Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

A Variational Approach to the Burridge-Knopoff Equation

A variational principle is obtained for the Burridge-Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation.

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method.

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.

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.

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).

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.

Research on the influence of fabrication parameters on the performance of buried ion-exchanged glass waveguides using the variational method

The variational method is proposed to analyze the influence of the fabrication parameters on the performance of buried K+-Na+ ion-exchanged Er3+-Yb3+ ions co-doped glass waveguide. The unknown parameters of the Hermite-Gaussian functions as the trial field distribution are determined based on the scalar variational principle. It is demonstrated that the results calculated in this paper agree with those measured in the experiment. The mode dimensions, the effective refractive index, and the overlap factor as the functions of the fabrication parameters are investigated. These results of the variational analysis are useful for the design and optimization of Er3+-Yb3+ ions co-doped waveguides.

Variational calculations of neutral bound excitons in GaAs quantum-well wires

The binding energy of an exciton bound to a neutral donor (D-0,X) in GaAs quantum-well wires is calculated variationally as a function of the wire width for different positions of the impurity inside the wire by using a two-parameter wavefunction. There is no artificial parameter added in our calculation. The results we have obtained show that the binding energies are closely correlated to the sizes of the wire, the impurity position, and also that their magnitudes are greater than those in the two-dimensional quantum wells compared. In addition, we also calculate the average interparticle distance as a function of the wire width. The results are discussed in detail.

Exact quantum master equation via the calculus on path integrals

An exact quantum master equation formalism is constructed for the efficient evaluation of quantum non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. A novel truncation scheme is further proposed and compared with other approaches to close the resulting hierarchically coupled equations of motion. The interplay between system-bath interaction strength, non-Markovian property, and required level of hierarchy is also demonstrated with the aid of simple spin-boson systems. (C) 2005 American Institute of Physics.

Variational calculations of ionized-donor-bound excitons in GaAs-AlxGa1-xAs quantum wells

Using a two-parameter wave function, we calculate variationally the binding energy of an exciton bound to an ionized donor impurity (D+,X) in GaAs-AlxGa1-xAs quantum wells for the values of the well width from 10 to 300 Angstrom, when the dopant is located in the center of the well and at the edge of the well. The theoretical results confirm that the previous experimental speculation proposed by Reynolds tit al. [Phys. Rev. B 40, 6210 (1989)] is the binding energy of D+,X for the dopant at the edge of the well. in addition, we also calculate the center-of-mass wave function of the exciton and the average interparticle distances. The results are discussed in detail.

An automata theoretic decision procedure for the propositional mu-calculus

The propositional mu-calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of Fischer and Ladner, the infinite looping construct of Streett, and the game logic of Parikh. We give an elementary time decision procedure, using a reduction to the emptiness problem for automata on infinite trees. A small model theorem is obtained as a corollary.