2,197 research outputs found
Delocalization in random polymer models
A random polymer model is a one-dimensional Jacobi matrix randomly composed
of two finite building blocks. If the two associated transfer matrices commute,
the corresponding energy is called critical. Such critical energies appear in
physical models, an example being the widely studied random dimer model. It is
proven that the Lyapunov exponent vanishes quadratically at a generic critical
energy and that the density of states is positive there. Large deviation
estimates around these asymptotics allow to prove optimal lower bounds on
quantum transport, showing that it is almost surely overdiffusive even though
the models are known to have pure-point spectrum with exponentially localized
eigenstates for almost every configuration of the polymers. Furthermore, the
level spacing is shown to be regular at the critical energy
Absence of continuous spectral types for certain nonstationary random models
We consider continuum random Schr\"odinger operators of the type with a deterministic background potential .
We establish criteria for the absence of continuous and absolutely continuous
spectrum, respectively, outside the spectrum of . The models we
treat include random surface potentials as well as sparse or slowly decaying
random potentials. In particular, we establish absence of absolutely continuous
surface spectrum for random potentials supported near a one-dimensional surface
(``random tube'') in arbitrary dimension.Comment: 14 pages, 2 figure
A family of Schr\"odinger operators whose spectrum is an interval
By approximation, I show that the spectrum of the Schr\"odinger operator with
potential for f continuous and , is an interval.Comment: Comm. Math. Phys. (to appear
Engineering liver
Interest in âengineering liverâ arises from multiple communities: therapeutic replacement; mechanistic models of human processes; and drug safety and efficacy studies. An explosion of micro- and nanofabrication, biomaterials, microfluidic, and other technologies potentially affords unprecedented opportunity to create microphysiological models of the human liver, but engineering design principles for how to deploy these tools effectively toward specific applications, including how to define the essential constraints of any given application (available sources of cells, acceptable cost, and user-friendliness), are still emerging. Arguably less appreciated is the parallel growth in computational systems biology approaches toward these same problemsâparticularly in parsing complex disease processes from clinical material, building models of response networks, and in how to interpret the growing compendium of data on drug efficacy and toxicology in patient populations. Here, we provide insight into how the complementary paths of engineering liverâexperimental and computationalâare beginning to interplay toward greater illumination of human disease states and technologies for drug development.National Institutes of Health (U.S.) (UH2TR000496)National Institutes of Health (U.S.) (R01-EB 010246)National Institutes of Health (U.S.) (R01-ES015241)National Institutes of Health (U.S.) (P30-ES002109
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