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...

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 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.

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...

An expression for the force on a sphere moving with a time-dependent velocity through an incompressible fluid in nonstationary, nonhomogeneous flow is obtained for the case of arbitrary slip on the surface of the sphere.

The systematic theory of multiple scattering which we gave in a previous paper is further elaborated for critical scattering. It is shown that in each order the multiple-scattering intensity near the critical point is in essence a contraction of consecutive uncorrelated single-scattering...

Thermodynamic and statistical mechanical arguments indicate that the temperature derivative of the dielectric constant of fluids diverges weakly at the critical point. Following a thermodynamic procedure proposed by Mistura, we derive an expansion for the static dielectric constant of fluids...

It is shown that the assumptions of causality and time-reversal invariance severely restrict the possibility to describe the fluctuations of a variable in a nonlinear Markovian system using a Langevin equation. In fact a theorem is proven which implies that a Langevin force which is independent...

The correlation function of temperature fluctuations around homogeneous stationary states of the ballast resistor is evaluated by extending the theory of thermal fluctuations around equilibrium states to non-equilibrium situations. It is found that equal-time temperature fluctuations become...