Generalized similarity, renormalization groups, and nonlinear clocks for multiscaling.

Fixed points of the renormalization group operator Rp,rX(t)≡X(rt)/rp are said to be p-self-similar. Here X(t) is an arbitrary stochastic process. The concept of a p-self-similar process is generalized via the renormalization group operator RF,GX(t)=F[X(G(t))], where F and G are bijections on (-∞,∞) and [0,∞), respectively. If X(t) is a fixed point of RF,G, then X(t) is said to be (F,G)-self-similar. We say Y(t) is (F,G)-X(t)-similar if RF,GX(t)=Y(t) in distribution. Exit time distributions and finite-size Lyapunov exponents were obtained for these latter processes. A power law multiscaling process is defined with a multipower-law clock. This process is employed to statistically represent diffusion in a nanopore, a monolayer fluid confined between atomically structured surfaces. The tools presented provide a straightforward method to statistically represent any multiscaling process in time.

Two-scale, three-phase theory for swelling drug delivery systems. Part I: constitutive theory.

Polymeric carriers used in drug delivery applications, such as hydroxypropyl methylcellulose, that swell significantly upon coming in contact with water (or biological fluid) have been historically difficult to model due to the complex interplay of forces. This article seeks to introduce a thermodynamically consistent framework in which to address such problems. Here, a constitutive theory is developed that is applicable to viscoelastic polymers carrying an initially elastic drug that subsequently dissolves when exposed to a viscous fluid. The theoretical model consists of three phases, the polymer, drug, and fluid. A novel form of Darcy's law is reported that clearly distinguishes between distortional and dilatational forces and accounts for the affect of polymer relaxation on fluid transport. A standard form of Fick's law is also derived.

Finite-size Lyapunov exponent for Levy processes.

The finite-size Lyapunov exponent (FSLE) is the exponential rate at which two particles separate from a distance of r to a x r (a>1) and provides a measure of dispersive mixing in chaotic systems. It is shown analytically that for particle trajectories governed by symmetric alpha -stable Levy motion, the FSLE is proportional to the diffusion coefficient and inversely proportional to r(alpha). This power law provides an easy method to determine the parameters for Levy processes and hence has applications to superdiffusion in the atmospheric, oceanic, and terrestrial sciences.

NMR imaging experiments for the verification of stochastic transport theory.

Nuclear magnetic resonance (NMR) imaging techniques were investigated as a means to obtain velocity field measurements for the verification of a stochastic transport theory. A modified stimulated-echo pulse sequence was used to make velocity images in an aperiodic heterogeneous porous medium. Construction of the velocity covariance from measurements of the fluctuating velocity has demonstrated that nuclear magnetic resonance imaging is a valuable tool for obtaining experimental data for the examination of existing stochastic transport theory.

On the thermodynamic stability of confined thin films under shear.

Thin films of monatomic fluid constrained between two plane-parallel structured solid walls have been modeled by Monte Carlo simulation under conditions (fixed temperature, chemical potential, and normal stress or load) prevailing in high-precision measurements of surface forces. Several states of the film, corresponding to different numbers of layers of fluid parallel with the walls, are generally consistent with these conditions, but only one is thermodynamically stable; the others are metastable. When the walls are properly aligned, epitaxial solid phases are stable. These melt under shear, eventually becoming metastable, whereupon a drainage (or imbibition) transition occurs, leading to a stable phase with fewer (or more) layers.

Fuel ethanol from cellulosic biomass.

Ethanol produced from cellulosic biomass is examined as a large-scale transportation fuel. Desirable features include ethanol's fuel properties as well as benefits with respect to urban air quality, global climate change, balance of trade, and energy security. Energy balance, feedstock supply, and environmental impact considerations are not seen as significant barriers to the widespread use of fuel ethanol derived from cellulosic biomass. Conversion economics is the key obstacle to be overcome. In light of past progress and future prospects for research-driven improvements, a cost-competitive process appears possible in a decade.

Mutualisms: Assessing the benefits to hosts and visitors.

A great number and variety of interactions are widely assumed to be mutualistic because the species involved exchange goods or services from which they appear to derive benefit. A familiar example is pollination, in which animal vectors receive food in the form of nectar and/or pollen, while the ovules of plants are fertilized. Unfortunately, most studies fail to demonstrate that both participants benefit in any significant way and therefore lack the information necessary to determine whether a given interaction is mutualistic. While mutualism is thought to be a common type of species interaction, there is still little evidence for this belief.

Shear forces in molecularly thin films.

Monte Carlo and molecular dynamics methods have been used to study the shearing behavior of an atomic fluid between two plane-parallel solid surfaces having the face-centered cubic (100) structure. A distorted, face-centered cubic solid can form epitaxially between surfaces that are separated by distances of one to five atomic diameters. Under these conditions a critical stress must be overcome to initiate sliding of the surfaces over one another at fixed separation, temperature, and chemical potential. As sliding begins, a layer of solid exits the space between the surfaces and the remaining layers become fluid.

Intra- and interspecific competition for mutualists: ants as a limited and limiting resource for aphids.

We present two years of experimental and descriptive data which support the hypothesis that fireweed aphids (Aphis varians) compete with intra-and interspecific aphid neighbors for the services of ant mutualists (Formica fusca and F. cinerea). Specifically, we have shown that ants are a Limited and Limiting resource for a tended aphid species. First, the presence of heavily aphid-infested fireweed shoots significantly reduced the number of ants tending neighboring conspecific populations on fireweed. Second, the presence of ant-tended aphids (Cinara sp.) on Engelmann spruce significantly reduced the number of ants tending neighboring aphid populations on fireweed. Third, the number of ants, and not just the presence of ants, had a significant effect on the fitness of fireweed aphids. Aphid populations tended by three or more F. cinerea exhibited significantly higher probabilities of persisting and growing through time than colonies tended by one or two ants. Aphid populations tended by F. fusca had a significantly higher probability of growing when tended by three or more ants only if they had declined in size during the previous week.