No abstract

(a) Relation to previous work. The connection between causality and dispersion relations for the S-matrix has been thoroughly investigated by Van Kampen, who has considered the scattering of a classical electromagnetic field 1) or of a Schrodinger particle 2) by a scatterer of finite radius. He has shown that the dispersion relations follow from a very small number of assumptions about the scatterer; the most essential one is a causality condition. In quantum field theory, the dispersion relations have also been derived from a set of general assumptions (although the assumptions concerning the interaction are more specific in this case), and a causality condition also plays an essential role 3).An entirely different approach has been taken in the derivations of dispersion relations for fixed momentum transfer which have been given by Khuri 4) and by Klein and Zemach 5) for the scattering of Schrodinger particles by a potential, and by Khuri and Treiman 6) for the scattering of Dirac particles by a potential. The form of the interaction is completely specified in these cases, and the derivations are based on the formal solution of the scattering integral equation, by means of a Fredholm expansion 4)s) or a Liouville-Neumann expansion 5). It has also been stressed that no explicit use is made of a causality condition. However, it is clear that many *) On leave of absence from Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brasil Physica 26 -209 -

Critical effects in semiclassical scattering, in which the standard approximations break down, are associated with forward peaking, rainbows, glories, orbiting and resonances. Besides giving rise to beautiful optical effects in the atmosphere, critical effects have important applications in many areas of physics. However, their interpretation and accurate treatment is difficult. This book, based on the Elliott Montroll Lectures, given at the University of Rochester, deals with the theory of these critical effects. After a preliminary chapter in which the problem of critical effects is posed, the next three chapters on coronae, rainbows and glories are written so as to be accessible to a broader audience. The main part of the book then describes the results obtained from the application of complex angular momentum techniques to scattering by homogeneous spheres. These techniques lead to practically usable asymptotic approximations, and to new physical insights into critical effects. A new conceptual picture of diffraction, regarded as a tunnelling effect, emerges. The final two chapters contain brief descriptions of applications to a broad range of fields, including linear and nonlinear optics, radiative transfer, astronomy, acoustics, seismology, atomic, nuclear and particle physics.

Recent studies indicate that the cell membrane, interacting with its attached cytoskeleton, is an important regulator of cell function, exerting and responding to forces. We investigate this relationship by looking for connections between cell membrane elastic properties, especially surface tension and bending modulus, and cell function. Those properties are measured by pulling tethers from the cell membrane with optical tweezers. Their values are determined for all major cell types of the central nervous system, as well as for macrophage. Astrocytes and glioblastoma cells, which are considerably more dynamic than neurons, have substantially larger surface tensions. Resting microglia, which continually scan their environment through motility and protrusions, have the highest elastic constants, with values similar to those for resting macrophage. For both microglia and macrophage, we find a sharp softening of bending modulus between their resting and activated forms, which is very advantageous for their acquisition of phagocytic functions upon activation. We also determine the elastic constants of pure cell membrane, with no attached cytoskeleton. For all cell types, the presence of F-actin within tethers, contrary to conventional wisdom, is confirmed. Our findings suggest the existence of a close connection between membrane elastic constants and cell function.

This is Paper I of a series on high-frequency scattering of a scalar plane wave by a transparent sphere (square potential well or barrier). It is assumed that (ka)⅓≫1,|N−1|½(ka)⅓≫1, where k is the wave-number, a is the radius of the sphere, and N is the refractive index. By applying the modified Watson transformation, previously employed for an impenetrable sphere, the asymptotic behavior of the exact scattering amplitude in any direction is obtained, including several angular regions not treated before. The distribution of Regge poles is determined and their physical interpretation is given. The results are helpful in explaining the reason for the difference in the analytic properties of scattering amplitudes for cutoff potentials and potentials with tails. Following Debye, the scattering amplitude is expanded in a series, corresponding to a description in terms of multiple internal reflections. In Paper I, the first term of the Debye expansion, associated with direct reflection from the surface, and the second term, associated with direct transmission (without any internal reflection), are treated, both for N > 1 and for N < 1. The asymptotic expansions are carried out up to (not including) correction terms of order (ka)−2. For N > 1, the behavior of the first term is similar to that found for an impenetrable sphere, with a forward diffraction peak, a lit (geometrical reflection) region, and a transition region where the amplitude is reduced to generalized Fock functions. For N < 1, there is an additional shadow boundary, associated with total reflection, and a new type of surface waves is found. They are related to Schmidt head waves, but their sense of propagation disagrees with the geometrical theory of diffraction. The physical interpretation of this result is given. The second term of the Debye expansion again gives rise to a lit region, a shadow region, and a Fock-type transition region, both for N > 1 and for N < 1. In the former case, surface waves make shortcuts across the sphere, by critical refraction. In the latter one, they excite new surface waves by internal diffraction.