Intermolecular Collisions Research Articles

The Vlasov–Maxwell–Boltzmann system with a uniform ionic background near Maxwellians

The two-species Vlasov–Maxwell–Boltzmann system is an important model for plasma physics describing the time evolution of dilute charged particles consisting of electrons and ions under the influence of the self-consistent internally generated Lorentz forces. In physical situations the ion mass is usually much larger than the electron mass so that the electrons move much faster than the ions. Thus, the ions are often described by a fixed ion background and only the electrons move. For such a simple case, the two-species Vlasov–Maxwell–Boltzmann system is reduced to the one-species Vlasov–Maxwell–Boltzmann system.Although the one-species Vlasov–Maxwell–Boltzmann system is a simplified model of the two-species Vlasov–Maxwell–Boltzmann system, its global well-posedness theory near a given global Maxwellian in the perturbative framework is more difficult than the two-species case, which is partially due to the slow-decay of the electromagnetic field and up to now, the problem on the construction of global in time solutions near a given global Maxwellian in the perturbative framework for the Cauchy problem of the one-species Vlasov–Maxwell–Boltzmann system with cutoff non-hard sphere intermolecular collisions remains unsolved. It is shown in this paper that the Cauchy problem of the one-species Vlasov–Maxwell–Boltzmann system with cutoff non-hard sphere intermolecular collisions including the cutoff inverse power law potentials is globally well-posed provided that the perturbative initial data satisfies certain regularity, smallness, and integrability conditions. Our analysis is based on a new time-velocity weighted energy method with two key technical parts: one is to introduce the exponentially weighted estimates into the cutoff Boltzmann operator and the other is to design a delicate temporal energy X(t)-norm to obtain its uniform bound. As a by-product of our analysis, we can also deduce certain temporal decay estimates on the global solutions constructed above for the same range of intermolecular collisions. Notice that even for the hard sphere model, although the global solutions have been successfully constructed in [8], its large time behaviors are unknown, cf. [8].

Spectrum structure and behavior of the Vlasov–Maxwell–Boltzmann system without angular cutoff

The spectrum structure and behavior of the Vlasov–Maxwell–Boltzmann (VMB) system with physical angular non-cutoff intermolecular collisions are studied in this paper. The analysis shows the effect of the Lorentz force induced by the electro-magnetic field leads to some different spectrum structure from the non-cutoff Boltzmann equation. The spectrum structure in high frequency, quite different from the VMB system with angular cutoff assumption, also illustrates the hyperbolic structure of the Maxwell equation. Furthermore, the large time behavior and optimal convergence rates to the equilibrium of the non-cutoff VMB system are established on the spectrum analysis.

Decomposition-based chemical reaction optimization (CRO) and an extended CRO algorithms for multiobjective optimization

Multiobjective optimization is an essential and challenging topic in the domains of science and engineering optimization. An effective decomposition-based chemical reaction optimization metaheuristic algorithm (MOCRO/D) for solving multiobjective optimization problems (MOPs) is proposed in this paper. In the proposed algorithm, each decomposed sub-problem is represented by a chemical molecule. All molecules are divided into a few groups and each molecule has several neighboring molecules. During the search, each molecule records its potential energy (optimal solution), the hits of number and the kinetic energy. MOCRO/D has four operators, i.e., on-wall ineffective collision, inter-molecular ineffective collision, decomposition, and synthesis. To explore the search space efficiently, polynomial mutation and multiple molecule collision operators are introduced in the inter-molecular collision and synthesis operator. The inter-molecular ineffective collision operator uses three molecules to collide, which can improve the information interacting with each other with a certain probability. The extended synthesis operator could increase the global search ability. Extended operators for MOCRO/D (MOECRO/D) are proposed that can better optimize the variables related problems. The proposed approach is compared with other metaheuristic algorithms available in the specialized literature. Results indicate that the proposed approach is competitive in most of the test instances.

A multi-flow regimes model for simulating gas transport in shale matrix

The gas transport in shale matrix is of great research interest for optimised shale gas recovery. Pores and pore-throats in the gas-bearing shale are nano-scale, and hence transport of gas is governed by the slippage effect and Knudsen diffusion rather than viscous flow. Hence a proper mathematical model is needed for full understanding of shale gas transport. In this paper, a mathematical model that considers multi-flow regimes is proposed based on gas molecular kinetics theory. The flow regimes transition from slip flow to Knudsen diffusion, and can be adequately described by introducing a corrected intermolecular collision frequency. The proposed mathematical model predictions are compared with experimental data and found to match very well. Furthermore, the gas mass flux contributed by different flow regimes with the variation of Knudsen number is analysed. The numerical simulation results indicate that with the increase in Knudsen number, viscous flow becomes weakened, and the slippage flow reaches a peak and then decreases gradually. The contribution to the gas mass flux due to Knudsen diffusion starts at the early stage of transition flow, and becomes dominant at the later stage of transition flow.

Equilibrating Effect of Maxwell-Type Boundary Condition in Highly Rarefied Gas

We study the equilibrating effects of the boundary and intermolecular collision in the kinetic theory for rarefied gases. We consider the Maxwell-type boundary condition, which has weaker equilibrating effect than the commonly studied diffuse reflection boundary condition. The gas region is the spherical domain in $\mathbb{R}^d$, $d=1,2$. First, without the equilibrating effect of collision, we obtain the algebraic convergence rates to the steady state of free molecular flow with variable boundary temperature. The convergence behavior has intricate dependence on the accommodation coefficient of the Maxwell-type boundary condition. Then we couple the boundary effect with the intermolecular collision and study their interaction. We are able to construct the steady state solutions of the full Boltzmann equation for large Knudsen numbers and small boundary temperature variation. We also establish the nonlinear stability with exponential rate of the stationary Boltzmann solutions. Our analysis is based on the explicit formulations of the boundary condition for symmetric domains.

Real gas transport through nanopores of varying cross-section type and shape in shale gas reservoirs

A model for real gas transport in nanopores of shale gas reservoirs (SGRs) was proposed on the basis of the weighted superposition of slip flow and Knudsen diffusion, where the ratios of the intermolecular collisions and the molecule–nanopore wall collisions to the total collisions are the weighted factors of slip flow and Knudsen diffusion, respectively. The present model takes account of slip effect and real gas effect, additionally, the effects of cross-section type and its shape of nanopores on gas transport are also considered in this paper. The present model is successfully validated against existing molecular simulation data collected from different sources in literature. The results show: (1) the present model is reasonable to describe all of the gas transport mechanisms known, including continuum flow, slip flow and transition flow in nanopores of SGRs; (2) the cross-section type and shape of nanopores both affect gas transport capacity: at the same cross-sectional area, gas transport capacity of nanopores with a circular cross section is greater than that with a rectangular cross section, and gas transport capacity of nanopores with a rectangular cross section decreases with an increasing aspect ratio; compared to the cross-section type, the effect of the cross-section shape on gas transport capacity is stronger; (3) a real gas effect improves gas transport capacity, which becomes more obvious with an increasing pressure and a decreasing pore size; (4) and compared to nanopores with a circular cross section, the effect of real gas effect on gas transport capacity of nanopores with a rectangular cross section is stronger, and the effect increases with an increasing aspect ratio. The proposed model can provide some theoretical support in numerical simulation of reservoir behavior in SGRs.

Thermally modulated biomolecule transport through nanoconfined channels.

In this work, a nanofluidic device containing both a feed cell and a permeation cell linked by nanopore arrays has been fabricated, which is employed to investigate thermally controlled biomolecular transporting properties through confined nanochannels. The ionic currents modulated by the translocations of goat antibody to human immunoglobulin G (IgG) or bovine serum albumin (BSA) are recorded and analyzed. The results suggest that the modulation effect decreases with the electrolyte concentration increasing, while the effects generated by IgG translocation are more significant than that generated by BSA translocation. More importantly, there is a maximum decreasing value in each modulated current curve with biomolecule concentration increasing for thermally induced intermolecular collision. Furthermore, the turning point for the maximum shifts to lower biomolecule concentrations with the system temperature rising (from 4°C to 45°C), and it is mainly determined by the temperature in the feed cell if the temperature difference exists in the two separated cells. These findings are expected to be valuable for the future design of novel sensing device based on nanopore and/or nanopore arrays.

Study of Convergence Time for Rarefied Gas Simulations Using an Unstructured DSMC Solver

This article studies the required convergence time for direct-simulation Monte Carlo (DSMC) simulations of rarefied gas flows. An arbitrary-geometry DSMC solver (RGS2D) with an efficient particle-tracking algorithm is introduced and employed for macro-/micro-scale flow applications. Convergence time study is performed by tracing different heat and flow parameters such as intermolecular collision rate, number of particles, drag coefficient, inlet/outlet mass flow rate, and distributions over the wall, i.e., pressure coefficient, skin friction coefficient, heat transfer coefficient, and wall collision rate. The results indicate that the required simulation time depends on the capturing parameter.

Convergence analysis of the direct simulation Monte Carlo based on the physical laws of conservation

Computational errors in the direct simulation Monte Carlo method can be categorized into four types; decomposition (or discretization), statistical, machine, and boundary condition errors. They arise due to variety of reasons including decoupling of movement and collision phases into two separate steps, finiteness of molecule numbers and domain cell-size, existence of statistical fluctuations and uncertainty, using machines to solve physical problems numerically, computational implementation of boundary conditions of approximate nature, and, finally, assumptions and simplifications adopted in the inter-molecular collision models. In this study, a verification method based on the physical laws of conservation, which are an exact consequence of the Boltzmann equation, is introduced in order to quantify the errors of the DSMC method. A convergence history according to the new verification method is then presented that can illustrate the effects of all type of errors during the simulation run. Convergence analysis indicates that the DSMC method can satisfy the conservation laws with an acceptable level of precision for the flow problems studied. Finally, it is shown that the overall deviation from conservation laws increases with decreasing sample size value and number of particles, and with increasing length of cells and time-step interval size.

A model for gas transport in microfractures of shale and tight gas reservoirs

A model for gas transport in microfractures of shale and tight gas reservoirs is established. Slip flow and Knudsen diffusion are coupled together to describe general gas transport mechanisms, which include continuous flow, slip flow, transitional flow, and Knudsen diffusion. The ratios of the intermolecular collision frequency and the molecule‐wall collision frequency to the total collision frequency are defined as the weight coefficients of slip flow and Knudsen diffusion, respectively. The model is validated by molecular simulation results. The results show that: (1) the model can reasonably describe the process of the mass transform of different gas transport mechanisms; (2) fracture geometry significantly impacts gas transport. Under the same fracture aperture, the higher the aspect ratio is, the stronger the gas transport capacity, and this phenomenon is more pronounced in the cases with higher gas pressure and larger fracture aperture. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2079–2088, 2015

一次元垂直衝撃波のDSMC解析における分子間衝突法に関する研究

一次元垂直衝撃波のDSMC解析における分子間衝突法に関する研究

Molecular free paths in nanoscale gas flows

Average distance traveled by gas molecules between intermolecular collisions, known as the mean free path (MFP), is a key parameter for characterizing gas flows in the entire Knudsen regime. Recent literature presents variations in MFP as a function of the surface confinement, which is in disagreement with the kinetic theory and leads to wrong physical interpretations of nanoscale gas flows. This controversy occurs due to erroneous definition and calculation practices, such as consideration of gas wall collisions, using local bins smaller than a MFP, and utilizing time frames shorter than a mean collision time in the MFP calculations. This study reports proper molecular MFP calculations in nanoscale confinements by using realistic molecular surfaces. We utilize molecular dynamics (MD) simulations to calculate gas MFP in three-dimensional periodic systems of various sizes and for force-driven gas flows confined in nano-channels. Studies performed in the transition flow regime in various size nano-channels and under a range of gas–surface interaction strengths have shown isotropic mean travelled distance and MFP values in agreement with the kinetic theory regardless of the surface forces and surface adsorption effects. Comparison of the velocity profiles obtained in MD simulations with the linearized Boltzmann solutions at predicted Knudsen values shows good agreement in the bulk of the channels, while deviations in the near wall region due to the influence of surface forces are reported.

Progress and future prospects for particle-based simulation of hypersonic flow

The direct simulation Monte Carlo method (DSMC) has evolved over 50 years into a powerful numerical technique for the computation of thermochemical nonequilibrium gas flows. In this context, nonequilibrium means that velocity and internal energy distribution functions are not in equilibrium forms due to a low number of intermolecular collisions within a fluid element. In hypersonic flow, nonequilibrium conditions occur at high altitude and in regions of flow fields with small length scales. This article highlights significant developments in particle simulation methods (since 2001) applied specifically to hypersonic flows, which now includes Molecular Dynamics in addition to DSMC. Experimental measurements that have led directly to improved DSMC models will be highlighted. Algorithm development for DSMC aimed at increasing computational efficiency is discussed with a focus on hybrid particle-continuum methods. New research that applies all-atom Molecular Dynamics simulation and trajectory-based DSMC simulation to normal shock waves is summarized. Finally, a discussion of state-resolved DSMC modeling is included with reference to future prospects for particle simulation methods and in particular for the DSMC method.

Optimal location of UPFC controller in transmission network using hybrid chemical reaction optimization algorithm

This paper presents a new hybrid chemical reaction optimization (HCRO) approach which is based on chemical reaction optimization (CRO) and differential evolution (DE) to find the optimal placement and parameter setting of unified power flow controller (UPFC) to achieve optimal performance of power system network. In the proposed algorithm, four elementary reactions, i.e., on-wall ineffective collision, inter-molecular ineffective collision, decomposition, and synthesis, are developed. Moreover, mutation operation of DE is integrated with inter-molecular ineffective collision and crossover operation is introduced in the inter-molecular collision, synthesis, and decomposition process to accelerate the convergence speed and improve the solution quality of CRO algorithm. Here, three different single objectives namely, minimization of the overall cost, transmission loss, voltage deviation and one multi-objective which simultaneously minimizes the transmission loss and voltage deviation are used. To verify the effectiveness, the proposed HCRO approach is implemented on IEEE 14-bus and IEEE 30-bus power systems. Moreover, to establish the superiority, the simulation results of the proposed HCRO technique are compared to the CRO and other previously reported algorithms published in the literature such as genetic algorithm (GA), particle swarm optimization (PSO), immune GA (IGA), immune PSO (IPSO) and hybrid immune algorithm (HIA). It is found that the results obtained by the proposed HCRO technique are superior to those obtained by other discussed algorithms.

An introduction to biomolecular simulations and docking

The biomolecules in and around a living cell – proteins, nucleic acids, lipids and carbohydrates – continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given biomolecule also samples (and is sampled by) a rapidly fluctuating local environment comprising other biopolymers, small molecules, water, ions, etc. that diffuse to within a few nanometres, leading to inter-molecular contacts that stitch together large supramolecular assemblies. Indeed, all biological systems can be viewed as dynamic networks of molecular interactions. As a complement to experimentation, molecular simulation offers a uniquely powerful approach to analyse biomolecular structure, mechanism and dynamics; this is possible because the molecular contacts that define a complicated biomolecular system are governed by the same physical principles (forces and energetics) that characterise individual small molecules, and these simpler systems are relatively well-understood. With modern algorithms and computing capabilities, simulations are now an indispensable tool for examining biomolecular assemblies in atomic detail, from the conformational motion in an individual protein to the diffusional dynamics and inter-molecular collisions in the early stages of formation of cellular-scale assemblies such as the ribosome. This text introduces the physicochemical foundations of molecular simulations and docking, largely from the perspective of biomolecular interactions.

Benzene diffusion on graphite described by a rough hard disk model

New insight into the nature of diffusion and the origin of friction of a prototype system for weak physisorption – benzene molecules, C6H6, adsorbed on the basal plane (0001) of graphite – has been obtained with quasi-elastic neutron scattering (QENS). Spectra were measured at relative adsorbate coverages between 0.1 and 1.0monolayers (ML) and at sample temperatures between 60K and 140K. Our experimental observations require a substantial modification of the model of interaction between benzene molecules and graphite surfaces: in contrast to recent studies we find only weak kinetic surface friction, but a substantial dissipative interaction during inter-molecular collisions. At coverages of up to 0.5ML the molecular dynamics are successfully modeled by a rough hard disk model, which we derive from a three-dimensional rough hard sphere model. At the full monolayer, three body and higher order collisions are dominant and the rough hard disk model breaks down, as expected.

Investigation of aerodynamic characteristics of rarefied flow around NACA 0012 airfoil using DSMC and NS solvers

In this study, rarefied supersonic and subsonic gas flow around a NACA 0012 airfoil is simulated using both continuum and particle approaches. Navier–Stokes equations subject to the first order slip/jump boundary conditions are solved under the framework of OpenFOAM package. The DSMC solver of the package, i.e., dsmcFoam, has been improved to include a newly presented “simplified Bernoulli trial (SBT)” scheme for inter-molecular collision modeling. The use of SBT collision model permits to obtain accurate results using a much lower number of simulator particles. We considered flow at different angles of attacks and Knudsen numbers at both the subsonic and supersonic regimes. The computed density and surface pressure distributions are compared with the experimental and numerical data and suitable accuracy was observed. We investigate variations of the lift and drag coefficients with the Knudsen number and angle of attack. At low Kn number in supersonic regime, our results for lift coefficient agree well with the linearized theory; however, the deviation starts as soon as the angle of attack goes beyond 15° or shock wave forms above the airfoil. Along with this, we have observed that drag coefficient increases with the Kn number increasing. We also investigated the effect of Kn number on the leading edge shock position and structure, drag polar (CL/CD), and slip velocity over the airfoil.

Computation of Hypersonic Flows Using the Direct Simulation Monte Carlo Method

The direct simulation Monte Carlo method has evolved over 50 years into a powerful numerical technique for the computation of complex, nonequilibrium gas flows. In this context, “nonequilibrium” means that the velocity distribution function is not in an equilibrium form due to a low number of intermolecular collisions within a fluid element. In hypersonic flow, nonequilibrium conditions occur at high altitude and in regions of flowfields with small length scales. In this paper, the theoretical basis of the direct simulation Monte Carlo technique is discussed. In addition, the methods used in direct simulation Monte Carlo are described for simulation of high-temperature, real gas effects and gas–surface interactions. Several examples of the application of direct simulation Monte Carlo to flows around blunt hypersonic vehicles are presented to illustrate current capabilities. Areas are highlighted where further research on the direct simulation Monte Carlo technique is required.

Direct Observation, Study, and Control of Molecular Superrotors

Extremely fast rotating molecules whose rotational energy is comparable with the molecular bond strength are known as "superrotors." It has been speculated that superrotors may exhibit a number of unique properties, yet only indirect evidence of these molecular objects has been reported to date. Here we demonstrate the first direct observation of molecular superrotors by detecting coherent unidirectional molecular rotation with extreme frequencies exceeding 10 THz. The technique of an "optical centrifuge" is used to control the degree of rotational excitation in an ultrabroad range of rotational quantum numbers, reaching as high as N = 95 in oxygen and N = 60 in nitrogen. State-resolved detection enables us to determine the shape of the excited rotational wave packet and quantify the effect of centrifugal distortion on the rotational spectrum. Femtosecond time resolution reveals coherent rotational dynamics with increasing coherence times at higher angular momentum. We demonstrate that molecular superrotors can be created and observed in dense samples under normal conditions where the effects of ultrafast rotation on many-body interactions, intermolecular collisions, and chemical reactions can be readily explored.

Mechanosignaling between central apparatus and radial spokes controls axonemal dynein activity

Cilia/flagella are conserved organelles that generate fluid flow in eukaryotes. The bending motion of flagella requires concerted activity of dynein motors. Although it has been reported that the central pair apparatus (CP) and radial spokes (RSs) are important for flagellar motility, the molecular mechanism underlying CP- and RS-mediated dynein regulation has not been identified. In this paper, we identified nonspecific intermolecular collision between CP and RS as one of the regulatory mechanisms for flagellar motility. By combining cryoelectron tomography and motility analyses of Chlamydomonas reinhardtii flagella, we show that binding of streptavidin to RS heads paralyzed flagella. Moreover, the motility defect in a CP projection mutant could be rescued by the addition of exogenous protein tags on RS heads. Genetic experiments demonstrated that outer dynein arms are the major downstream effectors of CP- and RS-mediated regulation of flagellar motility. These results suggest that mechanosignaling between CP and RS regulates dynein activity in eukaryotic flagella.