Inelastic Collisions Research Articles

Breather and nondegenerate solitons in the two-component modified Korteweg–de Vries equation

In this paper, we investigate the nonlinear dynamics of an interesting class of vector solitons in the two-component modified Korteweg–de Vries (mKdV) equation. We construct the nondegenerate solitons and the breather solutions of the two-component mKdV equation by applying a non-standard form of the Hirota direct method. Our study shows that the nondegenerate solitons and the breather solutions of the system consist of three profiles: single-hump, double-hump and flat-top, and the collisions among nondegenerate solitons are always standard inelastic collisions. An explicit form of the general breather solution of the two-component mKdV equation is presented.

Considering inelasticity in the real-time monitoring of particle size for twin-screw granulation via acoustic emissions

A recently developed process analytical technology (PAT) using artificial intelligence to form the framework of its model, combining frequency-domain acoustic emissions (AE) and elastic impact mechanics to accurately predict complex particle size distributions (PSD) in real-time. This model was modified in this study to give more accurate predictions for the more highly cohesive granules typical of pharmaceutical solid oral dosage formulations. AE spectra were collected from the granulated impacts of various formulations with ranging characteristics from largely elastic to highly inelastic collision responses. A viscoelastic (Hertzian spring-dashpot) and elastoplastic (Walton-Braun) contact force model were compared to understand how these different micro-mechanical approaches would affect the prediction accuracy of particle sizes relevant to granulation. Retraining the artificial intelligence model with the Walton-Braun transformation and a more comprehensive dataset of AE spectra spanning a broad range of granulated formulations showed the prediction error drop to as low as 2% compared to the original elastic version showing errors as large as 18.6% with representative formulations of the industry. The improved PAT shows good applicability to monitoring bimodal PSD that are typical of continuous twin-screw granulation.

Soliton dynamics to the Higgs equation and its multi-component generalization

In this paper, we study the coupled Higgs equation and its multi-component generalization based on the Hirota’s direct method. One and two-soliton solutions of the coupled Higgs equation are derived by the perturbation approach. We express the N-soliton solutions in the form of Pfaffians and demonstrate that the N-component coupled Higgs equation turns out to be the Pfaffian identity. One and two-soliton solutions of the multi-component coupled Higgs equation are obtained from the Pfaffians. Starting from the explicit solutions, parallel solitons, periodic and nearly periodic interactions, elastic and inelastic collisions are investigated.

Experimental Verification of and Physical Interpretation for Adsorption-Dependent Squeeze-Film Damping

The squeeze-film-damping effect is one of the main limits in many precision experiments, especially in the study of short-range interactions, and its physical mechanism is still not very clear. We develop a torsion pendulum to measure the damping effects caused by the thermal motion of residual gas between a cubic test mass and a pair of symmetric movable plates. The measured results are consistent with the model that synthesized the elastic and inelastic collisions by introducing a thermal accommodation coefficient (TAC). In our research, the pressure dependence of the TAC, which can be expressed as an exponential decay function, is also observed. This dependence may imply that the elastic collisions correspond to the simple bouncing of residual gas molecules, while the inelastic collisions correspond to the adsorption and desorption cycle of gas molecules on the surface. The method in this work and the discovered TAC pressure dependence are instructive for the analysis of residual-gas effects in weak-force measurements, as well as the deviation correction of rarefied gas pressure measurements based on the squeeze-film-damping effect.

Effect of ion-induced nuclear reactions on structure modification and radiolysis in LiF irradiated by 410 MeV 36S ions

The objective of this research is to study the structural damage in LiF crystals irradiated with 410 MeV 36S ions. We report on the appearance of a remarkable structural damage far (hundreds of μm) beyond the penetration depth (136 μm) of sulfur ions. Selective chemical etching on samples irradiated at room temperature revealed the formation of extended defects within the ion-irradiated zone and also beyond the range of sulfur ions. Based on AFM image analysis, the defects were identified as nano-size colloids (10 nm). In the irradiated zone, nanoindentation tests indicated a significant hardening effect. Annealing experiments showed manifestations of intense radiolysis both in the ion-irradiated and beyond the range areas with a maximum of around 620 K. Comparison of experimental results with those of performed model simulation using Monte-Carlo particle transport code FLUKA support the assumption that the cause of the observed long-range damage is irradiation by secondary particles created in inelastic nuclear collisions between incident sulfur ions and lithium and fluorine nuclei of the target atoms. Neutrons, γ-rays and protons are rated as the dominating components of the secondary particle flux. The results can be helpful for assessing the risks for damage delocalization and for reasonable selection of ions in the applications of ion technologies to optical materials like LiF.

Discussion on the transport processes in electrons with non-Maxwellian energy distribution function in partially-ionized plasmas

In a previous work (Alvarez Laguna et al 2022 Phys. Plasmas 29 083507), we have developed a non-linear moment model for electrons that self-consistently captures non-Maxwellian electron energy distribution function effects. The model does not rely in the local approximation and the transport coefficients are calculated by expanding the distribution function into Hermite polynomials and by taking moments of the Boltzmann equation, including the collision operator for elastic and inelastic collisions with arbitrary cross sections. This model captures the classical Fick’s, Fourier’s, and Ohm’s law as well as Soret, Dufour, and Peltier effects. In addition, novel non-local transport phenomena appear as a result of spatial gradients of the kurtosis of the distribution function. In this paper, we discuss on the transport effects by analyzing two collisional models: constant collision frequency and constant cross section. We estimate the order of magnitude of the transport processes in non-equilibrium electrons by analyzing the Langmuir probe measurements of a low-pressure argon inductively-coupled discharge. The results show that, under these conditions, the transport produced by the spatial gradients in the kurtosis of the distribution function produces a heat-flux contribution that is of the same order of magnitude as the Fourier and Dufour’s effects. These transport effects are beyond the local field or the electron gradient expansions, commonly used in the low-temperature plasma modeling.

Mass-velocity Formula and Mass-energy Relation Cannot Be Derived Based on Lorentz Velocity Transformation

The most important achievement of the Einstein's special relativity was to derive the mass-velocity formula and the famous mass-energy relation from the Lorentz velocity transformation formula. Based on the mass-velocity formula, the dynamics of special relativity was established. In this paper, six derivation methods of the mass-velocity formula in special relativity are re-analyzed, including the elastic collision and the inelastic collision of two particles, the particle splitting processes, and the force moment balance methods based on the Lorentz velocity transformation formula, as well as the method to consider the symmetry principle without using the Lorentz transformation formula. It is pointed out that all of them have serious problems so that they cannot hold actually. Besides, it is pointed out that the method of Hamiltonian action to derive the mass-velocity has nothing to do with the Lorentz velocity transformation and does not belong to the category of special relativity. Therefore, the conclusion of this paper is that it is impossible to derive the mass-velocity formula and the mass-energy relation based on the Lorentz velocity transformation formula. The mass-velocity formula can only be considered as an empirical formula which cannot be derived in theory and have nothing to do with special relativity. If the mass-velocity formula and the mass-energy relationship are correct, it just means that Einstein's special relativity is not true.

Plasma activation mechanisms governed by specific energy input: Potential and perspectives

AbstractIn a low‐temperature plasma, the electrons pick up energy from the electric field in collisions with atoms and molecules, gaining high kinetic energy that must be sufficient for ionizing reactions to sustain the plasma. For molecular gases, an average energy per heavy gas particle is thus available in the plasma, the specific energy input, yielding plasma activation by inelastic collisions. Following a distribution law, the probability for the activation mechanism can be described by an Arrhenius‐like equation. The potential of this approach is demonstrated on the basis of plasma polymerization and plasma CO2conversion. For perspective, energy efficiencies are discussed as a function of conversion indicating the optimum that can be achieved by electron impact activation compared with additional ways of energy transfer, probably depending on certain constraints.

Collision of C2 with NH and deuterated analogs in the interstellar medium. Scattering calculations

ABSTRACT Shephard’s interpolation potential energy surface and isotopic substitution were used to understand the mechanisms of chemical reactions; the NH + C2 reaction potential energy surface was constructed in this research and evaluated using ab-initio calculations. Classical trajectory simulations were used to calculate the reaction probability and cross-section. In addition, the rate constant by the nonlinear least-squares fitting was calculated. These were determined as a function of cross-section. In non-reactive trajectories for inelastic collisions, the scattering angle was estimated. The effects of the impact parameter and the relative velocity of particles on the reaction probability, transmitted energy, and dispersion angle were investigated. In addition, Isotopic substitution in the NH radical was evaluated for the effect of the mass of the target and incident particles on the cross-section, reaction probability, dispersion angle, and reaction rate. To calculate the kinetic isotope effect, the influence of the mass of colliding molecules on the observable properties was studied. Deuterated imidogen reacted faster than hydrogenated imidogen. These observations provided valuable insights into the details of the mechanisms, possible reactions of ND and NH + C2 , and deuterium fractionation.

Inelastic Collision Influencing the Rotational Dynamics of a Non-Rigid Asteroid (of Rubble Pile Type)

We have considered here a novel particular model for dynamics of a non-rigid asteroid rotation, assuming the added mass model instead of the concept of Viscoelastic Oblate Rotators to describe the physically reasonable response of a ‘rubble pile’ volumetric material of asteroid with respect to the action of a projectile impacting its surface. In such a model, the response is approximated as an inelastic collision in which the projectile pushes the ‘rubble pile’ parts of the asteroid together to form a mostly solidified plug in the crater during the sudden impact on the asteroid’s surface. Afterwards, the aforementioned ‘solidified plug’ (having no sufficient adhesion inside the after-impact crater) will be pushed outside the asteroid’s surface by centrifugal forces, forming a secondary rotating companion around the asteroid. Thus, according to the fundamental law of angular momentum conservation, the regime of the asteroid’s rotation should be changed properly. Namely, changes in rotational dynamics stem from decreasing the asteroid’s mass (due to the fundamental law of angular momentum conservation). As the main finding, we have presented a new solving procedure for a semi-analytical estimation of the total mass of the aforementioned ‘solidified plug’, considering the final spin state of rotation for the asteroid with minimal kinetic energy reduced during a long time period by the inelastic (mainly, tidal) dissipation. The asteroid is assumed to be rotating mainly along the maximal inertia axis with a proper spin state corresponding to minimal energy with a fixed angular momentum.

Semiclassical initial value representation: From Møller to Miller. II.

As shown by W. H. Miller in a seminal article [J. Chem. Phys. 53, 3578 (1970)], the most convenient and accurate semiclassical (SC) theory of molecular scattering in action-angle coordinates is based on the initial value representation (IVR) and the use of shifted angles, which are different from the natural angles usually used in the quantum and classical treatments. Here, we show for an inelastic molecular collision that the initial and final shifted angles define three-segment classical paths that are exactly those involved in the classical-limit of Tannor-Weeks quantum scattering theory [J. Chem. Phys. 98, 3884 (1993)], provided that the translational wave packets |g+⟩ and |g-⟩ into play in this theory are both taken at |0⟩. Assuming this to be the case, using van Vleck propagators, and applying the stationary phase approximation, Miller's SCIVR expression of S-matrix elements is found, with an additional cut-off factor canceling the energetically forbidden transition probabilities. This factor, however, is close to unity in most practical cases. Furthermore, these developments show that the Møller operators underlie Miller's formulation, thus confirming, for molecular collisions, the results recently established in the simpler case of light-induced rotational transitions [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. Last but not least, we show, based on the previous results, that for processes involving long-range anisotropic forces, implementing the Skinner-Miller method [Chem. Phys. Lett. 300, 20 (1999)] in shifted coordinates makes its predictions both easier and more accurate than in natural coordinates.

Residual gas damping noise in constrained volume in space-borne gravitational wave detection

The residual gas damping in the enclosure surrounding a free-fall test mass is an important limiting factor for the sensitivity of some space detection missions. We present a constrained volume damping model for space-borne gravitational wave detection, which depends on the escape time needed for a molecule to diffuse out of the gap between two adjacent surfaces. Using a completely inelastic molecular collision prediction, we calculate the escape times in the two most common constrained volumes, cylinder and cuboid, respectively. Both calculations agree well with Monte Carlo simulations. Additionally, the theoretical model of the residual gas damping presented in this work is in good agreement with the experimental results in the ground torsion pendulum test of LISA and its precursor LISA Pathfinder.

Importance of the radiations in water splitting for hydrogen generation

The review article examines the production of molecular hydrogen from the decomposition of water by various irradiation methods. The article shows different types of radiation: UV radiation, visible radiation, gamma radiation, X-ray radiation and neutron radiation. Electrons generated by radiation inside a nanoparticle of radius R suspense in fluid water are diffused with equal probability in all directions inside the particle and gradually lose their kinetic energy as a result of elastic and inelastic collisions. Some of these electrons are transported to the nanoparticle surface during the physical and physicochemical stages of the process and emitted into the water. It is extremely important for the formation of nanostructured materials after exposure to ordered nanostructure from the new phase with a period of a few nanometers, promoting the preservation of the properties of materials under high irradiation.

Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale

The relation between the energy-dependent particle and wave descriptions of electron-matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field from energy-filtered amplitude images of sample/vacuum interfaces with a special aberration-corrected electron microscope. The spatial field extension coincided with the energy-dependent self-coherence length of propagating wave packets that obeyed the time-dependent Schrödinger equation, and underwent a Goos-Hänchen shift. The findings support the view that wave packets are created by self-interferences during coherent-inelastic Coulomb interactions with a decoherence phase close to Δφ = 0.5 rad. Due to a strictly reciprocal dependence on energy, the wave packets shrink below atomic dimensions for electron energy losses beyond 1000 eV, and thus appear particle-like. Consequently, our observations inevitably include pulse-like wave propagations that stimulate structural dynamics in nanomaterials at any electron energy loss, which can be exploited to unravel time-dependent structure-function relationships on the nanoscale.

The energy dissipation mechanism of bi-metal Kevlar\ itanium fiber metal laminate under high-velocity impact

Fiber Metal Laminate (FML) is an impact resistant material widely used in marine and aerospace engineering structures that need to withstand impact damage, especially deck and bulkhead structures. To investigate the effect of titanium skin on energy dissipation, a series of ballistic impact experiments were performed on a bi-metal FML in this study. The FML were made of Ti–6Al–4V (TC4) skins and orthogonally woven Kevlar-129 fabric impregnated with E54-epoxy resin. Thus, this FML can be also called as bi-metal Kevlar/titanium FML. In addition, a numerical model based on stress wave theory is proposed to study the energy dissipation mechanism of the bi-metal FML under high-velocity ballistic impact. The residual ballistic velocity of the numerical model is verified by the experimental data in this paper and previous experimental data, showing that the numerical model is a more efficient method to analyze the energy dissipation mechanism of bi-metal FML. According to the numerical results, as the dominant energy dissipation, the perfectly inelastic collision of titanium skins dissipated 43%–62% and 17%–27% of total energy at the high-velocity penetration and ballistic limit, respectively. However, regardless of whether the FML has been penetrated, the compression-shear of Kevlar interlayer dissipated 24%–27% of total energy. Furthermore, the numerical calculations also show that the ballistic limit increases approximately linearly with the relative titanium skin thickness when the front titanium skin of the FML is thicker. Finally, this paper proposes a simple specific energy absorption prediction formula that helps to evaluate the energy dissipation capacity of FML.

The coupled modified Yajima–Oikawa system: Model derivation and soliton solutions

In this paper, we consider a coupled modified Yajima–Oikawa (YO) system which describes the nonlinear resonant interaction between one long wave (LW) and two short waves (SWs). It is shown that this coupled system can be derived from a three-component modified nonlinear Schrödinger equations through asymptotic reductions. Furthermore, the bright, dark multi-soliton and multi-breather solutions in terms of determinants are obtained respectively by virtue of the bilinear Kadomtsev–Petviashvili-hierarchy reduction technique. The detailed analysis of dynamical properties for one- and two-solitons and breathers is performed, which show the interesting collision properties for the bright and dark solitons. Particularly, differing from the modified YO system with the single SW component, two bright solitons can undergo inelastic collisions and two dark solitons can generate the bound state in the coupled modified YO system. Finally, general bright, dark multi-soliton and multi-breather solutions are presented for the multi-component modified YO system with multi short waves.

“Absolute zero” temperature in a vertically vibrated granular system

In thermodynamics, absolute zero is the coldest temperature and will never be reached because the thermal motion of microscopic particles never ceases. However, this situation could be changed for a collection of macroscopic particles. In the present paper, an experimental study was performed to explore the possible lowest temperature in a vertically vibrated granular system. It was found that the granular “absolute zero” temperature appears when the vibrating intensity is adjusted to about 4.6 times the gravitational acceleration. At this temperature, the macroscopic particles are arranged closely and behave like a rigid body without relative motions during the vibration. Near the absolute zero, inelastic collisions and energy transfer are responsible for the variation of granular temperature with time and vibrating parameters. Interestingly, the temperature variation reveals that the vibrated macroscopic particles are neither a crystal nor an amorphous system. This study introduces the granular entropy, including entropy generation and entropy flow, to describe the order of the vibrated particles. The entropy change could be illustrated by the temperature profiles of the granular system and its outside. It was also found that, unlike microscopic particles, which could maintain their entropy at a constant temperature, a granular system necessarily behaves completely disordered unless the system achieves the absolute zero granular temperature.

Interaction of chiral solitons in a Bose-Einstein Condensate under density-dependent gauge potential

The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.

Advanced γ-Ray Emission Studies of G15.4+0.1 with Fermi-LAT: Evidence of Escaping Cosmic Rays Interacting with Surrounding Molecular Clouds

We present an analysis of γ-ray emission in the direction of supernova remnant (SNR) G15.4+0.1 with 13 yr Fermi Large Area Telescope data. There are three point-like GeV sources in this region: one is spatially coincident with the TeV source HESS J1818-154 and is interpreted as the counterpart of HESS J1818-154. Its γ-ray spectrum can be well fitted by a single power law with an index of 2.3. The other two sources with log-parabola spectra are spatially coincident with dense regions of surrounding molecular clouds revealed by CO observations. Their γ-ray emission originates from hadronic π 0 decay due to inelastic collisions between nuclei in the clouds and cosmic rays accelerated in and escaping from SNR G15.4+0.1. The total energy of the escaping protons is about 1048 erg, assuming a point-like instantaneous injection. However, the inferred diffusion coefficients are lower than the typical Galactic value.

Elastic Interaction Between a Mesoscale Eddy‐Pair and an Axisymmetrical Eddy

AbstractWe investigate numerically the elastic interaction between an eddy‐pair and an axisymmetrical eddy in inviscid isochoric two‐dimensional (2D) flows, as well as in three‐dimensional (3D) flows under the quasi‐geostrophic (QG) approximation. The eddy‐pair is a straight moving Lamb‐Chaplygin dipole where the absolute value of either its positive or negative amount of vorticity equals the vorticity of the axisymmetrical eddy. The results for the 2D and 3D cases show that interactions with almost no vorticity exchange, or vorticity loss to the background field between ocean eddies, but causing changes in their displacement velocity, are possible. When the eddy‐pair approaches the axisymmetrical eddy, their respective potential flows interact, the eddy‐pair's trajectory acquires curvature and their vorticity poles separate. In the QG dynamics, the eddies suffer little vertical deformation, being the barotropic effects dominant. At the moment of highest interaction, the anticyclonic eddy of the pair elongates, simultaneously the cyclonic eddy of the pair evolves toward spherical geometry, and the axisymmetrical eddy acquires prolate ellipsoidal geometry in the vertically stretched QG space. Once the eddy‐pair moves away from the axisymmetrical eddy, its poles close, returning to their original geometry, and the anticyclonic and cyclonic eddies continue as an eddy‐pair with a straight trajectory but along a new direction. The interaction is sensitive to the initial conditions and, depending on the initial position of the eddy‐pair, as well as on small changes in the vorticity distribution of the axisymmetrical eddy, inelastic interactions may instead occur.