tensor field oor Sjinees
tensor field
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The same is true in general relativity, of tensor fields describing a physical property.
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We therefore can give a definition of tensor field, namely as a section of some tensor bundle.
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More generally, any covariant tensor field – in particular any differential form – on N may be pulled back to M using φ.
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As an advanced explanation of the tensor concept, one can interpret the chain rule in the multivariable case, as applied to coordinate changes, also as the requirement for self-consistent concepts of tensor giving rise to tensor fields.
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In general we can take sections of W, the tensor product of V with Ls, and consider tensor density fields with weight s.
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His prize essay was entitled Vector and Tensor Fields and was in two parts.
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More precisely, a tensor field assigns to any given point of the manifold a tensor in the space
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In the classical limit of Newtonian gravity, this has a simple interpretation: energy is being exchanged with gravitational potential energy, which is not included in the tensor, and momentum is being transferred through the field to other bodies.
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This is described by a tensor of type (2, 0) , in linear elasticity , or more precisely by a tensor field of type (2, 0) , since the stresses may vary from point to point.
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In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state , a tensor product of the states for each electromagnetic mode
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Through the direct analytic calculation it was shown that the real and imaginary parts of graphene conductivity, found recently on the basis of first principles of thermal quantum field theory using the polarization tensor in (2+1)-dimensional space-time, satisfy the Kramers-Kronig relations precisely.
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Mathisson proved that the variational equation can be solved when it has been defined so that the equations to be imposed upon the characteristic tensor will be compatible with the variations allowed in the fields.
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Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor , which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely.
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With this additional condition—the covariant divergence of the energy–momentum tensor, and hence of whatever is on the other side of the equation, is zero— the simplest set of equations are what are called Einstein's (field) equations:
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Christoffel not only contributed to all these fields, but his interests extended to orthogonal polynomials and continued fractions, and the applications of his work to the foundations of tensor analysis, to geodetical science, to the theory of shock waves, to the dispersion of light.
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15 sinne gevind in 6 ms. Hulle kom uit baie bronne en word nie nagegaan nie.