Inelastic Collision Model Research Articles

Reducing the computational complexity of implicit schemes in the modeling of kinetic inelastic collisions in a partially ionized plasma

AbstractModeling the time evolution of atomic number densities and the kinetic (non‐Maxwellian) electron energy distribution function under the action of electron impact collisions by classical approaches requires an implicit time‐stepping scheme to maintain numerical stability. The resulting linear system that must be iteratively solved at each time step incorporates a dense (nonsparse) matrix. For variables being propagated, the computational cost is . We present an alternative approach with a computational cost of , which is the same order as the computational cost of an explicit method for propagating a system of this type. The approach relies on a combination of classical iterative derivative evaluations, combinatorial approximations, and some ideas from deep machine learning.

Force of droplet impact on thin liquid films

Inertia-dominated droplet impact transfers momentum to a dry flat target within a short span of time t characterized by (droplet diameter D)/(impact speed U). We investigate experimentally how impact force dynamics change when a droplet hits a thin liquid film of thickness H, less than or approximately equal to the droplet diameter, atop the flat target. Impact force and morphology are recorded simultaneously by piezoelectric force sensing and high-speed video imaging. Compared with a dry surface, the force of droplet impact on a thin liquid film is found to follow the same initial tU/D scaling and reach a slightly higher peak value, but at a significantly later time. Modeling the impact process as a perfect inelastic collision between the droplet and a liquid column of height equal to the film thickness yields the proper timescale (H+D)/U to characterize temporal evolution of the impact force near the inertial peak and through its subsequent exponential decay. The impact crater penetration depth developing within the thin film over the same time span is also found to collapse to a self-similar form based on this characteristic timescale, which attests to the validity of the inelastic collision model in capturing the underlying impact flow physics.

The Gluon Exchange Model for diffractive and inelastic collisions

We propose a new model for a homogeneous description of hadron-hadron and hadron-nucleus collisions, the Gluon Exchange Model, fundamentally based on color octet (gluon) exchange. In proton-proton collisions we provide an exact description of the final state proton and neutron spectrum including the proton diffractive peak. In proton-nucleus reactions we find that the projectile proton diquark cannot survive in more than about half of multiple proton-nucleon processes and consequently must be very frequently disintegrated, leading to long transfers of baryon number over rapidity space.

Particle\u2013boundary interaction in a shear-driven cavity flow

The motion of a heavy finite-size tracer is numerically calculated in a two-dimensional shear-driven cavity. The particle motion is computed using a discontinuous Galerkin-finite-element method combined with a smoothed profile method resolving all scales, including the flow in the lubrication gap between the particle and the boundary. The centrifugation of heavy particles in the recirculating flow is counteracted by a repulsion from the shear-stress surface. The resulting limit cycle for the particle motion represents an attractor for particles in dilute suspensions. The limit cycles obtained by fully resolved simulations as a function of the particle size and density are compared with those obtained by one-way coupling using the Maxey–Riley equation and an inelastic collision model for the particle–boundary interaction, solely characterized by an interaction-length parameter. It is shown that the one-way coupling approach can faithfully approximate the true limit cycle if the interaction length is selected depending on the particle size and its relative density.

Modeling of inelastic collisions in a multifluid plasma: Ionization and recombination

A model for ionization and recombination collisions in a multifluid plasma is formulated using the framework introduced in previous work [H. P. Le and J.-L. Cambier, Phys. Plasmas 22, 093512 (2015)]. The exchange source terms for density, momentum, and energy are detailed for the case of electron induced ionization and three body recombination collisions with isotropic scattering. The principle of detailed balance is enforced at the microscopic level. We describe how to incorporate the standard collisional-radiative model into the multifluid equations using the current formulation. Numerical solutions of the collisional-radiative rate equations for atomic hydrogen are presented to highlight the impact of the multifluid effect on the kinetics.

Electron-impact dissociative double ionization ofN2and CO: Dependence of transition probability on impact energy

We present an experimental and computational analysis of dissociative double ionization of ${\mathrm{N}}_{2}$ and CO molecules under electron impact. Experiments are performed at three energies, viz. 1, 3, and 5 keV, in order to observe the effect of impact energy on the dissociative ionization kinematics. We compare the kinetic energy release (KER) distributions of the charge symmetric dissociation channels of ${\mathrm{N}}_{2}^{2+}$ and ${\mathrm{CO}}^{2+}$ at these impact energies. An approximately linear trend between the transition energy and the expected KER values is inferred on the basis of the calculated potential energy curves of the dications. Experimentally, the normalized differential KER cross sections for these channels show an increasing trend in the low KER range and a decreasing trend in the high KER range as the electron-impact energy is increased. This observation indicates that the transition probability for excitation to different molecular ion states is not only a function of energy difference between the ground and excited states, but also a complicated function of the impact energy. In addition, nature of the observed trend in the differential KER cross sections differs significantly from their differential transition probability, which are calculated using inelastic collision model for fast-electron-impact case.

Publisher's Note: “Modeling of inelastic collisions in a multifluid plasma: Excitation and deexcitation” [Phys. Plasmas 22, 093512 (2015)

Publisher's Note: “Modeling of inelastic collisions in a multifluid plasma: Excitation and deexcitation” [Phys. Plasmas <b>22</b>, 093512 (2015)

Modeling of inelastic collisions in a multifluid plasma: Excitation and deexcitation

We describe here a model for inelastic collisions for electronic excitation and deexcitation processes in a general, multifluid plasma. The model is derived from kinetic theory, and applicable to any mixture and mass ratio. The principle of detailed balance is strictly enforced, and the model is consistent with all asymptotic limits. The results are verified with direct Monte Carlo calculations, and various numerical tests are conducted for the case of an electron-hydrogen two-fluid system, using a generic, semi-classical model of collision cross sections. We find that in some cases, the contribution of inelastic collisions to the momentum and thermal resistance coefficients is not negligible, in contrast to the assumptions of current multifluid models. This fundamental model is also applied to ionization and recombination processes, the studies on which are currently underway.

WE‐F‐105‐01: On the Importance of Nuclear Models On the Accuracy of Fast Monte Carlo Methods for Proton‐Therapy

Purpose: Parallel architectures like graphical processor units (GPU) with high computational power allow dose distributions for proton beams to be calculated with Monte Carlo (MC) simulations within the time constraints of clinical practice. However, physical models often need to be simplified to exploit the full potential of GPUs. This study aims at evaluating comprehensively the impact on computation accuracy of the simplified model for nuclear inelastic collisions described by Fippel et al (Med Phys 2004) and used by Jia et al (PMB 2012). Methods: Three MC codes were used: 1) an in‐house version of Fippel's algorithm, which uses an empirical method to reproduce approximately ICRU 63 nuclear inelastic cross‐sections for oxygen; 2) an extension of PENELOPE to protons (PENH) that samples directly ICRU 63 cross sections (but neglects neutrons); 3) GEANT4 with Binary‐Cascade.The integral depth‐dose deposited by a 200 MeV proton beam into water was then calculated using those MC codes. The simulations were performed in water phantoms of dimensions 4.1×4.1×40, 8×8×40 and 60×60×40 cm3 with a scoring resolution of 1 mm in depth. Results: In the 4.1×4.1×40 cm3 phantom, deviations between Fippel's algorithm and GEANT4 were within 2%, whereas this bound grew up to 3% between PENH and GEANT4. However, when the phantom dimensions are increased, the deviations between PENH and GEANT4 remained within 3%, while they reached 5% for the 60×60×40 cm3 phantom using Fippel's method. Conclusion: Our in‐house implementation of Fippel's algorithm did not reproduce consistently GEANT4 results for varying phantom sizes. This was attributed to the over‐simplified sampling of the angular distributions of secondary protons resulting from nuclear inelastic reactions. However, this was not observed for PENH that implements an exact sampling of ICRU 63 cross‐sections. Therefore, the details of nuclear models may have a significant impact on accuracy. Kevin Souris is financed by the Walloon Region under the project name InVivoIGT, convention number 1017266. Kevin Souris is sponsored by a public‐private partnership IBA ‐ Walloon Region

Modeling and analysis of passive viscoelastic-legged rimless wheel that generates measurable period of double-limb support

Limit cycle walking including passive-dynamic walkers is generally modeled as a nonlinear hybrid dynamical system with state jumps. The inelastic collision model is usually derived on the assumption that the rear leg leaves the ground immediately after landing of the fore leg. This model is, however, inappropriate in the case of compliant-legged walkers. This paper then reconsiders the traditional collision model and discusses the conditions for transition to double-limb support (DLS) motion, which is not instantaneous through investigations of passive dynamic walking of a viscoelastic-legged rimless wheel. First, we experimentally confirm that measurable period of DLS motion emerges after landing of the fore leg, and develop the corresponding mathematical model. Second, we numerically analyze the fundamental properties of the generated passive-dynamic gaits. Furthermore, we discuss the conditions for transition to DLS motion and specify the computational procedures.

A variable hard sphere-based phenomenological inelastic collision model for rarefied gas flow simulations by the direct simulation Monte Carlo method

A modified phenomenological model is constructed for the simulation of rarefied flows of polyatomic non-polar gas molecules by the direct simulation Monte Carlo (DSMC) method. This variable hard sphere-based model employs a constant rotational collision number, but all its collisions are inelastic in nature and at the same time the correct macroscopic relaxation rate is maintained. In equilibrium conditions, there is equi-partition of energy between the rotational and translational modes and it satisfies the principle of reciprocity or detailed balancing. The present model is applicable for moderate temperatures at which the molecules are in their vibrational ground state. For verification, the model is applied to the DSMC simulations of the translational and rotational energy distributions in nitrogen gas at equilibrium and the results are compared with their corresponding Maxwellian distributions. Next, the Couette flow, the temperature jump and the Rayleigh flow are simulated; the viscosity and thermal conductivity coefficients of nitrogen are numerically estimated and compared with experimentally measured values. The model is further applied to the simulation of the rotational relaxation of nitrogen through low- and high-Mach-number normal shock waves in a novel way. In all cases, the results are found to be in good agreement with theoretically expected and experimentally observed values. It is concluded that the inelastic collision of polyatomic molecules can be predicted well by employing the constructed variable hard sphere (VHS)-based collision model.

Long-range interactions between ultracold atoms and molecules including atomic spin–orbit

We investigate theoretically the long-range electrostatic interactions between a ground-state homonuclear alkali-metal dimer and an excited alkali-metal atom taking into account its fine-structure. The interaction involves the combination of first-order quadrupole-quadrupole and second-order dipole-dipole effects. Depending on the considered species, the atomic spin-orbit may be comparable to the atom-molecule electrostatic energy and to the dimer rotational structure. Here we extend our general description in the framework of the second-order degenerate perturbation theory [M. Lepers and O. Dulieu, Eur. Phys. J. D, 2011] to various regimes induced by the magnitude of the atomic spin-orbit. A complex dynamics of the atom-molecule may take place at large distances, which may have consequences for the search for an universal model of ultracold inelastic collisions as proposed for instance in the study of Z. Idziaszek and P. S. Julienne [Phys. Rev. Lett.104, 2010, 113202].

Observation of fast collinear partitioning of theAu197 +Au197system into three and four fragments of comparable size

Collisions of a very heavy nonfusing nuclear system $^{197}\mathrm{Au}$$+$$^{197}\mathrm{Au}$ were studied at an energy of $15$ MeV/nucleon. An interesting process of violent reseparation of this heavy system into three or four fragments of comparable size was observed. In the case of ternary partitioning, either the projectile-like fragment (PLF) or target-like fragment (TLF) breaks up almost collinearly with the PLF-TLF separation axis. In the case of quaternary reactions, both PLF and TLF were observed breaking up along this direction. By comparison with a dynamical model of deep inelastic collisions it was concluded that the ternary and quaternary reactions occur in semiperipheral collisions, in a range of angular momenta corresponding to about $0.5--0.7$ of the maximum $L$ value for grazing collisions. The time elapsing from the scission of the binary PLF $+$ TLF system to the secondary scission of PLF or TLF was estimated to be of about $70--80$ fm/$c$ for the ternary reactions and $80--100$ fm/$c$ for the quaternary reactions.

A simple model for inelastic collisions

First Page

The Efficiency of Inelastic Collision Models with the Variable Sphere Molecular Model in the Direct Simulation Monte Carlo Method

The variable sphere (VS) molecular model for the inverse power law (IPL) potential is combined with the statistical inelastic cross section (SICS) and Borgnakke-Larsen (BL) models and the transport coefficients are estimated using the Monte Carlo integration technique for Wang-Chang-Uhlenbeck (WCU) theory. The VS model with SICS (VS-SICS) and BL (VS-BL) models are applied to the simulation of the normal shock wave structure in a nitrogen gas using the direct simulation Monte Carlo (DSMC) method, and then compared with the results of VSS model combined with the SICS model (VSS-SICS) and BL model (VSS-BL). Structures of number density, rotational temperature profiles, and rotational energy distribution in the VS-SICS and VS-BL models shock wave agree well with those of the VSS-SICS and VSS-BL models. The VS model demonstrated applicability to the inelastic molecular collision model.

Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation

The direct description of chemical reactions by the Boltzmann equation still involves some difficulties in the kinetic theory. In this paper, we describe diatomic molecular dissociation due to transitions of vibrational quantum states resulting from inelastic collisions. These can be described by the Wang Chang-Uhlenbeck (WCU) equation. To avoid direct evaluation of the strong nonlinear collision kernel of the WCU equation, we used a kinetic equation. For accurate description of the dissociation process, we describe improvements we made to the conventional inelastic collision model (the so-called Morse model). Combining this inelastic collision model with the gas mixture model by Oguchi, we formulated a model for representing diatomic molecular dissociations. We validated this model by simulating a hypersonic shock layer with diatomic molecular dissociation.

Rotational Collision Number and Rotationally Collision Cross Section of Inelastic Collision Model for Nitrogen Molecule in the Direct Simulation Monte Carlo Method

Transport coefficients and rotational collision number of nitrogen molecule were evaluated using the Monte Carlo integration with the classical trajectory calculation (CTC) for a set of equations in the Wang-Chang-Uhlenbeck (WCU) theory, and then the rotationally inelastic collision cross section for the statistical inelastic cross section (SICS) model was made so as to reproduce the rotational collision number of CTC. Transport coefficients and rotational collision number of SICS model with the rotationally inelastic cross section presented in this study were in reasonable agreement with those of CTC. SICS model was applied to the simulation of nitrogen normal shock wave structure and compared with CTC and experimental results. The density and translational structure in the shock wave were in reasonable agreement with those of CTC results. However, the structures of rotational temperature in the highly non-equilibrium state were in poor agreement with those of CTC.

Transport Coefficients of Inelastic Collision Model in the Direct Simulation Monte Carlo Method

The rotational energy gain function for Monte Carlo simulation of an inelastic molecular collision in rarefied gas flow is revised by analysis using a combination of Monte Carlo integration and classical trajectory calculation (CTC) for diatomic molecules. The rotational energy gain function presented here is combined with the statistical inelastic cross-section (SICS) model and applied to evaluation of the transport coefficients of nitrogen gas using the Wang-Chang-Uhlenbeck (WCU) theory. The normal shock wave structures for nitrogen determined by the proposed energy gain function, Parker’s energy gain function, and from experimental data are compared, and it is shown that the transport coefficients and shock wave structures given by the proposed function are in better agreement with the experimental results than Parker’s energy gain function.

Inter-particle heat transfer in a riser of gas–solid turbulent flows

Effects of the particle–particle heat transfer in a gas–solid turbulent flow in a riser were evaluated. An Eulerian/Lagrangian four-way interaction formulation including the particle collisions in conjunction with the k − τ and the k θ − τ θ model equations were used in the numerical simulation. Inter-particles and particle–wall interactions were accounted for with an inelastic collision model, where the restitution coefficient was evaluated for each collision. The special case when the flow initially contains two groups of hot and cold particles was treated in details. Particular attention was given to the nature of heat transfer to particles due to inter-particle interactions. The results showed that the effect of particle–particle heat transfer was more significant for smaller sizes, lower flow Reynolds numbers, and for higher loading ratios. Solid thermal properties, however, did not have a noticeable effect on the inter-particle heat transfer. The simulation results indicates that although the heat transferred to each group of hot and cold particles was significant, the mean values of gas and particle temperatures and suspension heat transfer was insensitive to the inter-particle heat transfer.

Transport Coefficients of Inelastic Collision Model in the Direct Simulation Monte Carlo Method (2nd Report, Modification of Parker's Energy Gain Function)

Transport Coefficients of Inelastic Collision Model in the Direct Simulation Monte Carlo Method (2nd Report, Modification of Parker's Energy Gain Function)