Time correlations for the parabolic Anderson model

We derive exact asymptotics of time correlation functions for the parabolic Anderson model with homogeneous initial condition and time-independent tails that decay more slowly than those of a double exponential distribution and have a finite cumulant generating function. We use these results to give precise asymptotics for statistical moments of positive order. Furthermore, we show what the potential peaks that contribute to the intermittency picture look like and how they are distributed in space. We also investigate for how long intermittency peaks remain relevant in terms of ageing properties of the model.Comment: 28 page

Precise asymptotics for the parabolic Anderson model with a moving catalyst or trap

We consider the solution $u\colon [0,\infty) \times\mathbb{Z}^d\rightarrow [0,\infty)$ to the parabolic Anderson model, where the potential is given by $(t,x)\mapsto\gamma\delta_{Y_t}(x)$ with $Y$ a simple symmetric random walk on $\mathbb{Z}^d$. Depending on the parameter $\gamma\in[-\infty,\infty)$, the potential is interpreted as a randomly moving catalyst or trap. In the trap case, i.e., $\gamma<0$, we look at the annealed time asymptotics in terms of the first moment of $u$. Given a localized initial condition, we derive the asymptotic rate of decay to zero in dimensions 1 and 2 up to equivalence and characterize the limit in dimensions 3 and higher in terms of the Green's function of a random walk. For a homogeneous initial condition we give a characterisation of the limit in dimension 1 and show that the moments remain constant for all time in dimensions 2 and higher. In the case of a moving catalyst ($\gamma>0$), we consider the solution $u$ from the perspective of the catalyst, i.e., the expression $u(t,Y_t+x)$. Focusing on the cases where moments grow exponentially fast (that is, $\gamma$ sufficiently large), we describe the moment asymptotics of the expression above up to equivalence. Here, it is crucial to prove the existence of a principal eigenfunction of the corresponding Hamilton operator. While this is well-established for the first moment, we have found an extension to higher moments.Comment: In honour of J\"urgen G\"artner on the occasion of his 60th birthday, 20 page

Anatol (December 11-12, 1964)

Program for Anatol (December 11-12, 1964)

Metodologias colaborativas de construção coletiva: análise dos resultados do curso de gestão social de bacias hidrográficas no contexto do projeto TSGA II

TCC(graduação) - Universidade Federal de Santa Catarina. Centro Tecnológico. Engenharia Sanitária e Ambiental.O presente trabalho buscou refletir e apresentar os resultados do curso de Gestão Social de Bacias Hidrográficas (GSBH) realizado nos municípios de Araranguá, Chapecó e Braço do Norte, no contexto do programa de capacitação do Projeto Tecnologias Sociais para a Gestão da Água II (TSGA II) em Santa Catarina. A água é um bem essencial à vida, é um recurso natural limitado que está presente em praticamente todos os processos ecológicos e sociais. Ela é, portanto, um bem comum da humanidade, dotado de valor ecológico, social e econômico. Por isso, sua gestão deve ser feita de forma participativa, qualificada, mediadora e estratégica, buscando entender e valorizar os contextos das comunidades locais inseridas nas bacias hidrográficas e suas relações com o ambiente. Os objetivos específicos deste trabalho são: a) sistematizar os resultados obtidos em cada uma das regiões; b) registrar a experiência de capacitação do Projeto TSGA II na Gestão Social de Bacias Hidrográficas; c) apresentar o acordo inicial construído nas regiões; d) construir um quadro síntese dos resultados em cada uma das regiões; e e) elaborar um reflexão teórica e metodológica para o avanço das Tecnologias Sociais de Gestão da Água. Para isso, foram utilizadas metodologias colaborativas de construção coletiva de conceitos e estratégias, tais como: a Pedagogia do Amor, a metodologia de Construção do Espírito da Lei das Águas e sinergia com as Leis Irmãs e a metodologia Open Space ou Espaço Aberto. Como resultados desse trabalho tem-se a apresentação dos acordos iniciais construídos coletivamente e a construção de um quadro síntese dos resultados obtidos durante os cursos de GSBH nas regiões de Araranguá, Chapecó e Braço do Norte. A expectativa deste trabalho é contribuir para a gestão dos recursos hídricos nas respectivas bacias hidrográficas, buscando sistematizar e devolver os resultados do curso aos participantes do curso, comitês de bacias e lideranças locais

On- and Off-Responses in the Inferior Colliculus of the Greater Horseshoe Bat to Pure Tones

1. The auditory threshold curve of averaged evoked potentials of the colliculus inferior in Rhinolophus /errum equinum to pure tone stimulation from 1 to 100 kHz is presented (Fig. 1). For pure tone frequencies lower than 14 ktIz thresholds steeply rise from 20 to 110 db. The steepness of the acoustical filter for 83.3 kHz signals and the frequency of the echoes heard by Greater Horseshoe Bats is accentuated by averaging methods. Because of averaging, evoked potentials thresholds are lowered by about 20 db compared to those obtained by non-averaging methods. 2. Prominent off-responses in evoked potentials appear for three stimulus frequency ranges: 3-10 kHz with a peak at 5 ktIz, 20-40 kHz with a peak at 20 kHz and 80.0-82.6 kHz with a peak at 81.5 kHz (Fig. 2). 3. It is unlikely that beat note frequencies play any role for echolocation. 4. The relevance of these results to echolocation in Horseshoe Bats is discussed, especially as to Doppler shift information contained in the constant frequency part of echoes

Fantasy’s Traumatic Take on the Bildungsroman: Reading Neil Gaiman

Neil Gaiman’s novelistic work presents a tell-tale combination of fantasy, trauma writing, and the bildungsroman. At their core, all of Gaiman’s novels chart journeys of becoming, using fantasy as a guise to facilitate renewed coming-of-age processes even in adult characters. This book examines the way Gaiman unites these seemingly paradoxical genres to great effect. Analysing the thoroughly postmodern writings of the author, Schnitzler teases out the different ways fantasy engages with the difficult subject of traumatic representations while building on the well-established structure of the bildungsroman