Spinless particles in screened Coulomb potential

We have obtained the analytic solutions of a relativistic spinless particle in a one-dimensional screened Coulomb potential and illustrate the existence of several genuine bound states. We also address the non-relativistic problem for the same potential and compare the energy spectra in the two cases. Comparisons with the results using the one-dimensional Dirac equation are also made. Numerical computations are done using Mathematica. © 2002 Elsevier Science B.V. All rights reserved

Eigenfunctions of spinless particles in a one-dimensional linear potential well

In the present paper, we work out the eigenfunctions of spinless particles bound in a one-dimensional linear finite range, attractive potential well, treating it as a time-like component of a four-vector. We show that the one-dimensional stationary Klein-Gordon equation is reduced to a standard differential equation, whose solutions, consistent with the boundary conditions, are the parabolic cylinder functions, which further reduce to the wellknown confluent hypergeometric functions. © Electronic Journal of Theoretical Physics. All rights reserved

Klein Paradox for bound states - A puzzling phenomenon

While Klien paradox is often encountered in the context of scattering of relativistic particles at a potential barrier,we presently discuss a puzzling situation that arises with the Klien-Gordon equation for bound states. With the usual minimal coupling procedure of introducing the interaction potential, a paradoxical situation results when the "hill" becomes a "well" ,simulating a bound state like situation.This phenomenal phenomenon for bound states is contrary to the convectional wisdom of quantum mechanics and is analogous to the well-known Klien paradox,a generic property of relativistic wave equation

Energy profile of the one-dimensional Klein–Gordon oscillator

In the present paper, we describe a method of introducing the harmonic oscillator potential into the Klein–Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly

Current Practices in Structural Analysis and Testing of Aero-Engine Main Shafts

AbstractGas turbine engines are widely used in both Military and Civil Aircrafts. The power generated at the turbine is transmitted to compressor through Engine main shafts. These shafts are classified as Class-I critical components of the engine. During the flight operating conditions engine main shafts are subjected to complex loading conditions, such as Torsional, Centrifugal, Thermal, Gyroscopic etc… The combination of these loads lead to multimode failure mechanisms, such as Low cycle Fatigue (LCF), High cycle Fatigue (HCF) and Ductile overload failures in shafts. Designing of shafts for structural integrity is very critical in single engine aircrafts, as the failure of any one shaft may result in the failure of engine, which in turn may lead to the catastrophic failure of the entire aircraft. The complex geometry of the shafts calls for combination of design tools for stress and life estimation of these parts (both analytical and finite element method (FEM)) backed up by extensive material and component test programs. In the present paper structural analysis and life estimation is carried out on Low Pressure Spool and Spline Coupling under various engine operating conditions. The design analysis cycle consists of several phases, such as Heat Transfer Analysis, Structural Analysis, Optimization and Fatigue Lifing. Detailed modeling and stress analysis carried out to evaluate the strength of the splines is also presented. This paper highlights the methodology of design subjected to clearance of stipulated MIL 5007 D/E specifications to ensure the structural integrity. Based on the stress analysis, a Stress Test Schedule is prepared to carry-out the testing at shaft fatigue rig facility. In the testing facility, mechanical testing of the shaft assembly is carried out to establish strength and fatigue life of the shafts. Brief results on the material tests carried out and fatigue life testing of full scale component are also presented

Simultaneous solution of Kompaneets equation and Radiative Transfer equation in the photon energy range 1 - 125 KeV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 KeV photon energy range. Diffuse radiation field is calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms $n, n^2$ and $\displaystyle \bigg({\frac {\partial n}{\partial x_k}}\bigg)$ where $n$ is photon phase density and $\displaystyle x_k= \bigg({\frac {h \nu} {k T_e}} \bigg)$, in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation $I^{MB}$ [1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at $\tau=0$ and reflected radiation $\tau=\tau_{max}$ are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.Comment: 31 pages, 8 figures, Accepte

Hydraulic jumps: Turbulence and air bubble entrainment

A free-surface flow can change from a supercritical to subcritical flow with a strong dissipative phenomenon called a hydraulic jump. Herein the progress and development in turbulent hydraulic jumps are reviewed with a focus on hydraulic jumps operating at large Reynolds numbers typically encountered in natural streams and hydraulic structures. The key features of the turbulent hydraulic jumps are the highly turbulent flow motion associated with some intense air bubble entrainment at the jump toe. The state-of-the-art on the topic is discussed based upon recent theoretical analyses and physical data

Comparison of 3He and129Xe MRI for evaluation of lung microstructure and ventilation at 1.5T

BACKGROUND: To support translational lung MRI research with hyperpolarized129Xe gas, comprehensive evaluation of derived quantitative lung function measures against established measures from3He MRI is required. Few comparative studies have been performed to date, only at 3T, and multisession repeatability of129Xe functional metrics have not been reported. PURPOSE/HYPOTHESIS: To compare hyperpolarized129Xe and3He MRI-derived quantitative metrics of lung ventilation and microstructure, and their repeatability, at 1.5T. STUDY TYPE: Retrospective. POPULATION: Fourteen healthy nonsmokers (HN), five exsmokers (ES), five patients with chronic obstructive pulmonary disease (COPD), and 16 patients with nonsmall-cell lung cancer (NSCLC). FIELD STRENGTH/SEQUENCE: 1.5T. NSCLC, COPD patients and selected HN subjects underwent 3D balanced steady-state free-precession lung ventilation MRI using both3He and129Xe. Selected HN, all ES, and COPD patients underwent 2D multislice spoiled gradient-echo diffusion-weighted lung MRI using both hyperpolarized gas nuclei. ASSESSMENT: Ventilated volume percentages (VV%) and mean apparent diffusion coefficients (ADC) were derived from imaging. COPD patients performed the whole MR protocol in four separate scan sessions to assess repeatability. Same-day pulmonary function tests were performed. STATISTICAL TESTS: Intermetric correlations: Spearman's coefficient. Intergroup/internuclei differences: analysis of variance / Wilcoxon's signed rank. Repeatability: coefficient of variation (CV), intraclass correlation (ICC) coefficient. RESULTS: A significant positive correlation between3He and129Xe VV% was observed (r = 0.860, P < 0.001). VV% was larger for3He than129Xe (P = 0.001); average bias, 8.79%. A strong correlation between mean3He and129Xe ADC was obtained (r = 0.922, P < 0.001). MR parameters exhibited good correlations with pulmonary function tests. In COPD patients, mean CV of3He and129Xe VV% was 4.08% and 13.01%, respectively, with ICC coefficients of 0.541 (P = 0.061) and 0.458 (P = 0.095). Mean3He and129Xe ADC values were highly repeatable (mean CV: 2.98%, 2.77%, respectively; ICC: 0.995, P < 0.001; 0.936, P < 0.001). DATA CONCLUSION:129Xe lung MRI provides near-equivalent information to3He for quantitative lung ventilation and microstructural MRI at 1.5T. LEVEL OF EVIDENCE: 3 Technical Efficacy Stage

Bubble Entrainment, Spray and Splashing at Hydraulic Jumps

The sudden transition from a high-velocity, supercritical open channel flow into a slow-moving sub-critical flow is a hydraulic jump. Such a flow is characterised by a sudden rise of the free-surface, with some strong energy dissipation and air entrainment, waves and spray. New two-phase flow measurements were performed in the developing flow region using a large-size facility operating at large Reynolds numbers. The experimental results demonstrated the complexity of the flow with a developing mixing layer in which entrained bubbles are advected in a high shear stress flow. The relationship between bubble count rates and void fractions was non-unique in the shear zone, supporting earlier observations of some form of double diffusion process between momentum and air bubbles. In the upper region, the flow consisted primarily of water drops and packets surrounded by air. Visually significant pray and splashing were significant above the jump roller. The present study is the first comprehensive study detailing the two-phase flow properties of both the bubbly and spray regions of hydraulic jumps, a first step towards understanding the interactions between bubble entrainment and droplet ejection processes

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem