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Vincenzo Vitelli
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Postdoctoral Fellow |
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My research interests are in the areas of 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. |
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Below
you find more details on two 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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Energy
Transport in Model Jammed Systems (with
N. Xu, M. Wyart, A. J. Liu, S. R. Nagel) We generate computer
models of jammed packings and calculate their energy diffusivity, a spectral
measure of transport that controls both sound attenuation and thermal
conductivity. The diffusivity of an isostatic packing is low and nearly
constant without any hint of the common divergence associated with long
wavelength phonons which are replaced in this system by extended and poorly
conducting modes. At higher packing fractions, plane wave-like states coexist
with the resonant modes localized in soft portions of the sample and
characterized by divergent Gruneisen parameters. Please click here for slides of a recent talk and a sound-bite. |
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