64 citations · 305 across the 72 of their papers we have counts for
37 papers · 1 filter
Gradient flow approach to Landau equation: A cross-product structure
Manh Hong Duong, Zihui He
We introduce a cross-product Landau gradient that commutes with Gaussian mollification. For the hard-potential interaction kernels of the form $A(|v-v_*|)\sim \langle v-v_*\rangle^…
Global Dynamics of Trait-Structured Generalised Lotka-Volterra Systems with Trait-Independent Interactions
Manh Hong Duong, Nataliya Balabanova, Blaine van Rensburg
We study the long time dynamics of a selection-mutation integro-differential Lotka-Volterra system of populations. In our model, fitness depends on a continuous phenotypic trai…
The Homogeneous Landau Equation with Regularised Thermal Noise
Manh Hong Duong, Zihui He, Zhengyan Wu
We introduce and analyze a fluctuating homogeneous Landau equation with regularised thermal noise. The model is motivated by the nonlocal gradient flow structure of the determinist…
Unified Formulation and Asymptotic Limits of Inhomogeneous Kinetic Models within GENERIC
Manh Hong Duong, Zihui He
In this paper, we study a general class of inhomogeneous kinetic models that unifies fundamental models in both the statistical physics of particles and of waves, namely the kineti…
Multi-species kinetic models: GENERIC formulation and Fisher information
Manh Hong Duong, Zihui He
In this paper, we study the GENERIC structures of multi-species spatially inhomogeneous Boltzmann and Landau equations with Bose-Einstein, Maxwell-Boltzmann, and Fermi-Dirac statis…
On a fuzzy Landau Equation: Part III. The grazing collision limit
Manh Hong Duong, Boris Golubkov, Zihui He
In this paper, we study the grazing limit from the non-cutoff fuzzy Boltzmann equations to the fuzzy Landau equation, where particles interact through delocalised collisions. We sh…
GENERIC formulation and small-angle limit for Kinetic wave equations
Manh Hong Duong, Zihui He
In this paper, we formulate the three-wave and four-wave kinetic equations into the GENERIC framework and formally derive a small-angle limit for the four-wave equation. This limit…
On a fuzzy Landau Equation: Part II. Solvability results
Manh Hong Duong, Zihui He
This article is the second in a series of our works on the fuzzy Landau equation, where particles interact via delocalised Coulomb collisions. In this work, we focus on the existen…
On a fuzzy Landau Equation: Part I. A variational approach
Manh Hong Duong, Zihui He
This article is the first in a series of works on the fuzzy Landau equation, where particles interact through delocalised Coulomb collisions. Here, we establish a variational chara…
Eco-evolutionary dynamics of a trait-structured predator-prey model
Manh Hong Duong, Fabian Spill, Blaine van Rensburg
The coupling between evolutionary and ecological changes (eco-evolutionary dynamics) has been shown to be relevant among diverse species, and is also of interest outside of ecology…
Adaptive Dynamics of Diverging Fitness Optima
Manh Hong Duong, Fabian Spill, Blaine van Rensburg
We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models…
Convergence to equilibrium for a degenerate McKean-Vlasov Equation
Manh Hong Duong, Amit Einav
In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean-Vlasov equation. We show that the solution to this equation is rel…
Model reduction of Brownian oscillators: quantification of errors and long-time behaviour
M. Colangeli, M. H. Duong, A. Muntean
A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in [Colangeli-Duong-Muntean, Journal of Physics A: Mathema…
Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems
Daniel Adams, Manh Hong Duong, Goncalo dos Reis
In this paper, we develop a natural operator-splitting variational scheme for a general class of non-local, degenerate conservative-dissipative evolutionary equations. The splittin…
Entropic regularisation of non-gradient systems
Daniel Adams, Manh Hong Duong, Goncalo dos Reis
The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framew…
Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures
Manh Hong Duong, Julian Tugaut
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as…
An operator splitting scheme for the fractional kinetic Fokker-Planck equation
Manh Hong Duong, Yulong Lu
In this paper, we develop an operator splitting scheme for the fractional kinetic Fokker-Planck equation (FKFPE). The scheme consists of two phases: a fractional diffusion phase an…
Mean field limits for non-Markovian interacting particles: convergence to equilibrium, GENERIC formalism, asymptotic limits and phase transitions
M. H. Duong, G. A. Pavliotis
In this paper, we study the mean field limit of interacting particles with memory that are governed by a system of interacting non-Markovian Langevin equations. Under the assumptio…
Persistence probability of a random polynomial arising from evolutionary game theory
Van Hao Can, Manh Hong Duong, Viet Hung Pham
In this paper, we obtain an asymptotic formula for the persistence probability in the positive real line of a random polynomial arising from evolutionary game theory. It correspond…
Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics
M. H. Duong, A. Lamacz, M. A. Peletier +2
In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quant…
On the distribution of the number of internal equilibria in random evolutionary games
Manh Hong Duong, Hoang Minh Tran, The Anh Han
In this paper, we study the distribution of the number of internal equilibria of a multi-player two-strategy random evolutionary game. Using techniques from the random polynomial t…
The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium
Manh Hong Duong, Julian Tugaut
In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial…
On the expected number of internal equilibria in random evolutionary games with correlated payoff matrix
Manh Hong Duong, Hoang Minh Tran, The Anh Han
The analysis of equilibrium points in random games has been of great interest in evolutionary game theory, with important implications for understanding of complexity in a dynamica…
On the fundamental solution and a variational formulation of a degenerate diffusion of Kolmogorov type
Manh Hong Duong, Hoang Minh Tran
In this paper, we construct the fundamental solution to a degenerate diffusion of Kolmogorov type and develop a time-discrete variational scheme for its adjoint equation. The so-ca…