Quantifying mixing in arbitrary fluid domains: a Padé approximation approach

On Padé Approximation of Some Practical Functions

Robust Padé Approximation via SVD

Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors; a Matlab code is provided. The success of this algorithm suggests that...

Quantifying Disorder through Conditional Entropy: An Application to Fluid Mixing

In this paper, we present a method to quantify the extent of disorder in a system by using conditional entropies. Our approach is especially useful when other global, or mean field, measures of disorder fail. The method is equally suited for both continuum and lattice models, and it can be made rigorous for the latter. We apply it to mixing and demixing in multicomponent fluid membranes, and sh...

Function approximation on arbitrary domains using Fourier extension frames

Fourier extension is an approximation scheme in which a function on an arbitary bounded domain is approximated using a classical Fourier series on a bounding box. On the smaller domain the Fourier series exhibits redundancy, and it has the mathematical structure of a frame rather than a basis. It is not trivial to construct approximations in this frame using function evaluations in points that ...

Control of mixing in fluid flow: a maximum entropy approach

In many technological processes a fundamental stage involves the mixing of two or more uids. As a result, optimal mixing protocols is a problem of both fundamental and practical importance. In this paper we formulate a prototypical mixing problem in a control framework, where the objective is to determine the sequence of uid ows that will maximize entropy. By developing the appropriate ergodic-...