Journal ArticleDOI
Fine phase mixtures as minimizers of energy
TLDR
In this article, the authors explore a theoretical approach to these fine phase mixtures based on the minimization of free energy and show that the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature.Abstract:
Solid-solid phase transformations often lead to certain characteristic microstructural features involving fine mixtures of the phases. In martensitic transformations one such feature is a plane interface which separates one homogeneous phase, austenite, from a very fine mixture of twins of the other phase, martensite. In quartz crystals held in a temperature gradient near the α-β transformation temperature, the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature. In this paper we explore a theoretical approach to these fine phase mixtures based on the minimization of free energy.read more
Citations
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On lower-semicontinuity of variational integrals
TL;DR: In this article, the relation between Morrey's quasiconvexity condition and lower semicontinuity of variational integrals is investigated, and it is shown how quasico-vexities naturally comes up in problems concerning stabilisation of sets of solutions of certain nonlinear systems under weak convergence.
Journal ArticleDOI
On Hessian matrices in the space BH
TL;DR: In this article, an extension of Alberti's result to second order derivatives was obtained, and it was shown that there exist u ∈ W1,1 (Ω) with ∇u ∈ BV(Ω;ℝN) and a constant C > 0 depending only on N such that and
Posted Content
Radial weak solutions for the Perona-Malik equation as a differential inclusion
Seonghak Kim,Baisheng Yan +1 more
TL;DR: In this article, the authors study the Perona-Malik type equation and show that, in all dimensions, there exist infinitely many radial weak solutions to the homogeneous Neumann boundary problem for any smooth nonconstant radially symmetric initial data.
Journal ArticleDOI
Variational Analysis of a Two-Dimensional Frustrated Spin System: Emergence and Rigidity of Chirality Transitions
TL;DR: In this article, the authors studied the discrete-to-continuum variational limit of the spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point.
Journal ArticleDOI
Elastic crystals with a triple point
TL;DR: In this paper, a generic Landau strain-energy function for a crystal with the coexisting tetragonal (t), orthorhombic (o), and monoclinic (m) phases is presented.
References
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Journal ArticleDOI
Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen
TL;DR: In this article, the Berechnung der dielektrizitatatkonstanten and der Leitfahigkeiten fur Elektriatitat and Warme der Mischkorper aus isotropen Bestandteilen behandelt.
Book
The theory of transformations in metals and alloys : an advanced textbook in physical metallurgy
Journal ArticleDOI
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
Book
The theory of transformations in metals and alloys
J.W. Christian,H. M. Otte +1 more
TL;DR: In this paper, the authors present a general introduction to the theory of transformation kinetics of real metals, including the formation and evolution of martensitic transformations, as well as a theory of dislocations.