arXiv subjects

Ngo Phuoc Nguyen Ngoc

Publications and source records attributed to Ngo Phuoc Nguyen Ngoc.

7 recordsLinked to original sources

arXiv2026

Recurrence, Transience, and the Rate of Escape for Elephant Random Walks with Two Memory Channels

We study the one-dimensional elephant random walk with two memory channels introduced by Saha [Phys.\ Rev.\ E \textbf{106}, L062105 (2022)] with memory parameter $p\in(0,1)$. Maulik, Roy and Sadhukhan [arXiv:2509.10225] proved recurrence for $p\le11/16$ and transience for $p>7/8$, leaving the range $11/16<p\le7/8$ open. We close this gap by proving that $p=11/16$ is the exact recurrence--transience threshold and by determining how fast the walk escapes from the origin throughout the transient regime. For $11/16<p<7/8$, we also show that the scaling limit obtained by Maulik, Roy and Sadhukhan is almost surely nonzero. At $p=7/8$, we prove that the walk is transient with zero asymptotic velocity and escapes at the scale $n/\sqrt{\log n}$.

math.PR↗

arXiv2026

Invariant measures of exclusion processes with a look-ahead rule

We study a one-dimensional exclusion process with a fixed jump length $I \ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local headway. We identify the class of rates admitting an explicit Ising-Gibbs invariant measure, with stationarity governed by pairwise balance rather than detailed balance. In the thermodynamic limit, we derive a closed-form stationary current that recovers the mean-field prediction for look-ahead traffic-flow models exactly when particles are uncorrelated, and quantifies the correlation-induced correction otherwise. The resulting fundamental diagram is right-skewed and non-concave, as in empirical traffic data, and for a preferred-spacing interaction-where the stationary headway distribution becomes bimodal-the mean-field approximation fails qualitatively. The closed-form current is confirmed by kinetic Monte Carlo simulations and by exact finite-size computations.

cond-mat.stat-mech↗

arXiv2026

Tandem Exclusion Process

We introduce the \emph{tandem exclusion process} (TEP), a one-dimensional stochastic lattice model motivated by tandem running in ants. Particles evolve through two cooperative local transitions, $110\to101$ at rate $α$ (leader advancement) and $101\to011$ at rate $β$ (follower recovery). We prove that the stationary measure on the dynamically active sector is the Gibbs measure $π\propto q^{H(η)}$, where $q=β/α$ and $H(η)$ counts neighboring occupied pairs, and derive exact closed-form expressions for the stationary current and spatial correlations using transfer-matrix methods. The current is asymmetric under particle--hole exchange $ρ\mapsto1-ρ$, with its maximum occurring at densities strictly larger than $1/2$, in contrast to the symmetric current $ρ(1-ρ)$ of the totally asymmetric simple exclusion process (TASEP). For $q>1$, cooperative dynamics enhances the current above the TASEP value and generates strong spatial clustering; in the limit $q\to\infty$, the current approaches $J\toαρ$, corresponding to nearly unconstrained collective transport. These results suggest that tandem coordination alone can substantially enhance collective transport efficiency at moderate and high densities, even without pheromone-mediated long-range communication.

cond-mat.stat-mech↗

arXiv2025

A Class of Exclusion Processes Capable of Exhibiting Current Reversal

A century after Ising introduced the Ising measure to study equilibrium systems, its relevance has expanded well beyond equilibrium contexts, notably appearing in non-equilibrium frameworks such as the Katz--Lebowitz--Spohn (KLS) model. In this work, we investigate a class of generalized asymmetric simple exclusion processes (ASEP) for which the Ising measure serves as the stationary state. We show that the average stationary current in these models can display current reversal and other unconventional behaviors, offering new insights into transport phenomena in non-equilibrium systems. Moreover, although long-range interaction rates often give rise to long-range interactions in the potential function, our model provides a counterexample: even with long-range interactions in the dynamics, the resulting potential remains short-ranged. Finally, our framework encompasses several well-known models as special cases, including ASEP, the KLS model, the facilitated exclusion process, the cooperative exclusion process, and the assisted exchange model.

cond-mat.stat-mech↗

arXiv2024

An Exactly Solvable Dual Bus Route Model

In 1998, O'Loan et al. introduced a simplified bus route model to illustrate bus dynamics. However, fluctuations in passenger numbers make it challenging to achieve an exact solution for the model's stationary state, as these fluctuations can impact bus behavior. In this study, we present an exactly solvable model for a dual bus route system that builds upon O'Loan et al.'s model. This dual model allows us to comprehensively analyze bus route dynamics. Our model introduces additional parameters not previously considered by O'Loan et al. to account for neighboring effects and align with an observation in the original model, which can influence the average stationary current and velocity of buses. When the neighboring effect is weak, our model behaves similarly to O'Loan et al.'s bus route model. However, with a strong neighboring effect, our model exhibits intriguing characteristics. Additionally, in some limiting cases, our model recovers well-known models such as the simple exclusion process, its generalization, the cooperative exclusion process, and the RNA polymerase model during the elongation stage.

cond-mat.stat-mech↗

arXiv2024

An exactly solvable model for RNA polymerase during the elongation stage

We consider a Markovian model for the kinetics of RNA Polymerase (RNAP) which provides a physical explanation for the phenomenon of cooperative pushing during transcription elongation observed in biochemical experiments on Escherichia coli and yeast RNAP. To study how backtracking of RNAP affects cooperative pushing we incorporate into this model backward (upstream) RNAP moves. With a rigorous mathematical treatment of the model we derive conditions on the mutual static and kinetic interactions between RNAP under which backtracking preserves cooperative pushing. This is achieved by exact computation of several key properties in the steady state of this model, including the distribution of headway between two RNAP along the DNA template and the average RNAP velocity and flux.

physics.bio-ph↗

arXiv2024

An Exactly Solvable Model for Single-Lane Unidirectional Ant Traffic

In 2002, Chowdhury et al. introduced a simplified model aimed at depicting the dynamics of single-lane unidirectional ant traffic. Despite efforts, an exact solution for the stationary state of this ant-trail model remains elusive. The primary challenge arises from inherent fluctuations in the total amount of pheromone along the ant-trail. These fluctuations significantly influence ant movement. Consequently, unlike conventional models involving driven interacting particles, the average velocity exhibits non-monotonic behavior with ant density. In this study, we propose an exactly solvable model for ant traffic whose dynamics is based on the one in Chowdhury et al.'s model, and then discuss the circumstances under which the non-monotonic trend of average velocity arises.

cond-mat.stat-mech↗