2005.
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Abstract. A one-dimensional (1-D), time-dependent, adaptive-grid MHD model with solar wind structure has been used in the past to study the interaction of shocks. In the present study, we wish to study some fundamental processes that may be associated with slow shock genesis and their possible interactions with other discontinuities. This adaptive-grid model, suitable for appropriate spatial and temporal numerical simulations, is used for this purpose because its finer grid sizes in the vicinity of the steep gradients at shocks make it possible to delineate the physical parameters on both sides of the shocks. We found that a perturbation with deceleration of solar wind will generate an ensemble consisting of a forward slow shock, a fast forward wave and a reverse slow shock. On the other hand, a perturbation with an increase in acceleration of solar wind will generate both a slow shock and a fast shock. These two perturbations, although not unique, may be representative of momentum and pressure changes at the solar surface. During the transition of a fast shock overtaking a slow shock from behind, the slow shock might disappear temporarily. Also, during the process of the merging of two slow shocks, a slow shock-like structure is formed first; later, the slow shock-like structure evolves into an intermediate shock-like structure. This intermediate shock-like structure then evolves into an intermediate wave and a slow shock-like structure. Finally, the slow shock-like structure evolves into a slow shock, but the intermediate wave disappears by interacting with the non-uniform solar wind. This complex behavior demonstrates the non-unique nature of the formation of slow shocks, intermediate shocks and their derivative structures. We emphasize the main aim of this work to be both: (a) non-unique input physical parameters to explain the paucity of observed slow shocks, as well as (b) the impossibility of backward tracing to the history of input boundary conditions in view of the present inability to describe unambiguous inputs at the Sun.
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Hollenbach, David. "The Physics of Molecular Shocks in YSO Outflows." Symposium - International Astronomical Union 182 (1997): 181–98. http://dx.doi.org/10.1017/s0074180900061647.
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Shock waves light up the jets, winds and outflows around YSOs and diagnose the physical conditions and processes resident in these regions. This paper discusses the differences between the jet/wind shock and the ambient shock, between C shocks and J shocks, and between the shocks produced by pure jets and by collimated wide angle winds. Basic shock physics is briefly reviewed, with a special focus on the temperature structure in shocks and the Wardle instability of C shocks. Application is made to the origin of shocked H2 emission and to H2O masers.
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Spiteri, Shaun. "Shock Absorber Applications." European Journal of Engineering Research and Science 4, no. 1 (January 18, 2019): 37–41. http://dx.doi.org/10.24018/ejers.2019.4.1.1005.
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Shock Absorbers are a part of everyday life and have many different applications and uses. They are used for bridges, highways, buildings and cars to absorb the impact from the bumps, earthquakes and high winds. Different applications require different types of shocks and different materials. A rubber shock absorber cannot be used on a vehicle while a cylindrical shock absorber cannot be used on a highway. All the situations require a specific shape and type of shocks to be used for the required tasks.
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Spiteri, Shaun. "Shock Absorber Applications." European Journal of Engineering and Technology Research 4, no. 1 (January 18, 2019): 37–41. http://dx.doi.org/10.24018/ejeng.2019.4.1.1005.
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Shock Absorbers are a part of everyday life and have many different applications and uses. They are used for bridges, highways, buildings and cars to absorb the impact from the bumps, earthquakes and high winds. Different applications require different types of shocks and different materials. A rubber shock absorber cannot be used on a vehicle while a cylindrical shock absorber cannot be used on a highway. All the situations require a specific shape and type of shocks to be used for the required tasks.
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Cha, Ji Hwan, and Maxim Finkelstein. "On New Classes of Extreme Shock Models and Some Generalizations." Journal of Applied Probability 48, no. 1 (March 2011): 258–70. http://dx.doi.org/10.1239/jap/1300198148.
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In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. A shock model which combines these two types is called a ‘combined shock model’. In this paper we study new classes of extreme shock models and, based on the obtained results and model interpretations, we extend these results to several specific combined shock models. For systems subject to nonhomogeneous Poisson processes of shocks, we derive the corresponding survival probabilities and discuss some meaningful interpretations and examples.
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Cha, Ji Hwan, and Maxim Finkelstein. "On New Classes of Extreme Shock Models and Some Generalizations." Journal of Applied Probability 48, no. 01 (March 2011): 258–70. http://dx.doi.org/10.1017/s0021900200007750.
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In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. A shock model which combines these two types is called a ‘combined shock model’. In this paper we study new classes of extreme shock models and, based on the obtained results and model interpretations, we extend these results to several specific combined shock models. For systems subject to nonhomogeneous Poisson processes of shocks, we derive the corresponding survival probabilities and discuss some meaningful interpretations and examples.
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HORNUNG, H. G., and D. W. SCHWENDEMAN. "Oblique shock reflection from an axis of symmetry: shock dynamics and relation to the Guderley singularity." Journal of Fluid Mechanics 438 (July 5, 2001): 231–45. http://dx.doi.org/10.1017/s0022112001004360.
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Oblique shock reflection from an axis of symmetry is studied using Whitham's theory of geometrical shock dynamics, and the results are compared with previous numerical simulations of the phenomenon by Hornung (2000). The shock shapes (for strong and weak shocks), and the location of the shock-shock (for strong shocks), are in good agreement with the numerical results, though the detail of the shock reflection structure is, of course, not resolved by shock dynamics. A guess at a mathematical form of the shock shape based on an analogy with the Guderley singularity in cylindrical shock implosion, in the form of a generalized hyperbola, fits the shock shape very well. The smooth variation of the exponent in this equation with initial shock angle from the Guderley value at zero to 0.5 at 90° supports the analogy. Finally, steady-flow shock reflection from a symmetry axis is related to the self-similar flow.
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Huete, C., J. G. Wouchuk, B. Canaud, and A. L. Velikovich. "Analytical linear theory for the shock and re-shock of isotropic density inhomogeneities." Journal of Fluid Mechanics 700 (April 30, 2012): 214–45. http://dx.doi.org/10.1017/jfm.2012.126.
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AbstractWe present an analytical model that describes the linear interaction of two successive shocks launched into a non-uniform density field. The re-shock problem is important in different fields, inertial confinement fusion among them, where several shocks are needed to compress the non-uniform target. At first, we present a linear theory model that studies the interaction of two successive shocks with a single-mode density perturbation field ahead of the first shock. The second shock is launched after the sonic waves emitted by the first shock wave have vanished. Therefore, in the case considered in this work, the second shock only interacts with the entropic and vortical perturbations left by the first shock front. The velocity, vorticity and density fields are later obtained in the space behind the second shock. With the results of the single-mode theory, the interaction with a full spectrum of random-isotropic density perturbations is considered by decomposing it into Fourier modes. The model describes in detail how the second shock wave modifies the turbulent field generated by the first shock wave. Averages of the downstream quantities (kinetic energy, vorticity, acoustic flux and density) are easily obtained either for two-dimensional or three-dimensional upstream isotropic spectra. The asymptotic limits of very strong shocks are discussed. The study shown here is an extension of previous works, where the interaction of a planar shock wave with random isotropic vorticity/entropy/acoustic spectra were studied independently. It is also a preliminary step towards the understanding of the re-shock of a fully turbulent flow, where all three of the modes, vortical, entropic and acoustic, might be present.
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Vimercati, Davide, Giulio Gori, and Alberto Guardone. "Non-ideal oblique shock waves." Journal of Fluid Mechanics 847 (May 21, 2018): 266–85. http://dx.doi.org/10.1017/jfm.2018.328.
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From the analysis of the isentropic limit of weak compression shock waves, oblique shock waves in which the post-shock Mach number is larger than the pre-shock Mach number, named non-ideal oblique shocks, are admissible in substances characterized by moderate molecular complexity and in the close proximity to the liquid–vapour saturation curve. Non-ideal oblique shocks of finite amplitude are systematically analysed, clarifying the roles of the pre-shock thermodynamic state and Mach number. The necessary conditions for the occurrence of non-ideal oblique shocks of finite amplitude are singled out. In the parameter space of pre-shock thermodynamic states and Mach number, a new domain is defined which embeds the pre-shock states for which the Mach number increase can possibly take place. The present findings are confirmed by state-of-the-art thermodynamic models applied to selected commercially available fluids, including siloxanes and hydrocarbons currently used as working fluids in renewable energy systems.
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Maleckar, M. M., M. C. Woods, V. Y. Sidorov, M. R. Holcomb, D. N. Mashburn, J. P. Wikswo, and N. A. Trayanova. "Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms." American Journal of Physiology-Heart and Circulatory Physiology 295, no. 4 (October 2008): H1626—H1633. http://dx.doi.org/10.1152/ajpheart.00706.2008.
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To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV−, reverse polarity is LV−) were applied to the ventricles in diastole. Experiments and simulations revealed that RV− shocks resulted in longer activation times compared with LV− shocks of the same strength. 3D simulations demonstrated that RV− shocks induced a greater volume of hyperpolarization at shock end compared with LV− shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.
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Knisley, S. B., W. M. Smith, and R. E. Ideker. "Prolongation and shortening of action potentials by electrical shocks in frog ventricular muscle." American Journal of Physiology-Heart and Circulatory Physiology 266, no. 6 (June 1, 1994): H2348—H2358. http://dx.doi.org/10.1152/ajpheart.1994.266.6.h2348.
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Effects of electrical shocks on myocardium are important for defibrillation. We measured effects of shocks (5 ms, 1–40 V/cm) in isolated frog ventricular strips. We recorded contraction strength and intracellular action potential (AP) with a shock-voltage cancellation technique to allow recordings immediately after shocks. Shocks of > or = 5 V/cm produced a dose- and latency-dependent prolongation of the AP ongoing during the shock. Stronger shocks of 28–40 V/cm decreased the duration, maximum diastolic potential, amplitude, and maximum rate of rise of the phase zero depolarization of paced APs that began after the shock. The contraction strength increased 43 and 59% during the 10 s after the stronger shocks. The transmembrane potential was shifted toward 0 mV immediately after the stronger shocks. We concluded that weak or strong shocks prolong the AP ongoing during the shock, whereas sufficiently strong shocks also shorten APs that begin after the shock. AP prolongation and shortening may be important for defibrillation and acceleration of tachycardia after failed cardioversion shocks.
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Tsurutani, B. T., L. Shan, G. S. Lakhina, C. Mazelle, X. Meng, A. Du, and Z. Liu. "Comment on “Non-interacting coronal mass ejections and solar energetic particles near the quadrature configuration of solar terrestrial relations observatory”: CME shocks are fast magnetosonic shocks and not intermediate Alfvén shocks." Astronomy & Astrophysics 656 (December 2021): A152. http://dx.doi.org/10.1051/0004-6361/202141029.
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Aims. The expression for the shock Mach number used by Ravishankar and Michalek (2020, A&A, 638, A42) is incorrect. We wish to provide a correct expression so they can redo their analyses. Methods. Coronal mass ejection (CME) shocks are fast magnetosonic shocks and not intermediate Alfvén shocks. We give the steps for calculating the shock normal, shock velocity, and, thus, the shock Mach number. We also mention that the shock properties, such as being quasi-perpendicular or quasi-parallel, are another important parameter for the shock acceleration of energetic particles. Results. We have corrected the errors existing in the Astronomy and Astrophysics literature concerning the mathematical expression for the Mach number for a CME shock. Hopefully, future authors will use the now-correct expression for the Mach number. Conclusions. The correct shock Mach number expression has been given to Ravishankar and Michalek. It is hoped that they will redo their calculations (including using other shock properties) to see if their 2020 conclusions still hold true or not.
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Baek, Jungho, and Ji-Yong Seo. "A Study on Unobserved Structural Innovations of Oil Price: Evidence from Global Stock, Bond, Foreign Exchange, and Energy Markets." Review of Pacific Basin Financial Markets and Policies 18, no. 01 (March 2015): 1550004. http://dx.doi.org/10.1142/s0219091515500046.
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This study examines the effects of oil shocks by their respective causes and of volatility spillover including leverage effects. Previous studies did not analyze oil factor by categorizing it into three components (supply shock, demand shock, and market shock) as determinants of rate of return in stock markets, a key issue in finance. Results show that oil shocks determine returns in the global stock market, bond market, foreign exchange market, and energy market, and that their effects vary by types of markets, levels of oil prices, and types of oil shocks. Second, the leverage effect of oil shocks and the spillover effect of volatility in demand shock and market shock are mostly statistically significant during periods characterized by high oil prices.
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Zhang, Congyao, Eugene Churazov, William R. Forman, and Natalia Lyskova. "Runaway merger shocks in galaxy cluster outskirts and radio relics." Monthly Notices of the Royal Astronomical Society 488, no. 4 (August 5, 2019): 5259–66. http://dx.doi.org/10.1093/mnras/stz2135.
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ABSTRACT Moderately strong shocks arise naturally when two subclusters merge. For instance, when a smaller subcluster falls into the gravitational potential of a more massive cluster, a bow shock is formed and moves together with the subcluster. After pericentre passage, however, the subcluster is decelerated by the gravity of the main cluster, while the shock continues moving away from the cluster centre. These shocks are considered as promising candidates for powering radio relics found in many clusters. The aim of this paper is to explore the fate of such shocks when they travel to the cluster outskirts, far from the place where the shocks were initiated. In a uniform medium, such a ‘runaway’ shock should weaken with distance. However, as shocks move to large radii in galaxy clusters, the shock is moving down a steep density gradient that helps the shock to maintain its strength over a large distance. Observations and numerical simulations show that, beyond R500, gas density profiles are as steep as, or steeper than, ∼r−3, suggesting that there exists a ‘habitable zone’ for moderately strong shocks in cluster outskirts where the shock strength can be maintained or even amplified. A characteristic feature of runaway shocks is that the strong compression, relative to the initial state, is confined to a narrow region just behind the shock. Therefore, if such a shock runs over a region with a pre-existing population of relativistic particles, then the boost in radio emissivity, due to pure adiabatic compression, will also be confined to a narrow radial shell.
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James, T. A., S. Viti, J. Holdship, and I. Jiménez-Serra. "Tracing shock type with chemical diagnostics." Astronomy & Astrophysics 634 (January 29, 2020): A17. http://dx.doi.org/10.1051/0004-6361/201936536.
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Aims. The physical structure of a shock wave may take a form unique to its shock type, implying that the chemistry of each shock type is unique as well. We aim to investigate the different chemistries of J-type and C-type shocks in order to identify unique molecular tracers of both shock types. We apply these diagnostics to the protostellar outflow L1157 to establish whether the B2 clump could host shocks exhibiting type-specific behaviour. Of particular interest is the L1157-B2 clump, which has been shown to exhibit bright emission in S-bearing species and HNCO. Methods. We simulate, using a parameterised approach, a planar, steady-state J-type shock wave using UCLCHEM. We compute a grid of models using both C-type and J-type shock models to determine the chemical abundance of shock-tracing species as a function of distance through the shock and apply it to the L1157 outflow. We focus on known shock-tracing molecules such as H2O, HCN, and CH3OH. Results. We find that a range of molecules including H2O and HCN have unique behaviour specific to a J-type shock, but that such differences in behaviour are only evident at low vs and low nH. We find that CH3OH is enhanced by shocks and is a reliable probe of the pre-shock gas density. However, we find no difference between its gas-phase abundance in C-type and J-type shocks. Finally, from our application to L1157, we find that the fractional abundances within the B2 region are consistent with both C-type and J-type shock emission.
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de Voil, Cedric. "Snack Shack or Snack Shock?" Nutrition and Health 16, no. 3 (July 2002): 249–50. http://dx.doi.org/10.1177/026010600201600310.
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Xu, Y. F., S. C. Hu, Y. Cai, and S. N. Luo. "Origins of plastic shock waves in single-crystal Cu." Journal of Applied Physics 131, no. 11 (March 21, 2022): 115901. http://dx.doi.org/10.1063/5.0080757.
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We investigate shock wave propagation in single-crystal Cu with large-scale molecular dynamics simulations. Plastic shock waves propagate via dislocation nucleation or growth. With decreasing particle velocity, a remarkable drop in plastic shock wave velocity relative to the linear shock velocity–particle velocity relation is observed in the elastic–plastic two-wave regime for different loading directions. This reduction can be attributed to the changes in the mechanisms of plastic shock wave generation/propagation, from the dislocation nucleation-dominant mode, to the alternating nucleation and growth mode, and to the growth-dominant mode. For weak shocks, the plastic shock advances at the speed of the growth of existing dislocations (below the maximum elastic shock wave speed), considerably slower than the dislocation nucleation front for strong shocks (above the maximum elastic shock wave speed).
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GOODMAN, JEREMY, and ANDREW MACFADYEN. "Ultra-relativistic geometrical shock dynamics and vorticity." Journal of Fluid Mechanics 604 (May 14, 2008): 325–38. http://dx.doi.org/10.1017/s0022112008001249.
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Geometrical shock dynamics, also called CCW theory, yields approximate equations for shock propagation in which only the conditions at the shock appear explicitly; the post-shock flow is presumed approximately uniform and enters implicitly via a Riemann invariant. The non-relativistic theory, formulated by G. B. Whitham and others, matches many experimental results surprisingly well. Motivated by astrophysical applications, we adapt the theory to ultra-relativistic shocks advancing into an ideal fluid whose pressure is negligible ahead of the shock, but is one third of its proper energy density behind the shock. Exact results are recovered for some self-similar cylindrical and spherical shocks with power-law pre-shock density profiles. Comparison is made with numerical solutions of the full hydrodynamic equations. We review relativistic vorticity and circulation. In an ultra-relativistic ideal fluid, circulation can be defined so that it changes only at shocks, notwithstanding entropy gradients in smooth parts of the flow.
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Wu, X. F., Z. G. Dai, Y. F. Huang, and T. Lu. "Optical Flash and Radio Flare in Wind Environment." Symposium - International Astronomical Union 214 (2003): 343–44. http://dx.doi.org/10.1017/s0074180900194720.
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The interaction of a relativistic fireball with its ambient medium is described through two shocks: a reverse shock that propagates into the fireball, and a forward shock that propagates into the medium. We here study very early afterglows from the reverse and forward shocks in winds. An optical flash arises from both the relativistic reverse and forward shock while a radio flare is produced by the forward shock.
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SCHWENDEMAN, DONALD W. "On converging shock waves of spherical and polyhedral form." Journal of Fluid Mechanics 454 (March 10, 2002): 365–86. http://dx.doi.org/10.1017/s0022112001007170.
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The behaviour of converging spherical shock waves is considered using Whitham's theory of geometrical shock dynamics. An analysis of converging shocks whose initial shape takes the form of regular polyhedra is presented. The analysis of this problem is motivated by the earlier work on converging cylindrical shocks discussed in Schwendeman & Whitham (1987). In that paper, exact solutions were reported for converging polygonal shocks in which the initial shape re-forms repeatedly as the shock contracts. For the polyhedral case, the analysis is performed both analytically and numerically for an equivalent problem involving shock propagation in a converging channel with triangular cross-section. It is found that a repeating sequence of shock surfaces composed of nearly planar pieces develops, although the initial planar surface does not re-form, and that the increase in strength of the shock at each iterate in the sequence follows the same behaviour as for a converging spherical shock independent of the convergence angle of the channel. In this sense, the shocks are stable and the result is analogous to that found in the two-dimensional case. A numerical study of converging spherical shocks subject to smooth initial perturbations in strength shows a strong tendency to form surfaces composed of nearly planar pieces suggesting that the stability result is fairly general.
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KEVLAHAN, N. K. R. "The vorticity jump across a shock in a non-uniform flow." Journal of Fluid Mechanics 341 (June 25, 1997): 371–84. http://dx.doi.org/10.1017/s0022112097005752.
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The vorticity jump across an unsteady curved shock propagating into a two-dimensional non-uniform flow is considered in detail. The exact general expression for the vorticity jump across a shock is derived from the gasdynamics equations. This general expression is then simplified by writing it entirely in terms of the Mach number of the shock MS and the local Mach number of the flow ahead of the shock MU.The vorticity jump is very large at places where the curvature of the shock is very large, even in the case of weak shocks. Vortex sheets form behind shock-shocks (associated with kinks in the shock front).The ratio of vorticity production by shock curvature to vorticity production by baroclinic effects is O(½(γ−1)M2U), where γ is ratio of specific heats, which is very small if the flow ahead of the shock is only weakly compressible. If, however, the tangential gradient along the shock of M2U is large then baroclinic production is significant; this is the case in turbulent flows with large gradients of turbulent kinetic energy ½M2U. The vorticity jump across a weak shock decreases in proportion to shock intensity if the flow ahead of the shock is rotational, rather than in proportion to the cube of shock intensity as is often assumed, and thus is not negligible. It is also shown that vorticity may be generated across a straight shock even if the flow ahead of the shock is irrotational. The importance of the contribution to the vorticity jump by non-uniformities in the flow ahead of the shock has not been recognized in the past.Examples are given of the vorticity jump across strong and weak shocks in a variety of flows exhibiting some properties of turbulence.
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MITROVIĆ, DARKO, and MARKO NEDELJKOV. "DELTA SHOCK WAVES AS A LIMIT OF SHOCK WAVES." Journal of Hyperbolic Differential Equations 04, no. 04 (December 2007): 629–53. http://dx.doi.org/10.1142/s021989160700129x.
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We discus the existence of delta shock waves obtained as a limit of two shock waves. For that purpose we perturb a prototype of weakly hyperbolic 2 × 2 system (sometimes called the "generalized pressureless gas dynamics model") by an additional term (called the "generalized vanishing pressure"). The obtained perturbed system is strictly hyperbolic and its Riemann problem is solvable. Since it is genuinely nonlinear, its solution consists of shocks and rarefaction waves combination. As perturbation parameter vanishes, the solution converges in the space of distribution. Specially, a solution consisting of two shocks converge to a delta function. Also, we give a formal definition of approximate solution and prove a kind of entropy argument. The paper finishes by a discussion about delta shock interactions for the original system.
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Sow Mondal, Shanwlee, Aveek Sarkar, Bhargav Vaidya, and Andrea Mignone. "Acceleration of Solar Energetic Particles by the Shock of Interplanetary Coronal Mass Ejection." Astrophysical Journal 923, no. 1 (December 1, 2021): 80. http://dx.doi.org/10.3847/1538-4357/ac2c7a.
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Abstract Interplanetary coronal mass ejection (ICME) shocks are known to accelerate particles and contribute significantly to solar energetic particle events. We have performed magnetohydrodynamic-particle in cell simulations of ICME shocks to understand the acceleration mechanism. These shocks vary in Alfvénic Mach numbers as well as in magnetic field orientations (parallel and quasi-perpendicular). We find that diffusive shock acceleration plays a significant role in accelerating particles in a parallel ICME shock. In contrast, shock drift acceleration (SDA) plays a pivotal role in a quasi-perpendicular shock. High-Mach shocks are seen to accelerate particles more efficiently. Our simulations suggest that background turbulence and local particle velocity distribution around the shock can indirectly hint at the acceleration mechanism. Our results also point toward a few possible in situ observations that could validate our understanding of the topic.
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Snow, B., and A. Hillier. "Intermediate shock sub-structures within a slow-mode shock occurring in partially ionised plasma." Astronomy & Astrophysics 626 (June 2019): A46. http://dx.doi.org/10.1051/0004-6361/201935326.
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Context. Slow-mode shocks are important in understanding fast magnetic reconnection, jet formation and heating in the solar atmosphere, and other astrophysical systems. The atmospheric conditions in the solar chromosphere allow both ionised and neutral particles to exist and interact. Under such conditions, fine sub-structures exist within slow-mode shocks due to the decoupling and recoupling of the plasma and neutral species. Aims. We study numerically the fine sub-structure within slow-mode shocks in a partially ionised plasma, in particular, analysing the formation of an intermediate transition within the slow-mode shock. Methods. High-resolution 1D numerical simulations were performed using the (PIP) code using a two-fluid approach. Results. We discover that long-lived intermediate (Alfvén) shocks can form within the slow-mode shock, where there is a shock transition from above to below the Alfvén speed and a reversal of the magnetic field across the shock front. The collisional coupling provides frictional heating to the neutral fluid, resulting in a Sedov-Taylor-like expansion with overshoots in the neutral velocity and neutral density. The increase in density results in a decrease of the Alfvén speed and with this the plasma inflow is accelerated to above the Alfvén speed within the finite width of the shock leading to the intermediate transition. This process occurs for a wide range of physical parameters and an intermediate shock is present for all investigated values of plasma-β, neutral fraction, and magnetic angle. As time advances the magnitude of the magnetic field reversal decreases since the neutral pressure cannot balance the Lorentz force. The intermediate shock is long-lived enough to be considered a physical structure, independent of the initial conditions. Conclusions. Intermediate shocks are a physical feature that can exist as shock sub-structure for long periods of time in partially ionised plasma due to collisional coupling between species.
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Melrose, D. B., and M. H. Pope. "Diffusive Shock Acceleration by Multiple Shocks." Publications of the Astronomical Society of Australia 10, no. 3 (1993): 222–24. http://dx.doi.org/10.1017/s1323358000025716.
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AbstractDiffusive shock acceleration produces a power law momentum distribution f(p)α p−b, with b ≥ 4 for a single shock, and b = 4 for a single strong shock. It has been shown that the distribution for acceleration at a sequence of identical shocks is flatter, approaching f(p)α p−3 below a high energy knee, for an arbitrarily large number of shocks. We show how this flatter distribution arises and discuss the range of momenta over which it extends after a finite number of shocks.
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Shrestha, Bishwas L., Eric J. Zirnstein, David J. McComas, Pontus Brandt, Alan Stern, Heather A. Elliott, Andrew R. Poppe, Kelsi N. Singer, and Anne Verbiscer. "Suprathermal H+ Pickup Ion Tails in the Outer Heliosphere." Astrophysical Journal 960, no. 1 (December 20, 2023): 35. http://dx.doi.org/10.3847/1538-4357/ad08b9.
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Abstract This study provides a detailed analysis of five distant interplanetary shocks observed by the Solar Wind Around Pluto instrument on board New Horizons, which exhibit the signature of a suprathermal H+ pickup ion (PUI) tail in the downstream distribution. These shocks were observed with a PUI data cadence of approximately 24 hr, covering a heliocentric distance range of 23.71–36.75 au. The shock compression ratio varies between approximately 1.4 and 3.2. The H+ PUI density and temperature show a gradual increase across the shock, while the H+ solar wind density shows erratic behavior without a distinct downstream compression. The H+ PUI cooling index variation across the shock displays different characteristics in each shock. This study demonstrates, for the first time, the variation of the number density of downstream H+ PUI tails with the shock compression ratio, revealing an increase in tail density with stronger shocks. Additionally, theoretical estimates of reflected PUI number densities derived from the electrostatic cross-shock potential agree very well with the observed H+ PUI tail densities for stronger shocks.
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Wu, C. C., S. T. Wu, and M. Dryer. "Generation and evolution of interplanetary slow shocks." Annales Geophysicae 14, no. 4 (April 30, 1996): 375–82. http://dx.doi.org/10.1007/s00585-996-0375-1.
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Abstract. It is well known that most MHD shocks observed within 1 AU are MHD fast shocks. Only a very limited number of MHD slow shocks are observed within 1 AU. In order to understand why there are only a few MHD slow shocks observed within 1 AU, we use a one-dimensional, time-dependent MHD code with an adaptive grid to study the generation and evolution of interplanetary slow shocks (ISS) in the solar wind. Results show that a negative, nearly square-wave perturbation will generate a pair of slow shocks (a forward and a reverse slow shock). In addition, the forward and the reverse slow shocks can pass through each other without destroying their characteristics, but the propagating speeds for both shocks are decreased. A positive, square-wave perturbation will generate both slow and fast shocks. When a forward slow shock (FSS) propagates behind a forward fast shock (FFS), the former experiences a decreasing Mach number. In addition, the FSS always disappears within a distance of 150R⊙ (where R⊙ is one solar radius) from the Sun when there is a forward fast shock (with Mach number ≥1.7) propagating in front of the FSS. In all tests that we have performed, we have not discovered that the FSS (or reverse slow shock) evolves into a FFS (or reverse fast shock). Thus, we do not confirm the FSS-FFS evolution as suggested by Whang (1987).
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Ruggeri, Tommaso, and Shigeru Taniguchi. "A complete classification of sub-shocks in the shock structure of a binary mixture of Eulerian gases with different degrees of freedom." Physics of Fluids 34, no. 6 (June 2022): 066116. http://dx.doi.org/10.1063/5.0094835.
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The shock structure in a binary mixture of polyatomic Eulerian gases with different degrees of freedom of a molecule is studied based on the multi-temperature model of rational extended thermodynamics. Since the system of field equations is hyperbolic, the shock-structure solution is not always regular, and discontinuous parts (sub-shocks) can be formed. For given values of the mass ratio and the specific heat of the constituents, we identify the possible sub-shocks as the Mach number M0 of the shock wave and the equilibrium concentration c0 of the constituents change. In the plane ( c0, M0), we identify the possible regions for the sub-shock formation. The analysis is obtained to verify when the velocity of the shock wave meets a characteristic velocity in the unperturbed or perturbed equilibrium states, which gives a necessary condition for the sub-shock formation. The condition becomes necessary and sufficient when the velocity of the shock becomes greater than the maximum characteristic velocity in the unperturbed state, namely, the regions with no sub-shocks, a sub-shock for only one constituent, or sub-shocks for both constituents are comprehensively classified. The most interesting case is that the lighter molecule has more degrees of freedom than that of the heavy one. In this situation, the topology of the various regions becomes different. We also solve the system of the field equations numerically using the parameters in various regions and confirm whether the sub-shocks emerge or not. Finally, the relationship between an acceleration wave in one constituent and the sub-shock in the other constituent is explicitly derived.
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Bulat, Pavel, Konstantin Volkov, and Igor Volobuev. "Interaction between Shock Waves Travelling in the Same Direction." Fluids 6, no. 9 (September 3, 2021): 315. http://dx.doi.org/10.3390/fluids6090315.
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In this paper, we study the intersection (interaction) between several steady shocks traveling in the same direction. The interaction between overtaking shocks may be regular or irregular. In the case of regular reflection, the intersection of overtaking shocks leads to the formation of a resulting shock, contact discontinuity, and some reflected discontinuities. The type of discontinuity depends on the parameters of incoming shocks. At the irregular reflection, a Mach shock forms between incoming overtaking shocks. Reflected discontinuities come from the points of intersection of the Mach stem with the incoming shocks. We also consider the possible types of shockwave configurations that form both at regular and irregular interactions of several overtaking shocks. The regions of existence of overtaking shock waves with different types of reflected shock and the intensity of reflected shocks are defined. The results obtained in the study can potentially be useful for designing supersonic intakes and advanced jet engines.
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Rahn, Daniela, and Enzo Weber. "PATTERNS OF UNEMPLOYMENT DYNAMICS IN GERMANY." Macroeconomic Dynamics 23, no. 1 (October 30, 2017): 322–57. http://dx.doi.org/10.1017/s1365100516001358.
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Using a structural vector autoregressive (SVAR) model, this paper provides deeper insight into unemployment dynamics in Germany. We identify a technology shock and two policy shocks that play a central role in business cycle research. Accordingly, we enrich the discussion on the sources of unemployment dynamics by considering demand-side impulses. The worker reallocation process varies substantially with the identified shocks. The job-finding rate plays a larger role after a technology shock and a monetary policy shock, whereas the separation rate appears to be the dominant margin after a fiscal policy shock. Technology shocks turn out to be relatively important for variations in the transition rates. Regarding policy shocks, our results point toward fiscal interventions as a promising instrument but with several limitations.
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Zhang, Congyao, Eugene Churazov, Klaus Dolag, William R. Forman, and Irina Zhuravleva. "Encounters of merger and accretion shocks in galaxy clusters and their effects on intracluster medium." Monthly Notices of the Royal Astronomical Society 494, no. 3 (April 17, 2020): 4539–47. http://dx.doi.org/10.1093/mnras/staa1013.
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ABSTRACT Several types/classes of shocks naturally arise during formation and evolution of galaxy clusters. One such class is represented by accretion shocks, associated with deceleration of infalling baryons. Such shocks, characterized by a very high Mach number, are present even in 1D models of cluster evolution. Another class is composed of ‘runaway merger shocks’, which appear when a merger shock, driven by a sufficiently massive infalling subcluster, propagates away from the main-cluster centre. We argue that, when the merger shock overtakes the accretion shock, a new long-living shock is formed that propagates to large distances from the main cluster (well beyond its virial radius), affecting the cold gas around the cluster. We refer to these structures as Merger-accelerated Accretion shocks (MA-shocks) in this paper. We show examples of such MA-shocks in one-dimensioanal (1D) and three-dimensional (3D) simulations and discuss their characteristic properties. In particular, (1) MA-shocks shape the boundary separating the hot intracluster medium (ICM) from the unshocked gas, giving this boundary a ‘flower-like’ morphology. In 3D, MA-shocks occupy space between the dense accreting filaments. (2) Evolution of MA-shocks highly depends on the Mach number of the runaway merger shock and the mass accretion rate parameter of the cluster. (3) MA-shocks may lead to the misalignment of the ICM boundary and the splashback radius.
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AL-Taee, Anwaar F., and Jamella H. Rasheed. "Expression of Heat Shock Protein HSP90 in Genomic-DNA of Chickpea (Cicer arietinum L.) Callus by Heat Shock Treatment." Academic Journal of Research and Scientific Publishing 3, no. 33 (January 5, 2022): 121–39. http://dx.doi.org/10.52132/ajrsp.e.2022.33.6.
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This study was able to detect of the expression activity of heat shock proteins HSP90 and heat transcription factors HSFs for the first time in callus cultures of chickpea, Cicer arietinum L., that exposed to abiotic shocks, grown on MS medium supplemented with 1.0 mg L-1 naphthalene acetic acid (NAA) and 2.0 mg L-1 benzyl adenine (BA). Heat shock proteins HSPs were constructed for increase of withstand long-term physical shocks, and production of resistant to heat chickpeas plants, this shock was enhancement of tolerance of chickpea callus to abiotic stresses (high - temperatures). Results enhanced the ability of chickpea callus to abiotic stresses bearing and induce of HSF genes to heat shock proteins HSP90 production quickly to removing denatured proteins, avoid apoptosis, thus, supporting tolerance to the sudden action of these shocks. Expression activity of heat shock genes and transcription factors by determined based on polymerase chain reaction qPCR, that explained the gene activity increasing at shocks intensity increased
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Bret, Antoine, and Asaf Pe’er. "On the Width of a Collisionless Shock and the Index of the Cosmic Rays It Accelerates." Astrophysical Journal 968, no. 2 (June 1, 2024): 100. http://dx.doi.org/10.3847/1538-4357/ad4bde.
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Abstract Despite being studied for many years, the structure of collisionless shocks is still not fully determined. Such shocks are known to be accelerators of cosmic rays (CRs), which, in turn, modify the shock structure. The shock width λ is known to be connected to the CR spectral index a. Here, we use an instability analysis to derive the shock width in the presence of CRs. We obtain an analytical expression connecting the shock width to the CR index and to the fraction of upstream particles that are accelerated. We find that when this fraction becomes larger than ∼30%, a new instability becomes dominant. The shock undergoes a transition where its width increases by a factor ∼8–10, and the CR acceleration effectively ends. Our analysis is valid for strong, nonrelativistic, and unmagnetized shocks. We discuss the implication of these results on the expected range of CR spectra and flux observed and on the structure of nonrelativistic collisionless shocks.
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Gedalin, M., and E. Griv. "Collisionless electrons in a thin high Mach number shock: dependence on angle and <font face="Symbol" ><b><i>b</i></b></font>." Annales Geophysicae 17, no. 10 (October 31, 1999): 1251–59. http://dx.doi.org/10.1007/s00585-999-1251-6.
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Abstract. It is widely believed that electron dynamics in the shock front is essentially collisionless and determined by the quasistationary magnetic and electric fields in the shock. In thick shocks the electron motion is adiabatic: the magnetic moment is conserved throughout the shock and v2^ ∝ B. In very thin shocks with large cross-shock potential (the last feature is typical for shocks with strong electron heating), electrons may become demagnetized (the magnetic moment is no longer conserved) and their motion may become nonadiabatic. We consider the case of substantial demagnetization in the shock profile with the small-scale internal structure. The dependence of electron dynamics and downstream distributions on the angle between the shock normal and upstream magnetic field and on the upstream electron temperature is analyzed. We show that demagnetization becomes significantly stronger with the increase of obliquity (decrease of the angle) which is related to the more substantial influence of the inhomogeneous parallel electric field. We also show that the demagnetization is stronger for lower upstream electron temperatures and becomes less noticeable for higher temperatures, in agreement with observations. We also show that demagnetization results, in general, in non-gyrotropic down-stream distributions.Key words. Interplanetary physics (interplanetary shocks; planetary bow shocks)
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Lee, Kiseok, Wensheng Kang, and Ronald A. Ratti. "OIL PRICE SHOCKS, FIRM UNCERTAINTY, AND INVESTMENT." Macroeconomic Dynamics 15, S3 (November 2011): 416–36. http://dx.doi.org/10.1017/s1365100511000496.
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This paper seeks to answer the following questions: Do oil price shocks affect firms' investment decisions? Do oil price shocks affect investment decisions differentially depending on firm-specific uncertainty? Over what time horizon do oil price shocks affect high-uncertainty firms? Is the intensity of the oil price shock important, or just its existence? It is found that oil price shocks depress firms' investment decisions, and do so differentially by depressing investment more for more uncertain firms. Oil shocks affect investment for at least the first and second year after the shock. In the short term, the mere existence of a shock drives most of the effect. In the long term, the intensity of the oil shock is also important. Bloom, Bond, and Van Reenan's result [Review of Economic Studies 74, 391–415 (2007)] regarding responsiveness to demand shocks being eroded at more uncertain firms for data on U.K. firms is replicated using data on U.S. firms and persists after oil shocks are considered.
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Cha, Ji Hwan, and Maxim Finkelstein. "On a Terminating Shock Process with Independent Wear Increments." Journal of Applied Probability 46, no. 2 (June 2009): 353–62. http://dx.doi.org/10.1239/jap/1245676092.
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In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. In this paper we combine an extreme shock model with a specific cumulative shock model. It is shown that the proposed setting can also be interpreted as a generalization of the well-known Brown–Proschan model that describes repair actions for repairable systems. For a system subject to a specific process of shocks, we derive the survival probability and the corresponding failure rate function. Some meaningful interpretations and examples are discussed.
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Cha, Ji Hwan, and Maxim Finkelstein. "On a Terminating Shock Process with Independent Wear Increments." Journal of Applied Probability 46, no. 02 (June 2009): 353–62. http://dx.doi.org/10.1017/s0021900200005507.
Full textAbstract:
In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. In this paper we combine an extreme shock model with a specific cumulative shock model. It is shown that the proposed setting can also be interpreted as a generalization of the well-known Brown–Proschan model that describes repair actions for repairable systems. For a system subject to a specific process of shocks, we derive the survival probability and the corresponding failure rate function. Some meaningful interpretations and examples are discussed.
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Draine, B. T. "MagnetoHydrodynamic shock waves in molecular clouds." Symposium - International Astronomical Union 147 (1991): 185–96. http://dx.doi.org/10.1017/s007418090023951x.
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The fluid dynamics of MHD shock waves in magnetized molecular gas is reviewed. The different types of shock solutions, and the circumstances under which the different types occur, are delineated. Current theoretical work on C∗- and J-type shocks, and on the stability of C-type shocks, is briefly described. Observations of the line emission from MHD shocks in different regions appear to be in conflict with theoretical expectations for single, plane-parallel shocks. Replacement of plane-parallel shocks by bow shocks may help reconcile theory and observation, but it is also possible that the observed shocks may not be “steady”, or that theoretical models have omitted some important physics.
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Draine, B. T. "MagnetoHydrodynamic shock waves in molecular clouds." Symposium - International Astronomical Union 147 (1991): 185–96. http://dx.doi.org/10.1017/s0074180900198894.
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The fluid dynamics of MHD shock waves in magnetized molecular gas is reviewed. The different types of shock solutions, and the circumstances under which the different types occur, are delineated. Current theoretical work on C∗- and J-type shocks, and on the stability of C-type shocks, is briefly described. Observations of the line emission from MHD shocks in different regions appear to be in conflict with theoretical expectations for single, plane-parallel shocks. Replacement of plane-parallel shocks by bow shocks may help reconcile theory and observation, but it is also possible that the observed shocks may not be “steady”, or that theoretical models have omitted some important physics.
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Zhang, Congyao, Eugene Churazov, and Irina Zhuravleva. "Pairs of giant shock waves (N-waves) in merging galaxy clusters." Monthly Notices of the Royal Astronomical Society 501, no. 1 (November 30, 2020): 1038–45. http://dx.doi.org/10.1093/mnras/staa3718.
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ABSTRACT When a subcluster merges with a larger galaxy cluster, a bow shock is driven ahead of the subcluster. At a later merger stage, this bow shock separates from the subcluster, becoming a ‘runaway’ shock that propagates down the steep density gradient through the cluster outskirts and approximately maintains its strength and the Mach number. Such shocks are plausible candidates for producing radio relics in the periphery of clusters. We argue that, during the same merger stage, a secondary shock is formed much closer to the main cluster centre. A close analogue of this structure is known in the usual hydrodynamics as N-waves, where the trailing part of the ‘N’ is the result of the non-linear evolution of a shock. In merging clusters, spherical geometry and stratification could further promote its development. Both the primary and the secondary shocks are the natural outcome of a single merger event and often both components of the pair should be present. However, in the radio band, the leading shock could be more prominent, while the trailing shock might conversely be more easily seen in X-rays. The latter argument implies that for some of the (trailing) shocks found in X-ray data, it might be difficult to identify their ‘partner’ leading shocks or the merging subclusters, which are farther away from the cluster centre. We argue that the Coma cluster and A2744 could be two examples in a post-merger state with such well-separated shock pairs.
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Vieu, T., S. Gabici, and V. Tatischeff. "Non-linear particle reacceleration by multiple shocks." Monthly Notices of the Royal Astronomical Society 510, no. 2 (December 10, 2021): 2529–37. http://dx.doi.org/10.1093/mnras/stab3564.
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ABSTRACT When the pressure of particles accelerated at shock waves is no longer negligible compared to the kinetic pressure of the gas, the linear theory of diffusive shock acceleration breaks down. This is expected in particular when the shock sweeps up pre-existing cosmic rays, or when multiple shocks reaccelerate successively the same particles. To describe these systems, one has to account for the non-linear backreaction of the particles on the magnetohydrodynamic flow. Using an up-to-date semi-analytical model of particle reacceleration at non-linear shocks, we show that the presence of pre-existing energetic particles strongly affects the shock profile, in such a way that the reacceleration of non-thermal particles or the acceleration of particles from the thermal bath becomes less efficient. We further describe the evolution of the distribution of particles after several shocks and study the properties of the asymptotic solution. We detail the case of identical shocks as well as more realistic scenarios, including the heating of the medium or superbubble environments. When the particles are efficiently confined in the acceleration region, it is generally found that the spectrum converges toward a concave solution after a few tens of shocks, with a spectral index around 3.5 at the highest energy. The post-shock cosmic ray pressure reaches an asymptotic value of about 4–5 per cent of the ram pressure of one shock. Most of the shock pressure is transferred to escaping particles.
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Marle, Allard Jan van, Artem Bohdan, Anabella Araudo, Fabien Casse, and Alexandre Marcowith. "Diffusive shock acceleration in relativistic, oblique shocks." Journal of Physics: Conference Series 2742, no. 1 (April 1, 2024): 012008. http://dx.doi.org/10.1088/1742-6596/2742/1/012008.
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Abstract Cosmic rays are charged particles that are accelerated to relativistic speeds by astrophysical shocks. Numerical models have been successful in confirming the acceleration process for (quasi-)parallel shocks, which have the magnetic field aligned with the direction of the shock motion. However, the process is less clear when it comes to (quasi-)perpendicular shocks, where the field makes a large angle with the shock-normal. For such shocks, the angle between the magnetic field and flow ensures that only highly energetic particles can travel upstream at all, reducing the upstream current. This process is further inhibited for relativistic shocks, since the shock can become superluminal when the required particle velocity exceeds the speed of light, effectively inhibiting any upstream particle flow. In order to determine whether such shocks can accelerate particles, we use the particle-in-cell (PIC) method to determine what fraction of particles gets reflected initially at the shock. We then use this as input for a new simulation that combines the PIC method with grid-based magnetohydrodynamics to follow the acceleration (if any) of the particles over a larger time-period in a two-dimensional grid. We find that quasi-perpendicular, relativistic shocks are capable of accelerating particles through the DSA process, provided that the shock has a sufficiently high Alfvénic Mach number.
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Newman, Byron Y. "Shock, Shock, and More Shock." Optometry - Journal of the American Optometric Association 75, no. 3 (March 2004): 145. http://dx.doi.org/10.1016/s1529-1839(04)70032-9.
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Zhou, X., W. M. Smith, D. L. Rollins, and R. E. Ideker. "Transmembrane potential changes caused by shocks in guinea pig papillary muscle." American Journal of Physiology-Heart and Circulatory Physiology 271, no. 6 (December 1, 1996): H2536—H2546. http://dx.doi.org/10.1152/ajpheart.1996.271.6.h2536.
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To study transmembrane potential (Vm) changes (delta Vm) caused by extracellular field stimulation, Vm was recorded in 10 guinea pig papillary muscles by a double-barrel microelectrode. A 10-ms shock was delivered during the action potential plateau or during diastole. Six shock strengths (1.8 +/- 0.4, 3.8 +/- 0.7, 5.6 +/- 0.9, 7.2 +/- 1.1, 11.1 +/- 1.9, and 17.8 +/- 1.5 V/cm) were given with both polarities. The tissue was then treated with either 30 microM tetrodotoxin (TTX; n = 5) or 30 microM TTX plus Ca(2+)-free (n = 5) perfusion. For shocks during the action potential plateau, delta Vm caused by the six potential gradients was 22.4 +/- 9.6, 43.6 +/- 17.4, 54.7 +/- 17.9, 60.4 +/- 18.1, 65.4 +/- 13.7, and 66.4 +/- 12.2 mV for shocks causing depolarization and 41.1 +/- 16.5, 68.3 +/- 22, 80.5 +/- 20.4, 84.0 +/- 19.5, 93.6 +/- 16.3, and 98.9 +/- 15.4 mV for shocks causing hyperpolarization. The relationship between delta Vm and shock potential gradient was not linear. During diastole, hyperpolarizing shocks induced initial hyperpolarization, then depolarization followed again by hyperpolarization. A new depolarization upstroke occurred immediately after the shock. After TTX or TTX plus Ca(2+)-free perfusion, point stimuli 10 times diastolic threshold could not induce an action potential, but a shock field of 1.8 +/- 0.2 V/cm still induced action potentials. The peak value of depolarization measured with respect to resting potential (-87 +/- 5 mV) during the hyperpolarizing shock decreased from +14 +/- 22 before to -66 +/- 30 mV with TTX perfusion (P < 0.01). The fast upstroke rate of depolarization both during and immediately after the end of hyperpolarizing shocks was inhibited by TTX perfusion. Thus 1) the relationship between delta Vm and shock potential gradient is not linear; 2) field but not point stimulation can induce an action potential when Na+ channels are inactivated; and 3) during diastole Na+ channels are activated twice by a 10-ms hyperpolarizing shock, once during shock-induced hyperpolarization and again immediately after the end of the shock.
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YANG, DOO YONG. "IMPACTS OF EXTERNAL SHOCKS ON ASIAN ECONOMIES: PANEL VECTOR AUTOREGRESSIVE REGRESSION WITH LATENT DYNAMIC COMPONENTS APPROACH." Singapore Economic Review 58, no. 04 (December 2013): 1350026. http://dx.doi.org/10.1142/s0217590813500264.
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This paper analyzes the effects of external shocks on emerging Asian economies. Since the Asian crisis of 1997–1998, the impact of external shocks on regional economies has grown important in the Asian business cycles as well as in the decision-making process of macroeconomic policies, as emerging Asian economies have become more integrated with the global economy. This paper designs a state-space representation of the panel vector autoregressive model with latent dynamic components in order to show the impulse response function of three external shocks including real income shock, financial shock, and long-term real interest rate shock. This paper finds the external real gross domestic product shock as a dominant one in emerging Asia. The shock has been persistent and has carried long-term effects on emerging Asia before and after the Asian crisis. Second, the external equity shock has also been an important factor influencing the business cycles in the region after the Asian crisis, while the effect has been insignificant before the Asian crisis. Last, the external monetary shock has presumably mitigated effectively by Asia's macroeconomic policy, but it has forced to give up monetary independency in the region.