Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Schemes for the Euler Equations under Gravitational Fields

This paper designs and analyzes positivity-preserving well-balanced (WB) central discontinuous Galerkin (CDG) schemes for the Euler equations with gravity. A distinctive feature of these schemes is that they not only are WB for a general known stationary hydrostatic solution, but also can preserve the positivity of the fluid density and pressure. The standard CDG method does not possess this feature, while directly applying some existing WB techniques to the CDG framework may not accommodate the positivity and keep other important properties at the same time. In order to obtain the WB and positivity-preserving properties simultaneously while also maintaining the conservativeness and stability of the schemes, a novel spatial discretization is devised in the CDG framework based on suitable modifications to the numerical dissipation term and the source term approximation. The modifications are based on a crucial projection operator for the stationary hydrostatic solution, which is proposed for the first time in this work. This novel projection has the same order of accuracy as the standard $L^2$-projection, can be explicitly calculated, and is easy to implement without solving any optimization problems. More importantly, it ensures that the projected stationary solution has the same cell averages on both the primal and dual meshes, which is a key to achieve the desired properties of our schemes. Based on some convex decomposition techniques, rigorous positivity-preserving analyses for the resulting WB CDG schemes are carried out. Several one- and two-dimensional numerical examples are performed to illustrate the desired properties of these schemes, including the high-order accuracy, the WB property, the robustness for simulations involving the low pressure or density, high resolution for the discontinuous solutions and the small perturbations around the equilibrium state.Comment: 57 page

Characteristics of intense winds in mountain area based on field measurement: Focusing on thunderstorm winds

Abstract With the development of mountain areas, more wind-sensitive infrastructures are constructed. In the design of these infrastructures, the wind loading cannot be accurately obtained from the code based on the flat area. Hence, it is of great importance to study the mountain wind characteristics. In this study, the wind field measurement was initiated in a mountain area of western China. After the examination of the measured data, two typical wind events including the thunderstorm wind and thermally developed wind are highlighted. To extract and separate these wind events, an automatic classification method is proposed. The thunderstorm wind is analyzed in order to capture the rapid variation of its maximum wind speed, mean temperature and mean humidity through the boxplot method while the analysis of thermally developed winds relies on the correlation between the mean wind speed and mean temperature. Since the thunderstorm wind is relatively more important for wind engineering, its wind characteristic is focused hereafter and analyzed in detail based on the ultrasonic anemometer data. The characteristics of the thermally developed wind and other wind will be the matter of further studies and investigations. Results show that the characteristics of the thunderstorm wind measured in the mountainous area have no significant difference in comparison with those in the flat area. Due to the limited data, the above results deserve further investigations when more measurements become available

A trehalose biosynthetic enzyme doubles as an osmotic stress sensor to regulate bacterial morphogenesis

The dissacharide trehalose is an important intracellular osmoprotectant and the OtsA/B pathway is the principal pathway for trehalose biosynthesis in a wide range of bacterial species. Scaffolding proteins and other cytoskeletal elements play an essential role in morphogenetic processes in bacteria. Here we describe how OtsA, in addition to its role in trehalose biosynthesis, functions as an osmotic stress sensor to regulate cell morphology in Arthrobacter strain A3. In response to osmotic stress, this and other Arthrobacter species undergo a transition from bacillary to myceloid growth. An otsA null mutant exhibits constitutive myceloid growth. Osmotic stress leads to a depletion of trehalose-6-phosphate, the product of the OtsA enzyme, and experimental depletion of this metabolite also leads to constitutive myceloid growth independent of OtsA function. In vitro analyses indicate that OtsA can self-assemble into protein networks, promoted by trehalose-6-phosphate, a property that is not shared by the equivalent enzyme from E. coli, despite the latter's enzymatic activity when expressed in Arthrobacter. This, and the localization of the protein in non-stressed cells at the mid-cell and poles, indicates that OtsA from Arthrobacter likely functions as a cytoskeletal element regulating cell morphology. Recruiting a biosynthetic enzyme for this morphogenetic function represents an intriguing adaptation in bacteria that can survive in extreme environments

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead