Direction indices for crystal lattices

Direction indices [uvw] of rational directions in crystal lattices are commonly restricted to integer numbers. This restriction is correct only when primitive unit cells are used. In the case of centred cells, however, direction indices may take fractional values too, because the first lattice node after the origin along a direction can have fractional coordinates in a centred basis. This evidence is very often overlooked and an undue simplification of direction indices to integer values is usually adopted. Although such a simplification does not affect the identification of the direction, it is potentially a source of confusion and mistakes in crystallographic calculations. A parallel is made with the incorrect restriction of Miller indices to relatively prime integers in centred cells.

The Influence of Higher Modes Vibrations on Local Cracks in Node of Lattice Girders Bridges / Wpływ Wyzszych Postaci Drgan Na Zaistnienie Lokalnych Spekan W Wezle Mostu Kratowego

Several previous investigations on failure of a certain type lattice girders railway bridge (on so called BJD line) have not convincingly explained reasons nor have they described potential hazards. This paper attempts to provide an answer, employing static, dynamic, and fatigue analysis of the structure, focusing on previously not analyzed vibrations of elements constituting a lattice node. Detailed models of two types of such nodes - damaged and non- damaged were compared, inside carefully defined limits of applicability.

A Novel Dynamics Lattice Boltzmann Method for Gas Flows

The lattice Boltzmann method (LBM), where discrete velocities are specifically assigned to ensure that a particle leaves one lattice node always resides on another lattice node, has been developed for decades as a powerful numerical tool to solve the Boltzmann equation for gas flows. The efficient implementation of LBM requires that the discrete velocities be isotropic and that the lattice nodes be homogeneous. These requirements restrict the applications of the currently-used LBM schemes to incompressible and isothermal flows. Such restrictions defy the original physics of Boltzmann equation. Much effort has been devoted in the past decades to remove these restrictions, but of less success. In this paper, a novel dynamic lattice Boltzmann method (DLBM) that is free of the incompressible and isothermal restrictions is proposed and developed to simulate gas flows. This is achieved through a coordinate transformation featured with Galilean translation and thermal normalization. The transformation renders the normalized Maxwell equilibrium distribution with directional isotropy and spatial homogeneity for the accurate and efficient implementation of the Gaussian-Hermite quadrature. The transformed Boltzmann equation contains additional terms due to local convection and acceleration. The velocity quadrature points in the new coordinate system are fixed while the correspondent points in the physical space change from time to time and from position to position. By this dynamic quadrature nature in the physical space, we term this new scheme as the dynamic quadrature scheme. The lattice Boltzmann method (LBM) with the dynamic quadrature scheme is named as the dynamic lattice Boltzmann method (DLBM). The transformed Boltzmann equation is then solved in the new coordinate system based on the fixed quadrature points. Validations of the DLBM have been carried with several benchmark problems. Cavity flows problem are used. Excellent agreements are obtained as compared with those obtained from the conventional schemes. Up to date, the DLBM algorithm can run up to Mach number at 0.3 without suffering from numerical instability. The application of the DLBM to the Rayleigh-Bernard thermal instability problem is illustrated, where the onset of 2D vortex rolls and 3D hexagonal cells are well-predicted and are in excellent agreement with the theory. In summary, a novel dynamic lattice Boltzmann method (DLBM) has been proposed with algorithm developed for numerical simulation of gas flows. This new DLBM has been demonstrated to have removed the incompressible and isothermal restrictions encountered by the traditional LBM.

COMPARING ENTROPIC AND MULTIPLE RELAXATION TIMES LATTICE BOLTZMANN METHODS FOR BLOOD FLOW SIMULATIONS

We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries. The Lattice BGK shows predictable stability and is the fastest method in terms of lattice node updates per second. The Multiple Relaxation Times LBM shows erratic stability which depends strongly on the relaxation times set chosen and is slightly slower. The Entropic LBM gives the best stability at the price of fewer lattice node updates per second. A parameter constraint optimization technique is used to determine which is the fastest model given a certain preset accuracy. It is found that the Lattice BGK performs best at most arterial flows, except for the high Reynolds number flow in the aorta, where the Entropic LBM is the fastest method due to its better stability. However we also conclude that the Entropic LBM with velocity/pressure inlet/outlet conditions shows much worse performance.