FE analysis of multi-cycle micro-forming through using closed-die upsetting models and forward extrusion models

Research in micro-forming leads to the investigation of the effects of heat generation in the workpiece and temperature changes in the tools during the forming. The results reported in this paper relate to the study of cold micro-forming processes which are usually ignored on its thermal characteristics. Two closed-die upsetting models were used for the simulation of the forming of micro-parts in single forming trial and in mass production (multi-cycle loading), respectively. An elastic-plastic finite element simulation was performed for a single forming trial. The heat transferred to the die, computed from the simulation, was then used as an input for the multi-cycle heat loading analysis in the die. Two materials: silver and low carbon steel, were used as the work material. The results show that the die saturation temperature could still go up to 100 °C for small size dies, which is significant for the forming of micro-parts. Forming errors due to the die-temperature changes were further computed, which forms a basis for developing considerations on the forming-error compensation. Using the same methods and procedures, forming of a micro-pin via forward extrusion was analysed

Automation of The Guiding Center Expansion

We report on the use of the recently-developed Mathematica package \emph{VEST} (Vector Einstein Summation Tools) to automatically derive the guiding center transformation. Our Mathematica code employs a recursive procedure to derive the transformation order-by-order. This procedure has several novel features. (1) It is designed to allow the user to easily explore the guiding center transformation's numerous non-unique forms or representations. (2) The procedure proceeds entirely in cartesian position and velocity coordinates, thereby producing manifestly gyrogauge invariant results; the commonly-used perpendicular unit vector fields $e_1,e_2$ are never even introduced. (3) It is easy to apply in the derivation of higher-order contributions to the guiding center transformation without fear of human error. Our code therefore stands as a useful tool for exploring subtle issues related to the physics of toroidal momentum conservation in tokamaks.Comment: 34 page

A macro-level model for investigating the effect of directional bias on network coverage

Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random walks that are biased towards their current heading. In this paper, we investigate whether or not complementing random walks with directional bias can decrease the expected discovery and coverage times in networks. To do so, we develop a macro-level model of a directionally biased random walk based on Markov chains. By focussing on regular, connected networks, the model allows us to efficiently calculate expected coverage times for different network sizes and biases. Our analysis shows that directional bias can significantly reduce coverage time, but only when the bias is below a certain value which is dependent on the network size.Comment: 15 page