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

Radiation and Environmental Biophysics: From Single Cells to Small Animals

In this chapter, two of very unique and novel radiation technologies for modern radiobiology studies are reviewed. First of all, it is concentrated on the developments of accelerator-based particle microbeam system, which has been effectively used for studying the puzzle of “radiation-induced bystander effect.” In addition, a recent published single-cell microbeam study, which is aiming to directly measure a cell’s radio-sensitivity combining microbeam system with self-referencing biosensor, is included. Then, toward the study of realistic irradiation scenarios in radiation biology in particular, such as a nuclear attack for homeland security concerns or a potential large-scale radiological event, there would be a major need to ascertain, within a few days, the radiation doses received by tens or hundreds of thousands of individuals. Specifically, biological tests would need to be established to estimate the likelihood of such radiation exposure to result in serious health consequences; tests that would then be applied to decide on the correct treatments that might mitigate the short- and long-term health effects of such radiation exposure. However, because of the complexity and difficulty of conducting tests in such circumstance, innovative irradiation systems and technology are required. So the new developments of small animal irradiation system for evaluating the radiation risk and carrying out animal model radiobiology experiments within the mimicked radiation scenarios are covered in the second half of this chapter

Pharmaceutical enterprises drug quality strategy Moran analysis considering government supervision and new media participation

The improvement of drug quality requires not only the supervision of government, but also the participation of new media. Therefore, this paper considers the impact of government regulation and new media reports on pharmaceutical enterprises, constructs a Moran Process evolutionary game model, and analyzes the evolution trajectory of pharmaceutical enterprises' choice of drug quality improvement strategy and drug cost reduction strategy. We obtain the conditions for the two strategies to achieve evolutionary stability under the dominance of external factors and the dominance of expected returns. To verify the theoretical results, we conduct a numerical simulation by the software MATLAB 2021b. The results show that, first of all, when the government penalty is high, the drug quality improvement strategy tends to become an evolutionary stable solution, increasing the penalty amount will help promote the improvement of drug quality. What's more, when the government penalty is low and the new media influence is low, the drug cost reduction strategy is easier to dominate. The higher the new media influence, the higher the probability that pharmaceutical enterprises choose the drug quality improvement strategy. Thirdly, when the number of pharmaceutical enterprises is lower than a threshold, the drug quality improvement strategy is easier to dominate. Finally, the drug quality improvement strategy is dominant when the quality cost factor is low and the government penalty is high, the drug cost reduction strategy is dominant when the quality cost factor is high and the government penalty is low. Above all, this paper provides countermeasures and suggestions for the drug quality improvement of pharmaceutical enterprises in practice

Superconvergent P1 honeycomb virtual elements and lifted P3 solutions

When solving the Poisson equation on honeycomb hexagonal grids, we show that the $P_1$ virtual element is three-order superconvergent in $H^1$-norm, and two-order superconvergent in $L^2$ and $L^\infty$ norms. We define a local post-process which lifts the superconvergent $P_1$ solution to a $P_3$ solution of the optimal-order approximation. The theory is confirmed by a numerical test

Isolation of AhDHNs from Arachis hypogaea L. and evaluation of AhDHNs expression under exogenous abscisic acid (ABA) and water stress

The peanut (Arachis hypogaea L.) is an important oil and cash crop all over the world. It is mostly planted in arid and semi-arid regions. To determine the mechanism by which dehydrins (DHNs) are regulated by abscisic acid (ABA) in peanuts, three Arachis hypogaea L. dehydrins (AhDHNs) were isolated from peanut plants and sequenced. By blasting the protein sequences of these AhDHNs, AhDHN1 was found belonging to the YnSKn subfamily. AhDHN2 and AhDHN3 were found belonging to the SKn and YnKn types, respectively. 100 μM ABA enhanced AhDHNs expression in peanut leaves. When peanut plants were treated with ABA and then with the ABA synthesis inhibitor sodium tungstate 12 h later, AhDHN expression was suppressed. However, AhDHN2 was inhibited by sodium tungstate at 2 h, though other AhDHNs were not. AhDHNs expressions increased greatly in peanut leaves treated with 30% polyethylene glycol (PEG). Sodium tungstate along with PEG inhibited the expression of AhDHNs. This study found that exogenous and endogenous ABA can both affect the expression of AhDHN independently. The differential expression of AhDHNs to exogenous ABA may be because of differences in the structure of different AhDHNs.Keywords: Arachis hypogaea L. dehydrins (AhDHNs), peanut, abscisic acid (ABA), expression, sodium tungstate, water stres

A new method of reconstructing Galactic three-dimensional structures using ultralong-wavelength radio observations

The free-free absorption of low frequency radio waves by thermal electrons in the warm ionized medium of our Galaxy becomes very significant at $\lesssim 10$ MHz (ultralong-wavelength), and the absorption strength depends on the radio frequency. Upcoming space experiments such as the Discovering Sky at the Longest wavelength (DSL) and Farside Array for Radio Science Investigations of the Dark ages and Exoplanets (FARSIDE) will produce high-resolution multi-frequency sky maps at the ultralong-wavelength, providing a new window to observe the Universe. In this paper we propose that from these ultralong-wavelength multi-frequency maps, the three-dimensional distribution of the Galactic electrons can be reconstructed. This novel and robust reconstruction of the Galactic electron distribution will be a key science case of those space missions. Ultralong-wavelength observations will be a powerful tool for studying the astrophysics relevant to the Galactic electron distribution, for example, the impacts of supernova explosions on electron distribution, and the interaction between interstellar atoms and ionizing photons escaped from the HII regions around massive stars. An animation shows the reconstructed results using {\tt NE2001} model as input test. On ArXiv, it is given in the directory: Ancillary files. In the paper the animation is linked to Fig. 5.Comment: 16 pages, 8 figures (including one animation, on ArXiv see the ancillary files), Accepted for publication in Ap