Efficient separation routines for the symmetric traveling salesman problem I: general tools and comb separation

This is the first of a series of two papers dedicated to efficient separation heuristics for violated inequalities in the context of solving to optimality instances of the Traveling Salesman Problem via branch-and-cut. In this paper we give the basic ideas behind these heuristics and design heuristics for comb separation. The second paper will deal with more complex inequalities such as Clique Tree, Star or Path and Ladder inequalities and give computational results. Received: September 1999 / Accepted: August 2001?Published online February 14, 2002     

Transcendance de l'invariant modulaire en caractéristique finie

Transcendence of the modular invariant in finite characteristic Abstract. Let J be the Fourier expansion at infinity of the modular invariant j associated to a Drinfeld module of rank 2 defined on the algebraic closure of and t an element of the completion of . Then at least one of the two elements t, J(t) is transcendental over .

Received: October 22, 1997; in final form January 21, 1998     

Improving chaos-based pseudo-random generators in finite-precision arithmetic

Nonlinear Dynamics - One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is to use the least significant bits or digits of finite-precision numbers defined...     

Hertz contact at finite friction and arbitrary profiles

Axisymmetric contact at finite Coulomb friction and arbitrary profiles is examined analytically and numerically for dissimilar linear elastic solids. Invariance and generality are aimed at and an incremental procedure is developed resulting in a reduced benchmark problem corresponding to a rigid flat indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values. Save for the influence of the coefficients of friction and contraction ratio, it is shown that at partial slip the evolving relative stick-slip contour is independent of any convex and smooth contact profile at monotonic loading. For flat and conical profiles with rounded edges and apices, results are illustrated for relations between force, depth and contact contours together with surface stress distributions. The solution for dissimilar solids in a full space is transformed to a half-space problem and solved for a combination of material parameters in order to first determine interface traction distributions. Subsequently, full field values for the two solids were computed individually. In order to predict initiation of fracture and plastic flow, results are reported for the location and magnitude of maximum tensile stress and effective stress, respectively, for a range of geometrical and material parameters. In two illustrations, predicted results are compared with experimental findings related to initiation of brittle fracture and load-depth relations at nanoindentation.     

Assessment of filtered gas–solid momentum transfer models via a linear wave propagation speed test

The propagation speeds of linear waves in gas–solid suspensions depend strongly on the solids volume fraction and the wave frequency. The latter is due to gas–solid momentum transfer and allows a simple test on filtered gas–solid momentum transfer models. Such models may predict linear wave propagation speeds different from those obtained with the non-filtered model at wave frequencies higher than the filter frequency, but not at wave frequencies lower than the filter frequency.     

Monte Carlo method of radiative transfer applied to a turbulent flame modeling with LES

Radiative transfer plays an important role in the numerical simulation of turbulent combustion. However, for the reason that combustion and radiation are characterized by different time scales and different spatial and chemical treatments, the radiation effect is often neglected or roughly modelled. The coupling of a large eddy simulation combustion solver and a radiation solver through a dedicated language, CORBA, is investigated. Two formulations of Monte Carlo method (Forward Method and Emission Reciprocity Method) employed to resolve RTE have been compared in a one-dimensional flame test case using three-dimensional calculation grids with absorbing and emitting media in order to validate the Monte Carlo radiative solver and to choose the most efficient model for coupling. Then the results obtained using two different RTE solvers (Reciprocity Monte Carlo method and Discrete Ordinate Method) applied on a three-dimensional flame holder set-up with a correlated-k distribution model describing the real gas medium spectral radiative properties are compared not only in terms of the physical behavior of the flame, but also in computational performance (storage requirement, CPU time and parallelization efficiency). To cite this article: J. Zhang et al., C. R. Mecanique 337 (2009).     

New 1,3,5-triphenyl-2-pyrazoline-containing 3-hydroxychromones as highly solvatofluorochromic ratiometric polarity probes

Two novel 1,3,5-triphenyl-2-pyrazoline moiety containing derivatives of 3-hydroxychromone were synthesized and studied by ¹H NMR, absorption and fluorescence spectroscopy. The prospects of practical application of these compounds exhibiting high solvatofluorochromism into analytical chemistry and biophysics as effective ratiometric polarity probes were discussed proceeding from the data on their fluorescent properties.