Distance traveled by random walkers before absorption in a random medium

We consider the penetration length $l$ of random walkers diffusing in a medium of perfect or imperfect absorbers of number density $\rho$. We solve this problem on a lattice and in the continuum in all dimensions $D$, by means of a mean-field renormalization group. For a homogeneous system in $D>2$, we find that $l\sim \max(\xi,\rho^{-1/2})$, where $\xi$ is the absorber density correlation length. The cases of D=1 and D=2 are also treated. In the presence of long-range correlations, we estimate the temporal decay of the density of random walkers not yet absorbed. These results are illustrated by exactly solvable toy models, and extensive numerical simulations on directed percolation, where the absorbers are the active sites. Finally, we discuss the implications of our results for diffusion limited aggregation (DLA), and we propose a more effective method to measure $l$ in DLA clusters.Comment: Final version: also considers the case of imperfect absorber

Self-gravitating Brownian systems and bacterial populations with two or more types of particles

We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multi-components gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a non universal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology

Phase transitions in self-gravitating systems and bacterial populations surrounding a central body

International audienceWe study the nature of phase transitions in a self-gravitating classical gas in the presence of a central body. The central body can mimic a black hole at the center of a galaxy or a rocky core (protoplanet) in the context of planetary formation. In the chemotaxis of bacterial populations, sharing formal analogies with self-gravitating systems, the central body can be a supply of ``food'' (chemoattractant). We consider both microcanonical (fixed energy) and canonical (fixed temperature) descriptions and study the inequivalence of statistical ensembles. At high energies (resp. high temperatures), the system is in a ``gaseous'' phase and at low energies (resp. low temperatures) it is in a condensed phase with a ``cusp-halo'' structure, where the cusp corresponds to the rapid increase of the density of the gas at the contact with the central body. For a fixed density $\rho_{*}$ of the central body, we show the existence of two critical points in the phase diagram, one in each ensemble, depending on the core radius $R_{*}$: for small radii $R_{*}R_{*}^{\rm CCP}$, there is no phase transition at all. We study how the nature of these phase transitions changes as a function of the dimension of space. We also discuss the analogies and the differences with phase transitions in the self-gravitating Fermi gas [P.H. Chavanis, Phys. Rev. E 65, 056123 (2002)]

Contribution of germline deleterious variants in the RAD51 paralogs to breast and ovarian cancers

International audienceRAD51 paralogs (RAD51B, RAD51C, RAD51D, XRCC2, and XRCC3) have recently been involved in breast and ovarian cancer predisposition: RAD51B, RAD51C, and RAD51D in ovarian cancer, RAD51B and XRCC2 in breast cancer. The aim of this study was to estimate the contribution of deleterious variants in the five RAD51 paralogs to breast and ovarian cancers. The five RAD51 paralog genes were analyzed by next-generation sequencing technologies in germline DNA from 2649 consecutive patients diagnosed with breast and/or ovarian cancer. Twenty-one different deleterious variants were identified in the RAD51 paralogs in 30 patients: RAD51B (n = 4), RAD51C (n = 12), RAD51D (n = 7), XRCC2 (n = 2), and XRCC3 (n = 5). The overall deleterious variant rate was 1.13% (95% confidence interval (CI): 0.72–1.55%) (30/2649), including 15 variants in breast cancer only cases (15/2063; 0.73% (95% CI: 0.34–1.11%)) and 15 variants in cases with at least one ovarian cancer (15/570; 2.63% (95% CI: 1.24–4.02%)). This study is the first evaluation of the five RAD51 paralogs in breast and ovarian cancer predisposition and it demonstrates that deleterious variants can be present in breast cancer only cases. Moreover, this is the first time that XRCC3 deleterious variants have been identified in breast and ovarian cancer cases