Branching Instabilities in Rapid Fracture: Dynamics and Geometry

We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of experimental data.Comment: 9 pages, 11 figure

Genealogy of catalytic branching models

We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate proportional to the number of catalyst individuals alive. The reactant forms a process in random medium. We describe asymptotically the genealogy of catalytic branching populations coded as the induced forest of $\mathbb{R}$-trees using the many individuals--rapid branching continuum limit. The limiting continuum genealogical forests are then studied in detail from both the quenched and annealed points of view. The result is obtained by constructing a contour process and analyzing the appropriately rescaled version and its limit. The genealogy of the limiting forest is described by a point process. We compare geometric properties and statistics of the reactant limit forest with those of the "classical" forest.Comment: Published in at http://dx.doi.org/10.1214/08-AAP574 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Improved Limits on B0B^{0} decays to invisible (+γ)(+\gamma) final states

We establish improved upper limits on branching fractions for B0 decays to final States 10 where the decay products are purely invisible (i.e., no observable final state particles) and for final states where the only visible product is a photon. Within the Standard Model, these decays have branching fractions that are below the current experimental sensitivity, but various models of physics beyond the Standard Model predict significant contributions for these channels. Using 471 million BB pairs collected at the Y(4S) resonance by the BABAR experiment at the PEP-II e+e- storage ring at the SLAC National Accelerator Laboratory, we establish upper limits at the 90% confidence level of 2.4x10^-5 for the branching fraction of B0-->Invisible and 1.7x10^-5 for the branching fraction of B0-->Invisible+gammaComment: 8 pages, 3 postscript figures, submitted to Phys. Rev. D (Rapid Communications

Stationary distribution for dioecious branching particle systems with rapid stirring

We study dioecious (i.e., two-sex) branching particle system models, where there are two types of particles, modeling the male and female populations, and where birth of new particles requires the presence of both male and female particles. We show that stationary distributions of various dioecious branching particle models are nontrivial under certain conditions, for example, when there is sufficiently fast stirring.Comment: Published in at http://dx.doi.org/10.1214/105051607000000276 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Measurement of the Branching Fraction for B- --> D0 K*-

We present a measurement of the branching fraction for the decay B- --> D0 K*- using a sample of approximately 86 million BBbar pairs collected by the BaBar detector from e+e- collisions near the Y(4S) resonance. The D0 is detected through its decays to K- pi+, K- pi+ pi0 and K- pi+ pi- pi+, and the K*- through its decay to K0S pi-. We measure the branching fraction to be B.F.(B- --> D0 K*-)= (6.3 +/- 0.7(stat.) +/- 0.5(syst.)) x 10^{-4}.Comment: 7 pages, 1 postscript figure, submitted to Phys. Rev. D (Rapid Communications

Relative rates of B meson decays into psi(2S) and J/psi mesons

We report on a study of the relative rates of B meson decays into psi(2S) and J/psi mesons using 1.3 fb^-1 of pbar p collisions at sqrt(s) = 1.96 TeV recorded by the D0 detector operating at the Fermilab Tevatron Collider. We observe the channels B^0_s -> psi(2S)phi, B^0_s -> J/psi phi, B^+/- -> psi(2S) K^+/-, and B^+/- -> J/psi K^+/- and we measure the relative branching fractions for these channels to be B(B^0_s -> psi(2S)phi)/B(B^0_s -> J/psi phi) = 0.55 +/- 0.11 (stat) +/- 0.07 (syst) +/- 0.06 (B), B(B^+/- -> psi(2S) K^+/-)/B(B^+/- -> J/psi K^+/-) = 0.65 +/- 0.04 (stat) +/- 0.03 (syst) +/- 0.07 (B) where the final error corresponds to the uncertainty in the J/psi and psi(2S) branching ratio into two muons.Comment: Published in Phys. Rev. D - Rapid Communicatio