14,830 research outputs found
Minimal surfaces from circle patterns: Geometry from combinatorics
We suggest a new definition for discrete minimal surfaces in terms of sphere
packings with orthogonally intersecting circles. These discrete minimal
surfaces can be constructed from Schramm's circle patterns. We present a
variational principle which allows us to construct discrete analogues of some
classical minimal surfaces. The data used for the construction are purely
combinatorial--the combinatorics of the curvature line pattern. A
Weierstrass-type representation and an associated family are derived. We show
the convergence to continuous minimal surfaces.Comment: 30 pages, many figures, some in reduced resolution. v2: Extended
introduction. Minor changes in presentation. v3: revision according to the
referee's suggestions, improved & expanded exposition, references added,
minor mistakes correcte
Universal Jamming Phase Diagram in the Hard-Sphere Limit
We present a new formulation of the jamming phase diagram for a class of
glass-forming fluids consisting of spheres interacting via finite-ranged
repulsions at temperature , packing fraction or pressure , and
applied shear stress . We argue that the natural choice of axes for the
phase diagram are the dimensionless quantities ,
, and , where is the temperature, is the
pressure, is the stress, is the sphere diameter,
is the interaction energy scale, and is the sphere mass. We demonstrate
that the phase diagram is universal at low ; at low
pressure, observables such as the relaxation time are insensitive to details of
the interaction potential and collapse onto the values for hard spheres,
provided the observables are non-dimensionalized by the pressure. We determine
the shape of the jamming surface in the jamming phase diagram, organize
previous results in relation to the jamming phase diagram, and discuss the
significance of various limits.Comment: 8 pages, 5 figure
Mutations and short geodesics in hyperbolic 3-manifolds
In this paper, we explicitly construct large classes of incommensurable
hyperbolic knot complements with the same volume and the same initial (complex)
length spectrum. Furthermore, we show that these knot complements are the only
knot complements in their respective commensurabiltiy classes by analyzing
their cusp shapes.
The knot complements in each class differ by a topological cut-and-paste
operation known as mutation. Ruberman has shown that mutations of hyperelliptic
surfaces inside hyperbolic 3-manifolds preserve volume. Here, we provide
geometric and topological conditions under which such mutations also preserve
the initial (complex) length spectrum. This work requires us to analyze when
least area surfaces could intersect short geodesics in a hyperbolic 3-manifold.Comment: This is the final (accepted) version of this pape
2D multi-objective placement algorithm for free-form components
This article presents a generic method to solve 2D multi-objective placement
problem for free-form components. The proposed method is a relaxed placement
technique combined with an hybrid algorithm based on a genetic algorithm and a
separation algorithm. The genetic algorithm is used as a global optimizer and
is in charge of efficiently exploring the search space. The separation
algorithm is used to legalize solutions proposed by the global optimizer, so
that placement constraints are satisfied. A test case illustrates the
application of the proposed method. Extensions for solving the 3D problem are
given at the end of the article.Comment: ASME 2009 International Design Engineering Technical Conferences &
Computers and Information in Engineering Conference, San Diego : United
States (2009
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