Any ll-state solutions of the Hulth\'en potential by the asymptotic iteration method

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 $l$ states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different $\delta$ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.Comment: 14 pages and 1 figur

Network of Earthquakes and Recurrences Therein

We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Data pertaining to the California region has been used in the study. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. The distribution of recurrence lengths and recurrence times are analyzed subsequently to extract information about the complex dynamics. We find that the unimodal feature of recurrence lengths helps to associate typical rupture lengths with different magnitude earthquakes. The out-degree of the network shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws are also obtained with recurrence time distribution agreeing with the Omori law.Comment: 17 pages, 5 figure

An Improvement of the Asymptotic Iteration Method for Exactly Solvable Eigenvalue Problems

We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the Nikiforov--Uvarov methods, which both solve the second order linear ordinary differential equations analytically.Comment: RevTex4, 8 page

Dirac Equation with Spin Symmetry for the Modified P\"oschl-Teller Potential in DD-dimensions

We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov-Uvarov method and the two-component spinor wavefunctions are obtain are in terms of the Jacobi polynomials. It is found that there exist only positive-energy states for bound states under spin symmetry, and the energy levels increase with the dimension and the potential range parameter $\alpha$.Comment: 9 pages and 1tabl

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solutions within the framework of the position-dependent effective mass radial Klein-Gordon equation with the scalar and vector Hulth\'{e}n potentials in any arbitrary $D$ dimension and orbital angular momentum quantum numbers $l.$ The Nikiforov-Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave ($l=0$) are identical with the ones obtained in literature.Comment: 25 pages, 1 figur

Новые синонимичные ряды существительных в последнем издании международной анатомической номенклатуры

МЕДИЦИНСКАЯ ТЕРМИНОЛОГИЯ СИСТЕМАТИЗИРОВАННАЯЛИНГВИСТИКАСИНОНИМ

Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry

The energy spectra and the corresponding two- component spinor wavefunctions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The $s-$wave ($\kappa = 0$ state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wavefunctions for this potential and other special types of this potential are obtained. Extension of this result to $\kappa \neq 0$ state is suggested.Comment: 18 page

Mixed reality simulation of rasping procedure in artificial cervical disc replacement (ACDR) surgery

<p>Abstract</p> <p>Background</p> <p>Until quite recently spinal disorder problems in the U.S. have been operated by fusing cervical vertebrae instead of replacement of the cervical disc with an artificial disc. Cervical disc replacement is a recently approved procedure in the U.S. It is one of the most challenging surgical procedures in the medical field due to the deficiencies in available diagnostic tools and insufficient number of surgical practices For physicians and surgical instrument developers, it is critical to understand how to successfully deploy the new artificial disc replacement systems. Without proper understanding and practice of the deployment procedure, it is possible to injure the vertebral body. Mixed reality (MR) and virtual reality (VR) surgical simulators are becoming an indispensable part of physicians’ training, since they offer a risk free training environment. In this study, MR simulation framework and intricacies involved in the development of a MR simulator for the rasping procedure in artificial cervical disc replacement (ACDR) surgery are investigated. The major components that make up the MR surgical simulator with motion tracking system are addressed. </p> <p>Findings</p> <p>A mixed reality surgical simulator that targets rasping procedure in the artificial cervical disc replacement surgery with a VICON motion tracking system was developed. There were several challenges in the development of MR surgical simulator. First, the assembly of different hardware components for surgical simulation development that involves knowledge and application of interdisciplinary fields such as signal processing, computer vision and graphics, along with the design and placements of sensors etc . Second challenge was the creation of a physically correct model of the rasping procedure in order to attain critical forces. This challenge was handled with finite element modeling. The third challenge was minimization of error in mapping movements of an actor in real model to a virtual model in a process called registration. This issue was overcome by a two-way (virtual object to real domain and real domain to virtual object) semi-automatic registration method.</p> <p>Conclusions</p> <p>The applicability of the VICON MR setting for the ACDR surgical simulator is demonstrated. The main stream problems encountered in MR surgical simulator development are addressed. First, an effective environment for MR surgical development is constructed. Second, the strain and the stress intensities and critical forces are simulated under the various rasp instrument loadings with impacts that are applied on intervertebral surfaces of the anterior vertebrae throughout the rasping procedure. Third, two approaches are introduced to solve the registration problem in MR setting. Results show that our system creates an effective environment for surgical simulation development and solves tedious and time-consuming registration problems caused by misalignments. Further, the MR ACDR surgery simulator was tested by 5 different physicians who found that the MR simulator is effective enough to teach the anatomical details of cervical discs and to grasp the basics of the ACDR surgery and rasping procedure</p