scholarly journals Exact Solution for Relativistic Trajectories Using Modal Transseries

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1505
Author(s):  
Luis Acedo ◽  
Abraham J. Arenas ◽  
Nicolas De La Espriella
Keyword(s):  
Exact Solution ◽  
Angular Momentum ◽  
High Precision ◽  
Limit Cycles ◽  
Fundamental Problem ◽  
Orbital Plane ◽  
Relativistic Effects ◽  
Geodesic Equation ◽  
Novel Method ◽  
Analytical Expressions

In this article, we design a novel method for finding the exact solution of the geodesic equation in Schwarzschild spacetime, which represents the trajectories of the particles. This is a fundamental problem in astrophysics and astrodynamics if we want to incorporate relativistic effects in high precision calculations. Here, we show that exact analytical expressions can be given, in terms of modal transseries for the spiral orbits as they approach the limit cycles given by the two circular orbits that appear for each angular momentum value. The solution is expressed in terms of transseries generated by transmonomials of the form e−nθ, n=1, 2, …, where θ is the angle measured in the orbital plane. Examples are presented that verify the effect of the solutions.

scholarly journals Numerical Solution of the Spinor-Spinor Bethe-Salpeter Equation in Functional Nonlinear Spinor Theory

1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Excited State ◽  
Variational Method ◽  
Numerical Solution ◽  
High Precision ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons ◽  
Functional Methods

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.

scholarly journals A novel method for high precision aortic constriction that allows for generation of specific cardiac phenotypes in mice

2018 ◽  
Vol 114 (12) ◽  
pp. 1680-1690 ◽  
Author(s):  
Arne O Melleby ◽  
Andreas Romaine ◽  
Jan Magnus Aronsen ◽  
Ioanni Veras ◽  
Lili Zhang ◽  
...  
Keyword(s):  
High Precision ◽  
Aortic Constriction ◽  
Novel Method

scholarly journals Testing viscous disc theory using the balance between stellar accretion and external photoevaporation of protoplanetary discs

2020 ◽  
Vol 497 (1) ◽  
pp. L40-L45
Author(s):  
Andrew J Winter ◽  
Megan Ansdell ◽  
Thomas J Haworth ◽  
J M Diederik Kruijssen
Keyword(s):  
Angular Momentum ◽  
Mass Loss ◽  
Central Star ◽  
Outer Edge ◽  
Momentum Transport ◽  
Angular Momentum Transport ◽  
Accretion Rates ◽  
Novel Method ◽  
Viscous Models ◽  
Protoplanetary Discs

ABSTRACT The nature and rate of (viscous) angular momentum transport in protoplanetary discs (PPDs) have important consequences for the formation process of planetary systems. While accretion rates on to the central star yield constraints on such transport in the inner regions of a PPD, empirical constraints on viscous spreading in the outer regions remain challenging to obtain. Here, we demonstrate a novel method to probe the angular momentum transport at the outer edge of the disc. This method applies to PPDs that have lost a significant fraction of their mass due to thermal winds driven by UV irradiation from a neighbouring OB star. We demonstrate that this external photoevaporation can explain the observed depletion of discs in the 3–5 Myr old σ Orionis region, and use our model to make predictions motivating future empirical investigations of disc winds. For populations of intermediate-age PPDs, in viscous models we show that the mass flux outwards due to angular momentum redistribution is balanced by the mass-loss in the photoevaporative wind. A comparison between wind mass-loss and stellar accretion rates therefore offers an independent constraint on viscous models in the outer regions of PPDs.

A Novel Method of Obtaining Honing Tool Profile for Machining Gears With Profile Modifications

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Michał Batsch
Keyword(s):  
Mathematical Model ◽  
Design Process ◽  
High Precision ◽  
Prediction Error ◽  
Industrial Applications ◽  
Helical Gears ◽  
Profile Deviation ◽  
Tool Profile ◽  
Novel Method ◽  
Two Parameter

Abstract In this study, a mathematical model of the honing process for helical gears with external teeth was developed. The proposed novel method of obtaining the two-parameter envelope of a family of surfaces proved useful in simulated machining by means of a tool with a profile deviation. Based on performed simulations and industrial applications, it was found that this method can be useful in predicting the accuracy of machined gear and therefore can be used in the design process of honing tool for high precision aerospace gears. For the example provided, the average absolute prediction error of machined tooth profile was 0.28 µm.

A Novel Lapping Method for High Precision Balls Based on Variable-Radius V-Groove

2013 ◽  
Vol 1 (4) ◽  
Author(s):  
Ping Zhao ◽  
Weigang Guo ◽  
Ming Feng ◽  
Binghai Lv ◽  
Qianfa Deng ◽  
...  
Keyword(s):  
High Precision ◽  
High Efficiency ◽  
Ball Bearing ◽  
Lower Plate ◽  
The Novel ◽  
Variable Radius ◽  
Novel Method ◽  
Set Up ◽  
High Consistency ◽  
Steel Balls

The precision ball is the most key component of ball bearing, which is widely used in many precision mechanical fields. This paper presents a variable-radius V-groove lapping method since this method can make the spin angle vary between 0 deg and 90 deg, and the lapping trajectory can cover the ball's surface. Based on this lapping method, an observation of lapping surface of balls experiment is set up in which blackened balls is brightened effectively only after 10 circulations of lower plate in 2 min. Next, another experiment is also done: A batch of G16 level steel balls has been lapped to G5 level in the machining experiment. All results illustrate that the novel method has properties of high efficiency, high precision, and high consistency, which needs further study and then it is likely to replace the traditional one in the future.

scholarly journals NEW EXACT TREATMENT OF THE PERTURBED COULOMB INTERACTIONS

2003 ◽  
Vol 18 (36) ◽  
pp. 2581-2586 ◽  
Author(s):  
OKAN ÖZER ◽  
BÜLENT GÖNÜL
Keyword(s):  
Perturbation Theory ◽  
Exact Solutions ◽  
Quantum Systems ◽  
External Potential ◽  
Coulomb Interactions ◽  
Exact Solvability ◽  
Hydrogenic Atom ◽  
Novel Method ◽  
Arbitrary Dimensions ◽  
Analytical Expressions

A novel method for the exact solvability of quantum systems is discussed and used to obtain closed analytical expressions in arbitrary dimensions for the exact solutions of the hydrogenic atom in the external potential ΔV(r) = br + cr2, which is based on the recently introduced supersymmetric perturbation theory.

The Quantum Mechanics of Cohesion

2007 ◽  
Vol 72 (2) ◽  
pp. 252-268
Author(s):  
Roy McWeeny
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Angular Momentum ◽  
Scalar Product ◽  
Hydrogen Molecule ◽  
Fundamental Problem ◽  
Ionic Species ◽  
General Context ◽  
Spin Angular Momentum ◽  
Actual Nature

We consider the fundamental problem of "what makes atoms stick together in molecules, crystals, or clusters?" The Heitler and London paper (1927) on the hydrogen molecule marked a first attempt to discuss, in terms of quantum mechanics, the interaction of two atoms with unpaired spins. The aim of this note is to show how the primitive concepts used eighty years ago still retain a certain validity even in a much more general context. We consider in fact the interaction of two arbitrary systems, each with a resultant spin angular momentum, and show how the interaction energy depends on the scalar product of the two resultants. The actual nature of the two systems is irrelevant: they may be atoms, molecules, or ionic species of any kind each described by a wave function which may be, in principle, exact. This provides a first step in the formulation of any general theory of cohesion.

Paper 2: Holographic Techniques in Engineering Metrology

1968 ◽  
Vol 183 (4) ◽  
pp. 5-12
Author(s):  
A. E. Ennos
Keyword(s):  
High Precision ◽  
Unique Feature ◽  
Three Dimensional ◽  
Laser Source ◽  
Coherent Light ◽  
Holographic Image ◽  
Dimensional Image ◽  
Engineering Component ◽  
Novel Method

Holography is a novel method of photography using coherent light from a laser source. Its unique feature is that it records a faithful three-dimensional image of the object. This allows one to compare the shape of an engineering component at one moment in time with its shape after some change has taken place, e.g. by deforming it under load. In some cases the holographic image of a ‘master’ component can be used as a template against which similar components can be matched with high precision. The techniques of holography, the interpretation of the results obtained, and the present limitations of the method will be discussed.

Sign in / Sign up

Export Citation Format

Share Document