Shock wave dynamics is a topic with a wide variety of applications ranging from removal of kidney stones to inertial confinement fusion. In reality, the shock front is most often followed by a decay in flow properties, and therefore it is of interest to better understand shock dynamic events for these situations. Thus, an experimental facility that can provide results that are accurate, highly controlled, affordable and with a quick turn-around time are needed. Here, we present the design of an exploding wire system that can be coupled to either a two-dimensional or a three-dimensional test section to provide the user with a multitude of settings to study shock dynamics emanating from shock waves with decaying flow properties behind the shock front. Schlieren photographs taken with an ultra-high speed camera are also presented to show that the exploding wire system functions as intended in both two- and three-dimensional setups.
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Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model
We consider a hyperbolic–parabolic system arising from a chemotaxis model in tumor angiogenesis, which is described by a Keller–Segel equation with singular sensitivity. It is known to allow viscous shocks (so-called traveling waves). We introduce a relative entropy of the system, which can capture how close a solution at a given time is to a given shock wave in almost [Formula: see text]-sense. When the shock strength is small enough, we show the functional is non-increasing in time for any large initial perturbation. The contraction property holds independently of the strength of the diffusion.
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- Award ID(s):
- 1614918
- PAR ID:
- 10209739
- Date Published:
- Journal Name:
- Mathematical Models and Methods in Applied Sciences
- Volume:
- 30
- Issue:
- 02
- ISSN:
- 0218-2025
- Page Range / eLocation ID:
- 387 to 437
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A<sc>bstract</sc> We study holographic renormalization group (RG) flows perturbed by a shock wave in dimensions
d ≥ 2. The flows are obtained by deforming a holographic conformal field theory with a relevant operator, altering the interior geometry from AdS-Schwarzschild to a more general Kasner universe near the spacelike singularity. We introduce null matter in the form of a shock wave into this geometry and scrutinize its impact on the near-horizon and interior dynamics of the black hole. Using out-of-time-order correlators, we find that the scrambling time increases as we increase the strength of the deformation, whereas the butterfly velocity displays a non-monotonic behavior. We examine other observables that are more sensitive to the black hole interior, such as the thermala -function and the entanglement velocity. Notably, thea -function experiences a discontinuous jump across the shock wave, signaling an instantaneous loss of degrees of freedom due to the infalling matter. This jump is interpreted as a ‘cosmological time skip’ which arises from an infinitely boosted length contraction. The entanglement velocity exhibits similar dependence to the butterfly velocity as we vary the strength of the deformation. Lastly, we extend our analyses to a model where the interior geometry undergoes an infinite sequence of bouncing Kasner epochs. -
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Abstract The ion foreshock is highly dynamic, disturbing the bow shock and the magnetosphere‐ionosphere system. To forecast foreshock‐driven space weather effects, it is necessary to model foreshock ions as a function of upstream shock parameters. Case studies in the accompanying paper show that magnetosheath ions sometimes exhibit strong field‐aligned asymmetry toward the upstream direction, which may be responsible for enhancing magnetosheath leakage and therefore foreshock ion density. To understand the conditions leading to such asymmetry and the potential for enhanced leakage, we perform case studies and a statistical study of magnetosheath and foreshock region data surrounding ∼500 Time History of Events and Macroscale Interactions during Substorms mission bow shock crossings. We quantify the asymmetry using the heat flux along the field‐aligned direction. We show that the strong field‐aligned heat flux persists across the entire magnetosheath from the magnetopause to the bow shock. Ion distribution functions reveal that the strong heat flux is caused by a secondary thermal population. We find that stronger asymmetry events exhibit heat flux preferentially toward the upstream direction near the bow shock and occur under larger IMF strength and larger solar wind dynamic pressure and/or energy flux. Additionally, we show that near the bow shock, magnetosheath leakage is a significant contributor to foreshock ions, and through enhancing the leakage the magnetosheath ion asymmetry can modulate the foreshock ion velocity and density. Our results imply that likely due to field line draping and compression against the magnetopause that leads to a directional mirror force, modeling the foreshock ions necessitates a more global accounting of downstream conditions.
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Abstract Initial hot spot temperatures and temperature evolutions for 4 polymer‐bound explosives under shock compression by laser‐driven flyer plates at speeds from 1.5–4.5 km s−1are presented. A new averaging routine allows for improved signal to noise in shock compressed impactor experiments and yields temperature dynamics which are more accurate than has been previously available. The PBX formulations studied here consist of either pentaerythritol tetranitrate (PETN), 1,3,5‐trinitro‐1,3,5‐triazinane (RDX), 2,4,6‐trinitrotoluene (TNT), or 1,3,5‐triamino‐2,4,6‐trinitrobenzene (TATB) in a 80/20 wt.% mixture with a silicone elastomer binder. The temperature dynamics demonstrate a unique shock strength dependence for each base explosive. The initial hot spot temperature and its evolution in time are shown to be indicative of chemistry occurring within the reaction zone of the four explosives. The number density of hot spots is qualitatively inferred from the spatially‐averaged emissivity and appears to increase exponentially with shock strength. An increased emissivity for formulations consisting of TNT and TATB is consistent with carbon‐rich explosives and in increased hot spot volume. Qualitative conclusions about sensitivity were drawn from the initial hot spot temperature and rate at which the number of hot spots appear to grow.
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ABSTRACT Tidal disruption events (TDEs) occur when a star gets torn apart by the strong tidal forces of a supermassive black hole, which results in the formation of a debris stream that partly falls back towards the compact object. This gas moves along inclined orbital planes that intersect near pericentre, resulting in a so-called ‘nozzle shock’. We perform the first dedicated study of this interaction, making use of a two-dimensional simulation that follows the transverse gas evolution inside a given section of stream. This numerical approach circumvents the lack of resolution encountered near pericentre passage in global three-dimensional simulations using particle-based methods. As it moves inward, we find that the gas motion is purely ballistic, which near pericentre causes strong vertical compression that squeezes the stream into a thin sheet. Dissipation takes place at the resulting nozzle shock, inducing a rise in pressure that causes the collapsing gas to bounce back, although without imparting significant net expansion. As it recedes to larger distances, this matter continues to expand while remaining thin despite the influence of pressure forces. This gas evolution specifies the strength of the subsequent self-crossing shock, which we find to be more affected by black hole spin than previously estimated. We also evaluate the impact of general relativistic effects, viscous dissipation, magnetic fields, and radiative processes on the nozzle shock. This study represents an important step forward in the theoretical understanding of TDEs, bridging the gap between our robust knowledge of the fallback rate and the more complex following stages, during which most of the emission occurs.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0218202520500104
