Everything about Tensor density
Generalization of tensor fields
In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing from one coordinate system to another, except that it is additionally multiplied or weighted by a power of the Jacobian determinant of the coordinate transition function or its absolute value. A tensor density with a single index is called a vector density. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. Sometimes tensor densities with a negative weight are called tensor capacity. A tensor density can also be regarded as a section of the tensor product of a tensor bundle with a density bundle. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Tensor densityA 5-minute orientation
- Skim a recent paper: Density-Based Affinity Propagation Tensor Clustering for Intelligent Fault Diagnosis of Train Bogie BearingInfluential work since 2022
- Pick up a classic book: Turbulence in the atmosphereThe most-reprinted book on the subject
- Read the landmark paper: Tensor part of the Skyrme energy density functional: Spherical nucleiCited 321 times
- Go sideways: Levi-Civita symbolA closely related topic
- Go sideways: PseudotensorA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Tensor part of the Skyrme energy density functional: Spherical nuclei
Metric tensor formulation of strain in density-functional perturbation theory
Improved tensor-product expansions for the two-particle density matrix
Energy density concept: A stress tensor approach
Nuclear tensor interaction in a covariant energy density functional
Tensor-Reduced Atomic Density Representations
Experimental characterization of the mesoscale dislocation density tensor
Density Matrix Renormalization Group with Tensor Processing Units
🆕 Influential since 2022
Density-Based Affinity Propagation Tensor Clustering for Intelligent Fault Diagnosis of Train Bogie Bearing
Tensor renormalization group study of (3+1)-dimensional ℤ2 gauge-Higgs model at finite density
Primordial black hole formation from a nonspherical density profile with a misaligned deformation tensor
Low-Rank Characteristic Tensor Density Estimation Part I: Foundations
Impact of tensor couplings with scalar mixing on covariant energy density functionals
đź“š Books worth reading
Turbulence in the atmosphereJohn C. Wyngaard · 2009
Information Processing in Medical ImagingJames C. Gee · 2013- 📕Applied data miningGuandong Xu · 2013
- 📕Altimetry data and the elastic stress tensor of subduction zonesMichele Caputo · 1985
A first course in noncommutative ringsT. Y. Lam · 1991
Lectures on lightStephen Colby Rand · 2010
Micromechanics of Composite MaterialsGeorge Dvorak · 2013
Introduction to Electromagnetic TheoryTai L. Chow · 2005
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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