Research, publications & Presentations

Chaotic behaviour of disordered nonlinear lattices, https://open.uct.ac.za/handle/11427/34029 

The research focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We report the effects of the type of the impurity (heterogeneity) parameter on the systems' transport properties and classify the transport mechanisms of the nonlinear versions of the models into various dynamical regimes. We also identify computationally efficient numerical integration techniques, including the so-called symplectic integrators, and implement them for studying these models. Finally, we perform an extensive numerical investigation of the dynamics of the considered models revealing that for their nonlinear versions chaotic transport persists and chaotic hotspots meander in the region of energy concentration supporting the theories governing the spreading mechanism.

• B. Senyange, C. Skokos, Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method, Physica D: Nonlinear Phenomena 432, 133154, 2022. https://www.sciencedirect.com/science/article/abs/pii/S016727892200001X 

• B. Senyange, J.J. du Plessis, B. M. Manda, C. Skokos, Properties of normal modes in a modified disordered Klein-Gordon lattice: From disorder to order, Nonlinear Phenomena in Complex Systems 23 (2), 65–71, 2020. https://doi.org/10.33581/1561-4085-2020-23-2-165-171 

• B. M. Manda, B. Senyange, C. Skokos, Chaotic wave-packet spreading in two-dimensional disordered nonlinear lattices, Phys. Rev. E 101 (3), 032206, 2020. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.032206 

• B. Senyange, B. M. Manda, C. Skokos, Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices, Phys. Rev. E 98, 2018. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.052229 

• B. Senyange, C. Skokos, Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices, EPJ 227, 625 – 643, 2018. https://link.springer.com/article/10.1140/epjst/e2018-00131-2 

• “Chaos in multidimensional disordered nonlinear lattices” (TALK), The 10th International Congress on Industrial and Applied Mathematics - ICIAM, Waseda University (Tokyo, Japan), August 20 – 25, 2023. https://iciam2023.org/ 

• “Localized and spreading chaos in multidimensional nonlinear disordered lattices” (POSTER), The 10th International Congress on Industrial and Applied Mathematics - ICIAM, Waseda University (Tokyo, Japan), August 20 – 25, 2023. https://iciam2023.org/ 

• “Chaotic behaviour of disordered nonlinear lattices” (TALK), The joint African-Nordic conference in Mathematicians 2023, Makerere University (Kampala, Uganda), August 1 – 4, 2023. https://news.mak.ac.ug/2023/07/the-joint-african-nordic-conference-in-mathematics/ 

• “Transitioning to remote engagement: the good, the bad and the unexpected experiences from an online course” (POSTER), Muni University Symposium, June 2023, Brazzaville (Republic of Congo), June, 2023.

• “Chaotic behaviour of disordered nonlinear lattices”, Pan African Congress of Mathematicians PACOM 2022, Brazzaville (Republic of Congo), August 1 – 6, 2022. https://www.pacom2022.com/

• “Chaotic behaviour of disordered nonlinear lattices”, Third International Conference on Integrable Systems & Nonlinear Dynamics, and school "Integrable and Nonlinear Days", Virtual (Yaroslavl, Russia), October 4 – 8, 2021. https://lomonosov-msu.ru/eng/event/6844/ 

• “Chaotic behaviour of disordered nonlinear lattices”, ICTP Statistical Physics of Complex systems conference, Virtual (Trieste, Italy), September 8 – 10, 2021. https://indico.ictp.it/event/9625/ 

• “Efficient integration schemes for multidimensional disordered nonlinear Hamiltonian lattices”, Nolineal conference 2020, Virtual, June 30 - July 2, 2021. http://www.gsc.upm.es/nolineal2020/ 

• “Symplectic integration techniques for disordered nonlinear Hamiltonian lattices”, The annual Southern Africa Mathematical Sciences Association (SAMSA) conference, Virtual, November 23 − 25, 2020.

• “Chaotic dynamics in disordered nonlinear lattices: Symplectic integrators”, The 62nd Annual Congress of South African Mathematical Society (SAMS), Cape Town (South Africa), December 2 − 4, 2019. https://uctcmc.eventsair.com/sams2019/ 

• “Chaotic dynamics in disordered nonlinear lattices: Symplectic integrators”, The International Congress on industrial and Applied Mathematics (ICIAM), Valencia (Spain), July 15 − 19, 2019. https://iciam2019.com/ 

• “Chaotic dynamics in disordered nonlinear lattices”, The International Congress on Industrial and Applied Mathematics (ICIAM), Valencia (Spain), July 15 − 19, 2019. https://iciam2019.com/ 

• “On characterising the dynamics of 1-D disordered nonlinear Hamiltonian lattices”, The annual Southern Africa Mathematical Sciences Association (SAMSA) conference, Palapye (Botswana), November 19 − 22, 2018. https://sites.google.com/a/biust.ac.bw/samsa2018/ 

• “Chaotic dynamics of one-dimensional disordered nonlinear lattices”, Nonlinear Localization in Lattices, Spetses (Greece), June 18 − 22, 2018. https://qcn.physics.uoc.gr/nll2018/ 

• “Chaotic dynamics of the disordered Klein-Gordon lattice”, The International Scientific Workshop: Recent Advances in Hamiltonian and Nonholonomic Dynamics, Moscow (Russia), June 15 − 18, 2017. http://hnh-conf.rcd.ru/ 

• “On the symplectic integration of the Klein-Gordon lattice model”, The 3rd EAUMP conference, Makerere University, Kampala (Uganda), October 26 − 28, 2016