Spin and orbital Hall effects for diffracting optical beams in gradient-index media

We examine the evolution of paraxial beams carrying intrinsic spin and orbital angular momenta (AM) in gradient-index media. A parabolic-type equation is derived which describes the beam diffraction in curvilinear coordinates accompanying the central ray. The center of gravity of the beam experiences transverse AM-dependent deflections -- the spin and orbital Hall effects. The spin Hall effect generates a transverse translation of the beam as a whole, in precise agreement with recent geometrical optics predictions. At the same time, the orbital Hall effect is significantly affected by the diffraction in the inhomogeneous medium and is accompanied by changes in the intrinsic orbital AM and deformations of the beam.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Coexistence in a One-Dimensional Cyclic Dominance Process

Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium processes in the stationary state. We exploit these insights to obtain asymptotically exact descriptions of the emerging reactive steady state in the regimes of high and low mutation rates. The results are compared to stochastic lattice simulations. Our methods and findings are potentially relevant for the spatio-temporal evolution of other non-equilibrium stochastic processes.Comment: 4 pages, 4 figures and 2 pages of Supplementary Material. To appear in Physical Review

Spatial fluctuations of a surviving particle in the trapping reaction

We consider the trapping reaction, $A+B\to B$, where $A$ and $B$ particles have a diffusive dynamics characterized by diffusion constants $D_A$ and $D_B$. The interaction with $B$ particles can be formally incorporated in an effective dynamics for one $A$ particle as was recently shown by Bray {\it et al}. [Phys. Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space dimension $d=1$, the asymptotic behaviour of the spatial fluctuation, $^{1/2}$, for a surviving $A$ particle in the perturbative regime, $D_A/D_B\ll 1$, for the case of an initially uniform distribution of $B$ particles. We show that, for $t\gg 1$, $^{1/2} \propto t^{\phi}$ with $\phi=1/4$. By contrast, the fluctuations of paths constrained to return to their starting point at time $t$ grow with the larger exponent 1/3. Numerical tests are consistent with these predictions.Comment: 10 pages, 5 figure

Survival probabilities in the double trapping reaction A +B -> B, B + C -> C

We consider the double trapping reaction A + B -> B, B + C -> C in one dimension. The survival probability of a given A particle is calculated under various conditions on the diffusion constants of the reactants, and on the ratio of initial B and C particle densities. The results are of more general form than those obtained in previous work on the problem.Comment: 5 page

DNA-encoded nucleosome occupancy is associated with transcription levels in the human malaria parasite Plasmodium falciparum.

BackgroundIn eukaryotic organisms, packaging of DNA into nucleosomes controls gene expression by regulating access of the promoter to transcription factors. The human malaria parasite Plasmodium falciparum encodes relatively few transcription factors, while extensive nucleosome remodeling occurs during its replicative cycle in red blood cells. These observations point towards an important role of the nucleosome landscape in regulating gene expression. However, the relation between nucleosome positioning and transcriptional activity has thus far not been explored in detail in the parasite.ResultsHere, we analyzed nucleosome positioning in the asexual and sexual stages of the parasite's erythrocytic cycle using chromatin immunoprecipitation of MNase-digested chromatin, followed by next-generation sequencing. We observed a relatively open chromatin structure at the trophozoite and gametocyte stages, consistent with high levels of transcriptional activity in these stages. Nucleosome occupancy of genes and promoter regions were subsequently compared to steady-state mRNA expression levels. Transcript abundance showed a strong inverse correlation with nucleosome occupancy levels in promoter regions. In addition, AT-repeat sequences were strongly unfavorable for nucleosome binding in P. falciparum, and were overrepresented in promoters of highly expressed genes.ConclusionsThe connection between chromatin structure and gene expression in P. falciparum shares similarities with other eukaryotes. However, the remarkable nucleosome dynamics during the erythrocytic stages and the absence of a large variety of transcription factors may indicate that nucleosome binding and remodeling are critical regulators of transcript levels. Moreover, the strong dependency between chromatin structure and DNA sequence suggests that the P. falciparum genome may have been shaped by nucleosome binding preferences. Nucleosome remodeling mechanisms in this deadly parasite could thus provide potent novel anti-malarial targets