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A Cut Finite Element Method for a Model of Pressure in Fractured Media

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arXiv 2020年

作者： Burman, Erik Hansbo, Peter Larson, Mats G. Department of Mathematics University College London LondonUK–WC1E 6BT United Kingdom Department of Mechanical Engineering Jönköping University JönköpingSE-55111 Sweden Department of Mathematics and Mathematical Statistics Umeå University UmeåSE-901 87 Sweden

We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion. Starting from a common background bulk mesh, that covers the domain, finite element spaces are constructed for the interface and bulk subdomains leading to efficient computations of the coupling terms. The crack pressure field also uses the bulk mesh for its representation. The interface conditions are a generalized form of conditions of Robin type previously considered in the literature which allows the modeling of a range of flow regimes across the fracture. The method is robust in the following way: 1. Stability of the formulation in the full range of parameter choices;and 2. Not sensitive to the location of the interface in the background mesh. We derive an optimal order a priori error estimate and present illustrating numerical examples. Copyright © 2020, The Authors. All rights reserved.

关键词： Mesh generation

A normal form for the onset of collapse: The prototypical example of the nonlinear schrödinger equation

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arXiv 2020年

作者： Chapman, S. Jon Kavousanakis, Mihalis E. Kevrekidis, I.G. Kevrekidis, P.G. Mathematical Institute University of Oxford AWB ROQ Woodstock Road OxfordOX2 6GG United Kingdom School of Chemical Engineering National Technical University of Athens Athens15780 Greece Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Department of Mathematics and Statistics University of Massachusetts AmherstMA01003-4515 United States

The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrödinger equation and systematically derive a normal form for the emergence of blowup solutions from stationary ones. While this is an extensively studied problem, such a normal form, based on the methodology of asymptotics beyond all algebraic orders, unifies both the dimension-dependent and power-law-dependent bifurcations previously studied;it yields excellent agreement with numerics in both leading and higher-order effects;it is applicable to both infinite and finite domains;and it is valid in all (subcritical, critical and supercritical) regimes. Copyright © 2020, The Authors. All rights reserved.

关键词： Nonlinear equations

SNAP – POP for Massive MIMO Systems

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SNAP – POP for Massive MIMO Systems

IEEE International Conference on Communications (ICC)

作者： Peter J. Smith Pawel A. Dmochowski Mark Hopper Harsh Tataria School of Mathematics and Statistics Victoria University of Wellington Wellington New Zealand School of Engineering and Computer Science Victoria University of Wellington Wellington New Zealand school of Mathematics University of Bristol Bristol U.K. Department of Electrical and Information Technology Lund University Lund Sweden

ISBN: (数字)9781728150895

ISBN: (纸本)9781728150901

Massive multiple-input multiple-output (MIMO) has gained a tremendous amount of attention as a key enabler of fifth-generation cellular systems. The majority of the vast literature on massive MIMO is based on fully digital processing, where each antenna element in the massive array is equipped with an up/down-conversion chain. Unlike previous works, we present a suite of greedy algorithms using pure analog processing which approach the performance of uplink digital zero-forcing (ZF) combining. Based on successive nulling and amplification processing (SNAP), the proposed techniques are evaluated in a multi-user context over a range of heterogeneous channel models. Rigorous comparisons are then made to other benchmark analog techniques, digital ZF and an upper bound on analog processing. The most promising approach is shown to have very low-complexity and robustness against a variety of channel conditions, while providing useful performance gains.

关键词： Interference Antennas MIMO communication Complexity theory Radio frequency Upper bound Signal to noise ratio

Origin and evolution of the multiply quantized vortex instability

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Physical Review Research 2022年第4期4卷 043104-043104页

作者： Sam Patrick August Geelmuyden Sebastian Erne Carlo F. Barenghi Silke Weinfurtner Department of Physics and Astronomy University of British Columbia Vancouver British Columbia Canada V6T 1Z1 Institute of Quantum Science and Engineering Texas A&M University College Station Texas 77840 USA School of Mathematical Sciences University of Nottingham University Park Nottingham NG7 2RD United Kingdom Vienna Center for Quantum Science and Technology Atominstitut TU Wien Stadionallee 2 1020 Vienna Austria Joint Quantum Centre Durham-Newcastle School of Mathematics Statistics and Physics Newcastle University Newcastle upon Tyne NE1 7RU United Kingdom Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems University of Nottingham Nottingham NG7 2RD United Kingdom

We show that the dynamical instability of quantum vortices with more than a single unit of circulation results from a superradiant bound state inside the vortex core. We then reveal a striking behavior of the system in the nonlinear regime. Counter to the expectation that the instability should produce well-separated vortices, the system evolves into a bound state of corotating singularities orbiting within a few healing lengths of each other, undergoing modulations in separation. During these modulations, kinetic energy is traded back and forth between sound waves and vortical degrees of freedom.

关键词： Vortices in superfluids Bose-Einstein condensates Quantum fluids & solids Superfluids Semiclassical methods

TEAM: TRIANGULAR-MESH ADAPTIVE AND MULTISCALE PROTON SPOT GENERATION METHOD

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International Journal of Particle Therapy

International Journal of Particle Therapy 2024年 12卷

作者： Chao Wang Bowen Lin Yuting Lin Suzanne M. Shontz Weizhang Huang Ronald Chen Hao Gao Department Of Radiation Oncology University of Kansas Medical Center Kansas City United States of America Department Of Intervention Medicine The Second Hospital of Shandong University Jinan China Department Of Electrical Engineering And Computer Science Institute For Information Sciences Bioengineering Program University of Kansas Lawrence United States of America Department Of Mathematics University of Kansas Lawrence United States of America

Reconfigurable curved metasurface for acoustic cloaking and illusion

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Physical Review B 2020年第2期101卷 024104-024104页

作者： Shi-Wang Fan Sheng-Dong Zhao Liyun Cao Yifan Zhu A-Li Chen Yan-Feng Wang Krupali Donda Yue-Sheng Wang Badreddine Assouar Institute of Engineering Mechanics Beijing Jiaotong University Beijing 100044 China Institut Jean Lamour CNRS Université de Lorraine Nancy 54000 France School of Mathematics and Statistics Qingdao University Qingdao 266071 China Department of Mechanics School of Mechanical Engineering Tianjin University Tianjin 300350 China

A severe limitation of current acoustic metasurfaces remains in their modest tunability to meet multifrequency requirements and alterable functionalities on demand. Here, a reconfigurable curved acoustic metasurface for acoustic cloaking and illusion is reported. The structure is composed of an array of tunable helical units to break this limitation and realize continuously versatile sound manipulations. We theoretically, numerically and experimentally investigate the channel length represented by the helical depth, which is used to achieve full 2π phase shift continuously over the frequency range from 2 to 7 kHz. As pragmatic examples, we present by full-wave numerical simulations the concept of a curved metasurface for the continuously tunable acoustic multifunction, including broadband carpet cloaking and ground illusion at a wide working band. Then, we experimentally demonstrate these functionalities by showing an excellent effect to restore the disturbed reflective field from a cloaked object or to mimic an arbitrary shaped ground.

关键词： Acoustic measurements Acoustic metamaterials Cloaking Finite-element method

Classification of datasets with imputed missing values: does imputation quality matter?

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arXiv 2022年

作者： Shadbahr, Tolou Roberts, Michael Stanczuk, Jan Gilbey, Julian Teare, Philip Dittmer, Sören Thorpe, Matthew Torné, Ramon Viñas Sala, Evis Lió, Pietro Patel, Mishal Rudd, James H.F. Mirtti, Tuomas Rannikko, Antti Sakari Aston, John A.D. Tang, Jing Schönlieb, Carola-Bibiane Selby, Ian Breger, Anna Weir-McCall, Jonathan R. Gkrania-Klotsas, Effrossyni Korhonen, Anna Jefferson, Emily Langs, Georg Yang, Guang Prosch, Helmut Preller, Jacobus Stanczuk, Jan Babar, Judith Sánchez, Lorena Escudero Wassin, Marcel Holzer, Markus Walton, Nicholas Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Data Science & Artificial Intelligence AstraZeneca Cambridge United Kingdom Department of Mathematics University of Manchester Manchester United Kingdom Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom Department of Radiology University of Cambridge Cambridge United Kingdom Clinical Pharmacology & Safety Sciences AstraZeneca Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pathology University of Helsinki Helsinki University Hospital Finland iCAN-Digital Precision Cancer Medicine Flagship Helsinki Finland Department of Urology University of Helsinki Helsinki University Hospital Helsinki Finland Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Faculty of Mathematics University of Vienna Austria Royal Papworth Hospital Cambridge Royal Papworth Hospital NHS Foundation Trust Cambridge United Kingdom Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Language Technology Laboratory University of Cambridge Cambridge United Kingdom Population Health and Genomics School of Medicine University of Dundee Dundee United Kingdom Department of Biomedical Imaging and Image-guided Therapy Computational Imaging Research Lab Medical University of Vienna Vienna Austria National Heart and Lung Institute Imperial College London London United Kingdom Contextflow GmbH Vienna Austria Institute of Astronomy University of Cambridge Cambridge United Kingdom

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data. All code and data used in this paper are also released publicly at [inserted upon publication]. © 2022, CC BY.

关键词： Classification (of information)

Finite element approximation of steady flows of colloidal solutions

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arXiv 2021年

作者： Bonito, Andrea Girault, Vivette Guignard, Diane Rajagopal, Kumbakonam R. Süli, Endre Texas A&M University Department of Mathematics 3368 TAMU College StationTX77843-3368 United States ParisF-75005 France University of Ottawa Department of Mathematics and Statistics 150 Louis-Pasteur Pvt OttawaONK1N 6N5 Canada Texas A&M University Department of Mechanical Engineering College StationTX77843-3123 United States Mathematical Institute University of Oxford Andrew Wiles Building Woodstock Road OxfordOX2 6GG United Kingdom

We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity gradient is assumed to be a monotone nonlinear function of the deviatoric part of the Cauchy stress tensor. We prove the existence of a weak solution to the problem, and under the additional assumption that the nonlinearity involved in the constitutive relation is Lipschitz continuous we also prove uniqueness of the weak solution. We then construct mixed finite element approximations of the system using both conforming and nonconforming finite element spaces. For both of these we prove the convergence of the method to the unique weak solution of the problem, and in the case of the conforming method we provide a bound on the error between the analytical solution and its finite element approximation in terms of the best approximation error from the finite element spaces. We propose first a Lions-Mercier type iterative method and next a classical fixed-point algorithm to solve the finite-dimensional problems resulting from the finite element discretisation of the system of nonlinear partial differential equations under consideration and present numerical experiments that illustrate the practical performance of the proposed numerical method. Copyright © 2021, The Authors. All rights reserved.

关键词： Stress tensor

Bond graphs unify stoichiometric analysis and thermodynamics

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arXiv 2020年

作者： Gawthrop, Peter J. Systems Biology Laboratory Department of Biomedical Engineering Melbourne School of Engineering University of Melbourne Victoria3010 Australia Systems Biology Laboratory School of Mathematics and Statistics University of Melbourne University of Melbourne Victoria3010 Australia

Whole-cell modelling is constrained by the laws of nature in general and the laws of thermodynamics in particular. This paper shows how one prolific source of information, stoichiometric models of biomolecular systems, can be integrated with thermodynamic principles using the bond graph approach to network thermodynamics. Copyright © 2020, The Authors. All rights reserved.

关键词： Thermodynamics