Menger curvature and rectifiability

For a Borel set E in R^n, the total Menger curvature of E, or c(E), is the integral over E^3 (with respect to 1-dimensional Hausdorff measure in each factor of E) of c(x,y,z)^2, where 1/c(x,y,z) is the radius of the circle passing through three points x, y, and z in E. Let H^1(X) denote the 1-dimensional Hausdorff measure of a set X. A Borel set E in R^n is purely unrectifiable if for any Lipschitz function gamma from R to R^n, H^1(E cap gamma(R)) = 0. It is said to be rectifiable if there exists a countable family of Lipschitz functions gamma_i from R to R^n such that H^1(E - union gamma_i(R)) = 0. It may be seen from this definition that any 1-set E (that is, E Borel and 0<H^1(E)<\infty) can be decomposed into two disjoint subsets E_irr and E_rect, where E_irr is purely unrectifiable and E_rect is rectifiable. Theorem. If E is a 1-set in R^n and c(E)^2 is finite, then E is rectifiable.Comment: 39 pages, 3 figures, published version, abstract added in migratio

Effective interactions in the colloidal suspensions from HNC theory

The HNC Ornstein-Zernike integral equations are used to determine the properties of simple models of colloidal solutions where the colloids and ions are immersed in a solvent considered as a dielectric continuum and have a size ratio equal to 80 and a charge ratio varying between 1 and 4000. At an infinite dilution of colloids, the effective interactions between colloids and ions are determined for ionic concentrations ranging from 0.001 to 0.1 mol/l and compared to those derived from the Poisson-Boltzmann theory. At finite concentrations, we discuss on the basis of the HNC results the possibility of an unambiguous definition of the effective interactions between the colloidal molecules.Comment: 26 pages, 15 figure

The orbital phases and secondary transit of Kepler-10b - A physical interpretation based on the Lava-ocean planet model -

The Kepler mission has made an important observation, the first detection of photons from a terrestrial planet by observing its phase curve (Kepler-10b). This opens a new field in exoplanet science: the possibility to get information about the atmosphere and surface of rocky planets, objects of prime interest. In this letter, we apply the Lava-ocean model to interpret the observed phase curve. The model, a planet with no atmosphere and a surface partially made of molten rocks, has been proposed for planets of the class of CoRoT-7b, i.e. rocky planets very close to their star (at few stellar radii). Kepler-10b is a typical member of this family. It predicts that the light from the planet has an important emission component in addition to the reflected one, even in the Kepler spectral band. Assuming an isotropical reflection of light by the planetary surface (Lambertian-like approximation), we find that a Bond albedo of \sim50% can account for the observed amplitude of the phase curve, as opposed to a first attempt where an unusually high value was found. We propose a physical process to explain this still large value of the albedo. The overall interpretation can be tested in the future with instruments as JWST or EChO. Our model predicts a spectral dependence that is clearly distinguishable from that of purely reflected light, and from that of a planet at a uniform temperature.Comment: Accepted in ApJ Letters, 17 pages, 3 figure

Can neutral and ionized PAHs be carriers of the UV extinction bump and the diffuse interstellar bands?

Up to now, no laboratory-based study has investigated polycyclic aromatic hydrocarbon (PAH) species as potential carriers of both the diffuse interstellar bands (DIBs) and the 2175 A UV bump. We examined the proposed correlation between these two features by applying experimental and theoretical techniques on two specific medium-sized/large PAHs (dibenzorubicene C30H14 and hexabenzocoronene C42H18) in their neutral and cationic states. It was already shown that mixtures of sufficiently large, neutral PAHs can partly or even completely account for the UV bump. We investigated how the absorption bands are altered upon ionization of these molecules by interstellar UV photons. The experimental studies presented here were realized by performing matrix isolation spectroscopy with subsequent far-UV irradiation. The main effects were found to be a broadening of the absorption bands in the UV combined with slight red shifts. The position of the complete pi - pi* absorption structure around 217.5 nm, however, remains more or less unchanged which could explain the observed position invariance of the interstellar bump for different lines of sight. This favors the assignment of this feature to the interstellar PAH population. As far as the DIBs are concerned, neither our investigations nor the laboratory studies carried out by other research groups support a possible connection with this class of molecules. Instead, there are reasonable arguments that neutral and singly ionized cationic PAHs cannot be made responsible for the DIBs.Comment: 11 pages, 7 figures, 1 tabl

Validation of a multiplex reverse transcription and pre-amplification method using TaqMan(®) MicroRNA assays.

Since the discovery of microRNAs (miRNAs), different approaches have been developed to label, amplify and quantify miRNAs. The TaqMan(&reg;) technology, provided by Applied Biosystems (ABIs), uses a stem-loop reverse transcription primer system to reverse transcribe the RNA and amplify the cDNA. This method is widely used to identify global differences between the expression of 100s of miRNAs across comparative samples. This technique also allows the quantification of the expression of targeted miRNAs to validate observations determined by whole-genome screening or to analyze few specific miRNAs on a large number of samples. Here, we describe the validation of a method published by ABIs on their web site allowing to reverse transcribe and pre-amplify multiple miRNAs and snoRNAs simultaneously. The validation of this protocol was performed on human muscle and plasma samples. Fast and cost efficient, this method achieves an easy and convenient way to screen a relatively large number of miRNAs in parallel

Mid-infrared laser light nulling experiment using single-mode conductive waveguides

Aims: In the context of space interferometry missions devoted to the search of exo-Earths, this paper investigates the capabilities of new single mode conductive waveguides at providing modal filtering in an infrared and monochromatic nulling experiment; Methods: A Michelson laser interferometer with a co-axial beam combination scheme at 10.6 microns is used. After introducing a Pi phase shift using a translating mirror, dynamic and static measurements of the nulling ratio are performed in the two cases where modal filtering is implemented and suppressed. No additional active control of the wavefront errors is involved. Results: We achieve on average a statistical nulling ratio of 2.5e-4 with a 1-sigma upper limit of 6e-4, while a best null of 5.6e-5 is obtained in static mode. At the moment, the impact of external vibrations limits our ability to maintain the null to 10 to 20 seconds.; Conclusions: A positive effect of SM conductive waveguide on modal filtering has been observed in this study. Further improvement of the null should be possible with proper mechanical isolation of the setup.Comment: Accepted in A&A, 7 pages, 5 figure

The bend stiffness of S-DNA

We formulate and solve a two-state model for the elasticity of nicked, double-stranded DNA that borrows features from both the Worm Like Chain and the Bragg--Zimm model. Our model is computationally simple, and gives an excellent fit to recent experimental data through the entire overstretching transition. The fit gives the first value for the bending stiffness of the overstretched state as about 10 nm*kbt, a value quite different from either B-form or single-stranded DNA.Comment: 7 pages, 1 figur