GENERAL SOLUTION FOR INTERACTION OF SOLITARY WAVES INCLUDING HEAD-ON COLLISIONS

A general solution of the Boussinesq equation is presented which solves the problem of interaction of any number of right-going and left-going solitary waves.The solution relies on the exact solu- tion of Gardner,Greene,Kruskal,and Miura(1967),and has the same degree of accuracy as that solution, but has a wider scope of application.It is much simpler than,but as accurate as,Hirota's exact solu- tion(1973)of the Boussinesq equation,to which the present solution is compared for the simplest case of two solitary waves in head-on collision.

ON HEAD-ON COLLISION BETWEEN TWO GKDV SOLITARY WAVES IN A STRATIFIED FLUID

In this paper,using the reductive perturbation method combined with the PLK method and two-parameter expansions,we treat the problem of head-on collision between two solitary waves described by the generalized Korteweg-de Vries equation (the gKdV equation) and obtain its second-order approximate solution.The results show that after the collision,the gKdV solitary waves preserve their profiles and during the collision,the maximum amplitute is the linear superposition of two maximum amplitudes of the impinging solitary waves.

Head-on collision of ring dark solitons in Bose-Einstein condensates

The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.

HEAD-ON COLLISION BETWEEN TWO mKdV SOLITARY WAVES IN A TWO-LAYER FLUID SYSTEM

In this paper, based on the equations presented in [2], the head-on collision between two solitary waves described by the modified KdV equation (the mKdVequation, for short) is investigated by using the reductive perturbation method combined with the PLK method. These waves propagate at the interface of a two-fluid system, in which the density ratio of the two fluids equals the square of the depth ratio of the fluids. The second order perturbation solution is obtained. It is found that in the case of disregarding the nonuniform phase shift, the solitary waves preserve their original profiles after collision, which agrees with Fornberg and Whitham's numerical result of overtaking collision[6] whereas after considering the nonuniform phase shift, the wave profiles may deform after collision.

Use of Finite Element Analysis for the Prediction of Driver Fatality Ratio Based on Vehicle Intrusion Ratio in Head-On Collisions

To estimate the aggressivity of vehicles in frontal crashes, national highway traffic safety administration (NHTSA) has introduced the driver fatality ratio, DFR, for different vehicle-to-vehicle categories. The DFR proposed by NHTSA is based on the actual crash statistical data, which makes it difficult to evaluate for other vehicle categories newly introduced to the market, as they do not have sufficient crash statistics. A finite element (FE) methodology is proposed in this study based on computational reconstruction of crashes and some objective measures to predict the relative risk of DFR associated with any vehicle-to-vehicle crash. The suggested objective measures include the ratios of maximum intrusion in the passenger compartments of the vehicles in crash, and the transmitted peak deceleration of the vehicles’ center of gravity, which are identified as the main influencing parameters on occupant injury. The suitability of the proposed method is established for a range of bullet light truck and van (LTV) categories against a small target passenger car with published data by NHTSA. A mathematical relation between the objective measures and DFR is then developed. The methodology is then extended to predict the relative risk of DFR for a crossover category vehicle, a light pick-up truck, and a mid-size car in crash against a small size passenger car. It is observed that the ratio of intrusions produces a reasonable estimate for the DFR, and that it can be utilized in predicting the relative risk of fatality ratios in head-on collisions. The FE methodology proposed in this study can be utilized in design process of a vehicle to reduce the aggressivity of the vehicle and to increase the on-road fleet compatibility in order to reduce the occupant injury out- come.

Head-on collision between two hydroelastic solitary waves with Plotnikov-Toland's plate model

Head-on collision between two hydroelastic solitary waves propagating at the surface of an incompressible and ideal fluid covered by a thin ice sheet is analytically studied by means of a singular perturbation method. The ice sheet is represented by the Plotnikov-Toland model with the help of the special Cosserat theory of hyperelastic shells and the Kirchhoff-Love plate theory,which yields the nonlinear and conservative expression for the bending forces. The shallow water assumption is taken for the fluid motion with the Boussinesq approximation. The resulting governing equations are solved asymptotically with the aid of the Poincaré-Lighthill-Kuo method,and the solutions up to the third order are explicitly presented. It is observed that solitary waves after collision do not change their shapes and amplitudes. The wave profile is symmetric before collision, and it becomes, after collision, unsymmetric and titled backward in the direction of wave propagation. The wave profile significantly reduces due to greater impacts of elastic plate and surface tension. A graphical comparison is presented with published results, and the graphical comparison between linear and nonlinear elastic plate models is also shown as a special case of our study.

Head-on Collision of Solitary Waves Described by the Toda Lattice Model in Granular Chain

We study the head-on collision of two solitary waves in a precompressed granular chain using the discrete element method.Our study takes the Toda chain solution as the initial condition for the simulations.The simulation covers the dynamical evolution of the collision process from the start of the incident wave to the end of the collision.The interaction has a central collision region of about five-grain width in which two solitary waves merge completely and share only one peak.Four stages,i.e.,the pre-in-phase traveling stage,lag-phase collision state,lead-phase collision state,and post-in-phase traveling stage,are identified to describe the complex collision processes.Our results may be helpful for explaining the existence of long-lived solitary waves seen in the simulations by Takato and Sen[Europhys.Lett.100(2012)24003].

Collisionless shock acceleration of protons in a plasma slab produced in a gas jet by the collision of two laser-driven hydrodynamic shockwaves

We have recently proposed a new technique of plasma tailoring by laser-driven hydrodynamic shockwaves generated on both sides of a gas jet[Marquès et al.,Phys.Plasmas 28,023103(2021)].In a continuation of this numerical work,we study experimentally the influence of the tailoring on proton acceleration driven by a high-intensity picosecond laser in three cases:without tailoring,by tailoring only the entrance side of the picosecond laser,and by tailoring both sides of the gas jet.Without tailoring,the acceleration is transverse to the laser axis,with a low-energy exponential spectrum,produced by Coulomb explosion.When the front side of the gas jet is tailored,a forward acceleration appears,which is significantly enhanced when both the front and back sides of the plasma are tailored.This forward acceleration produces higher-energy protons,with a peaked spectrum,and is in good agreement with the mechanism of collisionless shock acceleration(CSA).The spatiotemporal evolution of the plasma profile is characterized by optical shadowgraphy of a probe beam.The refraction and absorption of this beam are simulated by post-processing 3D hydrodynamic simulations of the plasma tailoring.Comparison with the experimental results allows estimation of the thickness and near-critical density of the plasma slab produced by tailoring both sides of the gas jet.These parameters are in good agreement with those required for CSA.

Production of the X(4014)as the Spin-2 Partner of X(3872)in e^(+)e^(-)Collisions

In 2021,the Belle collaboration reported the first observation of a new structure in theψ(2S)γfinal state produced in the two-photon fusion process.In the hadronic molecule picture,this new structure can be associatedwith the shallow isoscalar D*D* bound state and as such is an excellent candidate for the spin-2 partner of the X(3872)with the quantum numbers J^(PC)=2^(++)conventionally named X_(2).

Investigating the elliptic anisotropy of identified particles in p-Pb collisions with a multi-phase transport model

The elliptic azimuthal anisotropy coefficient(v_(2))of the identified particles at midrapidity(|η|<0.8)was investigated in p-Pb collisions at√s_(NN)=5.02 TeV using a multi-phase transport model(AMPT).The calculations of differential v_(2)based on the advanced flow extraction method of light flavor hadrons(pions,kaons,protons,andΛ)in small collision systems were extended to a wider transverse momentum(p_(T))range of up to 8 GeV/c for the first time.The string-melting version of the AMPT model provides a good description of the measured p_(T)-differential v_(2)of the mesons but exhibits a slight deviation from the baryon v_(2).In addition,we observed the features of mass ordering at low p_(T)and the approximate number-of-constituentquark(NCQ)scaling at intermediate p_(T).Moreover,we demonstrate that hadronic rescattering does not have a significant impact on v_(2)in p-Pb collisions for different centrality selections,whereas partonic scattering dominates in generating the elliptic anisotropy of the final particles.This study provides further insight into the origin of collective-like behavior in small collision systems and has referential value for future measurements of azimuthal anisotropy.

MD Simulation of Diffusion Behaviors in Collision Welding Processes of Al-Cu, Al-Al, Cu-Cu

To investigate the effects of material combinations and velocity conditions on atomic diffusion behavior near collision interfaces,this study simulates the atomic diffusion behavior near collision interfaces in Cu-Al,Al-Al and Cu-Cu combinations fabricated through collision welding using molecular dynamic(MD)simulation.The atomic diffusion behaviors are compared between similar metal combinations(Al-Al,Cu-Cu)and dissimilar metal combinations(Al-Cu).By combining the simulation results and classical diffusion theory,the diffusion coefficients for similar and dissimilar metal material combinations under different velocity conditions are obtained.The effects of material combinations and collision velocity on diffusion behaviors are also discussed.The diffusion behaviors of dissimilar material combinations strongly depend on the transverse velocity,whereas those of the similar material combinations are more dependent on the longitudinal velocity.These findings can provide guidance for optimizing welding parameters.

Properties of collective flow and pion production in intermediate-energy heavy-ion collisions with a relativistic quantum molecular dynamics model

The relativistic mean-field approach was implemented in the Lanzhou quantum molecular dynamics transport model(LQMD.RMF). Using the LQMD.RMF, the properties of collective flow and pion production were investigated systematically for nuclear reactions with various isospin asymmetries. The directed and elliptic flows of the LQMD.RMF are able to describe the experimental data of STAR Collaboration. The directed flow difference between free neutrons and protons was associated with the stiffness of the symmetry energy, that is, a softer symmetry energy led to a larger flow difference. For various collision energies, the ratio between the π^(-) and π^(+) yields increased with a decrease in the slope parameter of the symmetry energy. When the collision energy was 270 MeV/nucleon, the single ratio of the pion transverse momentum spectra also increased with decreasing slope parameter of the symmetry energy in both nearly symmetric and neutron-rich systems.However, it is difficult to constrain the stiffness of the symmetry energy with the double ratio because of the lack of threshold energy correction on the pion production.

Electromagnetic fields in ultra-peripheral relativistic heavy-ion collisions

Ultra-peripheral heavy-ion collisions(UPCs)offer unique opportunities to study processes under strong electromagnetic fields.In these collisions,highly charged fast-moving ions carry strong electromagnetic fields that can be effectively treated as photon fluxes.The exchange of photons can induce photonuclear and two-photon interactions and excite ions.This excitation of the ions results in Coulomb dissociation with the emission of photons,neutrons,and other particles.Additionally,the electromagnetic fields generated by the ions can be sufficiently strong to enforce mutual interactions between the two colliding ions.Consequently,the two colliding ions experience an electromagnetic force that pushes them in opposite directions,causing a back-to-back correlation in the emitted neutrons.Using a Monte Carlo simulation,we qualitatively demonstrate that the above electromagnetic effect is large enough to be observed in UPCs,which would provide a clear means to study strong electromagnetic fields and their effects.

Reachability-Based Confidence-Aware Probabilistic Collision Detection in Highway Driving

Risk assessment is a crucial component of collision warning and avoidance systems for intelligent vehicles.Reachability-based formal approaches have been developed to ensure driving safety to accurately detect potential vehicle collisions.However,they suffer from over-conservatism,potentially resulting in false–positive risk events in complicated real-world applications.In this paper,we combine two reachability analysis techniques,a backward reachable set(BRS)and a stochastic forward reachable set(FRS),and propose an integrated probabilistic collision–detection framework for highway driving.Within this framework,we can first use a BRS to formally check whether a two-vehicle interaction is safe;otherwise,a prediction-based stochastic FRS is employed to estimate the collision probability at each future time step.Thus,the framework can not only identify non-risky events with guaranteed safety but also provide accurate collision risk estimation in safety-critical events.To construct the stochastic FRS,we develop a neural network-based acceleration model for surrounding vehicles and further incorporate a confidence-aware dynamic belief to improve the prediction accuracy.Extensive experiments were conducted to validate the performance of the acceleration prediction model based on naturalistic highway driving data.The efficiency and effectiveness of the framework with infused confidence beliefs were tested in both naturalistic and simulated highway scenarios.The proposed risk assessment framework is promising for real-world applications.

Diagnosing ratio of electron density to collision frequency of plasma surrounding scaled model in a shock tube using low-frequency alternating magnetic field phase shift

A non-contact low-frequency(LF)method of diagnosing the plasma surrounding a scaled model in a shock tube is proposed.This method utilizes the phase shift occurring after the transmission of an LF alternating magnetic field through the plasma to directly measure the ratio of the plasma loop average electron density to collision frequency.An equivalent circuit model is used to analyze the relationship of the phase shift of the magnetic field component of LF electromagnetic waves with the plasma electron density and collision frequency.The applicable range of the LF method on a given plasma scale is analyzed.The upper diagnostic limit for the ratio of the electron density(unit:m^(-3))to collision frequency(unit:Hz)exceeds 1×10^(11),enabling an electron density to exceed 1×10^(20)m^(-3)and a collision frequency to be less than 1 GHz.In this work,the feasibility of using the LF phase shift to implement the plasma diagnosis is also assessed.Diagnosis experiments on shock tube equipment are conducted by using both the electrostatic probe method and LF method.By comparing the diagnostic results of the two methods,the inversion results are relatively consistent with each other,thereby preliminarily verifying the feasibility of the LF method.The ratio of the electron density to the collision frequency has a relatively uniform distribution during the plasma stabilization.The LF diagnostic path is a loop around the model,which is suitable for diagnosing the plasma that surrounds the model.Finally,the causes of diagnostic discrepancy between the two methods are analyzed.The proposed method provides a new avenue for diagnosing high-density enveloping plasma.

A self-organization formation configuration based assignment probability and collision detection

The formation control of multiple unmanned aerial vehicles(multi-UAVs)has always been a research hotspot.Based on the straight line trajectory,a multi-UAVs target point assignment algorithm based on the assignment probability is proposed to achieve the shortest overall formation path of multi-UAVs with low complexity and reduce the energy consumption.In order to avoid the collision between UAVs in the formation process,the concept of safety ball is introduced,and the collision detection based on continuous motion of two time slots and the lane occupation detection after motion is proposed to avoid collision between UAVs.Based on the idea of game theory,a method of UAV motion form setting based on the maximization of interests is proposed,including the maximization of self-interest and the maximization of formation interest is proposed,so that multi-UAVs can complete the formation task quickly and reasonably with the linear trajectory assigned in advance.Finally,through simulation verification,the multi-UAVs target assignment algorithm based on the assignment probability proposed in this paper can effectively reduce the total path length,and the UAV motion selection method based on the maximization interests can effectively complete the task formation.

Collision off-axis position dependence of relativistic nonlinear Thomson inverse scattering of an excited electron in a tightly focused circular polarized laser pulse

This paper presents a novel view of the impact of electron collision off-axis positions on the dynamic properties and relativistic nonlinear Thomson inverse scattering of excited electrons within tightly focused, circularly polarized laser pulses of varying intensities. We examine the effects of the transverse ponderomotive force, specifically how the deviation angle and speed of electron motion are affected by the initial off-axis position of the electron and the peak amplitude of the laser pulse. When the laser pulse intensity is low, an increase in the electron's initial off-axis distance results in reduced spatial radiation power, improved collimation, super-continuum phenomena generation, red-shifting of the spectrum's harmonic peak, and significant symmetry in the radiation radial direction. However, in contradiction to conventional understandings,when the laser pulse intensity is relatively high, the properties of the relativistic nonlinear Thomson inverse scattering of the electron deviate from the central axis, changing direction in opposition to the aforementioned effects. After reaching a peak, these properties then shift again, aligning with the previous direction. The complex interplay of these effects suggests a greater nuance and intricacy in the relationship between laser pulse intensity, electron position, and scattering properties than previously thought.

Age and geochemical evolution of granite magmatism in Olkhon region from Caledonian syncollisional ore-free granite to the rare metal granite and pegmatite of Middle Paleozoic intraplate setting

The detailed description of two granite complexes in the Olkhon subterrane is given.The Early Paleozoic Sharanur complex was formed by granitization of gneisses of the Olkhon series.It includes migmatites,granite-gneisses,granites and pegmatites of normal alkalinity;they belong to the type of syncollisional granites.The Middle Paleozoic Aya granite complex includes mother Aya massif of amazonite-bearing granites and several types of rare-metal pegmatites.They have elevated alkalinity,low of Ba,Sr,and high LILE and HFSE elements contents.The Aya pegmatites lie in northwest cracks of stretching and associated with the rise of the territory under the influence of the North Asian plume.These cracks and pegmatites mark the beginning of a new intraplate geodynamic setting.Two geochemical types are distinguished among the pegmatites of this complex.These are amazonite pegmatites of Li-F type with Ta mineralization and complex type pegmatite with Be-Rb-Nb-Ta and Li-F mineralization(the Ilixin vein).The Tashkiney pegmatite vein is similar to Ilixin,but lies in the gneisses of the Olkhon series.It shows high concentrations of Be,Nb,Ta,as well as W,Sn,but lacks Li and F,due to a greater depth and higher temperature of the melt crystallization of this pegmatite.

The study of intelligent algorithm in particle identification of heavy-ion collisions at low and intermediate energies

Traditional particle identification methods face timeconsuming,experience-dependent,and poor repeatability challenges in heavy-ion collisions at low and intermediate energies.Researchers urgently need solutions to the dilemma of traditional particle identification methods.This study explores the possibility of applying intelligent learning algorithms to the particle identification of heavy-ion collisions at low and intermediate energies.Multiple intelligent algorithms,including XgBoost and TabNet,were selected to test datasets from the neutron ion multi-detector for reaction-oriented dynamics(NIMROD-ISiS)and Geant4 simulation.Tree-based machine learning algorithms and deep learning algorithms e.g.TabNet show excellent performance and generalization ability.Adding additional data features besides energy deposition can improve the algorithm’s performance when the data distribution is nonuniform.Intelligent learning algorithms can be applied to solve the particle identification problem in heavy-ion collisions at low and intermediate energies.

Ovarian-adnexal reporting and data system ultrasound evaluation and pathological characteristics of ovarian collision tumor

BACKGROUND Collision tumor are neoplasms,including two histologically distinct tumors that coexist in the same mass without histological admixture.The incidence of collision tumor is low and is rare clinically.AIM To investigate ultrasound images and application of ovarian-adnexal reporting and data system(O-RADS)to evaluate the risk and pathological characteristics of ovarian collision tumor.METHODS This study retrospectively analyzed 17 cases of ovarian collision tumor diagnosed pathologically from January 2020 to December 2023.All clinical features,ultrasound images and histopathological features were collected and analyzed.The O-RADS score was used for classification.The O-RADS score was determined by two senior doctors in the gynecological ultrasound group.Lesions with O-RADS score of 1-3 were classified as benign tumors,and lesions with O-RADS score of 4 or 5 were classified as malignant tumors.RESULTS There were 17 collision tumors detected in 16 of 6274 patients who underwent gynecological surgery.The average age of 17 women with ovarian collision tumor was 36.7 years(range 20-68 years),in whom,one occurred bilaterally and the rest occurred unilaterally.The average tumor diameter was 10 cm,of which three were 2-5 cm,11 were 5-10 cm,and three were>10 cm.Five(29.4%)tumors with O-RADS score 3 were endometriotic cysts with fibroma/serous cystadenoma,and unilocular or multilocular cysts contained a small number of parenchymal components.Eleven(64.7%)tumors had an O-RADS score of 4,including two in category 4A,six in category 4B,and three in category 4C;all of which were multilocular cystic tumors with solid components or multiple papillary components.One(5.9%)tumor had an O-RADS score of 5.This case was a solid mass,and a small amount of pelvic effusion was detected under ultrasound.The pathology was high-grade serous cystic cancer combined with cystic mature teratoma.There were nine(52.9%)tumors with elevated serum carbohydrate antigen(CA)125 and two(11.8%)with elevated serum CA19-9.Histological and pathological results showed that epithelial-cell-derived tumors combined with other tumors were the most common,which was different from previous results.CONCLUSION The ultrasound images of ovarian collision tumor have certain specificity,but diagnosis by preoperative ultrasound is difficult.The combination of epithelial and mesenchymal cell tumors is one of the most common types of ovarian collision tumor.The O-RADS score of ovarian collision tumor is mostly≥4,which can sensitively detect malignant tumors.