Rate processes on fractals: Theory, simulations, and experiments

Distribution Theory on P.c.f. Fractals

We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure theorem showing that distributions are locally-finite sums of powers of the Laplacian applied to continuous functions, and an analysis of th...

Fractals and domain theory

We show that a measurement μ on a continuous dcpo D extends to a measurement μ̄ on the convex powerdomain CD iff it is a Lebesgue measurement. In particular, kerμ must be metrizable in its relative Scott topology. Moreover, the space ker μ̄ in its relative Scott topology is homeomorphic to the Vietoris hyperspace of kerμ, i.e., the space of nonempty compact subsets of kerμ in its Vietoris topolog...

Rate of mixing controls rate and outcome of autocatalytic processes: theory and microfluidic experiments with chemical reactions and blood coagulation.

This article demonstrates that the rate of mixing can regulate the rate and outcome of both biological and nonbiological autocatalytic reaction systems that display a threshold response to the concentration of an activator. Plug-based microfluidics was used to control the timing of reactions, the rate of mixing, and surface chemistry in blood clotting and its chemical model. Initiation of clott...

Localized harmonic motion imaging: theory, simulations and experiments.

Several techniques have been developed in an effort to estimate mechanical properties of tissues. These techniques typically estimate static or harmonic motion resulting from an externally or internally applied mechanical stimulus. In this paper, we discuss the advantages of utilizing a new technique that performs radiofrequency (RF) signal tracking to estimate the localized oscillatory motion ...

Sequential Auctions with Multi-Unit Demand: Theory, Experiments and Simulations