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Nonlinear responses from the interaction of two progressing waves at an interface

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arXiv 2017年

作者： Hoop, Maarten D.E. Uhlmann, Gunther Wang, Yiran Computational and Applied Mathematics and Earth Science Rice University United States Department of Mathematics University of Washington United States Institute for Advanced Study Hong Kong University of Science and Technology Department of Mathematics University of Helsinki Hong Kong Department of Mathematics University of Washington United States

For scalar semilinear wave equations, we analyze the interaction of two (distorted) plane waves at an interface between media of different nonlinear properties. We show that new waves are generated from the nonlinear interactions, which might be responsible for the observed nonlinear effects in applications. Also, we show that the incident waves and the nonlinear responses determine the location of the interface and some information of the nonlinear properties of the media. In particular, for the case of a jump discontinuity at the interface, we can determine the magnitude of the jump. Copyright © 2017, The Authors. All rights reserved.

关键词： Wave equations

Estimation of groundwater storage from seismic data using deep learning

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arXiv 2018年

作者： Lähivaara, Timo Malehmir, Alireza Pasanen, Antti Kärkkäinen, Leo Huttunen, Janne M.J. Hesthaven, Jan S. Department of Applied Physics University of Eastern Finland Kuopio Finland Department of Earth Sciences Uppsala University Uppsala Sweden Geological Survey of Finland Kuopio Finland Nokia Bell Labs Espoo Finland Department of Electrical Engineering and Automation Aalto University Espoo Finland Computational Mathematics and Simulation Science Ecole Polytechnique Fédérale de Lausanne Lausanne Switzerland

We investigate the feasibility of employing convolutional neural networks to estimate the amount of groundwater stored in an aquifer and delineate water-table level from active-source seismic data. The seismic data to train and test the neural networks are obtained by solving wave propagation in a coupled poroviscoelastic-elastic media. A discontinuous Galerkin method is used to model wave propagation whereas a deep convolutional neural network is used for the parameter estimation problem. In the numerical experiment, the primary unknowns, the amount of stored groundwater and water-table level, are estimated, while the remaining parameters, assumed to be of less of interest, are successfully marginalized in the convolutional neural networks-based solution. This study, through synthetic data, illustrates the potential of deep learning methods to extract additional aquifer information from seismic data, which otherwise would be impossible based on a set of reflection seismic sections or velocity tomograms. Copyright © 2018, The Authors. All rights reserved.

关键词： Wave propagation

Integral equation formulation of the biharmonic Dirichlet problem

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arXiv 2017年

作者： Rachh, M. Askham, T. Applied Mathematics Program Yale University New HavenCT06511 United States Department of Applied Mathematics University of Washington SeattleWA98195-3925 United States

We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation can be used. Not all potentials for the Dirichlet problem correspond to a potential for Stokes flow, and vice-versa, but we show that the integral representation can be augmented and modified to handle either simply or multiply connected domains. The resulting integral representation has a kernel which behaves better on domains with high curvature than existing representations. Thus, this representation results in more robust computational methods for the solution of the Dirichlet problem of the biharmonic equation and we demonstrate this with several numerical examples.31A10, 31A30, 65R20, 65N99 Copyright © 2017, The Authors. All rights reserved.

关键词： Integral equations

First integrated implosion experiment of three-axis cylindrical hohlraum at the SGⅢ laser facility

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arXiv 2018年

作者： Kuang, Longyu Li, Hang Jiang, Shaoen Jing, Longfei Zheng, Jianhua Li, Liling Lin, Zhiwei Zhang, Lu Li, Yulong Liu, Xiangming Peng, Xiaoshi Tang, Qi Zhan, Xiayu Cao, Zhurong Wang, Qiangqiang Deng, Bo Deng, Keli Hou, Lifei Du, Huabing Jiang, Wei Chen, Zhongjing Yang, Dong Wang, Feng Yang, Jiamin Gao, Lin Zhang, Haijun Zhang, Juan Xie, Jun Yuan, Guanghui He, Zhibing Zhou, Wei Wang, Yuancheng Huang, Xiaoxia Chen, Xu Deng, Caibo Zhang, Baohan Zheng, Jian Ding, Yongkun Laser Fusion Research Center China Academy of Engineering Physics P.O.Box 919-986 Mianyang621900 China CAS Key Laboratory of Basic Plasma Physics Department of Modern Physics University of Science and Technology of China Hefei230026 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

The first integrated implosion experiment of three-axis cylindrical hohlraum (TACH) was accomplished at the SGIII laser facility. 24 laser beams of the SGIII laser facility were carefully chosen and quasi-symmetrically injected into the TACH, in which a highly symmetric radiation filed was generated with a peak radiation temperature of ~190eV. Driven by the radiation field, the neutron yield of a deuterium gas filled capsule reached ~1×109, and the corresponding yield over clean (YOC) was ~40% for a convergence ratio (Cr) of ~17. The X-ray self-emission image of imploded capsule cores was nearly round, and the backscatter fraction of laser beams was less than 1.25%. This experiment preliminarily demonstrated the major performance of TACH, such as the robustness of symmetry, and a laser plasma instability (LPI) behavior similar to that of the outer ring of traditional cylindrical hohlraum. Copyright © 2018, The Authors. All rights reserved.

关键词： Laser beams

QTT-isogeometric solver in two dimensions

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arXiv 2018年

作者： Markeeva, L. Tsybulin, I. Oseledets, I. Center for Computational and Data-Intensive Science and Engineering Skolkovo Institute of Science and Technology Moscow Russia Department of Applied Math and Control Moscow Institute of Physics and Technology Moscow Russia Laboratory of Fluid Dynamics and Seismics Moscow Institute of Physics and Technology Moscow Russia Institute of Numerical Mathematics Russian Academy of Sciences Moscow Russia

Holographic viscoelastic hydrodynamics

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arXiv 2018年

作者： Buchel, Alex Baggioli, Matteo Department of Applied Mathematics Department of Physics and Astronomy University of Western Ontario LondonONN6A 5B7 Canada Perimeter Institute for Theoretical Physics WaterlooONN2J 2W9 Canada Crete Center for Theoretical Physics Institute for Theoretical and Computational Physics Department of Physics University of Crete Heraklion71003 Greece

Relativistic fluid hydrodynamics, organized as an effective field theory in the velocity gradients, has zero radius of convergence due to the presence of non-hydrodynamic excitations. Likewise, the theory of elasticity of brittle solids, organized as an effective field theory in the strain gradients, has zero radius of convergence due to the process of the thermal nucleation of cracks. Viscoelastic materials share properties of both fluids and solids. We use holographic gauge theory/gravity correspondence to study all order hydrodynamics of relativistic viscoelastic media. Copyright © 2018, The Authors. All rights reserved.

关键词： Holography

A finite element method with strong mass conservation for Biot's linear consolidation model

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arXiv 2017年

作者： Kanschat, Guido Riviere, Beatrice Heidelberg University Heideberg Germany Department of Computational and Applied Mathematics Rice University HoustonTX77005 United States

An H(div) conforming finite element method for solving the linear Biot equations is analyzed. Formulations for the standard mixed method are combined with formulation of interior penalty discontinuous Galerkin method to obtain a consistent scheme. Optimal convergence rates are obtained.65M60, 74F10 Copyright © 2017, The Authors. All rights reserved.

关键词： Galerkin methods

Some analysis of the knockoff filter and its variants

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arXiv 2017年

作者： Chen, Jiajie Hou, Anthony Hou, Thomas Y. School of Mathematical Sciences Peking University Department of Statistics Harvard University Applied and Computational Mathematics Caltech United States

In many applications, we need to study a linear regression model that consists of a response variable and a large number of potential explanatory variables and determine which variables are truly associated with the response. In 2015, Barber and Candès introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and proved that this method achieves exact FDR control. In this paper, we provide some analysis of the knockoff filter and its variants. Based on our analysis, we propose a PCA prototype group selection filter that has exact group FDR control and several advantages over existing group selection methods for strongly correlated features. Another contribution is that we propose a new noise estimator that can be incorporated into the knockoff statistic from a penalized method without violating the exchangeability property. Our analysis also reveals that some knockoff statistics, including the Lasso path and the marginal correlation statistics, suffer from the alternating sign effect. To overcome this deficiency, we introduce the notion of a good statistic and propose several alternative statistics that take advantage of the good statistic property. Finally, we present a number of numerical experiments to demonstrate the effectiveness of our methods and confirm our analysis. Copyright © 2017, The Authors. All rights reserved.

关键词： Statistics

Therapeutic Anticoagulation Delays Death in COVID-19 Patients: Cross-Sectional Analysis of a Prospective Cohort

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TH Open

TH Open 2020年第3期04卷 e263-e270页

作者： Filip Ionescu Giovi Grasso-Knight Edward Castillo Ehsun Naeem Ioana Petrescu Zaid Imam Vishal K. Patel Mangala Narasimhan Girish B. Nair Department of Internal Medicine Beaumont Health System Royal Oak Oakland University William Beaumont School of Medicine Michigan United States Division of Pulmonary and Critical Care Medicine Beaumont Health System Royal Oak Oakland University William Beaumont School of Medicine Michigan United States Department of Radiation Oncology Beaumont Health System Royal Oak Oakland University William Beaumont School of Medicine Michigan United States Department of Computational and Applied Mathematics Rice University Texas United States Division of Pulmonary and Critical Care Medicine North Well New York New York United States

A hypercoagulable state has been described in coronavirus disease 2019 (COVID-19) patients. Others have reported a survival advantage with prophylactic anticoagulation (pAC) and therapeutic anticoagulation (tAC), but these retrospective analyses have important limitations such as confounding by indication. We studied the impact of tAC and pAC compared with no anticoagulation (AC) on time to death in COVID-19. We performed a cross-sectional analysis of 127 deceased COVID-19 patients and compared time to death in those who received tAC (

关键词： anticoagulation COVID 19 novel coronavirus heparin