Plasma flow past a two-dimensional magnetic dipole

Plasma flow past a two dimensional magnetic dipol

Towards a gauge-polyvalent Numerical Relativity code

The gauge polyvalence of a new numerical code is tested, both in harmonic-coordinate simulations (gauge-waves testbed) and in singularity-avoiding coordinates (simple Black-Hole simulations, either with or without shift). The code is built upon an adjusted first-order flux-conservative version of the Z4 formalism and a recently proposed family of robust finite-difference high-resolution algorithms. An outstanding result is the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates (zero shift) without excision.Comment: to appear in Physical Review

Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid--fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition,however, the line tension does depend on the choice of the Gibbs dividing interfaces. We provide equations for the equilibrium contact angles which are form-invariant with respect to notional shifts of dividing interfaces which only change the description of the system. Conceptual consistency requires to introduce additional stiffness constants attributed to the line. We show how these constants transform as a function of the relative displacements of the dividing interfaces. The dependences of the contact angles on lens or drop volumes do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness constants of the line.Comment: 34 pages, 9 figure

Grand potential in thermodynamics of solid bodies and surfaces

Using the chemical potential of a solid in a dissolved state or the corresponding component of the chemical potential tensor at equilibrium with the solution, a new concept of grand thermodynamic potential for solids has been suggested. This allows generalizing the definition of Gibbs' quantity $\sigma$ (surface work often called the solid-fluid interfacial free energy) at a planar surface as an excess grand thermodynamic potential per unit surface area that (1) does not depend on the dividing surface location and (2) is common for fluids and solids.Comment: 6 page

Distribution of periphytic diatoms in the rivers of the Lake Ladoga basin (Northwestern Russia).

Relationships between distribution of periphytic diatoms and environmental variables in 19 rivers of the Lake Ladoga basin (Northwestern Russia) were examined using gradient analysis. On the basis of geology and river water chemistry, the Lake Ladoga basin could be separated into twomain parts, the northern and the southern sub-basin. The rivers in the northern sub-basin are slightly acidic and low in conductivity (mean value 53 mS cm–1); the rivers in the southern sub-basin have neutral to slightly alkaline waters with higher conductivities (mean value 168 mS cm–1). A detrended correspondence analysis (DCA)defined two groups of rivers generally corresponding to the two main parts of the Lake Ladoga basin. Fragilaria capucina var. rumpens, Frustulia saxonica and Tabellaria flocculosa were the typical species for the northern sub-basin, whereas Cocconeis placentula var. euglypta, Ulnaria ulna and Gomphonema parvulum were characteristic species for the southern sub-basin. A canonical correspondence analysis (CCA) identified conductivity, pH, bicarbonate, total phosphorus and water colour as the most important environmental variables related to changes in assemblage structure. Both DCA and CCA ordination showed that conductivity related to geology was the most important variable,while concentration of total phosphorus was the second most important variable.Weighted averaging was used to infer total phosphorus from relative biomass of diatoms. The predictive ability of the inference model was sufficiently strong with r2 = 0.71 and RMSEP = 1.9 mg L–1. These results strongly support the use of a diatom-based inference phosphorus model for indicating eutrophication in the rivers of the Lake Ladoga basin

Efficient implementation of finite volume methods in Numerical Relativity

Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be interpreted as an 'adaptive viscosity' modification of centered finite difference algorithms. These points are fully confirmed by 1D black-hole simulations. In the 3D case, evidence is found that the use of a conformal decomposition is a key ingredient for the robustness of black hole numerical codes.Comment: Revised version, 10 pages, 6 figures. To appear in Phys. Rev.