The Optimal Relaxation Parameter for the SOR Method Applied to the Poisson Equation in Any Space Dimensions

Abstract—The finite difference discretization of the Poisson equation with Dirichlet boundary conditions leads to a large, sparse system of linear equations for the solution values at the interior mesh points. This problem is a popular and useful model problem for performance comparisons of iterative methods for the solution of linear systems. To use the successive overrelaxation (SOR) method in these comparisons, a formula for the optimal value of its relaxation parameter is needed. In standard texts, this value is only available for the case of two space dimensions, even though the model problem is also instructive in higher dimensions. This note extends the derivation of the optimal relaxation parameter to any space dimension and confirms its validity by test calculations in three dimensions

Dynamics modeling and experimental modal analysis of bolt loosening for lightning rod

Lightning rods are effective to prevent lightning damage in power systems. However, under the influence of severe weather conditions, they often face failure problems, mainly manifested as tilt and fracture caused by bolt loosening which can result in significant economic losses. Therefore, it is very meaningful to detect the loosening of the lightning rod. The vibration-based method is an effective method for bolt loosening detection and is suitable for use on large lightning rods. This paper built a finite element model of the lightning rod Flange-Bolt Structure Unit (FBSU) based on the virtual material method, designed an effective acquisition test of the vibration signal under different loosening conditions of the lightning rod FBSU. The experimental results showed that it was effective to establish the dynamic model of the lightning rod FBSU by using the virtual material method. According to the measured vibration signal, the frequency response function was obtained by TIME MDOF method, and the preliminary judgment of bolt loosening can be realized. This study lays the foundation for the precise positioning and the extent of loosening detection of lightning rod bolt loosening, and also provides a guideline for the vibration test design of large bolted structures similar to lightning rods

Mitochondrial Membrane Remodeling

Mitochondria are key regulators of many important cellular processes and their dysfunction has been implicated in a large number of human disorders. Importantly, mitochondrial function is tightly linked to their ultrastructure, which possesses an intricate membrane architecture defining specific submitochondrial compartments. In particular, the mitochondrial inner membrane is highly folded into membrane invaginations that are essential for oxidative phosphorylation. Furthermore, mitochondrial membranes are highly dynamic and undergo constant membrane remodeling during mitochondrial fusion and fission. It has remained enigmatic how these membrane curvatures are generated and maintained, and specific factors involved in these processes are largely unknown. This review focuses on the current understanding of the molecular mechanism of mitochondrial membrane architectural organization and factors critical for mitochondrial morphogenesis, as well as their functional link to human diseases.Peer reviewe

Mitochondrial protein dysfunction in pathogenesis of neurological diseases

Mitochondria are essential organelles for neuronal function and cell survival. Besides the well-known bioenergetics, additional mitochondrial roles in calcium signaling, lipid biogenesis, regulation of reactive oxygen species, and apoptosis are pivotal in diverse cellular processes. The mitochondrial proteome encompasses about 1,500 proteins encoded by both the nuclear DNA and the maternally inherited mitochondrial DNA. Mutations in the nuclear or mitochondrial genome, or combinations of both, can result in mitochondrial protein deficiencies and mitochondrial malfunction. Therefore, mitochondrial quality control by proteins involved in various surveillance mechanisms is critical for neuronal integrity and viability. Abnormal proteins involved in mitochondrial bioenergetics, dynamics, mitophagy, import machinery, ion channels, and mitochondrial DNA maintenance have been linked to the pathogenesis of a number of neurological diseases. The goal of this review is to give an overview of these pathways and to summarize the interconnections between mitochondrial protein dysfunction and neurological diseases.Peer reviewe