2D ELASTICITY TENSOR INVARIANTS, INVARIANTS DEFINITE POSITIVE CRITERIA

2021 ◽  
Vol 10 (8) ◽  
pp. 2999-3012
Author(s):  
K. Atchonouglo ◽  
G. de Saxcé ◽  
M. Ban
Keyword(s):  
Group Action ◽  
Linear Elasticity ◽  
Orbit Space ◽  
Rotation Group ◽  
Elasticity Tensor ◽  
Tensor Invariants ◽  
Material Classification ◽  
The One ◽  
2D Elasticity ◽  
Space Description

In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.

scholarly journals Polynomial Invariants of the Euclidean Group Action on Multiple Screws

2021 ◽  
Author(s):  
◽  
Deborah Crook
Keyword(s):  
Group Action ◽  
Three Dimensions ◽  
Euclidean Group ◽  
Polynomial Invariants ◽  
Generating Sets ◽  
Special Euclidean Group ◽  
The One

<p>In this work, we examine the polynomial invariants of the special Euclidean group in three dimensions, SE(3), in its action on multiple screw systems. We look at the problem of finding generating sets for these invariant subalgebras, and also briefly describe the invariants for the standard actions on R^n of both SE(3) and SO(3). The problem of the screw system action is then approached using SAGBI basis techniques, which are used to find invariants for the translational subaction of SE(3), including a full basis in the one and two-screw cases. These are then compared to the known invariants of the rotational subaction. In the one and two-screw cases, we successfully derive a full basis for the SE(3) invariants, while in the three-screw case, we suggest some possible lines of approach.</p>

scholarly journals A Theoretical Prediction of the Acoustic Pressure Generated by Turbulence-Flame Front Interactions

1986 ◽  
Vol 108 (3) ◽  
pp. 315-321 ◽  
Author(s):  
R. G. Huff
Keyword(s):  
Wave Equation ◽  
Acoustic Pressure ◽  
Pressure Fluctuations ◽  
Orbit Space ◽  
Space Propulsion ◽  
Forcing Function ◽  
Homogeneous Wave ◽  
Gas Generators ◽  
The One ◽  
Nonhomogeneous Equation

The equations of momentum and continuity are combined and linearized yielding the one-dimensional nonhomogeneous acoustic wave equation. Three terms in the nonhomogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in earth-to-orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such system is presented.

Elastic constants and anisotropic pair correlations in solid hydrogen and deuterium

1979 ◽  
Vol 57 (2) ◽  
pp. 136-146 ◽  
Author(s):  
S. Luryi ◽  
J. Van Kranendonk
Keyword(s):  
Elastic Constants ◽  
Phonon Dispersion ◽  
Debye Model ◽  
Elasticity Tensor ◽  
Pair Correlations ◽  
Nearest Neighbours ◽  
Einstein Model ◽  
The One ◽  
Central Forces ◽  
Phonon Dispersion Relations

The anisotropic displacement–displacement correlation function for the two types of pairs of nearest neighbours in solid hep hydrogen and deuterium is studied. Two mechanisms contributing to the deviation of the pair distribution function from axial symmetry around the pair axis are identified. The one is due to the anisotropy of the phonon dispersion relations and is treated in a generalized Debye model parameterized in terms of the elastic constants. The elasticity tensor is decomposed into rotationally irreducible parts, and certain new relations between the elastic constants of hep crystals with central forces are derived. The other mechanism arises from the immediate, anisotropic environment of a pair and is treated using a generalized Einstein model. The relevance of these results for the interpretation of the microwave spectrum of pairs of orthohydrogen molecules in parahydrogen is also discussed.

The linear elasticity tensor of incompressible materials

2014 ◽  
Vol 20 (6) ◽  
pp. 643-662 ◽  
Author(s):  
Salvatore Federico ◽  
Alfio Grillo ◽  
Shoji Imatani
Keyword(s):  
Linear Elasticity ◽  
Elasticity Tensor ◽  
Incompressible Materials

scholarly journals OD REFLEKSJI DO KONSTRUOWANIA WIEDZY I WSPÓLNOTY KOMUNIKACYJNEJ: WYNIKI BADANIA W DZIAŁANIU

Neofilolog ◽  
2019 ◽  
Vol 1 (42/1) ◽  
pp. 95-109
Author(s):  
Wioletta Piegzik
Keyword(s):  
Action Research ◽  
Foreign Language ◽  
Language Learners ◽  
Group Action ◽  
Video Recording ◽  
The Other ◽  
Learning Behavior ◽  
Action Research Project ◽  
Foreign Language Learners ◽  
The One

The purpose of the following paper is to consider the development of reflection in foreign language learners. Based on the results of action research, we show to what extent the performance of group tasks affected the perception of reality and influenced changes in the communication and learning behavior of participants of an action research project. Reflection is analyzed on the basis of statements contained in student diaries and transcriptions from video recording of discussions. This means that on the one hand, we are interested in the opinions, conclusions and evaluations made by learners, but on the other hand, we attach importance to the coherence between formulated judgments and practical group action. It is not uncommon that declarations are not in accordance with the activities undertaken and that, in consequence, their value is questionable. The paper also points to difficulties associated with becoming a reflective person as well as the restrictions connected with the scientific measurements of this process.

scholarly journals Gaia DR2 distances to Collinder 419 and NGC 2264 and new astrometric orbits for HD 193 322 Aa,Ab and 15 Mon Aa,Ab

2019 ◽  
Vol 630 ◽  
pp. A119 ◽  
Author(s):  
J. Maíz Apellániz
Keyword(s):  
Total Mass ◽  
Binary Systems ◽  
Orbit Space ◽  
The Sun ◽  
Spatial Covariance ◽  
Multiple Systems ◽  
Star Catalog ◽  
Stellar Group ◽  
Galactic Clusters ◽  
The One

Context. On the one hand, the second data release of the Gaia mission (Gaia DR2) has opened a trove of astrometric and photometric data for Galactic clusters within a few kiloparsecs of the Sun. On the other hand, lucky imaging has been an operational technique to measure the relative positions of visual binary systems for a decade and a half. This time is sufficient to apply the results of the technique to the calculation of orbits of some massive multiple systems within ∼1 kpc of the Sun. Aims. As part of an ambitious research program to measure distances to Galactic stellar groups (including clusters) containing O stars, I start with two of the nearest examples: Collinder 419 in Cygnus and NGC 2264 in Monoceros. The main ionizing source for each cluster is a multiple system with an O-type primary: HD 193 322 and 15 Mon, respectively. For each of the two multiple systems, I aim to derive new astrometric orbits for the Aa,Ab components. Methods. First, I present a method that uses Gaia DR2 G + GBP + GRP photometry, positions, proper motions, and parallaxes to obtain the membership and distance of a stellar group and applied these values to Collinder 419 and NGC 2264. Second, I present a new code that calculates astrometric orbits by searching the whole seven-parameter orbit space and apply it to HD 193 322 Aa,Ab and 15 Mon Aa,Ab using, as input, literature data from the Washington Double Star Catalog and the AstraLux measurements recently presented by our group in another paper published this year. Results. I obtain Gaia DR2 distances of 1006+37−34 pc for Collinder 419 and 719 ± 16 pc for NGC 2264; the main contribution to the uncertainties comes from the spatial covariance of the parallaxes. The two NGC 2264 subclusters are at the same distance (within the uncertainties) and show a significant relative proper motion. The distances are shown to be robust. HD 193 322 Aa,Ab follows an eccentric (e = 0.58+0.03−0.04) orbit with a period of 44 ± 1 a and the three stars it contains have a total mass of 76.1+9.9−7.4M⊙. The orbit of 15 Mon Aa,Ab is even more eccentric (e = 0.770+0.023−0.030); it has a period of 108 ± 12 a and a total mass of 45.1+3.6−3.3M⊙ for its two stars.

On Certain Polynomials of Gaussian Type

1979 ◽  
Vol 31 (2) ◽  
pp. 274-281 ◽  
Author(s):  
Daniel Reich
Keyword(s):  
Group Action ◽  
Lie Group ◽  
Orbit Space ◽  
Partition Functions ◽  
Poincaré Polynomial ◽  
Complete Answer ◽  
Lie Group Action ◽  
Image Position ◽  
Positive Coefficients ◽  
Positive Integers

Introduction. We shall consider functions of the formwhere {ri} and {si} are sets of positive integers. Such functions were studied by E. Grosswald in [2], who took {si} to be pairwise relatively prime, and asked the following two questions:(a) When is ƒ(t) a polynomial?(b) When does ƒ(t) have positive coefficients?These questions arise naturally from the work of Allday and Halperin, who show in [1] that under suitable circumstance ƒ(t) will be the Poincare polynomial of the orbit space of a certain Lie group action. Grosswald gives a complete answer to (a), but (b) is a much harder question, and a complete answer is provided only for the case m = 2. His treatment involves the representation of the coefficients of ƒ(t) by partition functions, and uses a classical description by Sylvester of the semigroup generated by {si}.

scholarly journals Polynomial Invariants of the Euclidean Group Action on Multiple Screws

2021 ◽  
Author(s):  
◽  
Deborah Crook
Keyword(s):  
Group Action ◽  
Three Dimensions ◽  
Euclidean Group ◽  
Polynomial Invariants ◽  
Generating Sets ◽  
Special Euclidean Group ◽  
The One

<p>In this work, we examine the polynomial invariants of the special Euclidean group in three dimensions, SE(3), in its action on multiple screw systems. We look at the problem of finding generating sets for these invariant subalgebras, and also briefly describe the invariants for the standard actions on R^n of both SE(3) and SO(3). The problem of the screw system action is then approached using SAGBI basis techniques, which are used to find invariants for the translational subaction of SE(3), including a full basis in the one and two-screw cases. These are then compared to the known invariants of the rotational subaction. In the one and two-screw cases, we successfully derive a full basis for the SE(3) invariants, while in the three-screw case, we suggest some possible lines of approach.</p>

On the non-existence of semi-groups for some equations of continuum mechanics

1980 ◽  
Vol 86 (3-4) ◽  
pp. 303-306 ◽  
Author(s):  
N. S. Wilkes
Keyword(s):  
Group Theory ◽  
Continuum Mechanics ◽  
Linear Elasticity ◽  
Existence Of Solutions ◽  
Elasticity Tensor ◽  
Positive Definite ◽  
Semi Group

SynopsisLinear semi-group theory can be used to prove the existence of solutions to the equations of linear elasticity when the elasticity tensor is positive definite. Here, it is shown that this condition is also necessary for the existence of a semi-group. The method is also applied to linear dissipative equations.

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