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Structured time-delay models for dynamical systems with connections to Frenet-Serret frame

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arXiv 2021年

作者： Hirsh, Seth M. Ichinaga, Sara M. Brunton, Steven L. Kutz, J. Nathan Brunton, Bingni W. Department of Physics University of Washington SeattleWA United States Applied and Computational Mathematical Sciences Program University of Washington SeattleWA United States Department of Mechanical Engineering University of Washington SeattleWA United States Department of Applied Mathematics University of Washington SeattleWA United States Department of Biology University of Washington SeattleWA United States

Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode decomposition (DMD) on time-delay coordinates provide linear representations of strongly nonlinear systems, in the so-called Hankel alternative view of Koopman (HAVOK) approach. Curiously, the resulting linear model has a matrix representation that is approximately antisymmetric and tridiagonal with a zero diagonal;for chaotic systems, there is an additional forcing term in the last component. In this paper, we establish a new theoretical connection between HAVOK and the Frenet-Serret frame from differential geometry, and also develop an improved algorithm to identify more stable and accurate models from less data. In particular, we show that the sub- and super-diagonal entries of the linear model correspond to the intrinsic curvatures in Frenet-Serret frame. Based on this connection, we modify the algorithm to promote this antisymmetric structure, even in the noisy, low-data limit. We demonstrate this improved modeling procedure on data from several nonlinear synthetic and real-world examples. © 2021, CC BY.

关键词： Time delay

Two-dimensional Bose-Hubbard model for helium on graphene

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arXiv 2021年

作者： Yu, Jiangyong Lauricella, Ethan Elsayed, Mohamed Shepherd, Kenneth Nichols, Nathan S. Lombardi, Todd Kim, Sang Wook Wexler, Carlos Vanegas, Juan M. Lakoba, Taras Kotov, Valeri N. Del Maestro, Adrian Department of Physics University of Vermont BurlingtonVT05405 United States Materials Science Program University of Vermont BurlingtonVT05405 United States Department of Physics and Astronomy University of Missouri ColumbiaMO65211 United States Department of Mathematics & Statistics University of Vermont BurlingtonVT05405 United States Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996 United States Min H. Kao Department of Electrical Engineering and Computer Science University of Tennessee KnoxvilleTN37996 United States

An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a systems of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons (U ≈ ∞), repulsive nearest-neighbor (V > 0) and small attractive (V0 4He adsorbed on graphene deep in the commensurate solid phase with 1/3 of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system. Copyright © 2021, The Authors. All rights reserved.

关键词： Hubbard model

Gillespie algorithms for stochastic multiagent dynamics in populations and networks

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arXiv 2021年

作者： Masuda, Naoki Vestergaard, Christian L. Department of Mathematics State University of New York at Buffalo NY United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo NY United States Decision and Bayesian Computation Department of Neuroscience Cnrs Umr 3571 Department of Computational Biology Cnrs Usr 3756 Institut Pasteur Paris France

Many multiagent dynamics, including various collective dynamics occurring on networks, can be modeled as a stochastic process in which the agents in the system change their state over time in interaction with each other. The Gillespie algorithms are popular algorithms that exactly simulate such stochastic multiagent dynamics when each state change is driven by a discrete event, the dynamics is defined in continuous time, and the stochastic law of event occurrence is governed by independent Poisson processes. In the first main part of this volume, we provide a tutorial on the Gillespie algorithms focusing on simulation of social multiagent dynamics occurring in populations and networks. We do not assume advanced knowledge of mathematics (or computer science or physics). We clarify why one should use the continuous-time models and the Gillespie algorithms in many cases, instead of easier-to-understand discrete-time models. In the remainder of this volume, we review recent extensions of the Gillespie algorithms aiming to add more reality to the model (i.e., non-Poissonian cases) or to speed up the simulations. © 2021, CC BY.

关键词： Stochastic systems

An immersed interface method for incompressible flows and geometries with sharp features

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Journal of Computational Physics 2025年 537卷

作者： Michael J. Facci Ebrahim M. Kolahdouz Boyce E. Griffith Department of Mathematics University of North Carolina Chapel Hill NC USA Flatiron Institute Simons Foundation New York NY USA Department of Biomedical Engineering University of North Carolina Chapel Hill NC USA Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel Hill NC USA Computational Medicine Program University of North Carolina School of Medicine Chapel Hill NC USA McAllister Heart Institute University of North Carolina School of Medicine Chapel Hill NC USA

The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work using the IIM for fluid dynamics applications has focused on smooth interfaces, but boundaries with sharp features such as corners and edges can appear in practical analyses, particularly on engineered structures. The present study builds on our work to integrate finite element-type representations of interface geometries with the IIM. Initial realizations of this approach used a continuous Galerkin (CG) finite element discretization for the boundary, but as we show herein, these approaches generate large errors near sharp geometrical features. To overcome this difficulty, this study introduces an IIM approach using a discontinuous Galerkin (DG) representation of the jump conditions. Numerical examples explore the impacts of different interface representations on accuracy for both smooth and sharp boundaries, particularly flows interacting with fixed interface configurations. We demonstrate that using a DG approach provides accuracy that is comparable to the CG method for smooth cases. Further, we identify a time step size restriction for the CG representation that is directly related to the sharpness of the geometry. In contrast, time step size restrictions imposed by DG representations are demonstrated to be nearly insensitive to the presence of sharp features.

关键词： Discrete surface Finite element Fluid-structure interaction Immersed interface method Incompressible flow Jump condition Sharp geometry

Improving the robustness of the immersed interface method through regularized velocity reconstruction

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arXiv 2025年

作者： Sun, Qi Kolahdouz, Ebrahim M. Griffith, Boyce E. Department of Mathematics 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

Robust, broadly applicable fluid-structure interaction (FSI) algorithms remain a challenge for computational mechanics. Efforts in this area are driven by the need to enhance predictive accuracy and efficiency in FSI simulations, align with experimental observations, and unravel complex multiscale and multiphysics phenomena, while addressing challenges in developing more robust and efficient methodologies. In previous work, we introduced an immersed interface method (IIM) for discrete surfaces and an extension based on an immersed Lagrangia-Eulerian (ILE) coupling strategy for modeling FSI involving complex geometries. The ability of the method to sharply resolve stress discontinuities induced by singular immersed boundary forces in the presence of low-regularity geometrical representations makes it a compelling choice for three-dimensional modeling of complex geometries in diverse engineering applications. Although the IIM we previously introduced offers many desirable advantages, it also imposes a restrictive mesh factor ratio, requiring the surface mesh to be coarser than the fluid grid to ensure stability. This is because when the mesh factor ratio constraint is not satisfied, parts of the structure motion are not controlled by the discrete FSI system. This constraint can significantly increase computational costs, particularly in applications involving multiscale geometries with highly localized complexity or fine-scale features. To address this limitation, we devise a stabilization strategy for the velocity restriction operator inspired by Tikhonov regularization. This study demonstrates that using a stabilized velocity restriction operator in IIM enables a broader range of structure-to-fluid grid-size ratios without compromising accuracy or altering the flow dynamics. This advancement significantly broadens the applicability of the method to real-world FSI problems involving complex geometries and dynamic conditions, offering a robust and computationally effi

关键词： Mesh generation

Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

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Physical Review E 2021年第1期104卷 014127-014127页

作者： Michael A. Klatt Robert M. Ziff Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 91058 Erlangen Germany Center for the Study of Complex Systems and Department of Chemical Engineering University of Michigan Ann Arbor Michigan 48109 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δc. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δc is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ2〉, which is easier to determine than δc. Here, we compare δc to the second moment of the pore size 〈δ2〉, and indeed confirm that, for all porosities and all models considered, δc2 is to a good approximation proportional to 〈δ2〉. However, unlike 〈δ2〉, the permeability estimate based on δc2 does not predict the correct ranking of k for our models. Thus, we confirm 〈δ2〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targete

关键词： Geophysical networks Materials Patterns in complex systems

Choosing Appropriate Regression Model in the Presence of Multicolinearity

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Open Journal of statistics 2019年第2期9卷 159-168页

作者： Maruf A. Raheem Nse S. Udoh Aramide T. Gbolahan Department of Engineering and Mathematics Sheffield Hallam University Sheffield UK Department of Mathematics & Statistics University of Uyo Uyo Nigeria Department of Computer Science Sheffield Hallam University Sheffield UK

This work is geared towards detecting and solving the problem of multicolinearity in regression analysis. As such, Variance Inflation Factor (VIF) and the Condition Index (CI) were used as measures of such detection. Ridge Regression (RR) and the Principal Component Regression (PCR) were the two other approaches used in modeling apart from the conventional simple linear regression. For the purpose of comparing the two methods, simulated data were used. Our task is to ascertain the effectiveness of each of the methods based on their respective mean square errors. From the result, we found that Ridge Regression (RR) method is better than principal component regression when multicollinearity exists among the predictors.

关键词： Multicollinearity Adequacy Regression coefficients Variance Inflation Factor (VIF) Mean Square Error

Drake equation of search for extraterrestrial intelligence: A proposal for modification in the light of Dirac's large number hypothesis

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International Journal of Modern Physics D 2023年第15期32卷 2350094-2350094页

作者： Ray, Saibal Ray, Soham Al-Amri, Issa S. Maurya, S.K. Manith Banula, K.P. Centre for Cosmology Astrophysics and Space Science (CCASS) Gla University Uttar Pradesh Mathura 281406 India Biological Institute Tomsk State University Lenin Ave 36 Tomsk Oblast Tomsk 634050 Russian Federation Department of Biological Science and Chemistry University of Nizwa Nizwa Oman Department of Mathematics and Physical Science College of Arts and Science University of Nizwa Oman Smart Materials and Technologies Institute Tomsk International Science Program: Molecular Engineering Tomsk State University Lenin Ave 36 Tomsk Oblast Tomsk 634050 Russian Federation

In the light of Dirac's Large Number Hypothesis (LNH), we try to relate the Drake equation with the extra-terrestrial intelligence (ETI), specifically in terms of cognitive science. This argument has been drawn from the ratio of smallest time scale (i.e. 40 Hz oscillation in neuronal system of brain) to the smallest timescale (i.e. the Planck time in the present universe) which provides a very large dimensionless number 10⁴⁰. Under this LNH, we emphasize on the issue of the alien equation of Drake and provide a modified version of it by considering consciousness of the ETI. Thus, the Drake equation, which basically represents a statistical conjecture with random and arbitrary values, can be related with a feasible as well as applicable background philosophy. © 2023 World Scientific Publishing Company.

关键词： cognitive astrobiology consciousness Dirac's large number hypothesis Drake equation

Influence of artificial intelligence for diagnostic decision making using radiological imaging

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AIP Conference Proceedings 2023年第1期2603卷

作者： Praveen Kumar Misra G. Meena Devi S. A. Yuvaraj Mohd Zeeshan S. Fathhoor Rabbani Shvets Yuriy Yurievich Department of Mathematics and Statistics Dr. Shakuntala Misra National Rehabilitation University Lucknow 226017 India Department of Mathematics St. Joseph’s college of Engineering Chennai 600119 India Department of Electronics and Communication Engineering GRT Institute of Engineering and Technology Tiruttani 631209 India Department of Radio-Diagnosis Career Institute of Medical Sciences and Hospital Lucknow 226020 India Department of Physics C. Abdul Hakeem College (Autonomous) Melvisharam 632509 India Department of Economical Development Institute of Control of Science Trapeznikov RAS Financial University under the Government of Russion Federation Moscow 117997 Russia

Due to advancements in imaging technique, artificial intelligence requires less human intervention for binary and multi-class decision making, which is suited for the availability of medical data. Furthermore, the precision of prediction and autonomous decision-making are valued. As a result, the focus of this review is on the use of AI in radiological decision-making. The theory underpinning imaging internal body components and their use for disease diagnosis is first introduced, followed by numerous radiological procedures.

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