Nonlinear Partial Differential Equations in Applied Mathematics
应用数学中的非线性偏微分方程
基本信息
- 批准号:9704155
- 负责人:
- 金额:$ 9.82万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:1997
- 资助国家:美国
- 起止时间:1997-08-01 至 2000-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
9704155 Hunter The proposal is to study a number of nonlinear partial differential equations which model various physical and biological systems. The first equation is a free-boundary value problem which models the deposition of surfactant on a surface by a liquid droplet. There is a complex interaction between the motion of the droplet on the surface and the deposition of surfactant. The second equation is a system of reaction-diffusion equations which models an islet of beta-cells in the pancreas. The aim of Professor Hunter's research is to understand the collective dynamics of the beta-cells and the formation of spatial patterns in an islet. The third equation is a two dimensional Burgers equation which models the diffraction and reflection of weak shock waves in two space dimensions, where there are longstanding discrepancies between theory and experiment. The fourth equation is a modulation equation which describes the propagation of nonlinear gravitational waves in Einstein's theory of general relativity. Professor Hunter proposes to study this equation with the aim of understanding the formation of space-time singularities in a nonlinear gravitational wave. Mathematical models of physical and biological systems provide a way to understand, predict, and control the behavior of those systems. The proposed research involves the study of a number of mathematical models of systems of importance in engineering, biology, and basic science. One model describes the deposition of surfactant on a surface by droplets. Surface deposition has many applications in materials science, including the printing of very small structures on surfaces for the control of fluids, and as an experimental means of preparing liquid crystal display screens. A second model describes the collective behavior of beta-cells in the pancreas. These cells produce insulin and play a central role in diseases like diabetes. A third model describes the propagation of shock waves, which are generated by transonic or supersonic aircraft, in turbines, and in many other high-speed fluid flows. The mathematical theory of shock waves remains very poorly understood. The fourth model is a set of equations which describe the propagation of nonlinear gravitational waves in Einstein's general theory of relativity. The general theory of relativity is the fundamental physical theory of gravity, and it describes the large scale cosmological structure of the universe. The main obstacle to understanding the predictions of the theory is the nonlinearity of the Einstein equations. This work is directed towards an increased understanding of the effects of this nonlinearity.
9704155 猎人 该建议是研究一些非线性偏微分方程,模拟各种物理和生物系统。 第一个方程是一个自由边界值问题,它模拟了表面活性剂通过液滴在表面上的沉积。 液滴在表面的运动与表面活性剂的沉积之间存在着复杂的相互作用。第二个方程是反应扩散方程组,其模拟胰腺中的胰岛β细胞。亨特教授的研究目的是了解β细胞的集体动力学和胰岛中空间模式的形成。 第三个方程是二维Burgers方程,它模拟了弱激波在二维空间中的衍射和反射,其中理论和实验之间存在长期的差异。 第四个方程是一个调制方程,它描述了爱因斯坦广义相对论中的非线性引力波的传播。亨特教授提出研究这个方程,目的是了解非线性引力波中时空奇点的形成。 物理和生物系统的数学模型提供了一种理解、预测和控制这些系统行为的方法。拟议中的研究涉及一些数学模型的重要性,在工程,生物学和基础科学系统的研究。一种模型描述了表面活性剂通过液滴在表面上的沉积。 表面沉积在材料科学中有许多应用,包括在表面上印刷非常小的结构以控制流体,以及作为制备液晶显示屏的实验手段。第二个模型描述了胰腺中β细胞的集体行为。这些细胞产生胰岛素,并在糖尿病等疾病中发挥核心作用。第三个模型描述了跨音速或超音速飞机、涡轮机和许多其他高速流体流动中产生的冲击波的传播。 冲击波的数学理论仍然知之甚少。第四个模型是爱因斯坦广义相对论中描述非线性引力波传播的一组方程。 广义相对论是引力的基本物理理论,它描述了宇宙的大尺度宇宙学结构。 理解该理论预言的主要障碍是爱因斯坦方程的非线性。 这项工作是针对增加了解这种非线性的影响。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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John Hunter其他文献
matplotlib/matplotlib: REL: v3.4.0rc1
matplotlib/matplotlib:相对:v3.4.0rc1
- DOI:
10.5281/zenodo.4550144 - 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
Thomas A Caswell;Michael Droettboom;Antony Lee;Elliott Sales de Andrade;John Hunter;Tim Hoffmann;Eric Firing;Jody Klymak;David Stansby;Nelle Varoquaux;Jens Hedegaard Nielsen;Benjamin Root;Ryan May;Phil Elson;Jouni K. Seppänen;Darren Dale;Jae;Damon McDougall;Andrew D. Straw;Paul Hobson;Christoph Gohlke;Tony S Yu;Eric Ma;Adrien F. Vincent;Hannah;Steven Silvester;Charlie Moad;Nikita Kniazev;Elan Ernest;P. Ivanov - 通讯作者:
P. Ivanov
31st Annual Meeting and Associated Programs of the Society for Immunotherapy of Cancer (SITC 2016): late breaking abstracts
- DOI:
10.1186/s40425-016-0191-4 - 发表时间:
2016-12-01 - 期刊:
- 影响因子:10.600
- 作者:
Sonja Althammer;Keith Steele;Marlon Rebelatto;Tze Heng Tan;Tobias Wiestler;Guenter Schmidt;Brandon Higgs;Xia Li;Li Shi;Xiaoping Jin;Joyce Antal;Ashok Gupta;Koustubh Ranade;Gerd Binning;Joaquim Bellmunt;Ronald de Wit;David J. Vaughn;Yves Fradet;Jae Lyun Lee;Lawrence Fong;Nicholas J. Vogelzang;Miguel A. Climent;Daniel P. Petrylak;Toni K. Choueiri;Andrea Necchi;Winald Gerritsen;Howard Gurney;David I. Quinn;Stéphane Culine;Cora N. Sternberg;Yabing Mai;Markus Puhlmann;Rodolfo F. Perini;Dean F. Bajorin;Padmanee Sharma;Margaret K. Callahan;Emiliano Calvo;Joseph W. Kim;Filipo de Braud;Patrick A. Ott;Petri Bono;Rathi N. Pillai;Michael Morse;Dung T. Le;Matthew Taylor;Pavlina Spilliopoulou;Johanna Bendell;Dirk Jaeger;Emily Chan;Scott J. Antonia;Paolo A. Ascierto;Delphine Hennicken;Marina Tschaika;Alex Azrilevich;Jonathan Rosenberg;Ofer Levy;Christopher Chan;Gady Cojocaru;Spencer Liang;Eran Ophir;Sudipto Ganguly;Amir Toporik;Maya Kotturi;Tal Fridman Kfir;Benjamin M. Murter;Kathryn Logronio;Liat Dassa;Ling Leung;Shirley Greenwald;Meir Azulay;Sandeep Kumar;Zoya Alteber;Xiaoyu Pan;Arthur Machlenkin;Yair Benita;Andrew W. Drake;Ayelet Chajut;Ran Salomon;Ilan Vankin;Einav Safyon;John Hunter;Zurit Levine;Mark White;Rom Leidner;Hyunseok Kang;Robert Haddad;Neil H. Segal;Lori J. Wirth;Robert L. Ferris;F. Stephen Hodi;Rachel E. Sanborn;Thomas F. Gajewski;William Sharfman;Dan McDonald;Shivani Srivastava;Xuemin Gu;Penny Phillips;Chaitali Passey;Tanguy Seiwert;Tsadik Habtetsion;Gang Zhou;Donastas Sakellariou-Thompson;Cara Haymaker;Caitlin Creasy;Mark Hurd;Naohiro Uraoka;Jaime Rodriguez Canales;Scott Koptez;Patrick Hwu;Anirban Maitra;Chantale Bernatchez;Scott M. Coyle;Kole T. Roybel;Levi J. Rupp;Stephen P. Santoro;Stephanie Secrest;Michael Spelman;Hanson Ho;Tina Gomes;Tiffany Tse;Chia Yung-Wu;Jack Taunton;Wendell Lim;Peter Emtage;Tarsem Moudgil;Carmen Ballesteros-Merino;Traci Hilton;Christopher Paustian;Rom Leidner;David Page;Walter Urba;Bernard Fox;Bryan Bell;Ashish Patel;Tove Olafsen;Daulet Satpayev;Michael Torgov;Filippo Marchioni;Jason Romero;Ziyue Karen Jiang;Charles Zamilpa;Jennifer S. Keppler;Alessandro Mascioni;Fang Jia;Chen-Yu Lee;Jean Gudas;Ryan J. Sullivan;Yujin Hoshida;Theodore Logan;Nikhil Khushalani;Anita Giobbie-Hurder;Kim Margolin;Joanna Roder;Rupal Bhatt;Henry Koon;Thomas Olencki;Thomas Hutson;Brendan Curti;Shauna Blackmon;James W. Mier;Igor Puzanov;Heinrich Roder;John Stewart;Asim Amin;Marc S. Ernstoff;Joseph I. Clark;Michael B. Atkins;Howard L. Kaufman;Jeffrey Sosman;Sabina Signoretti;David F. McDermott;Abraham A. Anderson;Igor Puzanov;Mohammed M. Milhem;Robert H. I. Andtbacka;David Minor;Kevin S. Gorski;Daniel M. Baker;Omid Hamid;Howard L. Kaufman;Emmanuel Akporiaye;Brendan Curti;Yoshinobu Koguchi;Rom Leidner;Kim Sutcliffe;Kristie Conder;Walter Urba;Thomas Marron;Nina Bhardwaj;Linda Hammerich;Fiby George;Seunghee Kim-Schulze;Tibor Keler;Tom Davis;Elizabeth Crowley;Andres Salazar;Joshua Brody;Arta Monjazeb;Megan E. Daly;Jonathan Riess;Tianhong Li;William J. Murphy;Karen Kelly;Zhiwei Hu;Rulong Shen;Amanda Campbell;Elizabeth McMichael;Lianbo Yu;Bhuvaneswari Ramaswam;Cheryl A. London;Tian Xu;William Carson;Kathleen M. Kokolus;Elizabeth A. Repasky;Todd D. Schell;Joseph D. Drabick;David J. Messenheimer;Shawn Jensen;Bernard Fox;Mark Rubinstein;Kristina Andrijauskaite;Marzena Swiderska-syn;Kristin Lind;Agnes Choppin;Marina K. Roell;John Wrangle;Kristina Andrijauskaite;Marzena Swiderska-syn;Peter Rhode;Hing Wong;Mark Rubinstein;Shamim Ahmad;Mason Webb;Rasha Abu-Eid;Rajeev Shrimali;Vivek Verma;Atbin Doroodchi;Zuzana Berrong;David Yashar;Raed Samara;Mikayel Mkrtichyan;Samir Khleif;Steven Powell;Mark Gitau;Christopher Sumey;Andrew Terrell;Michele Lohr;Ryan K. Nowak;Steven McGraw;Ash Jensen;Miran Blanchard;Kathryn A. Gold;Ezra E. W. Cohen;Christie Ellison;Lora Black;John Lee;William Chad Spanos;Erik Wennerberg;Emily Schwitzer;Claire Lhuillier;Graeme Koelwyn;Rebecca Hiner;Lee Jones;Sandra Demaria;Vandeveer Amanda;John W. Greiner;Jeffrey Schlom;Michelle Bookstaver;Christopher M. Jewell;Christopher Paustian;Andrew Gunderson;Brian Boulmay;Rui Li;Bradley Spieler;Kyle Happel;Tarsem Moudgil;Zipei Feng;Carmen Ballesteros-Merino;Christopher Dubay;Brenda Fisher;Yoshinobu Koguchi;Sandra Aung;Eileen Mederos;Carlo B. Bifulco;Michael McNamara;Keith Bahjat;William Redmond;Augusto Ochoa;Hong-Ming Hu;Adi Mehta;Fridtjof Lund-Johansen;Bernard Fox;Walter Urba;Rachel E. Sanborn;Traci Hilton;Frank Bedu-Addo;Greg Conn;Michael King;Panna Dutta;Robert Shepard;Mark Einstein;Sylvia Adams;Ena Wang;Ping Jin;Yelena Novik;Debra Morrison;Ruth Oratz;Franco M. Marincola;David Stroncek;Judith Goldberg;Sandra Demaria;Silvia C. Formenti;Jérôme Galon;Bernhard Mlecnik;Florence Marliot;Fang-Shu Ou;Carlo B. Bifulco;Alessandro Lugli;Inti Zlobec;Tilman T. Rau;Iris D. Nagtegaal;Elisa Vink-Borger;Arndt Hartmann;Carol Geppert;Michael H. Roehrl;Prashant Bavi;Pamela S. Ohashi;Julia Y. Wang;Linh T. Nguyen;SeongJun Han;Heather L. MacGregor;Sara Hafezi-Bakhtiari;Bradley G. Wouters;Yutaka Kawakami;Boryana Papivanova;Mingli Xu;Tomonobu Fujita;Shoichi Hazama;Nobuaki Suzuki;Hiroaki Nagano;Kiyotaka Okuno;Kyogo Itoh;Eva Zavadova;Michal Vocka;Jan Spacek;Lubos Petruzelka;Bohuslav Konopasek;Pavel Dundr;Helena Skalova;Toshihiko Torigoe;Noriyuki Sato;Tomohisa Furuhata;Ichiro Takemasa;Marc Van den Eynde;Anne Jouret-Mourin;Jean-Pascal Machiels;Tessa Fredriksen;Lucie Lafontaine;Bénédicte Buttard;Sarah Church;Pauline Maby;Helen Angell;Mihaela Angelova;Angela Vasaturo;Gabriela Bindea;Anne Berger;Christine Lagorce;Prabhu S. Patel;Hemangini H. Vora;Birva Shah;Jayendrakumar B. Patel;Kruti N. Rajvik;Shashank J. Pandya;Shilin N. Shukla;Yili Wang;Guanjun Zhang;Giuseppe V. Masucci;Emilia K. Andersson;Fabio Grizzi;Luigi Laghi;Gerardo Botti;Fabiana Tatangelo;Paolo Delrio;Gennaro Cilberto;Paolo A. Ascierto;Franco Marincola;Daniel J. Sargent;Bernard A. Fox;Alain Algazi;Katy Tsai;Michael Rosenblum;Prachi Nandoskar;Robert H. I. Andtbacka;Amy Li;John Nonomura;Kathryn Takamura;Mary Dwyer;Erica Browning;Reneta Talia;Chris Twitty;Sharron Gargosky;Jean Campbell;Carmen Ballesteros-Merino;Carlo B. Bifulco;Bernard Fox;Mai Le;Robert H. Pierce;Adil Daud;Robyn Gartrell;Douglas Marks;Edward Stack;Yan Lu;Daisuke Izaki;Kristen Beck;Dan Tong Jia;Paul Armenta;Ashley White-Stern;Yichun Fu;Zoe Blake;Howard L. Kaufman;Bret Taback;Basil Horst;Yvonne M. Saenger;Steven Leonardo;Keith Gorden;Ross B. Fulton;Kathryn Fraser;Takashi O. Kangas;Richard Walsh;Kathleen Ertelt;Jeremy Graff;Mark Uhlik;Jennifer S. Sims;Liang Lei;Takashi Tsujiuchi;Jeffrey N. Bruce;Peter Canoll;Anthony W Tolcher;Evan W Alley;Gurunadh Chichili;Jan E Canoll;Paul Moore;Ezio Bonvini;Syd Johnson;Sadhna Shankar;James Vasselli;Jon Wigginton;John Powderly - 通讯作者:
John Powderly
matplotlib/matplotlib v3.1.3
matplotlib/matplotlib v3.1.3
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Thomas A Caswell;Michael Droettboom;Antony Lee;John Hunter;Eric Firing;David Stansby;J. Klymak;Tim Hoffmann;Elliott Sales de Andrade;Nelle Varoquaux;Jens Hedegaard Nielsen;Benjamin Root;Phil Elson;Ryan May;Darren Dale;Jae;Jouni K. Seppänen;Damon McDougall;Andrew D. Straw;Paul Hobson;Christoph Gohlke;Tony S Yu;Eric Ma;Adrien F. Vincent;Steven Silvester;Charlie Moad;Nikita Kniazev;P. Ivanov;Elan Ernest;Jan Katins - 通讯作者:
Jan Katins
Origin and growth of cysts of the jaws.
颌骨囊肿的起源和生长。
- DOI:
- 发表时间:
1967 - 期刊:
- 影响因子:1.4
- 作者:
Paul Toiler;John Hunter - 通讯作者:
John Hunter
Co-Designing Research for Sustainable Food Systems and Diets with Aboriginal Communities: A Study Protocol
与原住民社区共同设计可持续粮食系统和饮食研究:研究方案
- DOI:
10.3390/ijerph21030298 - 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
C. Lopes;S. Mihrshahi;John Hunter;R. Ronto;Renee Cawthorne - 通讯作者:
Renee Cawthorne
John Hunter的其他文献
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{{ truncateString('John Hunter', 18)}}的其他基金
DISSERTATION RESEARCH: The Evolution of the Hypocone in Microbats (Microchiroptera)
论文研究:微型蝙蝠(Microchiroptera)下锥体的进化
- 批准号:
1401775 - 财政年份:2014
- 资助金额:
$ 9.82万 - 项目类别:
Standard Grant
Quasi-linear hyperbolic and surface waves
准线性双曲波和表面波
- 批准号:
1312342 - 财政年份:2013
- 资助金额:
$ 9.82万 - 项目类别:
Standard Grant
Nonlinear hyperbolic waves and interfaces
非线性双曲波和界面
- 批准号:
1009538 - 财政年份:2010
- 资助金额:
$ 9.82万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Multi-Dimensional Problems for the Euler Equations of Compressible Fluid Flow and Related Problems in Hyperbolic Conservation Laws
FRG:合作研究:可压缩流体流动欧拉方程的多维问题及双曲守恒定律中的相关问题
- 批准号:
0243622 - 财政年份:2003
- 资助金额:
$ 9.82万 - 项目类别:
Standard Grant
Mathematical Sciences: Nonlinear Hyperbolic Waves
数学科学:非线性双曲波
- 批准号:
9404152 - 财政年份:1994
- 资助金额:
$ 9.82万 - 项目类别:
Continuing Grant
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Graphon mean field games with partial observation and application to failure detection in distributed systems
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Partial EIV 模型参数估计理论及其在测量数据处理中的应用研究
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图的l1-嵌入性以及partial立方图和多重median图的刻画
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- 批准年份:2012
- 资助金额:45.0 万元
- 项目类别:地区科学基金项目
相似海外基金
Conference: Recent advances in nonlinear Partial Differential Equations
会议:非线性偏微分方程的最新进展
- 批准号:
2346780 - 财政年份:2024
- 资助金额:
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Nonlinear Stochastic Partial Differential Equations and Applications
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- 批准号:
2307610 - 财政年份:2023
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2246031 - 财政年份:2023
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Toward a global analysis on solutions of nonlinear partial differential equations
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23K03165 - 财政年份:2023
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Topics in the Analysis of Nonlinear Partial Differential Equations
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- 批准号:
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- 资助金额:
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- 批准号:
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Expressivity of Structure-Preserving Deep Neural Networks for the Space-Time Approximation of High-Dimensional Nonlinear Partial Differential Equations with Boundaries
保结构深度神经网络的表达能力用于高维非线性有边界偏微分方程的时空逼近
- 批准号:
2318032 - 财政年份:2023
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非线性椭圆偏微分方程解的奇异性和结构
- 批准号:
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