ボーウェン マーク
准教授 (https://researchmap.jp/read0155708/)
(国際理工学センター)
政治経済学術院(政治経済学部)
兼任研究員 2018年-
博士
Mark Bowen, T. P. Witelski
European Journal of Applied Mathematics査読有り2018年-
Mark Bowen, B. Tilley
Physics of Fluids査読有り25(10)p.1021052013年-
Mark Bowen, J. R. King
Journal of Engineering Mathematics査読有り80(1)p.39 - 622013年-
Mark Bowen, B. Tilley
Physics of Fluids査読有り24(3)p.0321062012年-
Mark Bowen, T. P. Witelski
SIAM Journal of Applied Mathematics査読有り66(5)p.1727 - 17482006年-
B. Tilley, Mark Bowen
Journal of Fluid Mechanics査読有り541p.399 - 4082005年-
Mark Bowen, J. Sur, A. L. Bertozzi, R. P. Behringer
Physica D: Nonlinear Phenomena査読有り209p.36 - 482005年-
JB van den Berg, Mark Bowen, J R King, M M A El-Sheikh
European Journal of Applied Mathematics査読有り15(3)p.329 - 3462004年-
TP Witelski, Mark Bowen
Applied Numerical Mathematics査読有り45p.331 - 3512003年-
J R King, Mark Bowen
European Journal of Applied Mathematics査読有り12(3)p.321 - 3562001年-
Mark Bowen, J R King
European Journal of Applied Mathematics査読有り12(2)p.135 - 1572001年-
J Hulshof, J R King and Mark Bowen
Advances in Differential Equations査読有り6(9)p.1115 - 11522001年-
J Hulshof, J R King and Mark Bowen
SIAM Journal on Applied Mathematics査読有り62(1)p.149 - 1792001年-
AL Bertozzi, Mark Bowen
Modern Methods in Scientific Computing and Applications査読有りp.31 - 792002年-
Bowen, Mark;Tilley, B. S.
PHYSICS OF FLUIDS24(3)2012年-2012年
ISSN:1070-6631
Bowen, Mark;King, John R.
JOURNAL OF ENGINEERING MATHEMATICS80(1)p.39 - 622013年-2013年
ISSN:0022-0833
Witelski, Thomas; Bowen, Mark
Methods of Mathematical Modelling: Continuous Systems and Differential Equationsp.1 - 3052015年09月-2015年09月
概要:© Springer International Publishing Switzerland 2015. All rights are reserved. This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
(共著)
Springer2015年-
研究種別:
Self-similar behaviour in thin film flow2012年-0月-2014年-0月
配分額:¥910000
2017年度共同研究者:T. P. Witelski
研究成果概要:Working with Professor T. P. Witekski (Duke University, USA), we mathematically investigated the dynamics of a thin...Working with Professor T. P. Witekski (Duke University, USA), we mathematically investigated the dynamics of a thin liquid film draining from the edge of a (constrained) domain. Such problems frequently arise in industrial coating processes where domains are of finite extent.This work has now been published in EJAM (European Journal of Applied Mathematics):Pressure-dipole solutions of the thin-film equationM. BOWEN and T. P. WITELSKI European Journal of Applied Mathematicshttps://doi.org/10.1017/S095679251800013XPublished online: 02 April 2018
2014年度共同研究者:Burt Tilley
研究成果概要:An understanding of the dynamics of liquid jets is important in many applications such as in inkjet printing, for e...An understanding of the dynamics of liquid jets is important in many applications such as in inkjet printing, for example. Working with an international collaborator, we have been analytically and computationally investigating how externally applied temperature gradients can be used to better control (from the point-of-view of application to inkjet printers) both the printing speed and resolution.We have developed advanced computational methods that are capable of following the jet dynamics over many different length and time scales; we are also considering the application of parallelisation to the computations in order to improve the time taken for the simulations to run.The computations support additional analytical results, allowing us to understand, in particular, the approach to rupture of the jets (separation into droplets) and also how to control the initial instability of a uniform jet that leads to rupture.
2016年度共同研究者:T. P. Witelski
研究成果概要:We have considered self-similar sign-changing solutions to the thin-film equation on a semi-infinite domain with ze...We have considered self-similar sign-changing solutions to the thin-film equation on a semi-infinite domain with zero-pressure-type boundary conditions imposed at the fixed boundary. In particular, we have identified classes of both first- and second-kind compactly supported self-similar solutions and have explained how these solutions interact as parameters vary.
2018年度共同研究者:L. Smolka, T. P. Witelski
研究成果概要:1) Working with Professor T P Witelski (Duke University, USA), we have been studying out-diffusion solutions of the...1) Working with Professor T P Witelski (Duke University, USA), we have been studying out-diffusion solutions of the so-called thin film equation (a fourth order parabolic partial differential equation) on a finite multi-dimensional domain; this extends our recent previous work on the one-dimensional problem.While considering this problem, we decided first to make a preliminary study of the related problem for the lower (second) order porous medium equation. In this context, we have constructed analytically self-similar solutions that act as large time attractors for solutions defined on sectorial [quarter, half-plane and three-quarter-plane] domains. We have confirmed these results using numerical simulations.2) While working on this project, I established a new working relationship with Professor L. Smolka (Bucknell University, USA) looking at how thin films evolve in a periodic domain (corresponding physically to the external surface of a cylinder) under the combined effects of gravity (drainage) and thermal stresses (leading to a non-convex convective flux of fluid). The interaction of convective effects and surface tension (fourth order parabolic terms) yields solutions containing non-classical shock dynamics, such as undercompressive-compressive shock pairs and undercompressive shocks-rarefaction fans. We are currently writing up the results of this research for publication in the near future.
2019年度
研究成果概要:We have been analytically and computationally investigating the motion of a monolayer thin film (tether) held betwe...We have been analytically and computationally investigating the motion of a monolayer thin film (tether) held between two quasi-steady masses. The monolayer tether is assumed to be stretched by an externally imposed symmetric stagnation point flow and interesting dynamics arise due to the competition between surface tension and convective flow. In particular, we have been interested in whether the tether breaks in finite time and how such rupture occurs.Mathematical modelling of this phenomena leads to a higher-order non-autonomous nonlinear diffusion-convection equation containing a parameter that takes different values depending on the thickness of the monolayer film.We have analysed the behaviour of the evolution equation for general values of the parameter and have identified that for large enough values of the parameter rupture of the tether does not occur in finite time.We are now writing this research up for publication in the near future.
2015年度共同研究者:Thomas Witelski
研究成果概要:Working with an international collaborator, I have investigated the dynamics of a thin liquid film draining off of ...Working with an international collaborator, I have investigated the dynamics of a thin liquid film draining off of one edge of a flat substrate. Such a scenario frequently arises in the natural sciences, engineering and industry. We have also extended these results to the (non-physical) case where the solution (corresponding to film height) can change sign. The analytical results are supported by detailed numerical calculations.
科目名 | 開講学部・研究科 | 開講年度 | 学期 |
---|---|---|---|
Calculus A 01 | 政治経済学部 | 2021 | 秋クォーター |
Calculus B 01 | 政治経済学部 | 2021 | 冬クォーター |
Calculus C 01 | 政治経済学部 | 2021 | 春クォーター |
Calculus A | 基幹理工学部 | 2021 | 秋学期 |
Calculus A | 創造理工学部 | 2021 | 秋学期 |
Calculus A | 先進理工学部 | 2021 | 秋学期 |
Calculus B | 基幹理工学部 | 2021 | 春学期 |
Calculus B | 創造理工学部 | 2021 | 春学期 |
Calculus B | 先進理工学部 | 2021 | 春学期 |
Partial Differential Equations | 基幹理工学部 | 2021 | 春学期 |
Partial Differential Equations | 創造理工学部 | 2021 | 春学期 |
Partial Differential Equations | 先進理工学部 | 2021 | 春学期 |
Research Project B | 基幹理工学部 | 2021 | 春学期 |
Research Project B 【S Grade】 | 基幹理工学部 | 2021 | 春学期 |
Research Project C | 基幹理工学部 | 2021 | 秋学期 |
Research Project C 【S Grade】 | 基幹理工学部 | 2021 | 秋学期 |
Research Project A | 基幹理工学部 | 2021 | 秋学期 |
Research Project D | 基幹理工学部 | 2021 | 春学期 |
Calculus A (1) | 基幹理工学部 | 2021 | 秋クォーター |
Calculus A (1) | 創造理工学部 | 2021 | 秋クォーター |
Calculus A (1) | 先進理工学部 | 2021 | 秋クォーター |
Calculus B (1) | 基幹理工学部 | 2021 | 冬クォーター |
Calculus B (1) | 創造理工学部 | 2021 | 冬クォーター |
Calculus B (1) | 先進理工学部 | 2021 | 冬クォーター |
Calculus C (1) | 基幹理工学部 | 2021 | 春クォーター |
Calculus C (1) | 創造理工学部 | 2021 | 春クォーター |
Calculus C (1) | 先進理工学部 | 2021 | 春クォーター |
Survey of Modern Mathematical Sciences B | 基幹理工学部 | 2021 | 春クォーター |
Survey of Modern Mathematical Sciences B [S Grade] | 基幹理工学部 | 2021 | 春クォーター |
Research Project Spring | 基幹理工学部 | 2021 | 春学期 |
Research Project Fall | 基幹理工学部 | 2021 | 秋学期 |
Special Seminar | 基幹理工学部 | 2021 | 春学期 |
Research on Nonlinear Systems | 大学院基幹理工学研究科 | 2021 | 通年 |
Seminar on Nonlinear Systems A | 大学院基幹理工学研究科 | 2021 | 春学期 |
Seminar on Nonlinear Systems B | 大学院基幹理工学研究科 | 2021 | 秋学期 |
Seminar on Nonlinear Systems C | 大学院基幹理工学研究科 | 2021 | 春学期 |
Seminar on Nonlinear Systems D | 大学院基幹理工学研究科 | 2021 | 秋学期 |
2015年
概要:This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.