Self-action in Gravity

On a particle moving with variable acceleration in the flat space-time affects the self-force due to outgoing radiation. The gravitational fields bring an additional contribution to self-force due to scattering waves on the curved backgrounds. This force is not zero even for a particle at rest. A review of the self-interaction in the gravitational field is presented. We consider the self-force for the particle connected with the vector and scalar fields. Different backgrounds are considered -- black holes, stars, topological defects, and wormholes.Comment: 65 page

Semiclassical wormholes

Smooth-throat wormholes are treated on as possessing quantum fluctuation energy with scalar massive field as its source. Heat kernel coefficients of the Laplace operator are calculated in background of the arbitrary-profile throat wormhole with the help of the zeta-function approach. Two specific profile are considered. Some arguments are given that the wormholes may exist. It serves as a solution of semiclassical Einstein equations in the range of specific values of length and certain radius of wormhole's throat and constant of non-minimal connection.Comment: 28 pages, 4 figures, revtex

Van der Waals interaction between an atom with spherical plasma shell

We consider the van der Waals energy of an atom near the infinitely thin sphere with finite conductivity which model the fullerene. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of vacuum fluctuations in framework of the zeta-function approach. The energy for a single atom is obtained from this expression by consideration of the rare media. In the limit of the infinite radius of the sphere the Casimir-Polder expression for an atom and plate is recovered. For finite radius of sphere the energy of an atom monotonously falls down as $d^{-3}$ close to the sphere and $d^{-7}$ far from the sphere. For hydrogen atom on the surface of the fullerene $C_{60}$ we obtain that the energy is $3.8 eV$. We obtain also that the polarizability of fullerene is merely cube of its radius.Comment: 10 pages, 5 figure

Modeling of interstitial branching of axonal networks

A single axon can generate branches connecting with plenty synaptic targets. Process of branching is very important for making connections in central nervous system. The interstitial branching along primary axon shaft occurs during nervous system development. Growing axon makes pause in its movement and leaves active points behind its terminal. The new branches appear from these points. We suggest mathematical model to describe and investigate neural network branching process. The model under consideration describes neural network growth in which the concentration of axon guidance molecules manages axon's growth. We model the interstitial branching from axon shaft. Numerical simulations show that in the model framework axonal networks are similar to neural network.Comment: 12 pages, 7 figure