arXiv subjects

Hung Dang Nguyen

Publications and source records attributed to Hung Dang Nguyen.

4 recordsLinked to original sources

arXiv2026

Trend to equilibrium and Newtonian limit for the relativistic Langevin equation with singular potentials

We study a system of interacting particles in the presence of the relativistic kinetic energy, external confining potentials, singular repulsive forces as well as a random perturbation through an additive white noise. In comparison with the classical Langevin equations that are known to be exponentially attractive toward the unique statistically steady states, we find that the relativistic systems satisfy algebraic mixing rates of any order. This relies on the construction of Lyapunov functions adapting to previous literature developed for irregular potentials. We then explore the Newtonian limit as the speed of light tends to infinity and establish the validity of the approximation of the solutions by the Langevin equations on any finite time window.

math.PR↗

arXiv2026

Asymptotic analysis for the Generalized Relativistic Langevin Equation

In this paper, we study a non-Markovian generalized relativistic Langevin equation (GRLE). We show that when the memory kernel is a sum of exponentials, the GRLE is equivalent to a Markovian system with added variables. We establish the well-posedness and polynomial ergodicity, obtaining an algebraic rate of convergence to the unique Gibbs distribution. From the Markovian GRLE, we recover the relativistic underdamped Langevin dynamics in a small-noise limit, as well as the classical (non-relativistic) generalized Langevin dynamics in the Newtonian limit.

math.PR↗

arXiv2026

Ergodicity and asymptotic limits for Langevin interacting systems with singular forces and multiplicative noises

In this paper, we study systems of $N$ interacting particles described by the classical and relativistic Langevin dynamics with singular forces and multiplicative noises. For the classical model, we prove the ergodicity, obtaining an exponential rate of convergence to the invariant Boltzmann-Gibbs distribution, and the small-mass limit, recovering the $N$-particle interacting overdamped Langevin dynamics. For the relativistic model, we establish the ergodicity, obtaining an algebraic mixing rate of any order to the Maxwell-Jüttner distribution, and the Newtonian limit (that is when the speed of light tends to infinity), approximating a system of underdamped Langevin dynamics. The proofs rely on the construction of Lyapunov functions that account for irregular potentials and multiplicative noises.

math.PR↗

arXiv2021

Stability analysis of a novel Delay Differential Equation of HIV Infection of CD4$^+$ T-cells

In this paper, we investigate a novel 3-compartment model of HIV infection of CD4$^+$ T-cells with a mass action term by including two versions: one baseline ODE model and one delay-differential equation (DDE) model with a constant discrete time delay. Similar to various endemic models, the dynamics within the ODE model is fully determined by the basic reproduction term $R_0$. If $R_0<1$, the disease-free (zero) equilibrium will be asymptotically stable and the disease gradually dies out. On the other hand, if $R_0>1$, there exists a positive equilibrium that is globally/orbitally asymptotically stable within the interior of a predefined region. To present the incubation time of the virus, a constant delay term $τ$ is added, forming a DDE model. In this model, this time delay (of the transmission between virus and healthy cells) can destabilize the system, arising periodic solutions through Hopf bifurcation. Finally, numerical simulations are conducted to illustrate and verify the results.

q-bio.PE↗