Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory

The multiphase Whitham modulation equations with $N$ phases have $2N$ characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for coalescence, where two characteristics change from hyperbolic to elliptic via collision. Firstly, a linear theory develops the structure of colliding characteristics involving the topological sign of characteristics and multiple Jordan chains, and secondly a nonlinear modulation theory is developed for transitions. The nonlinear theory shows that coalescing characteristics morph the Whitham equations into an asymptotically valid geometric form of the two-way Boussinesq equation. That is, coalescing characteristics generate dispersion, nonlinearity and complex wave fields. For illustration, the theory is applied to coalescing characteristics associated with the modulation of two-phase travelling-wave solutions of coupled nonlinear Schr\"odinger equations, highlighting how collisions can be identified and the relevant dispersive dynamics constructed.Comment: 40 pages, 2 figure

The Modulation of Multiple Phases Leading to the Modified KdV Equation

This paper seeks to derive the modified KdV (mKdV) equation using a novel approach from systems generated from abstract Lagrangians that possess a two-parameter symmetry group. The method to do uses a modified modulation approach, which results in the mKdV emerging with coefficients related to the conservation laws possessed by the original Lagrangian system. Alongside this, an adaptation of the method of Kuramoto is developed, providing a simpler mechanism to determine the coefficients of the nonlinear term. The theory is illustrated using two examples of physical interest, one in stratified hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to illustrate how the criterion for the mKdV equation to emerge may be assessed and its coefficients generated.Comment: 35 pages, 5 figure

Projective equivalence of ideals in Noetherian integral domains

Let I be a nonzero proper ideal in a Noetherian integral domain R. In this paper we establish the existence of a finite separable integral extension domain A of R and a positive integer m such that all the Rees integers of IA are equal to m. Moreover, if R has altitude one, then all the Rees integers of J = Rad(IA) are equal to one and the ideals J^m and IA have the same integral closure. Thus Rad(IA) = J is a projectively full radical ideal that is projectively equivalent to IA. In particular, if R is Dedekind, then there exists a Dedekind domain A having the following properties: (i) A is a finite separable integral extension of R; and (ii) there exists a radical ideal J of A and a positive integer m such that IA = J^m.Comment: 20 page

Magnetohydrodynamic Simulation of Electromagnetic Pump in TC-1

The pilot molten lead-bismuth target circuit (TC-1) in university of Nevada Las Vegas (UNLV) was designed for beam power of 1 MW accelerator driven system (ADS). The TC-1 is a liquid lead-bismuth eutectic (LBE) circulation loop. Circulation of the liquid alloy is driven by an annular linear induction pump (ALIP). Experimental measurements of system parameters have yielded a surprisingly low pump efficiency of less than 1%. A numerical study of the pump efficiency is being conducted to determine which operational parameters are responsible for this low efficiency and to give insight into future EM pump design. The numerical study will first entail calculating the EM phenomena such as the induced current distribution, magnetic field and electromagnetic body forces using both analytic and numerical methods. These calculated EM forces will be incorporated into fluid flow calculations using a commercial code such as FEMLab and/or Fluent. Parametric studies of the EM and fluid flow phenomena in the pump will be carried out

Energy Disaggregation via Adaptive Filtering

The energy disaggregation problem is recovering device level power consumption signals from the aggregate power consumption signal for a building. We show in this paper how the disaggregation problem can be reformulated as an adaptive filtering problem. This gives both a novel disaggregation algorithm and a better theoretical understanding for disaggregation. In particular, we show how the disaggregation problem can be solved online using a filter bank and discuss its optimality.Comment: Submitted to 51st Annual Allerton Conference on Communication, Control, and Computin

Blind Identification via Lifting

Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.Comment: Submitted to the IFAC World Congress 2014. arXiv admin note: text overlap with arXiv:1303.671