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Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation

Journal of Dynamics and Differential Equations 1991年第2期3卷 179-197页

作者： Jolly, M.S. Kevrekidis, I.G. Titi, E.S. Program in Applied and Computational Mathematics Princeton University Princeton 08544 New Jersey United States Department of Mathematics Indiana University Bloomington 47405 Indiana United States Department of Chemical Engineering Princeton University Princeton 08544 New Jersey United States Mathematical Sciences Institute Cornell University Ithaca 14853 New York United States Department of Mathematics University of California Irvine 92717 California United States

It has been observed, in earlier computations of bifurcation diagrams for dissipative partial differential equations, that the use of certain explicit approximate inertial forms can give rise to numerical artifacts such as spurious turning points and inaccurate solution branches. These shortcomings were attributed to a lack of dissipation in the forms used. We show analytically and verify numerically that with an appropriate adjustment we can eliminate these numerical artifacts. The motivation for this adjustment is to enforce dissipation, while maintaining the same order of approximation. We demonstrate with computations that the most natural remedy, namely, preparation of the equation, can be highly sensitive to assumptions on the size of the absorbing ball. In addition, we show that certain implicit forms are dissipative without any adjustment. As an illustrative example we use here the Kuramoto-Sivashinsky equation. © 1991 Plenum Publishing Corporation.

关键词： dissipation Inertial manifold Kuramoto-Sivashinsky non-linear Galerkin method

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Bibliometric Analysis: Research Trends in Leaf Image Segmentation and Classification

Bibliometric Analysis: Research Trends in Leaf Image Segment...

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2024 International Conference on Artificial Intelligence and Mechatronics System, AIMS 2024

作者： Agustini, Eka Puji Gernowo, Rahmad Kurnianingsih Wibowo, Adi Warsito, Budi Doctoral Program of Information System School of Postgraduated Studies Diponegoro University Semarang Indonesia Doctoral Program of Information System Diponegoro University Semarang Indonesia Master of Applied Science Program Polytechnic Semarang Indonesia Diponegoro University Faculty of Science and Mathematics Department of Informatics Semarang Indonesia Faculty of Science and Mathematics Diponegoro Universitty Department of Statistics Semarang Indonesia

ISBN: (纸本)9798350350524

Exploring various phenomena and issues related to leaf images is paramount, particularly in segmentation and classification of such images. This study employs bibliometric analysis to delve into two overarching themes: The trends in publication and the evolution of publications, along with a keyword-based analysis. The research methodology unfolds in two stages: (1) data collection and (2) analysis. The dataset comprises 1,248 articles sourced from the Scopus database, covering the period from 1988 to 2023. The research findings unveil a noteworthy surge in publication trends, peaking at 231 documents in 2023. An in-depth examination of journal names demonstrates that studies on the segmentation and classification of leaf images are predominantly featured in computer science journals, exemplified by the publication of 589 documents. Furthermore, an analysis of frequently used keywords highlights 'Extraction' as the predominant term, employed a total of 364 times. This underscores that the research focus on leaf image segmentation and classification presents ample opportunities for researchers to delve more profoundly into the subject. © 2024 IEEE.

关键词： Image segmentation

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Bistable Helices

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Physical Review Letters 2000年第7期84卷 1631-1631页

作者： Raymond E. Goldstein Alain Goriely Greg Huber Charles W. Wolgemuth Department of Physics University of Arizona Tucson Arizona 85721 Program in Applied Mathematics University of Arizona Tucson Arizona 85721 Department of Mathematics University of Arizona Tucson Arizona 85721

We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom is developed using the natural frame of space curves, spanning from the inviscid limit to the viscously overdamped regime applicable to cellular biology. Aspects of front propagation found in flagella are discussed.

关键词：芽孢杆菌枯草/细胞学弹性鞭毛/化学鞭毛/生理学鞭毛/超微结构模型生物学运动(Motion) 沙门菌属/细胞学热力学转矩黏度

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Downlink analysis for a heterogeneous cellular network

Downlink analysis for a heterogeneous cellular network

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2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2014

作者： Madhusudhanan, Prasanna Restrepo, Juan G. Liu, Youjian Eugene Brown, Timothy X. Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO 80309-0425 United States Department of Applied Mathematics University of Colorado Boulder CO 80309-0425 United States Interdisciplinary Telecommunications Program University of Colorado Boulder CO 80309-0425 United States

ISBN: (纸本)9783901882630

In this paper, a comprehensive study of the downlink performance in a heterogeneous cellular network (or hetnet) is conducted. A general hetnet model is considered consisting of an arbitrary number of open-access and closed-access tier of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs of each tier have a constant transmission power, random fading coefficient with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability and average rate at an arbitrary mobile-station (MS), and average per-tier load are derived for the max-SINR connectivity model. Using stochastic ordering, interesting properties and simplifications for the hetnet downlink performance are derived by relating this connectivity model to the maximum instantaneous received power (MIRP) connectivity model, providing good insights about the hetnets and the downlink performance in these complex networks. Furthermore, the results also demonstrate the effectiveness and analytical tractability of the stochastic geometric approach to study the hetnet performance. © 2014 IFIP.

关键词： Fading channels

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Correlations in interacting electron liquids: Many-body statistics and hyperuniformity

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Physical Review B 2024年第10期110卷 104201页

作者： Haina Wang Rhine Samajdar Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Materials Institute Program in Applied and Computational Mathematics

Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to ordinary liquids. The structure factor of disordered hyperuniform systems often obeys the scaling relation S(k)∼Bkα with B,α>0 in the limit k→0. Ground states of d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this paper, we systematically address these questions by deriving the analytical small-k behaviors (and, associated, α and B) of the total and spin-resolved structure factors of quasi-one-dimensional, two-dimensional, and three-dimensional electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our paper thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple

关键词： Electronic structure Quantum many-body systems Two-dimensional electron gas

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Cholesterol allosteric modulation of the oxytocin receptor

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Biophysical Journal 2025年

作者： Marlow, Brennica Vogel, Alexander Kuenze, Georg Pankonin, Maik Reinhardt, Franziska Stadler, Peter F. Hildebrand, Peter W. Meiler, Jens Center for Structural Biology Vanderbilt University Nashville TN United States Institute for Drug Discovery Medical Faculty Leipzig University Leipzig Germany Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI Leipzig University Leipzig Germany Interdisciplinary Center for Bioinformatics Leipzig University Leipzig Germany Chemical and Physical Biology Program Vanderbilt University Nashville TN United States Department of Chemistry Vanderbilt University Nashville TN United States Institute of Medical Physics and Biophysics Medical Faculty Leipzig University Leipzig Germany Bioinformatics Group Institute of Computer Science Interdisciplinary Center of Bioinformatics Leipzig University Leipzig Germany Max-Planck-Institute for Mathematics in the Sciences Leipzig Germany Institute of Theoretical Chemistry University of Vienna Wien Austria Facultad de Ciencias Universidad National de Colombia Sede Bogota Colombia Santa Fe Institute New Mexico Santa Fe Mexico

G-protein coupled receptors are critical components in cellular signaling, mediating various physiological responses to external stimuli. Here, we investigate the intricate relationship between cholesterol and the oxytocin receptor (OXTR), focusing on the binding mechanisms and the allosteric cross talk of bound cholesterol to the orthosteric ligand binding pocket. Utilizing molecular docking and molecular dynamics simulations, we identify cholesterol binding sites both on the agonist-bound and antagonist-bound state, which show differing distributions and residence times of the cholesterol molecules. Importantly, both methods converge on several key sites, demonstrating strong predictive overlap. Notably, one such site, and several sites detected by our molecular dynamics approach, also coincide with electron density observed in an experimental cryo-EM map, providing orthogonal validation for computational predictions. Allosteric network analysis uncovers the distinct pathways through which cholesterol may affect ligand-mediated receptor signaling, highlighting the significance of one site on the extracellular leaflet between TM4 and TM5, and two sites on the intracellular leaflet between TM2, TM3, and TM4 and between TM4 and TM5 in transmitting allosteric signals to the orthosteric pocket. These findings provide insights into the impact of cholesterol on OXTR function, emphasizing specific binding sites and signaling paths for further experimental exploration. © 2025 Biophysical Society

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Estimating the mean and variance from the median, range, and the size of a sample

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BMC Medical Research Methodology 2005年第1期5.0卷 1-10页

作者： Hozo, Stela Pudar Djulbegovic, Benjamin Hozo, Iztok Indiana University Northwest Department of Mathematics Gary IN 46408 United States Interdisciplinary Oncology Program H. Lee Moffitt Cancer Center and Research Institute University of South Florida Tampa FL United States

Background: Usually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial. Methods: In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data. Results: We found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n ≤ 15). For moderately sized samples (15 70), the formula range/6 gives the best estimator for the standard deviation (variance). We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy. Conclusion: Using these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported. © 2005 Hozo et al;licensee BioMed Central Ltd.

关键词： Erythropoietin Cochrane Review Skewed Distribution Good Estimator Estimation Formula

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A reduced-order model for unsteady flow over circular cylinder

A reduced-order model for unsteady flow over circular cylind...

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作者： Ghommem, Mehdi Akhtar, Imran Hajj, Muhammad R. Puri, Ishwar K. Department of Engineering Science and Mechanics Virginia Tech. Blacksburg VA 24061 United States Interdisciplinary Center for Applied Mathematics Virginia Tech. Blacksburg VA 24061 United States

ISBN: (纸本)9781600867392

Proper orthogonal decomposition (POD) is performed on steady and unsteady flows past a circular cylinder. The unsteady flow considered here is obtained by adding a sinusoidal component to the steady mean flow. The results show that the first two modes in both flows are almost identical. On the other hand, the mean flow unsteadiness yields an additional mode. Consequently, the POD-based reduced-order models for the steady flow cannot be readily used to reproduce flow characteristics of the unsteady flow. A reformulation of the reduced-order model that makes use of the POD modes obtained from steady flow and that incorporates unsteadiness parameters is presented.

关键词： Steady flow

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On The Mechanism of Nucleation in Pulsed-laser Quenched Si Films on SiO 2

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MRS Online Proceedings Library 2021年第1期1245卷 1-6页

作者： Y. Deng Q. Hu U. J. Chung A. M. Chitu A. B. Limanov S. James Im Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York USA

We have investigated the solid nucleation mechanism in laser-quenched Si films on SiO2. Previously neglected experimental steps, consisting of BHF-etching and irradiation in vacuum, were implemented to reduce potential extrinsic influences. The resulting experimental findings and computational analysis lead us to conclude that solid nucleation consistently takes place heterogeneously at, and only at, the bottom liquid Si-SiO2 interface.

关键词： Si thin film nucleation & growth

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A note on Miura's transformation

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Journal of Mathematical Physics 1978年第6期20卷 999-1003页

作者： Ablowitz, Mark J. Kruskal, Martin Segur, Harvey Program in Applied Mathematics Princeton University Princeton NJ 08540 United States Aeronautical Research Associates of Princeton Inc. Princeton NJ 08540 50 Washington Road United States Department of Mathematics Clarkson College of Technology Potsdam NY 13676 United States

It has been observed by Miura that the solutions of the modified Korteweg-deVries equation can be mapped into those of the Korteweg-deVries equation. In this note we show that all of the solutions of the former, decaying sufficiently rapidly as |x|→∞, map into a sparse solution set of the KdV equation. We use certain results regarding the second Painlevé transcendent to exhibit this fact. © 1979 American Institute of Physics.

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