A Characterization of b‐Perfect Graphs

A b‐coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b‐chromatic number of a graph G is the largest integer k such that G admits a b‐coloring with k colors. A graph is b‐perfect if the b‐chromatic number is equal to the chromatic number for every induced subgraph of G. We prove that a graph is b‐perfect if and only if it does not contain as an induced subgraph a member of a certain list of 22 graphs. This entails the existence of a polynomial‐time recognition algorithm and of a polynomial‐time algorithm for coloring exactly the vertices of every b‐perfect graph. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:95–122, 2012     

Energy contracts management by stochastic programming techniques

We consider the problem of optimal management of energy contracts, with bounds on the local (time step) amounts and global (whole period) amounts to be traded, integer constraint on the decision variables and uncertainty on prices only. After building a finite state Markov chain by using vectorial quantization tree method, we rely on the stochastic dual dynamic programming (SDDP) method to solve the continuous relaxation of this stochastic optimization problem. An heuristic for computing sub optimal solutions to the integer optimization problem, based on the Bellman values of the continuous relaxation, is provided. Combining the previous techniques, we are able to deal with high-dimensional state variables problems. Numerical tests applied to realistic energy markets problems have been performed.     

Static model of a violin bow: influence of camber and hair tension on mechanical behavior

Experienced bow makers empirically know the influence of wood, tapering, and camber on the playing and tonal qualities of a bow. However, the way each parameter affects the bow mechanical behavior is not clearly established. An in-plane finite element model is developed to highlight the link between the adjustable design parameters and the mechanical behavior of a bow. This model takes into account geometric nonlinearity as well as compliance of the hair. Its validity is discussed from measurements on a bow. Results from simulations are compared to experimental results from previous studies. The consequences of adjusting hair tension and camber are then investigated.     

Generalization of the k-moment method using the maximum entropy principle. Application to the NBKM and full spectrum SLMB gas radiation models

The k-moment method is generalized by applying the maximum entropy principle to get several estimates of the k-distribution function on any kind of spectral interval as a function of the first two moments of the absorption coefficient. Corresponding formulations of the blackbody weighted band averaged transmission function of a gaseous uniform path are obtained. Different constraints involving the first and second order positive, first order negative and logarithmic moments are introduced together with a physical meaning whenever it is possible. Different sets of these constraints are considered to get maximum entropy estimates of the distributions functions: the Dirac, exponential, Gamma, inverse Gaussian and reciprocal inverse Gaussian k-distribution functions. Analytical formulas are provided for each of these distributions and for their associated transmission function, as a function of the mean and variance of the absorption coefficient. The methodology can be applied considering any spectral interval: narrow, wide, the full spectrum, continuous or not. Thus the resulting associated transmission and cumulative k-distribution functions can be utilized in the frame of a large variety of gas radiation models. Hence the k-moment method using the maximum entropy principle is assessed in the frame of the NBKM and full spectrum SLMB gas radiation models. A series of test cases implying comparisons with reference Line-by-Line results exhibits which maximum entropy k-distributions are likely to give the best estimations of narrow band or total emitted intensities, curves-of-growth of the total emission function and full spectrum cumulative k-distribution functions. In particular, the inverse Gaussian and Gamma k-distributions seem most of the time to perform very well.     

Influence of polarization filtering on image registration precision in underwater conditions

Underwater images often suffer from poor visibility due to photon scattering. However, in some cases, optical polarization filtering techniques can decrease the contribution of the scattered light and improve the visual image quality. In this Letter, the influence of these techniques for underwater image registration is analyzed, particularly when backscattered light is the main perturbation induced by the submarine environment. This analysis is performed using the Cramer-Rao bound and relies on a standard image formation model, taking into account various kinds of noises.     

A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate

We present a level set approach to the numerical simulation of the Stefan problem on non-graded adaptive Cartesian grids, i.e. grids for which the size ratio between adjacent cells is not constrained. We use the quadtree data structure to discretize the computational domain and a simple recursive algorithm to automatically generate the adaptive grids. We use the level set method on quadtree of Min and Gibou [C. Min, F. Gibou, A second order accurate level set method on non-graded adaptive Cartesian grids, J. Comput. Phys. 225 (2007) 300–321] to keep track of the moving front between the two phases, and the finite difference scheme of Chen et al. [H. Chen, C. Min, F. Gibou, A supra-convergent finite difference scheme for the poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids, J. Sci. Comput. 31 (2007) 19–60] to solve the heat equations in each of the phases, with Dirichlet boundary conditions imposed on the interface. This scheme produces solutions that converge supralinearly (∼1.5)$(\sim 1.5)$ in both the L¹$L^1$ and the L^∞$L^{\infty }$ norms, which we demonstrate numerically for both the temperature field and the interface location. Numerical results also indicate that our method can simulate physical effects such as surface tension and crystalline anisotropy. We also present numerical data to quantify the saving in computational resources.     

Polarized He spin-filters using MEOP for wide-angle polarization analysis

Polarized ³He spin-filters are currently employed on a wide range of neutron instruments at the ILL, primarily for diffraction, reflectometry and fundamental physics. A wide range of recent and ongoing improvements are enabling the implementation of this technique for wide-angle polarization analysis for inelastic measurements. These include

• Progress in metastability-exchange optical pumping (MEOP), resulting in on-beam polarization levels of up to 80%.

• 1st generation “Pastis-1” coils for rotating the neutron polarization at the sample position, allowing for “XYZ” polarization analysis.

• 2nd generation “Pastis-2” coils with no blind angles in the equatorial plane.

• Spin-filter cells with glued silicon windows, allowing for wide-angle “banana” cells with very low background scattering.

• Polarization-preserving capillaries for transferring polarized ³He gas into the cell without manual access.

The development of capillary transfer also allows for a completely new way of working with ³He spin-filters: connecting the cells on the instruments directly to the MEOP filling station several tens of meters away and allowing for quasi-continuous operation.     

Cyanuric chloride: an efficient reagent for the Lossen rearrangement

An efficient method for the Lossen rearrangement that uses 2,4,6-trichloro-1,3,5-triazine (TCT) as a promoter is reported. This procedure allowed the preparation of various carbamates, thiocarbamates, and ureas in good yields directly from the corresponding hydroxamic acids.