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Corrigendum to “Revisiting a magneto-elastic strange attractor” [J. Sound Vib. 333 (6) (2014) 1767–1780]

Journal of Sound and Vibration 2016年 367卷 256-256页

作者： Jee Ian Tam Philip Holmes Department of Mechanical and Aerospace Engineering Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

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Applying Graph Theory and Mathematical-computational Modelling to Study a Neurophysiological Circuit

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Open Journal of Modelling and Simulation 2021年第2期9卷 159-171页

作者： Camila de Andrade Kalil Maria Clícia Stelling de Castro Dilson Silva Célia Martins Cortez Postgraduate Program in Computational Sciences Rio de Janeiro State University Rio de Janeiro Brazil Department of Informatics and Computer Science Rio de Janeiro State University Rio de Janeiro Brazil Department of Applied Mathematics Rio de Janeiro State University Rio de Janeiro Brazil

The aim of the present study is to contribute to the knowledge about the functioning of the neuronal circuits. We built a mathematical-computational model using graph theory for a complex neurophysiological circuit consisting of a reverberating neuronal circuit and a parallel neuronal circuit, which could be coupled. Implementing our model in C++ and applying neurophysiological values found in the literature, we studied the discharge pattern of the reverberant circuit and the parallel circuit separately for the same input signal pattern, examining the influence of the refractory period and the synaptic delay on the respective output signal patterns. Then, the same study was performed for the complete circuit, in which the two circuits were coupled, and the parallel circuit could then influence the functioning of the reverberant. The results showed that the refractory period played an important role in forming the pattern of the output spectrum of a reverberating circuit. The inhibitory action of the parallel circuit was able to regulate the reverberation frequency, suggesting that parallel circuits may be involved in the control of reverberation circuits related to motive activities underlying precision tasks and perhaps underlying neural work processes and immediate memories.

关键词： Mathematical-computational Modelling Neurophysiological Circuit Reverberating Circuit Parallel Circuit

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An Atlas of Convection in Main-Sequence Stars

arXiv

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arXiv 2022年

作者： Jermyn, Adam S. Anders, Evan H. Lecoanet, Daniel Cantiello, Matteo Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States CIERA Northwestern University EvanstonIL60201 United States Department of Engineering Sciences and Applied Mathematics Northwestern University EvanstonIL60208 United States Department of Astrophysical Sciences Princeton University Princeton NJ08544 United States

Convection is ubiquitous in stars and occurs under many different conditions. Here we explore convection in main-sequence stars through two lenses: dimensionless parameters arising from stellar structure and parameters which emerge from the application of mixing length theory. We first define each quantity in terms familiar both to the 1D stellar evolution community and the hydrodynamics community. We then explore the variation of these quantities across different convection zones, different masses, and different stages of main-sequence evolution. We find immense diversity across stellar convection zones. Convection occurs in thin shells, deep envelopes, and nearly-spherical cores;it can be efficient of inefficient, rotationally constrained or not, transsonic or deeply subsonic. This atlas serves as a guide for future theoretical and observational investigations by indicating which regimes of convection are active in a given star, and by describing appropriate model assumptions for numerical simulations. © 2022, CC BY.

关键词： Stars

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Convective Penetration in Early-Type Stars

arXiv

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arXiv 2022年

Observations indicate that the convective cores of stars must ingest a substantial amount of material from the overlying radiative zone, but the extent of this mixing and the mechanism which causes it remain uncertain. Recently, Anders et al. (2021) developed a theory of convective penetration and calibrated it with 3D numerical hydrodynamics simulations. Here we employ that theory to predict the extent of convective boundary mixing in early-type main-sequence stars. We find that convective penetration produces enough mixing to explain core masses inferred from asteroseismology and eclipsing binary studies, and matches observed trends in mass and age. While there are remaining uncertainties in the theory, this agreement suggests that most convective boundary mixing in early-type main-sequence stars arises from convective penetration. Finally, we provide a fitting formula for the extent of core convective penetration for main-sequence stars in the mass range from 1.1 − 60Mo © 2022, CC BY.

关键词： Mixing

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An Informative Itinerary

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Science 2010年第5977期328卷 430页

作者： Iain D. Couzin The reviewer is at the Department of Ecology and Evolutionary Biology and the Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA.

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Adaptive tikhonov strategies for stochastic ensemble Kalman inversion

arXiv

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arXiv 2021年

作者： Weissmann, Simon Chada, Neil K. Schillings, Claudia Tong, Xin T. Interdisciplinary Center for Scientific Computing University of Heidelberg Heidelberg69120 Germany Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal KSA 23955 Saudi Arabia Mannheim School of Computer Science and Mathematics University of Mannheim Mannheim68131 Germany Department of Mathematics National University of Singapore Singapore119077 Singapore

Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov strategies for EKI. This work builds upon Tikhonov EKI (TEKI) which was proposed for a fixed regularization constant. By adaptively learning the regularization parameter, this procedure is known to improve the recovery of the underlying unknown. For the analysis, we consider a continuous-time setting where we extend known results such as well-posdeness and convergence of various loss functions, but with the addition of noisy observations. Furthermore, we allow a time-varying noise and regularization covariance in our presented convergence result which mimic adaptive regularization schemes. In turn we present three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning. We numerically test these schemes and the theory on linear and nonlinear partial differential equations, where they outperform the non-adaptive TEKI and *** Codes 65M32, 60G35, 65C35, 70F17 Copyright © 2021, The Authors. All rights reserved.

关键词： Continuous time systems

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Lithospheric foundering and underthrusting imaged beneath Tibet

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Nature Communications 2017年第1期8卷 1-10页

作者： Chen, Min Niu, Fenglin Tromp, Jeroen Lenardic, Adrian Lee, Cin-Ty A. Cao, Wenrong Ribeiro, Julia 318 Keith-Wiess Geology Lab Department of Earth Science Rice University 6100 Main Street Houston 77005 TX United States State Key Laboratory of Petroleum Resource Prospecting and Unconventional Natural Gas Institute China University of Petroleum Beijing 102249 China Department of Geosciences Princeton University Princeton 08544 NJ United States Program in Applied and Computational Mathematics Princeton University Princeton 08544 NJ United States

Long-standing debates exist over the timing and mechanism of uplift of the Tibetan Plateau and, more specifically, over the connection between lithospheric evolution and surface expressions of plateau uplift and volcanism. Here we show a T-shaped high wave speed structure in our new tomographic model beneath South-Central Tibet, interpreted as an upper-mantle remnant from earlier lithospheric foundering. Its spatial correlation with ultrapotassic and adakitic magmatism supports the hypothesis of convective removal of thickened Tibetan lithosphere causing major uplift of Southern Tibet during the Oligocene. Lithospheric foundering induces an asthenospheric drag force, which drives continued underthrusting of the Indian continental lithosphere and shortening and thickening of the Northern Tibetan lithosphere. Surface uplift of Northern Tibet is subject to more recent asthenospheric upwelling and thermal erosion of thickened lithosphere, which is spatially consistent with recent potassic volcanism and an imaged narrow low wave speed zone in the uppermost mantle. © 2017 The Author(s).

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Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

arXiv

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arXiv 2023年

作者： Beckers, Thomas Seidman, Jacob Perdikaris, Paris Pappas, George J. Department of Electrical and Systems Engineering University of Pennsylvania PhiladelphiaPA19104 United States graduate program in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems. © 2023, CC BY-NC-ND.

关键词： Hamiltonians

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DeePN2: A deep learning-based non-Newtonian hydrodynamic model

arXiv

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arXiv 2021年

作者： Fang, Lidong Ge, Pei Zhang, Lei Weinan, E. Lei, Huan Department of Computational Mathematics Science and Engineering Michigan State University MI48824 United States School of Mathematical Sciences Institute of Natural Sciences and MOE-LSC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing100080 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States Department of Statistics and Probability Michigan State University MI48824 United States

A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying micro-scale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure and heterogeneous interaction. DeePN2, a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN2 using more complex micro-structural models. We show that DeePN2 can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention. © 2021, CC BY.

关键词： Non Newtonian flow

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Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation

arXiv

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arXiv 2020年

作者： Puelz, Charles Danial, Zach Marinaro, Jon Raval, Jay Griffith, Boyce E. Peskin, Charles S. Courant Institute of Mathematical Sciences New York University Department of Emergency Medicine University of New Mexico Department of Pathology University of New Mexico Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Computational Medicine Program University of North Carolina McAllister Heart Institute University of North Carolina

This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno–arterial or veno–venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have been validated with experimental data [15]. We also show that the algebraic delay equations are forward Euler discretizations of the delay differential equations, with timesteps equal to transit times through model compartments. Numerical simulations are performed to compare different model types, to investigate the impact of plasma device port switching on the efficiency of the exchange process, and to study the sensitivity of the models to their parameters. Copyright © 2020, The Authors. All rights reserved.

关键词： Respiratory therapy

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