1,680 research outputs found
Excitable Delaunay triangulations
In an excitable Delaunay triangulation every node takes three states
(resting, excited and refractory) and updates its state in discrete time
depending on a ratio of excited neighbours. All nodes update their states in
parallel. By varying excitability of nodes we produce a range of phenomena,
including reflection of excitation wave from edge of triangulation, backfire of
excitation, branching clusters of excitation and localized excitation domains.
Our findings contribute to studies of propagating perturbations and waves in
non-crystalline substrates
Improvement of the robustness on geographical networks by adding shortcuts
In a topological structure affected by geographical constraints on liking,
the connectivity is weakened by constructing local stubs with small cycles, a
something of randomness to bridge them is crucial for the robust network
design. In this paper, we numerically investigate the effects of adding
shortcuts on the robustness in geographical scale-free network models under a
similar degree distribution to the original one. We show that a small fraction
of shortcuts is highly contribute to improve the tolerance of connectivity
especially for the intentional attacks on hubs. The improvement is equivalent
to the effect by fully rewirings without geographical constraints on linking.
Even in the realistic Internet topologies, these effects are virtually
examined.Comment: 14 pages, 10 figures, 1 tabl
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An Object-Orientated Approach to Hydrological Modelling using Triangular Irregular Networks
Discrete Geometric Structures in Homogenization and Inverse Homogenization with application to EIT
We introduce a new geometric approach for the homogenization and inverse
homogenization of the divergence form elliptic operator with rough conductivity
coefficients in dimension two. We show that conductivity
coefficients are in one-to-one correspondence with divergence-free matrices and
convex functions over the domain . Although homogenization is a
non-linear and non-injective operator when applied directly to conductivity
coefficients, homogenization becomes a linear interpolation operator over
triangulations of when re-expressed using convex functions, and is a
volume averaging operator when re-expressed with divergence-free matrices.
Using optimal weighted Delaunay triangulations for linearly interpolating
convex functions, we obtain an optimally robust homogenization algorithm for
arbitrary rough coefficients. Next, we consider inverse homogenization and show
how to decompose it into a linear ill-posed problem and a well-posed non-linear
problem. We apply this new geometric approach to Electrical Impedance
Tomography (EIT). It is known that the EIT problem admits at most one isotropic
solution. If an isotropic solution exists, we show how to compute it from any
conductivity having the same boundary Dirichlet-to-Neumann map. It is known
that the EIT problem admits a unique (stable with respect to -convergence)
solution in the space of divergence-free matrices. As such we suggest that the
space of convex functions is the natural space in which to parameterize
solutions of the EIT problem
An analysis of the dense packing of disks : a computer simulated approach
This thesis is concerned with the analysis of dense packing of hard disks. The Voronoi diagram and the geometric neighbours were first computed. The average number of geometric neighbours of a disk is six. It is thus more efficient to choose structural neighbours from among the geometric neighbours than from among all other disks.
Through the Monte Carlo simulation by Rosato et. al., disk configurations after pouring and subsequent shaking were provided for analysis. The mean number of geometric neighbours and the average coordination number were computed. The angular distribution of the structural neighbours was discussed. The packing fraction increases with number of shakes in a linear relationship. It seems to be packing into an ordered close packing after continued shaking.
A configuration constrained by two rigid vertical walls was analyzed. It was found the packing fraction is smallest in the vicinity of the wall and increased asymptotically to the mean packing fraction when moving away from the wall
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