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- Geoffrey R. Grimmett, Zhongyang Li
- Electr. J. Comb.
- 2013

The Fisher transformation acts on cubic graphs by replacing each vertex by a triangle. We explore the action of the Fisher transformation on the set of self-avoiding walks of a cubic graph. Iteration of the transformation yields a sequence of graphs with common critical exponents, and with connective constants converging geometrically to the golden mean. We… (More)

(2)] , (ln[) , , (ln[ 0 y x i y x T TE y x I TE y x f φ + − = ]. 1 [) , () , (2)] , (ln[) , , (ln[ 0 y x i y x T TE y x I TE y x f φ + − = Introduction: Recently radial methods have been investigated as a means to obtain MRI-dependent tissue parameters such as T2 and T1 from a single k-space data set 1,4. These methods permit the fast measurement of tissue… (More)

- Zhongyang Li, Serkan Butun, Koray Aydin
- ACS nano
- 2014

Nanostructured metals have received a significant amount of attention in recent years due to their exciting plasmonic and photonic properties enabling strong field localization, light concentration, and strong absorption and scattering at their resonance frequencies. Resonant plasmonic and metamaterial absorbers are of particular interest for applications… (More)

Bounds are proved for the connective constant µ of an infinite, connected, ∆-regular graph G. The main result is that µ ≥ √ ∆ − 1 if G is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which it is sharp.

- Zhongyang Li, Edgar Palacios, Serkan Butun, Koray Aydin
- Nano letters
- 2015

Ultrathin metasurfaces have recently emerged as promising materials that have huge potential to enable novel, flat optical components, and surface-confined, miniature photonic devices. Metasurfaces offer new degrees of freedom in molding the optical wavefronts by introducing abrupt and drastic changes in the amplitude, phase, and/or polarization of… (More)

The connective constant µ(G) of a graph G is the asymptotic growth rate of the number of self-avoiding walks on G from a given starting vertex. We survey three aspects of the dependence of the connective constant on the underlying graph G. Firstly, when G is cubic, we study the effect on µ(G) of the Fisher transformation (that is, the replacement of… (More)

- Zhongyang Li, Yingfang Ma, +5 authors Weili Zhang
- Optics express
- 2011

Coupling between superradiant and subradiant mode resonators in a metamaterial unit cell plays an important role in observing the sharp transparency peak due to destructive interference between the resonators. This effect is enhanced as the resonators are brought closer to each other in a conventional planar arrangement. We present a novel coupling scheme… (More)

Nanostructured photonic materials enable control and manipulation of light at subwavelength scales and exhibit unique optical functionalities. In particular, plasmonic materials and metamaterials have been widely utilized to achieve spectral transmission, reflection, and absorption filters based on localized or delocalized resonances arising from the… (More)

- Hasan Kocer, Serkan Butun, Zhongyang Li, Koray Aydin
- Scientific reports
- 2015

We show that a triple-layer metal-insulator-metal (MIM) structure has spectrally selective IR absorption, while an ultra-thin metal film has non-selective absorption in the near infrared wavelengths. Both sub-wavelength scale structures were implemented with an ultra-thin 6 nm Cr top layer. MIM structure was demonstrated to have near perfect absorption at λ… (More)

The control of light−material interactions at the nanoscale requires optical elements with sizes much smaller than the wavelength of light. Plasmonic nanostructures and optical metamaterials enable drastic control and manipulation of light at such small scales. However it is quite challenging to further reduce the size of resonant elements using… (More)