Graeme Milton                Graeme Milton on mountain top

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Distinguished Professor
Department of Mathematics
University of Utah
155 S 1400 E RM 233
Salt Lake City, Utah 84112


Office: JWB 310
Office hours and Schedule
Office phone: (801)581-6495
Phone messages: (801)581-6851
Fax: (801)581-4148

E-mail: milton@math.utah.edu

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Latest news: the group of Martin Wegener has produced the World's first Hall-effect reversal material, in the paper Experimental Evidence for Sign Reversal of the Hall Coefficient in Three-Dimensional Metamaterials based on a simplification of an interlocking ring design that in the papers Homogenization of the three-dimensional Hall effect and change of sign of the Hall-coefficient ( Hal.archives Version ) and Reversal of the Hall coefficient sign under homogenization , Marc Briane and I proved would reverse the Hall-effect back in 2007. This result (called by Wegener's group a "mind-boggling prediction") overturns the notion, found in many textbooks, that the Hall coefficient tells one the sign of the charge carrier. Inspiration for the geometry came from the chainmail artist Dylon Whyte and from joint work with Vincenzo Nesi. With D. Manceau we proved the reversal is impossible in two-dimensions.

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New book with four chapters coauthored with M.Cassier, O.Mattei, M. Milgrom, and A.Welters

Extending the Theory of Composites to Other Areas of Science

See the review of Pradeep Sharma

Only $80! Available here: Extending the Theory of Composites to Other Areas of Science

A preview of what is inside the book can be found in these slides

One can find on arXiv four chapters: Analyticity of the Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations with Maxence Cassier and Aaron Welters; Bounds for the response of viscoelastic composites under antiplane loadings in the time domain with Ornella Mattei; A rigorous approach to the field recursion method for two-component composites with isotropic phases with Maxence Cassier and Aaron Welters; The response of linear inhomogeneous systems to coupled fields: Bounds and perturbation expansions with Mordehai Milgrom.

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Our work on ideal climbing ropes (also available on ArXiv ) made it to the front cover of climbing magazine . Direct link here . A once in a lifetime achievement!

See also the news release of Lee Siegel

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See the news release by Paul Gabrielsen describing our work on analytic materials, New math tools for new materials , and the accompanying paper also available on ArXiv. This paper also reviews other exact solutions in inhomogeneous media and the subject of metamaterials, providing a proper historical perspective.

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See below some of the many articles related to our work on cloaking. It could be that our 2006 paper On the cloaking effects associated with anomalous localized resonance (submitted in October 2005) was the first to introduce the word "cloaking" into the scientific literature, outside computer science. With 12,815 downloads our paper Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance was the most downloaded paper in 2007 amongst all 12 journals of the Optical Society of America.

  • 'Cloaking device' idea proposed.
  • Now you see it, now you don't: cloaking device is not just sci-fi
  • Close encounters of the cloaking kind: now you see it, now you don't
  • Scientists working to make objects invisible.
  • Scientists set sights on invisibility cloaks.
  • Hiding behind Hermite polynomials.
  • Mathematics of a Novel Type of Active Cloaking.
  • Cloaking Device Concept Moves Beyond Theory.
  • Cloaking Technology May Protect From Natural Disasters.
  • A New Cloaking Method: This is not a 'Star Trek' or 'Harry Potter' Story (w/ Video).
  • New Cloaking Method.
  • Hidden from view.
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    See the articles below related to pentamode materials a new type of material that we devised in the 1995 paper Which Elasticity Tensors are Realizable? also available here

  • NKIT Researchers Succeed in Realizing a New Material Class
  • New material class developed: Pentamode metamaterial
  • Elastic Cloaking Material Makes Objects "Unfeelable"
  • This New Material Makes Things 'Invisible' To Touch!
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    Below is a figure from our landmark paper Optical and dielectric properties of partially resonant composites that marked the discovery of anomalous resonance and ghost sources

    (see also the introduction of a draft paper, doi:10.13140/RG.2.1.1477.5283 ). Figure 3 in paper Optical and dielectric properties of partially resonant composites,

    This later turned out to be the essential mechanism for explaining the so-called superlenses or perfect lenses, for which Sir John Pendry received the Kavli Prize. . Interestingly as shown in the paper Opaque perfect lenses for a point dipole source turned on within a distance d/2 of a "perfect lens" of thickness d and emitting constant power the long-time transmission is zero not one! All the power gets pumped into the anomalously resonant fields. In fact the source does not radiate behind the lens either: this is an example of cloaking due to anomalous resonance, first discovered in the paper On the cloaking effects associated with anomalous localized resonance. The literature and websites abound with explanations and figures that purport to explain superlensing of a point source without mentioning anomalous resonance. This is absurd since it is the anomalous resonance that sets the scale of resolution. Anomalous resonance is more than just a surface plasmon: it has the characteristic feature that the region of anomalous resonance depends on the source location, and that as the loss goes to zero the fields converge to a smooth field outside this region, but blow up to infinity with increasingly rapid oscillations inside the region. Whereas normal resonance is connected with poles of a response function anomalous resonance seems to be connected with essential singularities (see Transport Properties of a Three-Phase Composite Material: The Square Array of Coated Cylinders and Spectral Theory of a Neumann–Poincaré-Type Operator and Analysis of Cloaking Due to Anomalous Localized Resonance ). Anomalous resonance, and the associated cloaking, can also occur in magnetoelectric and thermoelectric systems and elastic systems.

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    Vita updated in September 2016

    40 Most Significant Papers

    Summary of Some Major Accomplishments

    Publications in the last 12 years

    Google citations

    Notable recognitions include a 1988 Sloan Fellowship , an inaugural 1988 Packard Fellowship , the 2003 Ralph E. Kleinman Prize of the Society for Industrial and Applied Mathematics, the 2007 William Prager Medal of the Society for Engineering Science, the 2012 first competitive Rolf Landauer Medal of the International ETOPIM Association, and most recently the 2015 Levi-Civita Prize

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    Translation, thanks to my Russian friends, of Dolin's 1961 Paper, that marks the birth of Transformation Optics

    To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling

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    Talk slides

    Course Information

    Research Interests

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