Browsing by Author "Li, Ming"

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    Full-color fluorescent carbon quantum dots
    (AAAS, 2020) Wang, Liang; Li, Weitao; Yin, Luqiao; Liu, Yijian; Guo, Huazhang; Lai, Jiawei; Han, Yu; Li, Gao; Li, Ming; Zhang, Jianhua; Vajtai, Robert; Ajayan, Pulickel M.; Wu, Minghong
    Quantum dots have innate advantages as the key component of optoelectronic devices. For white light–emitting diodes (WLEDs), the modulation of the spectrum and color of the device often involves various quantum dots of different emission wavelengths. Here, we fabricate a series of carbon quantum dots (CQDs) through a scalable acid reagent engineering strategy. The growing electron-withdrawing groups on the surface of CQDs that originated from acid reagents boost their photoluminescence wavelength red shift and raise their particle sizes, elucidating the quantum size effect. These CQDs emit bright and remarkably stable full-color fluorescence ranging from blue to red light and even white light. Full-color emissive polymer films and all types of high–color rendering index WLEDs are synthesized by mixing multiple kinds of CQDs in appropriate ratios. The universal electron-donating/withdrawing group engineering approach for synthesizing tunable emissive CQDs will facilitate the progress of carbon-based luminescent materials for manufacturing forward-looking films and devices.
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    Harmonic maps, heat flows, currents and singular spaces
    (1995) Li, Ming; Hardt, Robert M.
    This thesis studies some problems in geometry and analysis with techniques developed from non-linear partial differential equations, variational calculus, geometric measure theory and topology. It consists of three independent parts: Chapter I. We study energy minimizing harmonic maps into a complete Riemannian manifold. We prove that the singular set of such a map has Hausdorff dimension at most n-2, where n is the dimension of the domain. We will also give an example of an energy minimizing map from a surface to a surface that has a singular point. Thus the n-2 dimension estimate is optimal, in contrast to the n-3 dimension estimate of Schoen-Uhlenbeck (SU) for compact targets. Chapter II. Here we study a new intersection homology theory for currents on a space X with cone-like singularities. This homology is given by a new mass functional $M\sb{p}$ associated with the perversity index p. For X, it pairs with the intersection homology of Goresky-MacPherson, as well as the $L\sp2$-cohomology of J. Cheeger. We also give a deformation theorem and then prove the existence of $M\sb{p}$-minimizing currents in a given intersection homology class. Chapter III. We construct a weak solution for the heat flow associated with various quasiconvex functionals into homogeneous spaces, in particular, the p-harmonic map heat flow for any $p > 1.$ Our proof generalizes previous works (CHN), (CH2) which treated the case for $p \ge 2$ where the target is a sphere.
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    New algorithms for pathwidth computation
    (2004) Li, Ming; Dean, Nathaniel
    The notions of pathwidth and the closely related treewidth have become more and more important recently. The importance lies not only in theory but also in practice. Theoretically, lots of NP-hard problems become polynomially solvable when restricted in graphs with bounded pathwidth (or treewidth). Practically, pathwidth and treewidth have significant applications in many different fields such as searching games, VLSI design, matrix computation, etc. Computing pathwidth is an NP-complete problem for general graphs, but polynomially solvable for treewidth-bounded graphs. However, there is no known practical algorithm to compute pathwidth for treewidth-bounded graphs. In this dissertation, a new algorithm for computing pathwidth and finding an optimal pathwidth-decomposition for treewidth-bounded graph is presented. This algorithm uses an interval completion technique and the branch-and-bound method to make the pathwidth computation process more efficient, practical, and easy to implement. It can also be easily converted to a parallel algorithm. The data structure for implementing this algorithm is presented, and some computational results are shown. Some heuristic methods to approximate pathwidth for general graphs are also given, especially for series-parallel graphs.