## Gianne Derks |
## Preprints and Publications Gianne Derks## Preprints- C. Brown, G Derks, P. van Heijster, and D.J.B. Lloyd, "Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system". Submitted. ArXiV link.
- T.J. Bridges and G. Derks, "Dimension breaking of nonlinear elliptic PDEs: satisfying the spectral condition geometrically". Submitted. href="http://www.maths.surrey.ac.uk/personal/st/G.Derks/Publications/dim_breaking.pdf">Pdf preprint.
## Published papers- A. Nasim, J. Yates, G. Derks, C. Dunlop, "A spatially resolved mechanistic growth law for cancer drug development predicting tumour growing fractions", Cancer Research Communications crc-22-0032, 2022. Link to paper (Open Access)
- G. Derks, P.A. Glendinning, and A.C. Skeldon,"Creation of
discontinuities in circle maps",
*Proc. R. Soc. A*,**477**: 20200872, 2021. Link to paper (Open Access), ArXiV link. - J. Brooks, G. Derks, and D.J.B. Lloyd, "Existence of stationary
fronts in a system of two coupled wave equations with spatial
inhomogeneity".
*Nonlinearity*,**32**, pp 4147-4187, 2019. Link to paper (Open Access_, ArXiV link. - L. Cucurull-Sanchez, M. Chappell, V. Chelliah, A. Cheung, G. Derks, M. Penney, A. Phipps, R. Malik-Sheriff, J. Timmis, M. Tindall, P. van der
Graaf, P. Vicini, and J. Yates, "Best practices to maximise
the use and re-use of QSP models: Recommendations from the UK QSP
Network".
*CPT: Pharmacometrics & Systems Pharmacology*, 2019. Link to paper - M.P. Bailey, G. Derks, and A.C. Skeldon, "Circle maps with gaps: understanding the
dynamics of the two process model for sleep-wake
regulation".
*Eur. J. Appl. Math.*,**29**pp 845-868 2018. Link to paper - A.C. Skeldon and G. Derks, "Nonsmooth maps and the
fast-slow dynamics of sleep-wake regulation: Part 1", in:
Research Perspectives CRM Barcelona (Trends in Mathematics
series); Colombo A., Jeffrey M., Lazaro J., Olm
J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics,
**8**, Birkhauser, pp 167-170, 2017. link to paper -
A.C. Skeldon, G. Derks}, V. Booth, "Nonsmooth maps and the
fast-slow dynamics of sleep-wake regulation: Part 2", in: Research Perspectives CRM Barcelona (Trends in Mathematics series); Colombo A., Jeffrey M., Lazaro J., Olm
J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics,
**8**, Birkhauser, pp 171--175, 2017. link to paper - C. Gavin, P.J. Aston, G. Derks, "Extending Slow Manifolds Near a Degenerate
Transcritical Intersection in Three
Dimensions", in: Research Perspectives CRM Barcelona (Trends in Mathematics series); Colombo A., Jeffrey M., Lazaro J., Olm
J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics,
**8**, Birkhauser, pp 65-70, 2017. DOI link -
P.J. Aston, G. Derks, B.M. Agoram, and P.H. van
der Graaf, ``A Mathematical Analysis of Rebound in a Target-Mediated
Drug Disposition Model. II. With feedback'',
*Journal of Mathematical Biology*,**75**pp 33-85, 2017. journal link (open access); DOI link; Pdf preprint. -
J.P. Ward, J.L. Dunster, G. Derks, P. Mistry, J.D. Salazar.
``Predicting tyrosinaemia: a mathematical model of
4-hydroxyphenylpyruvate dioxygenase inhibition by nitisinone in rats'',
*Math. Med. Biol.*,**34**pp 335-390, 2017 Pdf preprint (pre-proof). -
C.J.K. Knight, G.Derks. "A stability criterion for the non-linear wave
equation with spatial inhomogeneity".
*Journal of Differential Equations*,**259**, pp 4745-4762, 2015 DOI link, ArXiV preprint, and preprint pdf. - A.C. Skeldon, G. Derks, and
D.J. Dijk. "Modelling changes in sleep timing and duration across the
lifespan: changes in circadian rhythmicity or sleep homeostasis?",
*Sleep Medicine Reviews*,**28**, pp 92-103, 2016 Pre Author version (pre proofs) at publisher, DOI link. - G. Derks. "Stability of Fronts in Inhomogeneous Wave Equations",
*Acta Applicandae Mathematicae*,**137**, pp 61-78, 2014. (This is a tutorial paper). Pdf preprint. Online-first link at Springer. - A.C. Skeldon, D.J. Dijk, G. Derks.
"Mathematical models for sleep-wake dynamics: comparison of the two
process model and a mutual inhibition neuronal model",
*PLOS ONE*, 9:e103877, 2014. PLOS ONE or preprints can be found at the arXiv or the University preprint server. - P.J. Aston, G. Derks, B.M. Agoram, and P.H. van
der Graaf, ``A Mathematical Analysis of Rebound in a Target-Mediated
Drug Disposition Model: I. Without feedback'',
*Journal of Mathematical Biology*,**68**, pp 1453-1478, 2013. DOI link; Pdf preprint. - C.J.K. Knight, G. Derks, A. Doelman, H. Susanto
"Stability of stationary fronts in a non-linear wave equation with
spatial inhomogeneity".
*Journal of Differential Equations*, 254, pp. 408-468, 2013. DOI link; Pdf preprint. - G. Derks, A. Doelman, C.J.K. Knight, and
H. Susanto, ``Pinned fluxons in a Josephson junction with a finite
length inhomogeneity''.
*Eur. J. Appl. Math.*,**23**, pp. 201-244, 2012. DOI link; Pdf preprint; arXiv preprint. - G. Derks and G. Gaeta, "A minimal model of
DNA dynamics in interaction with RNA-Polymerase",
*Physica D*, 240, pp. 1805-1817, 2011. DOI link; Pdf preprint. - P.J. Aston, G.Derks, A. Raji, B.M. Agoram, and
P.H. van der Graaf, ``Mathematical Analysis of the
Pharmacokinetic-Pharmacodynamic (PKPD) Behaviour of Monoclonal
Antibodies: Predicting
*in vivo*Potency''.*J. Th. Biol.*,**281**, pp. 113-121, 2011. DOI link; Pdf preprint. - G. Derks, S. Maad and B. Sandstede,
"Perturbations of embedded eigenvalues for the planar bilaplacian".
*J. Func. Anal.*,**260**, pp. 340-398, 2011. DOI link, arXiv, Pdf preprint. - U. Ebert, F. Brau, G. Derks, W. Hundsdorfer,
C.-Y. Kao, C. Li, A. Luque, B. Meulenbroek, S. Nijdam, V. Ratushnaya,
L. Schäfer, S. Tanveer, "Multiple scales in streamer discharges, with
an emphasis on moving boundary approximations".
*Nonlinearity***24**, pp. C1-C26, 2011. DOI link (free access in 2011) and cover illustration of Nonlinearity in 2011, related to this review. - H. Susanto and G. Derks, ``Localized mode interactions in
0-π Josephson junctions''.
*Phys. Rev B*,**82**, 132301, 2010 (4 pages). DOI link, PRB link, arXiv, Pdf preprint. - G. Derks, "Existence and Uniqueness of Solutions of Initial Value
Problems". In:
*Encyclopedia of Complexity and Systems Science*, R.A. Meyers (Ed.), pp 3255-3267, 2009. DOI link, Springer link link, google books. - G.Derks, "Book review: Geometric mechanics",
*Journal of Geometric Mechanics*, pp. 267 - 270, 2009. DOI link - K.B. Blyuss and G. Derks, ``Transverse intersection of invariant
manifolds in perturbed multi-symplectic systems''.
*Dynamical Systems*,**23**, pp 219 - 256, 2008. DOI link, pdf on University preprint server, pdf preprint. - G. Derks, U. Ebert and B. Meulenbroek.
``Laplacian instability of planar streamer ionization fronts -
an example of pulled front analysis''.
*Journal Nonl. Science*,**18**, pp 551 - 590, 2008. And an short erratum:*Journal Nonl. Science*,**18**, pp 591 - 592, 2008 pdf preprint, the final publication is available at www.springerlink.com with a short erratum. - Comment by U. Ebert and G. Derks, Phys. Rev. Lett. 101, 139501 (2008) on M. Arrayás, M.A. Fontelos, J.L. Trueba, Phys. Rev. Lett. 95, 165001 (2005). Link to journal, Surrey institutional repository, and Pdf.
- G. Derks, S. Maad and B. Sandstede.
``Perturbations of embedded eigenvalues for the bilaplacian on a
cylinder''.
*Discrete and Continuous Dynamical Systems A*,**21**, pp 801-821, 2008. DOI link, pdf preprint. - G. Derks, A. Doelman, S.A. van Gils, and H. Susanto, ``Stability
analysis of π-kinks in a 0-π Josephson junction''.
*SIAM J. Applied Dynamical Systems*,**6**, pp 99-141, 2007. pdf on University preprint server, link to journal for paper, pdf preprint. - G. Derks and G. Gottwald, ``A robust numerical method to study
oscillatory instability of gap solitary waves''.
*SIAM J. Applied Dynamical Systems*,**4**, pp 140-158, 2005. pdf on University preprint server, link to journal for paper, pdf preprint on arXiv preprint server. - H. Susanto, S.A. van Gils, A. Doelman, and G. Derks, `` Analysis on the stability of Josephson vortices at tricrystal boundaries: A 3φ
_{0}/2-flux case''.*Physical Review B*,**69**, 212503, 2004. link to journal for paper,pdf on University preprint server, pdf preprint. - G. Derks, A. Doelman, S.A. van Gils and T. Visser,
``Travelling waves in a singularly perturbed sine-Gordon equation''.
*Physica D***180**, pp 40-70, 2003. Link to journal for paper, pdf preprint. - K.B. Blyuss, T.J. Bridges and G. Derks, ``Transverse instability and
its long-term development for solitary waves of the
(2+1)-dimensional Boussinesq equation''.
*Phys. Rev. E***67**, 056626 (9 pages), 2003. pdf on University preprint server, Link to journal for paper, pdf preprint. - T.J. Bridges and G. Derks, ``Constructing the symplectic Evans Matrix
using maximally analytic individual vectors''.
*Roy. Soc. Edinburgh Proc. A***133**, pp 505-526 (2003). pdf preprint. -
T.J. Bridges, G. Derks and G. Gottwald,
``Stability and instability of solitary waves of the
fifth-order KDV equation: a numerical framework''.
*Physica D***172**, pp 190-216, 2002. Link to journal for paper, pdf preprint. - G.Derks and T. Ratiu, ``Unstable manifolds of relative equilibria in
Hamiltonian systems with dissipation''.
*Nonlinearity***15**, pp 531-549, 2002. Link to journal for paper, pdf preprint. - T.J. Bridges and G. Derks, ``Linear instability of solitary wave
solutions of the Kawahara equation and its generalizations''.
*SIAM J. Math. Anal.***33**, pp 1356-1378, 2002. pdf on University preprint server, DOI, gzipped postscript preprint. - T.J. Bridges and G. Derks, ``The symplectic Evans matrix, and the
instability of solitary waves and fronts''.
*Arch. Rat. Mech. Anal.***156**, pp 1-87, 2001. Link to journal for paper, pdf preprint. - T.J. Bridges and G. Derks,
``The symplectic Evans matrix and solitary wave instability''.
Conference proceedings
*Symmetry and Perturbation Theory 2001*, editors: D. Bambusi, G. Gaeta and M. Cadoni, World Scientific, pp 32-38, 2001. pdf preprint. - G. Derks,
``Families of relative equilibria in Hamiltonian systems with dissipation''.
Conference proceedings
*Symmetry and Perturbation Theory 1998*, editors: A. Degasperis and G. Gaeta, World Scientific, pp 38-58, 1999. pdf preprint. - T.J. Bridges and G. Derks, ``Unstable eigenvalues and the linearisation
about solitary waves and fronts with symmetry''.
*Proceedings of the Royal Society London*,**A:455**, pp 2427-2469, 1999. pdf on University preprint server, Link to journal for paper, gzipped postscript preprint. - T.J. Bridges and G. Derks, ``Hodge duality and the Evans
function''.
*Physics Letters A*,**251**, pp 363-372, 1999. Link to journal for paper, gzipped postscript preprint. - G.Derks and T. Ratiu, ``Attracting curves on families of stationary
solutions in two-dimensional Navier-Stokes and reduced
magnetohydrodynamics''.
*Proceedings of the Royal Society London*,**A:454**, pp 1406-1444, 1998. pdf on University preprint server, Link to journal for paper. - G. Derks and E. van Groesen, ``Dissipation in Hamiltonian systems:
Decaying cnoidal waves''.
*SIAM Journ. of Math. Anal.***27**, pp 1424-1447,1996. pdf on University preprint server, Link to journal for paper. - G. Derks, D. Lewis and T. Ratiu, ``Approximations with curves of relative
equilibria in Hamiltonian systems with dissipation''.
Nonlinearity
**8**, pp 1087-1113, 1995. Link to journal for paper. - D.H. Hepting, G. Derks, K.D. Edoh, R.D. Russell,
``Qualitative analysis of invariant tori in a dynamical system''.
In G.M. Nielson and D. Silver, editors,
*Visualization '95 Proceedings*. IEEE, IEEE Computer Society Press, Los Alamitos, California, pp 342-345, 1995. - G. Derks and S.A. van Gils, ``On the uniqueness of traveling waves in
perturbed Korteweg-de Vries equations''.
*Jap. Journ. of Indus. and Appl. Math.***10**, pp 413-430, 1993. - G. Derks and E. van Groesen,
``Energy propagation in dissipative systems.
Part II: Centrovelocity for nonlinear wave equations''.
*Wave Motion***15**, pp 159-172, 1992. Link to journal for paper. - G. Derks and T.P. Valkering, ``Approximation in a damped
Hamiltonian system by successive relative equilibria''.
*Jap. Journ. of Indus. and Appl. Math.***9**, pp 141-161, 1992. - G. Derks, E. van Groesen and T.P. Valkering,
``Decay of coherent structures
in dissipative Hamiltonian systems''. In:
*Integration of theory and applications in applied mechanics*. J.F. Dijksman, F.T.M. Nieuwstadt (eds.), Kluwer Academic Press, pp 329-340, 1990. - T.P. Valkering, G. Derks and E. van Groesen, ``Modeling one degree of
freedom behavior of dissipative {H}amiltonian systems with forcing''.
In:
*Proceedings of the international conference on 'Singular behavior and nonlinear dynamics'*. Proceedings**2**, World Scientific, 1989.
## Posters- G.Derks, P.J Aston B.M. Agoram, P.H. Van Der Graaf.
*Predicting rebound for mAbs using the TMDD model*. 7th Noordwijkerhout Symposium on Pharmacokinetics, Pharmacodynamics and Systems Pharmacology, Noordwijkerhout, the Netherlands, 23-25 April 2014. Pdf of poster. -
A. Raji, P.J. Aston, G. Derks, D.J.B. Lloyd,
B.M. Agoram, P.H. Van Der Graaf.
*Mathematical Analysis of PKPD Behaviour of Monoclonal Antibodies: Predicting in vivo Potency and Rebound*6th International Symposium on Measurement and Kinetics of In Vivo Drug Effects. Noordwijkerhout, Netherlands, April 21-24, 2010. Pdf of poster.
## Theses-
G. Derks,
*Coherent Structures in the Dynamics of Perturbed Hamiltonian Systems*. PhD-thesis, University of Twente, Enschede, The Netherlands, 1992. - G. Derks,
*Fractionele Integratie, Fractionele Differentiatie, Fractionele Sobolevruimten (Fractional Integration, Fractional Differentiation, Fractional Sobolev Spaces)*, Master's thesis, University of Technology, Eindhoven, The Netherlands, 1988 (in Dutch).
G.Derks@surrey.ac.uk Last modified: Tue Jan 24 13:27:11 GMT 2023 |