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Current reversal and particle separation in Brownian transport

Physical Review Research 2021年第3期3卷 033162-033162页

作者： Hai-Wei Hu Lin Du Liang-Hui Qu Zi-Lu Cao Zi-Chen Deng Ying-Cheng Lai School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China School of Aeronautics Northwestern Polytechnical University Xi'an 710072 China School of Electrical Computer and Energy Engineering Arizona State University Tempe Arizona 85287 USA Department of Physics Arizona State University Tempe Arizona 85287 USA

In transport of micro- or nanosized particles through a confined structure driven by thermal fluctuations and external forcing—a situation that arises commonly in a variety of fields in physical and biological sciences, efficient and controllable separation of particles of different sizes is an important but challenging problem. We study, numerically and analytically, the diffusion dynamics of Brownian particles through the biologically relevant setting of a spatially periodic structure, subject to static and temporally periodic forcing. Molecular dynamical simulations reveal that the mean velocity in general depends sensitively on the particle size. The phenomenon of current reversal is uncovered, where particles larger than or smaller than a critical size diffuse in exactly opposite directions. This striking behavior occurs in a wide range of the forcing amplitude and provides a mechanism to separate the Brownian particles of different sizes. Besides the forcing amplitude, other parametric quantities characterizing the forcing profile, such as the temporal asymmetry, can also be exploited to modulate or control the transport dynamics of particles of different sizes. To gain a theoretical understanding, we exploit the Fick-Jacobs approximation to obtain a one-dimensional description of the diffusion problem, which enables key quantities characterizing the diffusion process, such as the mean velocity, to be predicted. In the regime of weak forcing, a reasonable agreement between theory and numerical results is achieved. Beyond the weakly forcing regime, the diffusion approximation breaks down, causing the theoretical predictions to deviate from the numerical results, into which we provide physical insights. Our findings have potential applications in optimizing transport in microfluidic devices or through biological channels.

关键词： Brownian motion Classical transport Brownian dynamics Langevin equation Stochastic differential equations

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Aluminum Nitride Ring Resonator-Coupled Spin Defects in Hexagonal Boron Nitride for Integrated Quantum Photonics

Aluminum Nitride Ring Resonator-Coupled Spin Defects in Hexa...

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Conference on Lasers and Electro-Optics (CLEO)

作者： Henry C. Roberts Aadil Waseem Scott A. Wicker Hamza Abudayyeh Dong Seob Kim Zhida Liu Steven Randolph Xiaoqin Li Xiuling Li Department of Electrical and Computer Engineering Microelectronics Research Center The University of Texas at Austin Austin TX USA Department of Physics and Center for Complex Quantum Systems Center for Dynamics and Control of Materials and Texas Materials Institute The University of Texas at Austin Austin TX USA Center for Nanophase Materials Sciences Oak Ridge National Laboratory Oak Ridge TN USA

We report a new approach to generate waveguide-coupled emission from deterministically implanted boron vacancy spin defects in hBN using single-crystal AlN-on-sapphire ring resonators. This facilitates the eventual de... 详细信息

ISBN: (纸本)9798350369311

关键词： Boron Waveguide lasers Ring lasers Optical ring resonators Electro-optical waveguides Photonics Aluminum nitride

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On the Notch Sensitivity of Nacre: A Large-Scale Numerical Investigation

SSRN

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SSRN 2024年

作者： Yan, Yi Chen, Xiao Gao, Yuan Deng, Zi-Chen Feng, Xi-Qiao Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China Department of Materials Science and Technology National University of Singapore 117575 Singapore School of Mechanical Engineering Hebei University of Technology Tianjin300401 China Institute of Biomechanics and Medical Engineering AML Department of Engineering Mechanics Tsinghua University Beijing100084 China

The brick–mortar microstructure of nacre endows it with remarkable strength and fracture toughness. Notably, nacre demonstrates robustness against flaws and minor cracks, although its microstructural mechanisms remain elusive. A significant challenge is that the fracture behavior of nacre spans a wide range of length scales, from the mineral platelet less than 1 μm to a damage process zone extending several millimeters. In this study, we employ a multiscale tension-shear-chain (TSC) network model to simulate the large-scale fracture process of nacre's brick-and-mortar structure. In particular, we investigate how the fracture behavior of nacre is influenced by notches of varying sizes. Our large-scale simulations show that with the decrease in the preexisting-crack length, an independent crack initiation gradually replaces the precrack propagation during the fracture of nacre. This observation confirms the critical transition of fracture from the process dominated by fracture toughness to the one by strength, namely from notch sensitivity to insensitivity. Further investigations are carried out on the dependence of this fracture transition on constituent and microstructural parameters, including the interfacial cohesive strength and microstructural randomness. We also propose a scaling law formulating the relationship between these parameters and the notch sensitivity, which provides insight into nacre’s tolerance to flaws at a microscale level. Our findings could guide the design of nacre-inspired artificial materials for fracture prevention. © 2024, The Authors. All rights reserved.

关键词： Fracture toughness

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Combined Extension and Torsion of Hydrogels with Chemo-Mechanical Coupling: Revealing Negative Poynting Effect

SSRN

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SSRN 2024年

作者： Zheng, Chengxiang Hu, Minghui Wu, Tao Pasquale, Ciarletta Li, Qian Deng, Zichen School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi'An710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Xi'An710072 China MOX Department di Mathematica Polytechnic di Milano piazza Leonardo da Vinci 32 Milano20133 Italy China Electronic Product Reliability and Environmental Testing Research Institute China Guangdong Provincial Key Laboratory of Electronic Information Products Reliability Technology China

In this paper, combined extension and torsion of hydrogel subject to a chemo-mechanical coupled loading is described in the framework of continuum mechanics, where the free energy density consists of the elastic, mixing and chemical contributions. A simplified, closed-form and exactly analytical solution to the mechanical response is obtained, which accounts for the coupling effect of external loading, chemical potential and microstructural parameters, such as crosslinking degree, Flory parameter, etc. In particular, the effect of free swelling and microscopic diffusion on deformation of the hydrogel is discussed, reaching some fundamental conclusions. The classic negative Poynting effect is revealed that the cylinder tends to shorten on twisting, and an inhomogeneous deformation, induced by torsion, along the radial direction is demonstrated. Furthermore, the dynamic competition between external loading and solvent environment is revealed and investigated, where the direct connection between internal micro-physical parameters and macroscopic deformation is demonstrated. The theoretical results presented in this paper may provide predictions and guidance for the mechanical analysis and design of hydrogel cylinder subject to extension and torsion in a solvent. © 2024, The Authors. All rights reserved.

关键词： Torsional stress

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Mechanics and Thermodynamics of Multivalent-Binding Induced Shrinkage of Hydrogels

SSRN

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SSRN 2024年

作者： Rajendran, Barathan Chen, Xiao Wang, Xin Wu, Tao Goh, Kek Boon Department of Mechanical Engineering School of Engineering Monash University Malaysia Jalan Lagoon Selatan Bandar Sunway Selangor 47500 Malaysia Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing100084 China School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Xi’an710072 China

Understanding the fundamental mechanism of shrink hydrogel sensors necessitates a complete comprehension of analyte-centered multivalent binding that occurs within their salt-rich microenvironments. However, the mechanics and thermodynamics governing this phenomenon remain insufficiently understood. Here, we derive a theoretical framework that examines the formation of temporary cross–links between the polymeric chains induced by the specific binding interaction between the fixed receptors and the multivalent analytes. As a highlight of our theory, we use statistical thermodynamics to characterize the analyte transport and these multivalent complexations, allowing us to subsequently determine the mechanics of the shrinkage experienced by these hydrogel sensors. Consequently, our theory unveils the valency of the bindings, setting an upper bound for the performance of these shrink sensors;i.e., tuning the receptor density allows us to further modulate their performance. In summary, our theory tightly correlates the microscopic properties of the analyte and hydrogel to the macroscopic shrinking properties of these sensors, hence facilitating a structured design and optimization regime for advanced biomedical applications. © 2024, The Authors. All rights reserved.

关键词： Shrinkage

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CONVERGENCE on A SYMMETRIC ACCELERATED STOCHASTIC ADMM with LARGER STEPSIZES

arXiv

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arXiv 2021年

作者： Bai, Jianchao Han, Deren Sun, Hao Zhang, Hongchao School of Mathematics and Statistics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710129 China LMIB of the Ministry of Education School of Mathematical Sciences Beihang University Beijing100191 China School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710129 China Department of Mathematics Louisiana State University Baton RougeLA70803-4918 United States

In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly nonsmooth convex function and an average function of many smooth convex functions. Our proposed algorithm combines both ideas of ADMM and the techniques of accelerated stochastic gradient methods possibly with variance reduction to solve the smooth subproblem. One main feature of SAS-ADMM is that its dual variable is symmetrically updated after each update of the separated primal variable, which would allow a more flexible and larger convergence region of the dual variable compared with that of standard deterministic or stochastic ADMM. This new stochastic optimization algorithm is shown to have ergodic converge in expectation with O(1/T) convergence rate, where T is the number of outer iterations. Our preliminary experiments indicate the proposed algorithm is very effective for solving separable optimization problems from big-data applications. Finally, 3-block extensions of the algorithm and its variant of an accelerated stochastic augmented Lagrangian method are discussed in the appendix. © 2021, CC BY.

关键词： Convex optimization

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Reverse Aperiodic Resonance in Low- to High-Dimensional Bistable systems: A Complement to Stochastic Resonance Studies in Logic Circuits

arXiv

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arXiv 2024年

作者： Shen, Mengen Yang, Jianhua Sanjuán, Miguel A.F. Chen, Huatao Wang, Zhongqiu Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment School of Mechanical and Electrical Engineering China University of Mining and Technology Jiangsu Xuzhou221116 China Nonlinear Dynamics Chaos and Complex Systems Group Departamento de Física Universidad Rey Juan Carlos Tulipán s/n Móstoles Madrid28933 Spain Division of Dynamics and Control School of Mathematics and Statistics Shandong University of Technology Zibo255000 China School of Computer Science and Technology China University of Mining and Technology Jiangsu Xuzhou221116 China

As circuits continue to miniaturize, noise has become a significant obstacle to performance optimization. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively;however, current implementations are limited to basic logical functions such as OR, AND, NOR, and NAND, restricting broader applications. This paper introduces a three-dimensional (3D) coupling model to investigate the counterintuitive phenomena that arise in nonlinear systems under noise. Compared to the one-dimensional Langevin equation and the two-dimensional Duffing equation, the 3D coupling model features more adjustable parameters and coupling interactions, enhancing the system's dynamic behavior. The study demonstrates that increasing noise intensity triggers reverse aperiodic resonance, leading to signal phase reversal and amplitude amplification. This phenomenon is attributed to the motion of Brownian particles in a bistable potential well. Additionally, reverse aperiodic resonance addresses the lack of logical negation in traditional stochastic resonance systems by introducing noise-driven phase reversal, providing a novel alternative to conventional inverters. © 2024, CC BY.

关键词： Stochastic systems

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Experimental measurement of respiratory particles dispersed by wind instruments and analysis of the associated risk of infection transmission

arXiv

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arXiv 2022年

作者： Schlenczek, Oliver Thiede, Birte Turco, Laura Stieger, Katja Kosub, Jana M. Müller, Rudolf Scheithauer, Simone Bodenschatz, Eberhard Bagheri, Gholamhossein Göttingen37077 Germany Institute for Dynamics of Complex Systems University of Göttingen Göttingen37077 Germany Institute of Infection Control and Infectious Diseases University Medical Center Göttingen37075 Germany Institute for Music and Aerosols Bad Wünnenberg 33181 Germany Laboratory of Atomic and Solid State Physics Sibley School of Mechanical and Aerospace Engineering Cornell University IthacaNY14853 United States

Activities such as singing or playing a wind instrument release respiratory particles into the air that may contain pathogens and thus pose a risk for infection transmission. Here we report measurements of the size distribution, number, and volume concentration of exhaled particles from 31 healthy musicians playing 20 types of wind instruments using aerosol spectrometry and in-line holography in a strictly controlled cleanroom environment. We find that playing wind instruments carries a lower risk of airborne disease transmission than speaking or singing. We attribute this to the fact that the resonators of wind instruments act as filters for particles >10 μm in diameter. We have also measured the size-dependent filtering properties of different types of filters that can be used as instrument masks. Based on these measurements, we calculated the risk of airborne transmission of SARS-CoV-2 in different near- and far-field scenarios with and without masking and/or distancing. We conclude that in all cases where there is a possibility that the musician is infectious, the only safe measure to prevent airborne transmission of the disease is the use of well-fitting and well-filtering masks for the instrument and the susceptible person. © 2022, CC BY.

关键词： Aerosols

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Solving Fokker-Planck equation using deep learning

arXiv

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arXiv 2019年

作者： Xu, Yong Zhang, Hao Li, Yongge Zhou, Kuang Liu, Qi Kurths, Jürgen Department of Applied Mathematics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China Department of Engineering Mechanics Northwestern Polytechnical University Xi’an710072 China Center for Mathematical Sciences School of Mathematics and Statistics HuazhongUniversity of Science and Technology Wuhan430074 China Potsdam Institute for Climate Impact Research Potsdam14412 Germany Department of Physics Humboldt University Berlin Berlin12489 Germany

The probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation. A novel machine learning method is developed to solve the general FP equations based on deep neural networks. The proposed algorithm does not require any interpolation and coordinate transformation, which is different from the traditional numercial methods. The main novelty of this paper is that penalty factors are introduced to overcome the local optimization for the deep learning approach, and the corresponding setting rules are given. Meanwhile, we consider a normalization condition as a supervision condition to effectively avoid that the trial solution is zero. Several numerical examples are presented to illustrate performances of the proposed algorithm, including one- and two-dimensional systems. All the results suggest that the deep learning is quite feasible and effective to calculate the FP equation. Further, influences of the number of hidden layers, the penalty factors, and the optimization algorithm are discussed in detail. These results indicate that the performances of the machine learning technique can be improved through constructing the neural networks appropriately. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

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On the loss of orthogonality in low-synchronization variants of reorthogonalized block classical Gram-Schmidt

arXiv

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arXiv 2024年

作者： Carson, Erin Lund, Kathryn Ma, Yuxin Oktay, Eda Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University Sokolovská 49/83 Praha 8186 75 Czech Republic Computational Mathematics Theme Building R71 STFC Rutherford Appleton Laboratory Harwell Oxford Didcot OxfordshireOX11 0QX United Kingdom Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Department of Mathematics Chemnitz University of Technology Reichenhainer Str. 41 Chemnitz09126 Germany

Interest in communication-avoiding orthogonalization schemes for high-performance computing has been growing recently. This manuscript addresses open questions about the numerical stability of various block classical Gram-Schmidt variants that have been proposed in the past few years. An abstract framework is employed, the flexibility of which allows for new rigorous bounds on the loss of orthogonality in these variants. We first analyze a generalization of (reorthogonalized) block classical Gram-Schmidt and show that a "strong" intrablock orthogonalization routine is only needed for the very first block in order to maintain orthogonality on the level of the unit roundoff. Then, using this variant, which has four synchronization points per block column, we remove the synchronization points one at a time and analyze how each alteration affects the stability of the resulting method. Our analysis shows that the variant requiring only one synchronization per block column cannot be guaranteed to be stable in practice, as stability begins to degrade with the first reduction of synchronization points. Our analysis of block methods also provides new theoretical results for the single-column case. In particular, it is proven that DCGS2 from [Bielich, D. et al. Par. Comput. 112 (2022)] and CGS-2 from [Świrydowicz, K. et al, Num. Lin. Alg. Appl. 28 (2021)] are as stable as Householder QR. Numerical examples from the BlockStab toolbox are included throughout, to help compare variants and illustrate the effects of different choices of intraorthogonalization *** Codes 65-04, 65F25, 65G50, 65Y20 Copyright © 2024, The Authors. All rights reserved.

关键词： Subroutines

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