ボーウェン マーク (ボーウェン マーク)

写真a

所属

理工学術院 国際理工学センター(理工学術院)

職名

准教授

ホームページ

https://markbowen.jp/

プロフィール

I am an applied mathematician undertaking research into nonlinear partial differential equations, employing a combination of analytical and numerical techniques in their study. I am particularly interested in studying free boundary problems arising from thin film flows, including investigations of rupture phenomena and the effects of surface topography and driving forces upon the motion of the liquid. Such problems often yield evolution equations for the interfacial film thickness in the form of high-order degenerate parabolic equations combined with additional convective effects. In certain cases, the solutions to these equations may contain discontinuities; the selection criterion and stability of these ‘shocks’ is also both of mathematical and physical interest.

兼担 【 表示 / 非表示

  • 政治経済学術院   政治経済学部

学内研究所等 【 表示 / 非表示

  • 2020年
    -
    2022年

    理工学術院総合研究所   兼任研究員

学位 【 表示 / 非表示

  • 博士

 

研究分野 【 表示 / 非表示

  • 応用数学、統計数学

論文 【 表示 / 非表示

  • Pressure-dipole solutions of the thin-film equation

    Mark Bowen, T. P. Witelski

    European Journal of Applied Mathematics    2018年  [査読有り]

    DOI

  • Methods of Mathematical Modelling: Continuous Systems and Differential Equations

    Witelski, Thomas, Bowen, Mark

    Methods of Mathematical Modelling: Continuous Systems and Differential Equations     1 - 305  2015年09月

     概要を見る

    © 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.

    DOI

  • On self-similar thermal rupture of thin liquid sheets

    M. Bowen, B. S. Tilley

    PHYSICS OF FLUIDS   25 ( 10 ) 102105  2013年10月  [査読有り]

     概要を見る

    We consider the dynamics of a symmetrically heated thin incompressible viscous fluid sheet. We take surface tension to be temperature dependent and consequently the streamwise momentum equation includes the effects of thermocapillarity, inertia, viscous stresses, and capillarity. Energy transport to the surrounding environment is also included. We use a long-wave analysis to derive a single nondimensional system which, with appropriate choices of Reynolds number, recovers two previously studied cases. In both cases, we find conditions under which sufficiently large-amplitude initial temperature profiles induce film rupture in finite time, notably without the inclusion of disjoining pressures from van der Waals effects. When the Reynolds number is large, the similarity solution is governed by a balance of inertia and capillarity near the rupture location, analogous to the isothermal case. When the Reynolds number is small, the thermocapillary transients induce the same similarity solution over intermediate times that is found for the drainage of lamellae in foams. For O(1) Reynolds numbers, the dynamics are governed initially by the large Reynolds number evolution, and then a transition over several orders of magnitude in the sheet thickness needs to take place before the small Reynolds number similarity solution is observed. (C) 2013 AIP Publishing LLC.

    DOI

  • Dynamics of a viscous thread on a non-planar substrate

    Mark Bowen, John R. King

    Journal of Engineering Mathematics   80 ( 1 ) 39 - 62  2013年  [査読有り]

     概要を見る

    We derive a general reduced model for the flow of a slender thread of viscous fluid on a grooved substrate. Specific choices of the substrate topography allow further analytic progress to be made, and we subsequently focus on a convection-diffusion equation governing the evolution of viscous liquid in a wedge geometry. The model equation that arises also appears in the context of foam drainage, and we take the opportunity to review and compare the results from both applications. After summarising the constant mass results, we introduce a time-dependent fluid influx at one end of the wedge. The analytical results are supported by numerical computations. © 2012 Springer Science+Business Media B.V.

    DOI

  • Thermally induced van der Waals rupture of thin viscous fluid sheets

    Mark Bowen, B. S. Tilley

    PHYSICS OF FLUIDS   24 ( 3 )  2012年03月  [査読有り]

     概要を見る

    We consider the dynamics of a thin symmetric fluid sheet subject to an initial temperature profile, where inertia, viscous stresses, disjoining pressures, capillarity, and thermocapillarity are important. We apply a long-wave analysis in the limit where deviations from the mean sheet velocity are small, but thermocapillary stresses and heat transfer from the sheet to the environment are significant and find a coupled system of partial differential equations that describe the sheet thickness, the mean sheet velocity, and the mean sheet temperature. From a linear stability analysis, we find that a stable thermal mode couples the velocity to the interfacial dynamics. This coupling can be utilized to delay the onset of rupture or to promote an earlier rupture event. In particular, rupture can be induced thermally even in cases when the heat transfer to the surrounding environment is significant, provided that the initial phase shift between the initial velocity and temperature disturbances is close to phi = pi/2. These effects suggest a strategy that uses phase modulation in the initial temperature perturbation related to the initial velocity perturbation that assigns priority of the rupture events at particular sites over several spatial periods. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3693700]

    DOI

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書籍等出版物 【 表示 / 非表示

  • Methods of Mathematical Modelling: Continuous Systems and Differential Equations

    Witelski, Thomas, Bowen, Mark( 担当: 共著)

    Springer  2015年09月

  • Methods of Mathematical Modelling

    ( 担当: 共著)

    Springer  2015年

共同研究・競争的資金等の研究課題 【 表示 / 非表示

  • Self-similar behaviour in thin film flow

    研究期間:

    2012年04月
    -
    2014年03月
     

     概要を見る

    複数の国を拠点とする研究協力者たちと連携し、我々は、表面張力が引き起こす薄膜流の研究において生じる方程式の(自己相似)特解の同定に関して、目覚ましい進展を達成した。この研究については、多くの国際的学術誌で論文発表を行った。さらに、近い将来投稿される予定の論文も複数存在する。また、複数の国際会議でも口頭発表を行った

特定課題研究 【 表示 / 非表示

  • Dynamics of monolayer thin-film flows

    2019年  

     概要を見る

    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.

  • Drainage problems for the multidimensional thin film equation

    2018年   L. Smolka, T. P. Witelski

     概要を見る

    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.

  • Dynamics of constrained thin films and jets

    2017年   T. P. Witelski

     概要を見る

    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

  • Dynamics of multi-dimensional thin-film equations

    2016年   T. P. Witelski

     概要を見る

    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.  

  • Investigation of multi-dimensional thin-film equations

    2015年   Thomas Witelski

     概要を見る

    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.

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