氏名

ボーウェン マーク

ボーウェン マーク

職名

准教授 (https://researchmap.jp/read0155708/)

所属

(国際理工学センター)

連絡先

URL等

研究者番号
30534341

本属以外の学内所属

兼担

政治経済学術院(政治経済学部)

学内研究所等

理工学術院総合研究所(理工学研究所)

兼任研究員 2018年-

論文

Pressure-dipole solutions of the thin-film equation

Mark Bowen, T. P. Witelski

European Journal of Applied Mathematics査読有り2018年-

DOI

On self-similar thermal rupture of thin liquid sheets

Mark Bowen, B. Tilley

Physics of Fluids査読有り25(10)p.1021052013年-

Dynamics of a viscous thread on a non-planar substrate

Mark Bowen, J. R. King

Journal of Engineering Mathematics査読有り80(1)p.39 - 622013年-

Thermally induced van der Waals rupture of thin viscous fluid sheets

Mark Bowen, B. Tilley

Physics of Fluids査読有り24(3)p.0321062012年-

The linear limit of the dipole problem for the thin film equation

Mark Bowen, T. P. Witelski

SIAM Journal of Applied Mathematics査読有り66(5)p.1727 - 17482006年-

Thermocapillary control of rupture in thin viscous fluid sheets

B. Tilley, Mark Bowen

Journal of Fluid Mechanics査読有り541p.399 - 4082005年-

Nonlinear dynamics of two-dimensional undercompressive shocks

Mark Bowen, J. Sur, A. L. Bertozzi, R. P. Behringer

Physica D: Nonlinear Phenomena査読有り209p.36 - 482005年-

The self-similar solution for draining in the thin film equation

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-

ADI schemes for higher-order nonlinear diffusion equations

TP Witelski, Mark Bowen

Applied Numerical Mathematics査読有り45p.331 - 3512003年-

Moving boundary problems and non-uniqueness for the thin film equation

J R King, Mark Bowen

European Journal of Applied Mathematics査読有り12(3)p.321 - 3562001年-

Asymptotic behaviour of the thin film equation in bounded domains

Mark Bowen, J R King

European Journal of Applied Mathematics査読有り12(2)p.135 - 1572001年-

Intermediate asymptotics of the porous medium equation with sign changes

J Hulshof, J R King and Mark Bowen

Advances in Differential Equations査読有り6(9)p.1115 - 11522001年-

Anomalous exponents and dipole solutions for the thin film equation

J Hulshof, J R King and Mark Bowen

SIAM Journal on Applied Mathematics査読有り62(1)p.149 - 1792001年-

Thin film dynamics: theory and applications

AL Bertozzi, Mark Bowen

Modern Methods in Scientific Computing and Applications査読有りp.31 - 792002年-

Thermally induced van der Waals rupture of thin viscous fluid sheets

Bowen, Mark;Tilley, B. S.

PHYSICS OF FLUIDS24(3)2012年-2012年

DOIWoS

詳細

ISSN:1070-6631

Dynamics of a viscous thread on a non-planar substrate

Bowen, Mark;King, John R.

JOURNAL OF ENGINEERING MATHEMATICS80(1)p.39 - 622013年-2013年

DOIWoS

詳細

ISSN:0022-0833

Methods of Mathematical Modelling: Continuous Systems and Differential Equations

Witelski, Thomas; Bowen, Mark

Methods of Mathematical Modelling: Continuous Systems and Differential Equationsp.1 - 3052015年09月-2015年09月 

DOIScopus

詳細

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.

書籍等出版物

Methods of Mathematical Modelling

(共著)

Springer2015年-

外部研究資金

科学研究費採択状況

研究種別:

Self-similar behaviour in thin film flow

2012年-0月-2014年-0月

配分額:¥910000

学内研究制度

特定課題研究

Investigation of multi-dimensional thin-film equations

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.

Dynamics of constrained thin films and jets

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

Thermo-capillary control of viscous sheets and jets

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.

Dynamics of multi-dimensional thin-film equations

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.  

Drainage problems for the multidimensional thin film equation

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.

現在担当している科目

科目名開講学部・研究科開講年度学期
Calculus A基幹理工学部2019秋学期
Calculus A創造理工学部2019秋学期
Calculus A先進理工学部2019秋学期
Calculus B基幹理工学部2019春学期
Calculus B創造理工学部2019春学期
Calculus B先進理工学部2019春学期
Ordinary Differential Equations (2)基幹理工学部2019秋学期
Ordinary Differential Equations (2)創造理工学部2019秋学期
Ordinary Differential Equations (2)先進理工学部2019秋学期
Partial Differential Equations基幹理工学部2019春学期
Partial Differential Equations創造理工学部2019春学期
Partial Differential Equations先進理工学部2019春学期
Research Project B基幹理工学部2019春学期
Research Project B 【S Grade】基幹理工学部2019春学期
Research Project C基幹理工学部2019秋学期
Research Project C 【S Grade】基幹理工学部2019秋学期
Research Project A基幹理工学部2019秋学期
Research Project D基幹理工学部2019春学期
Calculus A (1)基幹理工学部2019秋クォーター
Calculus A (1)創造理工学部2019秋クォーター
Calculus A (1)先進理工学部2019秋クォーター
Calculus B (1)基幹理工学部2019冬クォーター
Calculus B (1)創造理工学部2019冬クォーター
Calculus B (1)先進理工学部2019冬クォーター
Calculus C (1)基幹理工学部2019春クォーター
Calculus C (1)創造理工学部2019春クォーター
Calculus C (1)先進理工学部2019春クォーター
Master's Thesis (Department of Pure and Applied Mathematics)大学院基幹理工学研究科2019通年
Research on Nonlinear Systems (Prof. Bowen)大学院基幹理工学研究科2019通年
Seminar on Nonlinear Systems A (Prof. Bowen)大学院基幹理工学研究科2019春学期
Seminar on Nonlinear Systems B (Prof. Bowen)大学院基幹理工学研究科2019秋学期
Seminar on Nonlinear Systems C (Prof. Bowen)大学院基幹理工学研究科2019春学期
Seminar on Nonlinear Systems D (Prof. Bowen)大学院基幹理工学研究科2019秋学期