A simple expansion method for numerically calculating the energy levels and the corresponding wave functions of a quantum particle in a two-dimensional infinite potential well with arbitrary shape ~quantum billiard! is presented. The method permits the study of quantum billiards in an introductory quantum mechanics course. According to the method, wave functions inside the billiard are expresse...

in this paper, two dimensional natural convection heat transfer in non-square cavities such as triangle, trapezoid, quadrant-circle and semi-circular are investigated via lattice boltzmann method. the prandtl number is taken as 0.71 that corresponds to that of air. the results show that, when the flow pattern consists of two rotating cell, there is a extremum point in the variations of the loca...

We compute accurately the golden critical invariant circles of several area-preserving twist maps of the cylinder. We define some functions related to the invariant circle and to the dynamics of the map restricted to the circle (for example, the conjugacy between the circle map giving the dynamics on the invariant circle and a rigid rotation on the circle). The global Hölder regularities of the...

A new star recognition method based on the Adaptive Ant Colony (AAC) algorithm has been developed to increase the star recognition speed and success rate for star sensors. This method draws circles, with the center of each one being a bright star point and the radius being a special angular distance, and uses the parallel processing ability of the AAC algorithm to calculate the angular distance...

We compare two established and a new method for the calculation of spectral bounds for Hessian matrices on hyperrectangles by applying them to a large collection of 1522 objective and constraint functions extracted from benchmark global optimization problems. Both the tightness of the spectral bounds and the computational effort of the three methods, which apply to C2 functions φ : R → R that c...