A mathematical framework for inverse wave problems in heterogeneous media

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations respresent parametrically the spatially varying mechanical properties of materials. Rocks, manufactured materials, and other wave propagation environments often exhibit spatial heterogeneity in mechanical properties at a wide variety of scales, and coefficient functions representing these properties must mimic this heterogeneity. We show how to choose domains (classes of nonsmooth coefficient functions) and data definitions (traces of weak solutions) so that optimization formulations of inverse wave problems satisfy some of the prerequisites for application of Newton's method and its relatives. These results follow from the properties of a class of abstract first-order evolution systems, of which various physical wave systems appear as concrete instances. Finite speed of propagation for linear waves with bounded, measurable mechanical parameter fields is one of the by-products of this theory

Review of analysis methods for rotating systems with periodic coefficients

Two of the more common procedures for analyzing the stability and forced response of equations with periodic coefficients are reviewed: the use of Floquet methods, and the use of multiblade coordinate and harmonic balance methods. The analysis procedures of these periodic coefficient systems are compared with those of the more familiar constant coefficient systems

Mobile impurities in integrable models

We use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin models we express two phenomenological parameters characterising renormalised inter- actions of mobile impurities with superfluid background: the number of depleted particles, $N$ and the superfluid phase drop $\pi J$ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of two-phonon scattering resulting in vanishing rates of inelastic processes such as viscosity experienced by the mobile impuritiesComment: 25 pages, minor corrections made to the manuscrip

Analysis of large power systems

Computer-oriented power systems analysis procedures in the electric utilities are surveyed. The growth of electric power systems is discussed along with the solution of sparse network equations, power flow, and stability studies

Modeling tensorial conductivity of particle suspension networks

Significant microstructural anisotropy is known to develop during shearing flow of attractive particle suspensions. These suspensions, and their capacity to form conductive networks, play a key role in flow-battery technology, among other applications. Herein, we present and test an analytical model for the tensorial conductivity of attractive particle suspensions. The model utilizes the mean fabric of the network to characterize the structure, and the relationship to the conductivity is inspired by a lattice argument. We test the accuracy of our model against a large number of computer-generated suspension networks, based on multiple in-house generation protocols, giving rise to particle networks that emulate the physical system. The model is shown to adequately capture the tensorial conductivity, both in terms of its invariants and its mean directionality