Cross-linking patterns and their images in swollen and deformed gels

Using the theory of elasticity of polymer gels we show that large-scale cross-link density patterns written into the structure of the network in the melt state, can be revealed upon swelling by monitoring the monomer density patterns. We find that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image (both types of deformation yield affinely stretched images in $\theta$ solvents). We show that in ordinary solids with spatially inhomogeneous profile of the shear modulus, isotropic stretching leads to distorted density image of this profile under isotropic deformation. Using simple physical arguments we demonstrate that the different response to isotropic stretching stems from fundamental differences between the theory of elasticity of solids and that of gels. Possible tests of our predictions and some potential applications are discussed.Comment: 16 pages, 3 figure

Microphase separation in correlated random copolymers

In this paper we present the results of a calculation of the phase diagram of a highly polydisperse multiblock copolymer in the weak segregation limit. The theory for polydisperse systems developed by Erukhimovich and Dobrynin [Erukhimovich, I.; Dobrynin, A.V. Macromol.Symp, 81, 253 (1994)] has been used. The model of the copolymer has the following characteristics: the blocklengths, as well as the molecule lengths are highly polydisperse (M(w)/M(n) = 2). The average number of blocks per molecule is very large and the effects of the finiteness of the blocklengths (the fluctuation corrections) are ignored. The resulting phase diagram shows some remarkable differences with the phase diagram of a regular monodisperse multiblock. Known differences are e.g. the order of the transition from the homogeneous state, and the variation of the period of the microstructure with the chi-parameter. Ln addition, we found a peculiar feature at the critical point: the phase boundaries have discontinuous derivatives.</p

Inverse Problem for an Electrical Dipole and the Lightning Location Passive Monitoring System

We solve the problem of the locating parameters, identifying equivalent dipole electromagnetic radiation source through measured horizontal magnetic and vertical electric components at some point of the infinite conducting ground. Methods based on analysis of measured signals are suggested. The problem under consideration, like any inverse problem of mathematical physics, is ill-conditioned. The consequences of this are the high sensitivity of the algorithm to the errors in the source data and calculation errors. All these circumstances do not allow to estimate the accuracy and reliability of the results obtained with the help of single-scale algorithms. The considered problem is contained in a complex of mathematical models of the practically important problem of forecasting the development of thunderstorm foci. Lightning meteorology focuses on investigating the lightning activities in different types of convective weather systems and the relationship of lightning to the dynamic and microphysical processes in thunderstorms. With the development and application of advanced lightning detection and location technologies, lightning meteorology has been developed into an important interdisciplinary between atmospheric electricity and meteorology. This paper reviews (1) methods to identify the dipole location and (2) possibilities to analyze the pre-radiation of thunderstorm clouds by the passive methods