scholarly journals Four equivalent properties of integrable billiards

2021 ◽  
Vol 241 (2) ◽  
pp. 693-719
Author(s):  
Alexei Glutsyuk ◽  
Ivan Izmestiev ◽  
Serge Tabachnikov
Keyword(s):  
Equivalent Properties

Classifying model-theoretic properties

2008 ◽  
Vol 73 (3) ◽  
pp. 885-905 ◽  
Author(s):  
Chris J. Conidis
Keyword(s):  
Model Theory ◽  
Computability Theory ◽  
Prime Model ◽  
Decidable Theory ◽  
Dense Sets ◽  
Equivalent Properties ◽  
The Relationship

AbstractIn 2004 Csima, Hirschfeldt, Knight, and Soare [1] showed that a set A ≤T 0′ is nonlow2 if and only if A is prime bounding, i.e., for every complete atomic decidable theory T, there is a prime model computable in A. The authors presented nine seemingly unrelated predicates of a set A, and showed that they are equivalent for sets. Some of these predicates, such as prime bounding, and others involving equivalence structures and abelian p-groups come from model theory, while others involving meeting dense sets in trees and escaping a given function come from pure computability theory.As predicates of A, the original nine properties are equivalent for sets; however, they are not equivalent in general. This article examines the (degree-theoretic) relationship between the nine properties. We show that the nine properties fall into three classes, each of which consists of several equivalent properties. We also investigate the relationship between the three classes, by determining whether or not any of the predicates in one class implies a predicate in another class.

A Strain Energy-Based Equivalent Layer Method for the Prediction of Critical Collapse Pressure of Flexible Risers

2018 ◽  
Author(s):  
Xiao Li ◽  
Xiaoli Jiang ◽  
Hans Hopman
Keyword(s):  
Strain Energy ◽  
Critical Pressure ◽  
Numerical Models ◽  
Fe Model ◽  
Collapse Pressure ◽  
Layer Method ◽  
Flexible Risers ◽  
Collapse Behavior ◽  
Equivalent Properties ◽  
Equivalent Layer

Flexible risers are one kind of flexible pipes that transport fluid between subsea facilities and topside structures. This pipe-like structure consists of multiple layers and its innermost carcass layer is designed for external hydrostatic pressure resistance. For the flexible risers used in ultra-deep water fields, the critical collapse pressure of the carcass layers is one of the dominant factors in their safety design. However, the complexity of the interlocked carcass design introduces significant difficulties and constraints into the engineering analysis. To facilitate the anti-collapse analysis, equivalent layer methods are demanded to help construct an equivalent pipe that performs a similar collapse behavior of the carcass. This paper proposes a strain energy based equivalent layer method which trying to bridge the equivalence between those two structures by considering equivalent geometric and material properties for the equivalent layer. Those properties are determined through strain energy equivalence and membrane stiffness equivalence. The strain energy of the carcass is obtained through numerical models and is then used in a derived equation set to calculate the equivalent properties for the equivalent layer. After all the equivalent properties have been determined, an equivalent layer FE model is built and used to predict the critical pressure of the carcass. The prediction result is compared to that of the full 3D carcass model as well as the equivalent models that built based on other existing equivalent methods, which shows that the proposed equivalent layer method gives a better performance on predicting the critical pressure of the carcass.

Cropped Steel Fiber Reinforced Chemically Bonded Ceramic (CBC) Composites

1987 ◽  
Vol 114 ◽  
Author(s):  
Sean Wise ◽  
Kevan Jones ◽  
Claudio Herzfeld ◽  
David D. Double
Keyword(s):  
Silica Fume ◽  
Steel Fiber ◽  
High Strength ◽  
Cement Matrix ◽  
Metal Fiber ◽  
Morphological Form ◽  
The Matrix ◽  
Compressive And Flexural Strengths ◽  
Equivalent Properties ◽  
Very High

ABSTRACTVery high strength castable chemically bonded ceramic (CBC) materials have been prepared which consist of finely chopped steel fibers and steel aggregate in a silica modified portland cement matrix. This paper examines the effect of metal fiber addition on compressive and flexural strengths. The overall chemistry of the matrix is held constant but the morphological form of silica used and the cure conditions are altered to examine their effect. Compressive strengths in excess of 500 MPa and flexural strengths in excess of 80 MPa can be obtained.It is found that flexural strength increases proportionally with fiber content over the range of 0 to 10% by volume. Compressive strengths are not affected. Use of silica fume in the mixes produces higher strengths at low temperatures than mixes which contain only crystalline silica. High temperature curing/drying (400°C), which produces the highest strengths, produces equivalent properties for formulations with and without silica fume. Higher water/cement ratios are found to reduce compressive strengths but have relatively little effect on the flexural properties.

scholarly journals Upscaling Fractured Heterogeneous Media: Permeability and Mass Exchange Coefficient

2005 ◽  
Vol 73 (1) ◽  
pp. 41-46 ◽  
Author(s):  
Moussa Kfoury ◽  
Rachid Ababou ◽  
Benoît Noetinger ◽  
Michel Quintard
Keyword(s):  
Large Scale ◽  
Fluid Transport ◽  
Heterogeneous Media ◽  
Porous Matrix ◽  
Exchange Coefficient ◽  
Flow Equations ◽  
Unit Scale ◽  
Homogenization Methods ◽  
Fracture Distribution ◽  
Equivalent Properties

In order to optimize oil recuperation, to secure waste storage, CO2 sequestration and describe more precisely many environmental problems in the underground, we need to improve some homogenization methods that calculate petrophysical parameters. In this paper, we discuss the upscaling of fluid transport equations in fractured heterogeneous media consisting of the fractures themselves and a heterogeneous porous matrix. Our goal is to estimate precisely the fluid flow parameters like permeability and fracture/matrix exchange coefficient at large scale. Two approaches are possible. The first approach consists in calculating the large-scale equivalent properties in one upscaling step, starting with a single continuum flow model at the local scale. The second approach is to perform upscaling in two sequential steps: first, calculate the equivalent properties at an intermediate scale called the ”unit scale,” and, second, average the flow equations up to the large scale. We have implemented the two approaches and applied them to randomly distributed fractured systems. The results allowed us to obtain valuable information in terms of sizes of representative elementary volume associated to a given fracture distribution.

Experiment Verification of Equivalent Model for Vibration Analysis of Honeycomb Sandwich Structure

2014 ◽  
Vol 624 ◽  
pp. 280-284 ◽  
Author(s):  
Xing Qian Zhao ◽  
Gang Wang ◽  
Dian Long Yu
Keyword(s):  
Sandwich Beam ◽  
Equivalent Model ◽  
Low Frequencies ◽  
Physical Experiments ◽  
Honeycomb Sandwich ◽  
Layer Effect ◽  
Experiment Verification ◽  
Equivalent Method ◽  
Equivalent Properties ◽  
Honeycomb Sandwich Structure

In this paper, a honeycomb sandwich beam and a plate are studied to verify a method of determining the equivalent properties of these structures. The responses of the structures are obtained from both numerical and physical experiments considering free-free boundary conditions. It is shown that a double-layer effect caused by the bonding-stretching process during manufacturing cannot be ignored. It is also found that at low frequencies, the equivalent method gives good agreement with measurements. However at higher frequency range, the response calculated using equivalent method shift towards higher frequency compared with measurements.

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