Time evolution towards q-Gaussian stationary states through unified Ito-Stratonovich stochastic equation

We consider a class of single-particle one-dimensional stochastic equations which include external field, additive and multiplicative noises. We use a parameter $\theta \in [0,1]$ which enables the unification of the traditional It\^o and Stratonovich approaches, now recovered respectively as the $\theta=0$ and $\theta=1/2$ particular cases to derive the associated Fokker-Planck equation (FPE). These FPE is a {\it linear} one, and its stationary state is given by a $q$-Gaussian distribution with $q = \frac{\tau + 2M (2 - \theta)}{\tau + 2M (1 - \theta)}<3$, where $\tau \ge 0$ characterizes the strength of the confining external field, and $M \ge 0$ is the (normalized) amplitude of the multiplicative noise. We also calculate the standard kurtosis $\kappa_1$ and the $q$-generalized kurtosis $\kappa_q$ (i.e., the standard kurtosis but using the escort distribution instead of the direct one). Through these two quantities we numerically follow the time evolution of the distributions. Finally, we exhibit how these quantities can be used as convenient calibrations for determining the index $q$ from numerical data obtained through experiments, observations or numerical computations.Comment: 9 pages, 2 figure

Many-body system with a four-parameter family of point interactions in one dimension

We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual $\delta$-function potential. We examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction. We follow McGuire who obtained exact solutions for the system when the interaction is the $\delta$-function potential. We find exact bound states with the four-parameter family. For the scattering problem, however, we have not been so successful. This is because, as we point out, the condition of no diffraction that is crucial in McGuire's method is not satisfied except when the four-parameter family is essentially reduced to the $\delta$-function potential.Comment: 8 pages, 4 figure

Chapter 16 Volcanic hazard vulnerability on São Miguel Island, Azores

AbstractIn recent years much progress has been made in researching a wide variety of extreme events on São Miguel. In addition there are a number of volcano-related risks that impact upon the people of São Miguel. Some of these may occur both before and during volcanic emergencies (e.g. earthquakes), whilst others render São Miguel dangerous even when its volcanoes are not erupting (e.g. flooding, landslides, tsunamis and health impacts, especially the effects of CO2seepage into dwellings). In this chapter we first define what vulnerability means to the people of São Miguel, and relate this to the cultural and economic characteristics of the island. The following aspects of vulnerability are discussed: (a) physical (i.e. housing, settlement and the characteristics of evacuation routes and plans); (b) demographic and economic; and (c) social and cultural and perceptual (i.e. whether people have an accurate cognition of risk). Particular areas of concern relate to housing: the identification of isolated dwellings that would be difficult to evacuate; the vulnerability/resilience of evacuation routes following recent infrastructure improvements; characteristics of the island's transient population; management of livestock under emergency conditions; local leadership roles; and educational outreach.</jats:p

The motion of two masses coupled to a massive spring

We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple elastic function can be inferred are discussed and the normal modes and normal frequencies obtained. An approximation procedure to the evaluation of the normel frequencies in the case of uniform elastic function and mass density is also discussed.Comment: Standard Latex file plus three eps figure

Fronts and interfaces in bistable extended mappings

We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the convolution with a function of bounded variation. We prove the existence of travelling wave interfaces, namely fronts, and the uniqueness of the corresponding selected velocity and shape. This selected velocity is shown to be the propagating velocity for any interface, to depend continuously on the couplings and to increase with the symmetry parameter of the local nonlinearity. We apply the results to several examples including discrete and continuous couplings, and the planar fronts' dynamics in multi-dimensional Coupled Map Lattices. We eventually emphasize on the extension to other kinds of fronts and to a more general class of bistable extended mappings for which the couplings are allowed to be nonlinear and the local map to be smooth.Comment: 27 pages, 3 figures, submitted to Nonlinearit

Fungitoxicidade de grupos químicos sobre Myrothecium roridum in vitro e sobre a mancha-de-mirotécio em algodoeiro.

O objetivo deste trabalho foi avaliar a fungitoxicidade de produtos pertencentes aos grupos dos benzimidazóis, triazóis, estrobilurinas, isoftalonitrilas e ditiocarbamatos sobre a germinação conidial e o crescimento micelial in vitro de isolados de Myrothecium roridum e, in vivo, sobre a severidade da mancha-de-mirotécio em plantas de algodoeiro. Nos testes in vitro os fungicidas foram solubilizados em meio BDA, utilizando-se as concentrações de 0,1, 1, 10 e 100 mg L-1 de ingrediente ativo. A fungitoxidade dos produtos foi avaliada por meio da ED50 (dose necessária para inibir 50% da germinação conidial ou crescimento micelial). Em casa de vegetação, estimou-se a severidade da mancha-de-mirotécio pela porcentagem de área foliar lesionada nas plantas de algodoeiro tratadas antes (preventivo) e depois (curativo) da inoculação do patógeno. Os fungicidas tiofanato metílico, carbendazim, metconazol, tiofanato metílico + clorotalonil, piraclostrobina + epoxiconazol, piraclostrobina + metiram, triflostrobina + propiconazol e tebuconazol inibiram com alta eficácia (ED50<1 mg L-1), ou com eficácia (ED50 entre 1 e 10 mg L-1), a germinação conidial e o crescimento micelial in vitro de M. roridum. Os fungicidas piraclostrobina + epoxiconazol, tebuconazol, metconazol e azoxistrobina + ciproconazol são os mais eficazes em testes in vivo. O tratamento preventivo é mais eficaz que o curativo

Volcanic hazard vulnerability on Sao Miguel Island, Azores

"In recent years much progress has been made in researching a wide variety of extreme events on S. Miguel. In addition there are a number of volcano-related risks which impact upon the people of S. Miguel. Some of these may occur both before and during volcanic emergencies (e.g. earthquakes), whilst others render S. Miguel dangerous even when its volcanoes are not erupting (e.g. flooding, landslides, tsunamis and health impacts, especially the effects of CO2 seepage into dwellings). In this chapter we first define what vulnerability means to the people of São Miguel, and relate this to the cultural and economic characteristics of the island. The following aspects of vulnerability are discussed: a. physical (i.e. housing, settlement and the characteristics of evacuation routes and plans); b. demographic and economic; c. social and cultural and perceptual (i.e. do people have an accurate cognition of risk). Particular areas of concern relate to housing; the identification of isolated dwellings which would be difficult to evacuate; the vulnerability/resilience of evacuation routes following recent infrastructure improvements; characteristics of the island's transient population; management of livestock under emergency conditions; local leadership roles and educational outreach.