On Nonlinear Rayleigh-Taylor Instabilities

Some of the mathematical properties of the interface between two incompressible inviscid and immiscible fluids with different densities under the influence of a constant gravity field 9 are investigated. The purpose of this paper is to prove that linearly unstable modes for Rayleigh-Taylor instabilities give birth to nonlinear instabilities for the full nonlinear system. The main ingredient is a general instability theorem in an analytic framework which enables us to go from linear to nonlinear instabilities.     

Partially correlated phase smearing

Under the appropriate circumstances the effect of partially correlated phase smearing on the sum and difference de Haas-van Alphen frequencies generated through magnetic interaction can be treated as if the phase distribution of the two interacting oscillations were fully correlated.     

Evaluation of an edge-based registration method: application to magnetic resonance first-pass myocardial perfusion data

Purpose

Quantification of cardiac magnetic resonance (CMR) myocardial perfusion remains time consuming since it requires manual interventions to compensate for motion. Thus, the aim of this study was to evaluate a semiautomated registration method.

Materials and Methods

A rigid edge-based registration algorithm was applied on 10 patients who had rest and stress CMR acquisitions on three slice levels (apical, midventricular and basal slices). Registration efficiency was assessed qualitatively by evaluating the quality of k-means maps in terms of symmetry and heart structures identification before and after registration and quantitatively by estimating noise amplitude within the myocardium. Finally, residual registration errors were manually estimated.

Results

Before registration, k-means maps were satisfactory for 15 of 30 slices at rest and for only 5 of 30 slices during stress. After registration, the k-means maps quality was satisfactory for 29 of 30 slices at rest and for 30 of 30 slices during stress. Moreover, registration reduced noise amplitude from 49±26 to 29±11 at rest (P<.01) and from 52±14 to 30±10 during stress (P<.01). The residual horizontal and vertical shifts were 0.06±0.12 and 0.04±0.08 mm at rest and 0.32±0.69 and 0.28±0.53 mm at stress.

Conclusion

The registration was successfully tested on rest and stress CMR perfusion data. It provides a valuable basis for quantitative evaluation of myocardial perfusion.     

Synthesis and characterization of 5-octylthieno[3,4-c]pyrrole-4,6-dione derivatives as new monomers for conjugated copolymers

An efficient route for the synthesis of 1-iodo-5-octyl-4H-thieno[3,4-c]pyrrole-4,6(5H)-dione as a key intermediate to build new electron-deficient monomers and related conjugated polymers is reported. Along these lines, two new low bandgap copolymers were synthesized from Stille or Suzuki coupling. These polymers were characterized and their properties compared to those of analogous conjugated polymers.     

Synthesis and Reactivity of New 1,1-Diphenyl-2,5-Dihydrophospholium Salts

Abstract

We describe the first synthesis of new 1,1-diphenyl-2,5-dihydrophospholium salts of type 1. These salts allow the access to interesting alkadienyl phosphine oxides 3 and trienes 4. Unfortunately we could not obtain the strong nucleophilic diylide 5.