Monte Carlo Simulation Modelling

Particle simulation of semiconductor devices is a rather new field which has started to catch the interest of the world's scientific community. It represents a time-continuous solution of Boltzmann's transport equation, or its quantum mechanical equivalent, and the field equation, without encountering the usual numerical problems associated with the direct solution.

This book discusses the general principles of the Monte Carlo method with an emphasis on techniques to decrease simulation time and increase accuracy.

Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise.

This thesis develops a pioneering methodology and a concept for identifying critical loads and load model parameters in large power networks based on their influence on power system stability. The research described in the thesis first develops an automatic load modelling tool (ALMT) that can be used to automatically build load model from actual measured power system data without human intervention and the benefits of the ALMY are explored. Secondly, it develops a pioneering framework based on Morris screening method for ranking power system load model parameters based on their influence on overall power system stability (voltage, frequency, transient and small disturbance stability) considering different load models and loading conditions. Thirdly, a novel probabilistic methodology for determining the accuracy levels of critical load model parameters has been developed.

This book highlights major problems in the statistical analysis of compositions that have been known for over a century, as well as the corresponding solutions that have been put forward by specialists over the past 30 years. The basic assumptions of normality or multi-normality are pointed out and methods to test and achieve them are also covered. The conventional major and trace element geochemistry and modeling equations are discussed, and are followed by a more sophisticated multidimensional approach to data handling.