Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces

It is well known that the complexity of the Delaunay triangulation of $n$ points in $\RR ^d$, i.e., the number of its simplices, can be $\Omega (n^{\lceil {d}/{2}\rceil })$. In particular, in $\RR ^3$, the number of tetrahedra can be quadratic. Put another way, if the points are uniformly distributed in a cube or a ball, the expected complexity of the Delaunay triangulation is only linear. The case of points distributed on a surface is of great practical importance in reverse engineering since most surface reconstruction algorithms first construct the Delaunay triangulation of a set of points measured on a surface. In this paper we bound the complexity of the Delaunay triangulation of points distributed on the boundary of a given polyhedron. Under a mild uniform sampling condition, we provide deterministic asymptotic bounds on the complexity of the three-dimensional Delaunay triangulation of the points when the sampling density increases. More precisely, we show that the complexity is $O(n^{1.8})$ for general polyhedral surfaces and $O(n\sqrt{n})$ for convex polyhedral surfaces. Our proof uses a geometric result of independent interest that states that the medial axis of a surface is well approximated by a subset of the Voronoi vertices of the sample points.     

The Structural Nature of the Nerve Functor for n-Groupoids

Given a left exact category B, the construction of the nerve functor _n for n-groupoids in B is related to a certain property of the category S-S i m p l _{n – 1} B of the split (n – 1)-truncated simplicial objects in B, which allows us to define the split n-truncated simplicial objects in B completely internally to S-S i m p l _{n – 1} B and thus to construct intrisincally from it the category S-S i m p l _n B.     

Two-mode dynamics in dispersed systems: the case of particle-stabilized foams studied by diffusing wave spectroscopy

The stabilization of aqueous foams solely by solid particles is an active field of research. Thanks to controlled particle chemistry and production devices, we are able to generate large volumes of such foams. We previously investigated some of their unique properties, especially the strongly reduced coarsening. Here we report another type of study on these foams: performing diffusing wave spectroscopy (DWS), we investigate for the first time the internal dynamics on the scales of both the particles and the bubbles. When compared to surfactant foams, unusual features are observed; in particular, two well-separated modes are found in the dynamics, both evolving with foam aging. We propose an interpretation of these specificities, taking into account both the scattering by free particles in the foam fluid (fast mode), and by the foam structure (slow mode). To validate our interpretation, we show that independent measurements of the interstitial fluid scattering length, obtained indirectly on the foam and directly on the drained liquid, are in good agreement. We have also identified the experimental conditions required to observe such two-process dynamics. Counter-intuitively, the fraction of free particles within the foam interstitial fluid has to be very low to get an optimal signature of these particles on the DWS correlation curves. This study also sheds light on the partitioning of the particles inside the foams and at the interfaces, as the foam ages. Lastly, the results shown here (obtained by analyzing the fluctuations of the transmitted light) implement the previous ones (obtained by analyzing the mean transmitted intensity), and prove that the foam structure is actually not fully frozen.     

Tetranuclear manganese(II) complexes of thiacalixarene macrocycles with trigonal prismatic six-coordinate geometries: synthesis, structure, and magnetic properties

Two tetranuclear manganese(II) complexes [Mn(II)4(thiaS)2] (1) and [Mn(II)4(thiaSO)2] (2) have been synthesized under solvothermal conditions in methanol with p-tert-butylthiacalix[4]arene (thiaS) and p-tert-butylsulfinylthiacalix[4]arene (thiaSO). For both complexes, the structure has been established from single-crystal X-ray diffraction. [Mn4(thiaS)2].H2O (1) crystallizes in the orthorhombic Immm (No. 71) space group with the following parameters: a = 18.213 (5) angstroms, b = 19.037 (5) angstroms, c = 29.159 (5) angstroms, V = 10110 (4) angstroms3, and Z = 4. [Mn4(thiaSO)2].H2O (2) crystallizes in the monoclinic C2/m (No. 12) space group with the following parameters: a = 33.046(1) angstroms, b = 19.5363 (8) angstroms, c = 15.7773 (9) angstroms, beta = 115.176 (2) degrees, V = 9218.3 (8) angstroms3, and Z = 4. The two complexes are neutral and are best described as manganese squares sandwiched between two thiacalixarene macrocycles. In both complexes, each manganese center is six-coordinated in a trigonal prismatic geometry with four phenoxo oxygen atoms plus two sulfur atoms for 1 or two oxygen atoms from SO groups for 2. The two tetranuclear complexes exhibit identical magnetic behaviors resulting from antiferromagnetic interactions between the four manganese centers. The simulation of the magnetic susceptibility was done considering a single exchange-coupling constant between the manganese(II) ions, J (H = -J(S1S2 + S2S3 + S3S4 + S1S4)). The best fits give the same result for the two complexes: g = 1.94 and J = -5.57 cm(-1).     

Charge transfer complexes and cation radical salts of azino-diselenadiazafulvalene

The synthesis and the redox behaviour of electroactive donor molecules incorporating an azino spacer group between a benzoselenazole core and another heterocyclic moiety, either a benzoselenazole one or a thiazole one, are reported. Neutral complexes were obtained with TCNQ and, for the first time with dithiadiazafulvalene or diselenadiazafulvalene derivatives, cation radical salts by electrocrystallization. Crystal structures data of these complexes are presented and their geometries compared with those deduced from theoretical calculations.     

Identification,synthesis and conformational study of a CN(R,S) synthon by-product: (5R, 10R)-5,10-diphenyl-1,6-diaza-3,8-dioxabicyclo[4.4.1]undecane

The title compound, containing a new heterocyclic skeleton, was identified by X-ray crystallography as the product of condensation of (R)-phenylglycinol with an excess of formaldehyde. The molecule adopts a rigid double twist-chair conformation in both solid and solution states.     

SUNSCREENS WITH BROAD-SPECTRUM ABSORPTION DECREASE THE trans TO cis PHOTOISOMERIZATION OF UROCANIC ACID IN THE HUMAN stratum corneum AFTER MULTIPLE UV LIGHT EXPOSURES

Abstract The trans to cis photoisomerization of urocanic acid (UCA) in skin is considered to play an important role in the mechanism of immunosuppression. We have investigated the effects of skin type and various sunscreens with low sun protection factor (SPF) on the UV-induced cis -UCA formation in human skin after exposure to artificial IJV light. The rate of cis -UCA formation depends little on the skin type and is reduced by topical application of sunscreens. The rate of cis -UCA formation decreases with increasing SPF and only broad-spectrum, highly protective sunscreens offer protection against the UV-induced formation of cis -UCA, which accumulates in the stratum corneum after multiple UV exposures. A theoretical approach to estimate the distribution of cis -UCA after irradiation indicates that this compound may diffuse into the deeper layers of the epidermis with D ∼ 10⁻¹⁷ m²/s, and that its elimination from the stratum corneum is mainly due to desquamation.     

High-resolution Fourier-transform infrared spectroscopy of the ν6 and Coriolis perturbation allowed ν10 modes of ketenimine

High-resolution FTIR spectra of the short lived species ketenimine have been recorded in the region 700-1300 cm(-1) and over 1500 transitions of the ν(10) and ν(6) modes have been assigned. Effective rotational and centrifugal distortion parameters for the v(10) = 1 and v(6) = 1 (excluding K(a) = 5) states were determined by co-fitting transitions, and treating strong a- and c-axis Coriolis interactions between them. Other perturbations attributed to interactions with the v(8) = 2 and v(12) = 1 + v(8) = 1 dark-states were also observed and treated. The ν(10) transitions are predicted to be inherently very weak, but are enhanced by an intensity stealing effect with the highly IR active ν(6) mode. A mechanism for this intensity stealing in ketenimine is also detailed.