Matthew Hunt | University of Warwick (original) (raw)
I am an applied mathematician specialising in classical continuum mechanics. I have specific specialisms in linear and nonlinear waves and industrial applied mathematics. I am interested in working with companies and other academics in mathematical modelling.
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Papers by Matthew Hunt
Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fie... more Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fields are considered. Both the effects of gravity and surface tension are included in the dynamic boundary condition. An asymptotic analysis (based on the assumptions of small depth and small free surface displacements) is presented. It is shown that the problem can be modelled by a Benjamin-Ono Kadomtsev-Petviashvili equation. Furthermore a fifth order Benjamin-Ono Kadomtsev-Petviashvili equation is derived to describe the flows in the particular case of values of the Bond number close to 1/3.
Hilbert transform in the nonlinear equation for magnetohydrodynamics (MHD) distinguishes it from ... more Hilbert transform in the nonlinear equation for magnetohydrodynamics (MHD) distinguishes it from the water wave model description. In this paper, we are interested in examining weakly nonlinear interfacial waves in 2 + 1 dimensions. First, we determine the wave solution in the linear case. Next, we derive the corresponding generalisation for the Kadomtsev-Petviashvili (KP) equation with the inclusion of an equilibrium magnetic field. The derived governing equation is a generalisation of the Benjamin-Ono (BO) equation called the Benjamin equation first derived in Benjamin (J.
A continuum thermal electrochemical model of a lithium ion battery is developed which accounts fo... more A continuum thermal electrochemical model of a lithium ion battery is developed which accounts for fast diffusion and conservation of charge in the solid phase. Continuum equations for conservation of charge, energy and lithium are derived for the electrolyte with the assumption of dilute electrolyte and Butler-Volmer kinetics as well as bulk temperature for the entire battery. The approach used is homogenisation with the underlying assumptions of small electrode particle size relative to size of the electrodes themselves, the model is derived systematically. The advantage of using homogenisation is that the coefficients are derived in terms of the microstructure and changes in the geometry can be investigated relatively easily. Comparisons to the standard electrochemical model [1] as well as the model by [2] are compared. Effects of Joule and entropic heating are considered to obtain a physics based model of a lithium ion battery.
In 1895, Korteweg and de Vries (KdV), [17], derived an equation describing the motion of waves us... more In 1895, Korteweg and de Vries (KdV), [17], derived an equation describing the motion of waves using the assumptions of long wavelength and small amplitude. Two implicit assumptions which they also made were irrotational and inviscid fluids. Comparing experiment and observation seems to suggest that these two assumptions are well justified. This paper removes the assumption of irrotationality in the case of electrohydrodynamics with an assumption of globally constant vorticity in the fluid. A study of the effect of vorticity on wave profiles and amplitudes is made revealing some unusual features. The velocity potential is an important variable in irrotational flow, the vertical component of velocity takes place of this variable in our analysis. This allows the bypassing of the Burns condition and also demonstrates that waves exist even for negative values of the vorticity. The linear and weakly nonlinear models are derived.
Doctoral Thesis Ucl, Jul 28, 2013
Two-dimensional free surface flows generated by a moving disturbance are considered. The flows ar... more Two-dimensional free surface flows generated by a moving disturbance are considered. The flows are
assumed to be potential. The effects of electric field, gravity and surface tension are included in the dynamic
boundary condition. The disturbance is chosen to be a distribution of pressure moving at a constant velocity. Both
linear and nonlinear results are presented. For some values of the parameters, the linear theory predicts unbounded
displacements of the free surface. It is shown that this nonuniformity is removed by developing a weakly nonlinear
theory. There are then solutions which are perturbations of a uniform stream and others which are perturbations of
solitary waves with decaying tails.
Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fie... more Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fields are considered. Both the effects of gravity and surface tension are included in the dynamic boundary condition. An asymptotic analysis (based on the assumptions of small depth and small free surface displacements) is presented. It is shown that the problem can be modelled by a Benjamin-Ono Kadomtsev-Petviashvili equation. Furthermore a fifth order Benjamin-Ono Kadomtsev-Petviashvili equation is derived to describe the flows in the particular case of values of the Bond number close to 1/3.
Hilbert transform in the nonlinear equation for magnetohydrodynamics (MHD) distinguishes it from ... more Hilbert transform in the nonlinear equation for magnetohydrodynamics (MHD) distinguishes it from the water wave model description. In this paper, we are interested in examining weakly nonlinear interfacial waves in 2 + 1 dimensions. First, we determine the wave solution in the linear case. Next, we derive the corresponding generalisation for the Kadomtsev-Petviashvili (KP) equation with the inclusion of an equilibrium magnetic field. The derived governing equation is a generalisation of the Benjamin-Ono (BO) equation called the Benjamin equation first derived in Benjamin (J.
A continuum thermal electrochemical model of a lithium ion battery is developed which accounts fo... more A continuum thermal electrochemical model of a lithium ion battery is developed which accounts for fast diffusion and conservation of charge in the solid phase. Continuum equations for conservation of charge, energy and lithium are derived for the electrolyte with the assumption of dilute electrolyte and Butler-Volmer kinetics as well as bulk temperature for the entire battery. The approach used is homogenisation with the underlying assumptions of small electrode particle size relative to size of the electrodes themselves, the model is derived systematically. The advantage of using homogenisation is that the coefficients are derived in terms of the microstructure and changes in the geometry can be investigated relatively easily. Comparisons to the standard electrochemical model [1] as well as the model by [2] are compared. Effects of Joule and entropic heating are considered to obtain a physics based model of a lithium ion battery.
In 1895, Korteweg and de Vries (KdV), [17], derived an equation describing the motion of waves us... more In 1895, Korteweg and de Vries (KdV), [17], derived an equation describing the motion of waves using the assumptions of long wavelength and small amplitude. Two implicit assumptions which they also made were irrotational and inviscid fluids. Comparing experiment and observation seems to suggest that these two assumptions are well justified. This paper removes the assumption of irrotationality in the case of electrohydrodynamics with an assumption of globally constant vorticity in the fluid. A study of the effect of vorticity on wave profiles and amplitudes is made revealing some unusual features. The velocity potential is an important variable in irrotational flow, the vertical component of velocity takes place of this variable in our analysis. This allows the bypassing of the Burns condition and also demonstrates that waves exist even for negative values of the vorticity. The linear and weakly nonlinear models are derived.
Doctoral Thesis Ucl, Jul 28, 2013
Two-dimensional free surface flows generated by a moving disturbance are considered. The flows ar... more Two-dimensional free surface flows generated by a moving disturbance are considered. The flows are
assumed to be potential. The effects of electric field, gravity and surface tension are included in the dynamic
boundary condition. The disturbance is chosen to be a distribution of pressure moving at a constant velocity. Both
linear and nonlinear results are presented. For some values of the parameters, the linear theory predicts unbounded
displacements of the free surface. It is shown that this nonuniformity is removed by developing a weakly nonlinear
theory. There are then solutions which are perturbations of a uniform stream and others which are perturbations of
solitary waves with decaying tails.