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Vector fields and connection on fibred manifolds

Dekrét, Anton (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] In a previous paper [Cas. Pestovani Mat. 115, No.4, 360-367 (1990)] the author determined the set of the vector fields on TM by which connections on TM can be constructed. In this paper, he generalizes some of such constructions to the case of vector fields on fibred manifolds, giving several examples.

Visco-elastic-plastic modelling

Koppová, Jana, Minárová, Mária, Sumec, Jozef (2017)

Proceedings of Equadiff 14

In this paper we deal with the mathematical modelling of rheological models with applications in various engineering disciplines and industry. We study the mechanical response of visco-elasto-plastic materials. We describe the basic rheological elements and focus our attention to the specific model of concrete, for which we derive governing equations and discuss its solution. We provide an application of rheological model involving rigid-plastic element as well - mechanical and mathematical model...

Viscosity solutions to a new phase-field model for martensitic phase transformations

Zhu, Peicheng (2015)

Application of Mathematics 2015

We investigate a new phase-field model which describes martensitic phase transitions, driven by material forces, in solid materials, e.g., shape memory alloys. This model is a nonlinear degenerate parabolic equation of second order, its principal part is not in divergence form in multi-dimensional case. We prove the existence of viscosity solutions to an initial-boundary value problem for this model.

Volume and area renormalizations for conformally compact Einstein metrics

Graham, Robin C. (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Let X be the interior of a compact manifold X ¯ of dimension n + 1 with boundary M = ∂ X , and g + be a conformally compact metric on X , namely g ¯ ≡ r 2 g + extends continuously (or with some degree of smoothness) as a metric to X , where r denotes a defining function for M , i.e. r > 0 on X and r = 0 , d r ≠ 0 on M . The restrction of g ¯ to T M rescales upon changing r , so defines invariantly a conformal class of metrics on M , which is called the conformal infinity of g + . In the present paper, the author considers conformally compact metrics...

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