On acceleration in three dimensions

The stochastic acceleration problem in two dimensions

We consider the motion of a particle in a two-dimensional spatially homogeneous mixing potential and show that its momentum converges to the Brownian motion on a circle. This complements the limit theorem of Kesten and Papanicolaou [4] proved in dimensions d ≥ 3.

On algebraically defined graphs in three dimensions

Let F be a field of characteristic zero or of a positive odd characteristic p. For a polynomial f ∈ F[x, y], we define a graph ΓF(xy, f) to be a bipartite graph with vertex partition P ∪L, P = F = L, and (p1, p2, p3) ∈ P is adjacent to [l1, l2, l3] ∈ L if and only if p2 + l2 = p1l1 and p3 + l3 = f(p1, l1). If f = xy, the graph ΓF(xy, xy ) has the length of a shortest cycle (the girth) equal to ...

Biology in three dimensions

Most things in biology spread out into three dimensions, and many biological web sites include three-dimensional images. But biologists want more than a look at something. They want to pick it up and look at it from all sides, which is where three-dimensional images that can be manipulated online really come into their own. One approach to such interactive images relies on VRML (virtual reality...

Collapsars in Three Dimensions

We present the results of 3-dimensional simulations of the direct collapse to a black hole of a rotating, 60M⊙, zero metallicity, population III star. Because the structure of this star (angular momentum, density and temperature profiles) is similar to many collapsar gamma-ray burst progenitors, these calculations have implications beyond the fate of population III stars. These simulations prov...

Supersymmetry in Three Dimensions