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

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

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

Experimental study of a liquid Xenon PET prototype module

A detector using liquid Xenon in the scintillation mode is studied for Positron Emission Tomography (PET). The specific design aims at taking full advantage of the liquid Xenon properties. It does feature a promising insensitive to any parallax effect. This work reports on the performances of the first LXe prototype module, equipped with a position sensitive PMT operating in the VUV range (178 nm).Comment: Proc. of the 7th International Workshops on Radiation Imaging Detectors (IWORID-7), Grenoble, France 4-7 July 200

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

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

Note on flat foliations of spherically symmetric spacetimes

It is known that spherically symmetric spacetimes admit flat spacelike foliations. We point out a simple method of seeing this result via the Hamiltonian constraints of general relativity. The method yields explicit formulas for the extrinsic curvatures of the slicings.Comment: 4 pages, to appear in PRD, reference added, typos correcte

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

Biodégradation anaérobie de l'acide crotonique par une biomasse bactérienne spécialisée dans la dégradation de l'acide butyrique

La connaissance, actuellement très limitée, du métabolisme des bactéries acétogènes intervenant dans la biodégradation anaérobie de l'acide butyrique et d'un de ses sous-produits, l'acide crotonique, est à l'origine de cette étude.Après avoir mis au point un réacteur anaérobie à biomasse fixée, cette dernière a, dans un premier temps, été adaptée à la biodégradation exclusive du butyrate. La dégradation du crotonate a ensuite été étudiée, selon différents protocoles expérimentaux (pulses de crotonate en alimentation continue avec du butyrate puis alimentation continue avec du crotonate). Des injections de crotonate ont également été effectuées en circuit fermé, avec une biomasse adaptée dans un premier temps à la dégradation d'un mélange d'AGV, le réacteur étant ensuite alimenté avec du propionate puis du butyrate seuls.Contrairement à ce que laissait penser la bibliographie, il a été constaté que les bactéries adaptées à la dégradation exclusive du butyrate sons très rapidement à même de dégrader le crotonate.Les résultats obtenus permettent d'approcher les spécificités bactériennes, la voie catabolique suivie par le crotonate, son mode de régulation enzymatique et les équilibres qui la gouvernent. C'est ainsi qu'il est possible de proposer un modèle explicatif relativement simple du mécanisme de biodégradation du crotonate.Volatile Fatty Acids (VFAs) are intermediate metabolites formed in the anaerobic biodegradation of organic matter. They are commonly found in sewage, municipal sanitary landfill leachate and effluents from agricultural and food-processing industries. A good knowledge of the microorganisms involved in VFA biodegradation is necessary to operate satisfactory biotreatment of those effluents.The objective of the present study is to better understand the metabolism of the anaerobic bacteria responsible for the degradation of butyric acid and one of its metabolites (crotonic acid), which is still poorly known.Syntrophomonaswolfei is one of the few butyrate-degrading acetogenic bacteria that bas been documented. First studios have shown that this microorganism is not capable of degrading crotonic acid (MCINERNEY et al., 1979, 1981). This is surprising since crotonyl-Coenzyme A, in its activated form, is an intermediate metabolite of n-butyrate ß-oxidation, which is the most common mechanism of butyrate biodegradation. In addition, ß-oxidatlon of crotonate is thermodynamically possible, even under standard conditions.These observations are al the origin of the present study, which investigates the anaerobic biodegradation of crotonate. Other Investigators have followed a similar approach and isolated S. wolfei in pure culture on crotonate.The degradation of crotonate was studied in a bench-scale up-flow anaerobic filter of twenty liters, operated in the dark, at 35 °C.A first set of experiments was carried out with a biomass exclusively adapted to the biodegradation of butyrate. Heat-expansed vermiculite was used as a packing medium. Various experimental protocols were successive followed. First, pulses of crotonate were injected into the reactor under conditions of continuous feeding with butyrate, and then, the reactor was continuously fed with crotonate. The objective was to determine whether a bacterial population exclusively adapted to butyrate biodegradation would be capable of degrading crotonate.It was found that crotonate was actually biodegraded in the reactor. Woth the first protocol, when pulses of crotonate were injected into the reactor, crotonate was totally removed in 55 hours (fig. 3). Butyrate and acetate concentrations increased as crotonate was degraded, but no significant increase in biogas production was observed. On the other hand, under the same conditions, it was found that iso-butyrate was not degraded, which is consistent with other published data (MCINERNEY et al., 1979, 1981 ; STIEB and SCHINK, 1985,1989).With the second protocol (continuous feeding with crotonate at 5.2 gg/l), crotonate was totally biodegraded in 48 hours after a 24 hours lag period. This biodegradation resulted in the accumulation of acetate and, in a lower extend, butyrate (fig.4).Following this stage, the reactor was fed with a higher crotonate concentration (12 g/l), and it was observed that crotonate was totally degraded in 20 hours, without any lag period (fig. 5).These results showed that butyrate-degrading bacteria were capable of degrading crotonate effectively after a short period of adaptation.Further experiments were conducted with a biomass previously adapted to the degradation of a mixture of VFAs (acetate, propionate, iso-butyrate, butyrate and caproate). Berl saddles were used as a support for bacterial growth. The reactor was operated in a recirculated batch mode and spiked with crotonate. Finally, the reactor was successively fed for four weeks with propionate and for two weeks with butyrate, before being spiked with crotonate.In all these experiments, crotonate biodegradation was observed, but, in contrast to the results obtained with the “vermiculite reactor”, no butyrate accumulation occured (fig.6).These results show that a bacterial population adapted to the degradation of a mixture of VFAs or to the degradation of individual VFAs such as propionate and n-butyrate, is capable of degrading crotonate.Based on the present study and on literature data, the following mechanism can be proposed for the biodegradation of crotonate (fig.7). The first stage is the activation of crotonate into crotonyl-Coenzyme A by an acetyl-CoA/crotonyl-CoA transferase, as recently isolated from S. wolfei (BEATY and MCINERNEY, 1987). When present at low concentrations, crotonate is probably directly degraded into acetate, as shown by the results obtained with the “selles de Berl reactor”, in which no intermediate metabolite has been detected. At higher concentrations, enzymatic sites may be saturated and an equilibrium be established with butyrate, which is then released into the medium. This has been shown by the accumulation of butyrate under conditions of continuous feeding with crotonate. In addition, another intermediate metabolite has been formed, which has not been identified in the present study. This product is most probably poly-ß-hydroxy-butyrate, which has been found in S.wolfei (MCINERNEY et al, 1979) although if is not very common in chemiotrophic bacteria

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page