Theory Of Inelastic Collisions Research Articles

A Project Report on Optimization of an Off Road Vehicle Ergonomics

Abstract: This paper contain the behaviour of A BAJA vehicle chassis which undergo the various load test like’’Front impact test, Side impact test, Rear impact test, Roll over impact”all the analysis of the test has been performed with the help of ANSYS WORKBENCH 18.1,where maximum deformation ,stress and strain calculated over duration of the particular impact.For the theoretical calculation we have use the INELASTIC COLLISION THEORY with this we have applied a force at a point .The boundary conditions and loading use different methodology. Study of ergonomics which help to give the ergonomically safer design according to the driver perspective. Keywords: Front impact test, Side impact test, Rear impact test, Roll over impact, Ansys Workbench ,ergonomic study

Approximation Solution for the Zener Impact Theory

Collisions can be classified as completely elastic or inelastic. Collision mechanics theory has gradually developed from elastic to inelastic collision theories. Based on the Hertz elastic collision contact theory and Zener inelastic collision theory model, we derive and explain the Hertz and Zener collision theory model equations in detail in this study and establish the Zener inelastic collision theory, which is a simple and fast calculation of the approximate solution to the nonlinear differential equations of motion. We propose an approximate formula to obtain the Zener nonlinear differential equation of motion in a simple manner. The approximate solution determines the relevant values of the collision force, material displacement, velocity, and contact time.

Thermodynamic Analysis of Brownian Motion-Induced Particle Agglomeration Using the Taylor-Series Expansion Method of Moments

On the basis of binary perfectly inelastic collision theory, the time evolutions of kinetic energy and surface area for a particle agglomerate system, due to Brownian motion, are investigated by using the Taylor series expansion technology. The asymptotic behaviors over a long time period show a significantly negative power function of time. The thermodynamic constraints of this system are then obtained according to the principle of maximum entropy, which establishes a relationship of inequality between the first three particle moments and some physical parameters (i.e., surface tension and temperature). In the thermodynamic equilibrium state, this function provides a new approach for estimating the effect of molecular structure on surface tension of liquid polymers.

Influence of interlayer technique on microstructure and mechanical properties of Ti/Al cladding plate manufactured via explosive welding

In this study, different series of TA2/5083 cladding plates with and without the 1060 interlayers (0.3 and 0.5 mm thick) were manufactured via explosive welding. From the perspective of dynamics and energy, the perfectly inelastic collision theory and the momentum conservation theory were applied to calculate collision velocity and kinetic energy loss of each layer, thereby analyzing and studying the action mechanism of an interlayer in Ti/Al explosive welding. Microstructural work and mechanical tests were carried out to research the effect of the interlayer technique on the comprehensive properties of TA2/5083 explosive clads. The results indicated that the use of the interlayer technique could significantly reduce the collision velocity and actually divided the total kinetic energy loss of the flyer plate through multiple collision processes, thereby solving the problem of excessive kinetic energy loss in direct welding. The cladding plate manufactured via direct welding presented the planar interfacial morphology where the continue melting layer accompanied by a slender microcrack were observed, while the cladding plates with the interlayers exhibited good quality of bonding without major defects. In addition, the typical microstructures near the TA2/1060 interfaces, such as vortex and melting block, were reported. Mechanical tests of the three cladding plates found that the values of microhardness near the interfaces were increased due to the work hardening in explosive welding. The TA2/5083 cladding plate with a 0.3 mm thick 1060 interlayer had the highest tensile and shear strength, showing the best quality welded joint. The fractographic study indicated that ductile fracture was the main character.

Thermodynamic analysis of Brownian coagulation based on moment method

In this article, the thermodynamic constraints of Brownian coagulation are proposed based on the binary perfectly inelastic collision theory and the principle of maximum entropy. The constraints can be expressed as inequalities with the Taylor series expansion method of moments. The inequalities establish the relationship between the physical parameters (such as temperature and specific surface energy) and the first three integral moments of particles. The inequalities are verified to determine the critical time for Brownian coagulation to reach the thermodynamic equilibrium. The critical time is proportional to the specific surface energy and inversely related to the temperature, which can be used to determine whether the particle size distribution reaches self-preserving form. Moreover, the critical states provide a new approach for detecting the particle specific surface energy with the moment method. The results further explain Brownian coagulation and offer opportunities to improve environmental quality from the viewpoint of thermodynamics.

Auger Effect Revisited: An Essay by Inelastic Collision Theory

This work presents an essay to the Auger Effect, by the Inelastic Collision Theory. Calculations of the energies of the electrons ejected for bands of the Auger spectrum of some molecules were made, to test of the model.

Completely Inelastic Collision to Confirm Maximum Punch Pressure Force of Cold Pressure Welding

The maximum punch pressure force (TMPPF) of cold welding pressure affects not only the performance of the welding bonding but also the amount of the area of welding bonding. If punch force is more bigger, it may be take place cracks, stress concentration and welding concave pits, which affect application of materials and increase incidence of faults. The process that punch pressure of cold welding pressure applied on sheet materials to attain welding bonding is simplified beam in cold pressure welding. Under normal circumstances it is an important method to TMPPF by the manner of experiment, but the method to attain TMPPF is limited. In the paper completely inelastic collision theory is applied to explain the process of cold welding pressure, the theory of completely inelastic collision offers principle theory to attain TMPPF. In this paper, two supposes are put forward, on the basis of two supposes the critical velocity is attained. At the same time, critical kinetic momentum or critical kinetic energy will be attained. On the basis of the law of conservation of energy, energy balance equation is attained, which will drop in calculating difficulty of the non-linear process of cold pressure welding and decrease calculated amount. In this paper on the basis of the process of collision all phases are analyzed. Indeed elastic-plastic deformation phase is completely inelastic collision phase, and from point of view of collision to calculate energy loss. At the same time, to suppose other plate is utter stiff can attain critical velocity, thus, to achieve the equation of TMPPF.

A ballistic-pendulum test stand to characterize small cold-gas thruster nozzles

This paper deals with the design, development and experimentation of a new test stand for the accurate and precise characterization of small cold-gas nozzles having thrust of the order of 0.1 N and specific impulse of the order of 10 s. As part of the presented research, a new cold-gas supersonic nozzle was designed and developed based on the quasi one-dimensional theory. The test stand is based on the ballistic-pendulum principle: in particular, it consists of a suspended gondola hosting the propulsion system and the sample nozzle. The propulsion system consists of an air tank, pressure regulator, solenoid valve, battery and digital timer to command the valve. The gondola is equipped with a fin, immersed in water, to provide torsional and lateral oscillation damping. A laser sensor measures the displacement of the gondola. The developed test stand was calibrated by using a mathematical model based on the inelastic collision theory. The obtained accuracy was of ∼1%. Sample experimental results are reported regarding the comparison of the new supersonic nozzle with a commercially available subsonic nozzle. The obtained measurements of thrust, mass flow rate and specific impulse are precise to a level of ∼3%. The broad goal of the presented research was to contribute to an upgraded design of a spacecraft simulator used for laboratory validation of guidance, navigation and control algorithms for autonomous docking manoeuvres.

Effect of Gravity and Electrolyte Concentration on the Fractal Structure of Colloidal Aggregates

The new method developed by Li et al. was used to calculate the energy between two colloidal particles, which could break through the limit that the surface potential to be taken as a constant as electrolyte concentration changes in the classic DLVO theory. Also in this research, both the Boltzmann theory of kinetic energy of colloidal particles and Monte Carlo method were used to simulate the movement of colloidal particles, and the inelastic collision theory was used to solve the problem of effective collision probability. By improving the DDA model, the relationship between the cohesion efficiency and the electrolyte concentration in gravity field was established successfully. The results showed that: (1) the curves of the fractal dimension changed with electrolyte concentration as gravity field presence was quite different from that as the gravity field absence. The curves were “L”-shaped as the gravity field absence; while, as the gravity field presence, the curves were “S”-shaped. (2) As the gravity field presence, the slow aggregating process could be divided into two sections: the sensitive and non-sensitive sections to electrolyte concentration. In the sensitive section, an inflexion of electrolyte concentration was found. (3) As the gravity field absence, the fractal dimension of aggregates was 1.86±0.01 for different sizes of colloidal particles as the aggregating process was fast under a higher electrolyte concentration condition. Comparatively, for a slow aggregating process of low electrolyte concentration, the fractal dimension increased to 2.01±0.02. However, under the same low electrolyte concentration, the fractal dimension of aggregates approached 3 as the gravity field presence.

Contact and Quasi-Static Impact of Hamilton System

Collisions and contacts of elastic materials are numerically and theoretically investigated. Using a two-dimensional spring-mass model with defect particles under the free boundary condition, we reproduce the Hertzian contact theory at equilibrium and the quasi-static theory for low speed impacts.

Simulation and theory of the impact of two-dimensional elastic disks

The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. This suggests that the elastic model cannot be used in the quasi-static limit. A new quasi-static theory of impacts is proposed, in which the effect of thermal diffusion is dominant. The abrupt decrease of COR has been found due to the plastic deformation of the disk, which is assisted by the initial internal motion.

The Impact of Two-Dimensional Elastic Disk

The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. The abrupt drop of COR is found due to the plastic deformation of the disk, which is assisted by the initial internal motion.(to be published in J. Phys. Soc. Jpn.)

Louis Goldstein

Louis Goldstein, a former group leader at the once-named Los Alamos Scientific Laboratory, died in Los Alamos, New Mexico, on 26 August 1999. He had broken his hip on 4 July, and died from the complications that followed.Louis was born in Dombrad, Hungary, on 25 March 1904. Barred as a Jew from attending a Hungarian university, he moved to Paris in the early 1920s. He earned a bachelor’s degree in physics from the University of Paris in 1926 and a doctor of science degree in theoretical physics from the same university in 1932. His thesis was entitled “The Quantum Theory of Inelastic Collisions.” He remained in Paris until the spring of 1939, when he emigrated to the US. Five years later, he became a US citizen.Shortly after arriving in the US, he began teaching theoretical physics at City College in New York City. From 1944 to 1946, he worked with the wave propagation group at Columbia University. In 1946, he moved to Los Alamos Scientific Laboratory, where he served as a group leader in the lab’s theoretical division. His position was unique: He was the sole member of his group, and his assignment was to work on whatever subject he chose!Among Louis’s first, and most appreciated, contributions to postwar research at Los Alamos were to the work of the low-temperature physics group. Shortly after World War II ended, preliminary investigations of thermonuclear reactions began at the lab. Experimentally, this effort required tritium, which made available, for the first time, pure helium-3. Louis was aware of Fritz London’s 1938 suggestion that helium-4 behaves anomalously at 2.17 K because it was a Bose–Einstein fluid. Knowing that 3He obeys Fermi–Dirac statistics, Louis recognized that it would show no such behavior. Other theorists had suggested that 3He would be hard to liquefy because of its high zero-point energy, but Louis was undeterred. Even before any 3He arrived at Los Alamos, he organized a crash course of experiments on liquid helium. It was therefore a rewarding experience for Louis when two of us (Grilly and Keller) and Stephen Sydoriak liquefied this isotope on 13 October 1948. Eleven months later, the team reported that liquid 3He exhibited no anomalous behavior down to a temperature of 0.84 K.In his later years, Louis continued to write many journal articles that explored the statistical thermodynamics of condensed phases of the stable helium isotopes, including the magnetic properties of solid 3He. He retired in 1971, but continued to be involved with the lab for many more years. He made a deep impression on his younger colleagues through his commitment to physics and to the integrity the subject requires and fosters. Physics for Louis was not merely important, but personally encompassing. His memory is cherished by everyone he mentored and influenced. Louis Goldstein PPT|High resolution© 2001 American Institute of Physics.

Quantum statistical effect on ionizing collisions of ultracold metastable Kr isotopes.

Ultracold ionizing collisions of laser-cooled Kr isotopes in the 1${\mathit{s}}_{5}$[4${\mathit{p}}^{5}$5s${:}^{3}$${\mathit{P}}_{2}$] metastable state are investigated. When the collision energy is reduced below the p-wave centrifugal barrier of 80 \ensuremath{\mu}K, the ratio of the ionizing collision rate between polarized and unpolarized $^{83}\mathrm{Kr}$ atoms is found to decrease. This is a direct evidence of the quantum interference of two identical Fermi particles. The experimental results are compared with the calculation based on the simplified inelastic collision theory.

A theory of inelastic collisions of atoms with multiply charged ions

A simple method is proposed for estimating cross sections for excitation and ionization in collision of atoms with fast multiply charged ions in cases in which the Born approximation is inapplicable. This method is analogous to the approximation of sudden excitations and allows direct generalization to collisions that lead to simultaneous excitation and ionization of two or more electrons. Ionization of a hydrogen atom and double ionization of a helium atom have been considered. Comparison with experiments is given.

Quantum theory of inelastic collisions of a diatomic molecule in a 2Π electronic state with an uncorrugated surface: Λ-doublet, spin-orbit, and polarization effects in NO (X 2Π)–Ag (111) scattering

The formalism is developed for scattering of a molecule in a 2Π electronic state by an infinitely massive, uncorrugated surface. A general development of the electrostatic interaction potential is used to obtain matrix elements of the potential between molecular rotational and fine-structure states, described in an intermediate Hund’s coupling case. Explicit expressions for the inelastic S-matrix elements are derived in the energy sudden limit. Semiclassical (high J) expressions for the potential matrix elements and sudden S-matrix elements are obtained. This formal work is then used to make several general predictions for collisions of NO (X 2Π) with Ag(111), which has been recently studied experimentally. In particular, we predict: (1) for moderate to high values of the final rotational quantum number, the molecules will be scattered so that J lies in the plane of the surface, (2) in the energy sudden limit the F1 and F2 rotational manifolds will be equally populated by collisions, (3) and, again in the energy sudden limit, preferential population will occur in either the two Λ-doublet levels which are symmetric with respect to reflection of the NO electronic wave function in the plane of rotation or in the two levels which are antisymmetric with respect to this operation.

A multi-trajectory theory of inelastic collisions

A systematic approximation scheme is presented for introducing multi-classical trajectories into the theory of inelastic collisions. In general, the translational and internal degrees of freedom are coupling through an interaction picture potential which is nonlocal in translational space and which has no diagonal elements in the internal space. For each different pair of internal states this potential has a unique classical trajectory generated by the Hamiltonian which is the arithmetic mean of the two appropriate (internal state) diagonal elements of the full system Hamiltonian. Localisation of this potential in translational position space produces a multi-trajectory eikonal theory. Finally, replacing the unique classical trajectories with fully parameterised trajectories gives a multi-trajectory version of the standard impact parameter approximation. Results for both atomic and molecular (adiabatic and diabatic) bases are presented.

Theory of inelastic collisions: an approach to the solution of the radial coupled equations

The radial second-order differential equations of the theory of collisions between atomic systems plus the boundary conditions at infinity are transformed to an equivalent system of first-order differential equations by introducing for each channel the Wronskian of the wavefunction and the Jost solution of the uncoupled equation (incoming and outgoing Jost solutions for open and closed channels, respectively). In the asymptotic region the Wronskian gives directly the value of the corresponding S-matrix element. By using the first-order Magnus-Fer approximation an approximate analytical expression for the S-matrix elements of the multichannel problem is obtained; the formula is also particularised to the two-channel problem.

Theory of inelastic collisions between low-lying excited- and ground-state Ne atoms

A quantum-mechanical study of low-energy inelastic collisions of excited- and ground-state Ne atoms has been undertaken. Close-coupling calculations of cross sections for the transitions $^{1}P_{1}\ensuremath{\rightarrow}^{3}P_{1}$, $^{1}P_{1}\ensuremath{\rightarrow}^{3}P_{2}$, $^{3}P_{1}\ensuremath{\rightarrow}^{3}P_{2}$, and $^{3}P_{0}\ensuremath{\rightarrow}^{3}P_{2}$ have been performed at collision energies below 3 eV. All cross sections exhibit a rapid falloff at low energies, reflecting barriers and repulsive walls present in the potential curves. Spin-orbit coupling is assumed to be the transition mechanism. Comparison with experimental data suggests that neglected rotational coupling might be important for some of the quite weak transitions at energies below about 0.1 eV.

A simple semiclassical model for E–V energy transfer in A+BC nonreactive collisions

The semiclassical theory of inelastic collisions between a diatom and a two-level atom is presented. The model is based on the well-known Dicke-like hamiltonian, whose usefulness for the collision problem is investigated. A simple analytical expression for the probability of vibronic energy exchange is derived.