This discussion document represents the work done during a four month post-doctoral period funded... more This discussion document represents the work done during a four month post-doctoral period funded by a Research and Consultancy Grant from the Uni-versity of Strathclyde. In this document we develop mathematical models of varying sophistication for the various stages of ...
In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting ... more In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting stents. The generalised model is capable of predicting drug release from a number of polymer-free systems including those that exhibit nanoporous, nanotubular and smooth surfaces. We derive analytical solutions which allow us to easily determine the important parameters that control drug release. Drug release profiles are provided, and we offer design recommendations so that the release profile may be tailored to achieve the desired outcome. The models presented here are not specific to drug-eluting stents and may also be applied to other biomedical implants that use nanoporous surfaces to release a drug.
This paper describes the development of an implicit finite difference method for solving transien... more This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5].
Previous studies have employed generic 3D-multiscale models to predict haemodynamic effects of th... more Previous studies have employed generic 3D-multiscale models to predict haemodynamic effects of the hybrid procedure in hypoplastic left heart syndrome. Patient-specific models, derived from image data, may allow a more clinically relevant model. However, such models require long computation times and employ internal pulmonary artery band [dint] dimension, which limits clinical application. Simpler, zero-dimensional models utilize external PAB diameters [dext] and provide rapid analysis, which may better guide intervention. This study compared 0-D and 3-D modelling from a single patient dataset and investigated the relationship dint versus dext and hemodynamic outputs of the two models. Optimum oxygen delivery defined at dint=2mm corresponded to dext=3.1 mm and 3.4 mm when models were matched for cardiac output or systemic pressure, respectively. 0-D and 3-D models when matched for PAB dimension produced close equivalence of hemodynamics and ventricular energetics. From this study we...
Journal of Mathematical Analysis and Applications, 2012
This paper presents an extension of the Eneström-Kakeya theorem concerning the roots of a polynom... more This paper presents an extension of the Eneström-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K , L) methods.
International Journal for Numerical Methods in Fluids, 1999
The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Tay... more The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Taylor (1968). This paper is concerned with demonstrating that a numerical method, GENSMAC, is capable of simulating this physical instability. A table of the parameter values (e.g. the Reynolds number, the Froude number, inlet width, inlet velocity and aspect ratio) is provided giving details of when buckling occurs and when it does not. This allows the deduction of a possible buckling condition in terms of the Reynolds number and the ratio of height of the jet to the inlet width, modifying a previous hypothesis. Visualization of jet buckling is provided. This work has been motivated by the need of industry to understand jet filling of containers; jet buckling can lead to air entrapment and this is undesirable. Copyright
... SEAN MCKEE AND TAO TANG Department of Mathematics, University of Strathclyde, Glasgow Gl 1XH,... more ... SEAN MCKEE AND TAO TANG Department of Mathematics, University of Strathclyde, Glasgow Gl 1XH, Scotland Dedicated to Professor AR Mitchell on the occasion of his 70th Birthday ... Downloaded from Page 2. 596 TERESA DIOGO, SEAN McKEE AND TAO TANG ...
Two-dimensional first-kind Volterra integral equations (VIEs) are studied. The first-kind equatio... more Two-dimensional first-kind Volterra integral equations (VIEs) are studied. The first-kind equations are reduced to second kind, and by obtaining an appropriate integral inequality, existence and uniqueness are demonstrated. The equivalent discrete integral inequality then permits convergence of discretization methods; and this is illustrated for the Euler method. Finally, a class of nonlinear telegraph equations is shown to be equivalent to (two-dimensional) Volterra integral equations, thereby providing existence and uniqueness results for this class of equations. Furthermore, the telegraph equation may be solved by the numerical method for two-dimensional VIEs, and a simple numerical example is given. †
A convergence analysis is presented for an implicit linear multistep method for solving integro-d... more A convergence analysis is presented for an implicit linear multistep method for solving integro-differential equations associated with multivalued maximal monotone mappings with special reference to an equation describing the wave induced motion of a body damped by Coulomb friction.
This paper is concerned with the study of the time-dependent water and air flow in a penstock cau... more This paper is concerned with the study of the time-dependent water and air flow in a penstock caused by closing the head gate. Two approximate techniques are employed. The first approach uses simple global arguments based on mass and momentum conservation, and the time-dependent Bernoulli equation is used to derive evolution equations for the fluxes of water and air through the various components of the system. To complement this approach, the time-dependent Nacier-Stokes equations were solved with a substantially reduced Reynolds number. Both approaches suggested that the pressure in the penstock remained abor>e 1 / 2 atm, answering a question posed by Electricorp, New Zealand.
A finite difference technique, based on a projection method, is developed for solving the dynamic... more A finite difference technique, based on a projection method, is developed for solving the dynamic threedimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tomé and McKee [32]; Tomé et al. ). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution.
This discussion document represents the work done during a four month post-doctoral period funded... more This discussion document represents the work done during a four month post-doctoral period funded by a Research and Consultancy Grant from the Uni-versity of Strathclyde. In this document we develop mathematical models of varying sophistication for the various stages of ...
In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting ... more In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting stents. The generalised model is capable of predicting drug release from a number of polymer-free systems including those that exhibit nanoporous, nanotubular and smooth surfaces. We derive analytical solutions which allow us to easily determine the important parameters that control drug release. Drug release profiles are provided, and we offer design recommendations so that the release profile may be tailored to achieve the desired outcome. The models presented here are not specific to drug-eluting stents and may also be applied to other biomedical implants that use nanoporous surfaces to release a drug.
This paper describes the development of an implicit finite difference method for solving transien... more This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5].
Previous studies have employed generic 3D-multiscale models to predict haemodynamic effects of th... more Previous studies have employed generic 3D-multiscale models to predict haemodynamic effects of the hybrid procedure in hypoplastic left heart syndrome. Patient-specific models, derived from image data, may allow a more clinically relevant model. However, such models require long computation times and employ internal pulmonary artery band [dint] dimension, which limits clinical application. Simpler, zero-dimensional models utilize external PAB diameters [dext] and provide rapid analysis, which may better guide intervention. This study compared 0-D and 3-D modelling from a single patient dataset and investigated the relationship dint versus dext and hemodynamic outputs of the two models. Optimum oxygen delivery defined at dint=2mm corresponded to dext=3.1 mm and 3.4 mm when models were matched for cardiac output or systemic pressure, respectively. 0-D and 3-D models when matched for PAB dimension produced close equivalence of hemodynamics and ventricular energetics. From this study we...
Journal of Mathematical Analysis and Applications, 2012
This paper presents an extension of the Eneström-Kakeya theorem concerning the roots of a polynom... more This paper presents an extension of the Eneström-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K , L) methods.
International Journal for Numerical Methods in Fluids, 1999
The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Tay... more The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Taylor (1968). This paper is concerned with demonstrating that a numerical method, GENSMAC, is capable of simulating this physical instability. A table of the parameter values (e.g. the Reynolds number, the Froude number, inlet width, inlet velocity and aspect ratio) is provided giving details of when buckling occurs and when it does not. This allows the deduction of a possible buckling condition in terms of the Reynolds number and the ratio of height of the jet to the inlet width, modifying a previous hypothesis. Visualization of jet buckling is provided. This work has been motivated by the need of industry to understand jet filling of containers; jet buckling can lead to air entrapment and this is undesirable. Copyright
... SEAN MCKEE AND TAO TANG Department of Mathematics, University of Strathclyde, Glasgow Gl 1XH,... more ... SEAN MCKEE AND TAO TANG Department of Mathematics, University of Strathclyde, Glasgow Gl 1XH, Scotland Dedicated to Professor AR Mitchell on the occasion of his 70th Birthday ... Downloaded from Page 2. 596 TERESA DIOGO, SEAN McKEE AND TAO TANG ...
Two-dimensional first-kind Volterra integral equations (VIEs) are studied. The first-kind equatio... more Two-dimensional first-kind Volterra integral equations (VIEs) are studied. The first-kind equations are reduced to second kind, and by obtaining an appropriate integral inequality, existence and uniqueness are demonstrated. The equivalent discrete integral inequality then permits convergence of discretization methods; and this is illustrated for the Euler method. Finally, a class of nonlinear telegraph equations is shown to be equivalent to (two-dimensional) Volterra integral equations, thereby providing existence and uniqueness results for this class of equations. Furthermore, the telegraph equation may be solved by the numerical method for two-dimensional VIEs, and a simple numerical example is given. †
A convergence analysis is presented for an implicit linear multistep method for solving integro-d... more A convergence analysis is presented for an implicit linear multistep method for solving integro-differential equations associated with multivalued maximal monotone mappings with special reference to an equation describing the wave induced motion of a body damped by Coulomb friction.
This paper is concerned with the study of the time-dependent water and air flow in a penstock cau... more This paper is concerned with the study of the time-dependent water and air flow in a penstock caused by closing the head gate. Two approximate techniques are employed. The first approach uses simple global arguments based on mass and momentum conservation, and the time-dependent Bernoulli equation is used to derive evolution equations for the fluxes of water and air through the various components of the system. To complement this approach, the time-dependent Nacier-Stokes equations were solved with a substantially reduced Reynolds number. Both approaches suggested that the pressure in the penstock remained abor>e 1 / 2 atm, answering a question posed by Electricorp, New Zealand.
A finite difference technique, based on a projection method, is developed for solving the dynamic... more A finite difference technique, based on a projection method, is developed for solving the dynamic threedimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tomé and McKee [32]; Tomé et al. ). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution.
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