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Phenomenological friction equation for turbulent flow of Bingham fluids

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Physical Review E 2017年第2期96卷 023107-023107页

作者： H. R. Anbarlooei D. O. A. Cruz F. Ramos Cecilia M. M. Santos A. P. Silva Freire Mechanical Engineering Program COPPE Federal University of Rio de Janeiro Rio de Janeiro Rio de Janeiro 21941-450 Brazil Department of Applied Mathematics Institute of Mathematics Federal University of Rio de Janeiro Rio de Janeiro Rio de Janeiro 21941-450 Brazil

Most discussions in the literature on the friction coefficient of turbulent flows of fluids with complex rheology are empirical. As a rule, theoretical frameworks are not available even for some relatively simple constitutive models. In the present work, a formula is proposed for the evaluation of the friction coefficient of turbulent flows of Bingham fluids. The developments combine a fresh analysis for the description of the microscales of Kolmogorov and the phenomenological turbulence model of Gioia and Chakraborty [G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006)]. The resulting Blasius-type friction equation is tested against some experimental data and shows good agreement over a significant range of Hedstrom and Reynolds numbers. Comments on pressure measurements in yielding fluids are made. The limits of the proposed model are also discussed.

关键词： Non-Newtonian fluids Turbulence Viscoplasticity

Capped p approximations for the composite 0 regularization problem

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arXiv 2017年

作者： Li, Qia Zhang, Na Guangdong Province Key Laboratory of Computational Science School of Data and Computer Sciences Sun Yat-sen University Guangzhou510275 China Department of Applied Mathematics College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China

The composite 0 function serves as a sparse regularizer in many applications. The algorithmic difficulty caused by the composite 0 regularization \(the 0 norm composed with a linear mapping\) is usually bypassed through approximating the 0 norm. We consider in this paper capped p approximations with p > 0 for the composite 0 regularization problem. For each p > 0, the capped p function converges to the 0 norm pointwisely as the approximation parameter tends to infinity. We point out that the capped p approximation problem is essentially a penalty method with an p penalty function for the composite 0 problem from the viewpoint of numerical optimization. Our theoretical results stated below may shed a new light on the penalty methods for solving the composite 0 problem and help the design of innovative numerical algorithms. We first establish the existence of optimal solutions to the composite 0 regularization problem and its capped p approximation problem under conditions that the data fitting function is asymptotically level stable and bounded below. Asymptotically level stable functions cover a rich class of data fitting functions encountered in practice. We then prove that the capped p problem asymptotically approximates the composite 0 problem if the data fitting function is a level bounded function composed with a linear mapping. We further show that if the data fitting function is the indicator function on an asymptotically linear set or the 0 norm composed with an affine mapping, then the composite 0 problem and its capped p approximation problem share the same optimal solution set provided that the approximation parameter is large enough. Copyright © 2017, The Authors. All rights reserved.

关键词： Constrained optimization

High-Reynolds-number turbulent cavity flow using the lattice Boltzmann method

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Physical Review E 2018年第4期98卷 043302-043302页

作者： L. A. Hegele, Jr. A. Scagliarini M. Sbragaglia K. K. Mattila P. C. Philippi D. F. Puleri J. Gounley A. Randles Department of Biomedical Engineering Duke University Durham North Carolina 27708 USA Department of Petroleum Engineering Santa Catarina State University Balneário Camboriú Santa Catarina 88336-275 Brazil CNR-IAC Institute for Applied Mathematics “M. Picone” 00185 Rome Italy Department of Physics and INFN University of “Tor Vergata” 00133 Rome Italy Department of Physics and Nanoscience Center University of Jyväskylä FI-40014 Jyväskylä Finland Department of Physics Tampere University of Technology FI-33101 Tampere Finland Mechanical Engineering Graduate Program Pontifical Catholic University of Paraná Curitiba Paraná 80215-901 Brazil

We present a boundary condition scheme for the lattice Boltzmann method that has significantly improved stability for modeling turbulent flows while maintaining excellent parallel scalability. Simulations of a three-dimensional lid-driven cavity flow are found to be stable up to the unprecedented Reynolds number Re=5×104 for this setup. Excellent agreement with energy balance equations, computational and experimental results are shown. We quantify rises in the production of turbulence and turbulent drag, and determine peak locations of turbulent production.

关键词： Transition to turbulence Lattice-Boltzmann methods

Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

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arXiv 2023年

作者： Alexeev, Yuri Amsler, Maximilian Barroca, Marco Antonio Bassini, Sanzio Battelle, Torey Camps, Daan Casanova, David Choi, Young Jai Chong, Frederic T. Chung, Charles Codella, Christopher Córcoles, Antonio D. Cruise, James Di Meglio, Alberto Duran, Ivan Eckl, Thomas Economou, Sophia Eidenbenz, Stephan Elmegreen, Bruce Fare, Clyde Faro, Ismael Fernández, Cristina Sanz Ferreira, Rodrigo Neumann Barros Fuji, Keisuke Fuller, Bryce Gagliardi, Laura Galli, Giulia Glick, Jennifer R. Gobbi, Isacco Gokhale, Pranav de la Puente Gonzalez, Salvador Greiner, Johannes Gropp, Bill Grossi, Michele Gull, Emanuel Healy, Burns Hermes, Matthew R. Huang, Benchen Humble, Travis S. Ito, Nobuyasu Izmaylov, Artur F. Javadi-Abhari, Ali Jennewein, Douglas Jha, Shantenu Jiang, Liang Jones, Barbara de Jong, Wibe Albert Jurcevic, Petar Kirby, William Kister, Stefan Kitagawa, Masahiro Klassen, Joel Klymko, Katherine Koh, Kwangwon Kondo, Masaaki Kürkçüoglu, Doga Murat Kurowski, Krzysztof Laino, Teodoro Landfield, Ryan Leininger, Matt Leyton-Ortega, Vicente Li, Ang Lin, Meifeng Liu, Junyu Lorente, Nicolas Luckow, Andre Martiel, Simon Martin-Fernandez, Francisco Martonosi, Margaret Marvinney, Claire Medina, Arcesio Castaneda Merten, Dirk Mezzacapo, Antonio Michielsen, Kristel Mitra, Abhishek Mittal, Tushar Moon, Kyungsun Moore, Joel Mostame, Sarah Motta, Mario Na, Young-Hye Nam, Yunseong Narang, Prineha Ohnishi, Yu-Ya Ottaviani, Daniele Otten, Matthew Pakin, Scott Pascuzzi, Vincent R. Pednault, Edwin Piontek, Tomasz Pitera, Jed Rall, Patrick Ravi, Gokul Subramanian Robertson, Niall Rossi, Matteo A.C. Rydlichowski, Piotr Ryu, Hoon Samsonidze, Georgy Sato, Mitsuhisa Saurabh, Nishant Sharma, Vidushi Sharma, Kunal Shin, Soyoung Slessman, George Steiner, Mathias Sitdikov, Iskandar Suh, In-Saeng Switzer, Eric D. Tang, Wei Thompson, Joel Todo, Synge Tran, Minh C. Trenev, Dimitar Trott, Christian Tseng, Huan-Hsin Tubman, Norm M. Tureci, Esin Valiñas, David García Vallecorsa, Sofia Wever, Christopher Wojciechowski, Konrad Wu, Xiaodi Yoo, Shinjae Yoshioka, Argonne National Laboratory LemontIL60439 United States Corporate Sector Research and Advance Engineering Robert Bosch GmbH Robert-Bosch-Campus 1 RenningenD-71272 Germany IBM Research RJ Rio de Janeiro20031-170 Brazil Centro Brasileiro de Pesquisas Físicas RJ Rio de Janeiro22290-180 Brazil CINECA via Magnanelli 6/3 BO Casalecchio di Reno40033 Italy Arizona State University TempeAZ United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Euskadi Donostia-San Sebastián20018 Spain Ikerbasque Basque Foundation for Science Bilbao48009 Spain Department of Physics Yonsei University Seoul03722 Korea Republic of University of Chicago ChicagoIL United States IBM Quantum IBM T.J. Watson Research Center Yorktown Heights NY10598 United States Cambridge Consultants part of Capgemini Invent Cambridge United Kingdom Geneva1211 Switzerland Virginia Tech BlacksburgVA24061 United States Los Alamos National Laboratory Los AlamosNM87545 United States Osaka University Osaka560-8531 Japan Department of Chemistry Chicago Center for Theoretical Chemistry University of Chicago ChicagoIL United States Fraunhofer ITWM Rheinland-Pfalz Kaiserslautern67663 Germany Infleqtion ChicagoIL60622 United States University of Illinois Urbana-Champaign United States University of Michigan Ann ArborMI48109 United States Research Office Oak Ridge National Laboratory One Bethel Valley Road Oak RidgeTN37831 United States Hyogo Kobe650-0047 Japan Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoONM5S 3H6 Canada Department of Physical and Environmental Sciences University of Toronto Scarborough TorontoONM1C 1A4 Canada Brookhaven National Laboratory UptonNY United States Rutgers University New BrunswickNJ United States IBM Quantum Almaden Research Center San JoseCA95120 United States Applied Mathematics and Computational Research Division

computational models are an essential tool for the design, characterization, and discovery of novel materials. computationally hard tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their resources for simulation, analysis, and data processing. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions. Copyright © 2023, The Authors. All rights reserved.

关键词： Characterization (materials science)

Application of the cut-off projection to solve a backward heat conduction problem in a two-slab composite system

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arXiv 2017年

作者： Tuan, Nguyen Huy Khoa, Vo Anh Truong, Mai Thanh Nhat Hung, Tran The Minh, Mach Nguyet Institute for Computational Science and Technology Ho Chi Minh city Viet Nam Mathematics and Computer Science Division Gran Sasso Science Institute L'Aquila Italy Institute for Numerical and Applied Mathematics University of Goettingen Germany Department of Electrical Electronic and Control Engineering Hankyong National University Gyeonggi Korea Republic of Department of Mathematics University of Hamburg Hamburg Germany Department of Mathematics and Statistics University of Helsinki Finland

The main goal of this paper is applying the cut-off projection for solving one-dimensional backward heat conduction problem in a two-slab system with a perfect contact. In a constructive manner, we commence by demonstrating the Fourier-based solution that contains the drastic growth due to the high-frequency nature of the Fourier series. Such instability leads to the need of studying the projection method where the cut-off approach is derived consistently. In the theoretical framework, the first two objectives are to construct the regularized problem and prove its stability for each noise level. Our second interest is estimating the error in L2-norm. Another supplementary objective is computing the eigen-elements. All in all, this paper can be considered as a preliminary attempt to solve the heating/cooling of a two-slab composite system backward in time. Several numerical tests are provided to corroborate the qualitative analysis.35K05, 42A20, 47A52, 65J20 Copyright © 2017, The Authors. All rights reserved.

关键词： Heat conduction

Qualitative symbolic perturbation 32

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Qualitative symbolic perturbation

32nd International Symposium on computational Geometry, SoCG 2016

作者： Devillers, Olivier Karavelas, Menelaos Teillaud, Monique Inria Centre de Recherche Nancy - Grand Est France CNRS Loria France Université de Lorraine France Mathematics and Applied Mathematics Department University of Crete Greece Institute of Applied and Computational Mathematics FORTH Greece

ISBN: (纸本)9783959770095

In a classical Symbolic Perturbation scheme, degeneracies are handled by substituting some polynomials in Ε for the inputs of a predicate. Instead of a single perturbation, we propose to use a sequence of (simpler) perturbations. Moreover, we look at their effects geometrically instead of algebraically;this allows us to tackle cases that were not tractable with the classical algebraic approach. © Olivier Devillers, Menelaos Karavelas, and Monique Teillaud.

关键词： Apollonius diagram Robustness issues Symbolic perturbations

Numerical local irreducible decomposition 6th

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Numerical local irreducible decomposition

6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015

作者： Brake, Daniel A. Hauenstein, Jonathan D. Sommese, Andrew J. Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

ISBN: (纸本)9783319328584

Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to produce a local irreducible decomposition. We define local witness sets and describe a numerical algebraic geometric approach for computing a numerical local irreducible decomposition for polynomial systems. Several examples are presented. © Springer International Publishing Switzerland 2016.

关键词： Geometry

Role of short-term dispersal on the dynamics of Zika virus in an extreme idealized environment

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Infectious Disease Modelling 2017年第1期2卷 21-34页

作者： Victor M.Moreno Baltazar Espinoza Derdei Bichara Susan A.Holechek Carlos Castillo-Chavez Simon A.Levin Mathematical Computational and Modeling Sciences CenterArizona State UniversityP.O.Box 873901TempeAZ 85287-3901United States Biodesign Center for Infectious Diseases and Vaccinology Biodesign InstituteArizona State UniversityTempeAZ 85287-5401United States School of Life Sciences Arizona State UniversityTempeAZ 85287-4501United States Department of Mathematics and Center for Computational and Applied Mathematics California State UniversityFullertonCA 92831United States Departamento the Ingenieria Biomedica Universidad de Los AndesBogotaColombia Rector's Office Yachay Tech UniversityUrcuquiEcuador

In November 2015,El Salvador reported their first case of Zika virus(ZIKV)infection,an event followed by an explosive outbreak that generated over 6000 suspected cases in a period of two *** agencies began implementing control measures that included vector control and recommending an increased use of ***,in response to the alarming and growing number of microcephaly cases in Brazil,the importance of avoiding pregnancies for two years was *** this paper,we explore the role of mobility within communities characterized by extreme poverty,crime and ***,the role of short term mobility between two idealized interconnected highly distinct communities is explored in the context of ZIKV *** make use of a Lagrangian modeling approach within a two-patch setting in order to highlight the possible effects that short-term mobility,within highly distinct environments,may have on the dynamics of ZIKV outbreak when the overall goal is to reduce the number of cases not just in the most affluent areas but *** depend on existing mobility patterns,levels of disease risk,and the ability of federal or state public health services to invest in resource limited areas,particularly in those where violence is *** results of simulations in highly polarized and simplified scenarios are used to assess the role of *** quickly became evident that matching observed patterns of ZIKV outbreaks could not be captured without incorporating increasing levels of *** number of distinct patches and variations on patch connectivity structure required to match ZIKV patterns could not be met within the highly aggregated model that is used in the simulations.

关键词： Vector-borne diseases Zika virus Residence times Multi-patch model

An approach with toric varieties for singular learning machines.

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arXiv 2017年

作者： Castillo-Villalba, M.P. González-Cervantes, J.O. Program of Computational Genomics Center for Genomic Sciences UNAM C.P. 62210 Cuernavaca Morelos Mexico Department of Mathematics Superior School of Physic and Mathematics National Polytechnical Institute IPN Zacatenco Mexico CityCP 07738 Mexico

The computational Algebraic Geometry applied in Algebraic Statistics;are beginning to exploring new branches and applications;in artificial intelligence and others areas. Currently, the development of the mathematics is very extensive and it is difficult to see the immediate application of few theorems in different areas, such as is the case of the Theorem 3.9 given in [10] and proved in part of here. Also this work has the intention to show the Hilbert basis as a powerful tool in data science;and for that reason we compile important results proved in works by, S. Watanabe [27], D. Cox, J. Little and H. Schenck [8], B. Sturmfels [16] and G. Ewald [10]. In this work we study, first, the fundamental concepts in Toric Algebraic Geometry. The principal contribution of this work is the application of Hilbert basis (as one realization of Theorem 3.9) for the resolution of singularities with toric varieties, and a background in Lattice Polytope. In the second part we apply this theorem to problems in statistical learning, principally in a recent area as is the Singular Learning Theory. We define the singular machines and the problem of Singular Learning through the computing of learning curves on these statistical machines. We review and compile results on the work of S. Watanabe in Singular Learning Theory, ref.;[17], [20], [21], also revising the important result in [26], about almost all Learning Machines are Singular, we formalize this theory with toric resolution morphism in a theorem proved here (Theorem 5.4), characterizing these Learning Machines as toric varieties, and we reproduce results previously published in Singular Statistical Learning seen in [19], [20], [23].MSC Codes 14M25, 52B20 Copyright © 2017, The Authors. All rights reserved.

关键词： Learning systems