Anisotropic random resistor networks: a model for piezoresistive response of thick-film resistors

A number of evidences suggests that thick-film resistors are close to a metal-insulator transition and that tunneling processes between metallic grains are the main source of resistance. We consider as a minimal model for description of transport properties in thick-film resistors a percolative resistor network, with conducting elements governed by tunneling. For both oriented and randomly oriented networks, we show that the piezoresistive response to an applied strain is model dependent when the system is far away from the percolation thresold, while in the critical region it acquires universal properties. In particular close to the metal-insulator transition, the piezoresistive anisotropy show a power law behavior. Within this region, there exists a simple and universal relation between the conductance and the piezoresistive anisotropy, which could be experimentally tested by common cantilever bar measurements of thick-film resistors.Comment: 7 pages, 2 eps figure

Nonadiabatic Superconductivity and Vertex Corrections in Uncorrelated Systems

We investigate the issue of the nonadiabatic superconductivity in uncorrelated systems. A local approximation is employed coherently with the weak dependence on the involved momenta. Our results show that nonadiabatic vertex corrections are never negligible, but lead to a strong suppression of $T_c$ with respect to the conventional theory. This feature is understood in terms of the momentum-frequency dependence of the vertex function. In contrast to strongly correlated systems, where the small ${\bf q}$-selection probes the positive part of vertex function, vertex corrections in uncorrelated systems are essentially negative resulting in an effective reduction of the superconducting pairing. Our analysis shows that vertex corrections in nonadiabatic regime can be never disregarded independently of the degree of electronic correlation in the system.Comment: 4 pages, 3 eps fig

Nonadiabatic Pauli susceptibility in fullerene compounds

Pauli paramagnetic susceptibility $\chi$ is unaffected by the electron-phonon interaction in the Migdal-Eliashberg context. Fullerene compounds however do not fulfill the adiabatic assumption of Migdal's theorem and nonadiabatic effects are expected to be relevant in these materials. In this paper we investigate the Pauli spin susceptibility in nonadiabatic regime by following a conserving approach based on Ward's identity. We find that a sizable renormalization of $\chi$ due to electron-phonon coupling appears when nonadiabatic effects are taken into account. The intrinsic dependence of $\chi$ on the electron-phonon interaction gives rise to a finite and negative isotope effect which could be experimentally detected in fullerides. In addition, we find an enhancement of the spin susceptibility with temperature increasing, in agreement with the temperature dependence of $\chi$ observed in fullerene compounds. The role of electronic correlation is also discussed.Comment: Revtex, 10 pages, 8 figures include

Longitudinal and transversal piezoresistive response of granular metals

In this paper, we study the piezoresistive response and its anisotropy for a bond percolation model of granular metals. Both effective medium results and numerical Monte Carlo calculations of finite simple cubic networks show that the piezoresistive anisotropy is a strongly dependent function of bond probability p and of bond conductance distribution width \Delta g. We find that piezoresistive anisotropy is strongly suppressed as p is reduced and/or \Delta g is enhanced and that it vanishes at the percolation thresold p=p_c. We argue that a measurement of the piezoresistive anisotropy could be a sensitive tool to estimate critical metallic concentrations in real granular metals.Comment: 14 pages, 7 eps figure

Influence de la déforestation sur le fonctionnement hydrologique de petits bassins versants tropicaux

Les régions tropicales subissent une déforestation importante. En Amérique du Sud,la forêt est généralement remplacée par une prairie, C'est pourquoi nous avons étudié le comportement hydrologique de 2 petits (1,5 ha) bassins versants. Un bassin (bassin B) est recouvert par une forêt primaire, tandis que le second (bassin A) a été défriché et transformé en prairie (Digitaria swazilandensis, programme ÉCÉREX, ORSTOM/CTFT). Ces bassins, situés en Guyane Française, sont proches (500 m), escarpés et principalement constitués par des sols à drainage vertical ralenti. Le climat est de type tmpical humide avec une température moyenne (26 °C) et des précipitations moyennes annuelles (3500 à 3900 mm/an) élevées. L'évapotranspiration réelle et potentielle de la forêt primaire sont respectivement égales à 1470 mm/an et 1565 mm/an, En période d'étiage, nous avons observé un écoulement permanent à l'exutoire du bassin A, alors que le bassin B en est dépourvu. Deux crues (24 mai 1992 et 15 mai 1993) ont été étudiées, simultanément sur les 2 bassins. Pendant les crues, nous avons prélevé des échantillons d'eau des précipitations (pluie et pluviolessivat), des ruisseaux et du sol. Sur ces sites, l'eau circulant dans les couches peu profondes du sol présente une concentration élevée en K+ et faible en Cl-. Une signature opposée caractérise l'eau des couches pmfondes du sol. L'analyse des relations existant entre les traceurs chimiques (K+, Cl-) et isotopique l80) ainsi l'étude des propriétés hydrodynamiques du sol permet de décomposer qualitativement l'hydrogramme de crue en 3 réservoirs: sol superficiel (écoulement hypodermique), sol intermédiaire (de 0 à - 0,4 m), sol profond (bassin B) ou nappe (bassin A). Une décomposition quantitative a été effectuée en utilisant des traceurs chimique (Cl-) et isotopique l80). Nous avons ainsi montré que les crues sur les 2 bassins sont dominées par l'écoulement issu des couches intermédiaires du sol qui représente environ la moitié de l'écoulement total de crue. Cependant,les mécanismes de génération des crues diffèrent sur les 2 bassins. Sur le bassin A, les couches profondes du sol sont saturées avant la crue et participent donc à la totalité de la crue. Au contraire, sur le bassin B, les couches profondes de sol atteignent la saturation peu de temps avant le pic de crue et participent donc essentiellement aux écoulement pendant la décrue. Ces résultats confirment les études hydrologiques réalisées précédemment (FRITSCH, 199Ù) et permettent d'identifier les mécanismes de genèse des crues et ainsi de mettre en évidence l'effet de la déforestation.The tropical regions are subjected to fast deforestation. In South America, the tropical rain forest is being replaced by grassland. Thus, we have studied the hydrological behaviour of two small (1.5 ha) watersheds. One basin (hereafter named "B" basin) is still covered by primary forest while the second one (hereafter named "A" basin) was cleared and transformed to grassland (Digitaria swazilandensis, ÉCÉREX program, supported by ORSTOM/CTFT). These basins, located in French Guyana, are close to one another (500 m), steep, and are principally constituted of soils showing lateral drainage. The tropical humid climate is characterized by a high mean interannual temperature (26¡C), which varies slightly from month to month, and by a high mean annual precipitation (3500 to 3900 mm yr-1). Precipitation mainly occurs during the main wet season from May to June and during a secondary wet season from December to January. Real evapotranspiration of the natural forest is 1470 mm yr-1 and potential evapotranspiration is 1565 mm yr-1. During the low-water level period, we have observed perennial runoff at the outlet at the "A" basin while the "B" basin is without permanent flow. We have studied two runoff events (24 May 1992 and 15 May 1993) in both basins. On 24 May 1992, the runoff event was caused by a rainfall lasting for about 10 hours. Total precipitation was 53.8 mm. The main event amounted to 32 mm. The main peak of the hydrograph corresponded to the heaviest rainfalls. On 15 May 1993, the runoff event was caused by a rain lasting for about 13 hours. Total precipitation was 64.0 mm. The main peak of the hydrograph (86.2 L s-1) corresponded again to the heaviest rainfalls. Spatial variability of the precipitation amount was high, especially for the most intense events that have the largest standard deviations. Interception by the canopy amounted to 5.3% of the rainfall in 1992 and 4.3% in 1993. High rapid runoff coefficients were observed, i.e., 0.28 for 24 May 1992 and 0.43 for 15 May 1993. No overland flow was observed in the watershed.Samples of rainwater, throughfall, stream water, and soil water were regularly collected in both watersheds during the runoff events. Temporal variations in the isotopic composition of the stream water at the outlet of the watershed paralleled variations in rainwater but with a distinct shift. The difference between the two signatures could be due to a mixture between:- Rainwater and water present in the watershed before the event and whose isotopic composition is different and variable over space. - Rainwater and water originating from various reservoirs whose contribution to the stream varies with time. The analysis of runoff events using the isotope tracer method revealed the existence in the stream of a mixture of water originating from rain and from one or several other reservoirs in the watershed. Isotope tracers alone were not sufficient to estimate the depth of the soil water contributing to the runoff event. On one hand, temporal variability in the isotopic composition of rainwater was very similar to the vertical spatial variability in the isotopic composition of soil water. On the other hand, surface evaporation in the watershed was negligible: the isotopic signature of water originating from soil during runoff events was the consequence of successive infiltrated rain events. Oxygen-18 content in rain water strongly varied with time but only slightly with space because of the small area of the watershed. Because of this temporal variability, an average isotope content of rainwater could not be used when calculating the contribution of "new water" at the outlet of the watershed.Using chemical and isotope tracers is a way to identify and quantify the contribution of the various water reservoirs to runoff. We were thus able to separate runoff hydrographs into simple components (water from superficial layer, intermediate layer and deep layer). In these watersheds, shallow water was characterized by relatively high concentration in potassium and very low concentration in chloride. An opposite signature characterized deep waterA "deep water" chemical tracer (chloride) - isotope tracer (18O) diagram shows the evidence of a hysteresis relationship:1. The decreasing limb of this relationship (rising segment of the hydrograph) is due to a decrease in heavy isotope content resulting from the decrease of oxygen-18 content in the precipitation and from the arrival of water from upper soil layers with low concentrations of chloride. 2. The increasing limb (falling segment of the hydrograph and recession) is associated with the arrival at the outlet of deep waters containing relatively high concentrations of chloride and heavy isotopes. Using chemical (Cl-) and isotope (18O) tracers, quantitative hydrograph separation was achieved with a simple 2- or 3- component conservative-mixing model. This information allowed qualitative hydrograph separation into 3 reservoirs: superficial soil layers, intermediate soil layers (0 to -0.4 m), deep soil layers ("B" watershed) or ground water ("A" watershed).Thus, the runoff event of both basins was dominated by the intermediate soil layers reservoir, which represents half of the total flow for both basins. However, the processes of runoff generation differ: in the "A" watershed, the deep soil layers were saturated before the rain: the contribution is significant throughout the runoff . In the "B" watershed, the deep soil layers become saturated a few times before the peak flow: their contribution dominates during the recession. These results confirm previous hydrological studies (Fritsch, 1990), which showed the high reactivity of the watershed, and give a better insight into the mechanisms involved.Some of these observations can also be used at a larger scale: 1. Identification of the reservoirs contributing to the runoff event by analyzing the relationships between oxygen-18 content and the flow rate, and between isotope and chemical tracers. 2. Simultaneous samplings along the stream in order to detect a possible zonation of the watershed. These samples must be taken during a runoff event as well as during a low-water level period to check whether the tracer concentrations in the continuous or discontinuous water table supplying the stream are heterogeneous. If the signature of the water table is heterogeneous or if the stream is supplied by several water tables with different chemical concentrations, the watershed must be divided into several homogeneous sub-watersheds

Band-filling effects on electron-phonon properties of normal and superconducting state

We address the effect of band filling on the effective electron mass $m^*$ and the superconducting critical temperature $T_c$ in a electron-phonon system. We compare the vertex corrected theory with the non-crossing approximation of the Holstein model within a local approximation. We identify two regions of the electron density where $m^*$ and $T_c$ are enhanced or decreased by the inclusion of the vertex diagrams. We show that the crossover between the enhancement at low density and the decrease towards half filling is almost independent of the microscopic electron-phonon parameters. These different behaviors are explained in terms of the net sign of the vertex diagrams which is positive at low densities and negative close to half filling. Predictions of the present theory for doped MgB$_2$, which is argued to be in the low density regime, are discussed.Comment: 13 revtex pages, figures eps include

Signature isotopique et chimique des précipitations (pluies et pluviolessivats) en Guyane française

Au cours de 2 crues survenues le 24 mai 1992 et le 15 mai 1993 sur 2 bassins versants, nous avons étudié la composition isotopique et chimique des précipitations (pluies et pluviolessivats) ainsi que leurs variations temporelle et spatiale. Les bassins étudiés (d'environ 1,5 ha) sont situés près de la ville de Sinnamary (Guyane Française) et sont proches l'un de l'autre (200 m). Un des bassins (bassin B) est recouvert par une forêt primaire, tandis que le second (bassin A) a été défriché et transformé en prairie (Digitaria swazilendensis, programme ÉCÉREX Orstom-CTFT). Le dispositif expérimental est composé de 31 pluviomètres sur le bassin B et de 3 pluviomètres sur le bassin A. Les hauteurs d'eau précipitées lors des événements étudiés sont importantes (environ 60 mm sur le bassin A). La hauteur d'eau précipitée est homogène spatialement sur le bassin A, alors qu'elle est très hétérogène sur le bassin B. La teneur instantanée des précipitations en18O est très variable temporellement, mais reste homogène spatialement, sur les 2 bassins. L'interception de la pluie par la canopée déstructure donc la hauteur d'eau précipitée sous forêt, mais pas sa signature isotopique. Le 24 mai 1992, nous avons observé une dilution de la composition chimique de la pluie et une diminution de son pH au cours du temps. Les pluviolessivats sont généralement plus concentrés que la pluie et leur pH est plus tamponné. Nous n'avons pas observé de corrélation entre la composition chimique de la pluie ou des pluviolessivats et l'intensité des précipitations. La variabilité spatiale de la composition chimique des pluviolessivats, étudiée lors de l'averse principale du 24 mai 1992, est très importante et 31 pluviomètres semblent insuffisants pour estimer précisément les apports au sol. L'effet de masse est respecté le 24 mai 1992, mais n'est pas visible le 15 mai 1993. La comparaison de l'évolution des teneurs intégrées en Cl- et en18O montre que l'événement pluvieux du 24 mai 1992 est issu d'une masse d'air unique, alors que celui du 15 mai 1993 est issu de plusieurs masses d'air différentes. On remarque également que la teneur intégrée en18O des pluviolessivats est légèrement supérieure à celle de la pluie en milieu ouvert. En l'absence d'évaporation (la composition isotopique des pluviolessivats est alignée sur la droite locale des eaux météoriques), cela s'explique par un mélange entre la pluie directe et de l'eau de pluie plus ancienne, retenue sur la canopée et de composition isotopique différente.Geochemical hydrograph separation methods are frequently employed because they allow one to determine the origin (spatial or temporal) of water that contributes to creating floods. This approach, based on mass balance equations, requires a good knowledge of the geochemical (isotopic and chemical) signals of the reservoirs that contribute to the flood. However, geochemical signals in precipitation, an obvious reservoir, may vary strongly over time. In forested watersheds, throughfall - and not direct rain - make up the input signal. The geochemical signal of throughfall may be different from that of rain and it may vary temporally and spatially. In order to clarify the use of geochemical tracers for hydrograph separation, we studied the isotopic (δ18O, δ2H) and chemical composition of precipitation (rain and throughfall) in two watersheds, as well as the spatial and temporal variations of this precipitation during two runoff events that occurred on May 24, 1992 and on May 15, 1993. The studied watersheds are located near the city of Sinnamary (French Guyana), 120 km south-west of Cayenne. They are small in size (1,5 ha) and close to each another (200 m). One basin (hereafter named B basin) is covered by primary forest, whereas the other (hereafter named A basin) was cleared and turned into grassland (Digitaria swazilendensis, ÉCÉREX program, supported by Orstom-CTFT). The climate is tropical-humid, characterised by high mean annual temperatures (26°C), which slightly varied from month to month, and high mean annual precipitation (3500 to 3900 mm.yr-1). Precipitation occurred primarily during the main wet season, centred around May and June, and during the secondary wet season from December to January. Given the small distance between the watersheds, the differences noted between the rain collected in the A basin and the throughfall collected in the B basin (amount, geochemical signal) were attributed to the forest cover (leaching, interception,...). The monitoring equipment consisted of 31 rain gauges in the B basin and 3 rain gauges in the A basin. Rainfall was important for the two studied rain events (about 60 mm in basin A). Average rainfall in the A basin is characterised by low coefficients of variation, whereas average water inputs in the B basin showed high coefficients of variation. Thus, the amount of incoming water was spatially homogeneous in basin A, but heterogeneous in basin B. In both basins, the instantaneous δ18O value for precipitation varied considerably over time, but it was still spatially homogeneous in both watersheds with the average δ18O value showing a low coefficient of variation. This result means that the interception of the rain by the canopy destroyed the structure of the precipitation amounts under the forest, but not the structure of its isotopic signal. On May 24, 1992, we noted a dilution of the chemical content of the rain and a decrease in its pH over the course of the event. The chemical contents of the throughfall were on the whole more concentrated than in the incident rain and the pH more buffered. We did not note any correlation between the chemical content of rain or throughfall and the intensity of precipitation. The chemical composition of throughfall, studied during the main shower on May 24, 1992, exhibited considerable spatial variation and 31 rain gauges did not seem to be enough to precisely estimate the amount reaching the soil. A continuous depletion in heavy isotopes (18O,2H) and some chemical species (e.g., Cl-) was noted for the first episode (May 24, 1992) but not for the second (May, 15, 1993). This depletion may be explained by water vapour condensation outside the Rayleigh distillation, or by mixing of different air masses. The comparison between the evolution of integrated values of δ18O and the integrated Cl- content versus the amount of accumulated precipitation proved that the rain event of May 24, 1992, was generated by a single air mass whereas the event of May 15, 1993 was generated by several air masses. We also noted that the integrated value of δ18O for throughfall was slightly more concentrated than the content of rain. In the absence of evaporation (the isotopic composition of the throughfall corresponded to the local meteoric line), this enrichment suggests that direct rain mixed with older water that was stored in the canopy and had a different isotopic composition.This study showed that the intensity and the geochemical signal of precipitation (rain and throughfall) vary greatly on a temporal scale in a tropical environment. It also showed that the amount of incoming water varied spatially under a forest cover, as did its geochemical (isotopic and chemical) signal. In order to achieve a stream hydrograph geochemical separation, it is necessary to collect the precipitation (rain and throughfall) with a short time step. It is also necessary to collect the throughfall across a concentrated network of rain gauges

Study of pressure effect on the magnetic penetration depth in MgB2_2

A study of the pressure effect on the magnetic penetration depth $\lambda$ in polycrystalline MgB$_{2}$ was performed by measuring the temperature dependence of the magnetization under an applied pressure of 0.15 and 1.13 GPa. We found that $\lambda^{-2}$ at low temperature is only slightly affected by pressure [$\frac{\Delta \lambda^{-2}}{\lambda^{-2}} = 1.5(9)$], in contrast to cuprate superconductors, where, in the same range of pressure, a very large effect on $\lambda^{-2}$ was found. Theoretical estimates indicate that most of the pressure effect on $\lambda^{-2}$ in MgB$_2$ arises from the electron-phonon interaction.Comment: 5 pages, 2 figure

Temporal Oscillation of Conductances in Quantum Hall Effect of Bloch Electrons

We study a nonadiabatic effect on the conductances in the quantum Hall effect of two-dimensional electrons with a periodic potential. We found that the Hall and longitudinal conductances oscillate in time with a very large frequencies due to quantum fluctuation.Comment: 8 pages, 4 figure

Electron-phonon renormalization in small Fermi energy systems

The puzzling features of recent photoemission data in cuprates have been object of several analysis in order to identity the nature of the underlying electron-boson interaction. In this paper we point out that many basilar assumptions of the conventional analysis as expected to fail in small Fermi energy systems when, as the cuprates, the Fermi energy $E_{\rm F}$ is comparable with the boson energy scale. We discuss in details the novel features appearing in the self-energy of small Fermi energy systems and the possible implications on the ARPES data in cuprates.Comment: 4 pages, 5 eps figures include