Passive scalars, three-dimensional volume-preserving maps, and chaos

1988 ◽  
Vol 50 (3-4) ◽  
pp. 529-565 ◽  
Author(s):  
Mario Feingold ◽  
Leo P. Kadanoff ◽  
Oreste Piro
Keyword(s):  
Three Dimensional ◽  
Passive Scalars ◽  
Volume Preserving

Closed-Form Primitives for Generating Volume Preserving Deformations

1993 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Closed Form ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Physical Systems ◽  
Mechanics Of Materials ◽  
Time Simulation ◽  
Infinite Variety ◽  
Volume Preserving ◽  
Three Dimensional Space

Abstract In this paper, methods for generating closed-form expressions for locally volume preserving deformations of general volumes in three dimensional space are introduced. These methods potentially have applications to computer aided geometric design, the mechanics of materials, and realistic real-time simulation and animation of physical processes. In mechanics, volume preserving deformations are intimately related to the conservation of mass. The importance of this fact manifests itself in design, and in the realistic simulation of many physical systems. Whereas volume preservation is generally written as a constraint on equations of motion in continuum mechanics, this paper develops a set of physically meaningful basic deformations which are intrinsically volume preserving. By repeated application of these primitives, an infinite variety of deformations can be written in closed form.

Fine Scale Structure of the Local Lyapunov Exponent

1997 ◽  
Vol 11 (16n17) ◽  
pp. 707-712
Author(s):  
Demin Yao
Keyword(s):  
Lyapunov Exponent ◽  
Three Dimensional ◽  
Scale Structure ◽  
Fine Scale ◽  
Spatial Function ◽  
Local Lyapunov Exponent ◽  
Chaotic Region ◽  
Scale Structures ◽  
Volume Preserving

Direct numerial calculations reveal the fine-scale structures of the local Lyapunov exponent as a spatial function in the chaotic region of a three-dimensional volume-preserving flow.

Volume-preserving time integrators for three-dimensional passive scalar advection

2003 ◽  
Vol 2003.1 (0) ◽  
pp. 31-32
Author(s):  
Nobuatsu TANAKA ◽  
Tsutomu KITAYAMA ◽  
Toshiteru Yamasaki
Keyword(s):  
Three Dimensional ◽  
Passive Scalar ◽  
Time Integrators ◽  
Volume Preserving

A volume preserving flow with essential coexistence of zero and non-zero Lyapunov exponents

2012 ◽  
Vol 33 (6) ◽  
pp. 1748-1785 ◽  
Author(s):  
JIANYU CHEN ◽  
HUYI HU ◽  
YAKOV PESIN
Keyword(s):  
Lyapunov Exponents ◽  
Smooth Manifold ◽  
Dense Subset ◽  
Three Dimensional ◽  
Frequency Vector ◽  
Almost Everywhere ◽  
Invariant Submanifolds ◽  
Hyperbolic Behavior ◽  
Volume Preserving ◽  
Full Volume

AbstractWe demonstrate essential coexistence of hyperbolic and non-hyperbolic behavior in the continuous-time case by constructing a smooth volume preserving flow on a five-dimensional compact smooth manifold that has non-zero Lyapunov exponents almost everywhere on an open and dense subset of positive but not full volume and is ergodic on this subset while having zero Lyapunov exponents on its complement. The latter is a union of three-dimensional invariant submanifolds, and on each of these submanifolds the flow is linear with Diophantine frequency vector.

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