Kinetic equation for the processes of local reorganization of molecular systems with charged species

A molecular dynamic theory based on the lattice-gas model for the local reorganization of multi-component systems containing charged species is considered. Expressions for the mono- and bimolecular stages of the elementary processes that describe chemical reactions and displacements and rotations of molecules in dense gases and liquids are derived, with consideration given to direct and indirect effects of the initiation of electron and proton transfer. The proposed kinetic equations describe small-scale restructuring of solutions containing components of different sizes under the influence of changes in the external parameters of the molecular system at the kinetic stage of evolution of the system. The theory retains the effects of direct spatial correlations in the distribution of all the components of the mixture with the help of pair distribution functions in the quasi-chemical approximation. The dynamics of the local reorganization of molecules includes the kinetic equations for the local densities and pair distribution functions. The equations derived are intended to describe liquid-phase reactions, ion charge exchange, mutual diffusion of components of different sizes in multicomponent solutions, extraction processes at liquid phase boundaries, and photochemical processes in condensed phases.     

Kinetic equations for non-Markovian processes with pearson distributions

Using orthogonal expansions of conventional probability densities, we obtain analytical expressions for the coefficients of kinetic equations describing non-Markovian processes with Pearson distributions.State Radioengineering Academy, Ryazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 7, pp. 695–704, July, 1995.     

Kinetic coefficients in the direct equations for nondifferential processes with aftereffect

Radiophysics and Quantum Electronics -     

Kinetic equations and nanocrystal growth in molecular beam epitaxy methods

The processes of nucleation and growth of GaN, Ge, and InAs nanoclusters in molecular beam epitaxy (conventional and nitrogen-ion-assisted) have been investigated by computer simulation methods. Physical models are proposed to explain the regularities of nanostructure evolution, depending on the epitaxy conditions. The role of nitrogen-ion irradiation, leading to radical changes in the epitaxial growth regime, is revealed.     

Kinetic equations for dense fluids

It is demonstrated that the kinetic equation of Davis's effective potential theory follows directly from the application of well-defined approximations to the three-body correlations involved in the second equation of the BBGKY hierarchy. The same, simple mathematical techniques involved in this demonstration are used to derive two other kinetic equations, one of which is a generalization to high densities of the Boltzmann equation. In order to facilitate its application to the calculation of the van Hove and other correlation functions, the kinetic equation of the effective potential theory is Fourier-Laplace transformed: explicit formulae are given for the matrix elements of all operators that occur in this equation.     

Faddeev-Born-Oppenheimer equations for molecular three-body systems: Adiabatic calculation of 9Be

The low-lying states of ⁹Be are calculated in the α-particle cluster model. The calculation is performed using a rotationally invariant molecular formulation of the three-body problem based on the Faddeev equations, which are solved for the α + n + α system in the adiabatic limit with the α-α interaction turned off. The resulting two-centre wave function is used to formulate an ansatz for the solution of the full hamiltonian of the system where all three particles interact. Unlike the traditional molecular approach, the ansatz we propose allows for the coupling between the movement of the light particle and the rotational motion of the heavy particles. This leads to a set of coupled ordinary differential equations for the three-body wave function that has good total angular momentum and parity. Although only one Born-Oppenheimer molecular energy curve is considered, all adiabatic corrections due to Coriolis coupling effects, mass polarization and derivatives of the two-centre wave function with respect to the separation distance between the α-particles are taken into account. Comparison with exact Faddeev results is presented for the ground-state energies of ⁹Be in a model problem where the α-α interaction is turned off. The validity of the molecular approach for small mass ratios between the heavy particle and the light particle is studied in a very general framework.     

Kinetic equations with soluble moment equations

If the moments of the kernel in a kinetic equation are polynomials, then the moment equations have a symmetry property, which permits the general solution in the form of a Laguerre series, and its coefficients (Laguerre moments) satisfy the same equations as the ordinary moments.     

Master equations for subordinated processes

We study Markov jump processes constructed by subordination of diffusion processes. The procedure can be viewed as a randomization or a coarse graining of time. We construct the master equation for the cases of finite and infinite total jump rates, and give a collection of explicitly solvable examples.     

Orthogonality properties of the coupled equations for rearrangement collisions

The orthogonality properties required for a rigorous formulation of the coupled equations method for reactions involving particle exchanges and rearrangements are presented without the explicit use of multichannel projection operators.     

Asymmetric systems described by a pair of local covariant wave equations

We obtain a class of asymmetric solutions of the integrability conditions for systems obeying the Leutwyler-Stern pair of covariant wave equations. The class of unequal-mass systems described by these solutions does not embed the particle-antiparticle system behaving as a relativistic harmonic oscillator.     

Kinetic energy functionals for molecular calculations

The orbitals and eigenvalues of a Kohn-Sham density functional theory calculation can be used to determine the kinetic potential, the functional derivative of the non-interacting kinetic energy. Thus, approproximate kinetic energy functionals can be systematically parameterized to improve their functional derivatives. Fitting procedures have been applied to various functional forms and the quality of the resulting functionals investigated using variationally optimized densities. The best functionals include the full correction of Weizsäcker and a modulation of the Thomas-Fermi p^5/3 term by a function of the distance from the nucleus. These atom-specific functionals predict virtually exact shell structure, and may be combined readily into a functional which supports molecular binding.     

Kinetic equations for autocorrelation functions in dilute gases

We show that in the case of a dilute gas of neutral particles kinetic equations for autocorrelation functions such as $$\left\langle {\hat f\left( {r,v,t} \right)\hat f\left( {r\prime v\prime ,t\prime } \right)} \right\rangle ,where\hat f\left( {r,v,t} \right) = \sum {_{i = 1}^N } \delta \left( {r - r_i \left( t \right)} \right)\delta \left( {v - v_i \left( {tt} \right)} \right)$$ , can be obtained in a very simple manner by the use of the truncated BBGKY hierarchy. The resulting equations correspond to the low-density limit of the results of van Leeuwen and Yip. Moreover, the derivation does not make use of the Bogoliubov adiabatic approximation, and therefore includes non-Markovian effects which can be important in describing light scattering from gases and the collisional narrowing of atomic dipole radiation. The resulting equations in the long-wavelength limit correspond to the non-Markovian Boltzmann equation for the self-correlation part and the non-Markovian, linearized Boltzmann equation for the total autocorrelation function.