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A useful representation for the radial part of the Coulomb Green's function is derived in the form of a double series in Laguerre polynomials with two free (arbitrary) parameters α and α′ . An appropriate choice of α and α′ leads to a cardinal simplification in calculations of matrix...
In order to form the intricate network of synaptic connections in the brain, the growth cones migrate through the embryonic environment to their targets using chemical communication. As a first step to study self-wiring, 2D model systems of neurons have been used. We present a simple model to...
It has been shown that the surface free energy for a smooth interface between a nematic liquid crystal (NLC) and an isotropic medium contains four different contributions: a standard anchoring term, an elastic term and two curvature terms. In this paper we show that the four coefficients that...
We study the nonlinear dynamical behavior of cavity polaritons in a semiconductor microcavity with a multiple quantum-well structure. It is shown numerically within the framework of the semiclassical model that for a sufficiently strong exciton-photon coupling and a sufficiently large number of...
The kinetic equation for high energy electrons in neutral gases is derived. The collision integral which fully takes into account both the scattering of high energy electrons and the growth of their number due to ionization processes is obtained.
Within the framework of a Landau expansion of the free energy we consider the transition into a non-uniform state. The order parameter ψ ( x ) is assumed to be of one-component type and the modulation period small to ensure the applicability of the Landau expansion in the derivatives of ψ. With...
We give the correct prescriptions for the terms involving ∂ x −1 δ ( x − y ), in the Hamiltonian structures of the AKNS and DNLS systems, necessary for the Jacobi identities to hold. We establish that the sl (2) and sl (3) AKNS systems are tri-Hamiltonians and construct two compatible...
A two-step detection strategy is suggested for the precise measurement of the optical phase shift. In the first step an unsharp , but unbiased , joint measurement of the phase and photon number is performed by heterodyning the signal field. Information coming from this step is then used for...
The different types of temperature-concentration phase diagrams of liquid crystal mixtures containing the Smectic A, the ferroelectric Smectic C ∗ , and the antiferroelectric Smectic C A ∗ phases, are worked out theoretically.
The morphological instabilities of two-dimensional hexagonal crystals in lipid monolayers are studied. Fluorescence microscopy indicates that beyond a critical size the faceted crystal develops into dendrites with unusual tip growth behavior, which is not consistent with the current theory of...
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