Massimiliano Giona

We generalize the multipole expansion and the structure of the Faxén operator in Stokes flows obtained for bodies with no-slip to generic boundary conditions, addressing the assumptions under which this generalization is conceivable. We show that a disturbance field generated by a body immersed in an ambient flow can be expressed, independently on the boundary conditions, as a multipole expansion, the coefficients of which are the moments of the volume forces. We find that the dualism between the operator giving the disturbance field of an nth order ambient flow and the nth order Faxén operator, referred to as the Hinch–Kim dualism, holds only if the boundary conditions satisfy a property that we call Boundary-Condition reciprocity (BC-reciprocity). If this property is fulfilled, the Faxén operators can be expressed in terms of the (m, n)th order geometrical moments of the volume forces (defined in the article). In addition, it is shown that in these cases, the hydromechanics of the fluid-body system is completely determined by the entire set of the Faxén operators. Finally, classical boundary conditions of hydrodynamic applications are investigated in light of this property: boundary conditions for rigid bodies, Newtonian drops at the mechanical equilibrium, porous bodies modeled by the Brinkman equations are BC-reciprocal, while deforming linear elastic bodies, deforming Newtonian drops, non-Newtonian drops, and porous bodies modeled by the Darcy equations do not have this property. For Navier-slip boundary conditions on a rigid body, we find the analytical expression for low order Faxén operators. By using these operators, the closed form expressions for the flow past a sphere with arbitrary slip length immersed in shear and quadratic flows are obtained.

The Central Limit Theorem stands as a milestone in probability theory and statistical physics, as the privileged, if not the unique, universal route to normal distributions. This article addresses and describes several other alternative routes to Gaussianity, stemming from physical interactions, related to particle-particle and radiative particle–photon elementary processes. The concept of conservative mixing transformations of random ensembles is addressed, as it represents the other main universal distributional route to Gaussianity in classical low-energy physics. Monadic ensemble transformations are introduced, accounting for radiative particle–photon interactions, and are intimately connected with the theory of random Iterated Function Systems. For Monadic transformations, possessing a thermodynamic constraint, Gaussianity represents the equilibrium condition in two limiting cases: in the low radiative-friction limit in any space dimension, and in the high radiative-friction limit, when the dimension of the physical space tends to infinity.