Related papers: Study of a confined Hydrogen-like atom by the Asym…
In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphisation requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and…
Several well-known statistical measures similar to \emph{LMC} and \emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom in both position ($r$) and momentum ($p$) spaces. Further, a more generalized form of these…
Intraatomic orbital hybridization and interatomic bond formation are the two fundamental processes when real atoms are condensed to form matter. Artificial atoms mimic real atoms by demonstrating discrete energy levels attributable to…
Analytical solutions of the Bohr Hamiltonian are obtained in the $\gamma$-unstable case, as well as in an exactly separable rotational case with $\gamma\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for…
In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any…
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the…
The Field Ion Microscope (FIM) can be used to characterize the atomic configuration of the apex of sharp tips. These tips are well suited for Scanning Probe Microscopy (SPM) since they predetermine SPM resolution and electronic structure…
This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state…
We describe a method to perform a single quantum measurement of an arbitrary observable of a single ion moving in a harmonic potential. We illustrate the measurement procedure with explicit examples, namely the position and phase…
Atom interferometers provide exquisite measurements of the properties of non-inertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing.…
An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48). The solution is created by analytically continuing the divergent…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. Boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional…
In this paper, a hybrid quasi-static atomistic simulation method at finite temperature is developed, which combines the advantages of MD for thermal equilibrium and atomic-scale finite element method (AFEM) for efficient equilibration. Some…
We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away…
In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition…