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GRFP/NSF and Beyond Pizza Seminar Baylor Mathematics pizza margherita: from subwavelength metaoptics to intracellular signaling pathways @academiabarilla.com qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 1 / 14 a background search for new energy motivations: Pipelines and fossil energy exhaustion... ) A new search web pictures qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 2 / 14 subwavelength metamaterials energy transform lights through subwavelength holes: Theory: Wave propagation control at the deep subwavelength scale in metamaterials, by F. Lemoult et. al., Nature (physics), 2013 Applications: Areas in the energy engineering, also electromagnetic radiation, seismology, and acoustics Designs of metamaterials that mold electromagnetics web pictures Researcher taps high-performance computers to design metamaterials that mold electromagnetics. qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 3 / 14 subwavelength metamaterials math models mathematical models @JMD Professor John Davis and his PDE book ) pg. 170: qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 4 / 14 subwavelength metamaterials partial differential equations Maxwell’s equations: James Clerk Maxwell (1831–1879) qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 5 / 14 subwavelength metamaterials partial differential equations paraxial Helmholtz equation: For a monochromatic beam, consider the complex envelope E of the complex wavefunction in the paraxial sense: 2iκEz = Exx + Eyy + Ezz ; (x; y) 2 D2; z > z0; where D2 is the transverse domain, z is the beam propagation direction, and κ = 2πν=c > 102 is the wave number of the light. Hermann Ludwig Ferdinand von Helmholtz (1821–1894) qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 6 / 14 subwavelength metamaterials partial differential equations Ritz and his criticism: Walther Ritz (1878 –1909) qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 7 / 14 subwavelength metamaterials Helmholtz in polar system our concern: 1 E = β E + E + E ; 0 < r ≤ R; z ≥ 0: z rr r r zz i) Paraxial Models; ii) Kerr Effects qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 8 / 14 subwavelength metamaterials multiscale configurations a “possible” resolution: Micro and Macro Regions qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 9 / 14 subwavelength metamaterials multiscale configurations multiscale scheme: Due to the singularity as r ! 0+; we replace the polar PDE by coupled partial differential equations in connected transverse domains. Definition (a decomposed system) Ez = β (2Err + Ezz + g(E)) ; 0 ≤ r < ~r; 1 E = β E + E + E ; ~r ≤ r ≤ R: z rr r r zz qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 10 / 14 subwavelength metamaterials multiscale configurations a multiscale infrastructure: Micro and Macro Grids qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 11 / 14 cancer treatments a cell biology model and its solution hes1 and p53-mdm2 intracellular signaling pathways: @q α n = κ r2 + q µ ; 2D ; qn qn h qqn x n @t 1 + (pn=p) @q c = κ r2q − µ q ; x 2D ; @t qc c q c c @p c = κ r2p + H (x)α q − µ p ; x 2D ; @t pc c 1 p c p c c @p n = κ r2p − µ p ; x 2D : @t pn n p n n qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 12 / 14 cancer treatments multiscale configurations high resolution multiscale computations: Can we do the computing and numerical analysis? qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 13 / 14 cancer treatments cell model computing and analysis what else to expect? Challenges are waiting! qin sheng (tim) pizza seminar @ mathematics Feb. 28, 2018 14 / 14.
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