Quenched invariance principle for random walks in balanced random environment

We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.Comment: Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo (in journal version) corrected in (26

Modeling tumor cell migration: from microscopic to macroscopic

It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study of the growth of real-size tumors with several millions of cells, it is best to use a macroscopic model having the form of a partial differential equation (PDE) for the density of cells. The difficulty is to predict the effect, at the macroscopic scale, of contact interactions that take place at the microscopic scale. To address this we use a multiscale approach: starting from a very simple, yet experimentally validated, microscopic model of migration with contact interactions, we derive a macroscopic model. We show that a diffusion equation arises, as is often postulated in the field of glioma modeling, but it is nonlinear because of the interactions. We give the explicit dependence of diffusivity on the cell density and on a parameter governing cell-cell interactions. We discuss in details the conditions of validity of the approximations used in the derivation and we compare analytic results from our PDE to numerical simulations and to some in vitro experiments. We notice that the family of microscopic models we started from includes as special cases some kinetically constrained models that were introduced for the study of the physics of glasses, supercooled liquids and jamming systems.Comment: Final published version; 14 pages, 7 figure

Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style

Fluorescent macrolide probes – synthesis and use in evaluation of bacterial resistance

This is the final version. Available on open access from the Royal Society of Chemistry via the DOI in this recordThe emerging crisis of antibiotic resistance requires a multi-pronged approach in order to avert the onset of a post-antibiotic age. Studies of antibiotic uptake and localisation in live cells may inform the design of improved drugs and help develop a better understanding of bacterial resistance and persistence. To facilitate this research, we have synthesised fluorescent derivatives of the macrolide antibiotic erythromycin. These analogues exhibit a similar spectrum of antibiotic activity to the parent drug and are capable of labelling both Gram-positive and -negative bacteria for microscopy. The probes localise intracellularly, with uptake in Gram-negative bacteria dependent on the level of efflux pump activity. A plate-based assay established to quantify bacterial labelling and localisation demonstrated that the probes were taken up by both susceptible and resistant bacteria. Significant intra-strain and -species differences were observed in these preliminary studies. In order to examine uptake in real-time, the probe was used in single-cell microfluidic microscopy, revealing previously unseen heterogeneity of uptake in populations of susceptible bacteria. These studies illustrate the potential of fluorescent macrolide probes to characterise and explore drug uptake and efflux in bacteria.Australian Postgraduate AwardInstitute for Molecular Biosciences Research Advancement AwardMedical Research Council (MRC)Gordon and Betty and Gordon Moore FoundationCampus France the Programme Hubert Curien FASIC 2018Wellcome TrustNHMR

I. Flux and color variations of the quadruply imaged quasar HE 0435-1223

aims: We present VRi photometric observations of the quadruply imaged quasar HE 0435-1223, carried out with the Danish 1.54m telescope at the La Silla Observatory. Our aim was to monitor and study the magnitudes and colors of each lensed component as a function of time. methods: We monitored the object during two seasons (2008 and 2009) in the VRi spectral bands, and reduced the data with two independent techniques: difference imaging and PSF (Point Spread Function) fitting.results: Between these two seasons, our results show an evident decrease in flux by ~0.2-0.4 magnitudes of the four lensed components in the three filters. We also found a significant increase (~0.05-0.015) in their V-R and R-i color indices. conclusions: These flux and color variations are very likely caused by intrinsic variations of the quasar between the observed epochs. Microlensing effects probably also affect the brightest "A" lensed component.Comment: 10 pages, 8 figure

Realising consilience: How better communication between archaeologists, historians and natural scientists can transform the study of past climate change in the Mediterranean

This paper reviews the methodological and practical issues relevant to the ways in which natural scientists, historians and archaeologists may collaborate in the study of past climatic changes in the Mediterranean basin. We begin by discussing the methodologies of these three disciplines in the context of the consilience debate, that is, attempts to unify different research methodologies that address similar problems. We demonstrate that there are a number of similarities in the fundamental methodology between history, archaeology, and the natural sciences that deal with the past ("palaeoenvironmental sciences"), due to their common interest in studying societal and environmental phenomena that no longer exist. The three research traditions, for instance, employ specific narrative structures as a means of communicating research results. We thus present and compare the narratives characteristic of each discipline; in order to engage in fruitful interdisciplinary exchange, we must first understand how each deals with the societal impacts of climatic change. In the second part of the paper, we focus our discussion on the four major practical issues that hinder communication between the three disciplines. These include terminological misunderstandings, problems relevant to project design, divergences in publication cultures, and differing views on the impact of research. Among other recommendations, we suggest that scholars from the three disciplines should aim to create a joint publication culture, which should also appeal to a wider public, both inside and outside of academia

The UA9 experimental layout

The UA9 experimental equipment was installed in the CERN-SPS in March '09 with the aim of investigating crystal assisted collimation in coasting mode. Its basic layout comprises silicon bent crystals acting as primary collimators mounted inside two vacuum vessels. A movable 60 cm long block of tungsten located downstream at about 90 degrees phase advance intercepts the deflected beam. Scintillators, Gas Electron Multiplier chambers and other beam loss monitors measure nuclear loss rates induced by the interaction of the beam halo in the crystal. Roman pots are installed in the path of the deflected particles and are equipped with a Medipix detector to reconstruct the transverse distribution of the impinging beam. Finally UA9 takes advantage of an LHC-collimator prototype installed close to the Roman pot to help in setting the beam conditions and to analyze the efficiency to deflect the beam. This paper describes in details the hardware installed to study the crystal collimation during 2010.Comment: 15pages, 11 figure, submitted to JINS