13 research outputs found
Quantum phases in entropic dynamics
In the Entropic Dynamics framework the dynamics is driven by maximizing
entropy subject to appropriate constraints. In this work we bring Entropic
Dynamics one step closer to full equivalence with quantum theory by identifying
constraints that lead to wave functions that remain single-valued even for
multi-valued phases by recognizing the intimate relation between quantum
phases, gauge symmetry, and charge quantization.Comment: Presented at MaxEnt 2017, the 37th International Workshop on Bayesian
Inference and Maximum Entropy Methods in Science and Engineering (July 9-14,
2017, Jarinu, Brazil
Multiscale Computations for Flow and Transport in Heterogeneous Media
Many problems of fundamental and practical importance have multiple scale solutions. The direct numerical solution of multiple scale problems is difficult to obtain even with modern supercomputers. The major difficulty of direct solutions is due to disparity of scales. From an engineering perspective, it is often sufficient to predict macroscopic properties of the multiple-scale systems, such as the effective conductivity, elastic moduli, permeability, and eddy diffusivity. Therefore, it is desirable to develop a method that captures the small scale effect on the large scales, but does not require resolving all the small scale features. The purpose of this lecture note is to review some recent advances in developing multiscale finite element (finite volume) methods for flow and transport in strongly heterogeneous porous media. Extra effort is made in developing a multiscale computational method that can be potentially used for practical multiscale for problems with a large range of nonseparable scales. Some recent theoretical and computational developments in designing global upscaling methods will be reviewed. The lectures can be roughly divided into four parts. In part 1, we review some homogenization theory for elliptic and hyperbolic equations. This homogenization theory provides a guideline for designing effective multiscale methods. In part 2, we review some recent developments of multiscale finite element (finite volume) methods. We also discuss the issue of upscaling one-phase, two-phase flows through heterogeneous porous media and the use of limited global information in multiscale finite element (volume) methods. In part 4, we will consider multiscale simulations of two-phase flow immiscible flows using a flow-based adaptive coordinate, and introduce a theoretical framework which enables us to perform global upscaling for heterogeneous media with long range connectivity