Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Data Descriptor : A European Multi Lake Survey dataset of environmental variables, phytoplankton pigments and cyanotoxins

Under ongoing climate change and increasing anthropogenic activity, which continuously challenge ecosystem resilience, an in-depth understanding of ecological processes is urgently needed. Lakes, as providers of numerous ecosystem services, face multiple stressors that threaten their functioning. Harmful cyanobacterial blooms are a persistent problem resulting from nutrient pollution and climate-change induced stressors, like poor transparency, increased water temperature and enhanced stratification. Consistency in data collection and analysis methods is necessary to achieve fully comparable datasets and for statistical validity, avoiding issues linked to disparate data sources. The European Multi Lake Survey (EMLS) in summer 2015 was an initiative among scientists from 27 countries to collect and analyse lake physical, chemical and biological variables in a fully standardized manner. This database includes in-situ lake variables along with nutrient, pigment and cyanotoxin data of 369 lakes in Europe, which were centrally analysed in dedicated laboratories. Publishing the EMLS methods and dataset might inspire similar initiatives to study across large geographic areas that will contribute to better understanding lake responses in a changing environment.Peer reviewe

A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L? constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first - and second-order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme. Dupire equation ; parameter identification ; optimal control ; optimality conditions ; SQP method ; primal-dual active set strateg

Phase Behavior of Aqueous Na-K-Mg-Ca-CI-NO3 Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na{sup +}, K{sup +}, Mg{sup 2+}, Ca{sup 2+}, Cl{sup -}, and NO{sub 3}{sup -} ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 C. The measurements have been performed using Oak Ridge National Laboratory's (ORNL) previously designed gravimetric isopiestic apparatus, which makes it possible to detect solid phase precipitation. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid-liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor-liquid and solid-liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems

Epstein Barr virus (EBV) encoded small RNAs: targets for detection by in situ hybridisation with oligonucleotide probes.

AIMS: To develop a rapid, sensitive, and specific non-isotopic in situ hybridisation (NISH) procedure for the detection of Epstein-Barr virus in formalin fixed, paraffin wax embedded tissues. METHODS: Two low molecular weight RNAs, designated EBER-1 and EBER-2 (Epstein-Barr encoded RNA), were used: cells latently infected with EBV secrete large amounts of EBERs. The method uses digoxigenin labelled anti-sense oligonucleotides, corresponding to sequences in EBER-1 and EBER-2. RESULTS: The use of these probes, in conjunction with high temperature microwave denaturation, ensured that the technique was considerably more sensitive than other in situ hybridisation techniques for detecting EBV. Furthermore, the hybridisation signal was morphologically distinct in that only the nucleus and not the nucleolus give a positive signal. No cross-hybridisation was observed with cells infected with other lymphotropic herpes viruses. CONCLUSION: The sensitivity, simplicity, and rapidity of this technique make it ideal for diagnostic use, and for studies investigating the role of this virus in neoplastic disease