32 citations · 84 across the 19 of their papers we have counts for
19 papers
Broadband quasistatic passive cloaking: bounds and limitations in the near-field regime
Maxence Cassier, Graeme W. Milton, Aaron Welters
We consider here several aspects of the following challenging question: is it possible to use a passive cloak to make invisible a dielectric inclusion on a finite frequency interva…
Effective Operators in the Theory of Composites: Hilbert Space Framework
Aaron Welters
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to intr…
Kharitonov's Theorem with Degree Drop: a Wronskian Approach
Jason Elsinger, Anthony Stefan, Aaron Welters
In this paper, we present a simplified proof of Kharitonov's Theorem, an important result on determining the Hurwitz stability of interval polynomials. Our new approach to the proo…
Complete characterization of symmetric Kubo-Ando operator means satisfying Molnár's weak associativity
Yury Grabovsky, Graeme W. Milton, Aaron Welters
We provide a complete characterization of a subclass of weakly associative means of positive operators in the class of symmetric Kubo-Ando means. This class, which includes the geo…
Matrix monotonicity and concavity of the principal pivot transform
Kenneth Beard, Aaron Welters
We prove the (generalized) principal pivot transform is matrix monotone, in the sense of the Löwner ordering, under minimal hypotheses. This improves on the recent results of J. E.…
On the Spectral Theory of Linear Differential-Algebraic Equations with Periodic Coefficients
Bader Alshammari, Aaron Welters
In this paper, we consider the spectral theory of linear differential-algebraic equations (DAEs) for periodic DAEs in canonical form, i.e., \begin{equation*} J \frac{df}{dt}+Hf=λWf…
Effective operators and their variational principles for discrete electrical network problems
Kenneth Beard, Anthony Stefan, Robert Viator +1
Using a Hilbert space framework inspired by the methods of orthogonal projections and Hodge decompositions, we study a general class of problems (called Z-problems) that arise in e…
Continuity of the roots of a nonmonic polynomial and applications in multivariate stability theory
Anthony Stefan, Aaron Welters
We study continuity of the roots of nonmonic polynomials as a function of their coefficients using only the most elementary results from an introductory course in real analysis and…
A Short Proof of the Symmetric Determinantal Representation of Polynomials
Anthony Stefan, Aaron Welters
We provide a short proof of the theorem that every real multivariate polynomial has a symmetric determinantal representation, which was first proved in J. W. Helton, S. A. McCullou…
Extension of the Bessmertnyi Realization Theorem for Rational Functions of Several Complex Variables
Anthony Stefan, Aaron Welters
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions o…
A rigorous approach to the field recursion method for two-component composites with isotropic phases
Maxence Cassier, Aaron Welters, Graeme W. Milton
In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we give a rigorous derivation of the field e…
On overdamping phenomena in gyroscopic systems composed of high-loss and lossless components
Alexander Figotin, Aaron Welters
Using a Lagrangian framework, we study overdamping phenomena in gyroscopic systems composed of two components, one of which is highly lossy and the other is lossless. The losses ar…
Analyticity of the Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations
Maxence Cassier, Aaron Welters, Graeme W. Milton
In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we derive the analyticity properties of the…
Pathological scattering by a defect in a slow-light periodic layered medium
Stephen P. Shipman, Aaron T. Welters
Scattering of electromagnetic fields by a defect layer embedded in a slow-light periodically layered ambient medium exhibits phenomena markedly different from typical scattering pr…
Speed-of-light limitations in passive linear media
Aaron Welters, Yehuda Avniel, Steven G. Johnson
We prove that well-known speed of light restrictions on electromagnetic energy velocity can be extended to a new level of generality, encompassing even nonlocal chiral media in per…
Lagrangian Framework for Systems Composed of High-Loss and Lossless Components
Alex Figotin, Aaron Welters
Using a Lagrangian mechanics approach, we construct a framework to study the dissipative properties of systems composed of two components one of which is highly lossy and the other…
Resonant electromagnetic scattering in anisotropic layered media
Stephen P. Shipman, Aaron T. Welters
The resonant excitation of an electromagnetic guided mode of a slab structure by exterior radiation results in anomalous scattering behavior, including sharp energy-transmission an…
Dissipative Properties of Systems Composed of High-Loss and Lossless Components
Alexander Figotin, Aaron Welters
We study here dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. A principal result of our studies is that all the…
On Explicit Recursive Formulas in the Spectral Perturbation Analysis of a Jordan Block
Aaron Welters
Let A(z) be an analytic square matrix and an eigenvalue of A(0) of multiplicity m. Then under the generic condition, the characteristic polynomial of A(z) evaluated at $λ_{…