Propagation Properties of Shock Waves in Polyurethane Foam based on Atomistic Simulations

Porous materials are widely used in the field of protection because of their excellent energy absorption characteristics.In this work,a series of polyurethane microscopic models are established and the effect of porosity on the shock waves is studied with classical molecular dynamics simulations.Firstly,shock Hugoniot relations for different porosities are obtained,which compare well with the experimental data.The pores collapse and form local stress wave,which results in the complex multi-wave structure of the shock wave.The microstructure analysis shows that the local stress increases and the local velocity decreases gradually during the process of pore collapse to complete compaction.Finally,it leads to stress relaxation and velocity homogenization.The shock stress peaks can be fitted with two exponential functions,and the amplitude of attenuation coefficient decreases with the increase of density.Besides,the pore collapse under shock or non-shock are discussed by the entropy increase rate of the system.The energy is dissipated mainly through the multiple interactions of the waves under shock.The energy is dissipated mainly by the friction between atoms under non-shock.

THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS

In this paper,we study the shock waves for a mixed-type system from chemotaxis.We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region.Under the generalized entropy conditions,we find that there are different shock wave structures for different parameters.To guarantee the uniqueness of the solutions,we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters.Finally,we construct the Riemann solutions in some solvable regions.

Research on the distribution characteristics of explosive shock waves at different altitudes

There are great differences in the distribution characteristics of shock waves produced by ammunition explosions at different altitudes.At present,there are many studies on plain explosion shock waves,but there are few studies on the distribution characteristics of plateau explosion shock waves,and there is still a lack of complete analysis and evaluation methods.This paper compares and analyzes shock wave overpressure data at different altitudes,obtains the attenuation effect of different altitudes on the shock wave propagation process and proposes a calculation formula for shock wave overpressure considering the effect of altitude.The data analysis results show that at the same TNT equivalent and the same distance from the measuring point,the shock wave overpressure at high altitude is lower than that at low altitude.With the increase in the explosion center distance of the measuring point,the peak attenuation rate of the shock wave overpressure at high altitudes is smaller than that at low altitudes,and the peak attenuation rate of the shock wave overpressure at high altitudes gradually intensifies with increasing proportional distance.The average error between the shock wave overpressure and measured shock wave overpressure in a high-altitude environment obtained by using the above calculation formula is 11.1389%.Therefore,this method can effectively predict explosion shock wave overpressure in plateau environments and provides an effective calculation method for practical engineering tests.

ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY

This paper is concerned with an ideal polytropic model of non-viscous and heatconductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions.Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.

Study on Collision Process of Opposing Unsteady Supersonic Jets and Shock Waves

Double pulsed-laser-ablation is a promising method to prepare nanoparticle composites. The backward movement of the plume after the collision with counter-propagating shock wave has been observed in experiments. In the present study, collision dynamics of the oppositely injected Si and Ge jets into a He background gas was numerically calculated as a simulation for double pulsed-laser-ablation. The experimentally observed backward movement was reproduced. The effect of distance between two jet exits on the distance of backward movement of the jet, BL, after the collision with the counter-propagating shock front was calculated to discuss the collision dynamics and to optimize the target distance for the experiment. We found that BL does not decrease monotonically with increasing distance between two jet exits, but has a maximum value at a certain distance. This behavior is discussed by calculating the expansion dynamics of an individual jet. Shock wave grows with time at the initial stage of the jet expansion and then attenuates;the density just behind the shock front for individual jet has a maximum value at a certain time and position. BL has a maximum value when the densities just behind the shock fronts for the individual jets have maximum values. This result is important for designing the appropriate distance between the two jet exits, i.e., the distance between the targets of double pulsed-laser-ablation.

NUMERICAL INVESTIGATION OF TOROIDAL SHOCK WAVES FOCUSING USING DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD

A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.

IMPROVEMENT OF MATERIALS WELDABILITY BY SHOCK WAVES

The weldability is an important property to metal materials. Materials weldability becomes worse with the yield strength increasing. The experimental results indicate that the specific shock waves treatment could improve the weldability of steels such as 16MnR, SM 58Q, e.g. increase the notch toughness of coarse grains zone in HAZ and decrease cold cracking sensibility. The work would explore initially the mechanisms of improvement of weldability by shock waves. The further study on the low alloy high strength steel WEL TEN80 indicates that the shock waves may increase the material weldability on this grade of trength.

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.

Propagation law of shock waves and gas flow in cross roadway caused by coal and gas outburst

In order to study the propagation law of shock waves and gas flow during coal and gas outburst,we analyzed the formation process of outburst shock waves and gas flow and established the numerical simulation models of the roadways with 45°intersection and 135°intersection to simulate the propagation of outburst gas flow and the process of gas transport.Based on the analysis of the simulation results,we obtained the qualitative and quantitative conclusions on the characteristics and patterns of propagation and attenuation of outburst shock waves and gas flow.With the experimental models,we investigated the outburst shock waves and gas flow in the roadways with the similar structures to the simulated ones.According to the simulation results,when the angle between the driving roadway and the adjacent roadway increased,the sudden pressure variation range in adjacent roadway and the influencing scope of gas flow increased and the sudden pressure variation duration decreased.The intersection between the driving roadway and the adjacent roadway has no effect on airflow reversal induced by the shock waves and gas flow.

Effects of bi-kappa distributed electrons on dust-ion-acoustic shock waves in dusty superthermal plasmas

The basic properties of dust-ion-acoustic （DIA） shock waves in an unmagnetized dusty plasma （containing inertial ions, kappa distributed electrons with two distinct temperatures, and negatively charged immobile dust grains） are investi- gated both numerically and analytically. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The effects of superthermal bi-kappa electrons and ion kinematic viscosity, which are found to modify the basic features of DIA shock waves significantly, are briefly discussed.

Dynamic Response of Stiffened Plates with Holes Subjected to Shock Waves and Fragments

The power field of shock waves and fragments is analyzed and set up, and the damage modes of stiffened plates are put forward. According to the structural characters of the stiffened plates investigated and the properties of the shock waves and fragments, the experiments on the shock waves acting on the stiffened plates (penetrated and non-penetrated by fragments) are mainly conducted. The dynamic response rules of stiffened plates with holes under shock waves and fragments loading are obtained. The results show that the penetration of fragments into stiffened plates hardly affects their deformation produced by shock waves..

An improved two-dimensional unstructured CE/SE scheme for capturing shock waves

In this paper, the accuracy of Chang＇s unstructured space-time conservation element and solution element （CE/SE） scheme is analysed for the first time. Based on a redefinition of conservation elements and solution elements, an improved two-dimensional （2D） unstructured CE/SE scheme with an adjustable parameter β is proposed to accurately capture shock waves. The new scheme can be applied to any type of grid without special treatnmnt. Compared with Chang＇s original parameter a, larger/5 dose not cost extra computational resources. Numerical tests reveal that the new scheme is not only clear in physical concept, compact and highly accurate but also more capable of capturing shock waves than the popular fifth-order accurate weighted essentially non-oscillatory scheme.

NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION

We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.

NUMERICAL SCHEMES WITH HIGH ORDER OF ACCURACY FOR THE COMPUTATION OF SHOCK WAVES

High order accurate scheme is highly desirable for Slow computation with shocks. After analysis has been made for the reason of the generation of non-physical oscillations around the shock in numerical computations, a third-order, upwind biased, shock capturing scheme was proposed. Also, a new shock fitting method, called pseudo shock fitting method, was suggested, which in principle can be with any order of accuracy. Test cases for one dimensional flows show that the new method is very satisfactory.

Ion-Acoustic Shock Waves in Nonextensive Electron-Positron-Ion Plasma

A rigorous theoretical investigation is made of ion-acoustic shock structures in an unmagnetized three-component plasma whose constituents are nonextensive electrons, nonextensive positrons, and inertial ions. The Burgers equation is derived by employing the reductive perturbation method. The effects of electron and positron nonextensivity and ion kinematic viscosity on the properties of these ion-acoustic shock waves are briefly discussed. It is found that shock waves with positive and negative potentials are obtained to depend on the plasma parameters. The entailment of our results may be useful to understand some astrophysical and cosmological scenarios including stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc., where effects of nonextensivity can play significant roles.

Positron-Acoustic Shock Waves in a Degenerate Multi-Component Plasma

A theoretical investigation on the propagation of positron-acoustic shock waves （PASWs） in an unmagnetized, collisionless, dense plasma （containing non-relativistic inertial cold positrons, non-relativistic or ultra-relativistic degenerate electron and hot positron fluids and nondegenerate positively charged immobile ions） is carried out by employing the reductive perturbation method. The Burgers equation and its stationary shock wave solution are derived and numerically analyzed. It is observed that the relativistic effect （i.e., the presence of non/ultra- relativistic electrons and positrons） and the plasma particle number densities play vital roles in the propagation of PASWs. The implications of our results in space and interstellar compact objects including non-rotating white dwarfs, neutron stars, etc. are briefly discussed.

SOME PROBLEMS ON JUMP CONDITIONS OF SHOCK WAVES IN 3-DIMENSIONAL SOLIDS

Based on the general conservation laws in continuum mechanics, the Eulerian and Lagrangian descriptions of the jump conditions of shock waves in 3-dimensional solids were presented respectively. The implication of the jump conditions and their relations between each other, particularly the relation between the mass conservation and the displacement continuity, were discussed. Meanwhile the shock wave response curves in 3- dimensional solids, i.e. the Hugoniot curves were analysed, which provide the foundation for studying the coupling effects of shock waves in 3-dimensional solids.

Synergetic effects of shock waves with polydeoxyribonucleotides on rotator cuff tendon tear in a rabbit model

This work aimed to investigate the synergetic therapeutic effects of polydeoxyribonucleotides(PDRN)combined with extracorporeal shock waves therapy(ESWT)and the effects of the therapy according to ESWT sequences on a chronic traumatic full-thickness rotator cuff tear(RCT)in rabbit models.For this purpose,thirty-two rabbits were randomly allocated into 4 groups.An excision was made to create a 5-mm sized full-thickness RCT right proximal to the insertion site on the supraspinatus.After 6 weeks,4 different procedures(normal saline,Group 1;PDRN injection,Group 2;PDRN injection before ESWT,Group 3;PDRN injection after ESWT,Group 4)were performed.PDRN injection and radial type ESWT were each performed 4 times per week.Gross morphology,Immunohistochemistry,and motion analysis were performed at 4 weeks after treatments.All parameters including tear size,Masson’s trichrome(MT)staining,anti-collagen 1 monoclonal antibody immunostaining(COL-1),proliferating cell nuclear antigen(PCNA),vascular endothelial growth factor(VEGF),anti-platelet endothelial cell adhesion molecule-1 polyclonal antibody(PECAM-1),and motion analysis,were significantly greater in Group 2,Group 3,and Group 4 than in Group 1.In Group 4,all parameters were significantly greater than in Group 2,and parameters including MT staining,COL-1,PCNA,PECAM-1,and fast walking time were significantly greater than Group 3.There were no significant differences between Group 2 and Group 3.This study demonstrated that PDRN injection alone and combined with ESWT were more effective than control treatment and applying ESWT before PDRN injection was also shown to yield better outcomes in parameters including angiogenesis,cell proliferation,and fast walking time in a rabbit model with chronic traumatic full-thickness RCT.Therefore,the application of ESWT before PDRN injection could be recommended for optimal outcomes of the conservative treatments when the patients with full-thickness RCT are not suitable in surgical treatment.

THE INTERACTIONS OF SHOCK WAVES OF NONSTRICTLY HYPERBOLIC SYSTEMS

The interaction of shock waves is investigated for the following nonstrictly hyperbolic system: [GRAPHICS] The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the dependence of interaction on the relative positions of the three states separated by shock waves. Several ideas are introduced to helo organize and clarify the new phenomena.

Theoretical Study of Coupling Mechanism between FBG and Shock Waves of Rock Burst

To achieve the monitor of rock burst in coal mine with fiber Bragg grating (FBG) sensing, the coupling mechanism between FBG and shock waves was theoretically analyzed. Based on Housner’s random shock model, the coupling mechanism between shock waves and FBG was theoretically analyzed. The result shows that the wave will change the period Ʌ and effective refractive index n of FBG, and further affect the initial wavelength value. The amplitude, phase and frequency of shock wave are directly related to the wavelength drifts of FBG. The transmitting velocity of shock wave in rock is affected by lithologic characteristics. The Elastic modulus, density and Poisson’s ratio of rock influence the initial wavelength value of FBG. This study provided a theoretical basis and practical application guidance for coal or rock burst monitoring with FBG sensing.