Aspects of diffusive-relaxation dynamics with a nonuniform, partially absorbing boundary in general porous media.

We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of the boundary geometry has been widely exploited, such as in biological and geophysical applications. We consider the situation where the critical assumptions which enable such applications break down.

Effects of inhomogeneous partial absorption and the geometry of the boundary on population evolution of molecules diffusing in general porous media.

We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese.

Two-dimensional NMR of diffusion systems.

We consider diffusion in porous media with well-connected pore space for which isolated-pore models are insufficient. Explicit pore-to-pore exchange parameters were introduced in recent 2D NMR experiments. However, such parameters capture only certain aspects of the interpore spin dynamic which, for single-fluid saturated media, are wholly determined by diffusion.

Nonresonant multiple spin echoes.

Nonresonant manipulation of nuclear spins can probe large volumes of sample situated in inhomogeneous fields outside a magnet, a geometry suitable for mobile sensors for the inspection of roads, buildings, and geological formations. However, the interference by Earth's magnetic field causes rapid decay of the signal within a few milliseconds for protons and is detrimental to this method. Here we describe a technique to suppress the effects of Earth's field by using adiabatic rotations and sudden switching of the applied fields.