We extend our previously developed scheme to evaluate the static mobility tensors of an arbitrary number of spheres in a viscous fluid, to the case of finite frequencies.

A Hamiltonian formalism for hydrodynamics of ideal fluids is developed with the help of Seliger and Whitham's variational principle. It is shown that a density distribution function in the phase space of the mass-density, momentum-density and energy-density fields obeys a Liouville-equation

We formulate a scheme describing the fluctuations in a system obeying the non-linear hydrodynamic equations. The random fluxes are assumed to be Gaussian processes with white noise. It is shown that the usual expressions for the systematic parts of the dissipative fluxes are consistent with this...

A general scheme is presented to evaluate the mobility tensors of an arbitrary number of spheres, immersed in a viscous fluid, in a power series expansion in R-1, where R is a typical distance between spheres. Some general properties of these (translational and rotational) mobility tensors are...

We derive by means of a canonical transformation the variational principle of Seliger and Whitham for the Eulerian description of ideal hydrodynamics from the more familiar variational principle that yields the equations of motion of an ideal fluid in the Lagrangian description.

The differential real space renormalization method, recently introduced by Hillhorst et al., is applied to the linear Ising chain. It is shown that chains with spatially homogeneous as well as inhomogeneous or quenched random interactions can be treated. For the first two cases the free energy...

The variational principles introduced by Kadanoff et al. in the renormalization theory are analyzed. It is shown that the values for the specific heat critical exponent α which can be found by a variational method are restricted to α 0 or α = 1 (first order transition). The reason is the...

A previously developed scheme—to evaluate the (translational and rotational) mobility tensors for an arbitrary number of spheres in an unbounded fluid—is extended to include the presence of a plane wall. General expressions for the friction tensors and the fluid velocity field are also obtained.

We have analyzed the implications of the energy of anisotropy of a ferromagnetic sphere suspended in a carrier fluid in its dynamics. The rotational viscosity, which for a particular geometry represents the increase of the viscosity of the system due to the presence of an external magnetic...