The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

scholarly journals Applications of KS - variables in celestial mechanics

BIBECHANA ◽  
1970 ◽  
Vol 7 ◽  
pp. 54-60
Author(s):  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Coordinate System ◽  
Celestial Mechanics ◽  
Restricted Problem ◽  
Three Dimensional ◽  
Orbital Elements ◽  
Circular Restricted Problem ◽  
Ks Variables ◽  
Three Dimensional Coordinate

This paper deals with the transformation of KS-Variables and canonically conjugate variables from sideral (inertial) to synodic (rotating) form and their applications in "the circular restricted problem of three bodies in three-dimensional coordinate system" to form generating solutions. Keywords: KS - transformation; KS - Variables; Orbital elements; Generating solutions DOI: 10.3126/bibechana.v7i0.4046BIBECHANA 7 (2011) 54-60

scholarly journals Modeling of dense well block point bar architecture based on geological vector information: A case study of the third member of Quantou Formation in Songliao Basin

2021 ◽  
Vol 13 (1) ◽  
pp. 39-48
Author(s):  
Chao Luo ◽  
Ailin Jia ◽  
Jianlin Guo ◽  
Wei Liu ◽  
Nanxin Yin ◽  
...  
Keyword(s):  
River Sediments ◽  
Three Dimensional ◽  
Songliao Basin ◽  
Point Bar ◽  
Meandering River ◽  
Architecture Model ◽  
The Third ◽  
Continuous Convergence ◽  
Vector Information ◽  
Architecture Modeling

Abstract Although stochastic modeling methods can achieve multiple implementations of sedimentary microfacies model in dense well blocks, it is difficult to realize continuous convergence of well spacing. Taking the small high-sinuosity meandering river sediments of the third member of Quantou Formation in Songliao Basin as an example, a deterministic modeling method based on geological vector information was explored in this article. Quantitative geological characteristics of point bar sediments were analyzed by field outcrops, modern sediments, and dense well block anatomy. The lateral extension distance, length, and spacing parameters of the point bar were used to quantitatively characterize the thickness, dip angle, and frequency of the lateral layer. In addition, the three-dimensional architecture modeling of the point bar was carried out in the study. The established three-dimensional architecture model of well X24-1 had continuous convergence near all wells, which conformed to the geological knowledge of small high-sinuosity meandering river, and verified the reliability of this method in the process of geological modeling in dense well blocks.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

Imaging Cracks in Bones Using Acoustic Nonlinearity: A Simulation Study

2011 ◽  
Vol 97 (5) ◽  
pp. 728-733
Author(s):  
Yang Liu ◽  
Xiasheng Guo ◽  
Zhao Da ◽  
Dong Zhang ◽  
Xiufen Gong
Keyword(s):  
Time Reversal ◽  
Three Dimensional ◽  
Harmonic Component ◽  
Ultrasonic Signal ◽  
Long Bone ◽  
Third Harmonic ◽  
Acoustic Nonlinearity ◽  
The Third ◽  
Nonlinear Approach ◽  
Radial Depth

This article proposes an acoustic nonlinear approach combined with the time reversal technique to image cracks in long bones. In this method, the scattered ultrasound generated from the crack is recorded, and the third harmonic nonlinear component of the ultrasonic signal is used to reconstruct an image of the crack by the time reversal process. Numerical simulations are performed to examine the validity of this approach. The fatigue long bone is modeled as a hollow cylinder with a crack of 1, 0.1, and 0.225 mm in axial, radial and circumferential directions respectively. A broadband 500 kHz ultrasonic signal is used as the exciting signal, and the extended three-dimensional Preisach-Mayergoyz model is used to describe the nonclassical nonlinear dynamics of the crack. Time reversal is carried out by using the filtered third harmonic component. The localization capability depends on the radial depth of the crack.

The Images of Dante’s Inferno in Fyodor Dostoevsky’s The House of the Dead

2021 ◽  
pp. 31-52
Author(s):  
Marina G. Kurgan ◽  
Keyword(s):  
Semantic Network ◽  
Three Dimensional ◽  
Personal Space ◽  
Divine Comedy ◽  
The Body ◽  
Dimensional Image ◽  
The Third ◽  
Character System ◽  
The Divine Comedy ◽  
The Dead

The House of the Dead was repeatedly compared with the first part of Dante’s The Divine Comedy even in F.M. Dostoevsky’s lifetime. However, his contemporaries usually focused on general analogies, while later scholars paid more attention to the narrative features or individual reminiscences. This research studies the main aspects of the artistic structure of the Dante code, constructing the space of Hell in Dostoevsky’s novel. 1. The organization of space. Alexander Petrovich Goryanchikov, the narrator in The House of the Dead, recreates a three-dimensional image that resembles a gradually narrowing funnel: from a bird’s-eye view, where the prison is seen in its entirety, the focus slowly descends, passing to smaller objects, and finally reaching the “three boards”, which limit Goryanchikov’s personal space. The same principle is employed to construct the space of Hell in Dante’s poem. In The House of the Dead, there is another significant indication of the spatial affinity of Dante’s hell and Dostoevsky’s katorga – active imagery associated with cobwebs and spiders. In the centre of the system of images associated with the designated semantic network is the parade- major, the head of the fortress and the owner of the inmate web. 2. The character system as an element constituting the space of Hell. The character system of The House of the Dead follows the compositional principle of Divine Comedy, where sinners are located in different circles in accordance with their main passion. There are three circles in the prison: the first is formal, according to the court decision; the second is informal, internal, formed by crafts and occupations; the third represents Goryanchikov’s perspective as an exponent of human and humane judgment, which distinguishes another person’s moral state. 3. Torment. The House of the Dead demonstrate a hierarchy in describing the tortures, while freedom becomes a fundamental category to embody the most important motif of physical and moral torment connecting Dostoevsky’s novel with Dante’s experience. The bodily torment ceases to be only the torment of the body to become a pain of the soul, comparable to physical torment, so the soul suffers and burns. Hell as a moral topos was the key for Dostoevsky. In The House of the Dead, he chooses the same way as Dante in The Divine Comedy: vivid corporeality conveys an esoteric metaphor of moral suffering and deep inner movements of the soul.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

scholarly journals Minimal Universal Model for Chaos in Laser with Feedback

2021 ◽  
Vol 31 (04) ◽  
pp. 2130013
Author(s):  
Riccardo Meucci ◽  
Stefano Euzzor ◽  
F. Tito Arecchi ◽  
Jean-Marc Ginoux
Keyword(s):  
Laser Physics ◽  
Nonlinear Oscillator ◽  
Three Dimensional ◽  
Universal Model ◽  
Type Formula ◽  
The Third ◽  
Proposed Model ◽  
Homoclinic Bifurcations ◽  
Electronic Implementation ◽  
Different Time Scales

We revisit the model of the laser with feedback and the minimal nonlinearity leading to chaos. Although the model has its origin in laser physics, with peculiarities related to the [Formula: see text] laser, it belongs to the class of the three-dimensional paradigmatic nonlinear oscillator models giving chaos. The proposed model contains three key nonlinearities, two of which are of the type [Formula: see text], where [Formula: see text] and [Formula: see text] are the fast and slow variables. The third one is of the type [Formula: see text], where [Formula: see text] is an intermediate feedback variable. We analytically demonstrate that it is essential for producing chaos via local or global homoclinic bifurcations. Its electronic implementation in the range of kilo Hertz region confirms its potential in describing phenomena evolving on different time scales.

Synthesis and third-order nonlinear optical properties of novel ethynyl-linked heteropentamer composed of four porphyrins and one pyrene

2009 ◽  
Vol 13 (02) ◽  
pp. 275-282 ◽  
Author(s):  
Ning Sheng ◽  
Jing Sun ◽  
Yongzhong Bian ◽  
Jianzhuang Jiang ◽  
Dong Xu
Keyword(s):  
Optical Properties ◽  
Nonlinear Optical ◽  
Three Dimensional ◽  
Spectroscopic Methods ◽  
Third Order ◽  
Zinc Compounds ◽  
Nlo Properties ◽  
Metal Free ◽  
The Third ◽  
Wide Range

Novel heteropentameric porphyrins-pyrene arrays, in which four meso-tetraphenyl porphyrins are linked to the center unit of pyrene by four acetylenyl bonds, were designed and synthesized. The newly synthesized heteropentameric compounds have been characterized by a wide range of spectroscopic methods. The third-order nonlinear optical (NLO) properties of both the metal-free and zinc compounds of the three-dimensional arrays were investigated by Z-scan experiments, showing enhanced NLO properties compared with that of the porphyrin and pyrene monomers.

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