Search Results (24)

The research reviews and contrasts two studies based on the gas-phase reaction OH + D₂(v, j). In these studies, Quasi-Classical Trajectory (QCT) calculations and the Gaussian Binning (GB) technique were used on the Wu–Schatz–Lendvay–Fang–Harding (WSLFH) potential energy surface. Large sample sizes allow for precise energy state distribution analysis across translational, vibrational, and rotational components in the products. A key observation is the influence of the vibrational and rotational excitation of D₂ on the total angular momentum (J′) of the HOD* product. This study reveals that increasing the vibrational level, vD₂, significantly shifts P(J′) distributions toward higher values, broadening them due to increased isotropy. In contrast, increasing the rotational level, jD₂, results in a smaller shift but introduces greater anisotropy, leading to a more selective distribution of J′ values. The dual Gaussian Binning selection—Vibrational-GB followed by Rotational-GB—further highlights a preference for either odd or even J′ values, depending on the specific excitation conditions. These findings have implications for the development of chemical lasers, as the excitation and emission properties of HOD* can be leveraged in the laser design. Future research aims to extend this study to a broader range of initial conditions, refining the understanding of reaction dynamics in controlled gas-phase environments. Full article

This paper addresses the challenge of solving quasi-variational inequalities (QVIs) by developing and analyzing a forward–backward–forward algorithm from a continuous and iterative perspective. QVIs extend classical variational inequalities by allowing the constraint set to depend on the decision variable, a formulation that is particularly useful in modeling various problems. A critical computational challenge in these settings is the expensive nature of projection operations, especially when closed-form solutions are unavailable. To mitigate this, we consider the moving set case and propose a forward–backward–forward algorithm that requires only one projection per iteration. Under the assumption that the operator is strongly monotone, we establish that the continuous trajectories generated by the corresponding dynamical system converge exponentially to the unique solution of the QVI. We extend Tseng’s well-known forward–backward–forward algorithm for variational inequalities by adapting it to the more complex framework of QVIs. We prove that it converges when applied to strongly monotone QVIs and derive its convergence rate. We perform numerical implementations of our proposed algorithm and give numerical comparisons with other related gradient projection algorithms for quasi-variational inequalities in the literature. Full article

The research presented by the author investigates a polyatomic reaction occurring in the gas phase. This study employs the Quasi-Classical Trajectory (QCT) approach using the Wu–Schatz–Lendvay–Fang–Harding (WSLFH) potential energy surface (PES), recognized as one of the most reliable PES models for this type of analysis. The substantial sample size enables the derivation of detailed results that corroborate previous findings while also identifying potential objectives for future experimental work. The Gaussian Binning (GB) technique is utilized to more effectively highlight the variation in the total angular momentum (J′) of the excited product molecule, HOD*. A key aim of the study is to explore the reaction dynamics due to their importance in excitation and emission processes, which may contribute to the development of a chemical laser based on this reaction. Increasing the vibrational level, v, of one reactant, D₂, significantly enhances the excitation of HOD* and shifts the P(J′) distributions towards higher J′ values, while also broadening the distribution. Although the current research focuses on a few initial conditions, the author plans to extend the study to encompass a wider range of initial conditions within the reaction chamber of this type of chemical laser. Full article

For many disciplines of science, all conceivable collisional cross-sections and reactions must be precisely known. Although recent decades have seen a trial of large-scale research to obtain such data, many essential atomic and molecular cross-section data are still missing, and the reliability of the existing cross-sections has to be validated. In this paper, we present projectile ionization, electron capture, and system breakdown cross-sections in carbon (C⁵⁺) ions and lithium (Li²⁺) ion collisions with atomic hydrogen based on the Monte Carlo models of classical and quasi-classical trajectories. According to our expectation, the QCTMC results show higher results in comparison to standard CTMC data, emphasizing the role of the Heisenberg correction constraint, especially in the low-energy regime. On the other hand, at high energy, the Heisenberg correction term has less influence as the projectile momentum increases. We present the total cross-sections of projectile ionization, electron capture, and system breakdown in C⁵⁺ ions and Li²⁺ ion collisions with atomic hydrogen in the impact energy range from 10 keV to 160 keV, which is of interest in astrophysical plasmas, atmospheric sciences, plasma laboratories, and fusion research. Full article

Three-body recombination reactions, in which two particles form a bound state while a third one bounces off after the collision, play significant roles in many fields, such as cold and ultracold chemistry, astrochemistry, atmospheric physics, and plasma physics. In this work, the dynamics of the recombination reaction for the N₃ system over a wide temperature range (5000–20,000 K) are investigated in detail using the quasi-classical trajectory (QCT) method based on recently developed full-dimensional potential energy surfaces. The recombination products are N₂(X) + N(⁴S) in the 1⁴A″ state, N₂(A) + N(⁴S) in the 2⁴A″ state, and N₂(X) + N(²D) in both the 1²A″ and 2²A″ states. A three-body collision recombination model involving two sets of relative translational energies and collision parameters and a time-delay parameter is adopted in the QCT calculations. The recombination process occurs after forming an intermediate with a certain lifetime, which has a great influence on the recombination probability. Recombination processes occurring through a one-step three-body collision mechanism and two distinct two-step binary collision mechanisms are found in each state. And the two-step exchange mechanism is more dominant than the two-step transfer mechanism at higher temperatures. N₂(X) formed in all three related states is always the major recombination product in the temperature range from 5000 K to 20,000 K, with the relative abundance of N₂(A) increasing as temperature decreases. After hyperthermal collisions, the formed N₂(X/A) molecules are distributed in highly excited rotational and vibrational states, with internal energies mainly distributed near the dissociation threshold. Additionally, the rate coefficients for this three-body recombination reaction in each state are determined and exhibit a negative correlation with temperature. The dynamic insights presented in this work might be very useful to further simulate non-equilibrium dynamic processes in plasma physics involving N₃ systems. Full article

The rate constants of elementary processes in the atom–diatom system $\mathrm{O}{(}^{3}P)+{\mathrm{H}}_2\left(v\right)$, including the processes of vibrational relaxation and dissociation, were studied using the quasiclassical trajectory method. All calculations were carried out along the ground potential energy surface (PES) ³$A^{″}$ that was approximated by a neural network. Approximation data were obtained using ab initio quantum chemistry methods at the extended multi-configuration quasi-degenerate second-order perturbation theory XMCQDPT2 in a basis set limit. The calculated cross-sections of the reaction channels are in good agreement with the literature data. A complete set of state-to-state rate constants was obtained for the metathesis reaction, the dissociation and relaxation of the H₂ molecule upon collision with an O atom. According to these data, Arrhenius approximations over a wide temperature range were obtained for the thermal rate constants of considered processes. Data obtained on the dissociation constants and VT relaxation of vibrationally excited H₂ molecules can be used in constructing kinetic models describing the oxidation of hydrogen at high temperatures or highly nonequilibrium conditions. Full article

We present Python Quasi-classical atom–molecule scattering (PyQCAMS v0.1.0), a new Python package for atom–diatom scattering within the quasi-classical trajectory approach. The input consists of the mass, collision energy, impact parameter, and pair-wise/three-body interactions. As the output, the code provides the vibrational quenching, dissociation, and reactive cross sections along with the rovibrational energy distribution of the reaction products. We benchmark the program for a reaction involving a molecular ion in a high-density ultracold gas, RbBa⁺ + Rb. Furthermore, we treat H₂ + Ca → CaH + H reactions as a prototypical example to illustrate the properties and performance of the software. Finally, we study the parallelization performance of the code by looking into the speedup of the program as a function of the number of CPUs used. Full article

For the control of fusion reactors, we need to accurately know all the possible reactions and collisional cross sections. Although large-scale trials have been performed over the last decades to obtain this data, many basic atomic and molecular cross section data are missing and the accuracy of the available cross sections need to be checked. Using the available measured cross sections and theoretical predictions of hydrogen atom ionization by proton impact, critical analysis of the data is presented. Moreover, we also present our recent classical results based on the standard classical trajectory Monte Carlo (CTMC) and quasi-classical trajectory Monte Carlo (C-QCTMC) models. According to our model calculations and comparison with the experimental data, recom-mended cross sections for ionization of hydrogen were presented in a wide range of pro-jectile impact energies. We found that, while in the low energy region, the experimental cross sections are very close to the C-QCTMC results, at higher energies, they are close to the results of our standard CTMC results. Full article

Recent advances in technology have led to a surge in interest in unmanned aerial vehicles (UAVs), which are remote-controlled aircraft that rely on cameras or sensors to gather information about their surroundings during flight. A UAV requires a path-planning technique that can swiftly recalculate a viable and quasi-optimal path in flight if a new obstacle or hazard is recognized or if the target is moved during the mission. In brief, the planning of UAV routes might optimize a specific problem determined by the application, such as the moving target problem (MTP), flight time and threats, or multiobjective navigation. The complexity of MTP ranges from NP-hard to NEXP-complete because there are so many probabilistic variables involved. Therefore, it is hard to detect a high-quality solution for this problem using traditional techniques such as differential calculus. Therefore, this paper hybridizes differential evolution (DE) with two newly proposed updating schemes to present a new evolution-based technique named hybrid differential evolution (HDE) for accurately tackling the MTP in a reasonable amount of time. Using Bayesian theory, the MTP can be transformed into an optimization problem by employing the target detection probability as the fitness function. The proposed HDE encodes the search trajectory as a sequence of UAV motion pathways that evolve with increasing the current iteration for finding the near-optimal solution, which could maximize this fitness function. The HDE is extensively compared to the classical DE and several rival optimizers in terms of several performance metrics across four different scenarios with varying degrees of difficulty. This comparison demonstrates the proposal’s superiority in terms of the majority of used performance metrics. Full article

Deep space missions, and particularly cislunar endeavors, are becoming a major field of interest for the space industry, including for the astrodynamics research community. While near-Earth missions may be completely covered by perturbed Keplerian dynamics, deep space missions require a different modeling approach, where multi-body gravitational interactions play a major role. To this end, the Restricted Three-Body Problem stands out as an insightful first modeling strategy for early mission design purposes, retaining major dynamical transport structures while still being relatively simple. Dynamical Systems Theory and classical Hamiltonian Mechanics have proven themselves as remarkable tools to analyze deep-space missions within this context, with applications ranging from ballistic capture trajectory design to stationkeeping. In this work, based on this premise, a Hamiltonian derivation of the Restricted Three-Body Problem co-orbital dynamics between two spacecraft is introduced in detail. Thanks to the analytical and numerical models derived, connections between the relative and classical Keplerian and CR3BP problems are shown to exist, including first-order linear solutions and an inherited Hamiltonian normal form. The analytical linear and higher-order models derived allow the theoretical finding and unveiling of natural co-orbital phase space structures, including relative periodic and quasi-periodic orbital families, which are further exploited for general proximity operation applications. In particular, a novel reduced-order, optimal low-thrust stationkeeping controller is derived in the relative Floquet phase space, hybridizing the classical State Dependent Ricatti Equation (SDRE) with Koopman control techniques for efficient unstable manifold regulation. The proposed algorithm is demonstrated and validated within several end-to-end low-cost stationkeeping missions, and comparison against classical continuous stationkeeping algorithms presented in the literature is also addressed to reveal its enhanced performance. Finally, conclusions and open lines of research are discussed. Full article

We study the transition from integrability to chaos for the three-particle Fermi–Pasta–Ulam–Tsingou (FPUT) model. We can show that both the quartic $\beta$-FPUT model ($\alpha =0$) and the cubic one ($\beta =0$) are integrable by introducing an appropriate Fourier representation to express the nonlinear terms of the Hamiltonian. For generic values of $\alpha$ and $\beta$, the model is non-integrable and displays a mixed phase space with both chaotic and regular trajectories. In the classical case, chaos is diagnosed by the investigation of Poincaré sections. In the quantum case, the level spacing statistics in the energy basis belongs to the Gaussian orthogonal ensemble in the chaotic regime, and crosses over to Poissonian behavior in the quasi-integrable low-energy limit. In the chaotic part of the spectrum, two generic observables obey the eigenstate thermalization hypothesis. Full article

We study the mechanism of scarring of eigenstates in rectangular billiards with slightly corrugated surfaces and show that it is very different from that known in Sinai and Bunimovich billiards. We demonstrate that there are two sets of scar states. One set is related to the bouncing ball trajectories in the configuration space of the corresponding classical billiard. A second set of scar-like states emerges in the momentum space, which originated from the plane-wave states of the unperturbed flat billiard. In the case of billiards with one rough surface, the numerical data demonstrate the repulsion of eigenstates from this surface. When two horizontal rough surfaces are considered, the repulsion effect is either enhanced or canceled depending on whether the rough profiles are symmetric or antisymmetric. The effect of repulsion is quite strong and influences the structure of all eigenstates, indicating that the symmetric properties of the rough profiles are important for the problem of scattering of electromagnetic (or electron) waves through quasi-one-dimensional waveguides. Our approach is based on the reduction of the model of one particle in the billiard with corrugated surfaces to a model of two artificial particles in the billiard with flat surfaces, however, with an effective interaction between these particles. As a result, the analysis is conducted in terms of a two-particle basis, and the roughness of the billiard boundaries is absorbed by a quite complicated potential. Full article

The hydrogen abstraction reaction OH + H₂S→H₂O + SH plays an important role in acid rain formation, air pollution and climate change. In this work, the product energy disposals of the reaction and its isotopic variants OD + H₂S and OD + D₂S are calculated on a new ab-initio-based ground electronic state potential energy surface (PES) using the quasi-classical trajectory method. The PES is developed by fitting a total of 72,113 points calculated at the level of UCCSD(T)-F12a/aug-cc-pVTZ and using the fundamental invariant-neural network method, resulting in a total RMSE of 4.14 meV. The product H₂O formed in the OH + H₂S reaction at 298 K is found to be largely populated in the first overtone states of its symmetric and asymmetric stretching modes, while the vibrational distributions of the products HOD and D₂O in the isotopically substituted reactions are visibly different. The computed product vibrational state distributions agree reasonably well with experimental results and are rationalized by the sudden vector projection model. Full article

Charge-exchange cross sections in Be⁴⁺ + H(1s) collisions are calculated using the three-body classical trajectory Monte Carlo method (CTMC) and the quasi-classical trajectory Monte Carlo method of Kirschbaum and Wilets (QCTMC) for impact energies between 10 keV/amu and 300 keV/amu. We present charge-exchange cross sections in the projectile n = 2 and nl = 2s, 2p states. Our results are compared with the previous quantum-mechanical approaches. We found that the QCTMC model is a powerful classical model to describe the state-selective charge-exchange cross sections at lower impact energies and the QCTMC results are in good agreement with previous observations. Full article

In this work, an application of the trajectory tracking algorithm proposed in the literature for underactuated marine vehicles is presented. The main difference relies on that here the dynamics of the vehicle are expressed in terms of some quasi-velocities (QV). This fact has a double meaning. First of all, it is shown that using the QV, it is possible to control a vehicle in the absence of one variable because the works related to marine vehicles have only concerned fully actuated systems. In addition, a controller using QV provides information that gives some insight into vehicle dynamics and that is not available in classical equations of motion. The simulations done on two 3-DOF models of different underwater vehicles and using two desired trajectories show performance of the considered control strategy. A discussion of the presented control scheme and selected control approaches from recent years was also conducted, and the benefits of the proposed approach were pointed out. Full article