20,274 research outputs found
Network-Configurations of Dynamic Friction Patterns
The complex configurations of dynamic friction patterns-regarding real time
contact areas- are transformed into appropriate networks. With this
transformation of a system to network space, many properties can be inferred
about the structure and dynamics of the system. Here, we analyze the dynamics
of static friction, i.e. nucleation processes, with respect to "friction
networks". We show that networks can successfully capture the crack-like shear
ruptures and possible corresponding acoustic features. We found that the
fraction of triangles remarkably scales with the detachment fronts. There is a
universal power law between nodes' degree and motifs frequency (for triangles,
it reads T(k)\proptok{\beta} ({\beta} \approx2\pm0.4)). We confirmed the
obtained universality in aperture-based friction networks. Based on the
achieved results, we extracted a possible friction law in terms of network
parameters and compared it with the rate and state friction laws. In
particular, the evolutions of loops are scaled with power law, indicating the
aggregation of cycles around hub nodes. Also, the transition to slow rupture is
scaled with the fast variation of local heterogeneity. Furthermore, the motif
distributions and modularity space of networks -in terms of withinmodule degree
and participation coefficient-show non-uniform general trends, indicating a
universal aspect of energy flow in shear ruptures
Topological Complexity of Frictional Interfaces: Friction Networks
Through research conducted in this study, a network approach to the
correlation patterns of void spaces in rough fractures (crack type II) was
developed. We characterized friction networks with several networks
characteristics. The correlation among network properties with the fracture
permeability is the result of friction networks. The revealed hubs in the
complex aperture networks confirmed the importance of highly correlated groups
to conduct the highlighted features of the dynamical aperture field. We found
that there is a universal power law between the nodes' degree and motifs
frequency (for triangles it reads T(k)\proptok{\beta} ({\beta}
\approx2\pm0.3)). The investigation of localization effects on eigenvectors
shows a remarkable difference in parallel and perpendicular aperture patches.
Furthermore, we estimate the rate of stored energy in asperities so that we
found that the rate of radiated energy is higher in parallel friction networks
than it is in transverse directions. The final part of our research highlights
4 point sub-graph distribution and its correlation with fluid flow. For shear
rupture, we observed a similar trend in sub-graph distribution, resulting from
parallel and transversal aperture profiles (a superfamily phenomenon)
Domination Integrity of Some Path Related Graphs
The stability of a communication network is one of the important parameters for network designers and users. A communication network can be considered to be highly vulnerable if the destruction of a few elements cause large damage and only few members are able to communicate. In a communication network several vulnerability measures like binding number, toughness, scattering number, integrity, tenacity, edge tenacity and rupture degree are used to determine the resistance of network to the disruption after the failure of certain nodes (vertices) or communication links (edges). Domination theory also provides a model to measure the vulnerability of a graph network. The domination integrity of a simple connected graph is one such measure. Here we determine the domination integrity of square graph of path as well as the graphs obtained by composition (lexicographic product) of two paths
The level of occlusion of included bark affects the strength of bifurcations in hazel (Corylus avellana L.)
Bark-included junctions in trees are considered a defect as the bark weakens the union between the branches. To more accurately assess this weakening effect, 241 bifurcations from young specimens of hazel (Corylus avellana L.), of which 106 had bark inclusions, were harvested and subjected to rupture tests. Three-point bending of the smaller branches acted as a benchmark for the relative strength of the bifurcations. Bifurcations with included bark failed at higher displacements, and their modulus of rupture was 24% lower than normally formed bifurcations, while stepwise regression showed that the best predictors of strength in these bark-included bifurcations were the diameter ratio and width of the bark inclusion, which explained 16.6% and 8.1% of the variability, respectively. Cup-shaped, bark-included bifurcations where included bark was partially occluded by xylem were found, on average, to be 36% stronger than those, where included bark was situated at the bifurcation apex. These findings show that there are significant gradations in the strength of bark-included bifurcations in juvenile hazel trees that relate directly to the level of occlusion of the bark into the bifurcation. It therefore may be possible to assess the extent of the defect that a bark-included bifurcation represents in a tree by assessing the relative level of occlusion of the included bark
On the growth behaviour of Hironaka quotients
We consider a finite analytic morphism \phi = (f,g) : (X,p)\to (\C^2,0)
where is a complex analytic normal surface germ and and are
complex analytic function germs. Let be a good
resolution of with exceptional divisor . We denote
the dual graph of the resolution . We study the behaviour of the
Hironaka quotients of associated to the vertices of . We show
that there exists maximal oriented arcs in along which the Hironaka
quotients of strictly increase and they are constant on the connected
components of the closure of the complement of the union of the maximal
oriented arcs
Topology counts: force distributions in circular spring networks
Filamentous polymer networks govern the mechanical properties of many
biological materials. Force distributions within these networks are typically
highly inhomogeneous and, although the importance of force distributions for
structural properties is well recognized, they are far from being understood
quantitatively. Using a combination of probabilistic and graph-theoretical
techniques we derive force distributions in a model system consisting of
ensembles of random linear spring networks on a circle. We show that
characteristic quantities, such as mean and variance of the force supported by
individual springs, can be derived explicitly in terms of only two parameters:
(i) average connectivity and (ii) number of nodes. Our analysis shows that a
classical mean-field approach fails to capture these characteristic quantities
correctly. In contrast, we demonstrate that network topology is a crucial
determinant of force distributions in an elastic spring network.Comment: 5 pages, 4 figures. Missing labels in Fig. 4 added. Reference fixe
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