Philip MJ Trevelyan

Welcome to my website. 


Research Interests

Turbulent and Potential Flow

Thin Films

Chemically Driven Instabilities

Reaction Diffusion Equations


Useful Links

Google Scholar: https://scholar.google.com/citations?hl=en&user=Ath_WSYAAAAJ [says 1327 citations, h-index 21]
Microsoft Academic: 
https://academic.microsoft.com/profile/e037e334-969j-42eg-8830-j4g6i7hg59hi/PhilipMJTrevelyan/publication/ [says 1144 citations]
Researchgate: 
https://www.researchgate.net/profile/Philip_Trevelyan [says 1102 citations, h-index 19, RG score 29.38]
Scorpus: 
https://www.scopus.com/authid/detail.uri?authorId=7801598562 [says 1016 citations, h-index 19]
Mendeley: 
https://www.mendeley.com/profiles/philip-trevelyan/?viewAsOther=true [says 1016 citations, h-index 19]
Publons: 
https://publons.com/researcher/3518403/philip-trevelyan [says 989 citations, h-index 19]
ORCiD: https://orcid.org/0000-0003-2780-6680



Contact Details

Email: ptrevelyan@gmail.com

Work Email: philip.trevelyan@southwales.ac.uk 
Work Webpage: 
http://staff.southwales.ac.uk/users/3932-ptrevely
LinkedIn: https://www.linkedin.com/in/philip-trevelyan-5b88a34b/?originalSubdomain=uk 

Work Address:
Faculty of Computing, Engineering and Science
Uiversity of South Wales
Pontypridd
CF37 1DL, UK

Office: J415
Phone: +44-1443-48-2275


Job History

Lecturer, Mathematics, Glamorgan/South Wales (2010-now).

Post-Doctoral Research Associate positions:
Chemically Driven Instabilities, Nonlinear Physical Chemistry Unit, Brussels (2006-2010).
Reactive Thin Films, Chemical Engineering, Imperial College London (2004-2006).
Heated Thin Films, Chemical Engineering, Leeds (2002-2004).
Thin Films, Chemistry Department, Leeds (1999-2002).


Modules Involved With

Current Modules (2020-21):
AM0S01 - Foundations of Mathematics
MS1S461 - Mathematics and Statistics for Computing
MS2S04 - Further Calculus
MS3S20 - Partial Differential Equations
MS3S29 - Final Year Project
MS4S03 - Numerical Methods for Geophysical Flows
MS4D01 - MMath Project

Previous Modules:
AM0H01 - Foundation Quantitative Methods
AM0H02 - Foundation Mathematics
AM1S50 - Mathematics for Mechanical and Aeronautical Engineers
AM2H41 - Engineering Mathematics 2
MS0D02 - Mathematical Applications and Investigations
MS0T03 - Mathematical Applications and Investigations
MS1S13 - Method and Techniques of Mathematics
MS2S16 - Algorithms


Publications

Journal Publications

54. J. Kent and P.M.J. Trevelyan, Rayleigh-Taylor Instabilities of Initially Linear Density Profiles with a Jump, in preparation for Transport in Porous Media.
53. P.M.J. Trevelyan and J. Kent, Large Time Growth Rates of Rayleigh-Taylor Instabilities in Porous Media, submitted to J. Eng. Math. in (2020).
52. M.J.A. Choudhury, P.M.J. Trevelyan and G.P. Boswell, Mathematical modelling of fungi-initiated siderophore-iron interactions, published in Mathematical Medicine & Biology.
https://doi.org/10.1093/imammb/dqaa008

51. S. Cowell, J. Kent and P.M.J. Trevelyan, Rayleigh-Taylor Instabilities in Miscible Fluids with Initially Piecewise Linear Density Profiles, J. Eng. Math., 121, 57-83, (2020).
https://doi.org/10.1007/s10665-020-10039-6
50. P.M.J. Trevelyan and A.J. Walker, Asymptotic Properties of Radial A+B→C reaction fronts, Phys. Rev. E. 98, 032118, (2018). 
https://doi.org/10.1103/PhysRevE.98.032118 [3 Citations]
49. M.J.A. Choudhury, P.M.J. Trevelyan and G.P. Boswell, A mathematical model of nutrient influence on fungal competition, Journal of Theoretical Biology, 438, 9-20, (2018). 
https://doi.org/10.1016/j.jtbi.2017.11.006
 [6 Citations]
48. M.J.A. Choudhury, P.M.J. Trevelyan and G.P. Boswell, Determining the kinematic properties of an advancing front using a decomposition method, IAENG, 46, 578-584, (2016).
http://www.iaeng.org/IJAM/issues_v46/issue_4/IJAM_46_4_23.pdf[1 Citation]
47. V. Loodts, P.M.J. Trevelyan, L. Rongy, A. De Wit, Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification, Phys. Rev. E. 94, 043115, (2016). 
https://doi.org/10.1103/PhysRevE.94.043115 [18 Citations]
46. P.M.J. Trevelyan, C. Almarcha and A. De Wit, Buoyancy-driven instabilities around miscible A+B→C reaction fronts: A general classification, Phys. Rev. E. 91, 023001, (2015). 
https://doi.org/10.1103/PhysRevE.91.023001 [40 Citations]
45. J. Gandhi and P.M.J. Trevelyan, Onset conditions for a Rayleigh-Taylor instability with step function density profiles, J. Engng. Math. 86, 31-48, (2014). 
https://doi.org/10.1007/s10665-013-9649-2 [7 Citations]
44. C. Almarcha, P. M. J. Trevelyan, P. Grosfils and A. De Wit, Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front, Phys. Rev. E. 88, 033009, (2013). 
https://doi.org/10.1103/PhysRevE.88.033009 [21 Citations]
43. J. Carballido-Landeira, P.M.J. Trevelyan, C. Almarcha and A. De Wit, Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convection modes, Phys. Fluids. 25, 024107, (2013).
https://doi.org/10.1063/1.4790192
 [39 Citations]
42. P.M.J. Trevelyan, Approximating the large time asymptotic reaction zone solution for fractional order kinetics AnBm, Discrete and Continuous Dynamical Systems – Series S, 5, 219-234, (2012). 
https://doi.org/10.3934/dcdss.2012.5.219 
[2 Citations]
41. L.A. Riolfo, Y. Nagatsu, S. Iwata, R. Maes, P.M.J. Trevelyan and A. De Wit, Experimental evidence of reaction-driven miscible viscous fingering, Phys. Rev. E., 85, 015304, (2012). 
https://doi.org/10.1103/PhysRevE.85.015304 [51 Citations]
40. P.M.J. Trevelyan, A. Pereira and S. Kalliadasis, Dynamics of a reactive thin film, Math. Model. Nat. Phenom., 7, 99-145, (2012).
https://doi.org/10.1051/mmnp/20127408
 [5 Citations]
39. C. Almarcha, Y. R’Honi, Y. De Decker, P. M. J. Trevelyan, K. Eckert, and A. De Wit, Convective mixing induced by acid-base reactions, J. Phys. Chem. B., 115, 9739-9744, (2011).
https://doi.org/10.1021/jp202201e
 [46 Citations]
38. P.M.J. Trevelyan, C. Almarcha and A. De Wit, Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells, J. Fluid Mech., 670, 38-65, (2011).
https://doi.org/10.1017/S0022112010005008
 [93 Citations] 
37. S. Kuster, L.A. Riolfo, A. Zalts, C. El Hasi, C. Almarcha, P.M.J. Trevelyan, A. De Wit and A. D’Onofrio, Differential diffusion effects on buoyancy-driven instabilities of acid-base fronts: the case of a color indicator, J. Phys. Chem. Chem. Phys., 13, 17295-17303 (2011).
https://doi.org/10.1039/C1CP21185D [36 Citations] 
36. M. Mishra, P.M.J. Trevelyan, C. Almarcha and A. De Wit, Influence of double diffusive effects on miscible viscous fingering, Phys. Rev. Lett., 105, 204501 (2010). 
https://doi.org/10.1103/PhysRevLett.105.204501 [69 Citations]
35. L. Rongy, P.M.J. Trevelyan and A. De Wit, Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers, Chem. Eng. Sci., 65, 2382-2391 (2010). 
https://doi.org/10.1016/j.ces.2009.09.022
 [24 Citations]
34. C. Almarcha, P.M.J. Trevelyan, L.A. Riolfo, A. Zalts, C. El Hasi, A. D’Onofrio and A. De Wit, Active role of a color indicator in buoyancy-driven instabilities of chemical fronts, J. Phys. Chem. Lett., 1, 752-757 (2010). 
https://doi.org/10.1021/jz900418d
 [57 Citations]
33. C. Almarcha, P.M.J. Trevelyan, P. Grosfils and A. De Wit, Chemically Driven Hydrodynamic Instabilities, Phys. Rev. Lett., 104, 044501 (2010). 
https://doi.org/10.1103/PhysRevLett.104.044501 [133 Citations]
32. S.H. Hejazi, P.M.J. Trevelyan, J. Azaiez and A. De Wit, Viscous fingering of a miscible reactive A+B→C interface: A linear stability analysis, J. Fluid Mech., 652, 501-528 (2010).
https://doi.org/10.1017/S0022112010000327
 [85 Citations]
31. P.M.J. Trevelyan, Analytical small time asymptotic properties of A+B→C fronts, Phys. Rev. E, 80, 046118 (2009). 
https://doi.org/10.1103/PhysRevE.80.046118 [9 Citations]
30. P.M.J. Trevelyan, Higher-order large-time asymptotics for a reaction of the form nA+mB→C, Phys. Rev. E, 79, 016105 (2009). 
https://doi.org/10.1103/PhysRevE.79.016105 [8 Citations]
29. C. Ruyer-Quil, P.M.J. Trevelyan, F. Giorgiutti-Dauphine, C. Duprat and S. Kalliadasis, Film flows down a fiber: Modeling and influence of streamwise viscous diffusion, Eur. Phys. J. Special Topics, 166, 89-92 (2009). 
https://doi.org/10.1140/epjst/e2009-00884-0 [9 Citations]
28. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Interfacial instabilities driven by chemical reactions, Eur. Phys. J. Special Topics, 166, 121-125 (2009). 
https://doi.org/10.1140/epjst/e2009-00891-1 [5 Citations]
27. P.M.J. Trevelyan, D.E. Strier and A. De Wit, Analytical asymptotic solutions of nA+mB→C reaction-diffusion equations in two-layer systems: A general study, Phys. Rev. E, 78, 026122 (2008). 
https://doi.org/10.1103/PhysRevE.78.026122 [11 Citations]
26. L. Rongy, P.M.J. Trevelyan and A. De Wit, Dynamics of A+B→C reaction fronts in the presence of buoyancy-driven convection, Phys. Rev. Lett., 101, 084503 (2008). 
https://doi.org/10.1103/PhysRevLett.101.084503 [62 Citations]
25. C. Ruyer-Quil, P.M.J. Trevelyan, F. Giorgiutti-Dauphine, C. Duprat and S. Kalliadasis, Modelling film flows down a fibre, J. Fluid Mech., 603, 431-462 (2008).
https://doi.org/10.1017/S0022112008001225
 [106 Citations]
24. P.M.J. Trevelyan, B. Scheid, C. Ruyer-Quil and S. Kalliadasis, Heated falling films, J. Fluid Mech., 592, 295-334 (2007).
https://doi.org/10.1017/S0022112007008476
 [77 Citations]
23. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Dynamics of a horizontal thin liquid film in the presence of reactive surfactants, Phys. Fluids, 19, 112102 (2007).
https://doi.org/10.1063/1.2775938
 [48 Citations]
22. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Interfacial hydrodynamic waves driven by chemical reactions, J. Engng. Math., 59, 207-220 (2007). 
https://doi.org/10.1007/s10665-007-9143-9 [14 Citations]
21. S. Saprykin, P.M.J. Trevelyan, R. Koopmans and S. Kalliadasis, Free-surface thin-film flows over uniformly heated topography, Phys. Rev. E, 75, 026306 (2007). 
https://doi.org/10.1103/PhysRevE.75.026306 [62 Citations]
20. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Thin Films in the Presence of Chemical Reactions, Fluid Dyn. Mater. Process., 3, 303-316 (2007). 
https://doi.org/10.3970/fdmp.2007.003.303 [5 Citations]
19. P.M.J. Trevelyan and S. Kalliadasis, Wave dynamics on a thin liquid film falling down a heated wall, J. Engng. Math., 50, 177-208 (2004). 
https://doi.org/10.1007/s10665-004-1016-x [48 Citations]
18. P.M.J. Trevelyan and S. Kalliadasis, Dynamics of a reactive falling film at large Peclet numbers. I Long-wave approximation, Phys. Fluids, 16, 3191-3208 (2004).
https://doi.org/10/1063/1.1767834
 [36 Citations]
17. P.M.J. Trevelyan and S. Kalliadasis, Dynamics of a reactive falling film at large Peclet numbers. II Nonlinear waves far from criticality: Integral-boundary-layer approximation, Phys. Fluids, 16, 3209-3226 (2004).
https://doi.org/10.1063/1.1767835
 [27 Citations]
16. P.M.J. Trevelyan, S. Kalliadasis, J.H. Merkin and S.K. Scott, Dynamics of a vertically falling film in the presence of a first-order chemical reaction, Phys. Fluids, 14, 2402-2421 (2002).
https://doi.org/10.1063/1.1485761
 [24 Citations]
15. P.M.J. Trevelyan, S. Kalliadasis, J.H. Merkin and S.K. Scott, Mass transport enhancement in regions bounded by rigid walls, J. Engng. Math., 42, 45-64 (2002). 
https://doi.org/10.1023/A:1014369607387 [10 Citations]
14. P.M.J. Trevelyan, S. Kalliadasis, J.H. Merkin and S.K. Scott, Circulation and reaction enhancement of mass transport in a cavity, Chem. Eng. Sci., 56, 5177-5188 (2001).
https://doi.org/10.1016/S0009-2509(01)00179-8
 [10 Citations]
13. L.M. Conroy, P.M.J. Trevelyan and D.B. Ingham, An analytical, numerical, and experimental comparison of the fluid velocity in the vicinity of an open tank with one and two lateral exhaust slot hoods and a uniform crossdraft, Ann. Occup. Hyg., 44, 407-419 (2000).
https://doi.org/10.1093/annhyg/44.6.407
 [12 Citations]
12. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Potential flow in a semi-infinite channel with multiple sub-channels using the Schwarz-Christoffel transformation, Comput. Meth. Appl. Mech. Eng., 189, 341-359 (2000).
https://doi.org/10.1016/S0045-7825(99)00299-6 
[4 Citations]
11. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, A numerical method for Schwarz-Christoffel conformal transformation with application to potential flow in channels with oblique sub-channels, CMES-Comp. Model. Eng., 1, 117-122 (2000).
https://doi.org/10/3970/cmes.2000.001.419
 

Conference Proceedings / Extended Abstracts

10. L.A. Riolfo, Y. Nagatsu, P.M.J. Trevelyan, A. De Wit, Chemically-driven miscible viscous fingering: how can a reaction destabilize typically stable displacements?, European Conference on Complex Systems, Springer Proceedings in Complexity, (2013).
https://doi.org/10.1007/978-3-319-00395-5_2 [2 Citations]
9. P.M.J. Trevelyan, D.E. Strier and A. De Wit, Asymptotic reaction-diffusion profiles in two-layer systems, Mathematics in Chemical Kinetics and Engineering. (Ghent, Belgium, February 2009).
pdf
8. A. Pereira, P.M.J. Trevelyan and S. Kalliadasis, Hydrodynamics of reactive thin films, Proceedings of the 22nd International Congress on Theretical Applied Mechanics, paper 1132. (Adelaide, Australia, August 2008).
pdf
7. S. Kalliadasis and P.M.J. Trevelyan, Dynamics of a reactive falling film at large Peclet numbers, Proceedings of the 21st International Congress on Theoretical Applied Mechanics, paper FM14_L10220 (Warsaw, Poland, August 2004).
pdf
6. Toth, Boissonade, Scott, Westerhoff, Jonnalagadda, Gaspar, Trevelyan, Showalter, Snita, Marek, Mayama, Dewel, Simon, Sorensen, Epstein, Satnoianu, Harrison, Merkin, Hemming, Hantz, Noszticzius, Miller, Hauser, Sielewiesiuk, General discussion, Faraday Discussions, 2002, 120, 407-419. (Manchester, UK, September 2001). 

link
5. P.M.J. Trevelyan, D.B. Ingham and L. Elliott, The effects of ventilation and sash handles on the flow in fume cupboards, Progress in Modern Ventilation, Proceedings of Ventilation 2000, 2, Proceedings of the 6th International Symposium on Ventilation for Contaminant Control, 2000, 2, 80-83.
 (Helsinki, Finland, June 2000).
link
4. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Boundary integral approach to determine the potential fluid flow in a channel with multiple sub-channels, in Proceedings of 2nd UK Conference on Boundary Integral Methods, (L. Wrobel, S.N. Chandler-Wilde, Eds.), Brunel University Press, 1999, 291-302.
ISBN 1-902316-00-2. (London, UK, September 1999).

3. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Boundary integrals applied to potential flow in channels/oblique sub-channels, Proceedings of the 1st International Conference on Boundary Element Techniques, (M.H. Aliabadi, Ed.), Queen Mary and Westfield College, University of London, 341-348. ISBN 0 904 188 531 (London, UK, July 1999).

2. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Effects of a ventilation duct on the performance of a fume cupboard, RoomVent98, 1998, 1, 385-391. (Stockholm, Sweden, June 1998).
link
1. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Ventilation near a fume cupboard, Proceedings of the Institution of Chemical Engineers, 1998, paper 140. (Newcastle, UK, April 1998).


Fun Stuff: Fractal Patterns

Consider the discrete mapping zn+1 = f(z, k). The points that lie inside the Mandelbrot set are the values of k (complex) which lead to |z| remaining finite as the integer n tends to infinity, starting from z0=0. The boundary of the Mandelbrot set is a fractal. Below some fractal patterns are sketched in the complex k plane (k=x+iy where x & y are real with i2 = -1) for some simple mapping functions.

Quadratic: zn+1 = zn2 + k
 
 

Notice that the fractal is symmetric about the real axis, i.e. θ=0 where θ is the angle from the real axis measured in the anti-clockwise direction. The boundary of the largest area is known to be the cardioid 2r=1-cos(θ) shifted along the real axis by ¼. In Cartesian coordinates this is given by 16(x2+y2) = 3 ± 2(3-8x)½. Also an infinite number of circles are attached to the cardioid. It is important to note that the Mandelbrot set is connected, however, if an insufficient resolution is used then some of the peninsulas can appear like islands.

Cubic: zn+1 = zn3 + k

We notice that this has 2 lines of symmetry, the real and imaginary axis, i.e. θ=0 & π/2. Further,  there are an infinite number of cardioids attached to the main boundary.
 

Quartic: zn+1 = zn4 + k


Now there are 3 lines of symmetry: θ=0, π/3 & 2π/3.
 


Quintic: zn+1 = zn5 + k

The 4 lines of symmetry are: θ=0, π/4, π/2 & 3π/4.

Sextic: zn+1 = zn6 + k

This has 5 lines of symmetry: θ=0, π/5, 2π/5, 3π/5 & 4π/5.

 


 These fractals were plotted using the output from a fortran 77 program like this:

      PROGRAM FRACTAL
IMPLICIT NONE
INTEGER I,J,ITERATION,N,M
PARAMETER(N=2000,M=50)
REAL*8 U,V,X,Y,P,Q
OPEN(99,FILE='Fractal_quad.dat')
25 FORMAT(2F9.5,I3)
DO 10, I=1,N
DO 20, J=1,N
C Define first point z(n)=U+iV and k=X+iY
U=0.D0
V=0.D0
X=I*3.2D0/(N-1.D0)-2.1D0
Y=J*2.8D0/(N-1.D0)-1.4D0
DO 30, ITERATION=1,M
C Calculate z(n+1) = z(n)**2 + k where z(n+1)=P+iQ
P=U**2-V**2+X
Q=2.D0*U*V+Y
U=P
V=Q
C If |z|>2 stop iterating
If (U**2+V**2.GT.4.D0) GOTO 100
30 CONTINUE
100 WRITE(99,25) X,Y,ITERATION
20 CONTINUE
10 CONTINUE
STOP
END

This program calculates the number of iterations required until the magnitude of z is greater than 2. This yields a measure of the rate of divergence for the points outside the Mandelbrot set. 


Mandelbrot sets are not the only type of fractals. Another type are Julia sets which are similar to the Mandelbrot sets, as they also come from a discrete mapping zn+1= f (zn, k). The difference between them is that the Mandelbrot set is the set of values of k which lead to |z| remaining finite (starting from z0=0) whilst the Julia set is the set of values of z0 that lead to |z| remaining finite for a given value of k. Thus for a given mapping, an infinite number of Julia sets can be obtained by choosing different values of k 

 

Below the Julia set for the quadratic mapping zn+1 = zn2 + k with k = -0.9 is illustrated where z=x+iy. The contours represent the number of iterations required until the magnitude of z is greater than 2, to measure the rate of divergence for the points outside the Julia set


Another example of a Julia set, using the same quadratic mapping zn+1 = zn2 + k, but now for k=0.36+0.36i yields a very different picture:


In this case the Julia set is almost empty.

The Julia set for the cubic mapping zn+1 = zn3 + k with k=-0.5+0.1i  is:


However, if we change k to -0.516+0.1i the Julia set becomes:



Finally, part of the Julia set is illustrated for the mapping

zn+1 = zn3 +1.75zn2  -0.495 +0.2i