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In this work, we propose a rapid optimization approach to examine its application potential for the design and performance prediction and optimization of a solid fuel ramjet (SFRJ) with a bluff body. For this, the shape of the bluff body is parameterized first using the non-uniform rational B-spline method. We then develop a model for predicting SFRJ performances by incorporating both levy motion-gradient descent and support vector regression methods. It is found that a faster prediction is achievable, while the average error is maintained to be less than 5%. We then develop a multi-objective optimization model by considering the full thrust and minimum total pressure loss (TPL). The optimization model is examined using the non-dominated sorting genetic algorithm. A cost parameter is also created to facilitate the tradeoffs between the thrust and TPL in the Pareto front, when different bluff-body design configurations are considered. The present results reveal that an increase in the cost parameter will elevate the turbulence intensity within the SFRJs while drawing the incoming air closer to the fuel surface, resulting in an increase in thrust and regression rate, but the TPL will also increase. When prioritizing the TPL reduction in the design stage, the optimized solution reduces TPL by 50%. Meanwhile, the net thrust is shown to be decreased by less than 3.5%. Furthermore, flow-field investigation reveals that the improved performance of the optimized SFRJ is due to more uniform flow velocity gradients around the bluff body and a reduced rear vortex, resulting in reduced momentum loss. Our proposed optimization approach's robustness has been further confirmed with consistent performances, as the ramjet inlet speed varies over a broad range. It shows that our approach has great potential to be applied for the SFRJ performance prediction and optimization, being operated under various conditions. [ABSTRACT FROM AUTHOR]

Machine learning (ML) is used to build a new computationally efficient data-driven dynamical model for single-phase and complex multicomponent particle–liquid turbulent flows in a stirred vessel. By feeding short-term trajectories of flow phases or components acquired experimentally for a given flow condition via a positron emission particle tracking (PEPT) technique, the ML model learns primary flow dynamics from the input driver data and predicts new long-term trajectories pertaining to new flow conditions. The model performance is evaluated over a wide range of flow conditions by comparing ML-predicted flow fields with extensive long-term experimental PEPT data. The ML model predicts the local velocities and spatial distribution of each flow phase and component to a high degree of accuracy, including conditions of impeller speeds, particle loadings and sizes within and without the range of the input driver datasets. A new flow analysis and modeling strategy is thus developed, whereby only short-term experiments (or alternatively high-fidelity simulations) covering a few typical flow situations are sufficient to enable the prediction of complex multiphase flows, significantly reducing experimental and/or simulation costs. [ABSTRACT FROM AUTHOR]

The interaction between the swarm individuals affects the dynamic behavior of the swarm, but it is difficult to obtain directly from outside observation. Therefore, the problem we focus on is inferring the structure of the interactions in the swarm from the individual behavior trajectories. Similar inference problems that existed in network science are named network reconstruction or network inference. It is a fundamental problem pervading research on complex systems. In this paper, a new method, called Motion Trajectory Similarity, is developed for inferring direct interactions from the motion state of individuals in the swarm. It constructs correlations by combining the similarity of the motion trajectories of each cross section of the time series, in which individuals with highly similar motion states are more likely to interact with each other. Experiments on the flocking systems demonstrate that our method can produce a reliable interaction inference and outperform traditional network inference methods. It can withstand a high level of noise and time delay introduced into flocking models, as well as parameter variation in the flocking system, to achieve robust reconstruction. The proposed method provides a new perspective for inferring the interaction structure of a swarm, which helps us to explore the mechanisms of collective movement in swarms and paves the way for developing the flocking models that can be quantified and predicted. [ABSTRACT FROM AUTHOR]

In a system of two tunable-frequency qubits, it is well-known that adiabatic tuning into strong coupling-interaction regions between the qubit subspace and the rest of the Hilbert space can be used to generate an effective controlled-Z rotation. We address the problem of determining a preferable adiabatic trajectory along which the qubit frequency is tuned and apply this to the flux-tunable transmon model. The especially minimal anharmonic nature of these quantum processors makes them good candidates for qubit control using non-computational states as long as higher-level leakage is properly addressed. While the statement of this method has occurred multiple times in the literature, there have been few discussions on which trajectories may be used. We present a generalized method for optimizing parameterized families of possible flux trajectories and provide examples of use on five test families of one and two parameters. [ABSTRACT FROM AUTHOR]

We introduce an optimization method for the cross-correlation operation in particle image velocimetry by locating the correlation peaks assisted with constraint conditions. In this study, an objective function was constructed to include the residual of the normalized cross-correlation term, a component in charge of spatial smoothness (inspired by the optical flow method as used in a previous study) and a component for temporal smoothness (inspired by the concept of trajectory selection in particle tracking velocimetry). Minimizing the objective function gives optimized velocity fields for a series of tracer images for spatiotemporal smoothness. The proposed method was examined in synthetic images of turbulent flow and Batchelor vortex and in a laboratory experiment of vortex rings. The effect of image background noises and the initial guess for the optimization process were examined and discussed. [ABSTRACT FROM AUTHOR]

We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allows individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows, which are typically based on sparse information from drifters and probes. [ABSTRACT FROM AUTHOR]

A biological organism, such as an octopus tentacle or elephant trunk, exhibits complex 3D spatial trajectories. Although soft manipulators showing 2D in-plane deformations have been extensively studied and applied in many areas, the design method of soft manipulators with a mathematical model that can follow a particular 3D spatial trajectory remains elusive. In this paper, we present a methodology to automatically design bio-inspired multi-segment pneu-net soft manipulators that can match complex 3D trajectories upon single pressurization. The 3D motions can be characterized by a combination of twisting, bending, and helical deformations, which are enabled by the design of the soft segments with programmable chamber orientations. To inverse design the soft manipulators with trajectory matching, we develop an analytical framework that takes into account the material nonlinearity, geometric anisotropy, and varying loading directions. The spatial trajectory can be reconstructed by combining with a 3D rod theory. In this sense, multi-segment soft manipulators with trajectory matching are inversely designed by varying the geometric and material parameters. We further demonstrate the grasping of complex objects using the designed soft manipulators. The proposed methodology has immense potential to design soft manipulators in 3D space and broaden their application. [ABSTRACT FROM AUTHOR]

Understanding the mass transfer between surface and subsurface water is essential in the fluvial environment. Transport across the sediment–water interface (SWI) can be strongly influenced by pore-scale vortices and coherent turbulent structures (sweep and ejection) near the interface. However, the functions of these hydrodynamic structures over the exchange at the interface and pore water movement in the bed are still unclear. In this paper, the pore-scale flow and transport across the SWI under dispersive and turbulent regimes were studied. The results show that pore-scale vortices are the main hydrodynamic form at the SWI in dispersive regimes, creating a transition layer and impeding interfacial transport. Periodic sweep and ejection prevail in turbulent regimes, which alter the structures of pore scale vortices, enhance interfacial transport, generate periodic pressure eruptions at the interface, and pulse the pore water to move vertically and periodically in the bed. Different forms of the dominant hydrodynamics structures near the interface will affect the residence time and trajectories of solutes in the bed. In dispersive regimes, the residence time of solutes exhibits a positive correlation with the Reynolds number due to the increasing penetration of solutes, while, in turbulent regimes, this correlation turns negative because of the unchanged penetration depth of solutes. The mechanism demonstration from numerical simulations clarifies the functions of pore-scale vortices and coherent turbulent structures on mass transfer between the surface and subsurface water, which can enhance the understanding of the role of sediments in the aquatic ecosystem. [ABSTRACT FROM AUTHOR]

Turbulent channel flow with a porous wall is investigated using direct numerical simulation, where the porous media domain consists of regular or random circular cylinder arrays. We compare the statistics and structure of the mean flow and turbulence in the channel flow with a bulk Reynolds number of 2500 and two porosities (φ = 0.6 and 0.8) for the porous media. It is shown that the random interface significantly affects the dynamics of turbulence and the time-averaged flow. More intense mixing is observed near the random interface due to augmented form-induced shear stresses. Due to the strong dependence of induced flow direction on the interface geometry, we segmented the flow field into two types of areas based on the slope angle formed by the top-layer cylinders: the windward area and leeward area. The conditional average of turbulence kinematic energy budget over each type of area reveals their respective role in turbulence transportation more explicitly. In addition, we use finite-time Lyapunov exponents to inspect the Lagrangian coherent structures in the flow fields, which reveal the preferential fluid trajectories in the random porous medium geometry. [ABSTRACT FROM AUTHOR]

In many practical multi-channel active noise control (ANC) applications, various constraints need to be satisfied, such as stability, enhancement, etc. One way to enforce these constraints is to add a regularization term to the Wiener filter formulation, which, by tuning only a single parameter, can over satisfy many constraints and degrade the ANC performance. Another approach for non-adaptive ANC filter design that can produce better ANC performance is to directly solve the constrained optimization problem formulated based on the H 2 / H ∞ control framework. However, such a formulation does not result in a convex optimization problem and its practicality can be limited by the significant computation time required in the solving process. In the presented work, the H 2 / H ∞ formulation is convexified and a global minimum is guaranteed. It is then further reformulated into a cone programming problem which can be solved using specialized algorithms. Results show that the proposed method can produce better noise control performance than the regularization method. Compared with the traditional H 2 / H ∞ formulation, the proposed method is more reliable and the computation time can be reduced by several orders, which, practically, provides a potential to extend its application to adaptive control. [ABSTRACT FROM AUTHOR]

This paper studies the Cartesian point-to-point optimal trajectory planning for space robots oriented to space maintenance operations. Aiming at the problems of poor stability, large base disturbance, and large joint variation in the motion planning of point-to-point maintenance in space, a planning method is proposed to minimize the base disturbance and the total joint angle variation under the jerk constraint on the premise of ensuring the accuracy of the end pose. First, the attitude of the space robot is described by the unit quaternion, and the velocity relationship between the joint angle, the end effector, and the base posture is introduced. Then, the joint trajectories were parameterized by a fifth degree polynomial, and a trajectory planning model with the minimum perturbation of the base and the minimum variation of the joint of the manipulator was established under the condition that the end effector satisfied the pose and the jerk constraint. Finally, a multi-objective optimization algorithm is proposed to deal with the trajectory optimization problem under nonlinear constraints. The simulation results show that the proposed trajectory planning method can optimize the base attitude and joint angle of the space manipulator under the premise of the optimal trajectory and stability of the terminal execution tool, which ensures the stability of the space robot's on-orbit service and reduces the energy consumption. [ABSTRACT FROM AUTHOR]

The theoretical discoveries of the Sanal flow choking [V. R. Sanal Kumar et al., "Sanal flow choking: A paradigm shift in computational fluid dynamics code verification and diagnosing detonation and hemorrhage in real‐world fluid‐flow systems," Global Challenges 4, 2000012 (2020)] and streamtube flow choking [V. R. Sanal Kumar et al., "Deflagration to detonation transition in chemical rockets with sudden expansion/divergence regions," AIAA Paper No. 2020-3520, 2020] achieved significant contemplation in all branches of science and engineering for resolving various unanswered scientific questions brought onward from the beginning of this era [V. R. Sanal Kumar et al., "A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers," AIP Adv. 8, 025315 (2018)]. The applications of these flow choking phenomena are more significant in aerospace industries [V. R. Sanal Kumar et al., "Nanoscale flow choking and spaceflight effects on cardiovascular risk of astronauts—A new perspective," AIAA Paper No. 2021-0357, 2021] and medical sciences [V. R. Sanal Kumar et al., "Lopsided blood-thinning drug increases the risk of internal flow choking leading to shock wave generation causing asymptomatic cardiovascular disease," Global Challenges 2021, 2000076]. Herein, as an offshoot of the Sanal flow choking phenomena, the proof of the concept of boundary-layer-blockage (BLB) persuaded external-flow-choking (EFC) at aircraft-in-ground (AIG)-effect is presented. When the aircraft's ground clearance is relatively low, the evolving BLB factor from both planes (the bottom surface of the aircraft and the ground) creates a transient fluid-throat, leading to the Sanal flow choking and supersonic flow development in the duct flow region. In this physical situation, the pressure ratio (Ptotal/Pstatic) at the external flow choking region is exclusively a function of the specific heat ratio of the fluid. The EFC is more prone for the low wing aircraft flying in the near vicinity to the ground and/or sea with relatively high subsonic Mach number and low angle of attack. At this flying condition, the underside of the aircraft (fuselage and/or wing) and the ground creates the convergent-divergent duct flow effect leading to the EFC at the critical total-to-static pressure ratio. The accurate estimation of the BLB factor at the location of the EFC at AIG effect is presented in this manuscript as a universal yardstick for two-dimensional (2D) in silico simulation. For establishing the proof of the concept of external flow choking and supersonic flow development and shock wave generation, the 2D in silico results are presented for both stationary and moving airfoils in ground effect. In silico results show that the airfoil at stationary position exhibits relatively higher BLB factor and an immediate occurrence of the EFC than the same airfoil moving with the identical inflow Mach number and Reynolds number. We could establish herein that the moving vehicle simulation is inevitable for capturing actual flow physics and further precise examination of the BLB factor and the possibilities of the occurrence of the EFC for credible trajectory optimization of high-speed ground-effect vehicles. [ABSTRACT FROM AUTHOR]

A time-jerk optimal deployment trajectory planning method of a large cable-strut deployable parabolic cylindrical antenna is proposed. First, in order to decouple the complex multi-loop mechanisms, the multi-loop basic mechanism of the deployable support structure is split into three single-loop linkages, and the geometric constraint model is established based on the Denavit–Hartenberg method. Then, the kinematic model with jerk characteristics of the basic mechanism is obtained by differentiation. By considering the basic mechanism into a motion element, the kinematic model of the deployable support structure is also established based on matrix coding and motion synthesis theory. Second, by using cubic splines and considering the comprehensive optimal performance of deployment time and system jerk, an antenna deployment trajectory optimization model is established. At last, for obtaining a high precision and stable optimal solution rapidly, the non-dominated sorting genetic algorithm-II is improved by introducing the expected solution preserving strategy. The experimental results show that the proposed approach is able to effectively solve real-parameter multi-objective problems and has better performance on convergence, diversity, and the degree of controlling self-adaptation. The optimal trajectory is efficient and has a smooth kinematic performance. [ABSTRACT FROM AUTHOR]

In the past few decades, "buzz-saw" noise was mostly measured and predicted along the shroud wall. Uniform or nonuniform axial flows were applied to the predictions. Besides, the strength of the "buzz-saw" noise was widely assumed to be identical along the radius. However, nonuniform background flows and distinct radial distributions of shock strength are observed in almost all transonic fans. A possible way to solve these problems is to couple the shock trajectory with the evolution of the shock wavefront. In case the state of background flow field varies slowly, the shock trajectory is depicted by geometric acoustics. Meanwhile, the evolution of the wavefront can be solved by the governing equation of the weak-shock. Under this framework, a method is proposed to tackle the prediction of the "buzz-saw" noise under nonuniform axial and radial flows. This method is first validated by the test data from the literature. Then, it is applied to predict the near-field noise generated by the ideal and four modified versions of NASA rotor 67. The results indicate that the nonuniform radial and axial flows introduced by the wall boundary have strong effects on the distribution of the "buzz-saw" noise. Additionally, the eccentric-force problem is revealed as a side effect of blade sorting, which is an efficient method to suppress the "buzz-saw" noise. A bi-pyramid blade sorting strategy is proposed to suppress the eccentric force introduced by other blade sorting strategies. [ABSTRACT FROM AUTHOR]

This study is a comprehensive acoustic description and analysis of the six vowels /i e a u o ɔ/ in the Towet dialect of the Papuan language Nungon ⟨yuw⟩ of northeastern Papua New Guinea. Vowel tokens were extracted from a corpus of audio speech recordings created for general language documentation and grammatical description. To assess the phonetic correlates of a claimed phonological vowel length distinction, vowel duration was measured. Multi-point acoustic analyses enabled investigation of mean vowel F1, F2, and F3; vowel trajectories, and coarticulation effects. The three Nungon back vowels were of particular interest, as they contribute to an asymmetrical, back vowel-heavy array, and /o/ had previously been described as having an especially low F2. The authors found that duration of phonologically long and short vowels differed significantly. Mean vowel formant measurements confirmed that the six phonological vowels form six distinct acoustic groupings; trajectories show slightly more formant movement in some vowels than was previously known. Adjacent nasal consonants exerted significant effects on vowel formant measurements. The authors show that an uncontrolled, general documentation corpus for an under-described language can be mined for acoustic analysis, but coarticulation effects should be taken into account. [ABSTRACT FROM AUTHOR]

The constrained adiabatic trajectory method (CATM) is reexamined as an integrator for the Schrödinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet, and the (t, t′) theories is presented in detail. Two points are then more particularly analyzed and illustrated by a numerical calculation describing the H2+ ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to integrate the system. [ABSTRACT FROM AUTHOR]

A quasi-classical study of the endoergic Au+(1S) + H2(X1Σg+) → AuH+ (2Σ+) + H(2S) reaction, and isotopic variants, is performed to compare with recent experimental results [F. Li, C. S. Hinton, M. Citir, F. Liu, and P. B. Armentrout, J. Chem. Phys. 134, 024310 (2011)]. For this purpose, a new global potential energy surface has been developed based on multi-reference configuration interaction ab initio calculations. The quasi-classical trajectory results show a very good agreement with the experiments, showing the same trends for the different isotopic variants of the hydrogen molecule. It is also found that the total dissociation into three fragments, Au++H+H, is the dominant reaction channel for energies above the H2 dissociation energy. This results from a well in the entrance channel of the potential energy surface, which enhances the probability of H-Au-H insertion. [ABSTRACT FROM AUTHOR]

Quasiclassical trajectory calculations are compared, with classical and Wigner sampling of transition state (TS) energy levels, for C2H5F≠→HF+C2H4 product energy partitioning and [Cl...CH3...Cl]- central barrier dynamics. The calculations with Wigner sampling are reported here for comparison with the previously reported calculations with classical sampling [Y. J. Cho et al., J. Chem. Phys. 96, 8275 (1992); L. Sun and W. L. Hase, J. Chem. Phys. 121, 8831 (2004)]. The C2H5F≠ calculations were performed with direct dynamics at the MP2/6-31G* level of theory. Classical and Wigner sampling give post-transition state dynamics, for these two chemical systems, which are the same within statistical uncertainties. This is a result of important equivalences in these two sampling methods for selecting initial conditions at a TS. In contrast, classical and Wigner sampling often give different photodissociation dynamics [R. Schinke, J. Phys. Chem. 92, 3195 (1988)]. Here the sampling is performed for a vibrational state of the ground electronic state potential energy surface (PES), which is then projected onto the excited electronic state’s PES. Differences between the ground and the excited PESs may give rise to substantially different excitations of the vibrational and dissociative coordinates on the excited state PES by classical and Wigner sampling, resulting in different photodissociation dynamics. [ABSTRACT FROM AUTHOR]

We report results of a classical trajectory calculation of the postquenching dynamics of OH A 2∑+ by H2. This is done by performing roughly 100 000 trajectories at previously identified conical intersections (CoIs) [B. C. Hoffman and D. R. Yarkony, J. Chem. Phys. 113, 10091 (2000)]. The initial momenta are sampled fully and partially microcanonically, corresponding to “adiabatic” and “diabatic” model of the dynamics, respectively. The trajectories are propagated on a new ground state ab initio-based potential energy surface. This surface is a permutationally invariant fit to roughly 23 000 electronic energies (multireference configuration interaction/correlation-consistent-augmented-triple-zeta basis) at configurations obtained mostly from direct-dynamics calculations (complete active space second order perturbation theory with correlation-consistent-augment double-zeta basis), also initiated at the CoIs. Final rovibrational state distributions of the ground electronic state OH product and the H-atom translational energy distributions for abstraction and insertion mechanisms are calculated and compared to experimental ones. Agreement for these observable quantities is good. The branching between reactive and nonreactive quenching is sensitive to the momenta sampling; very good agreement with experiment is obtained using the diabatic sampling but not with the adiabatic sampling. The calculated H2 rovibrational distributions (not measured experimentally) are also presented. [ABSTRACT FROM AUTHOR]

Transition path sampling has been established as a powerful tool for studying the dynamics of rare events. The trajectory generation moves of this Monte Carlo procedure, shooting moves and shifting modes, were developed primarily for rate constant calculations, although this method has been more extensively used to study the dynamics of reactive processes. We have devised and implemented three alternative trajectory generation moves for use with transition path sampling. The centering-shooting move incorporates a shifting move into a shooting move, which centers the transition period in the middle of the trajectory, eliminating the need for shifting moves and generating an ensemble where the transition event consistently occurs near the middle of the trajectory. We have also developed varied-perturbation size shooting moves, wherein smaller perturbations are made if the shooting point is far from the transition event. The trajectories generated using these moves decorrelate significantly faster than with conventional, constant sized perturbations. This results in an increase in the statistical efficiency by a factor of 2.5–5 when compared to the conventional shooting algorithm. On the other hand, the new algorithm breaks detailed balance and introduces a small bias in the transition time distribution. We have developed a modification of this varied-perturbation size shooting algorithm that preserves detailed balance, albeit at the cost of decreased sampling efficiency. Both varied-perturbation size shooting algorithms are found to have improved sampling efficiency when compared to the original constant perturbation size shooting algorithm. [ABSTRACT FROM AUTHOR]

We use the fewest switches nonadiabatic trajectory surface hopping approach to study the photodissociation of methane on its lowest singlet excited state potential surface (1 1T2) at 122 nm, with emphasis on product state branching and energy partitioning. The trajectories and couplings are based on CASSCF(8,9) calculations with an aug-cc-pvdz basis set. We demonstrate that nonadiabatic dynamics is important to describe the dissociation processes. We find that CH3(X 2A2″)+H and CH2(ã 1A1)+H2 are the major dissociation channels, as have been observed experimentally. CH3+H is mostly formed by direct dissociation that is accompanied by hopping to the ground state. CH2+H2 can either be formed by hopping to the ground state to give CH2(ã 1A1)+H2 or by adiabatic dissociation to CH2(b 1B1)+H2. In the latter case, the CH2(b 1B1) can then undergo internal conversion to the ground singlet state by Renner–Teller induced hopping. Less important dissociation mechanisms lead to CH2+H+H and to CH+H2+H. Intersystem crossing effects, which are not included, do not seem essential to describe the experimentally observed branching behavior. About 5% of trajectories involve a roaming atom mechanism which can eventually lead to formation of products in any of the dissociation channels. Branching fractions to give H and H2 are in good agreement with experiment, and the H atom translational energy distribution shows bimodal character which also matches observations. [ABSTRACT FROM AUTHOR]

We demonstrate that the ring-polymer molecular dynamics (RPMD) method is equivalent to an automated and approximate implementation of the “Im F” version of semiclassical instanton theory when used to calculate reaction rates in the deep-tunneling regime. This explains why the RPMD method is often reliable in this regime and also shows how it can be systematically improved. The geometry of the beads at the transition state on the ring-polymer potential surface describes a finite-difference approximation to the “instanton” trajectory (a periodic orbit in imaginary time βh on the inverted potential surface). The deep-tunneling RPMD rate is an approximation to the rate obtained by applying classical transition-state theory (TST) in ring-polymer phase-space using the optimal dividing surface; this TST rate is in turn an approximation to a free-energy version of the Im F instanton rate. The optimal dividing surface is in general a function of several modes of the ring polymer, which explains why centroid-based quantum-TSTs break down at low temperatures for asymmetric reaction barriers. Numerical tests on one-dimensional models show that the RPMD rate tends to overestimate deep-tunneling rates for asymmetric barriers and underestimate them for symmetric barriers, and we explain that this is likely to be a general trend. The ability of the RPMD method to give a dividing-surface-independent rate in the deep-tunneling regime is shown to be a consequence of setting the bead-masses equal to the physical mass. [ABSTRACT FROM AUTHOR]

A potential energy surface that describes the title reaction has been constructed by interpolation of ab initio data. Classical trajectory studies on this surface show that the total reaction rate is close to that predicted by a Langevin model, although the mechanism is more complicated than simple ion-molecule capture. Only the HCO++H product is observed classically. An estimate of the magnitude of rotational inelastic scattering is also reported. [ABSTRACT FROM AUTHOR]

The transition to spatial-temporal complexity exhibited by spiral waves under the effect of gravitational field in the Belousov–Zhabotinsky reaction is numerically studied on the basis of spiral tip dynamics. Successive transformations in tip trajectories are characterized as a function of the hydrodynamical parameter and attributed to a Ruelle–Takens–Newhouse scenario to chaos. The analysis describes the emergence of complexity in terms of the interplay between the evolution of the velocity field and concentration waves. In particular, (i) by mapping the tip motion in relation to some hydrodynamical pseudopotentials, the general mechanism by which the velocity field affects the tip trajectory is pointed out, and, (ii) by comparing the dynamical evolutions of local and mean properties associated with the inhomogeneous structures and to the velocity field, a surprising correlation is found. The results suggest that the reaction-diffusion-convection (RDC) coupling addresses the system to some general regimes, whose nature is imposed by the hydrodynamical contribution. More generally, RDC coupling would be formalized as the phenomenon that governs the system and drives it to chaos. [ABSTRACT FROM AUTHOR]

Multiconfiguration molecular mechanics (MCMM) was previously applied to calculate potential energies, gradients, and Hessians along a reaction path and in the large-curvature tunneling swath, and it was shown that one could calculate variational transition state theory rate constants with optimized multidimensional tunneling without requiring more than a few electronic structure Hessians. It was also used for molecular dynamics simulations of liquid-phase potentials of mean force as functions of a reaction coordinate. In the present article we present some improvements to the formalism and also show that with these improvements we can use the method for the harder problem of trajectory calculations on gas-phase bimolecular reactive collisions. In particular, we apply the MCMM algorithm to the model reaction OH+H2→H2O+H, for which we construct the global full-dimensional interpolated potential energy surfaces with various numbers of electronic structure Hessians and various molecular mechanics force fields, and we assess the quality of these fits by quasiclassical trajectory calculations. We demonstrate that chemical accuracy (1–2 kcal/mol) can be reached for a MCMM potential in dynamically important regions with a fairly small number of electronic structure Hessians. We also discuss the origins of the errors in the interpolated energies and a possible way to improve the accuracy. [ABSTRACT FROM AUTHOR]

A trajectory surface hopping algorithm is proposed, which stems from a mathematically rigorous analysis of propagation through conical intersections of potential energy surfaces. Since nonadiabatic transitions are only performed when a classical trajectory attains one of its local minimal surface gaps, the algorithm is called single switch surface hopping. Numerical experiments for a two mode Jahn–Teller system are presented, which illustrate the asymptotic justification of the method as well as its good performance in the physically relevant parameter range. [ABSTRACT FROM AUTHOR]

Projection of a Markov process with constant rates of transition to a small number of observable aggregated states can result in complex kinetics with memory. Here, we define the entropy production along a single sequence of aggregated states and show that it obeys detailed and integral fluctuation theorems. More importantly, we prove that projection shifts the distribution of entropy production over the ensemble of paths for a nonequilibrium process toward one characteristic of a system at equilibrium. This statement represents an analog of the second law of thermodynamics for path-dependent entropies and thus a new form of constraint of irreversible systems. Numeric examples are presented to illustrate these ideas. [ABSTRACT FROM AUTHOR]

In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action S is taken to be complex [Y. Goldfarb et al., J. Chem. Phys. 125, 231103 (2006)]. In the alternative formulation there is a significant reduction in the magnitude of the quantum force as compared with the conventional Bohmian formulation, at the price of propagating complex trajectories. In this paper we show that Bohmian mechanics with complex action is able to overcome the main computational limitation of conventional Bohmian methods—the propagation of wave functions once nodes set in. In the vicinity of nodes, the quantum force in conventional Bohmian formulations exhibits rapid oscillations that present a severe numerical challenge. We show that within complex Bohmian mechanics, multiple complex initial conditions can lead to the same real final position, allowing for the accurate description of nodes as a sum of the contribution from two or more crossing trajectories. The idea is illustrated on the reflection amplitude from a one-dimensional Eckart barrier. We believe that trajectory crossing, although in contradiction to the conventional Bohmian trajectory interpretation, provides an important new tool for dealing with the nodal problem in Bohmian methods. [ABSTRACT FROM AUTHOR]

The absolute integral cross sections for the formation of HeH+ and HeD+ from the collisions of HD+(v,j=1)+He have been examined over a broad range of vibrational energy levels v=0–13 at the center-of-mass collision energies (ET) of 0.6 and 1.4 eV using the vacuum ultraviolet (VUV) pulsed field ionization photoelectron secondary ion coincidence method. The ET dependencies of the integral cross sections for products HeH+ and HeD+ from HD+(v=0–4)+He collisions in the ET range of 0–3 eV have also been measured using the VUV photoionization guided ion beam mass spectrometric technique, in which vibrationally selected HD+(v) reactant ions were prepared via excitation of selected autoionization resonances of HD. At low total energies, a pronounced isotope effect is observed in absolute integral cross sections for the HeH++D and HeD++H channels with significant favoring of the deuteron transfer channel. As v is increased in the range of v=0–9, the integral cross sections of the HeH++D channel are found to approach those of HeD++H. The observed velocity distributions of products HeD+ and HeH+ are consistent with an impulsive or spectator-stripping mechanism. Detailed quasiclassical trajectory (QCT) calculations are also presented for HD+(v,j=1)+He collisions at the same energies of the experiment. The QCT calculations were performed on the most accurate ab initio potential energy surface available. If the zero-point energy of the reaction products is taken into account, the QCT cross sections for products HeH+ and HeD+ from HD+(v)+He are found to be significantly lower than the experimental results at ET values near the reaction thresholds. The agreement between the experimental and QCT cross sections improves with translational energy. Except for prethreshold reactivity, QCT calculations ignoring the zero-point energy in the products are generally in good agreement with experimental absolute cross sections. The experimental HeH+/HeD+ branching ratios for the HD+(v=0–9)+He collisions are generally consistent with QCT predictions. The observed isotope effects can be rationalized on the basis of differences in thermochemical thresholds and angular momentum conservation constraints. [ABSTRACT FROM AUTHOR]

Quasiclassical trajectory calculations have been carried out for H2(v1=high)+H2(v2=low) collisions within a three degrees of freedom model where five different geometries of the colliding complex were considered. Within this approach, probabilities for different competitive processes are studied: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. The purpose is to compare in detail with equivalent quantum-mechanical wave packet calculations [Bartolomei et al., J. Chem. Phys 122, 064305 (2005)], especially the behavior of the probabilities near reaction thresholds. Quasiclassical calculations compare quite well with the quantum-mechanical ones for collision induced dissociation as well as for the four center reaction, although quantum effects become very important near thresholds, particularly for lower v1’s and for the four center process. Less quantitative agreement is found for reactive dissociation and three-body complex formation. It is found that most quantum effects are due to differences between quantum and classical vibrational distributions of H2(v1=high). Zero point energy violation has been found in the classical reactive-dissociative probabilities. Extension of these findings to full-dimensional treatments is examined. [ABSTRACT FROM AUTHOR]

We use a constant velocity steered molecular dynamics (SMD) simulation of the stretching of deca-alanine in vacuum to demonstrate a technique that can be used to create a surrogate processes approximation (SPA) using the time series that come out of SMD simulations. In this article, the surrogate processes are constructed by first estimating a sequence of local parametric diffusion models along a SMD trajectory and then a single global model is constructed by piecing the local models together through smoothing splines (estimation is made computationally feasible by likelihood function approximations). The SPAs are then “bootstrapped” in order to obtain a plausible range of work values associated with a particular SMD realization. This information is then used to assist in estimating a potential of mean force constructed by appealing to the Jarzynski equality. When this procedure is repeated for a small number of SMD paths, it is shown that the global models appear to come from a single family of closely related diffusion processes. Possible techniques for exploiting this observation are also briefly discussed. The findings of this paper have potential relevance to computationally expensive computer simulations and experimental works involving optical tweezers where it is difficult to collect a large number of samples, but possible to sample accurately and frequently in time. [ABSTRACT FROM AUTHOR]

We investigate differential charging of high aspect ratio dielectric trenches under plasma exposure using a two-dimensional computational model. Rather than considering average fluxes, we track individual ion and electron trajectories within the electric field arising from surface charges on the trench, updating the potentials within the computational domain after each particle. Our results show that, as the trench width shrinks to 100 nm and below, the potentials within the trench oscillate over an ever-wider range. The stochastic charging behavior in turn leads to noticeable changes in the flux and energies of ions passing through the trench. [ABSTRACT FROM AUTHOR]

The use of the Ehrenfest method to simulate the relaxation of molecules in solution is explored. Using the cyanide ion dissolved in water as a test model, the independent trajectory (IT) and the bundle of trajectories (BT) approximations are shown to provide very different results for the time evolution of the vibrational populations of the solute. None of these approximations reproduce the Boltzmann equilibrium vibrational populations accurately. A modification of the Ehrenfest method based on the use of quantum correction factors is thus proposed to solve this problem. The simulations carried out using the modified Ehrenfest method provide IT and BT relaxation times which are closer to each other and which agree quite well with previous hybrid perturbative results. [ABSTRACT FROM AUTHOR]

The temporal evolution of the entropy of a mechanical system as described by a single trajectory is computed using the Clausius [Philos. Mag. 40, 122 (1868)] equality. This requires computing the maximal work that can be done by the system and comparing it to the actual work performed. A single trajectory suffices to determine the entropy when it is “typical,” meaning that average values of mechanical variables will not be different when computed using trajectories with different initial conditions. The results are illustrated for small rare gas clusters heated and compressed by an impact at a hard surface. [ABSTRACT FROM AUTHOR]

Trajectory calculations of collisional energy transfer between excited azulene and Kr are reported, and the results are compared with recent crossed molecular beam experiments by Liu et al. [J. Chem. Phys. 123, 131102 (2005); 124, 054302 (2006)]. Average energy transfer quantities are reported and compared with results obtained before for azulene-Ar collisions. A collisional energy transfer probability density function P(E,E′), calculated at identical initial conditions as experiments, shows a peak at the up-collision branch of P(E,E′) at low initial relative translational energy. This peak is absent at higher relative translational energies. There is a supercollision tail at the down-collision side of the probability distribution. Various intermolecular potentials are used and compared. There is broad agreement between experiment and computation, but there are some differences as well. [ABSTRACT FROM AUTHOR]

The effect of finite trajectory length on single molecule rotational correlation functions has been studied by utilizing time series analysis and numerical simulations. Correlation functions obtained from the trajectories of length less than 100 times the correlation time constant (τℓ) exhibit significant deviations from the true correlation function. The distributions of sample time constants (τF) and stretching exponents (βF) are mapped by fitting a large number of rotational trajectories to stretched exponentials. As the trajectory length gets smaller, the distributions become broader and asymmetric and their mean values deviate from the true value predicted by pure rotational diffusion. Analysis based on higher order spherical harmonics is suggested as a method for minimizing the effect of the trajectory length. The distributions of time constants for different higher order spherical harmonics are also compared. While the focus of the paper is on rotational correlation functions, the general conclusions apply to any dynamical process that yields an exponentially decaying correlation function. [ABSTRACT FROM AUTHOR]

Trajectory calculations run on global potential energy surfaces have shown that the topology of the entrance channel has strong implications on the dynamics of the title reactions. This may explain why huge differences are observed between the rate constants calculated from global dynamical methods and those obtained from local methods that employ the same potential energy surfaces but ignore such topological details. Local dynamics approaches such as transition state-based theories should then be used with caution for fine-tuning potential energy surfaces, especially for fast reactions with polyatomic species since the key statistical assumptions of the theory may not be valid for all degrees of freedom. [ABSTRACT FROM AUTHOR]

A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic two-dimensional system confirm the efficiency of this approach. The results are compared to the standard fixed transition state dividing surface that is well-known to suffer from recrossings and therefore requires trajectories to be evolved over a long time interval before they can reliably be classified as reactive or nonreactive. The moving dividing surface can be used to identify reactive trajectories in harmonic or moderately anharmonic systems with considerably lower numerical effort or even without any simulation at all. [ABSTRACT FROM AUTHOR]

We present a generalized formulation of the trajectory surface hopping method applicable to a general multidimensional system. The method is based on the Zhu-Nakamura theory of a nonadiabatic transition and therefore includes the treatment of classically forbidden hops. The method uses a generalized recipe for the conservation of angular momentum after forbidden hops and an approximation for determining a nonadiabatic transition direction which is crucial when the coupling vector is unavailable. This method also eliminates the need for a rigorous location of the seam surface, thereby ensuring its applicability to a wide class of chemical systems. In a test calculation, we implement the method for the DH2+ system, and it shows a remarkable agreement with the previous results of C. Zhu, H. Kamisaka, and H. Nakamura, [J. Chem. Phys. 116, 3234 (2002)]. We then apply it to a diatomic-in-molecule model system with a conical intersection, and the results compare well with exact quantum calculations. The successful application to the conical intersection system confirms the possibility of directly extending the present method to an arbitrary potential of general topology. [ABSTRACT FROM AUTHOR]

A method of controlling the particle trajectory in a microchannel is demonstrated. The method utilizes the dc-dielectrophoretic (dc-DEP) force created around an insulating hurdle in a microchannel under an applied dc electric field. This method does not require a complicated electrode array which is commonly used in the conventional ac-DEP system. The “proof-of-principle” experiments were carried out using a straight microchannel with a rectangle-shaped hurdle in the middle. The experiments showed that the trajectories of the micron-sized particles can be controlled by the DEP force under electric-field strengths of 5–20 kV/m. To compare with the experimental results, the particle motion was simulated using the Lagrangian tracking method, taking into consideration of the electrophoretic force, the dielectrophoretic force, and the dielectric interaction between the particle and the channel wall. The numerical simulation based on the finite-element method showed a reasonable agreement with the experimental data. [ABSTRACT FROM AUTHOR]