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A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion (2023)
Journal Article
Elatrash, L., Chadwick, E., El-Mazuzi, R., Christian, J. M., Wang, Y., Adamu, H. A., & Chadwick, E. (in press). A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion. Computers and Fluids, 266, https://doi.org/10.1016/j.compfluid.2023.106064

The problem studied was the non-reciprocal cyclic swimming motion of three spheres linked with axially aligned retractable arms in Stokes flow. The arms are assumed to be able to retract at a steady speed to half their length, and then at a later tim... Read More about A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion.

Existence, Smoothness and Uniqueness (in smooth space) of the Navier-Stokes equation by using a new Boundary Integral representation (2023)
Journal Article
Chadwick, E. Existence, Smoothness and Uniqueness (in smooth space) of the Navier-Stokes equation by using a new Boundary Integral representation. https://doi.org/10.48550/arXiv.2305.14219. Manuscript submitted for publication

Consider an exterior space-time domain where the incompressible Navier-Stokes equation and continuity equation hold with no bodies or force fields present, and smooth velocity at initial time. This is equivalent to the velocity being impulsively inst... Read More about Existence, Smoothness and Uniqueness (in smooth space) of the Navier-Stokes equation by using a new Boundary Integral representation.

An optimisation of a chordwise slot to enhance lateral flow control on a UCAV (2022)
Journal Article
Ali, U., Chadwick, E., & Sugar-Gabor, O. (2022). An optimisation of a chordwise slot to enhance lateral flow control on a UCAV. Incas Bulletin, 14(4), 3-17. https://doi.org/10.13111/2066-8201.2022.14.4.1

This research aims to optimise a chordwise slot so that lateral flow control of a flying wing configuration can be enhanced. This was achieved by maximising the airflow rate over the trailing edge control surfaces of the wing. A higher rate of airf... Read More about An optimisation of a chordwise slot to enhance lateral flow control on a UCAV.

Uniform flow past a closed body at low Reynolds number employing a novel matching in a boundary element formulation (2020)
Journal Article
Dang, B., & Chadwick, E. (2020). Uniform flow past a closed body at low Reynolds number employing a novel matching in a boundary element formulation. Engineering Analysis with Boundary Elements, 119, 95-104. https://doi.org/10.1016/j.enganabound.2020.07.008

Consider a two dimensional steady low Reynolds number flow past a circular cylinder. A boundary integral representation that matches an outer Oseen flow and inner Stokes flow is given, and the matching error is shown to be smallest when the outer dom... Read More about Uniform flow past a closed body at low Reynolds number employing a novel matching in a boundary element formulation.

The theory and application of Navier-Stokeslets (NSlets) (2019)
Journal Article
Chadwick, E. (2019). The theory and application of Navier-Stokeslets (NSlets). Physics of Fluids, 31(10), 107103. https://doi.org/10.1063/1.5119331

Consider a closed body moving in an unbounded fluid that decays to rest in the far-field and governed by the incompressible Navier-Stokes equations. By considering a translating reference frame, this is equivalent to a uniform flow past the body. A... Read More about The theory and application of Navier-Stokeslets (NSlets).

The theory and application of eulerlets (2019)
Journal Article
Chadwick, E., Christian, J., Kapoulas, A., & Chalasani, K. (2019). The theory and application of eulerlets. Physics of Fluids, 31(4), 047106. https://doi.org/10.1063/1.5088132

Consider a fixed body in a uniform flow field in the limit as the Reynolds number approaches infinity and the flow field remains steady. Instead of using standard techniques and theory for describing the problem, a new method is employed based upon t... Read More about The theory and application of eulerlets.

Modelling the electrical resistivity of concrete with varied water and chloride contents (2019)
Journal Article
Xiang, N., Wang, Y., Oleiwi, H., Chadwick, E., Yao, G., Augusthus Nelson, L., …Shabalin, I. (2020). Modelling the electrical resistivity of concrete with varied water and chloride contents. Magazine of Concrete Research, 72(11), 552-563. https://doi.org/10.1680/jmacr.18.00198

The electrical resistivity of concrete is an important property in the assessment of reinforcement corrosion in concrete and an essential parameter in the design and operation of cathodic protection for reinforced-concrete (RC) structures. Water and... Read More about Modelling the electrical resistivity of concrete with varied water and chloride contents.

Using eulerlets to model steady uniform flow past a circular cylinder (2018)
Journal Article
Chadwick, E., Christian, J., & Chalasani, K. (2018). Using eulerlets to model steady uniform flow past a circular cylinder. European Journal of Computational Mechanics, 27(5-6), 469-478. https://doi.org/10.1080/17797179.2018.1550960

Consider uniform, steady flow past a circular cylinder at Reynolds numbers 26, 36 and 40 before the flow becomes unsteady. Model the flow by using eulerlets, new Green’s functions for Euler flow. This is the first time this eulerlet model has been us... Read More about Using eulerlets to model steady uniform flow past a circular cylinder.

Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions (2017)
Journal Article
Kazem, S., Chadwick, E. A., & Hatam, A. (2018). Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions. Ain Shams Engineering Journal ASEJ / Ain Shams University, 9(4), 2587-2598. https://doi.org/10.1016/j.asej.2017.03.013

A class of basis functions so called well-conditioned RBF (WRBFs) has been introduced. This basis has been manipulated by adding cardinal functions to the conditionally negative definite RBFs of order 1, such as Multiquadric functions. The condition... Read More about Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions.

Experimental study and modelling of the thermal conductivity of sandy soils of different porosities and water contents (2017)
Journal Article
and water contents. Applied Sciences, 7(2), 119. https://doi.org/10.3390/app7020119

This paper at first reports an experimental work to test the thermal conductivity of formulated sandy soil specimens of different porosities and water contents. Both needle probe and hot-plate methods were conducted and compared. It has been confirme... Read More about Experimental study and modelling of the thermal conductivity of sandy soils of different porosities and water contents.

Flow control and high-lift performance for flying-wing manned Combat Air Vehicle Configurations by inserting lots (2016)
Journal Article
Ali, U., & Chadwick, E. (2016). Flow control and high-lift performance for flying-wing manned Combat Air Vehicle Configurations by inserting lots. International Journal of Multiphysics, 10(2), https://doi.org/10.21152/1750-9548.10.2.117

The objectives of the present study on Unmanned Combat Air Vehicles (UCAVs) are two-fold: first to control the flow by inserting leading-edge and cross-flow slots and analysing the viscous flow development over the outer panels of a flying-wing co... Read More about Flow control and high-lift performance for flying-wing manned Combat Air Vehicle Configurations by inserting lots.

The exponential function method for solving nonlinear ordinary differential equations with constant coefficients on a semi-infinite domain (2016)
Journal Article
Chadwick, E., Hatam, A., & Kazem, S. (2016). The exponential function method for solving nonlinear ordinary differential equations with constant coefficients on a semi-infinite domain. Proceedings Mathematical Sciences, 126(1), 79-97. https://doi.org/10.1007/s12044-015-0254-3

A new approach, named the Exponential Function Method (EFM) is used to obtain solutions to nonlinear ordinary differential equations with constant coefficients in a semi-infinite domain. The form of the solutions of these problems is considered to... Read More about The exponential function method for solving nonlinear ordinary differential equations with constant coefficients on a semi-infinite domain.

Using generating functions to convert an implicit (3,3) finite difference method to an explicit form on diffusion equation with different boundary conditions (2015)
Journal Article
Kazem, S., Chadwick, E., Hatam, A., & Deghan, M. (2015). Using generating functions to convert an implicit (3,3) finite difference method to an explicit form on diffusion equation with different boundary conditions. Numerical Algorithms, 71(4), 827-854. https://doi.org/10.1007/s11075-015-0026-2

In this article, our main goal is to develop an idea to convert an implicit (3,3) Ø-scheme finite difference method to an explicit form for both linear and nonlinear diffusion equations and also for nonlinear advection-diffusion equation with differe... Read More about Using generating functions to convert an implicit (3,3) finite difference method to an explicit form on diffusion equation with different boundary conditions.

Emotional intelligence in STEM (2014)
Journal Article
Singh, M., & Chadwick, E. (2014). Emotional intelligence in STEM. Mathematics today, Dec, 212-214

Using eulerlets to give a boundary integral formulation in euler flow and discussion on applications (2014)
Journal Article
Chadwick, E., & Kapoulas, A. (2014). Using eulerlets to give a boundary integral formulation in euler flow and discussion on applications. https://doi.org/10.3970/cmes.2014.102.331

Boundary element models in inviscid (Euler) flow dynamics for a manoeuvring body are difficult to formulate even for the steady case; Although the potential satisfies the Laplace equation, it has a jump discontinuity in twodimensional flow relating t... Read More about Using eulerlets to give a boundary integral formulation in euler flow and discussion on applications.

Gravitational theoretical development supporting MOND (2013)
Journal Article
Chadwick, E., Hodgkinson, T., & McDonald, G. (2013). Gravitational theoretical development supporting MOND. Physical Review D - Particles, Fields, Gravitation and Cosmology, 88(024036), https://doi.org/10.1103/PhysRevD.88.024036

Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein’s equation appropriately. A particular so... Read More about Gravitational theoretical development supporting MOND.

Assessing student teams developing mathematical models applied to business and industrial mathematics (2011)
Journal Article
Chadwick, E., Sandiford, K., & Percy, D. (2011). Assessing student teams developing mathematical models applied to business and industrial mathematics. MSOR Connections, 11(3), 22-24

Using case studies and group work, this project attempted to provide students with experience of business and industrial working practices and also to address the issue of how to solve practical mathematical problems. Students were organised into tea... Read More about Assessing student teams developing mathematical models applied to business and industrial mathematics.

Experimental verification of an Oseen flow slender body theory (2010)
Journal Article
Chadwick, E., Khan, H., Moatamedi, M., Mappin, M., & Penney, M. (2010). Experimental verification of an Oseen flow slender body theory. Journal of Fluid Mechanics, 654, 271-279. https://doi.org/10.1017/S0022112010001333

Consider uniform flow past four slender bodies with elliptical cross-section of constant ellipticity along the length of 0, 0.125, 0.25 and 0.375, respectively, for each body. Here, ellipticity is defined as the ratio of the semiminor axis of the e... Read More about Experimental verification of an Oseen flow slender body theory.

A slender body theory in oseen flow obtained by expanding the Oseenlets in the Green's integral representation (2009)
Journal Article
Chadwick, E. (2009). A slender body theory in oseen flow obtained by expanding the Oseenlets in the Green's integral representation. Fluid Dynamics Research, 41(4), 045508. https://doi.org/10.1088/0169-5983/41/4/045508

Consider steady, uniform flow at a small angle of incidence to a slender body. Let us assume that Oseen flow, the far field approximation obtained by linearizing the velocity about the uniform flow velocity, also holds in a near-field region that conti... Read More about A slender body theory in oseen flow obtained by expanding the Oseenlets in the Green's integral representation.