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Monotone Properties (monotone + property)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

Indecomposable quasi-characteristics scheme on pyramidal stencil and its application for numerical simulation of two-phase flows through heterogeneous porous medium

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2002
Do Young Kwak
Abstract A new high-resolution indecomposable quasi-characteristics scheme with monotone properties based on pyramidal stencil is considered. This scheme is based on consideration of two high-resolution numerical schemes approximated governing equations on the pyramidal stencil with different kinds of dispersion terms approximation. Two numerical solutions obtained by these schemes are analyzed, and the final solution is chosen according to the special criterion to provide the monotone properties in regions where discontinuities of solutions could arise. This technique allows to construct the high-order monotone solutions and keeps both the monotone properties and the high-order approximation in regions with discontinuities of solutions. The selection criterion has a local character suitable for parallel computation. Application of the proposed technique to the solution of the time-dependent 2D two-phase flows through the porous media with the essentially heterogeneous properties is considered, and some numerical results are presented. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 44,55, 2002 [source]

High-resolution monotone schemes based on quasi-characteristics technique

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2001
Do Young Kwak
Abstract In this article, we consider a new technique that allows us to overcome the well-known restriction of Godunov's theorem. According to Godunov's theorem, a second-order explicit monotone scheme does not exist. The techniques in the construction of high-resolution schemes with monotone properties near the discontinuities of the solution lie in choosing of one of two high-resolution numerical solutions computed on different stencils. The criterion for choosing the final solution is proposed. Results of numerical tests that compare with the exact solution and with the numerical solution obtained by the first-order monotone scheme are presented. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 262,276, 2001 [source]

Partition-based algorithm for estimating transportation network reliability with dependent link failures

JOURNAL OF ADVANCED TRANSPORTATION, Issue 3 2008
Agachai Sumalee
Evaluating the reliability of a transportation network often involves an intensive simulation exercise to randomly generate and evaluate different possible network states. This paper proposes an algorithm to approximate the network reliability which minimizes the use of such simulation procedure. The algorithm will dissect and classify the network states into reliable, unreliable, and un-determined partitions. By postulating the monotone property of the reliability function, each reliable and/or unreliable state can be used to determine a number of other reliable and/or unreliable states without evaluating all of them with an equilibrium assignment procedure. The paper also proposes the cause-based failure framework for representing dependent link degradation probabilities. The algorithm and framework proposed are tested with a medium size test network to illustrate the performance of the algorithm. [source]

What is the furthest graph from a hereditary property?

RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2008
Noga Alon
Abstract For a graph property P, the edit distance of a graph G from P, denoted EP(G), is the minimum number of edge modifications (additions or deletions) one needs to apply to G to turn it into a graph satisfying P. What is the furthest graph on n vertices from P and what is the largest possible edit distance from P? Denote this maximal distance by ed(n,P). This question is motivated by algorithmic edge-modification problems, in which one wishes to find or approximate the value of EP(G) given an input graph G. A monotone graph property is closed under removal of edges and vertices. Trivially, for any monotone property, the largest edit distance is attained by a complete graph. We show that this is a simple instance of a much broader phenomenon. A hereditary graph property is closed under removal of vertices. We prove that for any hereditary graph property P, a random graph with an edge density that depends on P essentially achieves the maximal distance from P, that is: ed(n,P) = EP(G(n,p(P))) + o(n2) with high probability. The proofs combine several tools, including strengthened versions of the Szemerédi regularity lemma, properties of random graphs and probabilistic arguments. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source]