Shock Wave Theory Research Articles

Coordination of distributed adaptive signal control and advisory speed optimization based on shockwave theory

AbstractThis paper presents a distributed adaptive signal control and advisory speed coordination method based on shockwave theory, which accommodates diverse traffic conditions. In order to assess signal control efficiency under various scenarios, an innovative evaluation index termed synthetic delay is introduced based on the analysis of traffic dynamics at intersections. Considering the formation and dissipation of queue, and flow fluctuation of incoming traffic, it automatically evaluates control delay and throughput with distinctive significances. The distributed adaptive control method calculates the optimal green time in real time to minimize total synthetic delay at intersections. Furthermore, the coordination of advisory speed with the signal control schemes is addressed to ensure smooth progressions for vehicles. The proposed method considers the saturation of traffic and upstream traffic flow changes, leading to adaptability to changing traffic scenarios and effective coordination of traffic control. Several simulations were conducted and compared with the proposed method with other control methods. The results demonstrate that the proposed methods reduce the control delay and increase intersection throughput remarkably under different traffic saturations, confirming their effectiveness.

Ejecta velocity and motion model of spherical aluminum alloy projectile hypervelocity impact on basalt

A series of small-scale impact cratering experiments were performed on basalt at velocities of 3.5–6.0 km s−1. The formation and motion process of ejecta were observed by high-speed and ultra-high-speed cameras. The momentum transfer coefficient values and cratering size were measured. Hydrodynamic simulations in 2D were carried out to replicate the impact conditions of the basalt and calibrate model parameters. The contribution of jet, central cratering, and spalling ejection to momentum enhancement was quantitatively analyzed by simulation. Simulation results show that: the mass and the momentum of the jet are less than 1 % of the projectile mass, and the initial momentum, can be ignored. For craters in small-sized basalt, the momentum enhancement mainly comes from the spall region ejecta. The formation mechanism of ejecta at different stages was analyzed based on the shock wave and jet theory. An analytical model is developed for estimating the velocity and motion of ejecta formation at different stages. The model calculation results of the speed of the ejecta formed in different stages are consistent with the numerical results. The maximum velocity of the ejecta formed in the jet and cratering stage depends on the initial impact velocity and the Hugoniot parameters of the projectile/target material. The minimum velocity of the spallation ejecta is linearly related to the spalling strength of the target. The model provides a fast and simple method to calculate the ejecta velocity and estimate the influence range of ejecta under different impact conditions.

A time-varying shockwave speed model for reconstructing trajectories on freeways using Lagrangian and Eulerian observations

Inference of detailed vehicle trajectories is crucial for applications such as traffic flow modeling, energy consumption estimation, and traffic flow optimization. Static sensors can provide only aggregated information, posing challenges in reconstructing individual vehicle trajectories. Shockwave theory is used to reproduce oscillations that occur between sensors. However, as the emerging of connected vehicles grows, probe data offers significant opportunities for more precise trajectory reconstruction. Existing methods rely on Eulerian observations (e.g., data from static sensors) and Lagrangian observations (e.g., data from connected vehicles) incorporating shockwave theory and car-following modeling. Despite these advancements, a prevalent issue lies in the static assignment of shockwave speed, which may not be able to reflect the traffic oscillations in a short time period caused by varying response times and vehicle dynamics. Moreover, driver dynamics while reconstructing the trajectories are ignored. In response, this paper proposes a novel framework that integrates Eulerian and Lagrangian observations for trajectory reconstruction on freeways. The approach introduces a calibration algorithm for time-varying shockwave speed. The shockwave speed calibrated by the CV is then utilized for trajectory reconstruction of other non-connected vehicles based on shockwave theory. Additionally, vehicle and driver dynamics are introduced to optimize the trajectory and estimate energy consumption by applying a vehicle movement model. The proposed method is evaluated using real-world datasets, demonstrating superior performance in terms of trajectory accuracy, reproducing traffic oscillations, and estimating energy consumption.

In-Plane crushing performance of bionic glass Sponge-Type honeycomb structures

Honeycomb structures are commonly adopted due to their superior energy absorption capacity. In this study, a new bionic glass sponge–type honeycomb structure (BSH) with a quadrilateral octagonal mesh microstructure inspired by the sea sponge structure was proposed. The in-plane crushing performance of the BSH with different geometrical parameters under different crushing speeds was investigated by ABAQUS/Explicit. The numerical findings suggested that the BSH displayed stronger energy absorption in contrast to the square, hexagonal and hierarchical honeycombs at both quasi-static and dynamic crushing conditions. More plastic hinges and more unit walls involved in deformation resulted in a high energy absorption capacity. In addition, three typical deformation modes of the BSH under different loading speeds were discussed, and the empirical model to predict the plateau stress of the BSH was established based on the shock wave theory. Finally, the effect of boundary segmentation parameter m on crushing performance was also illustrated. The energy absorption capacity reaches a maximum at m = 3 for quasi–static loading, whereas at m = 5 for dynamic loading. These findings provide valuable insights into the optimization of bionic honeycombs.

Theory and simulation of shock waves freely propagating through monoatomic non-Boltzmann gas

The effect of non-Boltzmann energy distributions on the free propagation of shock waves through a monoatomic gas is investigated via theory and simulation. First, the non-Boltzmann heat capacity ratio γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}, as a key property for describing shock waves, is derived from first principles via microcanonical integration. Second, atomistic molecular dynamics simulations resembling a shock tube setup are used to test the theory. The presented theory provides heat capacity ratios ranging from the well-known γ=5/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma = 5/3$$\\end{document} for Boltzmann energy-distributed gas to γ→1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\rightarrow 1$$\\end{document} for delta energy-distributed gas. The molecular dynamics simulations of Boltzmann and non-Boltzmann driven gases suggest that the shock wave propagates about 9% slower through the non-Boltzmann driven gas, while the contact wave appears to be about 4% faster if it trails non-Boltzmann driven gas. The observed slowdown of the shock wave through applying a non-Boltzmann energy distribution was found to be consistent with the classical shock wave equations when applying the non-Boltzmann heat capacity ratio. These fundamental findings provide insights into the behavior of non-Boltzmann gases and might help to improve the understanding of gas dynamical phenomena.Graphical abstract

Errors in Shock Wave Theory Can Impact Clinical Outcomes

Abstract The mechanical waves that are used therapeutically are well defined from the point of view of physics. The differences between focused and radial waves are very important, however there is enormous confusion in the literature. In the present bibliographic analysis we make a critical comment on a publication in which a pneumatic source is illustrated and presented as generating focused shock waves. We believe that every effort should be made to be strict in definitions, not only because science is based on the search for truth, but also because errors in shock wave theory can impact clinical outcomes.

Generation and modulation of shock waves in two-dimensional polariton condensates

Due to the ability of exciton-polariton condensates formed in semiconductor microcavities to be achieved at room temperature and their characteristics such as non-equilibrium and strong interactions, they have become an ideal platform for studying the nonlinear properties of non-equilibrium quantum systems. In 2013, the research group led by L. Dominici observed two-dimensional symmetric shock waves in the polariton condensate driven by coherent pump. However, owing to the characteristics of this system, theoretical researches have lagged behind. In one-dimensional polariton condensates, disregarding cross-interaction of the system, a type of asymmetric shock wave was respectively discovered by A. M. Kamchatnov in 2012 and A. M. Belounis in 2017. In 2023, utilizing the adiabatic approximation, our research team not only uncovered sparse wave, symmetric, and asymmetric shock waves in the system, but also revealed that the symmetric shock waves are triggered by cross-interaction. At present, there is no theoretical research on shock waves in two-dimensional polariton condensate. In this paper, spectral methods and fourth-order Runge-Kutta methods are used to explore the generation and control of shock waves in two-dimensional polariton condensates. It is found that when the cross-interaction between the condensate and the polariton thermal reservoir is quenched at high condensation rates, the initially prepared bright solitons can be modulated into two types of rotationally symmetric shock waves with different velocities, while the initial dark-like solitons can only transform into a single velocity rotationally symmetric shock wave. If quenching the external potential, the dark-like solitons can be transformed into anisotropic supersonic shock waves, and the dependence of shock wave on the width of the external potential is also shown. When the external potential and incoherent pumping are controlled at low condensation rates, multiple anisotropic shock waves can be excited in a uniform condensate, and their amplitudes can be used to control the wave number and amplitude of the shock waves and the range of widths for the external potential or incoherent pumping to excite shock waves is also demonstrated. The proposed methods in this paper not only provide theoretical guidance for the generation and control of shock waves in exciton-polariton condensates, but also find symmetric shock waves similar to experiments (<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.nature.com/articles/ncomms9993"><i>Nat. Commun.</i> <b>6</b> , 8993</ext-link>) without adopting any approximation, and open up a universal pathway for exciting shock waves in non-equilibrium or non-integrable systems, which may become a paradigm for transforming solitons into shock waves and significantly propel the rapid development of shock wave theory in different domains.

Perforation Characteristics of Three-Layer Steel Plates Subjected to Impact with Different Shapes and Velocities of Reactive Fragments

In this paper, the AUTODYN/Smoothed Particle Hydrodynamics (SPH) method was used to study the impact of reactive fragments on three-layer equidistant steel plates. The perforation characteristics of equidistant three-layer steel plates were investigated along with the parameters of combustion energy release from reactive fragments under varied impact velocities and shape conditions. The modification of the steel plates’ perforation diameter was investigated using the dimensional analysis approach. The shock wave pressure and chemical reaction characteristics were examined using the shock wave theory. The results show that within the examined impact velocity range, the perforation diameter initially increased and then decreased as the impact velocity of the reactive fragment rose. In addition, the perforation diameter was approximately 1.5–3 times the diameter of the reactive fragment. As the impact speed increased, the active reaction generated by the reactive fragments became more sufficient. The energy released contributed to the impact’s pressure rise; in addition, the temperature of the steel plate was raised in part by the reactive fragment impact, making the steel plate more prone to melting. The results of this investigation provide important support for a detailed understanding of the rules governing the failure of steel plates under the impact of reactive fragments as well as the combustion of reactive fragments under impact.

On the Theory of Shock Waves in Isotropically Hardening Plastic Media

On the Theory of Shock Waves in Isotropically Hardening Plastic Media

Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed type

This article is a survey of Cathleen Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed elliptic-hyperbolic type. The main focus is on Morawetz’s fundamental work on the nonexistence of continuous transonic flows past profiles, Morawetz’s program regarding the construction of global steady weak transonic flow solutions past profiles via compensated compactness, and a potential theory for regular and Mach reflection of a shock at a wedge. The profound impact of Morawetz’s work on recent developments and breakthroughs in these research directions and related areas in pure and applied mathematics are also discussed.

A safety-enhanced eco-driving strategy for connected and autonomous vehicles: A hierarchical and distributed framework

This paper presents a safety-enhanced eco-driving strategy for connected and autonomous vehicles (CAVs), which is implemented by a hierarchical and distributed framework. The driving risk field, shockwave theory, and motion planning and control method are integrated into this framework to optimize the trajectories of CAVs on a signalized arterial under mixed traffic flow, with the aim of reducing the driving risk and fuel consumption of CAVs simultaneously, while ensuring traffic efficiency. The optimization procedure is mainly composed of two parts: long-term trajectory planning based on optimal control and short-term trajectory control based on model predictive control, which makes the strategy more adaptable to the various traffic conditions. The results show that the proposed framework can effectively reduce the safety risk that vehicles are exposed to and their fuel consumption by 18%–24% and 20%–27%, respectively. Furthermore, it reveals that conventional eco-driving strategies may result in negative safety issues when only considering the impact of preceding vehicles on the eco-CAV. However, these negative impacts can be eliminated when the impacts of following vehicles on the eco-CAV are taken into account. In addition, the sensitivity analysis on the Market Penetration Rate (MPR) of CAVs and traffic demand is performed. The results show that the framework is robust and can work under various traffic conditions (including under-saturated and over-saturated ones) and different MPRs.

Asymptotic theory of not completely integrable soliton equations.

We develop the theory of transformation of intensive initial nonlinear wave pulses to trains of solitons emerging at asymptotically large time of evolution. Our approach is based on the theory of dispersive shock waves in which the number of nonlinear oscillations in the shock becomes the number of solitons at the asymptotic state. We show that this number of oscillations, which is proportional to the classical action of particles associated with the small-amplitude edges of shocks, is preserved by the dispersionless flow. Then, the Poincaré-Cartan integral invariant is also constant, and therefore, it reduces to the quantization rule similar to the Bohr-Sommerfeld quantization rule for a linear spectral problem associated with completely integrable equations. This rule yields a set of "eigenvalues," which are related to the asymptotic solitons' velocities and their characteristics. It is implied that the soliton equations under consideration give modulationally stable solutions; therefore, these "eigenvalues" are real. Our analytical results agree very well with the results of numerical solutions of the generalized defocusing nonlinear Schrödinger equation.

In-plane crushing response and energy absorption of two different arranged circular honeycombs

Circular honeycombs have been widely used in many fields due to their excellent mechanical properties recently, however, circular honeycombs with different arrangements have been rarely studied. In this paper, two circular honeycombs with different arrangements were designed and fabricated using a 3D printer. Both honeycombs were investigated by experiment and finite element (FE) analysis to compare their performance. It is worth noting that both honeycombs possess the same relative density. The accuracy of the FE models was validated by comparing them with experimental results and relevant reports. Subsequently, a series of numerical studies were conducted to analyse the in-plane dynamic crushing behaviour and energy absorption characteristics at different impact velocities. Based on different experiment deformation modes were identified from the observation of results respectively. Additionally, continuous circle honeycomb (CCH) exhibits a higher reaction force but is prone to fracture. On the other hand, spacing circle honeycomb (SCH) possesses a lower reaction force but offers greater stability due to its ability to flex and release force. As a result, SCH can effectively absorb energy and demonstrates superior crushing capacity compared to CCH. To investigate and compare the plateau stress and energy absorption of these honeycombs, the FE method was used, which also involved a detailed analysis of the impact velocity and relative density of the honeycomb. It was observed that the crushing stress and energy absorption of SCH were higher than those of CCH with the same impact velocity and relative density. According to the one dimensional shock wave theory, empirical formulas for two circular honeycombs to predict the plateau stress are given respectively with the maximum error lower than 12%. This paper aims to offer valuable insights for the design of different configurations, with the goal of improving the crashworthiness and energy absorption capacity of a specific honeycomb structure.

Numerical Simulation of Acoustic Wave Generated by DC Corona Discharge Based on the Shock Wave Theory

The audible noise generated by corona discharge has the N-type characteristic at the initial generation stage, and it is a typical shock wave. This shock wave usually only exists around the corona source with a tiny range, making it difficult to obtain its characteristics through experimental measurements. An electrosound-combined simulation of the corona discharge based on the shock wave theory was conducted, and the development process involving the corona discharge, shock wave, and sound wave was simulated. First, the corona was numerically simulated based on the 2D pin–plate axisymmetric hydrodynamic model. It was found that the plasma was mainly distributed near the axis of the corona field where the electric field changed violently, and the maximum value of the electric field appeared at the head of the discharge channel. Then, the plasma energy was equivalent to the explosive energy, and a plasma explosion shock model was established. It was found that the shock wave pressure had obvious positive and negative pressure zones, and the propagation velocity decays to the sound velocity gradually. Finally, the shock wave pressure derived by the explosion model was used as the acoustic source, and the acoustic wave propagation process was simulated. The simulated sound pressure waveform had the same characteristics as the relevant experimental measurement results, proving that the developed method possessed strong applicability and gave rise to a new angle for the simulation of corona-generated audible noise.

Spatiotemporal clustering for the impact region caused by a traffic incident: an improved fuzzy C-means approach with guaranteed consistency

Traffic incidents disrupt the normal flow of vehicles and induce nonrecurrent traffic congestion. It has been well accepted that the shape of the spatiotemporal region impacted by a traffic incident should be consistent with the propagation of shockwaves. Although there has been a variety of approaches that attempt to estimate the impact region of traffic incidents, most of them are not capable of producing results with guaranteed consistency. In this research, we propose an improved fuzzy clustering approach that integrates the domain knowledge of shockwave theory for freeway incidents to address this issue, which is new to the literature. Compared to the general clustering approaches, our improved fuzzy clustering approach takes control of the clustering process by leveraging the directional propagation of shockwaves in the form of constraints, which can guarantee the consistency. In addition, unlike existing studies that employ discrete variables to distinguish traffic status in case of traffic incidents, the fuzzy clustering approach uses the continuous variable to indicate the incident impact on vehicle speed. This can help to reduce the information loss and estimate the impact region more accurately. Numerical experiments are conducted to evaluate the performance of our approach using both simulation and real data. Results show that our approach is able to guarantee that the shape of the impact region is consistent with the propagation of shockwaves and achieve higher accuracy of the estimated delay induced by the incident than the current state-of-the-art approach.

Queue Length Estimation Based on Probe Vehicle Data at Signalized Intersections

Queue length is one of the important indexes to evaluate the operation efficiency of signalized intersection and also the key parameter of intersection signal control optimization. Traditional queue length estimation models are mostly based on fixed detection equipment, and the models assumptions are too harsh; there are certain limitations. Based on the probe vehicle data, this paper establishes a model of queue length estimation for signalized intersection based on shockwave theory. First, based on the speed and location data of the probe vehicle, the vehicle density is calculated to estimate the intersection stop line. A real-time calculation method of vehicle arrival rate is proposed to improve the applicability of the model. Then, based on the shockwave theory, the meeting time of the queue forming wave and the queue discharging wave are calculated after the green light is on. Finally, the queue length is summed in sections, including the distance between the last queued probe vehicle and the stop line during the red light period, the length of the subsequent vehicles arriving during the residual red light time, and the newly increased queue length within the queue discharging time. This paper uses the VISSIM software to simulate the actual intersection. The simulation results show that when the penetration of probe vehicle is 50%, 25%, and 10%, their corresponding mean absolute relative error are 11.27%, 27.77%, and 39.12%, respectively. It can be seen that with the increase of penetration, the error gradually decreases. The average absolute relative error is within the acceptable range. After analyzing the existing similar methods, although the accuracy of the method proposed in this paper does not reach the highest level, it has the advantages of simple operation, less computation, and good real-time computation. Relevant research results can provide support for traffic control at signalized intersections.

Multivariate time-varying Kalman filter approach for cycle-based maximum queue length estimation

Real-time queue length is a crucial information, increasingly needed for signal operation and signal optimization purposes. This paper proposes a novel multivariate time-varying Kalman filter approach to estimate the cycle-based maximum queue lengths in real-time by only using high-resolution vehicle loop detector data and signal timing data. The modeling framework builds on state changing points that can be identified at detector site and shockwave theory that models the propagation of traffic states in the space–time domain. The times at which traffic states change at the detector site, known as break points (e.g., free flow to jam condition, jam to saturation condition, etc.) are identified using high resolution detector data and the end of the queue is estimated using linear models that build on the shockwave theory. Nevertheless, this deterministic approach, which is previously proposed in the literature, does not account for measurements errors associated with traffic state changing points or the assumptions in the shockwave theory. Therefore, we propose a multivariate time-varying Kalman filter approach to produce a robust estimate for the cycle-based maximum queue length in both undersaturated and oversaturated conditions. Further, the developed algorithm can estimate the residual queue length and inform its occurrence in case of oversaturation. The proposed methodology can easily be adapted in practice, as it relies solely on measurements from a single loop detector that may be located close to the stop line.

Experimental and numerical investigation of vertical shock tube performance for blast load testing of geological media

In this paper, a new vertical shock tube test facility is described that has been designed and established for a research program aimed at studying the response of the geological media subjected to blast loading. In the present study, the vertical shock tube test facility is studied, and its performance is evaluated by characterizing generated blast waves considering two different diaphragm types; Aluminium and Lexan, and two driver gases; Nitrogen and Helium. The driver pressure in the vertical shock tube is varied by using Aluminium diaphragms of different thicknesses and groove depths and Lexan diaphragms of different thicknesses and numbers. The blast wave generated in the vertical shock tube is evaluated by studying its pressure loading profile, blast properties, Friedlander wave fit, trinitrotoluene equivalence, and by comparing it with idealized shock wave theory. The measured blast waves have properties that are a function of the driver pressure and driver gas. The positive-phase duration segment of the measured pressure wave is comparable to the blast waves in the actual free-field explosions. Based on the experimental results, the equations for the determination of driver pressure and peak-reflected overpressure considering Lexan diaphragms are also proposed. The profile of the measured pressure wave in the vertical shock tube demonstrated its capability in generating an air blast loading in controlled laboratory conditions. Finally, the three-dimensional finite element simulations are also performed, and results are validated with the experimental data.

Investigations on the quasi-static/dynamic mechanical properties of 3D printed random honeycombs under in-plane compression

The aim of this study was to reveal the effects of inertia and base material strain rate on the mechanical properties of 3D-printed random honeycombs. First, random honeycombs were established with various meso-structural parameters based on the Voronoi technique and then manufactured by 3D printing. Quasi-static compression tests were performed using a universal test machine. The results indicated that the random honeycombs exhibited a more uniform deformation mode which led to a gentle stress–strain curve when compared with the regular honeycombs. Furthermore, the strain rate effect of the base material was determined by Split Hopkinson Pressure Bar (SHPB) tests. Finite element models considering the base material strain rate were verified by the quasi-static compression and drop weight impact tests. Dynamic simulations were carried out to determine the critical velocity between the deformation mode and clarify its mechanisms. The second critical velocities increase as the cell size and cell wall thickness increased or as the strain rate effect of the base material is considered. The effects of inertia and base material strain rate on the mechanical properties were discussed. The dynamic stress enhancement is dominated by the strain rate effect of the base material and the inertia effect in the random and shock modes, respectively. Finally, an empirical model that includes the inertia effect and strain rate effect of the base material was proposed based on the 1D shock wave theory and the Johnson–Cook material model.

Estimating Demand Volume for Signalized Corridors Under Oversaturated Conditions Using Aggregated Probe Vehicle Speed Data

Measuring demand directly with vehicle sensors is not possible when demand is larger than capacity for an extended period, as the queue grows beyond the sensor, and the flow measurements at a given point cannot exceed the capacity of the section. The main objective of this study is to develop methods that could be implemented in practice based on readily available data. To this end, two methods are proposed: an innovative method based on shockwave theory and the volume delay function adapted from the Highway Capacity Manual (7th edition). Both methods primarily rely on probe vehicle speeds (e.g., from INRIX) as the input data and the capacity of the segment or bottleneck being analyzed. Probe vehicle data are used to determine the critical times when the queue reaches the end or beginning of a road segment. From these critical times, the shockwave speed for the boundary between congested (high density) traffic and arriving (low density) traffic is estimated. The proposed methods are tested with simulation data generated in VISSIM and validated based on volume data from the field. The field data are collected from a congested arterial in Virginia Beach, VA, and include the ground truth volumes and INRIX speed data aggregated at one-minute intervals. The results show that both methods are effective for estimating the demand volume and produce less than 4% error when tested with field data.