scholarly journals Large amplitude collective dynamic beyond the independent particle/quasiparticle picture

2019 ◽  
pp. 93-113
Author(s):  
Denis Lacroix
Keyword(s):  
Large Amplitude ◽  
Collective Dynamic ◽  
Independent Particle ◽  
Quasiparticle Picture

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

Теория гетерогенного катализа. Теория хемосорбции

2021 ◽  
Author(s):  
Василий Садовников
Keyword(s):  
Heterogeneous Catalysis ◽  
Potential Energy ◽  
Publishing House ◽  
Cell Number ◽  
Oil Refining ◽  
Lateral Interaction ◽  
Reaction Products ◽  
Crystal Face ◽  
Independent Particle ◽  
The Face

This monograph is a continuation of the monograph by V.V. Sadovnikov. Lateral interaction. Moscow 2006. Publishing house "Anta-Eco", 2006. ISBN 5-9730-0017-6. In this work, the foundations of the theory of heterogeneous catalysis and the theory of chemisorption are more easily formulated. The book consists of two parts, closely related to each other. These are the theoretical foundations of heterogeneous catalysis and chemisorption. In the theory of heterogeneous catalysis, an experiment is described in detail, which must be carried out in order to isolate the stages of a catalytic reaction, to find the stoichiometry of each of the stages. This experiment is based on the need to obtain the exact value of the specific surface area of the catalyst, the number of centers at which the reaction proceeds, and the output curves of each of the reaction products. The procedures for obtaining this data are described in detail. Equations are proposed and solved that allow calculating the kinetic parameters of the nonequilibrium stage and the thermodynamic parameters of the equilibrium stage. The description of the quantitative theory of chemisorption is based on the description of the motion of an atom along a crystal face. The axioms on which this mathematics should be based are formulated, the mathematical apparatus of the theory is written and the most detailed instructions on how to use it are presented. The first axiom: an atom, moving along the surface, is present only in places with minima of potential energy. The second axiom: the face of an atom is divided into cells, and the position of the atom on the surface of the face is set by one parameter: the cell number. The third axiom: the atom interacts with the surrounding material bodies only at the points of minimum potential energy. The fourth axiom: the solution of the equations is a map of the arrangement of atoms on the surface. The fifth axiom: quantitative equations are based on the concept of a statistically independent particle. The formation energies of these particles and their concentration are calculated by the developed program. The program based on these axioms allows you to simulate and calculate the interaction energies of atoms on any crystal face. The monograph is intended for students, post-graduate students and researchers studying work and working in petrochemistry and oil refining.

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