Spherical Box Research Articles

A New Ray Casting Algorithm Based on an Adjustable Threshold and Error Controlling

Volume rendering is an important visualization technique that can accurately display the interior information of data. The Ray-casting algorithm is simple and easy to realize, which often apply to area needs high quality resulting image. The new algorithm in this paper uses a spherical bounding box to remove useless rays, an adjustable threshold to skip the empty voxels and avoid unnecessary interpolation computing. To further accelerate the rendering speed, an adjustable error is set to change interpolation types. Experiment proves that the new algorithm effectively accelerates the rendering speed and guarantees the rendering quality.

Perturbation theory for confined systems

We discuss the application of perturbation theory to a system of particles confined in a spherical box. A simple argument shows that the particles behave almost independently in sufficiently strong confinement. We choose the helium atom with a moving nucleus as a particular example and compare results of first order with those for the nucleus clamped at the center of the box. We provide a suitable explanation for some numerical results obtained recently by other authors.

Quantum confinement under Neumann condition: Atomic H filled in a lattice of cavities

Energy spectrums of a nonrelativistic particle and an H-like atom in a spherical box of size R with general conditions of “not going out” through the box surface are explored. The lowest energy levels reconstruction is described from the point of view of their asymptotical behavior for large R. The role of von Neumann–Wigner level reflection/avoided crossing effect in this spectrum reconstruction is emphasized. The properties of atomic H ground state in a cell, formed by a spherical cavity with an outer potential shell and Neumann condition on the outward boundary, are studied in detail. Some of them turn out to be quite new. The relevance of such a cell to a cubic lattice of cavities, occupied by H, is discussed be means of first principles and assumptions of the Wigner–Seitz model.

Shannon and Fisher entropies for a hydrogen atom under soft spherical confinement

Abstract We calculate Shannon and Fisher entropies in the position and momentum space, and some complexity measures for a variationally described hydrogen atom confined in soft and hard spherical boxes of varying dimension r c and selected values of strength U 0 . We include calculations for a free particle trapped in impenetrable boxes. It is found that the Shannon entropy S r becomes negative for small cavity radii and large values of U 0 , due to the highly localized nature of the particle. For soft confinement and small cavity dimensions, the entropies change very rapidly over short radial intervals.

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

Abstract The ground state energy, some low-lying excited state energies and oscillator strengths for a hydrogen atom confined in both a Debye screening potential and finite impenetrable spherical box have been calculated. These have been calculated using a linear variational method based on B-spline basis functions. The results have been compared with those of other authors. The evaluated energies and oscillator strengths with respect to different plasma screening parameters with a certain confinement radii are discussed.

Evaluating dot–lead coupling in a non-parabolic quantum dot connected to two conducting leads

A manifestly novel approach is developed by considering excitons in a semiconductor non-parabolic quantum dot as hydrogen-atom-like quasi-particles confined in a spherical quantum box, the dot being connected to two conducting leads. In fact, the maximal dot–lead coupling energy is calculated in terms of maximum Fermi velocity within a new perspective.

Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems indDimensions

It is shown that the spanning set forL2([0,1])provided by the eigenfunctions{2sin(nπx)}n=1∞of the particle in a box in quantum mechanics provides a very effective variational basis for more general problems. The basis is scaled to[a,b], whereaandbare then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box inRdturns out to be appropriate also for problems that are softly confined byU-shaped potentials, including those with strong singularities atr=0. Specific examples are discussed in detail, along with some boundN-boson systems.

Unusually kicked dynamics: Hydrogen atom in a spherical box

Abstract In this paper we have examined the ionization of the ground state hydrogen atom in a spherical box with laser pulses of specific shapes. These shapes are predicted assuming correspondence under some conditions with the alternating kicking field. Unusually kicked dynamics is suggested. It is shown that such kicked dynamics leads to generalized Rabi oscillations with the positive energy states included and participation of the excited states. The correspondence with the real pulse is established emphasizing such unusually kicked dynamics. The approach is verified on the one-dimensional (1D) hydrogen atom and calculation of the known results for ionization probability.

EVALUATING DOT-LEAD COUPLING IN A NONPARABOLIC QUANTUM DOT CONNECTED TO TWO CONDUCTING LEADS

By considering excitons in a semiconductor nonparabolic quantum dot as hydrogen-atom-like quasi-particles confined in a spherical quantum box, the dot being connected to two semi-infinite conducting leads, we propose a theoretical-analytical approach by which the maximal dot-lead coupling energy is calculated in terms of the maximum Fermi velocity. In addition, numerical computations consistent with the above approach are carried out. Our results constitute a deep insight into the state of the art and agree with experimental data.

Dipole polarizabilities for a hydrogen atom confined in a penetrable sphere

Benchmark numerical results on the ground and excited state eigenvalues and the ground state static and dynamic dipole polarizabilities are reported for a hydrogen atom confined at the center of a spherical box with penetrable walls. The dynamic polarizabilities are negative except when the frequency of incident radiation is below the 1s–2p transition frequency or in the frequencies immediately below a 1s–np transition.

Application of variational Monte Carlo method to the confined helium atom

A new application of variational Monte Carlo method is presented to study the helium atom under the compression effect of a spherical box with radius (rc). The ground-state energies of the helium atom were calculated for different values of rc. Our calculations were extended to include Li + and Be 2+ ions. The calculations were based on the use of a compact accurate trial wave function with five variational parameters. To optimize variational parameters, we used the steepest descent method. The obtained results are in good agreement with previous results.

Generalization of the collision cone approach for motion safety in 3-D environments

Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.

Shell structure and orbit bifurcations in finite fermion systems

We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the “periodic orbit theory”. We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called “superdeformed” energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).

Discrete spectra for confined and unconfined −a/r + br2 potentials in d-dimensions

Exact solutions to the d-dimensional Schrödinger equation, d ⩾ 2, for Coulomb plus harmonic oscillator potentials V(r) = −a/r + br2, b > 0, and a ≠ 0 are obtained. The potential V(r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical box of radius R. With the aid of the asymptotic iteration method, the exact analytic solutions under certain constraints, and general approximate solutions, are obtained. These exhibit the parametric dependence of the eigenenergies on a, b, and R. The wave functions have the simple form of a product of a power function, an exponential function, and a polynomial. Polynomial solutions are found for differential equations of the form py″ + qy′ − ry = 0, where p, q, and r are given polynomials with degrees 4, 3, and 2, respectively.

Stochastic global optimization for robust point set registration

In this paper, we propose a new algorithm for pairwise rigid point set registration with unknown point correspondences. The main properties of our method are noise robustness, outlier resistance and global optimal alignment. The problem of registering two point clouds is converted to a minimization of a nonlinear cost function. We propose a new cost function based on an inverse distance kernel that significantly reduces the impact of noise and outliers. In order to achieve a global optimal registration without the need of any initial alignment, we develop a new stochastic approach for global minimization. It is an adaptive sampling method which uses a generalized BSP tree and allows for minimizing nonlinear scalar fields over complex shaped search spaces like, e.g., the space of rotations. We introduce a new technique for a hierarchical decomposition of the rotation space in disjoint equally sized parts called spherical boxes. Furthermore, a procedure for uniform point sampling from spherical boxes is presented. Tests on a variety of point sets show that the proposed registration method performs very well on noisy, outlier corrupted and incomplete data. For comparison, we report how two state-of-the-art registration algorithms perform on the same data sets.

Efficiency of random search procedures along the silicon cluster series: Sin (n = 5–10, 15, and 20)

The efficiency of the simplest isomeric search procedure consisting in random generation of sets of atomic coordinates followed by density functional theory geometry optimization is tested on the silicon cluster series (Si(5-10, 15, 20)). Criteria such as yield, isomer distributions and recurrences are used to clearly establish the performance of the approach with respect to increasing cluster size. The elimination of unphysical candidate structures and the use of distinct box shapes and theoretical levels are also investigated. For the smaller Si(n) (n=5-10) clusters, the generation of random coordinates within a spherical box is found to offer a reasonable alternative to more complex algorithms by allowing straightforward identification of every known low-lying local minima. The simple stochastic search of larger clusters (i.e. Si(15) and Si(20)) is however complicated by the exponentially increasing number of both low- and high-lying minima leading to rather arbitrary and non-comprehensive results.

Variational approach to the confined hydrogen atom with a moving nucleus

AbstractWe calculate the ground‐state energy and other physical properties of the hydrogen atom inside a spherical box with an impenetrable wall. We apply the variational method and show that the total, kinetic, and potential energies for the moving nucleus model are greater than those for the case in which the nucleus is clamped at the box center. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

On the variation of polarizability and hyperpolarizability of a confined atom with the strength of confinement: a case study of a helium atom

This paper is devoted to the study of variation of linear polarizability and nonlinear hyperpolarizability of a helium atom confined in an impenetrable spherical box with the strength of confinement. The calculation of polarizability and hyperpolarizabilities has been performed within density-functional theory (DFT). The ground-state densities required to carry out calculation of response properties have also been obtained by employing a variational approach within DFT. We find that polarizability decreases monotonically with decreasing confinement radius and interestingly the hyperpolarizability not only decreases but also undergoes a change of sign in the strong confinement regime.

A tale of two electrons: Correlation at high density

We review our recent progress in the determination of the high-density correlation energy E c in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke’s law atom (hookium). We also present results regarding two electrons on the surface of a sphere (spherium), and two electrons trapped in a spherical box (ballium). We also show that, in the large-dimension limit, the high-density correlation energy of two opposite-spin electrons interacting via a Coulomb potential is given by E c ∼ - 1 / ( 8 D 2 ) for any radial external potential V ( r ) , where D is the dimensionality of the space. This result explains the similarity of E c in the previous two-electron systems for D = 3 .

Linear and nonlinear electric properties of spatially confined LiH molecule, studied with the finite field method

The influence of spatial confinement on the electric properties: dipole moment ( μ), dipole polarizability ( α), first hyperpolarizability ( β) and second hyperpolarizability ( γ) of the LiH molecule was studied. The confining model potential is assumed in the form of a penetrable spherical box. The properties in question were calculated within the finite field approach, with an accurate, explicitly correlated wave function. We found all studied properties diminished under confinement.