Quantum and variational monte-carlo interaction potentials for li2 (x1-sigma-g+)

Optimized trial functions are used in quantum Monte Carlo and variational Monte Carlo calculations of the Li₂(X ¹Σ⁺_g) potential curve. The trial functions used are a product of a Slater determinant of molecular orbitals multiplied by correlation functions of electron—nuclear and electron—electron separation. The parameters of the determinant and correlation functions are optimized simultaneously by reducing the deviations of the local energy E_L (E_L  Ψ⁻¹_THΨ_T, where Ψ_T denotes a trial function) over a fixed sample. At the equilibrium separation, the variational Monte Carlo and quantum Monte Carlo methods recover 68% and 98% of the correlation energy, respectively. At other points on the curves, these methods yield similar accuracies.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

Adiabatic compression of plasma with purely toroidal rotation

A variational method is developed to find approximate solutions to the generalized Grad-Shafranov equations for an adiabatic compression of the plasma with toroidal rotation, via the expansion in Fourier series in poloidal angle of the flux surface coordinates. The numerical results, which are carried out by the present method and by the usual two-dimensional method for a static equilibrium state, agree well.

Variational method for adiabatic compression of plasma with poloidal and toroidal rotation

A variational method is developed for adiabatic compression of plasma with both poloidal and toroidal rotation.

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

The dynamical process of a coronal transient associated with an eruptive prominence .2. Analytical solutions in finite regions

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An application of adjoint variational method to the capillary instability in liquid

In this paper, applying the direct variational approach of first-order approximation to the capillary instability problem for the eases of rotating liquid column, toroid and films on both sides of cylinder, we have obtained the necessary and sufficient conditions for motion stability of the "cylindrical coreliquid-liquid-cylindrical shell" systems. The results obtained before are found to be special cases of the present investigation. At the same time, we have explained physical essence of rotating instability and settled a few disputes in previous investigations.

Exact solutions to collisionless external gas flows

This paper presents exact density, velocity and temperature solutions for two problems of collisionless gas flows around a flat plate or a spherical object. At any point off the object, the local velocity distribution function consists of two pieces of Maxwellian distributions: one for the free stream which is characterized by free stream density, temperature and average velocity, n0, T0, U0; and the other is for the wall and it is characterized by density at wall and wall temperature, nw,Tw. Directly integrating the distribution functions leads to complex but exact flowfield solutions. To validate these solutions, we perform numerical simulations with the direct simulation Monte Carlo (DSMC) method. In general, the analytical and numerical results are virtually identical. The evaluation of these analytical solutions only requires less than one minute while the DSMC simulations require several days.

Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].