### Article

## Hamiltonian Formulation of Ideal Ferrohydrodynamics

The Hamiltonian description of ferrohydrodynamics equation for a ideal nonconducting compressible magnetic fluid with frozen-in magnetization is presented.

In this paper the behavior (break-up and creation) of a magnetic fluid bridge between two coaxial cylinders in a magnetic field of a line

conductor for any values of wetting angles of a magnetic fluid is investigated.

We demonstrate that a piecewise linear slow-fast Hamiltonian system with an equilibrium of the saddle-center type can have a sequence of small parameter values for which a one-round homoclinic orbit to this equilibrium exists. This contrasts with the well-known findings by Amick and McLeod and others that solutions of such type do not exist in analytic Hamiltonian systems, and that the separatrices are split by the exponentially small quantity. We also discuss existence of homoclinic trajectories to small periodic orbits of the Lyapunov family as well as symmetric periodic orbits near the homoclinic connection. Our further result, illustrated by simulations, concerns the complicated structure of orbits related to passage through a non-smooth bifurcation of a periodic orbit.

In this paper the behavior of a finite magnetic fluid volume on a line conductor is investigated. Here we consider the problem of a magnetic fluid drop on a line conductor and the problem of a finite magnetic fluid volume on a horizontal plane near a vertical line conductor. The possibility of the fluid shape hysteresis for a cyclic increase and decrease of the current and of spasmodic drop thickness changes at certain values of the current is treated.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.