3,475 research outputs found
Phase Diagrams for Deformable Toroidal and Spherical Surfaces with Intrinsic Orientational Order
A theoretical study of toroidal membranes with various degrees of intrinsic
orientational order is presented at mean-field level. The study uses a simple
Ginzburg-Landau style free energy functional, which gives rise to a rich
variety of physics and reveals some unusual ordered states. The system is found
to exhibit many different phases with continuous and first order phase
transitions, and phenomena including spontaneous symmetry breaking, ground
states with nodes and the formation of vortex-antivortex quartets. Transitions
between toroidal phases with different configurations of the order parameter
and different aspect ratios are plotted as functions of the thermodynamic
parameters. Regions of the phase diagrams in which spherical vesicles form are
also shown.Comment: 40, revtex (with epsf), M/C.TH.94/2
From singularities to graphs
In this paper I analyze the problems which led to the introduction of graphs
as tools for studying surface singularities. I explain how such graphs were
initially only described using words, but that several questions made it
necessary to draw them, leading to the elaboration of a special calculus with
graphs. This is a non-technical paper intended to be readable both by
mathematicians and philosophers or historians of mathematics.Comment: 23 pages, 27 figures. Expanded version of the talk given at the
conference "Quand la forme devient substance : puissance des gestes,
intuition diagrammatique et ph\'enom\'enologie de l'espace", which took place
at Lyc\'ee Henri IV in Paris from 25 to 27 January 201
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