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

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

Interdigitation between surface-anchored polymer chains and an elastomer : consequences for adhesion promotion

We study the adhesion between a cross-linked elastomer and a flat solid surface where polymer chains have been end-grafted. To understand the adhesive feature of such a system, one has to study both the origin of the grafted layer interdigitation with the network, and the end-grafted chains extraction out of the elastomer when it comes unstuck from the solid surface. We shall tackle here the first aspect for which we develop a partial interdigitation model that lets us analytically predict a critical surface grafting density $\sigma^{*} \simeq P^{{1/10}}N^{-{3/5}}$ beyond which the layer no longer interdigitates with the elastomer. We then relate this result with recent adhesion measurements

Energy expenditure of extreme competitive mountaineering skiing.

PURPOSE: Multi-hour ski mountaineering energy balance may be negative and intake below recommendations. METHODS: Athletes on the 'Patrouille des Glaciers' racecourses (17 on course Z, 27 km, +2,113 m; 11 on course A, 26 km, +1,881 m) volunteered. Pre-race measurements included body mass, stature, VO2max, and heart rate (HR) vs VO2 at simulated altitude; race measurements HR, altitude, incline, location, and food and drink intake (A). Energy expenditure (EE) was calculated from altitude corrected HR derived VO2. RESULTS: Race time was 5 h 7 min ± 44 min (mean ± SD, Z) and 5 h 51 min ± 53 min (A). Subjects spent 19.2 ± 3.2 MJ (Z), respectively, 22.6 ± 2.9 MJ (A) during the race. Energy deficit was -15.5 ± 3.9 MJ (A); intake covered 20 ± 7 % (A). Overall energy cost of locomotion (EC) was 9.9 ± 1.3 J m(-1) kg(-1) (Z), 8.0 ± 1.0 J m(-1) kg(-1) (A). Uphill EC was 11.7 ± 1 J m(-1) kg(-1) (Z, 13 % slope) and 15.7 ± 2.3 J m(-1) kg(-1) (A, 19 % slope). Race A subjects lost -1.5 ± 1.1 kg, indicating near euhydration. Age, body mass, gear mass, VO2max and EC were significantly correlated with performance; energy deficit was not. CONCLUSIONS: Energy expenditure and energy deficit of a multi-hour ski mountaineering race are very high and energy intake is below recommendations

Sliding friction between an elastomer network and a grafted polymer layer: the role of cooperative effects

We study the friction between a flat solid surface where polymer chains have been end-grafted and a cross-linked elastomer at low sliding velocity. The contribution of isolated grafted chains' penetration in the sliding elastomer has been early identified as a weakly velocity dependent pull-out force. Recent experiments have shown that the interactions between the grafted chains at high grafting density modify the friction force by grafted chain. We develop here a simple model that takes into account those interactions and gives a limit grafting density beyond which the friction no longer increases with the grafting density, in good agreement with the experimental dataComment: Submitted to Europhys. Letter

Validation of the French Version of the "Patterns of Activity Measure" in Patients with Chronic Musculoskeletal Pain.

Background. The "Patterns of Activity Measure" (POAM-P) is a self-administered questionnaire that assesses "avoidance", "pacing" and "overdoing" activity patterns in chronic pain patients. Objectives. To adapt the POAM-P to French ("POAM-P/F") and test its validity and reliability in Chronic Musculo-Skeletal Pain patients (CMSP). Methods. We followed the recommended procedure for translation of questionnaires. Five hundred and ninety five inpatients, admitted to a tertiary rehab center in the French-speaking part of Switzerland for chronic pain after orthopedic trauma, were included (sex ratio M/F = 4.36, mean age 43 ± 12). Face, content and criterion validities, internal consistency and reliability were assessed. Data included: TAMPA Scale for Kinesiophobia (TSK), Chronic Pain Coping Inventory (CPCI), Pain Catastrophizing Scale (PCS), Brief Pain Inventory (BPI), Hospital Anxiety and Depression Scale (HADS). Results. Face and content validities were checked during the translation process. Correlations between POAM-P/F-avoidance and TSK, POAM-P/F-pacing and CPCI-pacing, POAM-P/F-overdoing and CPCI-task persistence were highly significant (r &gt; 0.3, p &lt; 10(-2)). The three subscales demonstrated excellent homogeneity (Cronbach's alpha coefficients &gt; 0.8) and test-retest reliability (Intraclass Correlation Coefficients &gt; 0.8). They correlated very differently with the other scales. Discussion and Conclusion. The three POAM-P/F subscales clearly assess different behaviors in CMSP. The POAM-P/F is a suitable questionnaire for classifying French speaking CMSP into avoiders, pacers or overdoers

Diagnostics for specific PAHs in the far-IR: searching neutral naphthalene and anthracene in the Red Rectangle

Context. In the framework of the interstellar polycyclic aromatic hydrocarbons (PAHs) hypothesis, far-IR skeletal bands are expected to be a fingerprint of single species in this class. Aims. We address the question of detectability of low energy PAH vibrational bands, with respect to spectral contrast and intensity ratio with ``classical'' Aromatic Infrared Bands (AIBs). Methods. We extend our extablished Monte-Carlo model of the photophysics of specific PAHs in astronomical environments, to include rotational and anharmonic band structure. The required molecular parameters were calculated in the framework of the Density Functional Theory. Results. We calculate the detailed spectral profiles of three low-energy vibrational bands of neutral naphthalene, and four low-energy vibrational bands of neutral anthracene. They are used to establish detectability constraints based on intensity ratios with ``classical'' AIBs. A general procedure is suggested to select promising diagnostics, and tested on available Infrared Space Observatory data for the Red Rectangle nebula. Conclusions. The search for single, specific PAHs in the far-IR is a challenging, but promising task, especially in view of the forthcoming launch of the Herschel Space Observatory.Comment: 13 pages, 13 figures, accepted for publication in A&

Visible photodissociation spectroscopy of PAH cations and derivatives in the PIRENEA experiment

The electronic spectra of gas-phase cationic polycyclic aromatic hydrocarbons (PAHs), trapped in the Fourier Transform Ion Cyclotron Resonance cell of the PIRENEA experiment, have been measured by multiphoton dissociation spectroscopy in the 430-480 nm spectral range using the radiation of a mid-band optical parametric oscillator laser. We present here the spectra recorded for different species of increasing size, namely the pyrene cation (C16H10+), the 1-methylpyrene cation (CH3-C16H9+), the coronene cation (C24H12+), and its dehydrogenated derivative C24H10+. The experimental results are interpreted with the help of time-dependent density functional theory calculations and analysed using spectral information on the same species obtained from matrix isolation spectroscopy data. A kinetic Monte Carlo code has also been used, in the case of pyrene and coronene cations, to estimate the absorption cross-sections of the measured electronic transitions. Gas-phase spectra of highly reactive species such as dehydrogenated PAH cations are reported for the first time