Search results for "Random walk"

showing 2 items of 132 documents

Random Walk and Diffusion

2014

The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.

symbols.namesakePartial differential equationHeterogeneous random walk in one dimensionDiffusion equationFourier transformLaplace transformDifferential equationMathematical analysissymbolsEinsteinRandom walkMathematics
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A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

2014

WOS:000346854900026 (Nº de Acesso Web of Science) We present an algorithm for two- and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algo…

ta113Parallelizable manifoldSEM image segmentationComputer scienceMatemáticasApplied MathematicsGeneral MathematicsFast marchingCapacitance extractionIntegrated circuitResolution (logic)CapacitanceImage (mathematics)law.inventionNon-Manhattan IClawFloating random walkPreprocessorRepresentation (mathematics)AlgorithmFast marching method
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