Stability of an oscillating tip in Non-Contact Atomic Force Microscopy: theoretical and numerical investigations

This paper is a theoretical and a numerical investigation of the stability of a tip-cantilever system used in Non-Contact Atomic Force Microscopy (NC-AFM) when it oscillates close to a surface. No additional dissipative force is considered. The theoretical approach is based on a variationnal method exploiting a coarse grained operation that gives the temporal dependence of the nonlinear coupled equations of motion in amplitude and phase of the oscillator. Stability criterions for the resonance peak are deduced and predict a stable behavior of the oscillator in the vicinity of the resonance. The numerical approach is based on results obtained with a virtual NC-AFM developped in our group. The effect of the size of the stable domain in phase is investigated. These results are in particularly good agreement with the theoretical predictions. Also they show the influence of the phase shifter in the feedback loop and the way it can affect the damping signal

Synchronization Based Approach for Estimating All Model Parameters of Chaotic Systems

The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of noise, enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system. The method is demonstrated using the Lorenz, Rossler chaos and hyperchaos models. Its possible application in decoding communications using chaos is discussed.Comment: 13 pages, 4 figure

Estimation de l'équivalent en eau du couvert nival au moyen d'images radar satellitaires

L'objectif de cette étude est de vérifier le potentiel des images radar à synthèse d'ouverture (RSO) pour estimer l'équivalent en eau du couvert nival sur le bassin de la rivière La Grande (Baie de James, Québec). Il s'agit d'un milieu dominé par une forêt ouverte d'épinettes noires, des brûlis et des tourbières. Cette information intéresse grandement Hydro-Québec qui gère plusieurs installations hydro-électriques dans cette région subarctique. Durant deux ans, six campagnes de terrain ont été réalisées sur le bassin de la rivière La Grande et une dizaine d'images RSO du satellite européen ERS-1 ont été acquises, étalonnées et géoréférencées, afin de déterminer la relation entre les coefficients de rétrodiffusion des images radar (hiver et automne) et la résistance thermique du couvert nival. Cette relation constitue la première partie d'un algorithme d'estimation de l'équivalent en eau. Elle utilise plus spécifiquement le rapport de rétrodiffusion, qui est la différence entre une image avec neige et une image sans neige. La deuxième partie de cette algorithme déduit l'équivalent en eau du couvert de neige à partir de sa résistance thermique et de sa densité, en se basant sur la relation physique établie par les mesures de terrain. L'équivalent en eau du couvert nival a donc été estimé pour quatre images de février et mars 1994 et 1995. L'erreur moyenne sur l'estimation de l'équivalent en eau de la neige au sol est de 2% à 3% (-5 à 7mm) sur l'ensemble des sites d'échantillonnage avec un écart-type de 14 à 19% (-35 à 45mm). Ces résultats ont encouragé Hydro-Québec à poursuivre la recherche avec les données du satellite canadien RADARSAT (opérationnel depuis le 1er avril 1996) et à développer un prototype pour la cartographie de l'équivalent en eau du couvert nival à partir d'images radar.The goal of this study was to evaluate the potential of synthetic aperture radar (SAR) images for estimating the snow water equivalent (SWE) on the La Grande river watershed (James Bay area, Québec). This information is of major interest for Hydro-Québec, which exploits many hydroelectric complexes throughout this subarctic region. The La Grande watershed is composed of moderately dense to opened black spruce forests, opened areas, burned areas and peat bogs. Over two years (1994-1995), six field campaigns were carried out on a study site located between the LG4 and Laforge1 reservoir, in the center of the La Grande river watershed. The field measurements were of two types: 20 snow lines (depth, snow water equivalent (SWE), density) and 8 snow profiles (depth, density, grain size, temperature, dielectric constant). With these data, the thermal resistance of the snowpack was calculated for every test-site, using the depth, density and thermal conductivity of each layer. Concurrently, more than 10 SAR images (European Satellite ERS-1) of the study site were acquired, calibrated and georeferenced. The backscattering coefficients of all winter images were extracted. Using a reference image (snow-free), backscattering ratios were calculated. They are the difference between a winter image and a snow-free image. This process is used to reduce the impact of vegetation and topography. Then, the relationship between the backscattering ratios and the snowpack thermal resistance of february and march 1994 are established, as the first part of an algorithm developed to estimate the snow water equivalent. The second part of the algorithm infers the snowpack water equivalent from its thermal resistance and density, based on the physical relationship established with field data. This approach is based on studies conducted by INRS-Eau in a southern Quebec agricultural area (BERNIER and FORTIN (1998)). The hypothesis are based on the following: - The snowpack characteristics influence the underlying soil temperature;- The dielectric constant of the soil varies with the soil temperature under 0°C;- The radar signal is influenced by the soil dielectric constant;- Thus, the snowpack characteristics (thermal resistance) influence the radar signal. However, due to variations of soil humidity on the date of the reference image (september 1994), two slightly different relationships were obtained. One for open areas and open forests and one for burned areas and peat bogs. This shows the importance of using a good reference image, with homogeneous soil conditions. It could be better to obtain an image later in the fall, when the soil is frozen. The relationships established here are preliminary, as they use a small dataset. It is estimated that a better regression should be obtained with the acquisition of more images and with a greater range of snow characteristics. However, the algorithm is applied to test the applicability of the method. First, the algorithm was applied on the test-sites, using the images from February and March of 1994 and 1995. The mean error on the estimation of the snow water equivalent is 2% to 3% ( 5 to 7mm), with a deviation of 14% to 19% ( 35 to 45mm). The results are comparable for both years, even if the algorithm is based on 1994 data only. Secondly, the algorithm is applied on the whole images. A classification of a Landsat-TM image is used to identify the land cover of every pixel, which determines the regression and the snow density to be used in the algorithm. Four maps of the SWE are produced and resampled to a resolution of 500m. These are compared with the field measurements from the four nearest Hydro-Quebec snow survey sites. The SWE measured by Hydro-Quebec are all within the most dominant SWE class of each map. Further validation of the results will be possible when the algorithm can be applied on a sub-watershed, which is the actual scale used by Hydro-Quebec. However, the results of this study were sufficiently promising to Hydro-Quebec to support a follow up research with data from the canadian satellite RADARSAT (operational since april 1996). Meanwhile, to improve the algorithm, it is important to obtain a good and homogeneous reference image, to better assess the impact of the land cover and to acquire a dataset with a greater range of snow characteristics

On the Hausdorff volume in sub-Riemannian geometry

For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function. We then prove that up to dimension 4 it is smooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4 on every smooth curve) but in general not C^5. These results answer to a question addressed by Montgomery about the relation between two intrinsic volumes that can be defined in a sub-Riemannian manifold, namely the Popp and the Hausdorff volume. If the nilpotent approximation depends on the point (that may happen starting from dimension 5), then they are not proportional, in general.Comment: Accepted on Calculus and Variations and PD

Latest Developments on HeII Co-Current Two-Phase Flow Studies

Large scale experiments were performed at CEA Grenoble with the support of CERN to simulate and understand the HeII cooling circuit of the LHC. This paper describes the latest results obtained in HeII co-current two-phase flow configuration. First we summarize thermal and hydraulic behaviour of flows obtained in a 40 mm I.D., 86 m long tube inclined at 1.4% which resembles closely the LHC heat exchanger tube. For low vapour velocities, the flow pattern is found to be stratified. A model based on this observation has been developed which fits very well the measured pressure losses. However the wetted surface predicted by the model underestimates the measured one, notably for high vapour velocities. In that case, liquid droplets entrainment takes place. Droplets landing on the tube wall increase the wetted surface. Thus we infer that for higher vapour velocities, the stratified two-phase flow model should not be applied anymore. In order to validate the range of availability of the model, and begin to draw a flow pattern map, a 20 mm I.D. horizontal test sector was built and experiments were performed. First results are presented here, including the observation of the stratified-annular flow transition

Tropical and subtropical actinorhizal plants

A maioria dos países tropicais enfrenta dois grandes problemas: o aumento constante da exploração das reservas florestais para extração de madeira ou lenha e a diminuição da fertilidade do solo para produção agrícola. O conceito geral é o de que plantas fixadoras de N2 podem evitar a propalada crise de madeira e alimentos. Juntas com um grande número de leguminosas fixadoras de N2, plantas actinorrízicas podem ter um papel importante na produção de madeira e recuperação de solos. As plantas actinorrízicas compreendem oito famílias de dicotiledôneas, todas elas representadas nos trópicos. Neste trabalho, as mais promissoras plantas actinorrízicas tropicais são brevemente apresentadas e a ênfase é dada principalmente à família Casuarinaceae. Esta família compreende quatro gêneros (Casuarina, Allocasuarina, Gymnostoma e gênero C), com 82 espécies, incluindo muitas árvores que podem produzir madeira de boa qualidade. As estirpes de Frankia que têm sido isoladas das Casuarinaceae crescem lentamente e são capazes de reduzir acetileno in vitro sob ar, o que indica uma capacidade de proteção contra o O2 muito mais eficiente do que no Rhizobium. Apenas as espécies do gênero Casuarina podem ser noduladas pela estirpe ORS 021001, isolada de Casuarina junghuhniana, o que sugere a existência de grupos de inoculação dentro da família Casuarinaceae. A fixação de N2 de Casuarina equisetifolia, crescida em microparcelas de 1 m2, na estação experimental de ORSTM, em Dakar, foi estimada através da comparação do N total em plantas não-inoculadas e plantas inoculadas com a estirpe ORS 021001. Extrapolando para um hectare, a fixação de N2 foi de 131 kg/N em um período de 6,5 meses. Usando o método de equivalência com adubo nitrogenado, a inoculação parece ser equivalente à aplicação de 288 kg de N/ha-1.Most tropical countries face two major problems: increasing overexploitation of wood reserves for timber or fuel wood and diminishing soil fertility for agricultural production. The present consensus is that N2 -fixing plants can help prevent the forthcoming wood and food crisis. Together with the vast group of N2 -fixing Leguminoseae, actinorhizal plants (AP) can play a major role in wood production and land regeneration. AP comprise eight families of dicotyledonous plants all of which are represented in the tropics. In this paper the most promising tropical AP are briefly presented and the emphasis is put mainly on Casuarinaceae. This family forms a group of four genera (Casuarina, Allocasuarina, Gymnostoma and genus C) with 82 species, including many trees that can yield wood of good quality. The Frankia strains that have been isolated from Casuarinaceae grow slowly and are able to reduce acetylene in vitro under air, which indicates that the protection against O2 is much more efficient in Frankia than in rhizobia. Only the species belonging to the Casuarina genus could be nodulated by strain ORS 021001, isolated from Casuarina junghuhniana, suggesting the existence of crossinoculation groups within the family Casuarinaceae. N2 fixation of Casuarina equisetifolia, grown in 1 m2 microplots at the ORSTOM experimental station of Dakar, was estimated by comparing total N in non-inoculated plants and plants inoculated with Frankia strain ORS 021001. Extrapolating to 1 hectare, N2 fixation was 131 kg for a 6.5-month period. Using the N fertilizer equivalence method, inoculation appeared to be equivalent to the application of 288 kg of N fertilizer per hectare

Magnetic structure of the antiferromagnetic half-Heusler compound NdBiPt

We present results of single crystal neutron diffraction experiments on the rare-earth, half-Heusler antiferromagnet (AFM) NdBiPt. This compound exhibits an AFM phase transition at $T_{\mathrm N}=2.18$~K with an ordered moment of $1.78(9)$~$\mu_{\mathrm B}$ per Nd atom. The magnetic moments are aligned along the $[001]$-direction, arranged in a type-I AFM structure with ferromagnetic planes, alternating antiferromagnetically along a propagation vector $\tau$ of $(100)$. The $R$BiPt ($R$= Ce-Lu) family of materials has been proposed as candidates of a new family of antiferromagnetic topological insulators (AFTI) with magnetic space group that corresponds to a type-II AFM structure where ferromagnetic sheets are stacked along the space diagonal. The resolved structure makes it unlikely, that NdBiPt qualifies as an AFTI.Comment: As resubmitted to PRB, corrected typos and changed symbols in Fig.

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate-dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present new results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, waveback velocity exhibits pronounced rate-dependence and the wavefront velocity does not. Moreover, the discrepancy between waveback velocity RCs is most significant for small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wavefront and waveback velocities. Our calculations show that waveback velocity rate-dependence is due to APD restitution, not memory.Comment: 17 pages, 7 figure

Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device

We observe competition between the modulation instability (MI) and stimulated Brillouin scattering (SBS) in a 9.2-GHz broadband SBS slow light device, in which a standard 20-km-long single-mode LEAF fibre is used as the SBS medium. We find that MI is dominant and depletes most of the pump power when we use an intense pump beam at ~1.55 {\mu}m, where the LEAF fibre is anomalously dispersive. The dominance of the MI in the LEAF-fibre-based system suppresses the SBS gain, degrading the SBS slow light delay and limiting the SBS gain-bandwidth to 126 dB \cdot GHz. In a dispersion-shifted highly nonlinear fibre, the SBS slow light delay is improved due to the suppression of the MI, resulting in a gain-bandwidth product of 344 dB \cdot GHz, limited by our available pump power of 0.82 W

Segregation and ordering at the (1×2) reconstructed Pt80Fe20(110) surface determined by low-energy electron diffraction

The surface of an ordered Pt80Fe20(110) crystal exhibits (1×2) and (1×3) reconstructions depending on the annealing treatment after ion bombardment. The (1×3) structure occurs after annealing in the range 750 to 900 K. Annealing above 1000 K leads to the (1×2) structure, which is, from the present result, unambiguously attributed to the same geometrical reconstruction as Pt(110) but with smaller relaxation amplitudes: a detailed low-energy electron-diffraction analysis concludes to a missing-row structure with row pairing in layers 2 and 4 accompanied by a buckling in layers 3 and 5. The top layer spacing is contracted by 13%, and further relaxations are detectable down to the fifth layer. The specific diffraction spots associated with the bulk chemical ordering along the dense [1¯10] rows are very weak: The I(V) analysis shows that this chemical ordering is absent in the outermost ‘‘visible’’ rows but gradually recovers over five to six layers deep. General Pt enrichment is found in the surface ‘‘visible’’ rows (in layers 1–3), but segregation and order yield a subtle redistribution of Pt and Fe atoms in deeper rows: For example, in layer 2, the visible row is Pt rich, whereas the other row (buried under layer 1) is enriched with Fe. Because of the many parameters considered, a fit procedure was applied to a large data basis to solve the structure; the results were confirmed and illustrated subsequently by a standard I(V) analysis for the most relevant parameters. The final r factors are RDE=0.36, RP=0.34, and RZJ=0.14 for two beam sets at normal and oblique incidence consisting of 26 and 21 beams, respectively