It is well known that the 4-equation formulation of the two-fluid model is ill-posed. As a result, it is impossible to differentiate between the errors originating from uncertainty in the empirical closure models and ...
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We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity, and surfa...
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We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity, and surface tension. The free boundary in our system develops sharp corners or singularities in certain parameter regimes, and this is an impediment to using existing “single-scale” numerical conformal mapping methods. The difficulty is due to the phenomenon of crowding, i.e., the tendency of nodes in the preimage plane to concentrate near the sharp regions of the boundary, leaving the smooth regions of the boundary poorly resolved. A natural idea is to exploit the scale separation between the sharp regions and smooth regions to solve for each region separately and then stitch the solutions together. However, this is not straightforward as conformal maps are rigid “global” objects, and it is not obvious how one would patch two conformal maps together to obtain a new conformal map. We develop a “multiscale” (i.e., adaptive) conformal mapping method that allows us to carry out this program of stitching conformal maps on different scales together. We successfully apply our method to the electromechanical model problem.
A new dynamic model for aircraft motions is presented. This model can be viewed as intermediate between a point-mass model, in which the body attitude angles are control-like, and a rigid-body model, in which the body...
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A new algorithm, discrete ascent optimal programming, for optimal power flow in distribution systems is presented. The new algorithm will converge to the same solution as the Lagrange multiplier approach, as demonstra...
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A new algorithm, discrete ascent optimal programming, for optimal power flow in distribution systems is presented. The new algorithm will converge to the same solution as the Lagrange multiplier approach, as demonstrated by example. An intuitive discussion illustrating the path of convergence is presented along with a theorem concerning convergence. The algorithm is explained with two DC examples which illustrate both unconstrained and constrained solutions. A switch placement design problem is also solved. Advantages of the new algorithm include its simplicity, ease of incorporating inequality constraints, and the ability to predict the number of steps required for convergence.
Dynamical systems ideas have recently gained increased momentum in the study of turbulent flows. The reason is that dynamical systems could be used to describe low dimensional structures, such as the coherent structur...
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Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely t...
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Machine learning is poised as a very powerful tool that can drastically improve our ability to carry out scientific research. However, many issues need to be addressed before this becomes a reality. This article focus...
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We present new algorithms for computing the H∞ optimal performance for a class of single-input/single-output (SISO) infinite-dimensional systems. The algorithms here only require use of one or two fast Fourier transf...
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In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of ...
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In this paper we study the existence and uniqueness of Nash equilibria (solution to competition-wise problems, with several controls trying to reach possibly different goals) associated to linear partial differential ...
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