Mathematical Sciences

Department staff

Dr Gyula Toth

Photo of Dr Gyula Toth

Lecturer in Applied Mathematics

  • 2017 - present: Lecturer in Applied Mathematics, Loughborough University, Loughborough, UK
  • 2014–2017: VISTA Postdoctoral Research Fellow of The Norwegian Academy of Science and Letters, University of Bergen, Bergen, Norway;
  • 2012– 2014: Postdoctoral Research Fellow of the Hungarian Academy of Sciences, Wigner Research Centre for Physics, Budapest, Hungary;
  • 2012: Ph.D. in Physics, Budapest University of Technology and Economics, Budapest, Hungary;
  • 2004: M.Sc. in Engineering Physics, Budapest University of Technology and Economics, Budapest, Hungary.


My main research field is theoretical and computational materials science, including:

  • Mean-field treatment of equilibrium crystal-liquid interfaces and the dynamics of complex solidification morphologies;
  • Analytic description of amorphous solids in the framework of classical density functional theories.
  • The fundamental understanding of the glass formation and the amorphous precursor-mediated crystal nucleation;
  • Developing a numerically efficient continuum theory describing pattern formation phenomena in multicomponent (complex) liquids;
  • Re-classification and extension of traditional hydrodynamic models: alternative interpretation of compressible and incompressible fluid flows, derivation of unified dynamic equations.
  • Finding the bridge between classical field theories and discrete microscopic models;
  • Implementing numerical algorithms for solving PDEs on massively parallel HPC devices (GPU programming).

Teaching 2017-18

  • MAB104 – Engineering Mathematics 3
  1. B. Korbuly, T. Pusztai, G.I. Tóth, H. Henry, M. Plapp, L. Gránásy: Orientation-field models for polycrystalline solidification: grain coarsening and complex growth forms, J. Cryst. Growth 457, 32-37 (2017).
  2. F. Podmaniczky, G.I. Tóth, G. Tegze, T. Pusztai, L. Gránásy: Phase-field crystal modeling of heteroepitaxy and exotic modes of crystal nucleation, J. Cryst. Growth 457, 24-31 (2017).
  3. F. Podmaniczky, G.I. Tóth, G. Tegze, L. Gránásy: Hydrodynamic theory of freezing: Nucleation and polycrystalline growth, Phys. Rev. E. 95, 052801 (2017).
  4. L. Rátkai, G.I. Tóth, L. Környei, T. Pusztai, L. Gránásy: Phase-field modeling of eutectic structures on the nanoscale: the effect of anisotropy, J. Mat. Sci. 52, 5544-5558 (2017).
  5. G. I. Tóth, J. Selvåg, B. Kvamme: A phenomenological continuum theory of asphaltene stabilized oil/water emulsion, Energy & Fuels 31, 1218-1225 (2017).
  6. F. Podmaniczky, G.I. Tóth, T. Pusztai, L. Gránásy: Investigating nucleation using the phase-field method, J. Indian Inst. Sci. 96, 161-178 (2016).
  7. G. I. Tóth, M. Zarifi and B. Kvamme: Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids, Phys. Rev. E 93, 013126 (2016).
  8. G.I. Tóth: Phase-field modeling of isothermal quasi-incompressible multicomponent liquids, Phys. Rev. E 94, 033114 (2016).
  9. F. Podmaniczky, G.I. Tóth, G. Tegze and L. Gránásy: Recent Developments in Modeling Heteroepitaxy/Heterogeneous Nucleation by Dynamical Density Functional Theory, Metall. Mat. Trans. A 46, 4908-4920 (2015).
  10. G .I. Tóth, B. Kvamme: Analysis of Ginzburg-Landau-type models of surfactant-assisted liquid phase separation, Phys. Rev. E 91, 032404 (2015).
  11. G .I. Tóth and B. Kvamme: Phase field modelling of spinodal decomposition in the oil/water/asphaltene system, Phys. Chem. Chem. Phys. 17, 20259 (2015).
  12. G. I. Tóth, T. Pusztai and L. Gránásy: Consistent multiphase-field theory for interface driven multidomain dynamics, Phys. Rev. B 92, 184105 (2015).
  13. L. Gránásy, L. Rátkai, A. Szállás, B. Korbuly, G. I. Tóth, L. Környei, T. Pusztai: Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites - A Review, Metall. Mat. Trans. A 40, 1-26 (2014).
  14. L. Gránásy, G.I. Tóth: Crystallization: Colloidal suspense, Nat. Phys. 10, 12-13 (2014).
  15. L. Gránásy, F. Podmaniczky, G.I. Tóth, G. Tegze, T. Pusztai: Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model, Chem. Soc. Rev. 43, 2159-2173 (2014).
  16. F. Podmaniczky, G. I. Tóth, T. Pusztai, L. Gránásy: Free energy of the bcc-liquid interface and the Wul_ shape as predicted by the phase-field crystal model, J. Cryst. Growth, 385(1), 148-153 (2014).
  17. G .I. Tóth, N. Provatas: Advanced Ginzburg-Landau theory of freezing: A density-functional approach, Phy. Rev. B. 90, 104101 (2014).
  18. G. I. Tóth, L. Gránásy, G. Tegze: Nonlinear hydrodynamic theory of crystallization, J. Phys.: Condens. Matter 26(5), 055001 (2013).
  19. 23. H. Emmerich, H. Löwen, R. Wittkowski, T. Gruhn, G.I. Tóth, G. Tegze, L. Gránásy: Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview, Adv. Phys. 61, 665-743 (2012).
  20. G. Tegze, G. I. Tóth: Osmotic convection-driven instability and cellular eutectic growth in binary systems, Acta Mater. 60, 1689-1694 (2012).
  21. G. I. Tóth, G. Tegze, T. Pusztai, L. Gránásy: Heterogeneous Crystal Nucleation: The Effect of Lattice Mismatch, Phys. Rev. Lett. 108, 025502 (2012).
  22. L. Gránásy, G. Tegze, G. I. Tóth, T. Pusztai: Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning, Philos. Mag. 91, 123-149 (2011).
  23. G. Tegze, L. Gránásy, G. I. Tóth, J. F. Douglas, T. Pusztai: Tuning the structure of nonequilibrium soft materials by varying the thermodynamic driving force for crystal ordering, Soft Matter 7, 1789-1799 (2011).
  24. G. Tegze, G. I. Tóth, L. Gránásy: Faceting and Branching in 2D Crystal Growth, Phys. Rev. Lett. 106, 195502 (2011).
  25. G. I. Tóth, T. Pusztai, G. Tegze, G. Tóth, L. Gránásy: Amorphous Nucleation Precursor in Highly Nonequilibrium Fluids, Phys. Rev. Lett. 107, 175702 (2011).
  26. G. I. Tóth, J. R. Morris, L. Gránásy: Ginzburg-Landau-Type Multiphase Field Model for Competing fcc and bcc Nucleation, Phys. Rev. Lett. 106, 045701 (2011).
  27. G. I. Tóth, G. Tegze, T. Pusztai, G. Tóth, L. Gránásy: Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D, J. Phys.: Condens. Matter 22, 364101 (2010).
  28. G. Tegze, L. Gránásy, G. I. Tóth, F. Podmaniczky, A. Jaatinen, T. Ala-Nissila, T. Pusztai: Diffusion-controlled anisotropic growth of stable and metastable crystal polymorphs in the phase-field crystal model, Phys. Rev. Lett. 103, 035702 (2009).
  29. G. Tegze, G. Bansel, G. I. Tóth, T. Pusztai, Z. Fan, L. Gránásy: Advanced operator-splitting based semi-implicit spectral method to solve the binary phase-field crystal equation with variable coefficients, J. Comp. Phys. 228, 1612-1623 (2009).
  30. G. I. Tóth, L. Gránásy: Crystal nucleation in the hard-sphere system revisited: Critical test of theoretical approaches, J. Phys. Chem. B 113, 5141-5148 (2009).
  31. W. Löser, R. Hermann, T. G. Woodcock, J. Fransaer, M. Krivilyov, L. Gránásy, T. Pusztai, G. I. Tóth, D. M. Herlach, D. Holland-Moritz, M. Kolbe, T. Volkmann: Nucleation and phase selection in undercooled melts: Magnetic alloys of industrial relevance, J. Jpn. Soc. Microgravity Appl. 25, 319-324 (2008).
  32. T. Pusztai, G. Tegze, G. I. Tóth, L. Környei, G. Bansel, Z. Fan, L. Gránásy: Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation, J. Phys.: Cond. Matter 20, 404205 (2008).
  33. G. I. Tóth, L. Gránásy: Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: I. Transitions in the one-phase liquid region, J. Chem. Phys. 127, 074709 (2007).
  34. G. I. Tóth, L. Gránásy: Phase-field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: II. Nucleation in the metastable liquid immiscibility region, J. Chem. Phys. 127, 074710 (2007).
  35. L. Gránásy, T. Pusztai, G. I. Tóth, G. Tegze, J. A.Warren, J. F. Douglas: Polycrystalline patterns in far-from-equilibrium freezing: a phase field study, Philos. Mag. 86, 3757-3778 (2006).
  36. L. Gránásy, T. Pusztai, T. Börzsönyi, G. Tóth, G. Tegze, J. A. Warren, J. F. Douglas: Phase field theory of crystal nucleation and polycrystalline growth: A review, J. Mater. Res. 21, 309-319 (2006). "Outstanding Meeting Paper - Review Article".
  37. G. Tegze, T. Pusztai, G. Tóth, L. Gránásy, A. Svandal, T. Buanes, T. Kuznetsova, B. Kvamme: Multi-scale approach to CO2-hydrate formation in aqueous solution: Phase field theory and molecular dynamics. Nucleation and growth, J. Chem. Phys. 124, 234710 (2006).
  38. B. Kvamme, A. Graue, E. Aspenes, T. Kuznetsova, L. Gránásy, G. Tóth, T. Pusztai, G. Tegze: Kinetics of solid hydrate formation by carbon dioxide: Phase-field theory of hydrate nucleation and magnetic resonance imaging, Phys. Chem. Chem. Phys. 6, 2327-2334 (2004).
  39. L. Gránásy, T. Pusztai, G. Tóth, Z. Jurek, M. Conti, B. Kvamme: Phase-field theory of crystal nucleation in the hard sphere liquid, J. Chem. Phys. 119, 10376-10382 (2003).