The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)

CIB W062 Symposium 2006 Study on Maximum Flow Rates and Sizing Method of Overflow Pipes in Water Tanks

Abstract When examining the standard of the air-gap in open tanks with overflow pipes, it is necessary to determine the height of the highest water level and maximum capacity of overflow pipe in tanks. However, it is not cleared not only to determine the height and the capacity, but also to decide the size of overflow pipe. Therefore, the experimental study was carried out for the purpose to obtain them. In this paper, it was reported the experiment result concerning the FRP water tank with overflow pipe of inside diameters 50 mm and 100 mm. As a result, empirical formulae of the height by incoming flow rates and inside diameters, and the maximum flow rate of overflow pipes are shown. Moreover, methods to decide the size of overflow pipes are proposed

Broad-band X-ray spectral evolution of GX 339-4 during a state transition

We report on X-ray and soft gamma-ray observations of the black-hole candidate GX 339-4 during its 2007 outburst, performed with the RXTE and INTEGRAL satellites. The hardness-intensity diagram of all RXTE/PCA data combined shows a q-shaped track similar to that observed in previous outbursts.The evolution in the diagram suggested that a transition from hard-intermediate state to soft-intermediate state occurred, simultaneously with INTEGRAL observations performed in March. The transition is confirmed by the timing analysis presented in this work, which reveals that a weak type-A quasi-periodic oscillation (QPO) replaces a strong type-C QPO. At the same time, spectral analysis shows that the flux of the high-energy component shows a significant decrease in its flux. However, we observe a delay (roughly one day) between variations of the spectral parameters of the high-energy component and changes in the flux and timing properties. The changes in the high-energy component can be explained either in terms the high-energy cut-off or in terms of a variations in the reflection component. We compare our results with those from a similar transition during the 2004 outburst of GX 339-4.Comment: 8 pages, 6 figures, accepted for publication in MNRAS Main Journa

Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes

The inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive a relationship between weak convergence of a Levy process to an infinite variance stable distribution when time approaches zero and weak convergence of a different Levy process as time approaches infinity. This allows us to get self contained conditions for a Levy process to converge to an infinite variance stable distribution as time approaches zero. We formulate our results both for general Levy processes and for the important class of tempered stable Levy processes. For this latter class, we give detailed results in terms of their Rosinski measures

Initial low/hard state, multiple jet ejections and X-ray/radio correlations during the outburst of XTE J1859+226

We have studied the 1999 soft X-ray transient outburst of XTE J1859+226 at radio and X-ray wavelengths. The event was characterised by strong variability in the disc, corona and jet - in particular, a number of radio flares (ejections) took place and seemed well-correlated with hard X-ray events. Apparently unusual for the `canonical soft' X-ray transient, there was an initial period of low/hard state behaviour during the rise from quiescence but prior to the peak of the main outburst - we show that not only could this initial low/hard state be an ubiquitous feature of soft X-ray transient outbursts but that it could also be extremely important in our study of outburst mechanisms.Comment: 12 pages, Accepted for publication in MNRA

A transient variable 6 Hz QPO from GX 339-4

We report the results of an observation with the Rossi X-ray Timing Explorer of the black hole candidate GX 339-4 during its 2002/2003 outburst. This observation took place during a spectral transition from the hard to the soft state. A strong (6% rms) transient quasi-periodic oscillation (QPO) appears suddenly in the power density spectrum during this observation. The QPO centroid is ~6 Hz, but it varies significantly between 5 and 7 Hz with a characteristic time scale of ~10 seconds, correlated with the 2-30 keV count rate. The appearance of the QPO is related to spectral hardening of the flux, due to a change in the relative contribution of the soft and hard spectral components. We compare this peculiar behavior with results from other systems that show similar low frequency QPO peaks, and discuss the results in terms of possible theoretical models for QPO production.Comment: Author list corrected, small typos fixe

Increased S-nitrosylation and proteasomal degradation of caspase-3 during infection contribute to the persistence of adherent invasive escherichia coli (AIEC) in immune cells

Adherent invasive Escherichia coli (AIEC) have been implicated as a causative agent of Crohn's disease (CD) due to their isolation from the intestines of CD sufferers and their ability to persist in macrophages inducing granulomas. The rapid intracellular multiplication of AIEC sets it apart from other enteric pathogens such as Salmonella Typhimurium which after limited replication induce programmed cell death (PCD). Understanding the response of infected cells to the increased AIEC bacterial load and associated metabolic stress may offer insights into AIEC pathogenesis and its association with CD. Here we show that AIEC persistence within macrophages and dendritic cells is facilitated by increased proteasomal degradation of caspase-3. In addition S-nitrosylation of pro- and active forms of caspase-3, which can inhibit the enzymes activity, is increased in AIEC infected macrophages. This S-nitrosylated caspase-3 was seen to accumulate upon inhibition of the proteasome indicating an additional role for S-nitrosylation in inducing caspase-3 degradation in a manner independent of ubiquitination. In addition to the autophagic genetic defects that are linked to CD, this delay in apoptosis mediated in AIEC infected cells through increased degradation of caspase-3, may be an essential factor in its prolonged persistence in CD patients

Protection by the NO-Donor SNAP and BNP against Hypoxia/Reoxygenation in Rat Engineered Heart Tissue

In vitro assays could replace animal experiments in drug screening and disease modeling, but have shortcomings in terms of functional readout. Force-generating engineered heart tissues (EHT) provide simple automated measurements of contractile function. Here we evaluated the response of EHTs to hypoxia/reoxygenation (H/R) and the effect of known cardiocytoprotective molecules. EHTs from neonatal rat heart cells were incubated for 24 h in EHT medium. Then they were subjected to 180 min hypoxia (93% N2, 7% CO2) and 120 min reoxygenation (40% O2, 53% N2, 7% CO2), change of medium and additional follow-up of 48 h. Time-matched controls (40% O2, 53% N2, 7% CO2) were run for comparison. The following conditions were applied during H/R: fresh EHT medium (positive control), the NO-donor S-nitroso-N-acetyl-D,L-penicillamine (SNAP, 10-7, 10-6, 10-5 M) or the guanylate cyclase activator brain type natriuretic peptide (BNP, 10-9, 10-8, 10-7 M). Frequency and force of contraction were repeatedly monitored over the entire experiment, pH, troponin I (cTnI), lactate dehydrogenase (LDH) and glucose concentrations measured in EHT medium. Beating activity of EHTs in 24 h-medium ceased during hypoxia, partially recovered during reoxygenation and reached time-control values during follow-up. H/R was accompanied by a small increase in LDH and non-significant increase in cTnI. In fresh medium, some EHTs continued beating during hypoxia and all EHTs recovered faster during reoxygenation. SNAP and BNP showed small but significant protective effects during reoxygenation. EHTs are applicable to test potential cardioprotective compounds in vitro, monitoring functional and biochemical endpoints, which otherwise could be only measured by using in vivo or ex vivo heart preparations. The sensitivity of the model needs improvement

The evolution of the timing properties of the black-hole transient GX 339-4 during its 2002/2003 outburst

We present the results of the timing and color analysis of more than two hundred RXTE/PCA observations of the bright black-hole transient GX 339-4 obtained during its 2002/2003 outburst. The color-intensity evolution of the system, coupled to the properties of its fast time variability, allow the identification of four separate states. Depending on the state, strong noise is detected, together with a variety of quasi-periodic oscillations at frequencies from 0.2 to 8 Hz. We present a characterization of the timing parameters of these states and compare them to what has been observed in other systems. These results, together with those obtained from energy spectra, point towards a common evolution of black-hole transients through their outbursts.Comment: 21 pages, 22 figures; accepted for publication in Astronomy & Astrophysics; small language changes, updated reference