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Science China Mathematics 2017年第10期60卷 1733-1752页

作者： LIU ChunGuang SHI ZuoQiang hou thomas yizhao Department of Mathematics Jinan University Yau Mathematical Sciences Center Tsinghua University Department of Computing and Mathematical Sciences California Institute of Technology

Based on the recently developed data-driven time-frequency analysis(hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we first run a local algorithm to get a good approximation of the instantaneous frequency. We then pass this instantaneous frequency to the global algorithm to get an accurate global intrinsic mode function(IMF)and instantaneous frequency. The two-level method alleviates the difficulty of the mode mixing to some *** also present a method to reduce the end effects.

关键词： sparse representation time-frequency analysis matching pursuit two-level method end effects

Sparse time-frequency representation of nonlinear and nonstationary data Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

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Science China Mathematics 2013年第12期56卷 2489-2506页

作者： hou thomas yizhao SHI ZuoQiang Department of Computing and Mathematical Sciences California Institute of Technology Mathematical Sciences Center Tsinghua University

Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data. These methods are inspired by the empirical mode decomposition method （EMD） and the recently developed compressed （compressive） sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a（t） cos（0（t））}, where a is assumed to be less oscillatory than cos（θ（t）） and θ ＇≥ 0. This problem can be formulated as a nonlinear ι0 optimization problem. We have proposed two methods to solve this nonlinear optimization problem. The first one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit. Convergence analysis has been carried out for the nonlinear matching pursuit method. Some numerical experiments are given to demonstrate the effectiveness of the proposed methods.

关键词： sparse representation time-frequency analysis data-driven

Exponentially Convergent Multiscale Finite Element Method

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Communications on Applied Mathematics and Computation 2024年第2期6卷 862-878页

作者： Yifan Chen thomas Y.hou Yixuan Wang Applied and Computational Mathematics CaltechPasadena 91106USA

We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave *** ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis *** most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity *** general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential ***,there are online and offline parts in the function representation provided by the *** online part depends on the right-hand side locally and can be computed in parallel *** offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.

关键词： Multiscale method Exponential convergence Helmholtz's equation Domain decomposition Nonlinear model reduction

Dynamics of self-hybridized exciton–polaritons in 2D halide perovskites

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Light(Science & Applications) 2024年第1期13卷 13-22页

作者： Surendra B.Anantharaman Jason Lynch Christopher E.Stevens Christopher Munley Chentao Li Jin hou Hao Zhang Andrew Torma thomas Darlington Francis Coen Kevin Li Arka Majumdar PJames Schuck Aditya Mohite Hayk Harutyunyan Joshua R.Hendrickson Deep Jariwala Department of Electrical and Systems Engineering University of PennsylvaniaPhiladelphiaPA19104USA KBR Inc. BeavercreekOH45431USA Air Force Research Laboratory Sensors DirectorateWright-Patterson Air Force BaseOH45433USA Department of Physics University of WashingtonSeattleWA98195USA Department of Physics Emory UniversityAtlantaGA30322USA Department of Chemical and Biomolecular Engineering Rice UniversityHoustonTX77005USA Department of Materials Science and Nanoengineering Rice UniversityHoustonTX77005USA Applied Physics Program Smalley‐Curl InstituteRice UniversityHoustonTX77005USA Department of Mechanical Engineering Columbia UniversityNew YorkNY10027USA Department of Electrical and Computer Engineering University of WashingtonSeattleWA98195USA

Excitons,bound electron–hole pairs,in two-dimensional hybrid organic inorganic perovskites(2D HOIPs)are capable of forming hybrid light-matter states known as exciton-polaritons(E–Ps)when the excitonic medium is confined in an optical *** the case of 2D HOIPs,they can self-hybridize into E–Ps at specific thicknesses of the HOIP crystals that form a resonant optical cavity with the ***,the fundamental properties of these self-hybridized E–Ps in 2D HOIPs,including their role in ultrafast energy and/or charge transfer at interfaces,remain ***,we demonstrate that>0.5µm thick 2D HOIP crystals on Au substrates are capable of supporting multiple-orders of self-hybridized E–P *** E–Ps have high Q factors(>100)and modulate the optical dispersion for the crystal to enhance sub-gap absorption and *** varying excitation energy and ultrafast measurements,we also confirm energy transfer from higher energy E–Ps to lower energy E–***,we also demonstrate that E–Ps are capable of charge transport and transfer at *** findings provide new insights into charge and energy transfer in E–Ps opening new opportunities towards their manipulation for polaritonic devices.

关键词： charge polar excitation

Two-grid Method of Expanded Mixed Finite Element Approximations for Parabolic Integro-differential Optimal Control Problems

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Acta Mathematicae Applicatae Sinica 2024年

作者： Yan-ping CHEN Jian-wei Zhou Tian-liang hou School of Science Nanjing University of Posts and Telecommunications School of Mathematics and Statistics Linyi University School of Mathematics and Statistics Beihua University

This paper aims to construct a two-grid scheme of fully discretized expanded mixed finite element methods for optimal control problems governed by parabolic integro-differential equations and discuss a priori error estimates. The state variables and co-state variables are discretized by the lowest order Raviart-thomas mixed finite element, and the control variable is approximated by piecewise constant functions. The time derivative is discretized by the backward Euler method. Firstly, we define some new mixed elliptic projections and prove the corresponding error estimates which play an important role in subsequent convergence ***, we derive a priori error estimates for all variables. Thirdly, we present a two-grid scheme and analyze its convergence. In the two-grid scheme, the solution of the parabolic optimal control problem on a fine grid is reduced to the solution of the parabolic optimal control problem on a much coarser grid and the solution of a decoupled linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy. At last, a numerical example is presented to verify the theoretical results.

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Practice of Barrier Measures against COVID-19 Among Diabetic People Followed at Departmental University Hospital Center Ouémé-Plateau, Benin, in 2021

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Open Journal of Epidemiology 2024年第2期14卷 249-259页

作者： Yèssito Corine Nadège houehanou Armand Wanvoègbe Akouodé thomas hounto Luc Béhanzin Maurice Agonnoudé David houéto Thierry Adoukonou National School of Public Health (ENATSE) University of Parakou Parakou Benin Department of Internal Medicine University Departmental Hospital Ou&#233me-Plateau Porto-Novo Benin

Introduction: COVID-19 is a pandemic disease caused by the coronavirus SARS-COV2 appeared in China in 2019. The aim of the study was to evaluate the practice of barrier measures against COVID-19 and to identify associated factors among diabetics followed at Departmental University Hospital Center Ouémé-Plateau, Benin, in 2021. Methods: This was a cross-sectional study conducted from June to August 2021, including diabetics aged 18 and over, hospitalized or received for medical visits in the department of medicine at the target hospital. Data were collected during an interview with each participant thanks to a questionnaire. “Good practice” was defined as regular practice of at least two of three barrier measures: hand washing, physical distancing and mask-wearing. Results: A total of 110 diabetics were included with a female predominance (55.5%) and a mean age of 57 ± 11.3 years. Among them, 89.1% washed their hands, 41.8% respected physical distancing and 12.7% wore a mask. The proportion of good practice was 47.3%. Only 5 practiced the three barrier measures. Only age group was associated with good practice. Conclusion: The study showed a low proportion of good practice of barrier measures against COVID-19 among diabetic people surveyed. It is important to continue the action for COVID-19 prevention among diabetic people in the targeted hospital and in other hospitals in Benin.

关键词： COVID-19 Barrier Measures Practice Diabetic People Benin

STABLE FOURTH-ORDER STREAM-FUNCTION METHODS FOR INCOMPRESSIBLE FLOWS WITH BOUNDARIES

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Journal of Computational Mathematics 2009年第4期27卷 441-458页

作者： thomas Y.hou BrianR.Wetton Department of Applied and Computational Mathematics California Institute of TechnologyPasadenaCA91125 USA Department of Mathematics University of British ColumbiaVancouverBCV6T 1Z2Canada

Fourth-order stream-function methods are proposed for the time dependent, incom- pressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the noslip condition. Formal error analysis is done for a simple model problem, showing that this extrapolation introduces numerical boundary layers at fifth-order in the stream-function. The fourth-order convergence in velocity of the proposed method for the full problem is shown numerically.

关键词： Incompressible flow Stream-function formulation Finite difference methods.

Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios

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Acta Mathematicae Applicatae Sinica 2002年第1期18卷 63-76页

作者： JφrgAarnes thomas Y.hou Department of Mathematics University of BergenJohs.Brunsgt.125008 BergenNorwayApplied Mathematics217-50CaltechPasadenaCA 91125

In this paper we study some nonoverlapping domain decomposition methods for solving a class of elliptic problems arising from composite materials and flows in porous media which contain many spatial scales. Our preconditioner differs from traditional domain decomposition preconditioners by using a coarse solver which is adaptive to small scale heterogeneous features. While the convergence rate of traditional domain decomposition algorithms using coarse solvers based on linear or polynomial interpolations may deteriorate in the presence of rapid small scale oscillations or high aspect ratios, our preconditioner is applicable to multiple-scale problems without restrictive assumptions and seems to have a convergence rate nearly independent of the aspect ratio within the substructures. A rigorous convergence analysis based on the Schwarz framework is carried out, and we demonstrate the efficiency and robustness of the proposed preconditioner through numerical experiments which include problems with multiple-scale coefficients, as well problems with continuous scales.

关键词： Multiscale elliptic problems Domain decomposition Schwarz methods Porous media

Vegetation classification at the association level under the China Vegetation Classification System: an example of six Stipa steppe formations in China

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Journal of Plant Ecology 2019年第6期12卷 1009-1024页

作者： Changcheng Liu thomas RWentworth Xianguo Qiao Ke Guo Dongjie hou State Key Laboratory of Vegetation and Environmental Change Institute of BotanyChinese Academy of SciencesBeijing 100093China Department of Plant and Microbial Biology North Carolina State UniversityBox 7612RaleighNC 27695-7612USA University of Chinese Academy of Sciences Beijing 100049China

Aims The latest China Vegetation Classification System(China-VCS)for natural/semi-natural vegetation has eight hierarchical levels:Association 详细信息

Aims The latest China Vegetation Classification System(China-VCS)for natural/semi-natural vegetation has eight hierarchical levels:Association

关键词： association China Vegetation Classification System consistent classification section cluster analysis ordination Stipa steppe

Phase behavior of rotationally asymmetric Brownian kites containing 90°internal angles

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Chinese Physics B 2021年第12期30卷 467-472页

作者： Huaqing Liu Yiwu Zong Zhanglin hou thomas G.Mason Kun Zhao Key Laboratory of Systems Bioengineering(Ministry of Education) School of Chemical Engineering and TechnologyTianjin UniversityTianjin 300072China Wenzhou Institute University of Chinese Academy of SciencesWenzhou 325001China Department of Physics and Astronomy University of California-Los AngelesLos AngelesCA 90095USA Department of Chemistry and Biochemistry University of California-Los AngelesLos AngelesCA 90095USA Physics Department Tianjin UniversityTianjin 300072China

Previous Monte Carlo simulations have shown that ordered tetratic phases can emerge in a dense two-dimensional Brownian system of rotationally asymmetric hard kites having 90°internal ***,there have been no experimental investigations yet to compare with these simulation ***,we have fabricated two types of micron-sized kites having internal angles of 72°-90°-108°-90°and 72°-99°-90°-99°,respectively,and we have experimentally studied their phase behavior in two-dimensional *** and in contrast to the Monte Carlo simulations,the experimental results show a phase sequence of isotropic fluid-hexagonal rotator crystal-square crystal as the area fractionφA increases for both types of *** observed square crystal displays not only a quasi-long-range translational order but also(quasi-)long-range 4-fold bond-and molecular-orientational order;these characteristics confirm that tetratic order can emerge even in dense Brownian systems of rotationally asymmetric particles.A model based on local polymorphic configurations(LPCs)is proposed to understand the origin of the square lattice order in these dense kite *** results in this study provide a new route to realize custom-designed self-assembly of colloids by controlling LPCs.

关键词： tetratic order colloidal kites two-dimentional system phase behavior