Phase-space approach to dynamical density functional theory

The authors consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. They show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, they obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.     

Varieties of interlaced bilattices

The paper contains some algebraic results on several varieties of algebras having an (interlaced) bilattice reduct. Some of these algebras have already been studied in the literature (for instance bilattices with conflation, introduced by M. Fitting), while others arose from the algebraic study of O. Arieli and A. Avron??s bilattice logics developed in the third author??s PhD dissertation. We extend the representation theorem for bounded interlaced bilattices (proved, among others, by A. Avron) to unbounded bilattices and prove analogous representation theorems for the other classes of bilattices considered. We use these results to establish categorical equivalences between these structures and well-known varieties of lattices.     

Simple Synthesis of P1P2-Diadenosine 5′-Pyrophosphate

Pyrophosphate-linked coenzymes play essential roles in several biochemical systems. Symmetrical diadenosine-5′-pyrophosphate (Ap2A) has been synthesized from adenosine-5′-phosphate in virtually quantitative yield. The simple procedure is carried out in anhydrous pyridine using adenosine phosphoromorpholidate and adenosine monophosphate bis-(tri-n-butylammonium salt) as coupling reagents.     

Statistical approach of the irreversible entropy variation

The constructal theory is based on the thought that flow architecture is a consequence of a principle of maximization of flow access, in time, and in flow configuration that is free to be realised. The principle of maxima for the variation of the entropy due to irreversibility represents a general principle of investigation for the stability of open systems, by which it is possible to predict some macroscopic shapes, originated by the spatial organisation, in Nature, both in living and in non-living objects. Its statistical meaning has recently been introduced. Here a statistical and dynamical interpretation for the entropy due to irreversibility is proposed as a foundation of the constructal theory.     

On the global “two-sided” characteristic Cauchy problem for linear wave equations on manifolds

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth “on each side” of the initial value hypersurface. A uniqueness result in Sobolev regularity \(H^{1/2+\varepsilon }_{\mathrm {loc}}\) is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.     

Heterogeneous Ziegler-Natta catalysts: On going progress for the polyolefin industry

A great deal of research and development efforts in Ziegler Natta catalysis has been put within the last ten years into the polyolefin industry. The exploitation of new catalysts, the introduction and consolidation of advanced polymerization process technologies and, finally, the development of a broader range and of a better tailoring of product grades, have made the polyolefin market an expression of a young, dynamic, technology-driven industry. In this context heterogeneous catalysts have played a key role. Many drawbacks of the catalysts of the previous generation have been overcome. However some problems have still to be solved in order to both further improve catalyst performance and reduce the residual areas of empiricism in catalyst design and manufacture.