The expressions for the 2nd-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities

In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding (TB) modelling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather `technical' and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-centre matrix element is aligned along the z-axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.Comment: 9 pages, no figure

Dilemma: Increase in Human Food Production or Use of Grasslands for Environmental and / or Social Purposes

In the title for this paper we find three major objectives: to feed the world, sustain the environment and provide resources for social purposes, and a dilemma. Even though the word ‘dilemma’ usually implies choice between undesirable alternatives, it is obvious that the alternatives here are not undesirable. Is the dilemma then, that we can only do one at the time, or that the consequences of favouring one over the other can lead to undesirable outcomes? It is my opinion that we are talking about the latter interpretation. It is the foreclosing of options by allowing one objective to dominate that concerns us and that poses a dilemma. How large this dilemma is depends on what we see the possibilities to be of using natural resources, i.e. grasslands in our case, to achieve all three objectives simultaneously

Automatic Generation of Matrix Element Derivatives for Tight Binding Models

Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a computer program they obviate the need to type all the required derivatives of all occuring matrix elements by hand.Comment: 11 pages, 2 figure

Human performance prediction in man-machine systems. Volume 1 - A technical review

Tests and test techniques for human performance prediction in man-machine systems task

Human performance prediction in man-machine systems. Part 2 - The test catalog

Human performance prediction in man machine systems - test catalog table

Enzymatic synthesis of L-pipecolic acid and L-proline

This article does not have an abstract

Magnetic and electronic Co states in layered cobaltate GdBaCo2O5.5-x

We have performed non-resonant x-ray diffraction, resonant soft and hard x-ray magnetic diffraction, soft x-ray absorption and x-ray magnetic circular dichroism measurements to clarify the electronic and magnetic states of the Co3+ ions in GdBaCo2O5.5. Our data are consistent with a 3+ Py Co HS state at the pyramidal sites and a 3+ Oc Co LS state at the octahedral sites. The structural distortion, with a doubling of the a axis (2ap x 2ap x 2ap cell), shows alternating elongations and contractions of the pyramids and indicates that the metal-insulator transition is associated with orbital order in the t2g orbitals of the 3+ Py Co HS state. This distortion corresponds to an alternating ordering of xz and yz orbitals along the a and c axes for the 3+ Py Co . The orbital ordering and pyramidal distortion lead to deformation of the octahedra, but the 3+ Oc Co LS state does not allow an orbital order to occur for the 3+ Oc Co ions. The soft x-ray magnetic diffraction results indicate that the magnetic moments are aligned in the ab plane but are not parallel to the crystallographic a or b axes. The orbital order and the doubling of the magnetic unit cell along the c axis support a non-collinear magnetic structure. The x-ray magnetic circular dichroism data indicate that there is a large orbital magnetic contribution to the total ordered Co moment

Minimum Decision Cost for Quantum Ensembles

For a given ensemble of $N$ independent and identically prepared particles, we calculate the binary decision costs of different strategies for measurement of polarised spin 1/2 particles. The result proves that, for any given values of the prior probabilities and any number of constituent particles, the cost for a combined measurement is always less than or equal to that for any combination of separate measurements upon sub-ensembles. The Bayes cost, which is that associated with the optimal strategy (i.e., a combined measurement) is obtained in a simple closed form.Comment: 11 pages, uses RevTe

Progressive Transient Photon Beams

In this work we introduce a novel algorithm for transient rendering in participating media. Our method is consistent, robust, and is able to generate animations of time-resolved light transport featuring complex caustic light paths in media. We base our method on the observation that the spatial continuity provides an increased coverage of the temporal domain, and generalize photon beams to transient-state. We extend the beam steady-state radiance estimates to include the temporal domain. Then, we develop a progressive version of spatio-temporal density estimations, that converges to the correct solution with finite memory requirements by iteratively averaging several realizations of independent renders with a progressively reduced kernel bandwidth. We derive the optimal convergence rates accounting for space and time kernels, and demonstrate our method against previous consistent transient rendering methods for participating media