The Structure of Typical Clusters in Large Sparse Random Configurations

The initial purpose of this work is to provide a probabilistic explanation of recent results on a version of Smoluchowski’s coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution of concentrations of particles in a medium where particles coalesce pairwise as time passes and each particle can only perform a given number of aggregations. Under appropriate assumptions, the concentrations of particles converge as time tends to infinity to some measure which bears a striking resemblance with the distribution of the total population of a Galton-Watson process started from two ancestors. Roughly speaking, the configuration model is a stochastic construction which aims at producing a typical graph on a set of vertices with pre-described degrees. Specifically, one attaches to each vertex a certain number of stubs, and then join pairwise the stubs uniformly at random to create edges between vertices. In this work, we use the configuration model as the stochastic counterpart of Smoluchowski’s coagulation equations with limited aggregations. We establish a hydrodynamical type limit theorem for the empirical measure of the shapes of clusters in the configuration model when the number of vertices tends to ∞. The limit is given in terms of the distribution of a Galton-Watson process started with two ancestors.     

Detection of acoustic waves by NMR using a radiofrequency field gradient

A B(1) field gradient-based method previously described for the detection of mechanical vibrations has been applied to detect oscillatory motions in condensed matter originated from acoustic waves. A ladder-shaped coil generating a quasi-constant RF-field gradient was associated with a motion-encoding NMR sequence consisting in a repetitive binomial 13;31; RF pulse train (stroboscopic acquisition). The NMR response of a gel phantom subject to acoustic wave excitation in the 20-200 Hz range was investigated. Results showed a linear relationship between the NMR signal and the wave amplitude and a spectroscopic selectivity of the NMR sequence with respect to the input acoustic frequency. Spin displacements as short as a few tens of nanometers were able to be detected with this method.     

Markovian Solutions of Inviscid Burgers Equation

For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller–Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infinitesimal generator. Previously known explicit solutions such as Frachebourg–Martin's (white noise initial velocity) and Carraro–Duchon's Lévy process intrinsic-statistical solutions (including Brownian initial velocity) are recovered as special cases.     

Fast rotation of a Bose-Einstein condensate

We study the rotation of a 87Rb Bose-Einstein condensate confined in a quadratic plus quartic potential. This trap configuration allows one to increase the rotation frequency of the gas above the trap frequency. In such a fast rotation regime we observe a dramatic change in the appearance of the quantum gas. The vortices which were easily detectable for a slower rotation become much less visible, and their surface density is well below the value expected for this rotation frequency domain. We discuss some possible tracks to account for this effect.     

Characterization of DNA chips on the molecular scale before and after hybridization with an atomic force microscope

Using two different 25-mer oligonucleotide probes covalently grafted on a silicon substrate, we demonstrate how efficient atomic force microscopy (AFM) can be for monitoring each step of DNA chip preparation: from probe immobilization to hybridization on the molecular scale. We observed the probe-molecule organization on the chip after immobilization, and the target molecules, which hybridized with probes could be individually identified. This article presents a method of straightforwardly identifying not only single and double DNA strands, but also, and more significantly, the hybridized part on them.     

A model for the calculation of noise transmission inside dwellings: application to aircraft noise

A numerical model of sound transmission inside dwellings has been developed. It is based on a decoupled method mixing integral, modal and geometric approaches. Kropp's formulation has been adapted to take balconies into account. Architectural effects such as projected roofs or nearby buildings have been analysed. Sound transmission is strongly affected by the angle of incidence of incoming waves. The proposed approach makes use of velocity fields on windows either computed or measured with a laser vibrometer. Comparisons between computations and measurements are reported.     

Dynamic contrast-enhanced MRI of vascular changes induced by the VEGF-signalling inhibitor ZD4190 in human tumour xenografts

Dynamic contrast-enhanced magnetic resonance imaging (DCEMRI) was used to examine the acute effects of treatment with an inhibitor of vascular endothelial growth factor (VEGF) signaling. ZD4190 is an orally bioavailable inhibitor of VEGF receptor-2 (KDR) tyrosine kinase activity, which elicits broad-spectrum antitumour activity in preclinical models following chronic once-daily dosing. Nude mice, bearing established (0.5-1.0 mL volume) human prostate (PC-3), lung (Calu-6) and breast (MDA-MB-231) tumor xenografts, were dosed with ZD4190 (p.o.) using a 1 day (0 and 22 h) or 7 day (0, 24, 48, 72, 96,120,144, and 166 h) treatment regimen. DCEMRI was employed 2 h after the last dose of ZD4190, using the contrast agent gadopentetate dimeglumine. Dynamic data were fit to a compartmental model to obtain voxelwise K(trans), the transfer constant for gadopentetate into the tumor. K(trans) was averaged over the entire tumor, and a multi-threshold histogram analysis was also employed to account for tumor heterogeneity. Reductions in K(trans) reflect reductions in flow, in endothelial surface area, and/or in vascular permeability. A vascular input function was obtained for each mouse simultaneously with the tumor DCEMRI data. ZD4190 treatment produced a dose-dependent (12.5-100 mg x kg(-1) per dose) reduction in K(trans) in PC-3 prostate tumors. At 100 mg x kg(-1), the largest concentration examined, ZD4190 reduced K(trans) in PC-3 tumors by 31% following 2 doses (1 day treatment regimen; p < 0.001) and by 53% following 8 doses (7 day regimen; p < 0.001). Comparative studies in the three models using a showed similar reductions in K(trans) for the lung and breast tumors using the histogram analysis, although the statistical significance was lost when K(trans) was averaged over the entire tumor. Collectively these studies suggest that DCEMRI using gadopentetate may have potential clinically, for monitoring inhibition of VEGF signaling in solid tumors.     

Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh–Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein–Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter (\(\rho _{0}\)) were explicitly plotted. The results show that, when the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter at \(r=1\) (\(\rho _{0}\)) vanish \((\rho _{0}=\epsilon =0)\), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing \(\rho _{0}\), the transition points are shifted to lower entropies. The same thing is observed when increasing \(\epsilon ^{2}\). In the absence of quintessence-like matter (\(\rho _{0}=0\)), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing \(\rho _{0}\) or \((\epsilon ^2)\).