Collision Theory Research Articles

Electrostatic forces acting on particle image velocimetry tracer particles in a plasma actuator flow

Dusty plasma effects were investigated for the results of plasma actuator particle image velocimetry experiments. Two particle charging theories, partially collisional and fully collisional theories, are used to estimate the charge on the particles. Secondary aerodynamic forces are shown to be weak in comparison to Stokes drag, and secondary dusty plasma effects are also weak compared to the electrostatic force. It is shown that the true air velocity can be calculated by extrapolating to the 0-nm particle size. Using the difference in velocity between the air and the particles, the Stokes drag force is calculated and found to be between 1 and 200 pN depending on particle size. The electrostatic force is also calculated and found to be almost equal and opposite to Stokes drag, but the charge and electric field components cannot be separated. Based on assumptions from published simulation results, the theories are shown to be within a factor of two in predicting the charge on a particle in a high pressure plasma.

Collision tumors of the thyroid: Review of literature and report of a case of papillary–Follicular collision tumor

It is a known fact that thyroid malignancies are the most common of endocrine malignancies. Furthermore, differentiated thyroid malignancies including the papillary and follicular types are the most common among these malignancies of the thyroid. However, it is extremely uncommon to get a combination of two primary malignancies within the same thyroid gland. These combinations can be classified into collision tumors, mixed tumors, and composite tumors. Whenever such tumors have been described, they have almost always been combinations of papillary carcinoma and medullary carcinoma. Recently, a couple of cases of combinations of papillary and follicular carcinomas are being reported. It is difficult to completely explain the occurrence of such tumor types together in the same gland. Various theories have been proposed to explain this simultaneous occurrence such as the stem cell theory, collision theory, and the hostage theory. It is now accepted that these tumors should be considered more aggressive and having a higher risk of recurrence as compared to either of the tumors occurring independently. Treatment should be patient specific and is directed by the more aggressive of the tumors; however, no standardized protocols for diagnosis or treatment have evolved due to lack of significant information on their behavior.

Students' visualisation of chemical reactions – insights into the particle model and the atomic model

This paper reports on an interview study of 18 Grade 10–12 students’ model-based reasoning of a chemical reaction: the reaction of magnesium and oxygen at the submicro level. It has been proposed that chemical reactions can be conceptualised using two models: (i) theparticle model, in which a reaction is regarded as the simple combination and rearrangement of reactant particles and does not involve any change in the identity of the reactants, and (ii) theatomic model, wherein a reaction involves the transformation of one chemical species into another. This paper suggests that although theparticle modellooks simpler than theatomic model, it can help to support the learning of some advanced chemical concepts such as energetics and collision theory. Therefore, it is postulated that students who reason using theparticle modelare able to demonstrate some advanced ideas about chemical reactions. The conceptualisation of reactions in terms of theatomic modeland theparticle modelallows a flexible understanding of students’ learning. Students’ representations of the reaction between magnesium and oxygen were analysed with reference to the two models. The models were found to be useful in assessing the students’ understanding of the reaction and revealing the novel ways that the students reasoned the chemical reaction. In addition, a student who used theparticle modelto represent the reaction was found to explain the reaction in terms of some energetics and kinetics concepts. The study offers insights for curriculum planners and teachers into the potential of these two models to help students understand chemical reactions.

Interface adhesion property between graphene film and surface of nanometric microstructure

The performance of graphene can be influenced by its surface mophology, while the surface morphology of graphene is closely related to the substrate. The adsorption and peeling process of graphene on a corrugated surface can provide a theoretical basis for the functional preparation and transfer of graphene. In this work, the adhesion properties and peeling process of graphene on nanostructured substrate are investigated by using molecular dynamics (MD) simulation. As an effective tool of atomic collision theory, MD simulation can provide detailed information about the adsorption configuration and peeling properties of graphene on the nanostructure surface, making up for the deficiency of experiment. The results indicate that graphene can conformably coat on the surface, partially adhere to or remain flat on the top of the stepped substrate. We find that the continuous transition occurs in the adsorption configuration of graphene on the stepped substrate, but the repeated process appears in the transition from partial adherence to conformable coating. When graphene coats on the nanostructured substrate conformably, the adsorption energy can reach its peak value. The adsorption configuration of graphene can change from suspension to partial adhesion after the adsorption energy has exceeded 360 eV -2. It is also shown that the average peeling force fluctuates periodically when the absorption configuration of graphene is conformably coated or suspended on the stepped substrate. Two kinds of behaviors can be noticed in the peeling process. The graphene can directly slide over the bottom while it is fully coated on the surface. The graphene is separated directly from the corrugated surface while it suspends or partially adheres to the surface. If the absorption configuration of graphene is in the suspension state, the average peeling force appears to change drastically within a section of peeling distance and then decreases immediately below zero. Although the flexural stiffness of graphene can be overcome, the interfacial friction between graphene and the substrate is also an essential factor affecting the final adsorption configuration. In this paper, we propose a theoretical formula for the average peeling force according to the changes of size parameters on the nanostructured substrate. The theoretical formula is validated by the simulation results. In addition, with the increase of peeling angle, the average peeling force first increases and then becomes smaller. As a result, a larger average peeling force can be found when the graphene with Stone-Wales defect structure is peeled from the flat substrate. With the increase of double vacancy defect, the maximum peeling force decreases in a certain range, whereas it increases beyond this range. This work can provide a theoretical reference for exploring the peeling property and the adhesion mechanism of graphene on nanostructure surface.

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.

SPH Particle Collisions for the Reduction of Particle Clustering, Interface Stabilisation and Wall Modelling

The pair-wise forces in the SPH momentum equation guarantee the conservation of momentum, but they cannot prevent particle clustering and wall penetration. Particle clustering may occur for several reasons. A fundamental issue is the tensile instability, which is caused by negative numerical pressures. Clustering may also occur due to certain properties of the kernel gradient. Discontinuities in the pressure and its gradient, due to surface tension and gravity, may cause particle instabilities near the interface between two fluids. Wall penetration is also a form of particle clustering. In this paper the particle collision concept is introduced to suppress particle clustering. Here, the use of kinematic conditions (motion) rather than dynamic conditions (forces) is explored. These kinematic conditions are obtained from kinetic collision theory. Conservation of momentum is maintained, and under elastic conditions conservation of energy as well. The particle collision model only becomes active when needed. It may be seen as a particle shifting method, in the sense that the velocities are changed, and as a consequence of that the particle positions change. It is demonstrated in several case studies that the particle collision model allows for realistic (low) viscosities. It was also found to stabilise the interface between two fluids up to high, realistic density ratios (1000:1) in typical liquid-gas applications. As such it can be used as a multi-fluid model. The concept allows for real wave speed ratios (and far beyond), which, as well as real viscosities, are essential in the modelling of heat transfer applications. The collisions with walls allow for no-slip conditions at real viscosities while wall penetration is suppressed. In summary, the particle collision model makes SPH more robust for engineering.

Self-Assembly through Noncovalent Preorganization of Reactants: Explaining the Formation of a Polyfluoroxometalate.

High-order elementary reactions in homogeneous solutions involving more than two molecules are statistically improbable and very slow to proceed. They are not generally considered in classical transition-state or collision theories. Yet, rather selective, high-yield product formation is common in self-assembly processes that require many reaction steps. On the basis of recent observations of crystallization as well as reactions in dense phases, it is shown that self-assembly can occur by preorganization of reactants in a noncovalent supramolecular assembly, whereby directing forces can lead to an apparent one-step transformation of multiple reactants. A simple and general kinetic model for multiple reactant transformation in a dense phase that can account for many-bodied transformations was developed. Furthermore, the self-assembly of polyfluoroxometalate anion [H2 F6 NaW18 O56 ]7- from simple tungstate Na2 WO2 F4 was demonstrated by using 2D 19 F-19 F NOESY, 2D 19 F-19 F COSY NMR spectroscopy, a new 2D 19 F{183 W} NMR technique, as well as ESI-MS and diffusion NMR spectroscopy, and the crucial involvement of a supramolecular assembly was found. The deterministic kinetic reaction model explains the reaction in a dense phase and supports the suggested self-assembly mechanism. Reactions in dense phases may be of general importance in understanding other self-assembly reactions.

Investigating the settling dynamics of cohesive silt particles with particle-resolving simulations

The settling of cohesive sediment is ubiquitous in aquatic environments, and the study of the settling process is important for both engineering and environmental reasons. In the settling process, the silt particles show behaviors that are different from non-cohesive particles due to the influence of inter-particle cohesive force. For instance, the flocs formed in the settling process of cohesive silt can loosen the packing, and thus the structural densities of cohesive silt beds are much smaller than that of non-cohesive sand beds. While there is a consensus that cohesive behaviors depend on the characteristics of sediment particles (e.g., Bond number, particle size distribution), little is known about the exact influence of these characteristics on the cohesive behaviors. In addition, since the cohesive behaviors of the silt are caused by the inter-particle cohesive forces, the motions of and the contacts among silt particles should be resolved to study these cohesive behaviors in the settling process. However, studies of the cohesive behaviors of silt particles in the settling process based on particle-resolving approach are still lacking. In the present work, three-dimensional settling process is investigated numerically by using CFD–DEM (Computational Fluid Dynamics–Discrete Element Method). The inter-particle collision force, the van der Waals force, and the fluid–particle interaction forces are considered. The numerical model is used to simulate the hindered settling process of silt based on the experimental setup in the literature. The results obtained in the simulations, including the structural densities of the beds, the characteristic lines, and the particle terminal velocity, are in good agreement with the experimental observations in the literature. To the authors’ knowledge, this is the first time that the influences of non-dimensional Bond number and particle polydispersity on the structural densities of silt beds have been investigated separately. The results demonstrate that the cohesive behavior of silt in the settling process is attributed to both the cohesion among silt particles themselves and the particle polydispersity. To guide to the macro-scale modeling of cohesive silt sedimentation, the collision frequency functions obtained in the numerical simulations are also presented based on the micromechanics of particles. The results obtained by using CFD–DEM indicate that the binary collision theory over-estimated the particle collision frequency in the flocculation process at high solid volume fraction.

On the theory of time dilation in chemical kinetics

The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying basic theories of chemical kinetics, which are transition state theory, collision theory, RRKM and Marcus theory, with the special theory of relativity. Boltzmann constant and energy spacing between permitted quantum levels of molecules are quantum mechanically proved to be Lorentz variant. The relativistic statistical thermodynamics has been developed to explain quasi-equilibrium existing between reactants and activated complex. The newly formulated Lorentz transformation of the rate constant from Arrhenius equation, of the collision frequency and of the Eyring and Marcus equations renders the rate of reaction to be Lorentz variant. For a moving observer moving at fractions of the speed of light along the reaction coordinate, the transition state possess less kinetic energy to sweep translation over it. This results in the slower transformation of reactants into products and in a stretched time frame for the chemical reaction to complete. Lorentz transformation of the half-life equation explains time dilation of the half-life period of chemical reactions and proves special theory of relativity and presents theory in accord with each other. To demonstrate the effectiveness of the present theory, the enzymatic reaction of methylamine dehydrogenase and radioactive disintegration of Astatine into Bismuth are considered as numerical examples.

A Theoretical Study on the Dynamics of the Reaction of CH Radicals with Water.

Quasi-classical trajectory (QCT) and RRKM-SSA calculations are carried out to gain insight into the dynamics of the title reaction. The barrier-less initiation step in this system is governed by the capture probability in the entrance channel to form an energized adduct once the centrifugal barrier is surmounted. The dynamics of the title reaction on its lowest doublet electronic state is studied at the DFT level of MPWB1K/6-31++g(2df,2p). An iteratively modified Shepard interpolation technique implemented in the GROW program suite was used to construct a global potential energy surface for the title reaction. The total and individual cross sections for the main products and corresponding reaction probabilities as a function of initial collision energy ranging from 0.4 kJ mol-1 to 52.5 kJ mol-1 are calculated. These data are used to calculate the total rate constant for the title reaction by means of collision theory. Our calculated QCT rate constant is compared with the calculated rate constant from RRKM-SSA method at the CCSD(T)/Aug-cc-pVTZ//MP2/6-31++g(2df,2p) level. The energy partitioning for the main products CH2O + H and HCOH + H and also for the reactants after nonreactive collisions as a function of initial collision energy are discussed.

Gas dynamic analogous exposure approach to interaction intensity in multiple-vehicle crash analysis: Case study of crashes involving taxis

Exposure is a frequency measure of being in situations in which crashes could occur. In modeling multiple-vehicle crash frequency, traditional exposure measures, such as vehicle kilometrage and travel time, may not be sufficiently representative because they may include situations in which vehicles rarely meet each other and multiple-vehicle crashes can never happen. The meeting frequency of vehicles should be a better exposure measure in such cases. This study aims to propose a novel Gas Dynamic Analogous Exposure (GDAE) to model multiple-vehicle crash frequency. We analogize the meeting frequency of vehicles with the meeting frequency of gas molecules because both systems consider the numbers of the meetings of discrete entities. A meeting frequency function of vehicles is derived based on the central idea of the classical collision theory in physical chemistry with consideration of constrained vehicular movement by the road alignments. The GDAE is then formulated on the basis of the major factors that contribute to the meeting frequency of vehicles. The proposed GDAE is a more representative proxy exposure measure in modeling of multiple-vehicle crash frequency because it further investigates and provides insight into the physics of the vehicle meeting mechanism. To demonstrate the applicability of the GDAE, zonal crash frequency models are constructed on the basis of multiple-vehicle crashes involving taxis in 398 zones of Hong Kong in 2011. The GDAE outperforms the conventional time exposure in multiple-vehicle crash modeling. To account for any unobservable heterogeneity and to cope with the over-dispersed count data, a random-parameter negative binomial model is established. Explanatory factors that contribute to the zonal multiple-vehicle crash risk involving taxis are identified. The proposed GDAE is a promising exposure measure for modeling multiple-vehicle crash frequency.

Spatial organization and interactions of harvester ants during foraging activity.

Local interactions, when individuals meet, can regulate collective behaviour. In a system without any central control, the rate of interaction may depend simply on how the individuals move around. But interactions could in turn influence movement; individuals might seek out interactions, or their movement in response to interaction could influence further interaction rates. We develop a general framework to address these questions, using collision theory to establish a baseline expected rate of interaction based on proximity. We test the models using data from harvester ant colonies. A colony uses feedback from interactions inside the nest to regulate foraging activity. Potential foragers leave the nest in response to interactions with returning foragers with food. The time series of interactions and local density of ants show how density hotspots lead to interactions that are clustered in time. A correlated random walk null model describes the mixing of potential and returning foragers. A model from collision theory relates walking speed and spatial proximity with the probability of interaction. The results demonstrate that although ants do not mix homogeneously, trends in interaction patterns can be explained simply by the walking speed and local density of surrounding ants.

Investigation on the optimal configuration design and discharge characteristics of the helicon plasma tube

Helicon discharge is characterized by its high ionization efficiency. In order to obtain the desired density, the configuration design of the helicon discharge tube is carried out, and the discharge characteristics are then studied to explore the correlation between the plasma parameters and the input discharge parameters. Finite‐length helicon discharge theory is employed to calculate the plasma resistance Rp, and then the optimal tube length Ls, the radius rp, and the tube–antenna gap d are confirmed. The partial and energy loss mechanisms of the tube are investigated based on low‐pressure discharge particle collision theory. The results show that, for a 10‐cm‐long Nagoya III type antenna, with a tube radius of 4 cm and length of 20 cm, the Rp versus ne curves have peak values at ne higher than 1012 cm−3 when the magnetic field intensity B0 ≥ 200 G. We find that a local minimum of Ploss exists when p0 is ∼1.5–3.0 mTorr; meanwhile, the radial confinement reduces Te and Ploss at constant p0.

A Semi-Empirical Formula of the Dependence of the Fluorescence Intensity of Naphthalene on Temperature and the Oxygen Concentration

Two-ring aromatics, such as naphthalene, are important fluorescent components of kerosene in the planar laser-induced fluorescent (PLIF) technique. Quantifying measurements of kerosene vapor concentrations by PLIF require a prior knowledge of the fluorescence intensity of naphthalene over a wide temperature and oxygen concentration range. To promote the application of PLIF, a semi-empirical formula based on the collision theory and experimental data at the laser wavelength of 266 nm and a pressure of 0.1 MPa is established to predict the fluorescence intensity of naphthalene at different temperatures and oxygen concentrations. This formula takes vibrational states, temperature, and oxygen quenching into account. Verified by published experimental data, the formula can predict the fluorescence intensity of naphthalene with an error less than 9%.

Three-dimensional Monte Carlo simulations of materials on the physical deposition process

The sputtering technique is largely used for the deposition of thin layers. In this study, the Monte Carlo (MC) method combined with the binary collision theory of hard spheres is used to simulate the energy, direction and topology of the film deposit. The effects of several parameters such as the substrate, target, pressure and the distance between substrate and target were analyzed. Our results showed that for large pressures or distances, energy and angular distributions are uniform and consequently the obtained film will be uniform. The obtained results are in agreement with other works, which validates our calculations.

The steady state collision of two compressible subsonic perfect flows

This paper is devoted to the mathematical theory for the steady state collision of two compressible subsonic irrotational flows issuing from two infinitely long nozzles. We established the existence, uniqueness and asymptotic behavior of the subsonic collision flow with a smooth interface for the steady Euler system in an important physical regime. More precisely, there exists a critical value, if the summation of the incoming mass fluxes in the inlets of the nozzles is less than the critical value, then there exists a unique smooth subsonic compressible collision flow. And furthermore, there exists a smooth interface which separates the two non-miscible compressible subsonic flows. In particular, a key observation is that the location of the interface can be determined uniquely by the incoming mass fluxes in the inlets of the nozzles. Finally, we showed some monotonic relationship between the location of the interface and the incoming mass fluxes.

Collisions in mechanics

This article presents a theory of collisions of continua either solid or not. The basic idea which is developed is that the system made of distinct continua is deformable because their relative positions change. The collisions we consider occur while the continua are evolving and the duration of the collisions is small compare to the duration of the whole motion. Thus they are assumed instantaneous. We do not focus on the fast and sophisticated phenomena which occur during collisions. We focus on summing up these phenomena in a coherent theory which gives the elements to pursue the description of the motion. This instantaneity assumption leaves large possibilities to engineers and scientists to develop numerous and useful predictive theories. The basis of the theory is illustrated with the collision of a point with an immobile obstacle. Then the theory is applied to collisions of solids, either rigid or deformable, then to collisions of solids and fluids. The thermal effects of collisions may produce phase change: the example of rain falling on a deeply frozen soil is investigated. Collisions may be so violent that they fracture the bodies: fracturation may also be predicted by the theory. From the theoretical point of view, let us mention that this theory proves that the paradoxes, i.e., illogic results, which are said to result from the equations of mechanics, as the Painleve–Jellet and Klein paradoxes, may be overcome in a clear and logic manner. Moreover these results are supported by experiments.

The Study of Ion Beam Assisted Deposition of CuInSe2 Absorber Films

Based on the selenium ion beam assisted magnetron sequential sputtering technology, low temperature deposition of CIS thin-film solar cells in high quality can be achieved. By comparing with the method of conventional gas phase atomic deposition, and through simulated analysis from the perspective of diffusion uniformity, numerical calculation on the depth of ion beam injection is proceeded. First, according to the classical collision theory in molecular dynamics, the theoretical calculation on the process of ion implantation is done; the concentration distribution of implanted selenium ions can be got by using TRIM program for simulation analysis. On this basis, the concentration distribution of selenium ion after diffusion can be further obtained. Finally, the calculation model is established; through comparison and analysis, when the selenium diffusion uniformity is same in the both conditions, the substrate temperature T1 needed for ion beam assisted deposition and the substrate temperature T2 needed for gas phase atomic deposition are respectively calculated. The calculation results show that on the premise of merely considering the depth of implanted ions, from the perspective of the diffusion uniformity, the selenium ion beam assisted deposition technique can obviously reduce the substrate temperature comparing with traditional vapor deposition technology.

A Development of the Principle of Virtual Laws and its Conceptual Framework in Mechanics as Fundamental Relationship between Physics and Mathematics

Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations (statics and dynamics) to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws (also known as the Principle of virtual velocity or of virtual work). I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris.

MQCT. I. Inelastic Scattering of Two Asymmetric-Top Rotors with Application to H2O + H2O.

A mixed quantum/classical theory (MQCT) for the inelastic collision of two asymmetric-top rotor molecules is developed. In this method, the quantum state-to-state transitions between the rotational states of molecules (internal) are treated quantum mechanically using the time-dependent Schrodinger equation, whereas their relative translational motion (responsible for scattering) is treated classically, using the average trajectory approach. Two versions of the formula for transition matrix elements are presented: a straightforward approach that uses numerical multidimensional quadrature over all the internal degrees of freedom and a more standard analytic approach that uses the expansion of the PES over the basis set of spherical harmonics. Adaptation to the case of identical molecules scattering is presented and is applied to the rotational excitation of two water molecules, H2O + H2O, using the PES from recent literature. Calculations of collisional excitation from the ground state of the system into a number of low-lying excited rotational states are carried out in a broad range of energies. Analysis of computed opacity functions shows a rather unusual scattering regime, dominated by a strong anisotropic long-range interaction (dipole-dipole). The coupled-states (CS) approximation is tested and found to agree semiquantitatively (within a factor of 2) with the fully coupled version of the method. Differential cross sections for the elastic scattering indicate a very narrow forward scattering peak.