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Stable memory with unstable synapses

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arXiv 2018年

作者： Susman, Lee Brenner, Naama Barak, Omri Interdisciplinary Program in Applied Mathematics Technion Israel Institute of Technology Haifa Israel Network Biology Research Laboratories Technion Israel Institute of Technology Haifa Israel Faculty of Chemical Engineering Technion Israel Institute of Technology Haifa Israel Rappaport Faculty of Medicine Technion Israel Institute of Technology Haifa Israel

What is the physiological basis of long-term memory? The prevailing view in neuroscience attributes changes in synaptic efficacy to memory acquisition. This view implies that stable memories correspond to stable connectivity patterns. However, an increasing body of experimental evidence points to significant, activity-independent dynamics in synaptic strengths. Motivated by these observations, we explore the possibility of memory storage within a global component of network connectivity, while individual connections fluctuate. We find a simple and general principle, stemming from stability arguments, that links eigenvalues in the complex plane to memories. Specifically, imaginary-coded memories are more resilient to noise and homeostatic plasticity than their real-coded counterparts. Memory representations are stored as time-varying attractors in neural state-space and support associative retrieval of learned information. Our results suggest a link between the properties of learning rules and those of network-level memory representations, and point at measurable signatures to be sought in experimental data. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

FIP-GNN: Graph neural networks for scalable prediction of grain-level fatigue indicator parameters

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arXiv 2024年

作者： Sim, Gyu-Jang Lee, Myoung-Gyu Latypov, Marat I. Department of Materials Science and Engineering & RIAM Seoul National University 1 Gwanak-ro Gwanak-gu Seoul08826 Korea Republic of Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

High-cycle fatigue is a critical performance metric of structural alloys for many applications. The high cost, time, and labor involved in experimental fatigue testing call for efficient and accurate computer models of fatigue life. We present FIP-GNN – a graph neural network for polycrystals that (i) predicts fatigue indicator parameters as grain-level inelastic responses to cyclic loading quantifying the local driving force for crack initiation and (ii) generalizes these predictions to large microstructure volume elements with grain populations well beyond those used in training. These advances can make significant contributions to statistically rigorous and computationally efficient modeling of high-cycle fatigue – a long-standing challenge in the field. © 2024, CC BY.

关键词： High-cycle fatigue

A First-Principles and Calphad-Assisted Phase-Field Model for Microstructure Evolution: Application to Mo-V Binary Alloy Systems

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SSRN

SSRN 2023年

作者： Thakur, Abhishek Kumar Kovacevic, Sasa Manga, Venkateswara Rao Deymier, Pierre Alix Muralidharan, Krishna Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Department of Civil and Environmental Engineering Imperial College London LondonSW7 2AZ United Kingdom Lunar and Planetary Laboratory University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics India

A multiscale computational framework combining the first-principles calculations and the CALPHAD approach with the phase-field method is presented to simulate the microstructure evolution in multicomponent steel alloys. We demonstrate the potential of the framework by predicting the microstructural evolution in elastically periodic arrays of the Mo-V binary sub-system. The framework utilizes the first-principles calculations using special quasi-random structures. Hitherto unavailable thermodynamic and material properties of the alloy are obtained by employing the first-principles calculations and the CALPHAD approach and fed into the phase-field model to predict the microstructure evolution at different temperatures within the miscibility gap region. In addition to the temperature and cooling rates, the model incorporates the role of mechanical fields in decomposition kinetics in the Mo-V binary alloy system. Regimes for temperatures and cooling rates at which spinodal decomposition occurs are identified. Applying external loading leads to directional phase separation in the Mo-V binary system. The elastic inhomogeneity in terms of material properties between the two phases initiates the directional alignment while eigenstrains and applied external loading control the degree of alignment. The framework developed is general and extendable to higher multicomponent sub-systems in steel alloys. © 2023, The Authors. All rights reserved.

关键词： Temperature

Aedes-AI: Neural network models of mosquito abundance

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arXiv 2021年

作者： Kinney, Adrienne C. Current, Sean Lega, Joceline Interdisciplinary Program in Applied Mathematics The University of Arizona TucsonAZ85721 United States Department of Mathematics The University of Arizona TucsonAZ85721 United States Department of Epidemiology and Biostatistics The University of Arizona TucsonAZ85721 United States BIO5 Institute The University of Arizona TucsonAZ85721 United States Department of Computer Science and Engineering The Ohio State University ColumbusOH43202 United States

We present artificial neural networks as a feasible replacement for a mechanistic model of mosquito abundance. We develop a feed-forward neural network, a long short-term memory recurrent neural network, and a gated recurrent unit network. We evaluate the networks in their ability to replicate the spatiotemporal features of mosquito populations predicted by the mechanistic model, and discuss how augmenting the training data with time series that emphasize specific dynamical behaviors affects model performance. We conclude with an outlook on how such equation-free models may facilitate vector control or the estimation of disease risk at arbitrary spatial scales. © 2021, CC BY-NC-ND.

关键词： Feedforward neural networks

An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure

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arXiv 2022年

作者： Kim, Keon Ho Bhalla, Amneet P.S. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering San Diego State University San DiegoCA United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary methods. The major difference between our approach and conventional immersed boundary methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well-characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations. © 2022, CC BY-SA.

关键词： Continuum mechanics

An Immersed Peridynamics Model of Fluid-Structure Interaction Accounting for Material Damage and Failure

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SSRN

SSRN 2022年

作者： Kim, Keon Ho Bhalla, Amneet Pal Singh Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering San Diego State University San DiegoCA United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary (IB) methods. The major difference between our approach and conventional IB methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations. © 2022, The Authors. All rights reserved.

关键词： Fluid structure interaction

Atomistic Characterization of Impact Bonding in Cold Spray Deposition of Copper

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SSRN

SSRN 2022年

作者： Nikravesh, Y. Latypov, Marat I. Frantziskonis, G. Muralidharan, Krishna Department of Civil and Architectural Engineering and Mechanics University of Arizona TucsonAZ85721 United States Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Lunar and Planetary Laboratory University of Arizona TucsonAZ85721 United States

Using classical molecular dynamics, we investigate the cold-spray additive manufacturing process involving copper particles impacting a copper substrate. Specifically, we develop fundamental insights into the interplay between particle size, particle velocity and ensuing penetration depth of the particle and the effective adhesion strength that binds the impinging particle with the substrate. Equally importantly, we also establish a quantitative constitutive relationship that governs the process variables (i.e., particle size, particle velocity), the resulting particle penetration depth and impact bonding energy. By examining the formation and evolution of adiabatic shear bands and dislocation densities within the particle and the substrate, as well as by examining the structural evolution of the impinging particle as a function of process variables in conjunction with observations of material jetting, we shed light on the deformation mechanisms that govern the cold spray process, and provide a fundamental basis for understanding the presence of a critical velocity that must be overcome in order to promote strong adhesion of the particle with the substrate. Further, by developing a comprehensive constitutive relationship that relates the process variables to the resulting penetration of the particle and the extent of impact bonding, we enable the ability to upscale information derived at the nanometric scales to experimental scales. This work thus serves as a steppingstone in not only answering fundamental interrelationships that govern the cold spray process, but also in the quest for developing comprehensive integrated computational materials engineering models for optimizing the process conditions underlying the cold spray process. © 2022, The Authors. All rights reserved.

关键词： Molecular dynamics

Benchmarking the Immersed Boundary Method for Viscoelastic Flows

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arXiv 2023年

作者： Gruninger, Cole Barrett, Aaron Fang, Fuhui Forest, M. Gregory Griffith, Boyce E. Department of Mathematics University North Carolina Chapel HillNC United States Department of Mathematics University of Utah Salt Lake CityUT United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime. Copyright © 2023, The Authors. All rights reserved.

关键词： Benchmarking

Composite B-Spline Regularized Delta Functions for the Immersed Boundary Method: Divergence-Free Interpolation and Gradient-Preserving Force Spreading

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arXiv 2024年

作者： Gruninger, Cole Griffith, Boyce E. Department of Mathematics University North Carolina Chapel HillNC United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

This paper presents an approach to enhance volume conservation in the immersed boundary (IB) method by employing regularized delta functions derived from composite B-splines. These delta functions are constructed using tensor product kernels, similar to the conventional IB method. However, the kernels are B-splines whose polynomial degree varies according to the normal and tangential directions of each velocity component. The conventional IB method, while effective for fluid-structure interaction applications, has long been challenged by poor volume conservation, particularly evident in simulations of pressurized, closed membranes. We demonstrate that composite B-spline regularized delta functions significantly enhance volume conservation through two complementary properties: they provide continuously divergence-free velocity interpolants and maintain the gradient character of forces corresponding to mean pressure jumps across interfaces. By correctly representing these forces as discrete gradients, they eliminate a key source of spurious flows that typically plague immersed boundary computations. Our approach maintains the local nature of the classical IB method, avoiding the computational overhead associated with the non-local Divergence-Free Immersed Boundary (DFIB) method’s construction of an explicit velocity potential which requires additional Poisson solves for interpolation and force spreading operations. Through a series of numerical experiments, we show that sufficiently regular composite B-spline kernels can maintain initial volumes to within machine precision. We provide a detailed analysis of the relationship between kernel regularity and the accuracy of force spreading and velocity interpolation operations. Our findings indicate that composite B-splines of at least C1 regularity produce results comparable to the DFIB method in dynamic simulations, with errors in volume conservation primarily dominated by truncation error of the employed time-stepping s

关键词： Delta functions