We explore the optimal time path of carbon sequestration and carbon abatement in stabilizing
CO₂ levels under uncertainty of climate impacts. Using a two-period sequential decision making
model, we analytically derive optimal rates for the two control variables, abatement and
sequestration rates. Uncertainty is assumed to affect the desired future...
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions...
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with formulations in terms of partial differential equations governing the conservative, advective-dispersive transport of mass concentrations in divergence form,...
We derive the fundamental solution of the linearized problem of the motion of a viscous uid around a rotating body when the axis of rotation of the body is not parallel to the velocity of the uid at infinity.
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain...