Time-dependent Distribution Function Research Articles

Molecular dynamics simulation and experimental verification of a biphasic solvent for CO2 capture

In the context of solvent-based carbon capture, researchers and industries are often interested in improvements in the efficiency of CO2 capture along with the reduction in the required energy. This study employs molecular dynamics (MD) simulation based on a reax force field and experimental investigation to study the effects and main mechanisms of a mutual amine absorbent including diethylenetriamine (DETA) and diethylethanolamine (DEEA), accompanied by NMP and water co-solvents, on the performance of CO2 capture in a phase change system. The implementation of time-dependent partial radial distribution functions (TD-PRDF, gαβrtm) and coordination number (CN) analyses revealed the significant formation of C-N bonds between carbon (C) derived from CO2 and nitrogen (N) within the solution. The direct relationship between changes in DETA molar ratios and CO2 loading, coupled with examining the catalytic role of DEEA in facilitating CO2 removal through protonation, has been thoroughly studied with MD. The experimental methodology was followed to validate the MD results. The optimum composition, DETA: DEEA: NMP with a molar ratio of 3:2.5:1, as determined through MD simulations exhibitsgαβr|tm = 9.848, CN=0.403 at tm= 1 ns. The stable C-N absorption bond length is calculated to be between 1.7 and 1.77 Å. Experimental results confirm a CO2 loading capacity of 0.93 mol/mol for this composition.

Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features.

Boltzmann's H-function H(t), often regarded as an analog of time-dependent entropy, holds a venerable place in the history of science. However, accurate numerical evaluation of H(t) for particles other than atoms is rare. To remove this lacuna, we generalize Boltzmann's H-function to a gas of molecules with orientational degrees of freedom and evaluate H(t) from the time-dependent joint probability distribution function f(p, L, t) for linear (p) and angular (L) momenta, evolving from an initial nonequilibrium state, by molecular dynamics simulations. We consider both prolate- and oblate-shaped particles, interacting via the well-known Gay-Berne potential and obtain the relaxation of the generalized molecular H(t) from initial (t = 0) nonequilibrium states. In the long-time limit, the H function saturates to its exact equilibrium value, which is the sum of translational and rotational contributions to the respective entropies. Both the translational and rotational components of H(t) decay nearly exponentially with time; the rotational component is more sensitive to the molecular shape that enters through the aspect ratio. A remarkable rapid decrease in the rotational relaxation time is observed as the spherical limit is approached, in a way tantalizingly reminiscent of Hu-Zwanzig hydrodynamic prediction with the slip boundary condition. In addition, we obtain H(t) analytically by solving the appropriate translational and rotational Fokker-Planck equation and obtain a modest agreement with simulations. We observe a remarkable signature of translation-rotation coupling as a function of molecular shape, captured through a physically meaningful differential term that quantifies the magnitude of translation-rotation coupling.

Heating mode transitions in capacitively coupled CF4 plasmas at low pressure

Abstract Capacitively coupled plasmas operated in CF4 at low pressure are frequently used for dielectric plasma etching. For such applications the generation of different ion and neutral radical species by energy dependent electron impact ionization and dissociation of the neutral background gas is important. These processes are largely determined by the space and time dependent electron energy distribution function and, thus, by the electron power absorption dynamics. In this work and based on a particle-in-cell/Monte Carlo collision model, we show that the electron heating mode in such plasmas is sensitive to changes of the gap at a constant pressure of 3 Pa. At a gap of 1.5 cm, the dominant mode is found to be a hybrid combination of the Drift-Ambipolar (DA) and the α-mode. As the gap is increased to 2 cm and 2.5 cm, the bulk power absorption and ambipolar power absorption decreases, and the DA mode decays. When the gap reaches 3 cm, the α-mode becomes more prominent, and at a gap of 3.75 cm the α-mode is dominant. These mode transitions are caused by a change of the electronegativity and are found to affect the discharge characteristics. The presence of the DA-mode leads to significant positive electron power absorption inside the bulk region and negative power absorption within the sheaths on time average, as electrons are accelerated from the bulk towards the collapsed sheath. The heating mode transitions result in a change from negative to positive total electron power absorption within the sheaths as the gap increases. When accounting for secondary electron emission, the transition of the heating mode can occur at shorter gaps due to the enhanced plasma density and decreased electronegativity.

Energy efficient F atom generation and control in CF4 capacitively coupled plasmas driven by tailored voltage waveforms

Abstract Neutral radicals generated by electron impact dissociation of the background gas play important roles in etching and deposition processes in low pressure capacitively coupled plasmas (CCPs). The rate and energy efficiency of producing a given radical depend on the space- and time-dependent electron energy distribution function (EEDF) in the plasma, as well as the electron energy dependent cross sections of the electron-neutral collisions that result in the generation of the radical. For the case of a CCP operated in CF4 gas, we computationally demonstrate that the energy efficiency of generating neutral radicals, such as F atoms can be improved by controlling the EEDF by using tailored voltage waveforms (TVW) instead of single-frequency driving voltage waveforms and that separate control of the radical density and the ion energy can be realized by adjusting the waveform shape at constant peak-to-peak voltage. Such discharges are often used for industrial etching processes, in which the F atom density plays a crucial role for the etch rate. Different voltage waveform shapes, i.e. sinusoidal waveforms at low (13.56 MHz) and high (67.8 MHz) frequencies, peaks- and sawtooth-up TVWs, are used to study their effects on the energy cost / energy efficiency of F atom generation by PIC/MCC simulations combined with a stationary diffusion model. The F atom density is enhanced by increasing the voltage amplitude in the single frequency cases, while the energy cost per F atom generation increases, i.e. the energy efficiency decreases, because more power is dissipated to the ions, as the sheath voltages and the ion energy increase simultaneously. In contrast, using TVWs can result in a lower energy cost and provide separate control of the F atom density and the ion energy. This is explained by the fact that tailoring the waveform shape in this way allows to enhance the high-energy tail of the EEDF during the sheath expansion phase by inducing a non-sinusoidal sheath motion, which results in acceleration of more electrons to high enough energies to generate F atoms via electron-neutral collisions compared to the single frequency cases. Similar effects of TVWs are expected for the generation of other neutral radicals depending on the electron energy threshold and the specific consequences of TVWs on the EEDF under the discharge conditions of interest.

Resolving Photoinduced Femtosecond Three-Dimensional Solute-Solvent Dynamics through Surface Hopping Simulations.

Photoinduced dynamics in solution is governed by mutual solute-solvent interactions, which give rise to phenomena like solvatochromism, the Stokes shift, dual fluorescence, or charge transfer. Understanding these phenomena requires simulating the solute's photoinduced dynamics and simultaneously resolving the three-dimensional solvent distribution dynamics. If using trajectory surface hopping (TSH) to this aim, thousands of trajectories are required to adequately sample the time-dependent three-dimensional solvent distribution functions, and thus resolve the solvent dynamics with sub-Ångstrom and femtosecond accuracy and sufficiently low noise levels. Unfortunately, simulating thousands of trajectories with TSH in the framework of hybrid quantum mechanical/molecular mechanical (QM/MM) can be prohibitively expensive when employing ab initio electronic structure methods. To tackle this challenge, we recently introduced a computationally efficient approach that combines efficient linear vibronic coupling models with molecular mechanics (LVC/MM) via electrostatic embedding [Polonius et al., JCTC 2023, 19, 7171-7186]. This method provides solvent-embedded, nonadiabatically coupled potential energy surfaces while scaling similarly to MM force fields. Here, we employ TSH with LVC/MM to unravel the photoinduced dynamics of two small thiocarbonyl compounds solvated in water. We describe how to estimate the number of trajectories required to produce nearly noise-free three-dimensional solvent distribution functions and present an analysis based on approximately 10,000 trajectories propagated for 3 ps. In the electronic ground state, both molecules exhibit in-plane hydrogen bonds to the sulfur atom. Shortly after excitation, these bonds are broken and reform perpendicular to the molecular plane on timescales that differ by an order of magnitude due to steric effects. We also show that the solvent relaxation dynamics is coupled to the electronic dynamics, including intersystem crossing. These findings are relevant to advance the understanding of the coupled solute-solvent dynamics of solvated photoexcited molecules, e.g., biologically relevant thio-nucleobases.

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

This paper presents the development of a third-order compact gas-kinetic scheme (GKS) for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme utilizes a time-dependent gas distribution function at a cell interface to not only calculate the fluxes needed for updating the cell-averaged flow variables but also to evaluate the flow variables at the cell interface. This leads to the evolution of cell-averaged gradients of flow variables. The success of this scheme heavily relies on the initial data reconstruction techniques, with an emphasis on their application to the tetrahedral mesh. Employing a conventional second-order unlimited least-square reconstruction directly on the cell-averaged flow variables of von Neumann neighbouring cells can introduce linear instability into the scheme. However, by using the updated cell-averaged gradients, the GKS with a third-order compact smooth reconstruction remains linearly stable under a large CFL number when applied to a tetrahedral mesh. To enhance the robustness of the high-order compact GKS for capturing a discontinuous solution, we propose a novel two-step multi-resolution weighted essentially non-oscillatory (WENO) reconstruction. This innovative approach overcomes the stability issues associated with a second-order compact reconstruction by incorporating a pre-reconstruction step. Additionally, it simplifies the third-order non-linear reconstruction process by adding a single large stencil to those used in the second-order one. A high-order wall boundary condition is achieved by fusing the constrained least-square technique with the WENO procedure, where a quadratic element is used in the reconstruction for cells with a curved boundary. Numerical tests involving both the second-order and third-order compact GKS are presented, encompassing both inviscid and viscous flows at both low and high speeds. The results demonstrate that the proposed third-order compact scheme possesses robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.

A new hard x-ray spectrometer for runaway electron measurements in tokamaks

Runaway electron gamma-ray detection system, a novel hard x-ray (HXR) spectrometer optimized for bremsstrahlung radiation measurement from runaway electrons in fusion plasmas, has been developed. The detector is based on a 1‘×1’ LaBr3:Ce scintillator crystal coupled with a photomultiplier tube. The system has an energy dynamic range exceeding 20 MeV with an energy resolution of 3% at 661.7 keV. The detector gain is stable even under severe loads, with a gain shift that stays below 3% at HXR counting rates in excess of 1 MCps. The performance of the system enables unprecedented studies of the time-dependent runaway electron energy distribution function, as shown in recent runaway electron physics experiments at the ASDEX Upgrade and COMPASS tokamaks.

The Effects of Viscosity and Capillarity on Nonequilibrium Distribution of Gas Bubbles in Swelling Liquid–Gas Solution

A detailed statistical description of the evolution of supersaturated-by-gas solution at degassing has been presented on the basis of finding the time-dependent distribution in radii of overcritical gas bubbles. The influence of solution viscosity and capillarity via internal pressure in the bubbles on this distribution has been considered until the moment when the gas supersaturation drops due to depletion and stops nucleation of new overcritical gas bubbles. This study is based on our previous results for the nonstationary growth rates of overcritical bubbles depending on gas supersaturation, diffusivity and solubility in solution, solution viscosity, and surface tension on bubble surface. Other important factors are linked with the initial rate of homogeneous gas bubble nucleation and coupling between diffusivity and viscosity in the solution. Here, we numerically studied how all these factors affect the time-dependent distribution function of overcritical bubbles in their radii, maximal and mean bubble radii, and the time-dependent swelling ratio of a supersaturated-by-gas solution in a wide range of solution viscosities.

Time evolution of electron distributions to bimodal steady states for electrons dilutely dispersed in theinert gases Ar, Kr, and Xe with deep Ramsauer Townsend minima in themomentum transfer cross section

The current paper considers the thermalization of an ensemble of electrons under the influence of an external electric field and dilutely dispersed in one of the inert gas moderators, Argon, Krypton or Xenon for which the electron momentum transfer cross sections have deep Ramsauer-Townsend minima. As a consequence, the steady state electron distribution functions are bimodal over a small range of external electric field strengths. The current work is directed towards the time evolution of the electron distribution function determined from the numerical solution of the Fokker-Planck equation. The kinetic theory of electrons dilutely dispersed in a heat bath of atoms at temperature T b has a very long history. The solution of the Fokker-Planck equation can be expressed as a sum of exponentials of the form where λ n are the eigenvalues of the Fokker-Planck operator. Alternatively, a finite difference algorithm is used to solve the time dependent Fokker-Planck equation to give the time dependent electron energy distribution function. We demonstrate the evolution of the initial Maxwellian into a nonequilibrium bimodal distribution which cannot be rationalized with either the Gibbs-Boltzmann entropy or the Tsallis nonextensive entropy. Instead, the time dependent approach of an initial Maxwellian to the bimodal distribution is described in terms of the Kullback-Leibler entropy. We also demonstrate the inapplicability of the Boltzmann entropy nor the Tsallis entropy for a model system with a power law momentum transfer cross section of the form, σ(x) = σ 0/x p , where is the reduced speed. This model with p = 2 is also employed to demonstrate a steady-state Kappa distribution which features prominently in space physics and other fields. For p > 2, we show distribution functions that increase without bound analogous to runaway electrons. The steady nonequilibrium distributions are interpreted as solutions of a Pearson ordinary differential equation.

Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid

Crystallization of supercooled liquids is mainly determined by two competing processes associated with the transition of particles (atoms) from liquid phase to crystalline one and, vice versa, with the return of particles from crystalline phase to liquid one. The quantitative characteristics of these processes are the so-called attachment rate and the detachment rate , which determine how particles change their belonging from one phase to another. In the present study, a correspondence rule between the rates and as functions of the size N of growing crystalline nuclei is defined for the first time. In contrast to the well-known detailed balance condition, which relates and at (where n c is the critical nucleus size) and is satisfied only at the beginning of the nucleation regime, the found correspondence rule is fulfilled at all the main stages of crystallization kinetics (crystal nucleation, growth and coalescence). On the example of crystallizing supercooled Lennard–Jones liquid, the rate was calculated for the first time at different supercooling levels and for the wide range of nucleus sizes . It was found that for the whole range of nucleus sizes, the detachment rate is only % less than the attachment rate . This is direct evidence that the role of the processes that counteract crystallization remains significant at all the stages of crystallization. Based on the obtained results, a kinetic equation was formulated for the time-dependent distribution function of the nucleus sizes, that is an alternative to the well-known kinetic Becker–Döring–Zeldovich–Frenkel equation.

All-Atom Nonadiabatic Semiclassical Mapping Dynamics for Photoinduced Charge Transfer of Organic Photovoltaic Molecules in Explicit Solvents.

Direct all-atom simulation of nonadiabatic dynamics in disordered condensed phases like liquid solutions and amorphous solids has been challenging. The first all-atom simulation of the photoinduced charge-transfer dynamics of a prototypical organic photovoltaic carotenoid-porphyrin-C60 molecular triad in explicit tetrahydrofuran is presented. Based on the Meyer-Miller mapping Hamiltonian, various semiclassical and mixed quantum-classical dynamics are employed, including the linearized semiclassical, symmetrical quasiclassical, mean-field Ehrenfest, classical mapping model, and spin-mapping model approaches. The all-atom nonadiabatic dynamics were compared to multi-state harmonic models with a globally shared bath, and the models built using the ensemble averages on the initial electronic state could reproduce the all-atom results. The solvent effect was found to be critical for the photoinduced charge transfer, and the time-dependent solute-solvent radial distribution functions revealed that only the nonadiabatic dynamics started with the effective forces on the initial electronic state could capture the correct nuclear dynamics. The proposed strategy for modeling condensed-phase nonadiabatic dynamics with atomistic details is readily applied to complex condensed-phase systems.

Time-resolved electron energy distribution functions at the substrate during a HiPIMS discharge with cathode voltage reversal

The time-dependent plasma properties of a high-power impulse magnetron sputtering plasma are investigated which include a positive ‘kick’ pulse on the sputtering target 2 μs after the main negative pulse, this reversing the voltage on the cathode. At a substrate 15 cm distant from the magnetron, the time-dependent electron energy distribution function (EEDF), plasma potential, potential commute time and plasma diffusion properties are measured using a single Langmuir probe. Results show that the positive pulse on the target expels plasma and raises the plasma potential across the chamber on the order of 1 to 2 μs, which is the time scale of the electron diffusion. The EEDF at the substrate fits a Druyvesteyn distribution during the main negative pulse rising slightly in average energy over time. The distribution is still Druyvesteyn and at the very start of the positive pulse, but then loses the higher energy electrons and drops in average electron energy as the positive pulse progresses. A Boltzmann equation solver, BOLSIG+, was used to predict the EEDF at the substrate during the positive pulse and it agrees best with the measurements assuming a value of 0.2 Td for the E/N (electric field/gas number density).

Dynamics in condensed phase for systems involving phase functions obeying Gaussian statistics

The study of non-equilibrium processes in condensed phase has been fascinating and has attracted considerable attention of experimentalists as well as theoreticians during the last few decades. Since the theoretical treatment using Liouville equation involves multi-dimensional phase space functions, it is very difficult to visualize and also to obtain analytical expressions for the time-dependent distribution functions in Liouville space, which has led to formulation of various reduced space descriptions. The bottleneck in describing the non-equilibrium processes in the reduced space lies in the appearance of coupled velocity and position correlation functions in the equations, which are difficult to evaluate in general. In this work, we have developed a scheme to decouple the complicated multi-point coupled correlation function into two-point velocity and position correlation functions for situations characterized by a time-dependent phase function obeying Gaussian distribution, by making use of the Novikov's theorem. As an illustrative application, we have investigated the problem of optically controlled solvation dynamics and obtained exact expressions for the non-equilibrium solvation time correlation functions showing explicit dependence on the excitation frequency, as observed experimentally. We have shown that the linear response theory result is valid as long as the energy gap obeys the Gaussian distribution, rescuing the linear response theory based result from the domain of validity for small fluctuations in solvation coordinate.

Grad's distribution functions-based gas kinetic scheme for simulation of flows beyond Navier–Stokes level

Conventional gas kinetic scheme (GKS) has been successfully utilized to obtain the accurate solution of Navier–Stokes (NS) equations. However, when it comes to flows beyond NS level, the conventional GKS is not reliable because its initial gas distribution function is approximated by the first-order Chapman–Enskog expansion, which merely recovers the NS equations. In order to make an extension for flows beyond NS level, we propose the Grad's distribution functions-based GKS in this paper. This scheme retains the advantage of conventional GKS and constructs the numerical fluxes through a time-dependent gas distribution function, which is derived from the integral solution of Boltzmann equation. In the present scheme, the initial gas distribution function in the local solution of Boltzmann equation is approximated by Grad's 13 and 26 distribution functions. Furthermore, the high-order moments in the initial Grad's distribution function are calculated by moment relationship directly, and thus, the solution of complicated partial differential equations for these high-order moments is avoided. Four benchmark numerical examples are tested to validate the performance of the present scheme, and the results demonstrate that the present scheme can not only recover NS solutions in the continuum region but also predict reasonable results for flows in the slip and transition regimes.

A compact high-order gas-kinetic scheme on unstructured mesh for acoustic and shock wave computations

Following the development of a third-order compact gas-kinetic scheme (GKS) for the Euler and Navier-Stokes equations (Ji et al. (2020) [40]), in this paper a higher-order compact GKS up to sixth order of accuracy will be constructed for the shock and acoustic wave computation on unstructured mesh. The compactness is defined by the physical domain of dependence for an unstructured triangular cell, which may involve the closest neighbors of neighboring cells. The compactness and high-order accuracy of the scheme are coming from the consistency between the high-order initial reconstruction and the high-order gas evolution model under GKS framework. The high-order evolution solution at a cell interface provides not only a time-accurate flux function, but also the time-evolving flow variables. Therefore, the cell-averaged flow variables and their gradients can be explicitly updated at the next time level from the moments of the same time-dependent gas distribution function. Based on the cell averaged flow variables and their cell-averaged derivatives, the nonlinear high-order compact reconstruction can be obtained for these variables in the evaluation of local equilibrium and non-equilibrium states. The current nonlinear reconstruction is a combination of WENO and ENO methodology, which is specifically suitable for compact GKS on unstructured mesh with a high-order (≥4) accuracy. The initial piecewise discontinuous reconstruction is used for the determination of non-equilibrium state and an evolved smooth reconstruction for the equilibrium state. The evolution model in GKS is based on a relaxation process from non-equilibrium to equilibrium state. The time-accurate gas distribution function provides the Navier-Stokes (NS) flux function directly without separating the inviscid and viscous terms, which simplifies the numerical discretization of the NS equations directly on unstructured mesh. Based on the time-accurate flux solver, the two-stage fourth-order time discretization can be applied to get a fourth-order time-accurate solution with only two stages, which reduces two reconstructions in comparison with the same order Runge-Kutta time stepping method. The current high-order GKS can uniformly capture acoustic and shock waves without identifying troubled cells and implementing additional limiting procedure. In addition, the fourth- up to sixth-order compact GKS can use almost the same time step as a second-order shock capturing scheme in most flow problems. The fourth-order GKS on unstructured mesh will be used in the computations from low speed incompressible viscous flow to the high Mach number shock interaction. The accuracy, efficiency, and robustness of the scheme have been validated. The main conclusion of the paper is that beyond the first-order Riemann solver, the use of high-order gas evolution model seems have advantages in the development of high-order schemes.

Inferring time-dependent distribution functions from kinematic snapshots

ABSTRACT We propose a method for constructing the time-dependent phase space distribution function (DF) of a collisionless system from an isolated kinematic snapshot. In general, the problem of mapping a single snapshot to a time-dependent function is intractable. Here, we assume a finite series representation of the DF, constructed from the spectrum of the system’s Koopman operator. This reduces the original problem to one of mapping a kinematic snapshot to a discrete spectrum rather than to a time-dependent function. We implement this mapping with a convolutional neural network. The method is demonstrated on two example models: the quantum simple harmonic oscillator and a self-gravitating isothermal plane. The latter system exhibits phase space spiral structure similar to that observed in Gaia Data Release 2.

Realization of Self-Preserving Size Distribution Theory for the Evolution of Tropospheric Atmospheric Aerosols Through an Inverse Gaussian Distribution

AbstractThe inverse Gaussian distributed method of moments (IGDMOM; J. Atmospheric Sci. 77 (9): 3011-3031, 2020) was developed to analytically solve the kinetic collection equation (KCE) for the first time. Using the IGDMOM, we obtained both new analytical and asymptotic solutions to the KCE. This is shown for both the free molecular and continuum regime collision frequency functions. The new analytical solutions are highly suitable for demonstrating the self-preserving size distribution (SPSD) theory. The SPSD theory is considered one of the most elegant research works in atmospheric science for aerosols or small cloud droplets. It was initially discovered by Friedlander (J. Meteorology 17 (5): 479-483, 1960) and then developed by Lee (J. Colloid Interface Sci. 92 (2): 315-325, 1983) with an assumption of the time-dependent lognormal size distribution function. In this study, we demonstrate that the SPSD theory of coagulating atmospheric aerosols can be presented in a simpler and more rigorous theoretical way, which is realized through the introduction of the IGDMOM for describing aerosol size distributions. Using the IGDMOM, the new formulas for the SPSD, as well as the time required for aerosols to reach the SPSD, are analytically provided and verified. Furthermore, we discover that the SPSD of atmospheric aerosols undergoing coagulation is only determined using a shape factor variable, 𝛺, which is composed of the first three moments at an initial stage. This study has critical implications for developing tropospheric atmospheric aerosol or small cloud droplet dynamics models and further verifies the SPSD theory from the viewpoint of theoretical analysis.

Ultrafast formation of a transient two-dimensional diamondlike structure in twisted bilayer graphene

Due to the absence of matching carbon atoms at honeycomb centers with carbon atoms in adjacent graphene sheets, theorists predicted that a sliding process is needed to form AA, AB, or ABC stacking when directly converting graphite into sp3 bonded diamond. Here, using twisted bilayer graphene, which naturally provides AA and AB stacking configurations, we report the ultrafast formation of a transient 2D diamond-like structure (which is not observed in aligned graphene) under femtosecond laser irradiation. This photo-induced phase transition is evidenced by the appearance of new bond lengths of 1.94A and 3.14A in the time-dependent differential pair distribution function using MeV ultrafast electron diffraction. Molecular dynamics and first principles calculation indicate that sp3 bonds nucleate at AA and AB stacked areas in moire pattern. This work sheds light on the direct graphite-to-diamond transformation mechanism, which has not been fully understood for more than 60 years.

A HWENO reconstruction based high-order compact gas-kinetic scheme on unstructured mesh

As an extension of a fourth-order compact gas kinetic scheme (GKS) on structured mesh [24], this work is about the development of a third-order compact GKS on unstructured mesh for the compressible Euler and Navier-Stokes solutions. Based on the time accurate high-order gas-kinetic evolution solution, the time-dependent gas distribution function at a cell interface in GKS provides not only the flux function and its time derivative, but also the time accurate flow variables there at the next time level. As a result, besides updating the conservative flow variables inside each control volume through the interface fluxes, the cell averaged first-order spatial derivatives of flow variables can be obtained as well using the updated flow variables at the closed cell interfaces around that cell through the divergence theorem. Therefore, with the cell-averaged flow variables and their first-order spatial derivatives inside each cell, the Hermite WENO (HWENO) techniques can be naturally implemented for the compact high-order reconstruction at the beginning of the next time step. Following the reconstruction technique in [64], a new HWENO reconstruction on triangular mesh is designed in the current scheme. Combined with the two-stage temporal discretization and second-order time accurate flux function, a third-order compact scheme on unstructured mesh has been constructed. Accurate solutions can be obtained for both inviscid and viscous flows without sensitive dependence on the quality of triangular mesh. The robustness and accuracy of the scheme have been validated through many cases, including strong shocks in the hypersonic viscous flow and smooth Navier-Stokes solution.

Sub-nanosecond secondary geminate recombination in mercury halides HgX2 (X = I, Br) investigated by time-resolved x-ray scattering

In this work, we present a detailed investigation on the recombination dynamics of mercury halides HgX2 (X = I, Br) in acetonitrile solution after UV-induced photodissociation. The study is performed by combining time-resolved wide-angle x-ray scattering (TRWAXS) and optical transient absorption spectroscopy. Up to 68% of the UV (266 nm) photodissociated HgX and X radicals that escape the solvent cage surrounding parent HgX2 recombine within a nanosecond after photodissociation. In contrast to classical primary geminate recombination, occurring on much faster time scales, we interpret the sub-nanosecond recombination channel as secondary geminate recombination (SGR), also referred to as diffusion-limited geminate recombination. The family of triatomic mercury halides therefore represents an important class of molecules to study chemical mechanisms of solvent-dependent SGR by TRWAXS. The methodology described here allows for direct mapping of the time-dependent inter-radical distance distribution function, a critical parameter for the assessment of the SGR dynamics in solution phase and solvation in general.