5,589 research outputs found
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
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 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
Integer polyhedra for program analysis
Polyhedra are widely used in model checking and abstract interpretation. Polyhedral analysis is effective when the relationships between variables are linear, but suffers from imprecision when it is necessary to take into account the integrality of the represented space. Imprecision also arises when non-linear constraints occur. Moreover, in terms of tractability, even a space defined by linear constraints can become unmanageable owing to the excessive number of inequalities. Thus it is useful to identify those inequalities whose omission has least impact on the represented space. This paper shows how these issues can be addressed in a novel way by growing the integer hull of the space and approximating the number of integral points within a bounded polyhedron
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