56,862 research outputs found
Variational Methods and Planar Elliptic Growth
A nested family of growing or shrinking planar domains is called a Laplacian
growth process if the normal velocity of each domain's boundary is proportional
to the gradient of the domain's Green function with a fixed singularity on the
interior. In this paper we review the Laplacian growth model and its key
underlying assumptions, so that we may consider a generalization to so-called
elliptic growth, wherein the Green function is replaced with that of a more
general elliptic operator--this models, for example, inhomogeneities in the
underlying plane. In this paper we continue the development of the underlying
mathematics for elliptic growth, considering perturbations of the Green
function due to those of the driving operator, deriving characterizations and
examples of growth, developing a weak formulation of growth via balayage, and
discussing of a couple of inverse problems in the spirit of Calder\'on. We
conclude with a derivation of a more delicate, reregularized model for
Hele-Shaw flow
Mineralogy of the Martian surface from Mariner 6/7 infrared spectrometer data
The Mariner 6/7 Infrared Spectrometer (IRS) experiment data from the 1969 Mars flyby encounters represent a valuable source of information about the IR reflection/emission spectrum of Mars in the 1.9 and 14.4 micron region. During 1990, the wavelength calibration of the IRS data was completely redone, using information from inflight spectra of Mars taken through a polystyrene film and from the locations of Martian CO2 bands. The response functions of the two instruments were then rederived using laboratory black body spectra. Also, a particular approach was taken to study the IRS data in which the effects of uncertain wavelength and intensity calibration can be minimized. This involves doing ratios of spectra. These are of particular value when applied to study contrasts between various albedo domains on the Mars surface and between spectra with differing emission angle. The latter provide a means of assessing the contribution of the atmosphere and airborne dust to the spectra. Given here are graphs showing two near infrared radiance spectra for very different albedo regions and a ratio of two spectra obtained at very different total solar pathlength (airmass)
Theory of voltammetry in charged porous media
We couple the Leaky Membrane Model, which describes the diffusion and
electromigration of ions in a homogenized porous medium of fixed background
charge, with Butler-Volmer reaction kinetics for flat electrodes separated by
such a medium in a simple mathematical theory of voltammetry. The model is
illustrated for the prototypical case of copper electro-deposition/dissolution
in aqueous charged porous media. We first consider the steady state with three
different experimentally relevant boundary conditions and derive analytical or
semi-analytical expressions for concentration profiles, electric potential
profiles, current-voltage relations and overlimiting conductances. Next, we
perform nonlinear least squares fitting on experimental data, consider the
transient response for linear sweep voltammetry and demonstrate good agreement
of the model predictions with experimental data. The experimental datasets are
for copper electrodeposition from copper(II) sulfate solutions in a variety of
nanoporous media, such as anodic aluminum oxide, cellulose nitrate and
polyethylene battery separators, whose internal surfaces are functionalized
with positively and negatively charged polyelectrolyte polymers.Comment: 39 pages, 12 figures, 5 tables; clarified where other parameters are
taken from and fixed typo
Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media
Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic
ion transport in charged porous media under periodic fluid flow by an
asymptotic multi-scale expansion with drift. The microscopic setting is a
two-component periodic composite consisting of a dilute electrolyte continuum
(described by standard PNP equations) and a continuous dielectric matrix, which
is impermeable to the ions and carries a given surface charge. Four new
features arise in the upscaled equations: (i) the effective ionic diffusivities
and mobilities become tensors, related to the microstructure; (ii) the
effective permittivity is also a tensor, depending on the electrolyte/matrix
permittivity ratio and the ratio of the Debye screening length to the
macroscopic length of the porous medium; (iii) the microscopic fluidic
convection is replaced by a diffusion-dispersion correction in the effective
diffusion tensor; and (iv) the surface charge per volume appears as a
continuous "background charge density", as in classical membrane models. The
coefficient tensors in the upscaled PNP equations can be calculated from
periodic reference cell problems. For an insulating solid matrix, all gradients
are corrected by the same tensor, and the Einstein relation holds at the
macroscopic scale, which is not generally the case for a polarizable matrix,
unless the permittivity and electric field are suitably defined. In the limit
of thin double layers, Poisson's equation is replaced by macroscopic
electroneutrality (balancing ionic and surface charges). The general form of
the macroscopic PNP equations may also hold for concentrated solution theories,
based on the local-density and mean-field approximations. These results have
broad applicability to ion transport in porous electrodes, separators,
membranes, ion-exchange resins, soils, porous rocks, and biological tissues
Tuning the stability of Electrochemical Interfaces by Electron Transfer reactions
The morphology of interfaces is known to play fundamental role on the
efficiency of energy-related applications, such light harvesting or ion
intercalation. Altering the morphology on demand, however, is a very difficult
task. Here, we show ways the morphology of interfaces can be tuned by driven
electron transfer reactions. By using non-equilibrium thermodynamic stability
theory, we uncover the operating conditions that alter the interfacial
morphology. We apply the theory to ion intercalation and surface growth where
electrochemical reactions are described using Butler-Volmer or coupled
ion-electron transfer kinetics. The latter connects microscopic/quantum
mechanical concepts with the morphology of electrochemical interfaces. Finally,
we construct non-equilibrium phase diagrams in terms of the applied driving
force (current/voltage) and discuss the importance of engineering the density
of states of the electron donor in applications related to energy harvesting
and storage, electrocatalysis and photocatalysis.Comment: 10 pages, 6 figure
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