Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality

We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic formulations for binary mixtures based on \emph{general reversible-irreversible couplings} and the associated mathematical attempts to formulate a \emph{non-equilibrium variational principle} in which these non-equilibrium couplings can be identified as minimizers. Based on this, we investigate two microscopic binary mixture formulations fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible fluid formulation without fluid flow; (b) a momentum-driven formulation for quasi-static and incompressible velocity fields. In both cases we state two novel, reliably upscaled equations for binary mixtures/multiphase fluids in strongly heterogeneous systems by systematically taking thermodynamic features such as free energies into account as well as the system's heterogeneity defined on the microscale such as geometry and materials (e.g. wetting properties). In the context of (a), we unravel a \emph{universality} with respect to the coarsening rate due to its independence of the system's heterogeneity, i.e. the well-known ${\cal O}(t^{1/3})$-behaviour for homogeneous systems holds also for perforated domains. Finally, the versatility of phase field equations and their \emph{thermodynamic foundation} relying on free energies, make the collected recent developments here highly promising for scientific, engineering and industrial applications for which we provide an example for lithium batteries

Rate of Convergence of Phase Field Equations in Strongly Heterogeneous Media towards their Homogenized Limit

We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such free energies in homogeneous environments found a broad interest over the last decades and hence is now widely accepted and applied in both science and engineering. Here, we focus on strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we present a general formal derivation of upscaled phase field equations for arbitrary free energy densities and give a rigorous justification by error estimates for a broad class of polynomial free energies. The error between the effective macroscopic solution of the new upscaled formulation and the solution of the microscopic phase field problem is of order $\epsilon^1/2$ for a material given characteristic heterogeneity $\epsilon$. Our new, effective, and reliable macroscopic porous media formulation of general phase field equations opens new modelling directions and computational perspectives for interfacial transport in strongly heterogeneous environments

Concerns of Contemporary Adolescents

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68176/2/10.1177_019263656504930006.pd

New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials

We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we study these equations in porous media whose electric permittivities show a contrast compared to the electric permittivity of the electrolyte phase. Our main result is the derivation of convenient low-dimensional equations, that is, of effective macroscopic porous media Poisson-Nernst-Planck equations, which reliably describe ionic transport. The contrast in the electric permittivities between liquid and solid phase and the heterogeneity of the porous medium induce strongly oscillating electric potentials (fields). In order to account for this special physical scenario, we introduce a modified asymptotic multiple-scale expansion which takes advantage of the nonlinearly coupled structure of the ionic transport equations. This allows for a systematic upscaling resulting in a new effective porous medium formulation which shows a new transport term on the macroscale. Solvability of all arising equations is rigorously verified. This emergence of a new transport term indicates promising physical insights into the influence of the microscale material properties on the macroscale. Hence, systematic upscaling strategies provide a source and a prospective tool to capitalize intrinsic scale effects for scientific, engineering, and industrial applications

Shoot Morphology of Eleven Alfalfa Populations

Alfalfa (Medicago sativa L.) is a major component of feed for dairy and beef cattle and one of the most productive forage species in North America. Alfalfa has been planted on millions of acres. More than 100 varieties have been developed in North America over the past 100 years. However, historically, alfalfa persistence under grazing in semiarid rangeland has generally been poor. Recently, it was discovered that naturally-selected populations of predominantly yellow-flowered alfalfa have been proven to be adapted to rangelands of western South Dakota and adjacent areas. A study was initiated in May 2006 to evaluate persistence and vigor of eleven alfalfa populations (conventional-hay type, pasture type, pure falcata, and predominately falcata) by transplanting seedlings into native and tame grasslands in South Dakota. The objective of this experiment was to investigate shoot morphology of eleven alfalfa populations in tame grasslands. The experiment was a randomized complete block design with three replications of five plants in 1.2 m long single-row plots. For each population, aboveground biomass of all plants was harvested and ten stems were randomly selected on July 25, 2008. For each stem, the morphological characteristics measured included: a) length & basal diameter, b) number of nodes, branches, pods, c) ratios of leaf to stem, branch to stem, reproductive to vegetative biomass. The results showed that pure falcata cultivar Don had the shortest and thinnest stem, the highest proportion of total stem weight in leaves and reproductive to vegetative biomass ratio, but the lowest stem total biomass. Naturally-selected predominately falcata population from Wind River Seed Co. had the longest, thickest, heaviest, most branched and pods produced stem compared to the other populations

Invisible and Silent Along the Blue Highways

If you are to achieve equal educational opportunities, you as educational leaders, must be the people who confront the stereotypes: you must be the leaders who deliver the rhetoric of equality

Supervisory Controller Synthesis for Non-terminating Processes is an Obliging Game

We present a new algorithm to solve the supervisory control problem over non-terminating processes modeled as $\omega$-regular automata. A solution to this problem was obtained by Thistle in 1995 which uses complex manipulations of automata. We show a new solution to the problem through a reduction to obliging games, which, in turn, can be reduced to $\omega$-regular reactive synthesis. Therefore, our reduction results in a symbolic algorithm based on manipulating sets of states using tools from reactive synthesis

Abstraction-Based Output-Feedback Control with State-Based Specifications

We consider abstraction-based design of output-feedback controllers for non-linear dynamical systems against specifications over state-based predicates in linear-time temporal logic (LTL). In this context, our contribution is two-fold: (I) we generalize feedback-refinement relations for abstraction-based output-feedback control to systems with arbitrary predicate and observation maps, and (II) we introduce a new algorithm for the synthesis of abstract output-feedback controllers w.r.t. LTL specifications over unobservable state-based predicates. Our abstraction-based output-feedback controller synthesis algorithm consists of two steps. First, we compute a finite state abstraction of the original system using existing techniques. This process typically leads to an abstract system with non-deterministic predicate and observation maps which are not necessarily related to each other. Second, we introduce an algorithm to compute an output-feedback controller for such abstract systems. Our algorithm is inspired by reactive synthesis under partial observation and utilizes bounded synthesis

AN EXPERIMENTALIST CRITIQUE OF PROGRAMMED INSTRUCTION

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72136/1/j.1741-5446.1962.tb00100.x.pd