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
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Book ChapterDOI
Minimizing sequences for nonconvex functionals, phase transitions and singular perturbations
TL;DR: In this paper, the singularly perturbed functional minimization problem is studied and it is shown that the minimizer is nearly periodic with period proportional to e. Connections with solid-solid phase transitions in crystals are indicated.
Journal ArticleDOI
Helical Miura Origami
TL;DR: In this paper, the phase space of all closed Miura origami structures is characterized, and it is shown that these structures are generically rigid to deformations that preserve cylindrical symmetry but are multistable.
Proceedings ArticleDOI
Anisotropic diffusions of image processing from Perona–Malik on
TL;DR: An overview of nonlinear anisotropic diffusion in image processing can be found in this article, where an overview of the main reasons for the desire to harness the power of NIMO diffusion is discussed.
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Lower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics
TL;DR: This work states a general relaxation result in terms of Young measures and shows the difficulty of having a relaxation in $L^p$ in an integral form, contrary to what happens for local functionals, nonpositive integrands may ...
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Numerical approximation of relaxed variational problems.
TL;DR: In this article, the authors consider the case when φ(x, u, ·) : IR → IR is not quasiconvex (in the sense of Morrey [19]) so that the minimum in (P) is generally not achieved.
References
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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.