1,596 research outputs found
Self-consistent calculation of electric potentials in Hall devices
Using a first-principles classical many-body simulation of a Hall bar, we
study the necessary conditions for the formation of the Hall potential: (i)
Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions,
and (iii) confinement to a finite system. By propagating thousands of
interacting electrons over million time-steps we capture the build-up of the
self-consistent potential, which resembles results obtained by
conformal-mapping methods. As shown by a microscopic model of the current
injection, the Hall effect is linked to specific boundary conditions at the
particle reservoirs.Comment: 6 pages, 7 figure
Persistent Homology and String Vacua
We use methods from topological data analysis to study the topological
features of certain distributions of string vacua. Topological data analysis is
a multi-scale approach used to analyze the topological features of a dataset by
identifying which homological characteristics persist over a long range of
scales. We apply these techniques in several contexts. We analyze N=2 vacua by
focusing on certain distributions of Calabi-Yau varieties and Landau-Ginzburg
models. We then turn to flux compactifications and discuss how we can use
topological data analysis to extract physical informations. Finally we apply
these techniques to certain phenomenologically realistic heterotic models. We
discuss the possibility of characterizing string vacua using the topological
properties of their distributions.Comment: 32 pages, 12 pdf figure
Density-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps
of simply-connected open surfaces in . Using a natural principle
of density diffusion in physics, we propose an effective algorithm for
computing density-equalizing flattening maps with any prescribed density
distribution. By varying the initial density distribution, a large variety of
mappings with different properties can be achieved. For instance,
area-preserving parameterizations of simply-connected open surfaces can be
easily computed. Experimental results are presented to demonstrate the
effectiveness of our proposed method. Applications to data visualization and
surface remeshing are explored
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