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Department of Mathematical Sciences

Staff

Prof Wojtek Zakrzewski, PhD

Contact Prof Wojtek Zakrzewski (email at w.j.zakrzewski@durham.ac.uk)

Research Groups

  • Biomathematics
  • Mathematical Physics

Research Interests

  • Mathematical physics

Selected Publications

Articles: magazine

Journal papers: academic

  • Delisle L.,, Hussin V., & Zakrzewski W.J. (2013). Constant curvature solutions of Grassmannian sigma models: (2) Non-holomorphic solutions. Journal of Geometry and Physics 71: 1-10.
  • Adam C.,, Ferreira L.A.,, da Hora E.,, Wereszczynski A., & Zakrzewski W.J., (2013). Some aspects of self-duality and generalised BPS theories. Journal of High Energy Physics 2013(8): 62.
  • Chakrabarti, B., Piette, B.M.A.G. & Zakrzewski, W.J. (2012). Spontaneous polaron transport in biopolymers. Europhysics letters 97(4): 47005.
  • Ferreira, LA, Klimas, P & Zakrzewski, WJ (2011). Some (3+1) dimensional vortex solutions of the $CP^N$ model. Physical Review D 83(10): 105018.
  • Ferreira, LA & Zakrzewski, WJ (2011). The concept of quasi-integrability: a concrete example. Journal of High Energy Physics 2011(5): 130.
  • Zakrzewski, W.J. (2010). A class of (1+1) dim models that generalize the Sine-Gordon model and some of their properties. Yaderna Fisica 73: 587-594.
  • Hussin, V., Yurdusen, I. & Zakrzewski, W.J. (2010). Canonical surfaces associated with projectors in Grassmannian sigma models. Journal of Mathematical Physics 51(10): 103509.
  • Brizhik, L. Eremko, A. Piette, B. & Zakrzewski, W.J. (2010). Ratchet dynamics of large polarons in asymmetric diatomic molecular chains. Journal of physics: condensed matter 22(15): 155105.
  • Stichel, PC & Zakrsewski, WJ (2010). Self-gravitating darkon fluid with anisotropic scaling. The European Physical Journal C 70(3): 713-721.
  • Piette, B.M.A.G., Liu, J., Peeters, K., Smertenko, A., Hawkins, T., Deeks, M., Quinlan, R., Zakrzewski, W.J. & Hussey, P.J. (2009). A Thermodynamic Model of Microtubule Assembly and Disassembly. PLoS ONE 4(8): e6378.
  • Stichel, P.C. & Zakrzewski, W.J. (2009). Can cosmic acceleration be caused by exotic massless particles? Physical Review D 80: 083513.
  • Piette B. & Zakrzewski, W.J. (2009). Scattering of sine-Gordon Breathers on a Potential Well. Physical Review E Statistical, Nonlinear and Soft Matter Physics 79(4): 046603.
  • Lukierski, J., Stichel, P.C. & Zakrzewski, W.J. (2008). Acceleration-extended symmetries in nonrelativistic space-time with a cosmological constant. European Journal of Physics C 55: 119-124.
  • Al-Alawi, J. & Zakrzewski, W.J. (2008). Scattering of Topological Solitons on Barriers and Holes of Deformed Sine-Gordon Models. Journal of Physics A 41: 315206.
  • Piette, B. & Zakrzewski, W.J. (2008). Skyrme Model with Different Mass Terms. Physical Review D 77: 074009 (.
  • Ferreira, L.A., Piette, B. & Zakrzewski, W.J. (2008). Wobbles and other kink-breather solutions of the Sine Gordon model. Physical Review E 77: 036613.
  • Ferreira, Luiz Agostinho & Zakrzewski, W.J. (2007). A simple formula for the conserved charges of soliton theories. Journal of High Energy Physics 09: 015.
  • Lukierski, J., Stichel, P.C. & Zakrzewski, W.J. (2007). Acceleration-extended Galilean symmetries with central charges and their dynamical realisations. Physics Letters B 650: 203.
  • Brizhik, L., Eremko, A., Piette, B. & Zakrzewski, W.J. (2007). Adiabatic self-trapped states in carbon nanotubes. J. Phys Cond. Mat 19: 306205.
  • Piette, B. & Zakrzewski, W.J. (2007). Dynamical properties of a Soliton in a Potential Well. Journal of Physics A: Mathematical and Theoretical 40(2 ): 329-346.
  • Admunsen, D., Cova, R.J. & Zakrzewski, W.J. (2007). Non ${\pi\over N}$ Scattering of $CP^1$ solitons. Canadian Journal of Physics 85: 1431-1445.
  • Al-Alawi, J. & Zakrzewski, W.J. (2007). Q-ball scattering on barriers and holes in 1 and 2 Spatial dimensions. Journal of Physics A 42: 245201.
  • Collins, J.C. & Zakrzewski, W.J. (2007). Scattering of a two skyrmion configuration on potential holes or barriers in a model Landau-Lifshitz equation. Journal of Physics A 42: 165102.
  • Piette, B. & Zakrzewski, W.J. (2007). Scattering of Sine-Gordon kinks on potential wells. Journal of Physics A: Mathematical and Theoretical 40(22): 5995-6010.
  • Al-Alawi, J. & Zakrzewski, W.J. (2007). Scattering of Topological Solitons on Barriers and Holes in Two $\lambda \phi^4$ Models. Journal of Physics A 40: 11319-11332.
  • Bratek, L. Brizhik, L., Eremko, A., Piette, B., Watson, M. & Zakrzewski, W.J. (2007). Self-trapped electron states in carbon nanotubes. Physica D 228(2): 130-139.
  • Hartmann, B. & Zakrzewski, W.J. (2007). Soliton solutions of the nonlinear Schr\"odinger equation with nonlocal Coulomb and Yukawa interactions. Physics Letters A 366: 540-544.
  • Zakrzewski, W.J. (2007). Surfaces in ${\mathbb R}^{N^2-1}$ based on harmonic maps $S^2\rightarrow CP^{N-1}$. Journal of Mathematical Physics 48: 113520.
  • Lukierski, J., Stichel, P.C. & Zakrzewski, W.J. (2006). Exotic Galilean conformal symmetry and its dynamical realisations. Physics Letters A357: 1-5.
  • Brizhik, L. Eremko, A., Piette, B. & Zakrzewski, W.J. (2006). Charge and energy transfer by solitons in low-dimensional nanosystems with helical structure. Chemical Physics 324(1): 259-266.
  • Yu. Gaididei,, P.L. Christiansen, & W.J. Zakrzewski (2006). Conformational transformations induced by the charge-curvature interaction. Physical Review E74: 021914.
  • Brizhik, L. Eremko, A., Piette, B. & Zakrzewski, W.J. (2006). Electron self-trapping on a nano-circle. Physica D: Nonlinear Phenomena 218(1): 36-55.
  • Lukierski, J., Prochnicka, I., Stichel, P.C. & Zakrzewski, W.J. (2006). Galilean exotic planar supersymmetries and nonrelativistic wave equations. Physics Letters B 639: 383-396.
  • Lukierski, J., Prochnicka, I., Stichel, P.C. & Zakrzewski, W.J. (2006). Galilean exotic planar supersymmetries and nonrelativistic wave equations. Physics Letters B 639: 383-396.
  • A.M. Grundland,, A. Strasburger, & W.J. Zakrzewski (2006). Surfaces immersed in $su{N+1}$ Lie algebras obtained from the $C P^{N}$ sigma models. Journal of Physics A 39: 9187-9213.
  • Hussin, V. & Zakrzewski, W.J. (2006). Susy $CP\sp{N-1}$ model and surfaces in ${R}^{N^2-1}$. Journal of Physics A 39: 14231-14240.
  • B. Hartmann & W.J. Zakrzewski (2006). The transition of 2 dimensional solitons to 1 dimensional on a hexagonal lattice. Journal of Nonlinear Mathematical Physics 13: 111-116.
  • Walet, N. & Zakrzewski, W.J. (2005). A simple model of the charge transfer in DNA-like substances. Nonlinearity 18(6): 2615-2636.
  • W.J. Zakrzewski (2005). Laplacians on Lattices. Journal of Nonlinear Mathematical Physics 12: 530-538.
  • Amundsen, D., Cova, R.J. & Zakrzewski, W.J. (2005). Modified ${\pi\over N}$ Scattering on $T_2$. WSEAS Transactions on Mathematics 3: 304-311
  • Piette, B. & Ward, R.S. (2005). Planar Skyrmions: vibrational modes and dynamics. Physica D: Nonlinear Phenomena 201(1-2): 45-55.
  • R.J. Cova & W.J. Zakrzewski (2005). Scattering of periodic solitons. Revisita Mexicana de Fisica 50: 527-535.
  • Brand, J., Piette, B. & Zakrzewski, W.J. (2005). Scattering of topological solitons on holes and barriers. Journal of Physics. A 38(IOP): 1403-1412.
  • B. Hartmann & W.J. Zakrzewski (2005). Solitons and Deformed Lattices. Journal of Nonlinear Mathematical Physics 12: 88-104.
  • P.C. Stichel & W.J. Zakrzewski (2003). A new type of Conformal Dynamics. Annals of Physics. 310 (2003) 158-180
  • A.M. Grundland & W.J. Zakrzewski (2003). CP^{N-1} Harmonic Maps and the Weierstrass Problem. Journal of Mathematical Physics 44(8): 3370-3382.
  • Hartmann, B. & Zakrzewski, W.J. (2003). Electrons on Hexagonal Lattices and Applications to Nanotubes. Physical Review B 68(18): 184302.
  • Lukierski, J, Stichel, P & Zakrzewski, W.J. (2003). Noncommutative planar particle dynamics with gauge interactions. Annals of Physics 306(1): 78-95.
  • Brizhik, L., Eremko, A., Piette, B. & Zakrzewski, W.J. (2003). Spontaneous Localisation of Electrons in Two-dimensional Lattices within the Adiabatic Approximation. Journal of Mathematical Physics (44): 3689-3697.
  • Brizhik, L., Eremko, A., Piette, B. & Zakrzewski, W.J. (2003). Spontaneous Localization of Electrons in Lattices with Non-Local Interactions. Physical Review B(68): 104301.
  • Brizhik, L., Eremko, A., Piette, B. & Zakrzewski, W.J. (2003). Static solutions of a D-dimensional Modified Nonlinear Schroedinger Equation. Nonlinearity 16(4): 1481-1497.
  • T.A. Ioannidou, V.B. Kopeliovich & W.J. Zakrzewski (2002). Approximate Analytical Solutions of the Baby Skyrme Model. 'Journal of Experimental and Theoretical Physics 95 (2002) 572-580'
  • Chu, C.S., Lukierski, J. & Zakrzewski, W.J. (2002). Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories. Nuclear Physics B 632(1-3): 219-239.
  • Wospakrik,H. Zakrzewski & W.J. (2001). Alternative SU(N) Skyrme Models and Their Solutions.
  • Brizhik, L Piette, B. & Zakrzewski, W.J. (2001). Electron Self-Trapping in Anisotropic Two Dimensional Lattices. Ukr. Fiz. Journal (46): 503-511.
  • Lukierski,J. Stichel, P.C. Zakrzewski & W.J. (2001). From Gauging Nonrelativistic Translations to N body Dynamics.
  • Stichel, P.C. & Zakrzewski, W.J. (2001). Possible confinement mechanisms for nonrelativistic particles on a line.
  • Ioannidou, T. Piette, B. , Sutcliffe, P. & Zakrzewski, W.J. (2001). Skyrmions and Rational Maps. Nonlinearity (14): C1-C5.
  • Sutcliffe, P. Zakrzewski & W.J. (2001). Skyrmions from Harmonic Maps.
  • Brizhik, L., Eremko, A. & Piette, B.M.A.G. (2001). Solitonic Electron States in a Discrete Two-Dimensional Lattice.
  • Brizhik, L., Eremko, A., Piette, B.M.A.G. & Zakrzewski, W.J. (2001). Spontaneously Localized Electron States in a Discrete Anisotropic Two-Dimensional Lattice. Physica D(159): 71-90.
  • Eslami,P. Sarbishei, M. Zakrzewski & W.J. (2000). Baby Skyrme Models for a Class of Potentials.
  • Zakrzewski W, B.M.A.G. Piette & A. Kudryavtsev (2000). Interactions of Skyrmions with Domain Walls. Physical Review D 61 025016
  • Kopeliovich,V.B. Stern, B.E. Zakrzewski & W.J. (2000). Skyrmions from SU(3) Harmonic Maps and Their Quantization.
  • Lukierski,J. Stichel, P.C. Zakrzewski & W.J. (2000). Translational Chern-Simons Action and New Planar Dynamics.
  • Zakrzewski, W.J., Lukierski, J. & Stichel, P.C. (1999). (2 + 1)-Dimensional Models with a Chern-Simons-Like Term and Noncommutative Geometry.
  • Zakrzewski W & J. Dziarmaga (1999). Diffusion of overdamped classical solitons. Physics Letters A 251 193-198
  • Zakrzewski, W.J. & Kopeliovich, V.B. (1999). Flavoured Multiskyrmions.
  • Zakrzewski, W.J. & Dziarmaga, J. (1999). Noise driven diffusion of solitons.
  • Ioannidou, T., Piette, B.M.A.G. & Zakrzewski, W.J. (1999). Spherically Symmetric Solutions of the SU(N) Skyrme Models. Journal of Mathematical Physics 40: 6223-6233.
  • Ioannidou, T., Piette, B.M.A.G. & Zakrzewski, W.J. (1999). SU(N) Skyrmions and Harmonic Maps. Journal of Mathematical Physics (40): 6353-6365.
  • Zakrzewski, W.J. & Ioannidou, T. (1998). A note on Ward's chiral model.
  • Zakrzewski, W.J. & Burzlaff, J. (1998). CP2 soliton scattering: the collective coordinate approximation.
  • Zakrzewski, W.J. & Ioannidou, T. (1998). Lagrangian formulation of the general modified chiral model.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1998). Localized solutions in a 2 dimensional landau-lifshitz model. Physica D(119): 314-326.
  • Piette, B.M.A.G., Kudryavtsev, A. & Zakrzewski, W.J. (1998). Mesons, baryons and waves in the baby skyrmion model. Eur. Phys. J C(1): 333-341.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1998). Metastable stationary solutions of the radial d dimensional sine-Gordon model. Nonlinearity (11): 1103-1110.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1998). Numerical integration of (2+1) dimensional PDEs for valued functions. J. Comp. Phys (145): 359-381.
  • Piette, B.M.A.G., Kudryavtsev, A. & Zakrzewski, W.J. (1998). Skyrmions and domain walls in (2+1) dimensions. Nonlinearity (11): 783-795.
  • Piette, B.M.A.G., Bogolubsky, I.L. & Zakrzewski, W.J. (1998). Solitons of a general gauged S^2 model with a mass term. Phys. Lett B(432): 151-158.
  • Zakrzewski, W.J., Thomova, Z. & Winternitz, P. (1998). Solutions of (2+1) dimensional spin systems.
  • Zakrzewski, W.J. & Ioannidou, T. (1998). Solutions of the modified chiral model in (2+1) dimensions.
  • Zakrzewski, W.J. & Dziarmaga, J. (1998). What happens with an initially kicked soliton?.
  • Zakrzewski, W.J, Lukierski, J. & Stichel, P. (1997). A Galilean invariant (2+1) dimensional model with a Chern-Simmons like term.
  • Zakrzewski, W.J, Rutenberg, A. & Zapotocky, M. (1997). Dynamical multiscaling in quenched skyrme systems.
  • Leznov, A.N., Piette, B.M.A.G. & Zakrzewski, W.J (1997). On the integrability of pure skyrme models in 2 dimensions. J.Math.Phys (38): 3007-3011.
  • Zakrzewski, W.J. & Cova, R.J (1997). Soliton scattering in the model on a torus.
  • Zakrzewski, W.J. & Burzlaff, J. (1996). CP2 Soliton Scattering: Simulations and Mathematical Underpinning.
  • Zakrzewski, W.J., Belov, N.A. & Leznov, A.N. (1996). Discrete Symmetry and its Use to Find Mulitsoliton Solutions of the Equations of Anisotropic Heisenberg Ferromagnets.
  • Zakrzewski, W.J. & Papanicolaou, N. (1996). Dynamics of Magnetic Bubbles in a Skyrme Model.
  • Zakrzewski, W.J., Belov, N.A. & Leznov, A.N. (1996). Generalization of the Toda Chain System to the Elliptic Curve Case.
  • Zakrzewski, W.J., Grundland, A.M. & Winternitz, P. (1996). On the Solutions of the CP1 Model in (2+1) Dimensions.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1996). Shrinking of Solitons in the 2+1 Dimensional S2 Sigma Model. Nonlinearity (9): 897-910.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1996). Some Aspects of Soliton Unwindings.
  • Zakrzewski, W.J. (1995). A modified discrete Sine-Gordon model.
  • Zakrzewski, W.J., Lukierski, J. & Ruegg, H. (1995). Classical and Quantum Mechanics of Free -relativistic Particles.
  • Zakrzewski, W.J., Lukierski, J. & Ruegg, H. (1995). Classical and Quantum Mechanics of Free -relativistic Systems.
  • Zakrzewski, W.J., Leznov, A.N. & Mukhtarov, M.A. (1995). Discrete Symmetry and Solution of the Principal Chiral Field Problem.
  • Piette, B.M.A.G., Schroers, B.J. & Zakrzewski, W.J. (1995). Dynamics of Baby Skyrmions. Nuclear Physics B(439): 205-238.
  • Zakrzewski, W.J. & Papanicolaou (1995). Dynamics of Interacting Magnetic Vortices in a Model Landau-Lifshitz Equation.
  • Zakrzewski, W.J. & M. Zapotocky (1995). Kinetics of phase ordering with topological textures.
  • Piette, B.M.A.G., Schroers, B.J. & Zakrzewski, W.J. (1995). Multisolitons in a two-dimensional Skyrme Model. Zeitschrift fur Physik C(65): 165-174.
  • Zakrzewski, W.J. & Cova, R.J. (1995). Skyrmions in (2+1) Dimensions.
  • Piette, B.M.A.G., Tchrakian, D.H. & Zakrzewski, W.J. (1994). Chern-Simons solitons in a model. Phys. Lett
  • Zakrzewski, W.J., Below, N.A. & Leznov, A.N. (1994). On the solutions of the anisotropic Heisenberg equation.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1994). Some aspects of the scattering of skyrmions in (2+1) dimensions. (7): 231-244.

Journal papers: professional

  • Brizhik, L, Eremko, A,, Piette, B.M.A.G., & # Zakrzewski, W.J., (2004). Solitons in alpha-helical proteins. Phys. Rev E 70,: 2615-2626.

Conference papers

  • Brizhik, L., Eremko, A. Piette, B. & Zakrzewski, W.J. (2010), Ratchet effect of Davydov's solitons in nonlinear low-dimensional nanosystems, International Journal of Quantum Chemistry 110: Molecular Self-Organization in Micro-, Nano-, and Macro-Dimensions: From Molecules to Water, to Nanoparticles, DNA and Proteins”. Kiev, Wiley, 25-37.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1994), General Structures in (2+1) Dimensional Models, in Spatschek, K.H. & Mertens, F.G. eds, Nonlinear Coherent Structures in Physics and Biology Plenum Press, 283-286.

Edited works: conference proceedings

  • Brizhik, L., Eremko, A., Piette, B. & Zakrzewski, W.J. (2009). Davydov's solitons in zigzag carbon nanotubes. Molecular Self-Organization in Micro-, Nano-, and Macro-Dimensions: From Molecules to Water, to Nanoparticles, DNA and Proteins, Wiley.
  • Brizhik, L. Eremko, A. Ferreira, L.A. Piette, B. & Zakrzewski, W.J. (2009). Some Properties of Solitons. SelfOrganization of Molecular Systems, Kiev.
  • Ferreira, L.A. Piette, B. & Zakrzewski, W.J. (2008). Dynamics of the topological structures in inhomogeneous media.
  • Brizhik, L. Eremko, A. Piette, B. & Zakrzewski, W. (2008). Effects of Periodic electromagnetic Field on Charge Transport in Macromolecules. Frohlich Symposium, Biophysical Aspects of Cancer: Electromagnetic Mechanisms.
  • Piette, B. & Zakrzewski, W.J. (2008). Scattering of sine-Gordon Kinks and Breathers on a Finite Width Well. Dynamic Systems and Applications, Atlanta, Georgia, USA.
  • Piette, B. & Zakrzewski, W.J. (2008). Some Aspects of Dynamics of Topological Solitons. 22nd Max Born Symposium,, Wroclaw.
  • Kopeliovich, V.B., Piette, B. & Zakrzewski, W.J. (2006). Mass Terms in the Skyrme Model. Quark 2006, St' Petersbourg, Russia.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (2000). Nontopological structures in the baby-Skyrme model. Solitons, Properties, Dynamics, Interactions and Applications,, Springer.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1999). Skyrmions and Domain Walls. Properties, Dynamics, Interactions and Applications,, Springer.
  • Ioannidou, T., Piette, B.M.A.G. & Zakrzewski, W.J. (1999). SU(N) Skyrmions and two dimensional CPN Rational Maps. New symmetries and integrable models, Karpacz.
  • Ioannidou, T., Piette, B.M.A.G. & Zakrzewski, W.J. (1999). Three Dimensional Skyrmions and Harmonic Maps. Halifax.
  • Piette, B.M.A.G. & Zakrzewski, W.J (1997). Soliton-like structures in two dimensions and their properties.
  • Piette, B.M.A.G. & Zakrzewski, W.J. (1995). Scattering of extended structures in (2+1) dimensional models,. World Scientific.

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