Sun, 27 Jul 2008 07:19:13 BST CiteULike: norris's Milton http://www.citeulike.org/user/norris/author/Milton CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/norris/article/2815420 <i></i> Minimization variational principles for acoustics, elastodynamics, and electromagnetism in lossy inhomogeneous bodies at fixed frequency Graeme Milton Pierre Seppecher Guy Bouchitt´e 2008-05-20T09:09:45-00:00 no-tag http://www.citeulike.org/user/norris/article/2358145 <i>Journal of Engineering Materials and Technology, Vol. 117, No. 4. (1995), pp. 483-493.</i><br /><br />It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor. Which Elasticity Tensors are Realizable? Graeme Milton Andrej Cherkaev doi:10.1115/1.2804743 Journal of Engineering Materials and Technology, Vol. 117, No. 4. (1995), pp. 483-493. 2008-02-09T16:31:43-00:00 1995 Journal of Engineering Materials and Technology 117 4 483 493 ASME anisotropy metamaterial http://www.citeulike.org/user/norris/article/2332035 <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 462, No. 2074. (October 2006), pp. 3027-3059.</i><br /><br />Regions of anomalous localized resonance, such as occurring near superlenses, are shown to lead to cloaking effects. This occurs when the resonant field generated by a polarizable line or point dipole acts back on the polarizable line or point dipole and effectively cancels the field acting on it from outside sources. Cloaking is proved in the quasistatic limit for finite collections of polarizable line dipoles that all lie within a specific distance from a coated cylinder having a shell permittivity ϵs≈−ϵm≈−ϵc where ϵm is the permittivity of the surrounding matrix, and ϵc is the core permittivity. Cloaking is also shown to extend to the Veselago superlens outside the quasistatic regime: a polarizable line dipole located less than a distance d/2 from the lens, where d is the thickness of the lens, will be cloaked due to the presence of a resonant field in front of the lens. Also a polarizable point dipole near a slab lens will be cloaked in the quasistatic limit. On the cloaking effects associated with anomalous localized resonance Graeme Milton Nicolae-Alexandru Nicorovici doi:10.1098/rspa.2006.1715 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 462, No. 2074. (October 2006), pp. 3027-3059. 2008-02-04T23:29:57-00:00 2006 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462 2074 3027 3059 cloaking metamaterial http://www.citeulike.org/user/norris/article/1748706 <i>New J. Phys., Vol. 9, No. 10. (October 2007), 359.</i> New metamaterials with macroscopic behavior outside that of continuum elastodynamics Graeme Milton doi:10.1088/1367-2630/9/10/359 New J. Phys., Vol. 9, No. 10. (October 2007), 359. 2007-10-10T06:49:41-00:00 2007 New J. Phys. 1367-2630 9 10 359 Institute of Physics Publishing metamaterial http://www.citeulike.org/user/norris/article/2329507 <i>Applied Physics Letters, Vol. 91, No. 11. (2007)</i><br /><br />  Nonmagnetic cloak with minimized scattering Wenshan Cai Uday Chettiar Alexander Kildishev Vladimir Shalaev Graeme Milton Applied Physics Letters, Vol. 91, No. 11. (2007) 2008-02-04T13:30:26-00:00 2007 Applied Physics Letters 91 11 AIP cloaking metamaterial http://www.citeulike.org/user/norris/article/2291081 <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, No. 2079. (March 2007), pp. 855-880.</i><br /><br />In this paper, we suggest a new perspective, where Newton's second law of motion is replaced by a more general law which is a better approximation for describing the motion of seemingly rigid macroscopic bodies. We confirm a finding of Willis that the density of a body at a given frequency of oscillation can be anisotropic. The relation between the force and the acceleration is non-local (but causal) in time. Conversely, for every response function satisfying these properties, and having the appropriate high-frequency limit, there is a model which realizes that response function. In many circumstances, the differences between Newton's second law and the new law are small, but there are circumstances, such as in specially designed composite materials, where the difference is enormous. For bodies which are not seemingly rigid, the continuum equations of elastodynamics govern behaviour and also need to be modified. The modified versions of these equations presented here are a generalization of the equations proposed by Willis to describe elastodynamics in composite materials. It is argued that these new sets of equations may apply to all physical materials, not just composites. The Willis equations govern the behaviour of the average displacement field whereas one set of new equations governs the behaviour of the average-weighted displacement field, where the weighted displacement field may attach zero weight to ‘hidden’ areas in the material where the displacement may be unobservable or not defined. From knowledge of the average-weighted displacement field, one obtains an approximate formula for the ensemble averaged energy density. Two other sets of new equations govern the behaviour when the microstructure has microinertia, i.e. where there are internal spinning masses below the chosen scale of continuum modelling. In the first set, the average displacement field is assumed to be observable, while in the second set an average-weighted displacement field is assumed to be observable. On modifications of Newton's second law and linear continuum elastodynamics Graeme Milton John Willis doi:10.1098/rspa.2006.1795 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, No. 2079. (March 2007), pp. 855-880. 2008-01-25T17:45:07-00:00 2007 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463 2079 855 880 cloaking metamaterial http://www.citeulike.org/user/norris/article/2236337 <i>(7 Dec 2007)</i><br /><br />We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of springs and point masses, both in the three-dimensional case and in the two-dimensional case. Specifically we construct networks which realize any response matrix which is compatible with the known symmetry properties and thermodynamic constraints of response matrices. Due to a mathematical equivalence we also obtain a characterization of the response matrices of discrete acoustic networks. Realizable response matrices of multiterminal electrical, acoustic, and elastodynamic networks at a given frequency Graeme Milton Pierre Seppecher (7 Dec 2007) 2008-01-15T20:54:11-00:00 2007 metamaterial http://www.citeulike.org/user/norris/article/1172262 <i>preprint (2006)</i> On cloaking for elasticity and physical equations with a transformation invariant form G Milton M Briane J Willis preprint (2006) 2007-03-18T22:51:25-00:00 2006 preprint phonons