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Vincenzo Vitelli
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Assistant Professor Soft Condensed Matter Theory Group |
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My research interests are in the areas of soft condensed matter theory
and statistical mechanics with an emphasis, over the last few years, on the
physics of frustrated and amorphous materials. I have contributed to
elucidate the properties of crystalline, liquid crystalline and He films
confined on in-homogeneously curved substrates. Current work is addressing
energy transport and vibrational dynamics in jammed packings of soft spheres
just above the onset of mechanical rigidity. These simple models offer
insights into the physics of granular materials and glasses. I have recently applied concepts and methods originating in condensed matter theory to the study of weak gravitational lensing. |
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Below
you find more details on three problems that I am currently investigating: |
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Geometric
Theory of Columnar Order on Curved Surfaces (with
C.D. Santangelo, R. D. Kamien and D. R. Nelson) We study geometrically
frustrated systems composed by thin self-assembled columns such as the ones
generated in block-copolymer systems. In the limit of vanishing compressional
strain, the normals to the columns converge (diverge) in regions of positive
(negative) Gaussian curvature, in analogy to the focusing of light rays by a
lens. This simple observation is the basis for a versatile analytical
approach that we have developed to calculate the geometric interaction
between dislocations and Gaussian curvature in columnar as well as crystalline
monolayers. The resulting geometrical forces play an important role in stress
relaxation dynamics, elastic instabilities, and melting. Please click here for our paper and poster.
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The stochastic geometry of the cosmic shear (with
B. Jain and R. D. Kamien) Shear fields due to weak gravitational lensing have characteristic coherent patterns. We describe the topological defects in shear fields in terms of the curvature of an imaginary surface whose height function is given by the lensing potential. The resulting defects can be identified as umbilical points of the potential surface produced by ellipsoidal halos. At large redshifts, statistical properties such as the abundance of defects can be readily expressed in terms of the correlation function of the lensing potential. On the right, we show a simulated lensing shear map
overlayed on the contour plot of the (projected) mass distribution fluctuations that generated it. Defects of positive and negative 1/2 index are indicated by black and red dots respectively. Please click here for our paper.
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Energy
transport, localization and anharmonicity in model amorphous solids (with
N. Xu, M. Wyart, A. J. Liu and S. R. Nagel) We use the Kubo formula to calculate the frequency dependence of the energy diffusivity
for jammed sphere packings under compression. At the Boson peak frequency, we find a sharp
crossover from a Rayleigh scattering regime to a diffusivity that is
nearly frequency independent. At the crossover, the vibrational modes are
quasi-localized resonances trapped in under-coordinated portions of the
sample and hence very susceptible to tiny pressure perturbations, as
indicated by their large Gruneisen parameters. As the system is
decompressed towards the jamming transition, the crossover frequency
shifts to zero with a characteristic scaling that depends on the average
connectivity of the jammed packing. Please click here for slides of a recent talk and a sound-bite. |
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