Distribution (differential geometry)

About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.

Random matrix theory and higher genus integrability: the quantum chiral Potts model

Abstract: We perform a random matrix theory (RMT) analysis of the quantum fourstate chiral Potts chain for different sizes of the chain up to size L = 8. Ou ra nalysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ‘higher genus integrability’.

Flow Manifold Optimization for a Uniform Velocity Distribution in a Laminated Microreactor with Micro-Pin-Fin Arrays

Abstract: Velocity uniformity in reaction channels has a significant effect on the performance of laminated microreactors with micro-pin-fin arrays (MPFAR) for hydrogen production. The hydrogen production efficiency can be improved by optimizing the structure of flow manifolds. The relationship between the flow manifold structure and the velocity distribution in the reaction channel with MPFAR is established by an equivalent electrical resistance network model validated via simulation. The effects of the flow manifold structure on the velocity distribution are investigated. The results show that the velocity distribution can be improved by increasing the y-direction coordinate Ypi of the flow manifold inlet tube. The flow manifold structure is optimized for better velocity distribution in reaction channels with different MPFAR widths.

Group Testing for Longitudinal Data

Abstract: We consider how to test for group differences of shapes given longitudinal data. In particular, we are interested in differences of longitudinal models of each group’s subjects. We introduce a generalization of principal geodesic analysis to the tangent bundle of a shape space. This allows the estimation of the variance and principal directions of the distribution of trajectories that summarize shape variations within the longitudinal data. Each trajectory is parameterized as a point in the tangent bundle. To study statistical differences in two distributions of trajectories, we generalize the Bhattacharyya distance in Euclidean space to the tangent bundle. This not only allows to take second-order statistics into account, but also serves as our test-statistic during permutation testing. Our method is validated on both synthetic and real data, and the experimental results indicate improved statistical power in identifying group differences. In fact, our study sheds new light on group differences in longitudinal corpus callosum shapes of subjects with dementia versus normal controls.

Multiscale singular value manifold for rotating machinery fault diagnosis

Abstract: Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.

Reduction by λ –symmetries and σ –symmetries: a Frobenius approach

Abstract: Different kinds of reduction for ordinary differential equations, such as λ –symmetry and σ –symmetry reductions, are recovered as particular cases of Frobenius reduction theorem for distribution of vector fields. This general approach provides some hints to tackle the reconstruction problem and to solve it under suitable assumptions on the distribution involved in the reduction process.