186 research outputs found
Mechanics and force transmission in soft composites of rods in elastic gels
We report detailed theoretical investigations of the micro-mechanics and bulk
elastic properties of composites consisting of randomly distributed stiff
fibers embedded in an elastic matrix in two and three dimensions. Recent
experiments published in Physical Review Letters [102, 188303 (2009)] have
suggested that the inclusion of stiff microtubules in a softer, nearly
incompressible biopolymer matrix can lead to emergent compressibility. This can
be understood in terms of the enhancement of the compressibility of the
composite relative to its shear compliance as a result of the addition of stiff
rod-like inclusions. We show that the Poisson's ratio of such a composite
evolves with increasing rod density towards a particular value, or {\em fixed
point}, independent of the material properties of the matrix, so long as it has
a finite initial compressibility. This fixed point is in three
dimensions and in two dimensions. Our results suggest an important
role for stiff filaments such as microtubules and stress fibers in cell
mechanics. At the same time, our work has a wider elasticity context, with
potential applications to composite elastic media with a wide separation of
scales in stiffness of its constituents such as carbon nanotube-polymer
composites, which have been shown to have highly tunable mechanics.Comment: 10 pages, 8 figure
Prodsimplicial-Neighborly Polytopes
Simultaneously generalizing both neighborly and neighborly cubical polytopes,
we introduce PSN polytopes: their k-skeleton is combinatorially equivalent to
that of a product of r simplices. We construct PSN polytopes by three different
methods, the most versatile of which is an extension of Sanyal and Ziegler's
"projecting deformed products" construction to products of arbitrary simple
polytopes. For general r and k, the lowest dimension we achieve is 2k+r+1.
Using topological obstructions similar to those introduced by Sanyal to bound
the number of vertices of Minkowski sums, we show that this dimension is
minimal if we additionally require that the PSN polytope is obtained as a
projection of a polytope that is combinatorially equivalent to the product of r
simplices, when the dimensions of these simplices are all large compared to k.Comment: 28 pages, 9 figures; minor correction
Construction and Analysis of Projected Deformed Products
We introduce a deformed product construction for simple polytopes in terms of
lower-triangular block matrix representations. We further show how Gale duality
can be employed for the construction and for the analysis of deformed products
such that specified faces (e.g. all the k-faces) are ``strictly preserved''
under projection. Thus, starting from an arbitrary neighborly simplicial
(d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose
projection to the last dcoordinates yields a neighborly cubical d-polytope. As
an extension of thecubical case, we construct matrix representations of
deformed products of(even) polygons (DPPs), which have a projection to d-space
that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both
cases the combinatorial structure of the images under projection is completely
determined by the neighborly polytope Q: Our analysis provides explicit
combinatorial descriptions. This yields a multitude of combinatorially
different neighborly cubical polytopes and DPPs. As a special case, we obtain
simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler
(2000) as well as of the ``projected deformed products of polygons'' that were
announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets
arbitrarily close to 9.Comment: 20 pages, 5 figure
QCD Thermodynamics with Improved Actions
The thermodynamics of the SU(3) gauge theory has been analyzed with tree
level and tadpole improved Symanzik actions. A comparison with the continuum
extrapolated results for the standard Wilson action shows that improved actions
lead to a drastic reduction of finite cut-off effects already on lattices with
temporal extent . Results for the pressure, the critical temperature,
surface tension and latent heat are presented. First results for the
thermodynamics of four-flavour QCD with an improved staggered action are also
presented. They indicate similarly large improvement factors for bulk
thermodynamics.Comment: Talk presented at LATTICE96(finite temperature) 4 pages, LaTeX2e
file, 6 eps-file
Algorithms for Highly Symmetric Linear and Integer Programs
This paper deals with exploiting symmetry for solving linear and integer
programming problems. Basic properties of linear representations of finite
groups can be used to reduce symmetric linear programming to solving linear
programs of lower dimension. Combining this approach with knowledge of the
geometry of feasible integer solutions yields an algorithm for solving highly
symmetric integer linear programs which only takes time which is linear in the
number of constraints and quadratic in the dimension.Comment: 21 pages, 1 figure; some references and further comments added, title
slightly change
Reconstructing a Simple Polytope from its Graph
Blind and Mani (1987) proved that the entire combinatorial structure (the
vertex-facet incidences) of a simple convex polytope is determined by its
abstract graph. Their proof is not constructive. Kalai (1988) found a short,
elegant, and algorithmic proof of that result. However, his algorithm has
always exponential running time. We show that the problem to reconstruct the
vertex-facet incidences of a simple polytope P from its graph can be formulated
as a combinatorial optimization problem that is strongly dual to the problem of
finding an abstract objective function on P (i.e., a shelling order of the
facets of the dual polytope of P). Thereby, we derive polynomial certificates
for both the vertex-facet incidences as well as for the abstract objective
functions in terms of the graph of P. The paper is a variation on joint work
with Michael Joswig and Friederike Koerner (2001).Comment: 14 page
Thermodynamics of Four-Flavour QCD with Improved Staggered Fermions
We have calculated the pressure and energy density in four-flavour QCD using
improved fermion and gauge actions. We observe a strong reduction of finite
cut-off effects in the high temperature regime, similar to what has been noted
before for the SU(3) gauge theory. Calculations have been performed on
and 16^4 lattices for two values of the quark mass,
and 0.1. A calculation of the string tension at zero temperature yields a
critical temperature for the smaller
quark mass value.Comment: 12 pages, LaTeX2e File, 11 encapsulated postscript file
MSLICE Sequencing
MSLICE Sequencing is a graphical tool for writing sequences and integrating them into RML files, as well as for producing SCMF files for uplink. When operated in a testbed environment, it also supports uplinking these SCMF files to the testbed via Chill. This software features a free-form textural sequence editor featuring syntax coloring, automatic content assistance (including command and argument completion proposals), complete with types, value ranges, unites, and descriptions from the command dictionary that appear as they are typed. The sequence editor also has a "field mode" that allows tabbing between arguments and displays type/range/units/description for each argument as it is edited. Color-coded error and warning annotations on problematic tokens are included, as well as indications of problems that are not visible in the current scroll range. "Quick Fix" suggestions are made for resolving problems, and all the features afforded by modern source editors are also included such as copy/cut/paste, undo/redo, and a sophisticated find-and-replace system optionally using regular expressions. The software offers a full XML editor for RML files, which features syntax coloring, content assistance and problem annotations as above. There is a form-based, "detail view" that allows structured editing of command arguments and sequence parameters when preferred. The "project view" shows the user s "workspace" as a tree of "resources" (projects, folders, and files) that can subsequently be opened in editors by double-clicking. Files can be added, deleted, dragged-dropped/copied-pasted between folders or projects, and these operations are undoable and redoable. A "problems view" contains a tabular list of all problems in the current workspace. Double-clicking on any row in the table opens an editor for the appropriate sequence, scrolling to the specific line with the problem, and highlighting the problematic characters. From there, one can invoke "quick fix" as described above to resolve the issue. Once resolved, saving the file causes the problem to be removed from the problem view
Towards Minimal Barcodes
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a polyhedral complex K (an object subdivided into cells which are polytopes) and an initial order of the set of vertices, we are concerned with the general problem of searching for filters (an order of the rest of the cells) that provide a minimal barcode representation in the sense of having minimal number of “k-significant” intervals, which correspond to homology classes with life-times longer than a fixed number k. As a first step, in this paper we provide an algorithm for computing such a filter for k = 1 on the Hasse diagram of the poset of faces of K
Polytopality and Cartesian products of graphs
We study the question of polytopality of graphs: when is a given graph the
graph of a polytope? We first review the known necessary conditions for a graph
to be polytopal, and we provide several families of graphs which satisfy all
these conditions, but which nonetheless are not graphs of polytopes. Our main
contribution concerns the polytopality of Cartesian products of non-polytopal
graphs. On the one hand, we show that products of simple polytopes are the only
simple polytopes whose graph is a product. On the other hand, we provide a
general method to construct (non-simple) polytopal products whose factors are
not polytopal.Comment: 21 pages, 10 figure
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