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On the Numerical Solution of Some Eikonal Equations:An Elliptic Solver Approach

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Chinese Annals of Mathematics,Series B 2015年第5期36卷 689-702页

作者： Alexandre CABOUSSAT Roland GLOWINSKI tsorng-whay pan Haute Ecole de Gestion de Genève University of Applied Sciences Department of Mathematics University of Houston

The steady Eikonal equation is a prototypical first-order fully nonlinear equation. A numerical method based on elliptic solvers is presented here to solve two different kinds of steady Eikonal equations and compute solutions, which are maximal and minimal in the variational sense. The approach in this paper relies on a variational argument involving penalty, a biharmonic regularization, and an operator-splitting-based time-discretization scheme for the solution of an associated initial-value problem. This approach allows the decoupling of the nonlinearities and differential *** experiments are performed to validate this approach and investigate its convergence properties from a numerical viewpoint.

关键词： Eikonal equations Maximal solutions Regularization methods Operator slalitting Finite element methods

Numerical Simulation of Red Blood Cell Suspensions Behind a Moving Interface in a Capillary

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Numerical Mathematics(Theory,Methods and Applications) 2014年第4期7卷 499-511页

作者： Shihai Zhao tsorng-whay pan Department of Mathematics University of HoustonHoustonTexas 77204USA

Computational modeling and simulation are presented on the motion of red blood cells behind a moving interface in a *** methodology is based on an immersed boundary method and the skeleton structure of the red blood cell(RBC)membrane is modeled as a spring *** by the nature of the problem,the computational domain is moving with either a designated RBC or an interface in an infinitely long two-dimensional channel with an undisturbed flow field in front of the computational *** tanking-treading and the inclination angle of a cell in a simple shear flow are briefly discussed for the validation *** then present and discuss the results of the motion of red blood cells behind a moving interface in a capillary,which show that the RBCs with higher velocity than the interface speed form a concentrated slug behind the moving interface.

关键词： Red blood cells moving domain immersed boundary method

A DLM/FD/IB Method for Simulating Compound Cell Interacting with Red Blood Cells in a Microchannel

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Chinese Annals of Mathematics,Series B 2018年第3期39卷 535-552页

作者： Shihai ZHAO Yao YU tsorng-whay pan Roland GLOWINSKI Department of Mathematics Dongbei University of Finance and EconomicsDalian 116023LiaoningChina CGG HoustonTX 77072USA Department of Mathematics University of HoustonHoustonTX 77204USA Department of Mathematics Hong Kong Baptist UniversityHong KongChina

In this article, a computational model and related methodologies have been tested for simulating the motion of a malaria infected red blood cell （iRBC for short） in Poiseuille flow at low Reynolds numbers. Besides the deformability of the red blood cell membrane, the migration of a neutrally buoyant particle （used to model the malaria parasite inside the membrane） is another factor to determine the iRBC motion. Typically an iRBC oscillates in a Poiseuille flow due to the competition between these two factors. The interaction of an iRBC and several RBCs in a narrow channel shows that, at lower flow speed, the iRBC can be easily pushed toward the wall and stay there to block the channel. But, at higher flow speed, RBCs and iRBC stay in the central region of the channel since their migrations axe dominated by the motion of the RBC membrane.

关键词： Compound cell Red blood cells Elastic spring model Fictitious domainmethod Immersed boundary method Microchannel

MODELING,SIMULATION,AND OPTIMIZATION OF SURFACE ACOUSTIC WAVE DRIVEN MICROFLUIDIC BIOCHIPS

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Journal of Computational Mathematics 2010年第2期28卷 149-169页

作者： Harbir Antil Roland Glowinski Ronald H.W.Hoppe Christopher Linsenmann tsorng-whay pan Achim Wixforth Department of Mathematics University of Houston Institute of Mathematics University of Augsburg Institute of Physics University of Augsburg

We will be concerned with the mathematical modeling, numerical simulation, and shape optimization of micro fluidic biochips that are used for various biomedical applications. A particular feature is that the fluid flow in the fluidic network on top of the biochips is in- duced by surface acoustic waves generated by interdigital transducers. We are thus faced with a multiphysics problem that will be modeled by coupling the equations of piezoelectricity with the compressible Navier-Stokes equations. Moreover, the fluid flow exhibits a multiscale character that will be taken care of by a homogenization approach. We will discuss and analyze the mathematical models and deal with their numerical solution by space-time discretizations featuring appropriate finite element approximations with respect to hierarchies of simplicial triangulations of the underlying computational domains. Simulation results will be given for the propagation of the surface acoustic waves on top of the piezoelectric substrate and for the induced fluid flow in the microchannels of the fluidic network. The performance of the operational behavior of the biochips can be significantly improved by shape optimization. In particular, for such purposes we present a multilevel interior point method relying on a predictor-corrector strategy with an adaptive choice of the continuation steplength along the barrier path. As a specific example, we will consider the shape optimization of pressure driven capillary barriers between microchannels and reservoirs.

关键词： Microfluidic biochips Mathematical modeling Numerical simulation Shape optimization Multiphysics Multiscale problems.

Engineering atomic Rb-N configurations to tune radical pathways for highly selective photocatalytic H2O2 synthesis coupled with biomass valorization

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Journal of Energy Chemistry 2025年第1期100卷 215-225页

作者： Jiaye Li Shuang pan Yihuang Chen Qiong Liu College of Chemistry and Materials Engineering Wenzhou University Guangdong Provincial Key Laboratory of Chemical Measurement and Emergency Test Technology (China) Institute of Analysis Guangdong Academy of Sciences (China National Analytical CenterGuangzhou)

Photocatalytic oxygen reduction for hydrogen peroxide （H2O2） synthesis presents a green and costeffective production ***,achieving highly selective H2O2synthesis remains challenging,necessitating precise control over free radical reaction pathways and minimizing undesirable oxidative ***,we report for the visible light-driven simultaneous co-photocatalytic reduction of O2to H2O2and oxidation of biomass using the atomic rubidium-nitride modified carbon nitride（CNRb）.The optimized CNRb catalyst demonstrates a record photoreduction rate of 8.01 mM h-1for H2O2generation and photooxidation rate of 3.75 mM h-1for furfuryl alcohol to furoic acid,achieving a remarkable solar-to-chemical conversion （SCC） efficiency of up to 2.27%.Experimental characterizations and DFT calculation disclosed that the introducing atomic Rb–N configurations allows for the high-selective generation of superoxide radicals while suppressing hydroxyl free radical *** is because the Rb–N serves as the new alternative site to perceive a stronger connection position for O2adsorption and reinforce the capability to extract protons,thereby triggering a high selective redox product *** study holds great potential in precisely regulating reactive radical processes at the atomic level,thereby paving the way for efficient synthesis of H2O2coupled with biomass valorization.

关键词： Atomic economy Radical pathway regulation Rubidium atom coordination Biomass valorization

Simulating the dynamics of fluid-cylinder interactions

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第2期6卷 97-109页

作者： pan tsorng-whay GLOWINSKI Roland JOSEPH Daniel D. Department of Mathematics University of Houston Houston Texas 77204-3008 USADepartment of Mathematics University of Houston Houston Texas 77204-3008 USADepartment of Aerospace Engineering and Mechanics University of Minnesota Minnesota MN 55455 USA

We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined with a finite element method and an operator splitting technique. As expected, a settling truncated cylinder turns its broadside perpendicular to the main stream direction and the center of mass moves to the central axis of the channel. In the case of two truncated cylinders, they first move around each other for a while and then stay together in a "T" shape. After the "T" shape has been formed for a long enough time, we found no vortex shedding behind the cylinders. When simulating the fluidization of 60 truncated cylinders, we captured the features of interactions among fluidized cylinders as observed in experiments.

关键词： Particulate flow Finite element methods Operator-splitting methods Fictitious domain methods

The role of axon guidance molecules in the pathogenesis of epilepsy

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Neural Regeneration Research 2025年第5期20卷 1244-1257页

作者： Zheng Liu Chunhua pan Hao Huang Department of Neurology Affiliated Hospital of Zunyi Medical UniversityZunyiGuizhou ProvinceChina

Current treatments for epilepsy can only manage the symptoms of the condition but cannot alter the initial onset or halt the progression of the disease. Consequently, it is crucial to identify drugs that can target novel cellular and molecular mechanisms and mechanisms of action. Increasing evidence suggests that axon guidance molecules play a role in the structural and functional modifications of neural networks and that the dysregulation of these molecules is associated with epilepsy susceptibility. In this review, we discuss the essential role of axon guidance molecules in neuronal activity in patients with epilepsy as well as the impact of these molecules on synaptic plasticity and brain tissue remodeling. Furthermore, we examine the relationship between axon guidance molecules and neuroinflammation, as well as the structural changes in specific brain regions that contribute to the development of epilepsy. Ample evidence indicates that axon guidance molecules, including semaphorins and ephrins, play a fundamental role in guiding axon growth and the establishment of synaptic connections. Deviations in their expression or function can disrupt neuronal connections, ultimately leading to epileptic seizures. The remodeling of neural networks is a significant characteristic of epilepsy, with axon guidance molecules playing a role in the dynamic reorganization of neural circuits. This, in turn, affects synapse formation and elimination. Dysregulation of these molecules can upset the delicate balance between excitation and inhibition within a neural network, thereby increasing the risk of overexcitation and the development of epilepsy. Inflammatory signals can regulate the expression and function of axon guidance molecules, thus influencing axonal growth, axon orientation, and synaptic plasticity. The dysregulation of neuroinflammation can intensify neuronal dysfunction and contribute to the occurrence of epilepsy. This review delves into the mechanisms associated with

关键词： axon guidance drug-resistant epilepsy epilepsy nerve regeneration nervous system diseases neural pathways neuroinflammatory diseases neuronal plasticity neurons synaptic remodeling

Co-production of hydrogen, oxygen, and electricity via an integrated solar-driven system with decoupled water electrolyzer and Na-Zn ion battery

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Journal of Energy Chemistry 2025年第1期100卷 621-627页

作者： Fei Lv Longjie Liu Jiazhe Wu Pengfei Wang Lixia pan Dengwei Jing Yubin Chen International Research Center for Renewable Energy State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University

Combining water electrolysis and rechargeable battery technologies into a single system holds great promise for the co-production of hydrogen （H2） and ***,the design and development of such systems is still in its ***,an integrated hydrogen-oxygen （O2）-electricity co-production system featuring a bipolar membrane-assisted decoupled electrolyzer and a Na-Zn ion battery was established with sodium nickelhexacyanoferrate （NaNiHCF） and Zn2+/Zn as dual redox *** decoupled electrolyzer enables to produce H2and O2in different time and space with almost 100%Faradaic efficiency at 100 mA ***,the charged NaNiHCF and Zn electrodes after the electrolysis processes formed a Na-Zn ion battery,which can generate electricity with an average cell voltage of 1.75 V at 10 m A *** connecting Si photovoltaics with the modular electrochemical device,a well-matched solar driven system was built to convert the intermittent solar energy into hydrogen and electric energy with a solar to hydrogen-electricity efficiency of 16.7%,demonstrating the flexible storage and conversion of renewables.

关键词： Hydrogen Electricity Decoupled water electrolyzer Na-Zn ion battery Solar energy

Sky location of massive black hole binaries in the foreground of Galactic white dwarf binaries

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Science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 97-108页

作者： pan Guo Hong-Bo Jin Cong-Feng Qiao Yue-Liang Wu The International Centre for Theoretical Physics Asia-Pacific University of Chinese Academy of Sciences The School of Physical Sciences University of Chinese Academy of Sciences Institute for Frontiers in Astronomy and Astrophysics Beijing Normal University National Astronomical Observatories Chinese Academy of Sciences Institute of Theoretical Physics Chinese Academy of Sciences

For space-based gravitational wave （GW） detection,the main noise source for massive black hole binaries （MBHBs） is attributed to approximately 10～7double white dwarf binaries in the *** a GW source,the amplitude of the detector response,recorded by a space-based gravitational wave detector,exhibits a modulation effect with a year period when observing the source from various orbital *** the adverse conditions mentioned above,where there is a strong foreground noise and annual modulation in the signals,we employed the wavelet transform and the strong-amplitude relevant orbital position search methods,which allows the weak MBHB sources to achieve higher locating *** detail,for two MBHB sources of lower intensity,the precision of luminosity distance,represented by the ratio ?DL/DLat the 95%confidence level,is enhanced by factors of ～*** angular resolutions,denoted by??s,are enhanced by a factor of ～*** improvements increase the number of detectable GW sources,facilitate multi-messenger follow-up observations and provide constraints on the cosmological constant.

关键词： space-based gravitational wave detection gravitational waves massive black hole binaries