First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

Partial survival and inelastic collapse for a randomly accelerated particle

We present an exact derivation of the survival probability of a randomly accelerated particle subject to partial absorption at the origin. We determine the persistence exponent and the amplitude associated to the decay of the survival probability at large times. For the problem of inelastic reflection at the origin, with coefficient of restitution $r$, we give a new derivation of the condition for inelastic collapse, $r<r_c=e^{-\pi/\sqrt{3}}$, and determine the persistence exponent exactly.Comment: 6 page

Studying the scale and q^2 dependence of K^+-->pi^+e^+e^- decay

We extract the K^+-->pi^+e^+e^- amplitude scale at q^2=0 from the recent Brookhaven E865 high-statistics data. We find that the q^2=0 scale is fitted in excellent agreement with the theoretical long-distance amplitude. Lastly, we find that the observed q^2 shape is explained by the combined effect of the pion and kaon form-factor vector-meson-dominance rho, omega and phi poles, and a charged pion loop coupled to a virtual photon-->e^+e^- transition.Comment: 8 pages, 3 figure

Effects of pressure, oxygen concentration, and forced convection on flame spread rate of Plexiglas, Nylon and Teflon

Experiments were conducted in which the burning of cylindrical materials in a flowing oxidant stream was studied. Plexiglas, Nylon, and Teflon fuel specimens were oriented such that the flames spread along the surface in a direction opposed to flowing gas. Correlations of flame spread rate were obtained that were power law relations in terms of pressure, oxygen concentration, and gas velocity

A nonperturbative Real-Space Renormalization Group scheme

Based on the original idea of the density matrix renormalization group (DMRG), i.e. to include the missing boundary conditions between adjacent blocks of the blocked quantum system, we present a rigorous and nonperturbative mathematical formulation for the real-space renormalization group (RG) idea invented by L.P. Kadanoff and further developed by K.G. Wilson. This is achieved by using additional Hilbert spaces called auxiliary spaces in the construction of each single isolated block, which is then named a superblock according to the original nomenclature. On this superblock we define two maps called embedding and truncation for successively integrating out the small scale structure. Our method overcomes the known difficulties of the numerical DMRG, i.e. limitation to zero temperature and one space dimension.Comment: 13 pages, 5 figures, late

Cable compliance

The object of the investigation was to solve mechanical problems using cable-in-bending and cable-in-torsion. These problems included robotic contacts, targets, and controls using cable compliance. Studies continued in the use of cable compliance for the handicapped and the elderly. These included work stations, walkers, prosthetic knee joints, elbow joints, and wrist joints. More than half of these objects were met, and models were made and studies completed on most of the others. It was concluded that the many different and versatile solutions obtained only opened the door to many future challenges

Biomass partitioning and gas exchange parameters in different Musa cultivars as influenced by natural shade

Poster presented at Tropentag 2011 Development on the Margin. Bonn (Germany), 3-7 Oct 2011