Intermittency on catalysts

The present paper provides an overview of results obtained in four recent papers by the authors. These papers address the problem of intermittency for the Parabolic Anderson Model in a \emph{time-dependent random medium}, describing the evolution of a ``reactant'' in the presence of a ``catalyst''. Three examples of catalysts are considered: (1) independent simple random walks; (2) symmetric exclusion process; (3) symmetric voter model. The focus is on the annealed Lyapunov exponents, i.e., the exponential growth rates of the successive moments of the reactant. It turns out that these exponents exhibit an interesting dependence on the dimension and on the diffusion constant.Comment: 11 pages, invited paper to appear in a Festschrift in honour of Heinrich von Weizs\"acker, on the occasion of his 60th birthday, to be published by Cambridge University Pres

Intermittency on catalysts: three-dimensional simple symmetric exclusion

We continue our study of intermittency for the parabolic Anderson model $\partial u/\partial t = \kappa\Delta u + \xi u$ in a space-time random medium $\xi$, where $\kappa$ is a positive diffusion constant, $\Delta$ is the lattice Laplacian on $\Z^d$, $d \geq 1$, and $\xi$ is a simple symmetric exclusion process on $\Z^d$ in Bernoulli equilibrium. This model describes the evolution of a \emph{reactant} $u$ under the influence of a \emph{catalyst} $\xi$. In G\"artner, den Hollander and Maillard (2007) we investigated the behavior of the annealed Lyapunov exponents, i.e., the exponential growth rates as $t\to\infty$ of the successive moments of the solution $u$. This led to an almost complete picture of intermittency as a function of $d$ and $\kappa$. In the present paper we finish our study by focussing on the asymptotics of the Lyaponov exponents as $\kappa\to\infty$ in the \emph{critical} dimension $d=3$, which was left open in G\"artner, den Hollander and Maillard (2007) and which is the most challenging. We show that, interestingly, this asymptotics is characterized not only by a \emph{Green} term, as in $d\geq 4$, but also by a \emph{polaron} term. The presence of the latter implies intermittency of \emph{all} orders above a finite threshold for $\kappa$.Comment: 38 page

A response to a letter from David Perkins concerning the question of whether nt mutants involve tryptophan pyrrolase

A response to a letter from David Perkins concerning the question of whether nt mutants involve tryptophan pyrrolas

Church and State

The problem of Church and State is one which is entirely Christian, though in its practical applications it also concerns others. The very nature of the case is one which presupposes the side by side existence of both institutions. It was only when Christ came and established the Church in the world and still said, “My kingdom is not of the world, (John 18 , 36) , that the problem of the relation the one bears to the other first arose

Adequação da metodologia Kjeldahl para determinação de nitrogênio total e proteína bruta.

bitstream/item/37465/1/CT63.pd

Alcance de los estudios sobre la pesca deportiva de los istiophoridae en Venezuela

On effectue l'analyse historique (1961-89) de la CPUE des poissons porte-épée capturés par la pêche sportive dans le principal port de plaisance du pays (Playa Grande Yatching Club). Bien qu'il existe une variabilité interannuelle accusée de la production, on peut observer que l'indice d'abondance du Makaire blanc (#Tetrapturus albidus) a baissé de façon continue ces dernières années, presqu'à son plus faible niveau historique. En ce qui concerne le Makaire bleu (#Makaira nigricans), la hausse de la CPUE, qui avait commencé au début des années quatre-vingt, s'est interrompue, et montrait déjà ces dernières années une tendance décroissante. Bien qu'encore faible, la CPUE du voilier (#Istiophorus albicans$) s'est stabilisée dans le courant de la décennie en cours. Exception faite de cette dernière espèce, on n'a pas observé d'individus sexuellement matures dans les échantillons. Chez les deux espèces de Makaires, les femelles atteignent une taille supérieure à celle des mâles, contrairement au voilier chez lequel il ne semble pas exister de différentiation sexuelle à cet égar

Neurospora crassa qa-2 gene fragment.

Neurospora crassa qa-2 gene fragment

A solid-reagent dispenser for use in the azocoll protease assay (and other insoluble substrate analyses).

A solid-reagent dispenser for use in the azocoll protease assay (and other insoluble substrate analyses)

Observations of the Sunyaev-Zel'dovich effect at high angular resolution towards the galaxy clusters A665, A2163 and CL0016+16

We report on the first observation of the Sunyaev-Zel'dovich effect with the Diabolo experiment at the IRAM 30 metre telescope. A significant brightness decrement is detected in the direction of three clusters (Abell 665, Abell 2163 and CL0016+16). With a 30 arcsecond beam and 3 arcminute beamthrow, this is the highest angular resolution observation to date of the SZ effect.Comment: 23 pages, 8 figures, 6 tables, accepted to New Astronom