Stability of an encapsulated bubble shell

The stability of an encapsulated bubble filled with gas is studied where gas is allowed to diffuse out of the bubble. A mechanistic model that takes into account shell stiffness and surface tension is considered. A critical shell radius for loss of mechanical stability is derived based on a technique adapted for small radius, where surface tension effects become substantial. A new parameter is defined that determines the relative importance of surface tension forces and shell stiffness for shell stability. The developed technique allows to predict, for a given bubble population and gas saturation level of the surrounding liquid, a range of bubble sizes which may collapse in time. Surface tension effects are dominant in determining the critical radius but have a negligible effect on the minimal radius for collapse. The influence of the surface tension on the stability of the shell is illustrated for Optison, a typical ultrasound contrast agent.     

Vibrational energy relaxation rates of H2 and D2 in liquid argon via the linearized semiclassical method

The vibrational energy relaxation (VER) rates for H2 and D2 in liquid argon (T=152 K, rho=1.45x1022 cm-3) are calculated using the linearized semiclassical (LSC) method (J. Phys. Chem. 2003, 107, 9059, 9070). The calculation is based on Fermi's golden rule. The VER rate constant is expressed in terms of the quantum-mechanical force-force correlation function, which is then estimated using the LSC method. A local harmonic approximation (LHA) is employed in order to compute the multidimensional Wigner integrals underlying the LSC approximation. The H2-Ar and D2-Ar interactions are described by the three-body potential of Bissonette et al. (J. Phys. Chem. A 1996, 105, 2639). The LHA-LSC-based VER rate constants for both D2 and H2 are found to be about 2-3 orders of magnitude slower than those obtained experimentally. However, their ratio agrees quantitatively with the corresponding experimental result. In contrast, the classical VER rate constants are found to be 8-9 orders of magnitude slower than those obtained experimentally, and their ratio is found to be qualitatively different from the corresponding experimental result.     

THE EFFECT OF LIPOSOMES'' MEMBRANE COMPOSITION ON THE BINDING OF THE PHOTOSENSITIZERS HPD AND PHOTOFRIN II

Abstract— Photofrin II (PF-II) is the commercial name of the active photosensitizer which is used in photodynamic therapy of cancer. The effect of the composition of lipid membranes on the binding of PF-II was studied and compared to hematoporphyrin derivative (Hpd), which is a complex mixture of porphyrins and from which PF-II is separated. We find that increasing the content of cholesterol in the bilayer decreases the partitioning of PF-II into the bilayer, similar to what we have found earlier with Hpd. However, inserting DMPC or DPPC into the membrane, which was shown to decrease the binding of Hpd, causes the opposite trend with PF-H. A membrane fluidizer such as benzyl alcohol also has different effects on the membrane binding of Hpd and PF-II. The rate of binding of PF-II to a lipid membrane is about 10 times lower than that of Hpd. These results as well as I^- quenching of the fluorescence of the two porphyrins indicate that PF-II is immersed less homogeneously and deeper in the bilayer than Hpd. The unique additive-dependent binding of PF-II to lipid membranes calls for care in using Hpd as a model photosensitizer.     

Numerical radius of positive matrices

We study some properties of the numerical radius of matrices with non-negative entries, and explicit ways to compute it. We also characterize positive matrices with equal spectral and numerical radii, i.e., positive spectral matrices.     

The numerical radius and specttural matrices

In this paper we investigate spectral matrices, i.e., matrices with equal spectral and numerical radii. Various characterizations and properties of these matrices are given.