Numerical aspects of improvement of the unsteady pipe flow equations

The paper presents an analysis of some recently proposed improvements of the water hammer equations, which concern the friction term in the momentum equation. A comparison of the experimental data and numerical results shows that the required damping and smoothing of the pressure wave cannot be obtained by modification of the friction factor only. In order to evaluate the significance of the introduced improvements into the momentum equation, the accuracy of the numerical solution has been analysed using the modified equation approach. The analysis shows why the physical dissipation process observed in the water hammer phenomenon cannot be reproduced with the commonly used source term in Darcy–Weisbach form, representing friction force in the momentum equation. Therefore, regardless of the proposed form of the friction factor for unsteady flow, the model of water hammer improved in such a way keeps its hyperbolic character. Consequently, it cannot ensure the expected effects of damping and smoothing of the calculation head oscillations. Copyright © 2007 John Wiley & Sons, Ltd.     

Nonlinear diffusion and Nelson-Brown movement

The nonlinear diffusion process, which can be described as the Nelson-Brown motion, is considered. The obtained equation becomes the classical linear diffusion equation for small relaxation times, and for long relaxation times it is transferred into the Schrödinger-like equation. The possible nonequilibrium stationary states are discussed.     

Imaging electron trajectories in a laser-wakefield cavity using betatron X-ray radiation

We demonstrate that betatron x-ray radiation accurately provides direct imaging of electrons trajectories accelerated in laser wakefields. Experimental far field x-ray beam profiles reveal that electrons can follow similar transverse trajectories with typical excursions of 1.5 microm+/-0.5 microm in the plane of laser polarization and 0.7 microm+/-0.2 microm in the plane perpendicular.     

Formation of Amphiphilic Molecules from the Most Common Marine Polysaccharides,toward a Sustainable Alternative?

Marine polysaccharides are part of the huge seaweeds resources and present many applications for several industries. In order to widen their potential as additives or bioactive compounds, some structural modifications have been studied. Among them, simple hydrophobization reactions have been developed in order to yield to grafted polysaccharides bearing acyl-, aryl-, alkyl-, and alkenyl-groups or fatty acid chains. The resulting polymers are able to present modified physicochemical and/or biological properties of interest in the current pharmaceutical, cosmetics, or food fields. This review covers the chemical structures of the main marine polysaccharides, and then focuses on their structural modifications, and especially on hydrophobization reactions mainly esterification, acylation, alkylation, amidation, or even cross-linking reaction on native hydroxyl-, amine, or carboxylic acid functions. Finally, the question of the necessary requirement for more sustainable processes around these structural modulations of marine polysaccharides is addressed, considering the development of greener technologies applied to traditional polysaccharides.     

A simple constructive approach to quadratic BSDEs with or without delay

This paper provides a simple approach for the consideration of quadratic BSDEs with bounded terminal conditions. Using solely probabilistic arguments, we retrieve the existence and uniqueness result derived via PDE-based methods by Kobylanski (2000) [14]. This approach is related to the study of quadratic BSDEs presented by Tevzadze (2008) [19]. Our argumentation, as in Tevzadze (2008) [19], highly relies on the theory of BMO martingales which was used for the first time for BSDEs by Hu et al. (2005) [12]. However, we avoid in our method any fixed point argument and use Malliavin calculus to overcome the difficulty. Our new scheme of proof allows also to extend the class of quadratic BSDEs, for which there exists a unique solution: we incorporate delayed quadratic BSDEs, whose driver depends on the recent past of the Y$Y$ component of the solution. When the delay vanishes, we verify that the solution of a delayed quadratic BSDE converges to the solution of the corresponding classical non-delayed quadratic BSDE.     

Decompositions of the free additive convolution

We introduce and study a new type of convolution of probability measures, denoted μν and called the s-free additive convolution, which is defined by the subordination functions associated with the free additive convolution. We derive an alternating decomposition of μν for compactly supported μ and ν, using another convolution called orthogonal additive convolution. This decomposition leads to two types of ‘complete’ alternating decompositions of the free additive convolution μ?ν. More importantly, we develop an operatorial approach to the subordination property and introduce the associated notion of s-free independence. Moreover, we establish relations between convolutions associated with the main notions of noncommutative independence (free, monotone and boolean). Finally, our result leads to natural decompositions of the free product of rooted graphs.