NASA Logo, External Link
Facebook icon, External Link to NASA STI page on Facebook Twitter icon, External Link to NASA STI on Twitter YouTube icon, External Link to NASA STI Channel on YouTube RSS icon, External Link to New NASA STI RSS Feed AddThis share icon
 

Record Details

Record 45 of 9054
The Topology of Symmetric Tensor Fields
Author and Affiliation:
Levin, Yingmei(Stanford Univ., Physics Dept., Stanford, CA United States)
Batra, Rajesh(Stanford Univ., Aeronautics and Astronautics Dept., Stanford, CA United States)
Hesselink, Lambertus(Stanford Univ., Electrical Engineering and Aeronautics and Astronautics Depts., Stanford, CA United States)
Levy, Yuval(Israel Inst. of Tech., Faculty of Aerospace Engineering, Haifa, Israel)
Abstract: Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Publication Date: Jan 01, 1997
Document ID:
20000012445
(Acquired Feb 06, 2000)
Subject Category: COMPUTER PROGRAMMING AND SOFTWARE
Document Type: Technical Report
Contract/Grant/Task Num: NAG2-911; NSF ECS-92-15145
Financial Sponsor: NASA Ames Research Center; Moffett Field, CA United States
National Science Foundation; Washington, DC United States
Organization Source: Stanford Univ.; Physics Dept.; Stanford, CA United States
Description: 13p; In English; Original contains color illustrations
Distribution Limits: Unclassified; Publicly available; Unlimited
Rights: Copyright
NASA Terms: TOPOLOGY; SYMMETRY; COMBINATORIAL ANALYSIS; MAGNETIC FIELDS; REYNOLDS STRESS; SCIENTIFIC VISUALIZATION; STRESS TENSORS; TENSORS; ANALOGIES; BIAS; DEFORMATION; DIFFERENTIAL EQUATIONS; EIGENVALUES; EIGENVECTORS; MAGNETIC CORES; SINGULARITY (MATHEMATICS); SYMBOLS; TURBULENCE MODELS; TURBULENT FLOW
Availability Source: Other Sources
› Back to Top
Find Similar Records
NASA Logo, External Link
NASA Official: Gerald Steeman
Site Curator: STI Program
Last Modified: August 22, 2011
Contact Us