57 resultados para Integrals, Generalized.
em CentAUR: Central Archive University of Reading - UK
Resumo:
A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.
Resumo:
We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost.
Resumo:
Background: Functional magnetic resonance imaging (fMRI) holds promise as a noninvasive means of identifying neural responses that can be used to predict treatment response before beginning a drug trial. Imaging paradigms employing facial expressions as presented stimuli have been shown to activate the amygdala and anterior cingulate cortex (ACC). Here, we sought to determine whether pretreatment amygdala and rostral ACC (rACC) reactivity to facial expressions could predict treatment outcomes in patients with generalized anxiety disorder (GAD).Methods: Fifteen subjects (12 female subjects) with GAD participated in an open-label venlafaxine treatment trial. Functional magnetic resonance imaging responses to facial expressions of emotion collected before subjects began treatment were compared with changes in anxiety following 8 weeks of venlafaxine administration. In addition, the magnitude of fMRI responses of subjects with GAD were compared with that of 15 control subjects (12 female subjects) who did not have GAD and did not receive venlafaxine treatment.Results The magnitude of treatment response was predicted by greater pretreatment reactivity to fearful faces in rACC and lesser reactivity in the amygdala. These individual differences in pretreatment rACC and amygdala reactivity within the GAD group were observed despite the fact that 1) the overall magnitude of pretreatment rACC and amygdala reactivity did not differ between subjects with GAD and control subjects and 2) there was no main effect of treatment on rACC-amygdala reactivity in the GAD group.Conclusions: These findings show that this pattern of rACC-amygdala responsivity could prove useful as a predictor of venlafaxine treatment response in patients with GAD.
Resumo:
This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.