Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems

This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in IFE functions. With the enhanced stability due to the added penalty, not only these IFE methods can be proven to have the optimal convergence rate in the H1-norm provided that the exact solution has sufficient regularity, but also numerical results indicate that their convergence rates in both the H1-norm and the L2-norm do not deteriorate when the mesh becomes finer which is a shortcoming of the classic IFE methods in some situations. Trace inequalities are established for both linear and bilinear IFE functions that are not only critical for the error analysis of these new IFE methods, but also are of a great potential to be useful in error analysis for other IFE methods

Application Analysis of PLC Technology in Electrical Engineering and Its Automation Control

At present, China's science and technology in the continuous development, in this process of the birth of many new technologies, in addition, computer technology is constantly applied in people's production and life, effectively promoted the development o f management and production services in various industries.At present, PLC technology is widely used in electrical engineering and automation control, and has obvious advantages, which can ensure the sustainable development of electrical engineering and automation control. This article mainly analyzes the application of PLC technology in electrical engineering and its automation control

Thermal Performance Analysis of an Underground Closed Chamber with Human Body Heat Sources under Natural Convection

In this article, a combined experimental and numerical study has been performed to investigate the thermal performance of a mine refuge chamber (MRC) under natural convection. In the current study, a 20-hour heating experiment is carried out in a fifty-person MRC laboratory and the heat lamps are utilized to simulate the human heat loss. A new analytical model is proposed to predict the air temperature and validated against the experimental data. Sensitivity analysis is performed to further investigate the effects of the thermal parameters of the rock. Results indicated that: (1) two different air temperature increase stages, rapid and slow increase stages, are observed in the MRC; (2) A new analytical method for predicting the air temperature in MRC under natural convection is proposed, it shows that the air temperature increasing trend becomes slow with the increase of the thermal conductivity, density and specific heat capacity of the rock; (3) the surface heat transfer coefficient on the vertical walls reaches the largest and it increases linearly with air temperature.Peer reviewe

Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions

AbstractWe derive optimal L2 error estimates for semi-discrete finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions. A new projection is introduced and used in the error analysis

Mouse modeling of the MDM2/MDMX−p53 signaling axis

It is evident that p53 activity is critical for tumour prevention and stress response through its transcriptional activation of genes affecting cellular senescence, apoptosis, cellular metabolism, and DNA repair. The regulation of p53 is highly complex, and MDM2 and MDMX are thought to be critical for deciding the fate of p53, both through inhibitory binding and post-translational modification. Many mouse models have been generated to study the regulation of p53 in vivo, and they have altered our interpretations of how p53 is regulated by MDM2 and MDMX. Although MDM2 is absolutely required for p53 regulation, certain functions are dispensable under unstressed conditions, including the ability of MDM2 to degrade p53. MDMX, on the other hand, may only be required in select situations, like embryogenesis. These models have also clarified how cellular stress signals modify the p53-inhibiting activities of MDM2 and MDMX in vivo. It is clear that more work will need to be performed to further understand the contexts for each of these signals and the requirements of various MDM2 and MDMX functions. Here, we will discuss what we have learned from mouse modelling of MDM2 and MDMX and underscore the ways in which these models could inform future therapies