We propose a phase-space formulation for the nonlinear Schrödinger equation with a white-noise potential in order to shed light on two problems: the rate of dispersion and the singularity formation. Our main tools are the energy laws and the variance identity. The method is completely elementary. For the problem of dispersion, we show that in the absence of dissipation the ensemble-average disp...

At IMM the advantages of an alternative synthesis route for biodiesel under supercritical conditions in micro-structured reactors applying heterogeneous catalysts are currently under investigation. Target of the development work is to build a pilot plant with an annual production capacity of 40 t which covers all process engineering steps and verifies their functionality in laboratory and field...

We study continuum percolation on certain negatively dependent point processes on R. Specifically, we study the Ginibre ensemble and the planar Gaussian zero process, which are the two main natural models of translation invariant point processes on the plane exhibiting local repulsion. For the Ginibre ensemble, we establish the uniqueness of infinite cluster in the supercritical phase. For the ...

This paper describes recent progress made in the use of high pressure or supercritical fluids to process polymers into three-dimensional tissue engineering scaffolds. Three current examples are highlighted: foaming of acrylates for use in cartilage tissue engineering; plasticization and encapsulation of bioactive species into biodegradable polyesters for bone tissue engineering; and a novel las...

We study random walks on supercritical percolation clusters on wedges in Z, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. Häggström and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on Z is equivalent to the (a.s.) exis...

In this paper, supercritical carbon dioxide (SC CO2) was first reported to help prepare unique flexible free-standing graphene oxide/nanofiber (GC) films. A novel hierarchical superior electrode material with polypyrrole (PPy) deposited on GO/CNF-SC (GC-SC) films was prepared via an in situ polymerization process. Our experimental results indicate that SC CO2 can not only enlarge the space betw...

monolithic aerogels of high molecular weight polyethylene (mw= 3x106- 6x106 g/mol) have been prepared by solvent extraction with supercritical carbon dioxide from thermoreversible gels prepared in decalin. these low density and highly porous aerogels present an apparent porosity up to 90%. the aerogel morphology observed by scanning electron microscopy (sem) is characterized by spherulitic stru...

enzyme efficiency was investigated in the lipase-catalyzed hydrolysis of canola oil in supercritical carbon dioxide (scco2). immobilized lipase from mucor miehie (lipozyme im) was used as the catalyst and the results showed that enzyme efficiency dropped at high pressures indicating a possible change in enzyme microstructure. therefore, scanning electron microscopy (sem) was used as a supplemen...