17,331 research outputs found
Effects of electrostatic correlations on electrokinetic phenomena
Classical theory of the electric double layer is based on the fundamental
assumption of a dilute solution of point ions. There are a number of situations
such as high applied voltages, high concentration of electrolytes, systems with
multivalent ions, or solvent-free ionic liquids where the classical theory is
often applied but the fundamental assumptions cannot be justified. Perhaps the
most basic assumption underlying continuum models in electrokinetics is the
mean-field approximation, that the electric field acting on each discrete ion
is self-consistently determined by the local mean charge density. This paper
considers situations where the mean-field approximation breaks down and
electrostatic correlations become important. A fourth-order modified Poisson
equation is developed that accounts for electrostatic correlations and captures
the essential features in a simple continuum framework. The theory is derived
variationally as a gradient approximation for non-local electrostatics, in
which the dielectric permittivity becomes a differential operator. The only new
parameter is a characteristic length scale for correlated ion pairs. The model
is able to capture subtle aspects of more detailed simulations based on Monte
Carlo, molecular dynamics, or density functional theory and allows for the
straightforward calculation of electrokinetic flows in correlated liquids, for
the first time. Departures from classical Helmholtz-Smoluchowski theory are
controlled by the dimensionless ratio of the correlation length to the Debye
screening length. Charge-density oscillations tend to reduce electro-osmotic
flow and streaming current, and over-screening of the surface charge can lead
to flow reversal. These effects also help to explain the apparent
charge-induced thickening of double layers in induced-charge electrokinetic
phenomena
Helicoidal minimal surfaces of prescribed genus, I
For every genus g, we prove that S^2 x R contains complete, properly
embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids
of any prescribed pitch. We also show that as the radius of the S^2 tends to
infinity, these examples converge smoothly to complete, properly embedded
minimal surfaces in Euclidean 3-space R^3 that are helicoidal at infinity. In a
companion paper, we prove that helicoidal surfaces in R^3 of every prescribed
genus occur as such limits of examples in S^2 x R.Comment: 53 pages, 5 figure
Nagata compactification for algebraic spaces
We prove the Nagata compactification theorem for any separated map of finite
type between quasi-compact and quasi-separated algebraic spaces, generalizing
earlier results of Raoult. Along the way we also prove (and use) absolute
noetherian approximation for such algebraic spaces, generalizing earlier
results in the case of schemes.Comment: 49 pages, various clarifications and bugfixe
Late Quaternary Mediterranean Outflow Water: implications from radiogenic Nd, Sr, Pb isotopes and clay minerals
Mediterranean Outflow Water (MOW) is characterised by higher temperatures and salinities than other ambient water masses. MOW spreads at water depths between 500 and 1500 m into the eastern North Atlantic and has been a source of salinity for the Atlantic Meridional Overturning Circulation. We used high-resolution Nd and Pb isotope records of past ambient seawater obtained from authigenic ferromanganese coatings of sediments in three gravity cores at 577, 1745 and 1974 m water depths in the Gulf of Cadiz and along the Portuguese margin complemented by a selection of surface sediments to reconstruct the extent and pathways of MOW over the past 23 000 years. In addition, radiogenic Nd, Pb and Sr isotope ratios obtained from total digestion of the residual clay fraction of the leached samples were used to evaluate any changes in the endmember compositions. The surface and downcore seawater Nd isotope data from all water depths exhibit only a very small variability close to the present day composition of MOW but do not reflect the present day Nd isotopic stratification of the water column as determined from a nearby open ocean hydrographic station, which is most likely the consequence of downslope sediment transport in the nepheloid boundary layer as well as the small variations in the Nd endmember compositions. In contrast, the seawater Pb isotope records show significant and systematic variations, which provide evidence for a significantly different pattern of the MOW pathways between 20 000 and 12 000 years ago compared with the subsequent period of time. A deeper situated MOW during the Last Glacial Maximum (LGM) raised during the early deglaciation with its shallowest position around Heinrich event H1, followed by a moderate deepening and the establishment of present-day MOW hydrography. The radiogenic isotope signatures of the residual clay fractions document a pulse of sediment input from the north during Heinrich event H1 around 14.8 ka, but other than that exhibit little varibility over time suggesting surprisingly constant sedimentary endmember compositions and mixing ratios since the LGM
Critical Behaviour of the Fuzzy Sphere
We study a multi-matrix model whose low temperature phase is a fuzzy sphere
that undergoes an evaporation transition as the temperature is increased. We
investigate finite size scaling of the system as the limiting temperature of
stability of the fuzzy sphere phase is approached. We find on theoretical
grounds that the system should obey scaling with specific heat exponent
\alpha=1/2, shift exponent \bar \lambda=4/3 and that the peak in the specific
heat grows with exponent \bar \omega=2/3. Using hybrid Monte Carlo simulations
we find good collapse of specific heat data consistent with a scaling ansatz
which give our best estimates for the scaling exponents as \alpha=0.50 \pm
0.01,\bar \lambda=1.41 \pm 0.08 and \bar \omega=0.66 \pm 0.08 .Comment: 30 pages, 10 figure
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