Supercritical super-Brownian motion with a general branching mechanism and travelling waves

We consider the classical problem of existence, uniqueness and asymptotics of monotone solutions to the travelling wave equation associated to the parabolic semi-group equation of a super-Brownian motion with a general branching mechanism. Whilst we are strongly guided by the probabilistic reasoning of Kyprianou (2004) for branching Brownian motion, the current paper offers a number of new insights. Our analysis incorporates the role of Seneta-Heyde norming which, in the current setting, draws on classical work of Grey (1974). We give a pathwise explanation of Evans' immortal particle picture (the spine decomposition) which uses the Dynkin-Kuznetsov N-measure as a key ingredient. Moreover, in the spirit of Neveu's stopping lines we make repeated use of Dynkin's exit measures. Additional complications arise from the general nature of the branching mechanism. As a consequence of the analysis we also offer an exact X(log X)^2 moment dichotomy for the almost sure convergence of the so-called derivative martingale at its critical parameter to a non-trivial limit. This differs to the case of branching Brownian motion and branching random walk where a moment `gap' appears in the necessary and sufficient conditions.Comment: 34 page

Dynamics of a suspension of interacting yolk-shell particles

In this work we study the self-diffusion properties of a liquid of hollow spherical particles (shells)bearing a smaller solid sphere in their interior (yolks). We model this system using purely repulsive hard-body interactions between all (shell and yolk) particles, but assume the presence of a background ideal solvent such that all the particles execute free Brownian motion between collisions,characterized by short-time self-diffusion coefficients D0s for the shells and D0y for the yolks. Using a softened version of these interparticle potentials we perform Brownian dynamics simulations to determine the mean squared displacement and intermediate scattering function of the yolk-shell complex. These results can be understood in terms of a set of effective Langevin equations for the N interacting shell particles, pre-averaged over the yolks' degrees of freedom, from which an approximate self-consistent description of the simulated self-diffusion properties can be derived. Here we compare the theoretical and simulated results between them, and with the results for the same system in the absence of yolks. We find that the yolks, which have no effect on the shell-shell static structure, influence the dynamic properties in a predictable manner, fully captured by the theory.Comment: 5 pages, 1 figur

Allelic variation of low molecular weight glutenin subunits composition and the revealed genetic diversity in durum wheat Triticum turgidum L. ssp. durum

Low molecular weight glutenin subunits (LMW-GS) play an important role in determining the bread-making characteristics of dough in the end-use quality of wheat. In this study, A total of 149 worldwide-originated durum wheat were used to analyze the composition of LMW-GS using MALDI-TOF-MS. Based on the allelic variation of glutenin subunits, the genetic diversity was evaluated for the 149 durum wheat. Five types of alleles were identified at the Glu-A3 locus with Glu-A3e, Glu-A3a/c, Glu-A3f, Glu-A3d and Glu-A3b accounting for 43.0%, 16.1%, 12.8%, 10.1% and 7.4 % of the accessions, respectively. Five types of alleles were identified at the Glu-B3 locus: Glu-B3d (60.4%), Glu-B3b (6.0%), Glu-B3c (6.0%), Glu-B3h (2.7%) and Glu-B3f (0.7%). Two novel alleles encoding abnormal subunits 40500 Da and 41260 Da were identified at the Glu-A3 and Glu-B3 loci, respectively. Further studies are needed to match these novel alleles to previously discovered novel alleles. Moreover, the genetic diversity analysis indicated that great genetic variation existed in durum wheat among encoding loci of glutenin subunits, released periods of varieties and different geographical origins. The results provide more important information of potential germplasm for the improvement of durum wheat and common wheat

The Λ(1405)\Lambda(1405) in resummed chiral effective field theory

We study the unitarized meson-baryon scattering amplitude at leading order in the strangeness $S=-1$ sector using time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral effective field theory. By solving the coupled-channel integral equations with the full off-shell dependence of the effective potential and applying subtractive renormalization, we analyze the renormalized scattering amplitudes and obtain the two-pole structure of the $\Lambda(1405)$ resonance. We also point out the necessity of including higher-order terms.Comment: 16 pages, 3 figures, 5 table