Minimal surfaces from circle patterns: Geometry from combinatorics

We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational principle which allows us to construct discrete analogues of some classical minimal surfaces. The data used for the construction are purely combinatorial--the combinatorics of the curvature line pattern. A Weierstrass-type representation and an associated family are derived. We show the convergence to continuous minimal surfaces.Comment: 30 pages, many figures, some in reduced resolution. v2: Extended introduction. Minor changes in presentation. v3: revision according to the referee's suggestions, improved & expanded exposition, references added, minor mistakes correcte

Optical Absorptivity versus Molecular Composition of Model Organic Aerosol Matter

Aerosol particles affect the Earth’s energy balance by absorbing and scattering radiation according to their chemical composition, size, and shape. It is generally believed that their optical properties could be deduced from the molecular composition of the complex organic matter contained in these particles, a goal pursued by many groups via high-resolution mass spectrometry, although: (1) absorptivity is associated with structural chromophores rather than with molecular formulas, (2) compositional space is a small projection of structural space, and (3) mixtures of polar polyfunctional species usually exhibit supramolecular interactions. Here we report a suite of experiments showing that the photolysis of aqueous pyruvic acid (a proxy for aerosol α-dicarbonyls absorbing at λ > 300 nm) generates mixtures of identifiable aliphatic polyfunctional oligomers that develop absorptions in the visible upon standing in the dark. These absorptions and their induced fluorescence emissions can be repeatedly bleached and retrieved without carbon loss or ostensible changes in the electrospray mass spectra of the corresponding mixtures and display unambiguous signatures of supramolecular effects. The nonlinear additivity of the properties of the components of these mixtures supports the notion that full structural speciation is insufficient and possibly unnecessary for understanding the optical properties of aerosol particles and their responses to changing ambient conditions

Long-term strict raw food diet is associated with favourable plasma b-carotene and low plasma lycopene concentrations in Germans

Dietary carotenoids are associated with a reduced risk of chronic diseases. Raw food diets are predominantly plant-based diets that are practised with the intention of preventing chronic diseases by virtue of their high content of beneficial nutritive substances such as carotenoids. However, the benefit of a long-term adherence to these diets is controversial since little is known about their adequacy. Therefore, we investigated vitamin A and carotenoid status and related food sources in raw food diet adherents in Germany. Dietary vitamin A, carotenoid intake, plasma retinol and plasma carotenoids were determined in 198 (ninety-two male and 106 female) strict raw food diet adherents in a cross-sectional study. Raw food diet adherents consumed on average 95 weight% of their total food intake as raw food (approximately 1800 g/d), mainly fruits. Raw food diet adherents had an intake of 1301 retinol activity equivalents/d and 16·7 mg/d carotenoids. Plasma vitamin A status was normal in 82% of the subjects ($1·05mmol/l) and 63$0·88 mmol/l). In 77% of subjects the lycopene status was below the reference values for average healthy populations (,0·45mmol/l). Fat contained in fruits, vegetables and nuts and oil consumption was a significant dietary determinant of plasma carotenoid concentrations (b-carotene r 0·284; P,0·05; lycopene r 0·168; P¼0·024). Long-term raw food diet adherents showed normal vitamin A status and achieve favourable plasma b-carotene concentrations as recommended for chronic disease prevention, but showed low plasma lycopene levels. Plasma carotenoids in raw food adherents are predicted mainly by fat intake

Thermochromism of Model Organic Aerosol Matter

Laboratory experiments show that the optical absorptivity of model organic matter is not an intrinsic property, but a strong function of relative humidity, temperature, and insolation. Suites of representative polyfunctional C_(x)H_(y)O_(z) oligomers in water develop intense visible absorptions upon addition of inert electrolytes. The resulting mixtures reach mass absorption cross sections σ(532 nm) ~ 0.1 m^(2)/gC in a few hours, absorb up to 9 times more solar radiation than the starting material, can be half-bleached by noon sunlight in ~ 1 h, and can be repeatedly recycled without carbon loss. Visible absorptions red-shift and evolve increasingly faster in subsequent thermal aging cycles. Thermochromism and its strong direct dependences on ionic strength and temperature are ascribed to the dehydration of >CH−C(OH)C═C< unsaturations by a polar E1 mechanism, and bleaching to photoinduced retrohydration. These transformations are deemed to underlie the daily cycles of aerosol absorption observed in the field, and may introduce a key feedback in the earth’s radiative balance