Thin-film limits of functionals on A-free vector fields

Thin-film Limits of Functionals on A-free Vector Fields

This paper deals with variational principles on thin films with linear PDE constraints represented by a constant-rank operator A, and studies the effective behavior, in the sense of Γ-convergence, of integral functionals as the thickness of the domain tends to zero. The limit integral functional turns out to be determined by the A-quasiconvex envelope of the original energy density and is const...

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Limits on the performance of dispersive thin-film stacks.

Dispersive thin-film stacks are interesting as compact, cost-effective devices for temporal dispersion compensation and wavelength multiplexing. Their performance depends on the total group delay or spatial shift that can be achieved. For general multilayer stacks, no analytic model exists relating the performance to the stack parameters such as the refractive indices and the number of layers. ...

Dimension reduction for functionals on solenoidal vector fields

We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happ...

Thin Film Limits in Magnetoelastic Interactions