RESEARCH ACTIVITY

My research interests are:

- Applied Mathematics and Calculus of Variations
- Variational analysis of atomistic and continuous physical models
- Analysis of problems with multiple scales
- Homogenization and Gamma-convergence
- Time-discrete variational schemes (minimizing movements)
- Geometric minimizing movements
- Vanishing-viscosity limits of gradient flow systems / Bifurcation
- Quasi static limits, vanishing viscosity approximations
- Fracture Mechanics
- Finite difference approximations
- Nematic elastomers, Nonlinear elasticity
- Variational inequalities and Set-valued Analysis
- Random homogenization and Percolation

Calculus of Variations and PDEs: My research activity basically covers:
- evolution of physical systems driven by interfacial type energies in presence of dissipation, by coupling the minimizing movements scheme for geometric evolutions due to Almgren, Taylor and Wang and a discrete-to-continuum analysis via Gamma-convergence. This new approach has been recently introduced by Braides, Gelli and Novaga to study the motion of discrete interfaces of nearest neighbors interacting ferromagnetic systems;
- chirality transitions in frustrated ferromagnetic spin chains and possible links with the Theory of Liquid Crystals;
- homogenization of discrete energies associated to random spin systems via Gamma-convergence and Percolation results;
- vanishing-viscosity limits of gradient flow systems, delayed bifurcation, multiscale analysis, Balanced Viscosity solutions, vanishing inertia and viscosity limits, variational approach via time-discrete minimization schemes (minimizing movements);
- finite difference approximation of functionals in Fracture Mechanics, point clouds, quantitative analysis;
- relaxation of elastic energies related to nematic elastomers, non-standard growth.

Variational and Set-Valued Analysis: My research activity basically covers:
- existence and regularity results for a class of stochastic weighted variational inequalities in non-pivot Hilbert spaces with application to the random traffic equilibrium problem;

Publications

[1] G. Scilla, Variational problems with percolation: rigid spin systems. Adv. Math. Sci. Appl. 23 (2013), 187-207. (PDF)

[2] A. Braides and G. Scilla, Motion of discrete interfaces in periodic media. Interfaces Free Bound. 15 (2013), 451-476. (PDF)

[3] G. Scilla, Motion of discrete interfaces in low contrast periodic media. Netw. Heterog. Media 9 (2014), 169-189. (PDF)

[4] A. Braides and G. Scilla, Nucleation and backward motion of discrete interfaces. C. R. Acad. Sci. Paris (2013), Vol. 351, Issues 21-22, 803-806. (PDF          


[5] A. Barbagallo and G. Scilla, Stochastic weighted variational inequalities in non-pivot Hilbert spaces with applications to a transportation modelJ. Math. Anal. Appl. 457 (2) (2018), 1118-113410.1016/j.jmaa.2017.07.067

[6] G. Scilla and V. Vallocchia, Chirality transitions in frustrated ferromagnetic spin chains: a link with the gradient theory of phase transitions,  J. Elasticity 132(2) (2018), 271-293  (PDF)  

[7] G. Scilla and F. Solombrino. Delayed loss of stability in singularly perturbed finite-dimensional gradient flows,  Asymptot. Anal. 110 (1-2) (2018), 1-19 (PDF)

[8] G. Scilla and F. Solombrino, Multiscale analysis of singularly perturbed finite dimensional gradient flows: the minimizing movement approach,  Nonlinearity 31(11) (2018), 5036-5074. (PDF

[9] G. Scilla and F. Solombrino, A variational approach to the quasistatic limit of viscous dynamic evolutions in finite dimension, J. Differential Equations 267 (2019), 6216-6264. (PDF

[10] G. Scilla and B. Stroffolini, Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers, To appear on Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. (2020) (PDF)

[11] G. Scilla, Variational motion of discrete interfaces (PhD Thesis, 2014). (PDF)

Submitted preprints 

[12] G. Scilla, Motion of discrete interfaces on the triangular lattice. Submitted paper 2018 (PDF)

[13] V. Crismale, G. Scilla and F. Solombrino, A derivation of Griffith functionals from discrete finite-difference models, Submitted paper (2019). (PDF)

Works in progress / Projects

[14] A. Braides, G. Scilla and A. Tribuzio, Nucleation and backward motion of anisotropic discrete interfaces. In progress.

[15] M. Caroccia, M. Ruf, G. Scilla and F. Solombrino, Discrete approximations on point clouds of functionals in Fracture Mechanics, In progress.