Statistical mechanics of the nonlinear Schrödinger equation

We investigate the statistical mechanics of a complex fieldø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian $$H(\phi ) = \int_\Omega {[\frac{1}{2}|\nabla \phi |^2 - (1/p) |\phi |^p ] dx}$$ is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, whenΩ is the circle and theL ² norm of the field (which is conserved by the dynamics) is bounded byN, the Gibbs measureυ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only ifp andN are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, asN and the temperature are varied.     

The cycloaddition way to novel deoxy disaccharide analogs

A novel heterocycloaddition merges 2-thiono-3-ketolactones with carbohydrate glycals to afford materials which resemble disaccharides with an O-glycosidic linkage at the anomeric center and a thioether linking both C-2 and C-2′, thus creating a third heterocyclic ring. Upon desulfurization, these novel cycloadducts afford materials which are models for 2-deoxydisaccharides. Studies with two keto lactones and seven glycals are described.     

Influence of structure and solubility of chain transfer agents on the RAFT control of dispersion polymerisation in scCO2

Reversible addition–fragmentation chain transfer (RAFT) dispersion polymerisation of methyl methacrylate (MMA) is performed in supercritical carbon dioxide (scCO₂) with 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT) present as chain transfer agent (CTA) and surprisingly shows good control over PMMA molecular weight. Kinetic studies of the polymerisation in scCO₂ also confirm these data. By contrast, only poor control of MMA polymerisation is obtained in toluene solution, as would be expected for this CTA which is better suited for acrylates. In this regard, we select a range of CTAs and use them to determine the parameters that must be considered for good control in dispersion polymerisation in scCO₂. A thorough investigation of the nucleation stage during the dispersion polymerisation reveals an unexpected “in situ two-stage” mechanism that strongly determines how the CTA works. Finally, using a novel computational solvation model, we identify a correlation between polymerisation control and degree of solubility of the CTAs. All of this ultimately gives rise to a simple, elegant and counterintuitive guideline to select the best CTA for RAFT dispersion polymerisation in scCO₂.

RAFT dispersion polymerisation of methyl methacrylate is performed in scCO₂ with 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT) present as chain transfer agent (CTA) and surprisingly shows good control over PMMA molecular weight.