24,140 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
Driven colloidal suspensions in confinement and density functional theory: Microstructure and wall-slip
We theoretically investigate general properties of driven (sheared) colloidal
suspensions in confinement, based on methods of classical density functional
theory. In the absence of an exact closed (Smoluchowski-) equation for the
one-particle density under shear, we formulate a set of general conditions for
approximations, and show that a simple closure fulfills them. The exact
microscopic stress tensor is identified. Exemplifying the situation near a wall
(oriented parallel to the direction of shear), we note that the microscopic
shear stress is not necessarily homogeneous. Formulating a second equation
additional to the Smoluchowski equation, we achieve a homogeneous shear stress,
and thereby compute the local flow velocity near the wall. This finally leads
to a slip length of the complex fluid at the wall.Comment: 11 pages, 8 figure
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