The Experts below are selected from a list of 66366 Experts worldwide ranked by ideXlab platform
Wenan Yong - One of the best experts on this subject based on the ideXlab platform.
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accuracy of the viscous stress in the lattice boltzmann equation with simple boundary conditions
Physical Review E, 2012Co-Authors: Wenan YongAbstract:Based on the theory of asymptotic analysis, we prove that the viscous stress tensor computed with the lattice Boltzmann equation (LBE) in a two-dimensional domain is indeed second-order accurate in space. We only consider simple bounce-back boundary conditions which can be reduced to the periodic boundary conditions by using the method of image. While the LBE with nine velocities on two-dimensional square lattice (i.e., the D2Q9 model) and with the Bhatnagar-Gross-Krook collision model is used as an example in this work, our proof can be extended to the LBE with any Linear Relaxation collision models in both two and three dimensions.
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accuracy of the viscous stress in the lattice boltzmann equation with simple boundary conditions
Physical Review E, 2012Co-Authors: Wenan YongAbstract:Based on the theory of asymptotic analysis, we prove that the viscous stress tensor computed with the lattice Boltzmann equation (LBE) in a two-dimensional domain is indeed second-order accurate in space. We only consider simple bounce-back boundary conditions which can be reduced to the periodic boundary conditions by using the method of image. While the LBE with nine velocities on two-dimensional square lattice (i.e., the D2Q9 model) and with the Bhatnagar-Gross-Krook collision model is used as an example in this work, our proof can be extended to the LBE with any Linear Relaxation collision models in both two and three dimensions.
Ali Ridha Mahjoub - One of the best experts on this subject based on the ideXlab platform.
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critical extreme points of the 2 edge connected subgraph polytope
2006Co-Authors: Jean Fonlupt, Ali Ridha MahjoubAbstract:In this paper we study the extreme points of the polytope P(G), the Linear Relaxation of the 2-edge connected spanning subgraph polytope of a graph G. We introduce a partial ordering on the extreme points of P(G) and give necessary conditions for a non-integer extreme point of P(G) to be minimal with respect to that ordering. We show that, if X is a non-integer minimal extreme point of P(G), then G and X can be reduced, by means of some reduction operations, to a graph G' and an extreme point X of P(G') where G' and X'satisfy some simple properties. As a consequence we obtain a characterization of the perfectly 2-edge connected graphs, the graphs for which the polytope P(G) is integral.
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the k edge connected subgraph problem i polytopes and critical extreme points
Linear Algebra and its Applications, 2004Co-Authors: Didi M Biha, Ali Ridha MahjoubAbstract:Abstract In this paper we consider the Linear Relaxation of the k -edge connected subgraph polytope, P ( G , k ), given by the trivial and the so-called cut inequalities. We introduce an ordering on the fractional extreme points of P ( G , k ) and describe some structural properties of the minimal extreme points with respect to that ordering. Using this we give sufficient conditions for P ( G , k ) to be integral.
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on the Linear Relaxation of the 2 node connected subgraph polytope
Discrete Applied Mathematics, 1999Co-Authors: Ali Ridha Mahjoub, Charles NocqAbstract:In this paper, we study the Linear Relaxation P(G) of the 2-node connected subgraph polytope of a graph G. We introduce an ordering on the fractional extreme points of P(G) and we give a characterization of the minimal extreme points with respect to that ordering. This yields a polynomial method to separate a minimal extreme point of P(G) from the 2-node connected subgraph polytope. It also provides a new class of facet defining inequalities for this polytope.
Heather Ratcliffe - One of the best experts on this subject based on the ideXlab platform.
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resonance broadening due to particle scattering and mode coupling in the quasi Linear Relaxation of electron beams
Journal of Geophysical Research, 2014Co-Authors: N H Bian, Eduard P Kontar, Heather RatcliffeAbstract:Of particular interest for radio and hard X-ray diagnostics of accelerated electrons during solar flares is the understanding of the basic nonLinear mechanisms regulating the Relaxation of electron beams propagating in turbulent plasmas. In this work, it is shown that in addition to scattering of beam electrons, scattering of the beam-generated Langmuir waves via for instance mode coupling can also result in broadening of the wave-particle resonance. We obtain a resonance-broadened version of weak turbulence theory with mode coupling to ion sound modes. Resonance broadening is presented here as a unified framework which can quantitatively account for the reduction and possible suppression of the beam instability due to background scattering of the beam electrons themselves or due to scattering of the beam-generated Langmuir waves in fluctuating plasmas. Resonance broadening being essentially equivalent to smoothing of the electron phase space distribution is used to construct an intuitive physical picture for the stability of inverted populations of fast electrons that are commonly observed in situ to propagate in the solar wind.
Hongwei Jiao - One of the best experts on this subject based on the ideXlab platform.
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A Note on a Class of Optimization Problems in System Engineering
2016Co-Authors: Hongwei Jiao, Jingben Yin, Yongqiang ChenAbstract:Abstract. In this technical note, we develop an approach to globally solve a class of optimization problems in system engineering based on the recent paper ([1]). Actually the problem we investigated is more general, since we extend numerators and denominators of Linear ratios to generalized polynomial functions. And we give a new Linear Relaxation method for obtaining the lower bound of problems. Our approach is easy to be implemented, since it need not additional special program to the upper and lower bound for numerator and denominator of each generalized polynomial ratio
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a practicable branch and bound algorithm for sum of Linear ratios problem
European Journal of Operational Research, 2015Co-Authors: Hongwei Jiao, Sanyang LiuAbstract:This article presents a practicable algorithm for globally solving sum of Linear ratios problem (SLR). The algorithm works by globally solving a biLinear programming problem (EQ) that is equivalent to the problem (SLR). In the algorithm, by utilizing convex envelope and concave envelope of biLinear function, the initial nonconvex programming problem is reduced to a sequence of Linear Relaxation programming problems. In order to improve the computational efficiency of the algorithm, a new accelerating technique is introduced, which provides a theoretical possibility to delete a large part of the investigated region in which there exists no global optimal solution of the (EQ). By combining this innovative technique with branch and bound operations, a global optimization algorithm is designed for solving the problem (SLR). Finally, numerical experimental results show the feasibility and efficiency of the proposed algorithm.
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global optimization of generalized Linear fractional programming with nonLinear constraints
Applied Mathematics and Computation, 2006Co-Authors: Hongwei Jiao, Yunrui Guo, Peiping ShenAbstract:This paper presents a branch-and-bound algorithm for globally solving a wide class of generalized Linear fractional programming problems (GLFP). This class includes such problems as: minimizing a sum, or error for product of a finite number of ratios of Linear functions, Linear multiplicative programming, polynomial programming, etc. – over nonconvex feasible region. First a problem (Q) is derived which is equivalent to problem (GLFP). In the algorithm, lower bounds are derived by solving a sequence of Linear Relaxation programming problems, which is based on the construction of the Linear lower bounding functions for the objective function and constraint functions of problem (Q) over the feasible region. Convergent property of the presented algorithm is proved and numerical results are given to show the feasibility of the proposed algorithm.
Ignacio E Grossmann - One of the best experts on this subject based on the ideXlab platform.
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global optimal scheduling of crude oil blending operations with rtn continuous time and multiparametric disaggregation
Industrial & Engineering Chemistry Research, 2014Co-Authors: Pedro M Castro, Ignacio E GrossmannAbstract:This paper addresses the modeling of crude oil operations in refineries assuming that all properties blend Linearly. Guidelines are given on how to generate a Resource-Task Network superstructure that implicitly handles the complex logistics, while extending the scope of a well-known continuous-time formulation to variable recipe tasks with multiple input materials. The new single time grid formulation has the advantage of avoiding computationally inefficient big-M constraints, unlike previously proposed unit-specific and priority-slot based models. Through the solution of a set of test problems from the literature, we show that the resulting mixed-integer nonLinear programs can be solved close to global optimality by the commercial solver GloMIQO for the objective of gross margin maximization but not for operating cost minimization. We also show that adopting a two-step MILP-NLP algorithm where the mixed-integer Linear Relaxation is derived from multiparametric disaggregation can reduce the optimality ga...
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optimality based bound contraction with multiparametric disaggregation for the global optimization of mixed integer biLinear problems
Journal of Global Optimization, 2014Co-Authors: Pedro M Castro, Ignacio E GrossmannAbstract:We address nonconvex mixed-integer biLinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer Linear Relaxation of the biLinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal).
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tightening the Linear Relaxation of a mixed integer nonLinear program using constraint programming
Integration of AI and OR Techniques in Constraint Programming, 2009Co-Authors: Sylvain Mouret, Ignacio E Grossmann, Pierre PestiauxAbstract:This paper aims at solving a nonconvex mixed integer nonLinear programming (MINLP) model used to solve a refinery crude-oil operations scheduling problem. The model is mostly Linear but contains biLinear products of continuous variables in the objective function. It is possible to define a Linear Relaxation of the model leading to a weak bound on the objective value of the optimal solution. A typical method to circumvent this issue is to discretize the continuous space and to use Linear Relaxation constraints based on variables lower and upper bounds (e.g. McCormick convex envelopes) on each subdivision of the continuous space. This work explores another approach involving constraint programming (CP). The idea is to use an additional CP model which is used to tighten the bounds of the continuous variables involved in biLinear terms and then generate cuts based on McCormick convex envelopes. These cuts are then added to the mixed integer Linear program (MILP) during the search leading to a tighter Linear Relaxation of the MINLP. Results show large reductions of the optimality gap of a two step MILP-NLP solution method due to the tighter Linear Relaxation obtained.