F Ur Mathematik in Den Naturwissenschaften Leipzig a Gamma-convergence Result for the Two- Gradient Theory of Phase Transitions a ?-convergence Result for the Two-gradient Theory of Phase Transitions
نویسندگان
چکیده
The generalization to gradient vector elds of the classical double-well, singularly perturbed func-tionals, I" (u;) := Z 1 " W(ru) + "jr 2 uj 2 dx; where W() = 0 if and only if = A or = B, and A ? B is a rank-one matrix, is considered. Under suitable constitutive and growth hypotheses on W it is shown that I" ?-converge to +1 otherwise, where K is the (constant) interfacial energy per unit area.
منابع مشابه
für Mathematik in den Naturwissenschaften Leipzig Global Existence for a Nonlinear System in Thermoviscoelasticity with Nonconvex Energy
A three-dimensional thermoviscoelastic system derived from the balance laws of momentum and energy is considered. To describe structural phase transitions in solids, the stored energy function is not assumed to be convex as a function of the deformation gradient. A novel feature for multi-dimensional, nonconvex, and non-isothermal problems is that no regularizing higher order terms are introduc...
متن کاملA homogenization result in the gradient theory of phase transitions
A homogenization problem arising in the gradient theory of fluid-fluid phase transitions is addressed in the vector-valued setting by means of Γ-convergence.
متن کاملF Ur Mathematik in Den Naturwissenschaften Leipzig Regularity and Optimal Design Results for Elastic Membranes Regularity and Optimal Design Results for Elastic Membranes
The eeective energy of a mixture of two elastic materials in a thin lm is characterized using Gamma-limit techniques. For cylindrical shaped inclusions it is shown that 3D-2D asymptotics and optimal design commute from a variational viewpoint. Regularity of local minimizers for the resulting design is addressed.
متن کاملساختار فاز میدانهای پیمانهای شبکهای دو بعدی U(N) با کنش مختلط
We study the phase structure of two dimensional pure lattice gauge theory with a Chern term. The symmetry groups are non-Abelian, finite and disconnected sub-groups of SU(3). Since the action is imaginary it introduces a rich phase structure compared to the originally trivial two dimensional pure gauge theory. The Z3 group is the center of these groups and the result shows that if we use one ...
متن کاملF Ur Mathematik in Den Naturwissenschaften Leipzig a Nonlocal Anisotropic Model for Phase Transitions Part Ii: Asymptotic Behaviour of Rescaled Energies a Nonlocal Anisotropic Model for Phase Transitions
we study the asymptotic behaviour as " ! 0, of the nonlocal models for phase transition described by the scaled free energy F " (u) := 1 4" Z J " (x 0 ? x) ? u(x 0) ? u(x) 2 dx 0 dx + 1 " Z W ? u(x) dx ; where u is a scalar density function, W is a double-well potential which vanishes at 1, J is a non-negative interaction potential and J " (h) := " ?N J(h="). We prove that the functionals F " c...
متن کامل