1,481 research outputs found
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 -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 for a material given
characteristic heterogeneity . 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 -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 -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
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