Research
Research
I work in the field of Mathematical Physics, both on Solid and Fluid Mechianics. In particular I am interested in thin structures as rods and membranes, in porous media and in second gradient fluids; often these topics are studied with the Calculus of Variations of with a semi-analytical and semi-numerical approach. In particular, my research interests involve:
Optimization of the geometry of porous media
Self-contact and non-interpenetration of matter for elastic rods
Multi-scale homogenization
Variational problems for nematic liquid crystals
Stability for complex fluids
Instabilities and wrinkles of soft matter
Kirchhoff-Plateau problem
P. Colli, C. Lonati, L. Lussardi, Effective interface conditions for phenotype-structured models in presence of basement membranes and cell linings.
C. Lonati, L. Preziosi, Optimal paths for cell migration in triply periodic surfaces.
C. Lonati, S. P. Venkata, M. Destrade, V. Balbi, Wrinkles of a bilayered cylinder under tension.
G. Giantesio, A. Girelli, C. Lonati, A. Marzocchi, A. Musesti, Linear and nonlinear stability of second-gradient fluids.
C. Lonati, A. Marzocchi, A refinement through geodesic distance of Möbius energy for tubes.
2026
C. Lonati, L. Preziosi, Geometric characteristics of cubically symmetric and triply periodic scaffolds for optimal cell migration, submitted.
G. Bevilacqua, C. Lonati, L. Lussardi, A. Marzocchi, Existence and uniqueness of minimizers for axisymmetric nematic films, submitted. [arxiv]
C. Lonati, On some hierarchical systems in Mechanics: liquid crystals, wrinkles and poroelastic media, submitted.
R. Penta, C. Lonati, L. Miller, A. Marzocchi, Poroelasticity derived from the microstructure for intrinsically incompressible constituents, Zeitschrift für angewandte Mathematik und Physik, 77, 22. [journal]
G. Bevilacqua, C. Lonati, L. Lussardi, A. Marzocchi, A variational analysis of nematic axisymmetric films: the covariant derivative case, Calculus of Variations and partial differential equations, 65, 14. [arxiv] [journal]
2025
G. Giantesio, A. Girelli, C. Lonati, A. Marzocchi, A. Musesti, B. Straughan, Thermal convection in a sixth order generalized Navier - Stokes fluid, Studies in Applied Mathematics, 155, 2. [journal]
G. Giantesio, A. Girelli, C. Lonati, A. Marzocchi, A. Musesti, B. Straughan, Thermal convection in a higher velocity gradient and higher temperature gradient fluid, Journal of Mathematical Fluid Mechanics, 27, 47. [arxiv][journal]
C. Lonati, A. Marzocchi, Self-contact preventing energy for tubular rods, Journal of Nonlinear Science, 35, 34. [arxiv] [journal]
2024
C. Lonati, A. Marzocchi, On self-contact and non-interpenetration of elastic rods, Mathematics and Mechanics of solids, 30, 2. [journal]
2023