1,064 research outputs found
Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model
Using a popular vertex-based model to describe a spatially disordered planar
epithelial monolayer, we examine the relationship between cell shape and
mechanical stress at the cell and tissue level. Deriving expressions for stress
tensors starting from an energetic formulation of the model, we show that the
principal axes of stress for an individual cell align with the principal axes
of shape, and we determine the bulk effective tissue pressure when the
monolayer is isotropic at the tissue level. Using simulations for a monolayer
that is not under peripheral stress, we fit parameters of the model to
experimental data for Xenopus embryonic tissue. The model predicts that
mechanical interactions can generate mesoscopic patterns within the monolayer
that exhibit long-range correlations in cell shape. The model also suggests
that the orientation of mechanical and geometric cues for processes such as
cell division are likely to be strongly correlated in real epithelia. Some
limitations of the model in capturing geometric features of Xenopus epithelial
cells are highlighted.Comment: 29 pages, 10 figures, revisio
De Sitter Uplift with Dynamical Susy Breaking
We propose the use of D-brane realizations of Dynamical Supersymmetry
Breaking (DSB) gauge sectors as sources of uplift in compactifications with
moduli stabilization onto de Sitter vacua. This construction is fairly
different from the introduction of anti D-branes, yet allows for tunably small
contributions to the vacuum energy via their embedding into warped throats. The
idea is explicitly exemplified by the embedding of the 1-family DSB
model in a local warped throat with fluxes, which we discuss in detail in terms
of orientifolds of dimer diagrams.Comment: 26 pages, 16 figures. v3: version accepted in JHEP with minor
corrections in the introduction and extra reference
Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible
We analyze the computational complexity of the many types of
pencil-and-paper-style puzzles featured in the 2016 puzzle video game The
Witness. In all puzzles, the goal is to draw a simple path in a rectangular
grid graph from a start vertex to a destination vertex. The different puzzle
types place different constraints on the path: preventing some edges from being
visited (broken edges); forcing some edges or vertices to be visited
(hexagons); forcing some cells to have certain numbers of incident path edges
(triangles); or forcing the regions formed by the path to be partially
monochromatic (squares), have exactly two special cells (stars), or be singly
covered by given shapes (polyominoes) and/or negatively counting shapes
(antipolyominoes). We show that any one of these clue types (except the first)
is enough to make path finding NP-complete ("witnesses exist but are hard to
find"), even for rectangular boards. Furthermore, we show that a final clue
type (antibody), which necessarily "cancels" the effect of another clue in the
same region, makes path finding -complete ("witnesses do not exist"),
even with a single antibody (combined with many anti/polyominoes), and the
problem gets no harder with many antibodies. On the positive side, we give a
polynomial-time algorithm for monomino clues, by reducing to hexagon clues on
the boundary of the puzzle, even in the presence of broken edges, and solving
"subset Hamiltonian path" for terminals on the boundary of an embedded planar
graph in polynomial time.Comment: 72 pages, 59 figures. Revised proof of Lemma 3.5. A short version of
this paper appeared at the 9th International Conference on Fun with
Algorithms (FUN 2018
Geographica: A Benchmark for Geospatial RDF Stores
Geospatial extensions of SPARQL like GeoSPARQL and stSPARQL have recently
been defined and corresponding geospatial RDF stores have been implemented.
However, there is no widely used benchmark for evaluating geospatial RDF stores
which takes into account recent advances to the state of the art in this area.
In this paper, we develop a benchmark, called Geographica, which uses both
real-world and synthetic data to test the offered functionality and the
performance of some prominent geospatial RDF stores
Two-dimensional localized structures in harmonically forced oscillatory systems
Two-dimensional spatially localized structures in the complex Ginzburg–Landau equation with 1:1 resonance are studied near the simultaneous presence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcation on one of them. The bifurcation structures of steady circular fronts and localized target patterns are computed in the Turing-stable and Turing-unstable regimes. In particular, localized target patterns grow along the solution branch via ring insertion at the core in a process reminiscent of defect-mediated snaking in one spatial dimension. Stability of axisymmetric solutions on these branches with respect to axisymmetric and nonaxisymmetric perturbations is determined, and parameter regimes with stable axisymmetric oscillons are identified. Direct numerical simulations reveal novel depinning dynamics of localized target patterns in the radial direction, and of circular and planar localized hexagonal patterns in the fully two-dimensional system
A note on near hexagons with lines of size 3
We classify all finite near hexagons which satisfy the following properties for a certain t(2) is an element of {1, 2, 4}: (i) every line is incident with precisely three points; (ii) for every point x, there exists a point y at distance 3 from x; (iii) every two points at distance 2 from each other have either 1 or t(2) + 1 common neighbours; (iv) every quad is big. As a corollary, we obtain a classification of all finite near hexagons satisfying (i), (ii) and (iii) with t(2) equal to 4
Constitutive Model for Material Comminuting at High Shear Rate
The modeling of high velocity impact into brittle or quasibrittle solids is
hampered by the unavailability of a constitutive model capturing the effects of
material comminution into very fine particles. The present objective is to
develop such a model, usable in finite element programs. The comminution at
very high strain rates can dissipate a large portion of the kinetic energy of
an impacting missile. The spatial derivative of the energy dissipated by
comminution gives a force resisting the penetration, which is superposed on the
nodal forces obtained from the static constitutive model in a finite element
program. The present theory is inspired partly by Grady's model for comminution
due to explosion inside a hollow sphere, and partly by analogy with turbulence.
In high velocity turbulent flow, the energy dissipation rate is enhanced by the
formation of micro-vortices (eddies) which dissipate energy by viscous shear
stress. Similarly, here it is assumed that the energy dissipation at fast
deformation of a confined solid gets enhanced by the release of kinetic energy
of the motion associated with a high-rate shear strain of forming particles.
For simplicity, the shape of these particles in the plane of maximum shear rate
is considered to be regular hexagons. The rate of release of free energy
density consisting of the sum of this energy and the fracture energy of the
interface between the forming particle is minimized. The particle sizes are
assumed to be distributed according to Schuhmann's power law. It is concluded
that the minimum particle size is inversely proportional to the (2/3)-power of
the shear strain rate, that the kinetic energy release is to proportional to
the (2/3)-power, and that the dynamic comminution creates an apparent material
viscosity inversely proportional to the (1/3)-power of the shear strain rate.Comment: 13 pages, 2 figure
Partitioning Regular Polygons into Circular Pieces I: Convex Partitions
We explore an instance of the question of partitioning a polygon into pieces,
each of which is as ``circular'' as possible, in the sense of having an aspect
ratio close to 1. The aspect ratio of a polygon is the ratio of the diameters
of the smallest circumscribing circle to the largest inscribed disk. The
problem is rich even for partitioning regular polygons into convex pieces, the
focus of this paper. We show that the optimal (most circular) partition for an
equilateral triangle has an infinite number of pieces, with the lower bound
approachable to any accuracy desired by a particular finite partition. For
pentagons and all regular k-gons, k > 5, the unpartitioned polygon is already
optimal. The square presents an interesting intermediate case. Here the
one-piece partition is not optimal, but nor is the trivial lower bound
approachable. We narrow the optimal ratio to an aspect-ratio gap of 0.01082
with several somewhat intricate partitions.Comment: 21 pages, 25 figure
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