Finite-size effects due to Goldstone particles in lattice gauge theory

We study the finite-size effects associated with the appearance of a light, i.e. Goldstone, particle in the Kogut-Susskind lattice gauge theory. We analytically study the order parameter $\text{(}\text{X}\text{X)}$ and the two-meson propagator in the strong coupling limit on a finite lattice. We give their explicit interpolations between the broken phase of the infinite-volume limit and the symmetric one of the finite system. We argue that the results obtained in the strong coupling limit are more general.     

An Extension of Generalized Linear Models to Finite Mixture Outcome Distributions

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the analysis of categorical and count outcomes when standard generalized linear models (GLMs) cannot adequately express variability observed in the data. We propose an extension of GLMs where the response follows a finite mixture distribution and the regression of interest is linked to the mixture’s mean. This approach may be preferred over a finite mixture of regressions when the population mean is of interest; here, only one regression must be specified and interpreted in the analysis. A technical challenge is that the mixture’s mean is a composite parameter that does not appear explicitly in the density. The proposed model maintains its link to the regression through a certain random effects structure and is completely likelihood-based. We consider typical GLM cases where means are either real-valued, constrained to be positive, or constrained to be on the unit interval. The resulting model is applied to two example datasets through Bayesian analysis. Supporting the extra variation is seen to improve residual plots and produce widened prediction intervals reflecting the uncertainty. Supplementary materials for this article are available online.     

Combined operando studies of new electrode materials for Li-ion batteries

The performances of Li-ion batteries depend on many factors amongst which the important ones are the electrode materials and their structural and electronic evolution upon cycling. For a better understanding of lithium reactivity mechanism of many materials the combination of X-Ray Powder Diffraction (XRPD) and Transmission Mössbauer Spectroscopy (TMS) providing both structural and electronic information during the electrochemical cycling has been carried out. Thanks to the design of a specific electrochemical cell, derived from a conventional Swagelock cell, such measurements have been realised in operando mode. Two examples illustrate the greatness of combining XRPD and TMS for the study of LiFe_0.75Mn_0.25PO₄ as positive electrode and TiSnSb as negative electrode. Different kinds of insertion or conversion reactions have been identified leading to a better optimization and design of performing electrodes.     

Decomposition for adjustable robust linear optimization subject to uncertainty polytope

We present in this paper a general decomposition framework to solve exactly adjustable robust linear optimization problems subject to polytope uncertainty. Our approach is based on replacing the polytope by the set of its extreme points and generating the extreme points on the fly within row generation or column-and-row generation algorithms. The novelty of our approach lies in formulating the separation problem as a feasibility problem instead of a max–min problem as done in recent works. Applying the Farkas lemma, we can reformulate the separation problem as a bilinear program, which is then linearized to obtained a mixed-integer linear programming formulation. We compare the two algorithms on a robust telecommunications network design under demand uncertainty and budgeted uncertainty polytope. Our results show that the relative performance of the algorithms depend on whether the budget is integer or fractional.     

Diisothiocyanates as heterodienophiles or dipolarophiles in the presence of α‐thioxothioamides or mesoionic thiazoles

Reactions of α‐thioxothioamides ( 1 ) with diisothiocyanates were carried out in the hope of generating the N,N′‐bis(1,3‐thiazoline‐2‐thiones) ( A ). Although that purpose could not be achieved, we succeeded in preparing the monocycloadducts 7 from the phenylene‐1,2‐diisothiocyanate ( 4 ). The benzimidazole derivatives 8 and 9 were also characterized and a mechanism was assumed to account for this intramolecular process. On the other hand, the regioselective synthesis of the N,N′‐biimidazole ( 13 ) containing the phenylene bridge was performed by the treatment of the 5‐aminothiazolium chloride ( 2 ) with the diisothiocyanate ( 4 ) in a basic medium. The mesoionic derivative 13 probably arises from the monoimidazolium‐4‐thiolate ( 12 ) which was shown to react with the salt 2 under similar conditions to give the primary cycloadduct 14 as an intermediate towards the bis(imidazolium) ( 13 ). © 2001 John Wiley & Sons, Inc. Heteroatom Chem 12:617–624, 2001     

Addition of isocyanides to α‐(methylthio)‐benzylidenamidinium iodides: A surprising access to 2‐(dialkylamino)imidazoles and 3,5‐diamino‐2H‐pyrrolium salts

A number of 2‐(dialkylamino)‐5‐(methylthio)imidazoles 2 are obtained by treating the formamidinium iodides 1a,b with isocyanides R³ NC under mild conditions. Reduction of these species can occur in the reaction medium to furnish the corresponding imidazoles 3 . In some cases, double cycloaddition across the imine bond of starting salts 1 also provides the (azetidin‐1‐yl‐methylene)ammonium iodides 4 . Reactions with tert‐butyl and isopropyl isocyanides in refluxing acetonitrile convert the acetamidinium iodide 1c into the 3,5‐diamino‐2H‐pyrrolium salts 7 . Mechanisms are suggested to account for these ring‐closure processes. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:370–376, 2000     

Uranium and fluorine cycles in the nuclear industry

In the nuclear fuel cycle, fluorine is currently not recycled. In this paper, we have examined the possible routes to implement such a cycle. Because UF₆ deconversion requires an excess of water, aqueous HF is produced. Two alternatives are then possible: either separate HF from H₂O or recycle the HF-H₂O in the deconversion process. Alternative UF₆ deconversion could also be implemented to resorb the high UF₆ inventory.