Analytical Study of Reinforced Concrete Horizontally Curved Beam of Rectangular Hollow Section

This research is devoted to study the behavior of Horizontally Curved Reinforced Concrete Beam (HCRCB) of hollow and solid section theoretically by finite element method, the 20-node isoparametric brick element has been used to represent the concrete and the reinforcement idealized as an axial members imbedded within the concrete elements, a parametric study of 210 beams with different cross sections had been done included the effect of wall thickness, and the effect of flange depth on the behavior of HCRCB as well as two techniques of rearrangement the concrete in the hollow core to strengthen the beam. From the analytical results it was concluded that rearranging the core area improved the ultimate load capacity for beams with shear span to effective depth ratio (a/d) more than 2 and the effect is reversed for beams with (a/d) less than 2. Also the technique of adding the hollow core area to the top and bottom flange represent the optimal and produce the maximum increment in the ultimate load which equal to 57%. While the technique of adding the hollow core area to the outside perimeter produced 20% increase in the ultimate load. Keywords: Three Dimensional Analysis, Reinforced Concrete Horizontally Curved Beam, Hollow Sectio

Two approximate formulae for the binding energies in Lambda hypernuclei and light nuclei

Two approximate formulae are given for the binding energies in Lambda-hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller and the Gaussian central potentials. Those easily programmable formulae combine the eigenvalues of the transformed Jacobi eigenequation and an application of the hypervirial theorems.Comment: Accepted for publication in Europhysics Letter

Variational collocation for systems of coupled anharmonic oscillators

We have applied a collocation approach to obtain the numerical solution to the stationary Schr\"odinger equation for systems of coupled oscillators. The dependence of the discretized Hamiltonian on scale and angle parameters is exploited to obtain optimal convergence to the exact results. A careful comparison with results taken from the literature is performed, showing the advantages of the present approach.Comment: 14 pages, 10 table

Renormalization--Group Solutions for Yukawa Potential

The self--similar renormalization group is used to obtain expressions for the spectrum of the Hamiltonian with the Yukawa potential. The critical screening parameter above which there are no bound states is also obtained by this method. The approach presented illustrates that one can achieve good accuracy without involving extensive numerical calculations, but invoking instead the renormalization--group techniques.Comment: 1 file, 12 pages, RevTe

Accurate energy spectrum for double-well potential: periodic basis

We present a variational study of employing the trigonometric basis functions satisfying periodic boundary condition for the accurate calculation of eigenvalues and eigenfunctions of quartic double-well oscillators. Contrary to usual Dirichlet boundary condition, imposing periodic boundary condition on the basis functions results in the existence of an inflection point with vanishing curvature in the graph of the energy versus the domain of the variable. We show that this boundary condition results in a higher accuracy in comparison to Dirichlet boundary condition. This is due to the fact that the periodic basis functions are not necessarily forced to vanish at the boundaries and can properly fit themselves to the exact solutions.Comment: 15 pages, 5 figures, to appear in Molecular Physic

Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well--established method based on a power--series expansions weighted by a Gaussian factor with an adjustable parameter (the so--called Hill--determinant method)

Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential functionV(x,y,z;Z2, λ,β)= ?Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calculations using this expansion and the Hill-determinant approach are reported for a large class of potential functions and for various values of the perturbation parametersZ2, λ, and β. PACS No.:03.6

Stable forward shooting for eigenvalues and expectation values

Internal differentiation techniques are used to produce a simple but highly accurate forwardsshootingmethod foreigenvaluesandexpectationvaluesof the Schrödinger equation. A multi-well potential is used as a test case