Ruggero Gabbrielli
- Contact Details
- Complex Materials Theory Group
- Department of Chemistry
- Princeton University
- Frick Chemistry Laboratory, Room 159
- Washington Road
- Princeton, NJ 08544
- tel +1 609 258 9381
- Qualifications
- Ph.D. Mechanical Engineering, University of Bath
- Laurea Mechanical Engineering, University of Florence
- Research interests
- Cell aggregates and soap films (require Java). The geometry of cellular materials. Ground state for cellular material and aggregates of equisized soft particles.
The Kelvin problem
(video 1 video 2 video 3 comics),
modelling of foams, the three-dimensional structure of bubbles in monodisperse foams, disorder in foams,
n-dimensional honeycombs, periodic tilings from point sets, low-dimensional non-lattice sphere packings and coverings, spatial distribution of points,
periodic point sets (require Java). Applications: foam modelling, cell aggregates, metal crystallites, grain structure and boundaries, cosmology.
- Triply periodic surfaces (require Java). Trigonometric approximations by implicit functions of minimal surfaces and surfaces of constant curvature.
Optimization of low volume fraction porous materials (stress levelling). Modelling of structures using triply periodic surfaces. Stress-leveling analysis of porous materials.
Application: bone substitutes, architecture.
Modelling and three-dimensional printing of functionally graded materials.
- Pattern formation applied to optimization problems in mathematics (sphere coverings and quantizers), physics (structure
of condensed matter and metallurgy), chemistry (crystallography), engineering (foam modelling, surface and volume mesh generation).
Swift-Hohenberg equation, Brusselator reaction-diffusion system.
- Auxetics (require Java). Bifurcation and geometric instabilities in solid mechanics. The internal geometry of
negative Poisson's ratio structures.
- Publications
- R. Gabbrielli, S. Hutzler, D. Weaire, A. Meagher, K. Brakke. An experimental realisation of the Weaire-Phelan structure in monodisperse liquid foam
Phil. Mag. Lett. 92:1 (2012), pp. 1-6.
- F.P.W. Melchels, K. Bertoldi, R. Gabbrielli, A.H. Velders, J. Feijen, D.W. Grijpma. Mathematically defined tissue engineering scaffold architectures prepared by stereolithography
Biomaterials 31:27 (2010), pp. 6909-6916.
- R. Gabbrielli. A new counter-example to Kelvin's conjecture on minimal surfaces
Phil. Mag. Lett. 89:8 (2009), pp. 483-491.
- R. Gabbrielli and M. O'Keeffe. A new simple tiling, with unusual properties, by a polyhedron with 14 faces
Acta Cryst. A64 (2008), pp. 430-431.
- R. Gabbrielli, I.G. Turner, C.R. Bowen. Development of modelling methods for materials to be used as bone substitutes Key Eng. Mat. 361-363 (2008), pp. 903-906.
- 3D Gallery (require Java)
- P42 and P42a: Two new periodic partitions of space that use polyhedra with 13 and 14 faces. P42 is also the simplest example of a hexagonal micellar phase (see lyotropic liquid crystals). P42a has less surface area than the partition by truncated octahedra. 3D also available as open and closed-cell foams.
- rug: A new simple tiling by a polyhedron with 14 faces. Better than Williams' polyhedron at approximating the actual distribution of polygons found in uniform mixtures of soap bubbles.
- P8: A polyhedron with 13 faces that fills space with its mirror image. Halfway between the rhombic dodecahedron and the truncated octahedron. This is the Wigner-Seitz cell of solid nitrogen.
- Q12: A new space-filling polyhedron with 12 faces. There are many known dodecahedral space-fillers. This one has never been described before.
- Comparison between Lord Kelvin's truncated octahedron, the Weaire-Phelan structure and the P42a partition.
- Classification of periodic models for foams based on symmetry.
- Affine nodal gyroid periodic surfaces: Obtained from an approximation by implicit functions of Schoen's G minimal surface.
- Weaire-Phelan foam: The partition of space into regions of equal volume having the lowest known surface area.
- Gallery
- All the pictures have been created with 3dt (Gavrog) + Sunflow renderings: P42a rug P8
- A few more pictures on P8 in a plain html page and in flash with more info
- Movies
- The movies below show how pattern-forming equations (in this case the Swift-Hohenberg equation) are able to find low energy lattices and nonlattices.
- Here two isosurfaces of the BCC lattice are shown. The lattice points are at the centre of the green surfaces.
The white surface is 5% off the absolute minima.
- Same with A15, a nonlattice. Also here.
- Presentations and Posters
- The Kelvin Problem Bioceramics 20 Periodic Triangulations from Pattern Forming Equations
- Curriculum Vitae
- CV
- Funding
- 2011-2014 € 149,380 Marie Curie Fellowship - FP7 COFUND; Construction sets sponsored by GEOMAG
- Links
- Javaview is a 3D geometry viewer and a mathematical visualization software. The 3d objects in this website use this format unless differently specified.
- The Surface Evolver is an interactive program for the modelling of liquid surfaces shaped by various forces and constraints.
- The Gavrog Project is a package for the analysis of periodic nets and tilings. It contains 3dt and Systre.
- K3DSurf is a program to visualize and manipulate mathematical models in three, four, five and six dimensions.
It supports parametric equations and isosurfaces.
- vcs computes Voronoi diagrams in three dimensions also with periodic boundary conditions.
Last updated on 22 April 2012