相关论文: The energy scaling behavior of a class of incompat…
Motivated by complex microstructures in the modelling of shape-memory alloys and by rigidity and flexibility considerations for the associated differential inclusions, in this article we study the energy scaling behaviour of a simplified…
Domain branching near the boundary appears in many singularly-perturbed models for microstructure in materials and was first demonstrated mathematically by Kohn and M\"uller for a scalar problem modeling the elastic behavior of shape-memory…
We investigate the scaling behaviour of a singular perturbation model within the geometrically linearized theory of elasticity involving data of higher lamination order. We study boundary data which are of staircase type and show rather…
We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms…
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion…
We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusion of fixed volume. Motivated by models for boundary…
The objective of this article is to compare different surface energies for multi-well singular perturbation problems associated with martensitic phase transformations involving higher order laminates. We deduce scaling laws in the singular…
For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…
In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on…
In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of $\mathcal{A}$-free operators and for a singularly perturbed $T_3$-structure for the divergence…
Energy functionals describing phase transitions in crystalline solids are often non-quasiconvex and minimizers might therefore not exist. On the other hand, there might be infinitely many gradient Young measures, modelling microstructures,…
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…
We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling law in the singular perturbation parameter. In these…
We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two…
In this work, singularly perturbed energies arising from discrete $J_1$-$J_3$-models are studied. The energies under consideration consist of a non-convex bulk term and a higher-order regularizing term and are subject to incompatible…
We consider an energy functional combining the square of the local oscillation of a one--dimensional function with a double well potential. We establish the existence of minimal heteroclinic solutions connecting the two wells of the…
The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous…
Turbulent flows are observed in low-Reynolds active fluids. They are intrinsically different from the classical inertial turbulence and behave distinctively in two- and three-dimensions. Understanding the behaviors of this new type of…