Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)

Avoidance of common problems on ponds and lakes.

This report looks at the events that results in fish deaths on ponds and lakes, and how to control and avoid them. Problems include de-oxygenation of the water, algal growth, water temperature, excessive fish stocks, excessive weed growth and excessive zooplankton

Problems for the conservation of freshwater fish genetic resources in India and some possible solutions

Many interconnected problems involved for the conservation of freshwater fish genetic resources of India are enumerated. Some possible solutions to the problems are also discussed.

Analytical strategies to solve problems in industrial and official laboratories

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