Double Shock Wave Research Articles

Exploration of nonlinear traveling wave phenomena in quintic conformable Benney-Lin equation within a liquid film

<abstract><p>In this article, we use the modified extended direct algebraic method (mEDAM) to explore and analyze the traveling wave phenomena embedded in the quintic conformable Benney-Lin equation (CBLE) that regulates liquid film dynamics. The proposed transformation-based approach developed for nonlinear partial differential equations (PDEs) and fractional PDEs (FPDEs), efficiently produces a plethora of traveling wave solutions for the targeted CBLE, capturing the system's nuanced dynamics. The methodically determined traveling wave solutions are in the form of rational, exponential, hyperbolic and trigonometric functions which include periodic waves, bell-shaped kink waves and signal and double shock waves. To accurately depict the wave phenomena linked to these solutions, we generate 2D, 3D, and contour graphs. These visualizations not only improve understanding of the CBLE model's dynamics, but also provide a detailed way to examine its behavior. Moreover, the use of the proposed techniques contributes to a better understanding of the other FPDEs' distinct characteristics, enhancing our comprehension of their underpinning dynamics.</p></abstract>

Multi-phase Modeling on Spall and Recompression Process of Tin Under Double Shockwaves

Multi-phase Modeling on Spall and Recompression Process of Tin Under Double Shockwaves

Bifurcation Analysis of Travelling Waves and Multi-rogue Wave Solutions for a Nonlinear Pseudo-Parabolic Model of Visco-Elastic Kelvin-Voigt Fluid

Through this article, we focus on the extension of travelling wave solutions for a prevalent nonlinear pseudo-parabolic physical Oskolkov model for Kevin-Voigt fluids by using two integral techniques. First of all, we explore the bifurcation and phase portraits of the model for different parametric conditions via a dynamical system approach. We derive smooth waves of the bright bell and dark bell, periodic waves, and singular waves of dark and bright cusps, in correspondence to homoclinic, periodic, and open orbits with cusp, respectively. Each orbit of the phase portraits is envisaged through various energy states. Secondly, with the help of a prevalent unified scheme, an inventive version of exact analytic solutions comprising hyperbolic, trigonometric, and rational functions can be invented with some collective parameters. The unified scheme is an excitably auspicious method to procure novel interacting travelling wave solutions and to obtain multipeaked bright and dark solitons, shock waves, bright bell waves with single and double shocks, combo waves of the bright-dark bell and dark-bright bell with a shock, dark bell into a double shock wave, and bright-dark multirogue type wave solutions of the model. The dynamics of the procured nonlinear wave solutions are also presented through 2-D, 3-D, and density plots with specified parameters.

Simulation and analysis of the 3D double shock-induced recompression of spall using a hybrid PAGOSA with FLIP + MPM

In this work, an innovative hybrid algorithm PAGOSA with FLIP + MPM is first presented by coupling PAGOSA with the particle FLIP + MPM, and applied to systematically exploring the 3D recompression of spall induced by double-shock waves in ductile materials as the few existing studies are currently limited to the pure longitudinal recompression of spall, and ignore the 3D effects. This algorithm solves the difficulties the grid-based methods encounter when applied to capturing the fracture in material. We first validate the capabilities of PAGOSA with FLIP + MPM to predict different fracture/fragmentation cases by solving two benchmark problems and comparing with the analytical solutions or the experiment results. The convergences and the infinity-norm errors are also investigated. Subsequently, the 3D effects are demonstrated by simulating the spallation in material using PAGOSA with FLIP + MPM and comparing with those in the longitudinal cases. Some factors that affect the spallation with 3D effects are also discussed. Finally, the recompressions of spall in material with/without 3D effects are systematically simulated and analyzed. The recompression of spall driven by a high explosive is also simulated to show the ability of PAGOSA with FLIP + MPM to handle this kind of problem. The conditions that can lead to a recompression of spall are explored. Numerical results show that PAGOSA with FLIP + MPM can accurately predict different fracture cases, that the 3D effects play an important role in fracture/fragmentation, and the recompression of spall is very sensitive to the occurrence conditions, shows great differences when considering 3D effects in real applications. Moreover, the present hybrid method can be easily extended to other grid-based techniques employed for fracture in materials.

Dynamic response of density-graded foam subjected to soft impact

The density-graded foam materials are gaining traction due to their enhanced impact and blast resistance capacities. However, current knowledge in the impact response of density-graded foam is limited to rigid impact, which narrows the design space of target materials. In particular, three main issues remain unclear, i.e., (1) how to quantify soft impact response, (2) what is the reduction of deformation and transferred stress from soft impact as compared to rigid impact, (3) whether density-graded foam can reduce the transferred stress from soft impact. To address these knowledge gaps, an analytical model based on the double shock wave theory is established by using a deformable projectile impinging onto a density-graded foam target. The dynamic stress at the supported end is analyzed for uniform, positive, and negative density gradients. The results indicate that the deformation process due to impact from deformable projectile is vastly different from that of traditional rigid projectile, with the former causing 27.42% smaller deformation and 9.87% stress reduction of the graded foam target, and three separate velocities can be observed throughout the soft impact process. The findings indicate lower mechanical requirements of target materials for soft projectile impact protections, potentially leading to weight and cost savings.

Vortex evolution and flame propagation driven by oblique shock wave in supersonic reactive mixing layer

Vortex evolution and flame propagation of supersonic reactive mixing layer with the interaction of single/double oblique shock waves are researched by employing direct numerical simulation methods. The vortex dynamics are found to be modulated by oblique shock waves, resulting in mixing enhancement of vorticity values. Notably, wider range of vortex scale distribution induced by double oblique shock waves leads to intense entrainment and nibbling process of large and small scale structures, which can remarkably increase the mixing level of hydrogen and airstreams. The analysis of vorticity transport equation indicates that compressing effects induced by shock waves are responsible for the increase of vortex strength. By tracking the vortex braid dynamical evolution process, it is revealed that local auto-ignition induced by double shock waves can accelerate the consumption of hydrogen and finally lead to high efficiency combustion. Since complex background waves are inherently present in confined space of Rocket-based Combined Cycle (RBCC) engine, the newly observed mixing enhancement mechanism for double shocked-reactive mixing layer can provide a guidance for the future design of mixing strategy using the inherent wave structures in RBCC combustor chambers.

The acceleration mechanism of shock wave induced by millisecond-nanosecond combined-pulse laser on silicon

The velocity variation law of shock wave induced by millisecond-nanosecond combined-pulse laser has been investigated experimentally. The pulse delay and laser energy are important experimental variables. The method of laser shadowgraphy is used in the experiment. Experimental results show that when the pulse delay is 2.4 ms, the ms and ns laser energy density is 301 J cm−2 and 12 J cm−2, respectively, the velocity of shock wave is 1.09 times faster than that induced by single ns pulse laser. It is inferred that the shock wave propagates in the plasma is faster than that in air. When the ms and ns laser energy density is 414.58 and 24 J cm−2, the velocity of shock wave shows rising trend with pulse delay in a range of 1.4 ms > Δt > 0.8 ms. It is indicated that with the increase of ns laser energy, the laser energy absorbed by laser-supported absorption wave increases. The mechanism of inverse bremsstrahlung absorption acts with target surface absorption simultaneously during the ns laser irradiation. Thus, the phenomenon of the double shock wave is induced. The numerical results of the phenomenon were accordance with experiment. The results of this research can provide a reference for the field of laser propulsion.

Acceleration of cosmic rays by double shock waves in galaxy clusters: application to radio relics

Context. Radio relics in galaxy clusters are known to be good laboratories for verification of the applicability of the diffusive shock acceleration (DSA) model in its canonical version. The need for such verification stems from the inconsistencies in the shock properties resulting from radio observations compared to X-ray observations. Aims. In this article we aim to explore how the presence of a second shock in the vicinity of a relic modifies the spectrum of accelerated electrons and decipher which of the involved parameters can have a significant impact on their shape. Methods. We analytically studied DSA of cosmic rays in two stationary shocks aiming to investigate the change of the distribution function. The latter eventually leads to spectrum slope deviations visible in different observations and simulations that do not appear to be explained by the case wherein cosmic rays interact with a single shock wave. Results. We obtain a complex distribution function f(x, p) depending on many parameters (distance between two shocks, compression ratios, spatial diffusion coefficients, injection value, etc.). This function reveals modifications that occur because of the coupled acceleration in both shocks. Apparently, deviations in the particle spectrum from the pure power law depend on a few parameters such as Q1/Q2, κ1/κ2, r1/r2, and L. Although we do not verify this idea by taking a particular cluster as an example, we demonstrate a potential cause of spectral disturbances in radio relics. In general terms, our findings appear to correlate with results from the literature when the distance between the shocks is of the order of the width of a radio relic and κ1/κ2 ∝ 3.

Experimental study of different pulse delays on the phenomenon of double shock waves induced by a millisecond-nanosecond combined-pulse laser.

We study the motion morphology, distance, and velocity of plasma and laser-induced shock waves induced by a millisecond-nanosecond (ms-ns) combined-pulse laser with different pulse delays on silicon. The laser shadowgraph method is used, and the phenomenon of double laser-induced shock waves has been found while the pulse delay is 1.2-1.8 ms. The controlling variable method is used to study this phenomenon, and it is found that it is mainly related to the ignition of the laser-supported absorption wave induced by the ms laser. Moreover, the plasma expansion velocity increases with the increase of pulse delay, the axial propagation distance of laser-induced shock waves increases monotonically with pulse delay, and the velocity of laser-induced shock waves decreases with the increase of pulse delay.

Impact response and energy absorption of functionally graded foam under temperature gradient environment

As an effective strategy to enhance the energy absorption and impact resistance capacities of foam materials, density-gradient design has been widely proposed as a viable solution. However, the influence of thermal environment on the impact response and energy absorption of functionally graded foam still remains unclear. In the present paper, an analytical model based on the double shock wave theory is presented to examine the impact performance of density-graded foam rods under temperature gradient environments. A density-graded foam with one end supported and the other end struck by a block of mass is presented to evaluate their impact performances. Both the positive and negative density-gradient models with power-law profiles along the axial direction of the foam rod are considered. The proposed theoretical representation is validated against several previous models, including a finite element (FE) simulation. It is demonstrated that the temperature gradient may lead to transformations in the deformation pattern for the positive and negative density-graded foams. Moreover, the temperature gradient can enlarge the impact resistance property in most cases and can reduce the energy absorption capacity of density-graded foams.

Calculation of a deuterium double shock Hugoniot from ab initio simulations.

We calculate the equation of state of dense deuterium with two ab initio simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, in the density range of 0.67 < or = rho < or = 1.60 g cm(-3). We derive the double shock Hugoniot and compare with the recent laser-driven double shock wave experiments by Mostovych et al. [Phys. Rev. Lett. 85, 3870 (2000)]. We find excellent agreement between the two types of microscopic simulations, but a significant discrepancy with the laser-driven shock measurements.

Effects of lithotripter fields on development of chick embryos

Chick embryos at 72 h incubation were subjected to three double shock waves from a Wolf Model 2137.50 Electrohydraulic Lithotripter. The pressure amplitude at the embryo was adjusted by variation of the distance from the source to the embryo. After a total of 120 h of incubation, they were assessed for developmental abnormalities. Early deaths, delayed deaths and malformations were all significantly increased at pressures of 10 MPa with suggestions of possible effects at lower pressure levels.

Double shock fronts for hyperbolic systems of conservation laws in multidimensional space

The existence of a unique double shock front for hyperbolic systems of conservation laws in several space variables is established, extending an earlier result of Metivier. An example of a double shock wave arising from physical applications is given.

Effect of high electron-proton temperature ratios on the double shock wave structure in the solar wind

Effect of high electron-proton temperature ratios on the double shock wave structure in the solar wind

The double shock wave structure in the solar wind

A one-dimensional model of the double shock structure in an inviscid, perfectly conducting fluid is presented. A magnetic field parallel to the discontinuity surfaces is included in the analysis. The range of ambient and driver gas parameters for which a double shock is possible is determined, and in particular, the effect of the magnetic field on these critical curves is examined. Theoretical shock profiles for typical solar wind conditions are discussed. Mariner 2 data for the high velocity stream of October 7–8, 1962, are compared with the results of the one-dimensional model. We show that the peak in the density should precede the peak in the magnetic field strength. This feature is in agreement with Mariner 2 data. The model yields values of temperature and pressure in the shocked gases that are higher than observed.