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Current reversal and particle separation in Brownian transport

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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

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

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SSRN

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

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

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SSRN

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

CONVERGENCE on A SYMMETRIC ACCELERATED STOCHASTIC ADMM with LARGER STEPSIZES

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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

Mechanics and Thermodynamics of Multivalent-Binding Induced Shrinkage of Hydrogels

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SSRN

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

Discernibility of topological variations for networked LTI systems based on observed output trajectories

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arXiv 2022年

作者： Hao, Yuqing Wang, Qingyun Duan, Zhisheng Chen, Guanrong Department of Dynamics and Control Beihang University Beijing100191 China State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science College of Engineering Peking University Beijing100871 China Department of Electronic Engineering City University of Hong Kong Hong Kong

In this paper, the possibility of detecting topological variations by observing output trajectories from networked linear time-invariant systems is investigated, where the network topology can be general, but the nodes have identical higher-dimensional dynamics. A necessary and sufficient condition on the discernibility of topological variations is derived, in terms of the eigenspaces of the original and the modified network configuarations. By taking the specific network structures into consideration, some lower-dimensional conditions are derived, which reveal how the network topologies, sensor locations, node-system dynamics and output, as well as inner interactions altogether affect the discernibility. Furthermore, the output discernibility of topological changes for networked multi-agent systems is revisited, showing that some criterion reported in the literature does not hold. Consequently, a modified necessary and sufficient condition is established. The effectiveness of the results is demonstrated through several examples. © 2022, CC BY-NC-ND.

关键词： Network topology

Evolutionary dynamics on graphs: Efficient method for weak selection

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Physical Review E 2009年第4期79卷 046707-046707页

作者： Feng Fu Long Wang Martin A. Nowak Christoph Hauert Program for Evolutionary Dynamics Harvard University Cambridge Massachusetts 02138 USA Center for Systems and Control State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing 100871 China Department of Organismic and Evolutionary Biology and Department of Mathematics Harvard University Cambridge Massachusetts 02138 USA Department of Mathematics University of British Columbia Vancouver British Columbia Canada V6T 1Z2

Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity—a prominent feature of scale-free networks—generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2×2 games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies.

关键词： dynamics

controllability of kronecker product networks

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arXiv 2019年

A necessary and sufficient condition is derived for the controllability of Kronecker product networks, where the factor networks are general directed graphs. The condition explicitly illustrates how the controllability of the factor networks affects the controllability of the composite network. For the special case where at least one factor network is diagonalizable, an easily-verifiable condition is explicitly expressed. Furthermore, the controllability of higher-dimensional multi-agent systems is revisited, revealing that some controllability criterion reported in the literature does not hold. Consequently, a modified necessary and sufficient condition is established. The effectiveness of the new conditions is demonstrated through several examples. Copyright © 2019, The Authors. All rights reserved.

关键词： Multi agent systems

Solving Fokker-Planck equation using deep learning

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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