Research
I am interested in developing mathematical models describing the joint evolution of active and passive populations. We investigate two distinct descriptions:
(1) a continuous one with deterministic dynamics (i.e. a PDE system coupling fast-slow flows in porous media via Forchheimer-like equations coupled with diffusion via non-linear interaction terms),
(2) a discrete one with Monte Carlo stochastic dynamics (i.e. a gas dynamics formalism involving two species driven by different dynamics competing via simple exclusion processes for the same lattice).
Our ultimate goal is to unite these descriptions into a multiscale, hybrid (coupled deterministic/stochastic) evolution system. We provide mathematical analysis and simulation results for parts of the proposed models.
Collaboration
This work is done jointly with my supervisor Prof. Adrian Muntean (Karlstad, Sweden), Prof. Emilio Cirillo (Rome, Italy) together with Assoc. Prof. Matteo Colangeli (L'Aquila, Italy).
Bio
I graduated my Master 2 in Applied Mathematics with the University of Orleans (France). After that, I have enrolled a PhD position at Gran Sasso Science Institute, L'Aquila, Italy in 2016. Via a double degree agreement, I became a PhD student in Mathematics with also Karlstad University.
Selected publications
TKT Thieu, M. Colangeli, A. Muntean. Uniqueness and stability with respect to parameters of solutions to a fluid-like driven system for active--passive pedestrian dynamics, accepted for publication in Journal of Mathematical Analysis and Applications, 2020.
VA Khoa, TKT Thieu, ER Ijioma, "On a pore-scale stationary diffusion equation: scaling effects and correctors for the homogenization limit", accepted for publication in Discrete & Continuous Dynamical Systems Series B, 2020.
ENM Cirillo, M. Colangeli, A. Muntean and TKT Thieu, "When diffusion faces drift: consequences of exclusion processes for bi - directional pedestrian flows", in Physica D: Nonlinear Phenomena, Vol. 413, no. 132651, 2020.
M. Colangeli, A. Muntean, O. Richardson, TK Thieu, "Modeling interactions between active and passive agents moving through heterogeneous environments," in G. Libelli, N. Bellomo (Eds), Crowd Dynamics, vol. 1: Theory, Models and Safety Problems (pp. 211-- 254). Modeling and Simulation in Science, Engineering and Technology, Boston, Birkh, 2019.
ENM Cirillo, M. Colangeli, A. Muntean, TKT Thieu, "A lattice model for active - passive pedestrian dynamics: a quest for drafting effects", in Mathematical Biosciences and Engineering, Vol. 17, 1, pp. 460-477, 2019.
TKT Thieu, M. Colangeli, A. Muntean, "Weak solubility of a fluid-like driven system for active-passive pedestrian dynamics", in Nonlinear Studies, Vol. 26, no. 4, pp. 991-1006, 2019.