We describe a class of mechanical systems for which the “method of controlled Lagrangians” provides a family of control laws that stabilize an unstable (relative) equilibrium. The controlled Lagrangian approach involves making modifications to the Lagrangian for the uncontrolled system such that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the close...

This article deals with the distribution of the view of a random environment as seen by an observer whose location at each moment is determined by the environment. The main application is in statistical fluid mechanics, where the environment consists of a random velocity field and the observer is a particle moving in the velocity field, possibly subject to molecular diffusion. Several results o...

In hierarchical models of gravitational clustering, virialized haloes are biased tracers of the matter distribution. As discussed by Mo & White (1996), this bias is nonlinear and stochastic. They developed a model which allows one to write down analytic expressions for the mean of the bias relation, in the initial Lagrangian, and the evolved, Eulerian, spaces. We provide analytic expressions fo...

In hierarchical models of gravitational clustering, virialized haloes are biased tracers of the matter distribution. As discussed by Mo & White (1996), this bias is nonlinear and stochastic. They developed a model which allows one to write down analytic expressions for the mean of the bias relation, in the initial Lagrangian, and the evolved, Eulerian, spaces. We provide analytic expressions fo...

Environmental context Iron-containing combustion particles are likely to contribute environmental iron deposition, while atmospheric acidic processing of such can promote their dissolution. Here we report the surface-mediated dissolution from ashes generated by biomass burning power plants and kilns. Examination process at several environmentally relevant pHs, suggests that pH has little impact...

There are many important theorems in number theory asserting that a sequence of arithmetic quantities of some kind is uniformly distributed. N. Katz has discovered a remarkable pattern in the finer aspects of distribution of many of these sequences, which we will describe below. Suppose for each n ≥ 1 we have a set Sn = {0 ≤ θ1 ≤ θ2 ≤ · · · ≤ θνn ≤ 1} of “angles” (normalized so that 2π = 1). We...