Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability

A real hyperbolic system is considered that applies near the onset of the oscillatory instability in large spatial domains. The validity of that system requires that some intermediate scales (large compared with the basic wavelength of the unstable modes but small compared with the size of the system) remain inhibited; that condition is analysed in some detail. The dynamics associated with the hyperbolic system is fully analysed to conclude that it is very simple if the coefficient of the cross-nonlinearity is such that , while the system exhibits increasing complexity (including period-doubling sequences, quasiperiodic transitions, crises) as the bifurcation parameter grows if ; if then the system behaves subcritically. Our results are seen to compare well, both qualitatively and quantitatively, with the experimentally obtained ones for the oscillatory instability of straight rolls in pure Rayleigh - Bénard convection

Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.

Non-volatile molecular memory elements based on ambipolar nanotube field effect transistors

We have fabricated air-stable n-type, ambipolar carbon nanotube field effect transistors (CNFETs), and used them in nanoscale memory cells. N-type transistors are achieved by annealing of nanotubes in hydrogen gas and contacting them by cobalt electrodes. Scanning gate microscopy reveals that the bulk response of these devices is similar to gold-contacted p-CNFETs, confirming that Schottky barrier formation at the contact interface determines accessibility of electron and hole transport regimes. The transfer characteristics and Coulomb Blockade (CB) spectroscopy in ambipolar devices show strongly enhanced gate coupling, most likely due to reduction of defect density at the silicon/silicon-dioxide interface during hydrogen anneal. The CB data in the ``on''-state indicates that these CNFETs are nearly ballistic conductors at high electrostatic doping. Due to their nanoscale capacitance, CNFETs are extremely sensitive to presence of individual charge around the channel. We demonstrate that this property can be harnessed to construct data storage elements that operate at the few-electron level.Comment: 6 pages text, 3 figures and 1 table of content graphic; available as NanoLetters ASAP article on the we

The Spatial Distribution of the Galactic First Stars II: SPH Approach

We use cosmological, chemo-dynamical, smoothed particle hydrodynamical simulations of Milky-Way-analogue galaxies to find the expected present-day distributions of both metal-free stars that formed from primordial gas and the oldest star populations. We find that metal-free stars continue to form until z~4 in halos that are chemically isolated and located far away from the biggest progenitor of the final system. As a result, if the Population III initial mass function allows stars with low enough mass to survive until z=0 (< 0.8 Msol), they would be distributed throughout the Galactic halo. On the other hand, the oldest stars form in halos that collapsed close to the highest density peak of the final system, and at z=0 they are located preferentially in the central region of the Galaxy, i.e., in the bulge. According to our models, these trends are not sensitive to the merger histories of the disk galaxies or the implementation of supernova feedback. Furthermore, these full hydrodynamics results are consistent with our N-body results in Paper I, and lend further weight to the conclusion that surveys of low-metallicity stars in the Galactic halo can be used to directly constrain the properties of primordial stars. In particular, they suggest that the current lack of detections of metal-free stars implies that their lifetimes were shorter than a Hubble time, placing constraints on the metal-free initial mass function.Comment: Accepted by ApJ. Emulate ApJ styl

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

GePEToS : A Geant4 Monte Carlo simulation package for Positron Emission Tomography

GePEToS is a simulation framework developed over the last few years for assessing the instrumental performance of future PET scanners. It is based on Geant4, written in Object-Oriented C++ and runs on Linux platforms. The validity of GePEToS has been tested on the well-known Siemens ECAT EXACT HR+ camera. The results of two application examples are presented : the design optimization of a liquid Xe micro-PET camera dedicated to small animal imaging as well as the evaluation of the effect of a strong axial magnetic field on the image resolution of a Concorde P4 micro-PET camera.Comment: 5 pages, 12 figures, submitted to IEEE Transactions on Nuclear Scienc

Principal Component Analysis of the Time- and Position-Dependent Point Spread Function of the Advanced Camera for Surveys

We describe the time- and position-dependent point spread function (PSF) variation of the Wide Field Channel (WFC) of the Advanced Camera for Surveys (ACS) with the principal component analysis (PCA) technique. The time-dependent change is caused by the temporal variation of the $HST$ focus whereas the position-dependent PSF variation in ACS/WFC at a given focus is mainly the result of changes in aberrations and charge diffusion across the detector, which appear as position-dependent changes in elongation of the astigmatic core and blurring of the PSF, respectively. Using >400 archival images of star cluster fields, we construct a ACS PSF library covering diverse environments of the $HST$ observations (e.g., focus values). We find that interpolation of a small number ($\sim20$) of principal components or ``eigen-PSFs'' per exposure can robustly reproduce the observed variation of the ellipticity and size of the PSF. Our primary interest in this investigation is the application of this PSF library to precision weak-lensing analyses, where accurate knowledge of the instrument's PSF is crucial. However, the high-fidelity of the model judged from the nice agreement with observed PSFs suggests that the model is potentially also useful in other applications such as crowded field stellar photometry, galaxy profile fitting, AGN studies, etc., which similarly demand a fair knowledge of the PSFs at objects' locations. Our PSF models, applicable to any WFC image rectified with the Lanczos3 kernel, are publicly available.Comment: Accepted to PASP. To appear in December issue. Figures are degraded to meet the size limit. High-resolution version can be downloaded at http://acs.pha.jhu.edu/~mkjee/acs_psf/acspsf.pd

Light Propagation in Inhomogeneous Universes. IV. Strong Lensing and Environmental Effects

We study the gravitational lensing of high-redshift sources in a LCDM universe. We have performed a series of ray-tracing experiments, and selected a subsample of cases of strong lensing (multiple images, arcs, and Einstein rings). For each case, we identify a massive galaxy that is primarily responsible for lensing, and studied how the various density inhomogeneities along the line of sight (other galaxies, background matter) affect the properties of the image. The matter located near the lensing galaxy, and physically associated with it, has a small effect. The background matter increases the magnification by a few percents at most, while nearby galaxies can increase it by up to about 10 percent. The effect on the image separation is even smaller. The only significant effect results from the random alignment of physically unassociated galaxies, which can increase the magnification by factors of several, create additional images, and turn arcs into rings. We conclude that the effect of environment on strong lensing in negligible in general, and might be important only in rare cases. We show that our conclusion does not depend on the radial density profile of the galaxies responsible for lensing.Comment: 23 pages, 7 figures (one in color). Accepted for publication in The Astrophysical Journal. Minor typos correcte

Unexpected Scaling of the Performance of Carbon Nanotube Transistors

We show that carbon nanotube transistors exhibit scaling that is qualitatively different than conventional transistors. The performance depends in an unexpected way on both the thickness and the dielectric constant of the gate oxide. Experimental measurements and theoretical calculations provide a consistent understanding of the scaling, which reflects the very different device physics of a Schottky barrier transistor with a quasi-one-dimensional channel contacting a sharp edge. A simple analytic model gives explicit scaling expressions for key device parameters such as subthreshold slope, turn-on voltage, and transconductance.Comment: 4 pages, 4 figure

Choix multicritère de procédés d'épuration des eaux usées municipales

Les stations d'épuration des eaux usées municipales du Québec, comme ailleurs au Canada et aux États Unis, sont en général peu efficaces sur le plan énergétique. Il est donc possible de concevoir des hypothèses de chaînes épuratoires améliorées au plan de leur efficacité énergétique et de leur performance globale en y introduisant, d'une part, diverses MEEE et, d'autre part, certains procédés unitaires améliorant l'épuration. Cependant, le problème de choisir, parmi ces hypothèses de chaînes d'épuration, celle correspondant au procédé le plus adéquat pour prendre en charge une situation donnée, demeure entier. Cet article analyse ce problème de choix pour les stations d'épuration de capacité comprise entre 5,000 m3/d (≈ 5000 personnes) et 100,000 m3/d (≈ 100,000 personnes). En faisant l'hypothèse, d'un côté, que l'ajout des mesures d'efficacité énergétique peut améliorer la consommation énergétique d'une chaîne d'épuration, et d'un autre côté, que l'insertion de segments de procédés peut contribuer à améliorer leur performance globale, nous avons élaboré, à partir des stations d'épuration de types Biofiltration, Physico-chimique, Réacteurs Biologiques séquentiels (deux variantes), Boues activées et Étangs aérés, six (6) hypothèses de chaînes épuratoires (chaînes 1 à 6) respectant les exigences opérationnelles et épuratoires et nous les avons comparées entre elles, sur la base d'une analyse multicritère d'aide à la décision, en vue d'en déterminer les plus performantes. Cette analyse multicritère intègre les aspects techniques, énergétiques, économiques, etc. et prend en compte les préférences du(des) décideur(s) dans le processus de choix. Les résultats obtenus montrent que, parmi les six hypothèses de chaînes étudiées, les trois premières positions sont occupées par les chaînes 3, 1 et 4 respectivement. Ce type d'analyse pourrait jouer un rôle complémentaire à une étude technico-économique visant le choix de technologies d'épuration.Quebec municipal wastewater treatment facilities, like those elsewhere in Canada and the United States, generally are low efficiency energy consumers (ELECTRIC POWER RESEARCH INSTITUTE (EPRI), 1993; OWEN, 1982; ONTARIO-HYDRO, 1993; METCALF and EDDY, INC., 1992, SASSEVILLE et al., 1995). The work of METCALF and EDDY, INC. (1992) and of EPRI (1993) concluded that it would be possible to substantially reduce electricity demand and to improve the utilization of electrical energy in the municipal wastewater treatment processes by introducing Electricity Saving Measures (ESMs) in the processes and their management.In the province of Quebec, given the potential savings linked to the reduction of electricity consumption in municipal wastewater treatment facilities, and the progressive expansion of the province's wastewater treatment facilities, the adoption of energetically efficient wastewater treatment technologies is particularly timely. SASSEVILLE et al. (1995) estimated that it would be possible to save 5 M $at the present level of wastewater treatment, based on a cost of about 24 M$ for the 400 GWh of electricity annually consumed in the municipal wastewater treatment facilities. This saving would come solely from the implementation of appropriate energy-saving measures.In hypothesizing on one hand that adding energy-saving measures can improve the energy consumption of a wastewater treatment chain, and on the other hand that the introduction of segments of processes can contribute in improving overall performance, we have elaborated from existing wastewater treatment facilities six hypotheses of liquid treatment chains that respect operational and regulation requirements, on the basis of the experience developed in the operation of municipal wastewater treatment facilities. The six hypothetical treatment chains were elaborated from facilities of the following types: biofiltration (chain 1), physico-chemical (chain 2), sequencing biological (batch) reactors system A (chain 3), sequencing biological (batch) reactors system B (chain 4), activated sludge (chain 5) and aerated lagoons (chain 6). The energy-saving measures utilized in the elaboration of these hypothetical treatment chains were chosen on the basis of a conjunctive analysis (KIBI et al., 1997). However, the problem of choosing among these treatment chains the one corresponding to the most adequate process for a particular situation is still present. The present article analyzes this choice for wastewater treatment facilities of a capacity between 5 000 m3/d (≈ 5 000 persons) and 100 000 m3/d (≈ 100 000 persons).How then to choose the most efficient of these hypothetical municipal wastewater treatment chains?Generally, the choice of the treatment technologies is done on the basis of single-criterion mathematical models: for example, the reduction of construction costs, or of exploitation and maintenance costs (ECKENFELDER, 1982; PINEAU et al., 1985; WANG and WANG, 1979; TYTECA et al., 1977). There are other approaches based on dynamic simulation models or on technological and econometric analyses (HYDRO-QUÉBEC, 1993; MACRAE 1989; LESSARD, 1989; BROCKTON, 1987; HOLDREN, 1987; FOSBERG and MUKHOPADHYAY, 1981; REID, CROWTHER and PARTNERS, 1978; KLEMETSON and GRENNEY, 1976).These different approaches are often insufficient to distinguish the real value of the different technological options. Furthermore, they do not take into account many important factors (technological, economic, financial and environmental, ergonomic and socio-political) that affect their implementation and should be considered in identifying an acceptable and viable solution.The multicriteria approach of decision-making advocated in this article can mitigate this difficulty. It will take into account key factors in the conception and operation of treatment technologies, especially energy and environmental factors, likely to give rise to efficient treatment facilities from both an energy and a treatment point of view. However the analysis of decisional factors to consider in this multicriteria analysis gives rise to a particular problem. They affect the decision that can be appreciated by deterministic relationships, offering a high level of certainty as to its evaluation, while others have a non-deterministic nature (uncertainty and imprecision). Research using the multicriteria analysis approach has been performed in similar situations over the last twenty years, in some cases applied to the environmental and energy sectors (e.g. KEENEY and NAIR 1977; ROY and VINCKE 1981; TEGHEM and KUNSCH 1985; SIMOS 1990; HANSON 1991; ROUSSEAU and MARTEL 1994). Here again, these approaches have limits since the cases were treated either in a situation of certainty or a situation of uncertainty and imprecision. The proposed model deals with the case of certainty and uncertainty at the same time, therefore improving the applicability of the multicriteria approach in the situation under study. The solution retained consists of applying this type of modelling in order to classify from the best to the worst, the six hypothetical treatment chains. This approach utilizes in the modelling process, fourteen evaluation criteria, various criteria weights, quantitative and qualitative evaluations, as well as the indifference, preference and veto thresholds. The main steps of the model are the construction of evaluated outclass relationships and the exploitation of these outclass relationships. The multicriteria aggregation procedure utilizes an elaborated mathematical model based upon the methods of ELECTRE III (Roy, 1978) and PROMETHEE II (BRANS et al., 1984), as well as the works of DÉROT et al. (1994). The ranking of these treatment chain hypotheses, elaborated on an empirical level in consultation with the operators and others involved in wastewater treatment and obtained on the basis of this procedure, can discriminate among their overall performance characteristics rather well. It also emphasizes their energy efficiency, since the energy criteria have on average in the analysis a weight that is 28% higher than the other evaluation criteria. The results obtained show that the hypothetical chain 3 is ranked first, chain 1 occupies the second rank, whereas chain 4 is in the third rank. The last three ranks are occupied respectively by chains 6, 5 and 2.In a decisional and strategic approach, the first three treatment chain hypotheses can be considered overall as being the highest achievers. This result signifies that in the scope of investments related to the expansion of treatment facilities and the construction of facilities with a flow rate contained within the considered range, these three treatment chains (when considering different modification hypotheses), should be preferred over the other chains when the emphasis is on their overall performance including energy efficiency. However, other analyses would be necessary in the case of the construction of a new wastewater treatment facility with a flow rate above the level considered in this study.Generally, the results of this analysis can assist in discriminating among the behaviors of the technologies considered, and in judging their relative performance in the investments of the construction of new wastewater treatment facilities, in addition to a technico-economic analysis. Overall, the multicriteria model described in this study identified a compromise solution between evaluations of a different and conflicting nature. This result demonstrates that this type of analysis is appropriate for tackling multidimensional problems