Prossimo seminario S.P.I.E.Dini – Valerio Corica | Next S.P.I.E.Dini seminar - Valerio Corica

[Federico Thiella]

English version below

Buongiorno a tutti,

Il prossimo seminario di S.P.I.E.Dini sarà tenuto da Valerio Corica, dottorando in matematica presso La Sapienza — Università di Roma

📅 Data e ora: Giovedì 11 Dicembre 2025 alle ore 15:30  in Aula Tricerri - DIMAI

Titolo: Energetic behaviour of dislocations of semicoherent interfaces

Abstract: A dislocation is a one-dimensional singularity in an elastic deformation that encodes a mismatch in the underlying displacement field.

Mathematically, it arises as a defect set where strain incompatibility concentrates, and it represents a fundamental example of line defects in continuum models of solids.

In the applied analysis literature, several approaches have been developed; here we focus on the one introduced by Lauteri and Luckhaus in their study of the interaction between two crystalline lattices rotated by an angle [Lauteri–Luckhaus, preprint (2016)].

In their seminal work, they established the scaling predicted by Read and Shockley in the 1950s [Read–Shockley, Phys. Rev. 1950], without assumptions on the defect distribution and introducing several deep ideas.

We propose a Lauteri–Luckhaus–type energy tailored to semi-coherent interfaces.

In this setting, the analogue of the Read–Shockley law is given by the classical van der Merwe model [van der Merwe, Proc. Phys. Soc. 1963], whose energetic behavior we rigorously confirm.

We also introduce a linearized model that enables us to prove the analogous logarithmic scaling in higher dimensions through a slicing procedure.

Based on joint work with Emanuele Spadaro (Sapienza).

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Vi aspettiamo,
A presto,

Federico e Matteo

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Good morning everyone,

The next S.P.I.E.Dini seminar will be held by Valerio Corica, a PhD student in mathematics at La Sapienza — University of Rome

📅 Date and time: Thursday, December 11, 2025, at 3:30 PM in Room Tricerri - DIMAI


Title: Energetic behaviour of dislocations of semicoherent interfaces

Abstract: A dislocation is a one-dimensional singularity in an elastic deformation that encodes a mismatch in the underlying displacement field.

Mathematically, it arises as a defect set where strain incompatibility concentrates, and it represents a fundamental example of line defects in continuum models of solids.

In the applied analysis literature, several approaches have been developed; here we focus on the one introduced by Lauteri and Luckhaus in their study of the interaction between two crystalline lattices rotated by an angle [Lauteri–Luckhaus, preprint (2016)].

In their seminal work, they established the scaling predicted by Read and Shockley in the 1950s [Read–Shockley, Phys. Rev. 1950], without assumptions on the defect distribution and introducing several deep ideas.

We propose a Lauteri–Luckhaus–type energy tailored to semi-coherent interfaces.

In this setting, the analogue of the Read–Shockley law is given by the classical van der Merwe model [van der Merwe, Proc. Phys. Soc. 1963], whose energetic behavior we rigorously confirm.

We also introduce a linearized model that enables us to prove the analogous logarithmic scaling in higher dimensions through a slicing procedure.

Based on joint work with Emanuele Spadaro (Sapienza).

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Anyone interested in presenting their work or having suggestions is welcome to email us at federico...@unifi.it matteo....@unifi.it

We look forward to seeing you,
See you soon,

Federico and Matteo