The influence of external fluctuations on the bifurcational behavior of two-dimensional dynamical systems exhibiting limit cycles is investigated. Studying both exactly and approximately solvable examples it is shown that the variances of the external fluctuations occur as additional bifurcation...

We present a general theorem for the force multipole moments of arbitrary order induced in a spherically symmetric particle immersed in a fluid whose motion satisfies the linear Navier-Stokes equation for steady incompressible viscous flow. The multipole moments are expressed in terms of the...

Exact first and second order statistics of a damped mechanical oscillator with a fluctuating frequency and driven by a fluctuating force are obtained. All the cumulants of the fluctuating frequency are assumed to be delta correlated, while those of the driving force are of arbitrary form. The...

Self-consistent field equations for the dipole moments of point polarizable atoms in slabs of cubic lattices with a uniform applied electric field are constructed. Results of Toeplitz operator theory are used to characterize the ranges of atomic polarizability for which there are unique...

A new class of groups is defined for describing the symmetry of spin arrangements in magnetic crystals. The general structure of these new groups, which we name wreath groups, is determined in a mathematically rigorous manner. Wreath groups are particularly suitable for describing incommensurate...

The Wigner function of a two-dimensional electron gas in an arbitrary magnetic field perpendicular to the plane in which the electrons are confined is constructed rigorously. The function is useful in taking various statistical averages and illuminates the roles played by the hyperbolic...

A microscopic foundation of the theory of static isothermal homogeneous deformation is given for classical (ionic) crystals which may have atomic electric dipoles and which may be in a structurally modulated (slightly distorted) phase. Special effects due to the dipoles and the modulations are...

The Landau equation is obtained, for a system of particles of arbitrary statistics, by expanding the semiclassical Boltzmann collision integral in the scattering angle. The equation is next cast into the Fokker-Planck form. Both the nonrelativistic and the relativistic cases are considered. In...

A boundary condition for the distribution operator of a dilute polyatomic gas at a gas-solid interface is presented. The derivation is based on the methods of nonequilibrium thermodynamics in connection with the general reciprocity postulate for the interface. The boundary condition consists of...

The present paper gives an extension of the Provotorov theory of magnetic resonance saturation to finite temperatures. Such an extension is not straightforward because at finite temperatures when line-shape and resonance frequency become temperature dependent the weak coupling expansion in a...