In General > s.a. electronic technology; fluids [complex fluids]; optical technology [photonic crystal].
* Idea: Materials whose bulk properties result from unusual arrangements of more elementary matter.
* Examples: Suspensions; Photonic crystals (> see technology); Left-handed structures, with negative μ and ε, made of Cu wires and rings.
* Applications: Proposed invisibility cloak designs for light [@ news sr(06)may]; Acoustic metamaterials, for example to improve medical ultrasound imaging, protect buildings from earthquakes, or obtain a negative index of refraction that might lead to super-resolution lenses and invisibility cloaks for sound waves.
@ General references: Banerjee 11 [r CP(12)]; news pw(12)aug [light-tunable metamaterial].
@ Acoustic metamaterials: Guenneau et al NJP(07) [for sound focusing and confinement]; Liang & Li PRL(12); Haberman & Guild PT(16)jun.
@ Left-handed metamaterials: Smith et al PRL(00) [ε, μ < 0]; news pn(00)mar; news pw(07)mar [for 813-nm infrared light]; > s.a. Refraction.
@ Applications: news nat(13)aug; Smolyaninov PhyB(14)-a1403 [experimental model of a toy, quantum big bang]; news cosmos(19)mar [solving Fredholm integral equations of the second kind]; news pt(19)apr [analog computers made with dielectric structures].

Foams > s.a. fluids [complex fluids]; spacetime foam; multiverse [bubbles].
* Idea: A set of cells (bubbles) that fill a region of space; In soap foams and other fluids, film surfaces have constant mean curvature, whose value is related to the pressure difference across them; Most of them contain mostly air (95%) and some liquid (5%), yet behave like springy solids; Three films meet along lines at 120° angles (Plateau border), and four films meet symmetrically at single points (Maraldi angle); Topological dynamics is described by a small set of moves; > s.a. Aboav-Weaire Law.
* Phase transition: They have a phase transition of sorts as the liquid content varies, with critical point occuring when it is so high (roughly 37% by volume) that the air bubbles are completely spherical and only touch each other at one point, when bubbles cease to be stacked in a semi-solid and begin to float freely inside a flowing liquid.
* Types: Dry foams are made of polyhedral bubbles, while wet foams have rounder bubbles because liquid inflates the bubble faces and vertices.
* Examples: Beer; Galaxy distribution; Soap; Polycrystals, which can be considered as a solid type of foam.
* Applications: Liquid foams can be used to block ultrasound transmission.
@ General references: Klarreich AS(00)mar [soap foam]; Perkowitz ThSc(00)mar; Weaire & Hutzler 01; Banhart & Weaire PT(02)jul [metal foams]; Diebels & Steeb PRS(02) [elastic moduli]; Durian & Raghavan PT(10)may [reasons for stability]; Lespiat et al PRL(11) [similarities between foams and granular matter]; Barmak et al PRB(11) + Kohn Phy(11) [grain boundary character distribution in polycrystals, irreversibility and critical phenomena]; Young 11; news pw(12)feb [Weaire-Phelan foam in the lab]; news pw(13)may [new mathematical model].
@ Related topics: Lovett 94 [soap films]; Hass & Schlafly AS(96) [soap double bubbles]; focus Phy(14) [using foam to block ultrasound transmission]; news cn(14)jul [what makes the perfect beer foam].
> Online resources: see Trinity College Dublin group site.

Granular Matter > s.a. condensed matter [clusters and nanoparticles].
* Idea: A type of metamaterial; Examples are sand, powders, nuts, sugar, coal; Normal ground is about 40% air.
* Properties: Some are shared with solids (they support a load), others with liquids (they pour); Characteristics do not depend on T, because typically E \(\gg\) kT; Some show a type of hysteresis in the opening and closing of microscopic bonds.
* Importance: Mixing, sifting, mining, erosion process; galaxies?
* Description: These materials are inherently dissipative, which renders key concepts of statistical mechanics, such as thermal equilibrium, inapplicable; One proposal (Edwards et al 1989) was to use the volume in the role of the energy, another (Blumenfeld et al 2016) to replace the volume with the connectivity function.
* Jamming transition: A phase transition analogous to the melting of an ordinary solid.
* Brazil nut problem: How do they find their way to the top of a bowl, while smaller nuts filter to the bottom?
@ Books: Mehta ed-94; Ristow 00 [r PT(01)apr]; Duran 00 [r PT(01)apr]; Mehta 07; Aste et al ed-07; Aranson & Tsimring 09 [r PT(10)may]; Andreotti et al 13 [r CP(14)]; Herminghaus 13 [wet granular matter].
@ General references: Jaeger et al PT(96)apr, RMP(96); Jaeger & Nagel AS(97); Arenzon JPA(99) [replica theory]; Kakalios AJP(05)jan [RL]; Aranson & Tsimring RMP(06) [patterns and collective behavior]; Al-Raoush PhyA(07) [microstructure properties]; Lespiat et al PRL(11) [similarities between foams and granular matter]; Boyer et al PRL(11) + de Bruyn Phy(11) [unifying liquid and granular flow]; Porter et al PT(15)nov [granular crystals]; Blumenfeld et al PRL(16) + McNamara Phy(16) [reformulation replacing the volume function with a connectivity function]; Bililign et al PRL(19) [hints of an equation of state].
@ Thermodynamics: news pt(17)jul [powders]; Smart PT(17)sep [grain arrangements in packings].
@ Jamming transition: Coniglio et al PhyA(04); Coulais et al PRL(14) + Daniels Phy(14) [experiments on elasticity of a model soil]; O'Hern Phy(16) [re Gardner phase transition thought to occur between the glass and jamming transitions].
@ Related topics: Umbanhowar et al Nat(96)aug + pn(96)sep [particle-like excitations]; Shinbrot et al Nat(99)feb + pn(99)mar [chaotic mixing]; Falcon et al PRL(99) + pn(99)jul [low gravity clustering]; Hong et al PRL(01) [Brazil nut problem]; Valverde et al CP(03) [Hurst rescaled range analysis]; Coniglio et al PhyA(04) [Edwards' theory]; Tighe & Sperl GM(07)phy/06 [Hagen's 1852 paper on pressure and motion]; Rice MS(12) [in air flow, simulations]; Puckett & Daniels PRL(13) [temperaturelike variables]; Asenjo et al PRL(14) [number of packings, entropy]; Yu et al PRL(20) [experiments in near-zero gravity].
> Related topics: see fluids [complex fluids]; gas [clustering in granular gas]; spheres [sphere packings]; analog gravity models.

Other Types of Metamaterials > s.a. Compressibility [negative]; light [superscattering].
@ General references: Rapoport et al Nat(97)jun + news pn(97)jul [hollow nanoparticle lubricants]; Khaldoun et al Nat(05)sep + pn(05)nov [quicksand]; Bohr & Olsen EPL(11)-a1004 + news sn(10)apr [rope geometry]; Chawla 16 [fibrous materials]; Pratapa et al PRL(19) [origami with tunable mechanical properties].
@ Suspensions: news pw(11)feb [and viscous fluids, gel-like materials]; news sn(12)jul [corn starch thickens when perturbed].
@ Invisibility cloaks: Alù & Engheta PRE(05)cm [transparency with plasmonic coatings]; Leonhardt & Philbin pw(06)sep; Weder JPA(08)-a0704 [theoretical analysis]; Lai et al PRL(09) + Philbin Phy(09); Lai et al PRL(09) [illusion optics]; Guevara et al OE(09)-a0907 [broadband]; news sn(09)dec [charged particles reveal objects]; news pw(10)nov [flexible metamaterial]; news pw(10)nov, Nat(10)dec; Zhang et al PRL(11) [for visible light]; news bbc(12)may; news pw(12)nov [adaptable invisibility cloak]; news pw(13)mar [ultrathin metascreen]; Monticone & Alù PRX(13) [over the entire electromagnetic spectrum, and global scattering]; McCall CP(13); news sci(15)sep; > s.a. optical technology.

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