713 research outputs found
Hyperbolic planforms in relation to visual edges and textures perception
We propose to use bifurcation theory and pattern formation as theoretical
probes for various hypotheses about the neural organization of the brain. This
allows us to make predictions about the kinds of patterns that should be
observed in the activity of real brains through, e.g. optical imaging, and
opens the door to the design of experiments to test these hypotheses. We study
the specific problem of visual edges and textures perception and suggest that
these features may be represented at the population level in the visual cortex
as a specific second-order tensor, the structure tensor, perhaps within a
hypercolumn. We then extend the classical ring model to this case and show that
its natural framework is the non-Euclidean hyperbolic geometry. This brings in
the beautiful structure of its group of isometries and certain of its subgroups
which have a direct interpretation in terms of the organization of the neural
populations that are assumed to encode the structure tensor. By studying the
bifurcations of the solutions of the structure tensor equations, the analog of
the classical Wilson and Cowan equations, under the assumption of invariance
with respect to the action of these subgroups, we predict the appearance of
characteristic patterns. These patterns can be described by what we call
hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of
the planforms that were used in [1, 2] to account for some visual
hallucinations. If these patterns could be observed through brain imaging
techniques they would reveal the built-in or acquired invariance of the neural
organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table
Control of long-range correlations in turbulence
The character of turbulence depends on where it develops. Turbulence near
boundaries, for instance, is different than in a free stream. To elucidate the
differences between flows, it is instructive to vary the structure of
turbulence systematically, but there are few ways of stirring turbulence that
make this possible. In other words, an experiment typically examines either a
boundary layer or a free stream, say, and the structure of the turbulence is
fixed by the geometry of the experiment. We introduce a new active grid with
many more degrees of freedom than previous active grids. The additional degrees
of freedom make it possible to control various properties of the turbulence. We
show how long-range correlations in the turbulent velocity fluctuations can be
shaped by changing the way the active grid moves. Specifically, we show how not
only the correlation length but also the detailed shape of the correlation
function depends on the correlations imposed in the motions of the grid. Until
now, large-scale structure had not been adjustable in experiments. This new
capability makes possible new systematic investigations into turbulence
dissipation and dispersion, for example, and perhaps in flows that mimic
features of boundary layers, free streams, and flows of intermediate character.Comment: This paper has been accepted to Experiments in Fluids. 25 pages, 10
figure
Quantum Spin Ice and dimer models with Rydberg atoms
Quantum spin ice represents a paradigmatic example on how the physics of
frustrated magnets is related to gauge theories. In the present work we address
the problem of approximately realizing quantum spin ice in two dimensions with
cold atoms in optical lattices. The relevant interactions are obtained by
weakly admixing van der Waals interactions between laser admixed Rydberg states
to the atomic ground state atoms, exploiting the strong angular dependence of
interactions between Rydberg p-states together with the possibility of
designing step-like potentials. This allows us to implement Abelian gauge
theories in a series of geometries, which could be demonstrated within state of
the art atomic Rydberg experiments. We numerically analyze the family of
resulting microscopic Hamiltonians and find that they exhibit both classical
and quantum order by disorder, the latter yielding a quantum plaquette valence
bond solid. We also present strategies to implement Abelian gauge theories
using both s- and p-Rydberg states in exotic geometries, e.g. on a 4-8 lattice.Comment: 26 pages, 16 figure
Molecular dynamics simulation study of grain boundary migration in nanocrystalline Pd
We present a new methodology for measuring the grain boundary mobility for curved boundaries using molecular-dynamics simulation of grain growth in a small, specifically tailored Pd nanocrystalline structure. In the model system, the boundaries move under the forces provided by their curvature and in the presence of the triple junctions. As a consequence of grain boundary migration the boundary area per unit volume is reduced and the mean grain size of grains increases with time. Our investigation shows that at elevated temperatures the activation energy for grain growth in this specifically tailored microstructure is very close to that of grain boundary diffusion. These findings suggest that the migration mechanism of curved grain boundaries might be mediated by short distance diffusion of atoms in the grain boundaries
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