arXiv subjects

Kevin Chen

Publications and source records attributed to Kevin Chen.

57 records · Page 4Linked to original sources

arXiv2015

The optical applications of 3D sub-wavelength block-copolymer nanostructured functional materials

A method to engineer the refractive indices of functional materials (TiO2, ZnO, SnO2, SiO2), by nanostructuring in the deep sub-wavelength regime (<20nm), is presented. Block-copolymer templating combined with a wet processing route is used to realize 3D functional nanostructures with continuously adjustable refractive indices from 1.17 to 2.2. Wet processing accessed refractive index engineering can be applied to address a variety of realizability concerns in attaining design specified refractive index values and refractive index gradients in 1D, 2D, and 3D that arise as the results of optical design techniques such as thin film optimization methods, transformation optics and conformal mapping. Refractive index optimized multi-layer anti-reflection coatings on crystalline silicon, which reduce light reflections from 38% down to ~3% with a wide angular span, are demonstrated with the developed wet processing route. A high temperature oxygen free fiber optic hydrogen sensor realized by accessing nano-engineering enabled refractive indices is also presented. The functionality of the sensor is characterized with a fiber Bragg grating, transmission based interrogation, and optical frequency domain reflectometry. The latter demonstrates the potential of the developed sensor for the detection of chemical gradients for applications such as in high temperature hydrogen driven fuel cells.

cond-mat.mes-hall↗

arXiv2011

Non-equilibrium allele frequency spectra via spectral methods

A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amounts of data from many related populations require high-performance algorithms to determine the likelihood of different demographic scenarios that could have shaped the observed neutral single nucleotide polymorphism (SNP) allele frequency spectrum. In many areas of applied mathematics, Fourier Transforms and Spectral Methods are firmly established tools to analyze spectra of signals and model their dynamics as solutions of certain Partial Differential Equations (PDEs). When spectral methods are applicable, they have excellent error properties and are the fastest possible in high dimension. In this paper we present an explicit numerical solution, using spectral methods, to the forward Kolmogorov equations for a Wright-Fisher process with migration of K populations, influx of mutations, and multiple population splitting events.

q-bio.PE↗

arXiv2009

On the Chudnovsky-Seymour-Sullivan Conjecture on Cycles in Triangle-free Digraphs

For a simple digraph $G$ without directed triangles or digons, let $β(G)$ be the size of the smallest subset $X \subseteq E(G)$ such that $G\setminus X$ has no directed cycles, and let $γ(G)$ be the number of unordered pairs of nonadjacent vertices in $G$. In 2008, Chudnovsky, Seymour, and Sullivan showed that $β(G) \le γ(G)$, and conjectured that $β(G) \le γ(G)/2$. Recently, Dunkum, Hamburger, and Pór proved that $β(G) \le 0.88 γ(G)$. In this note, we prove that $β(G) \le 0.8616 γ(G)$.

math.CO↗