A model to account for observed solar flare statistics in terms of a superposition of independent random flaring elements (assumed to be sites of magnetic reconnection in the coronal magnetic field and hence termed ‘‘ separators ’’) is described. A separator of length l is assumed to flare as a Poisson process in time, with a rate ðlÞ inversely proportional to the Alfvén transit time for the st...

In pipeline-riser systems, pressure fluctuations which result from the formation of large liquid slugs and gas surges due to operational changes or low mass flow rate from production wells and the profile of pipeline-riser systems often lead to trips at the inlet of the separator; and thereby, the problem causes a a loss of the production.In this study, on a sample deep-water oil field off the ...

We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any fixed ddimensional Euclidean space. The separator is applied in obtaining 2O( √ n) time exact algorithms for a class of NP-complete geometric problems, whose previous algorithms take nO( √ n) time . One of those problems is the well known disk cover...

We present I/O-efficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r > 0, a vertex separator of size O(N/ √ r) that partitions G into O(N/r) subgraphs of size at most r and boundary size O( √ r) can be computed in O(sort(N)) I/Os. This bound holds provided that M ≥ 56r log B. Together...

It has been widely acknowledged that the Goldman-Hodgkin-Katz (GHK) equation fully explains membrane potential behavior. The fundamental facet of the GHK equation lies in its consideration of permeability of membrane to ions, when the membrane serves as a separator for separating two electrolytic solutions. The GHK equation describes that: variation of membrane permeability to ion in accordance...

The notion of staircase separator, introduced in 2], greatly facilitates the design of divide-and-conquer algorithms for problems on rectangles. We generalize the concept of staircase separator to k-perfect staircase separator, namely a set of staircase separators which partitions a set S of n axis-parallel, disjoint rectangles into k subsets of (almost) equal size. We derive an optimal O(log n...

(1) p(x) = ∏ C ΨC(xC) ∏ S ΦS(xS) where ΨC(xC ) is the potential for a clique C , and ΦS(xS) is the potential for a separator S. After Junction Tree algorithm, the clique potential ΨC(xC) becomes the marginal probability for clique C . Thus, we are able to achieve a representation that is a product of marginals, and yet is also a representation of the joint probability. After we initialize maxim...