About

Tri Nguyen is an Assistant Research Professor in the Department of Nuclear Engineering at Penn State University. The department is recognized as one of the top-ranked nuclear engineering programs in the United States, with a strong emphasis on experimental research. The department offers educational programs for undergraduate, master's, and doctoral students, supported by facilities such as the Radiation Science and Engineering Center (RSEC), which includes the Breazeale Reactor, the country's first and longest operating licensed nuclear research reactor. This access to an operating research reactor provides unique research and educational opportunities. The department's focus areas include nuclear science and applications, nuclear materials, nuclear thermal hydraulics, reactor physics and advanced reactor design, plasma physics and engineering, nuclear security, safeguards, and safety, as well as the nuclear fuel cycle. Tri Nguyen's research and contributions are aligned with these areas, leveraging the department's resources to advance nuclear engineering knowledge and education.

Research topics

• Physics
• Geology
• Astronomy
• Remote sensing
• Applied mathematics
• Quantum mechanics
• Pure mathematics
• Mathematical analysis
• Mathematics
• Mathematical physics
• Optics
• Geometry

Selected publications

• Remarks on Landau damping

  ArXiv.org · 2025-05-15

  preprintOpen access1st authorCorresponding

  We provide few remarks on nonlinear Landau damping that concerns decay of the electric field in the classical Vlasov-Poisson system near spatially homogenous equilibria. In particular, this includes the analyticity framework, à la Grenier-Nguyen-Rodnianski, for non specialists, treating the analytic case studied by Mouhot-Villani, among other remarks for plasmas confined on a torus and in the whole space. Finally, we also establish the nonlinear Landau damping for a family of Vlasov-Riesz systems, which are new and surprisingly include the borderline Vlasov-Dirac-Benney system in the sharp analytic spaces.

  PublisherOA PDFDOI

• Boosting Insect Pest Recognition with Deep-Wide Learning

  SSRN Electronic Journal · 2025-01-01

  preprintOpen access1st authorCorresponding
  PublisherDOI

• Linear Landau Damping for the Vlasov-Maxwell System in $$\mathbb{R}^3$$

  Annals of PDE · 2025-09-24 · 1 citations

  articleOpen access

  In this work, we consider the relativistic Vlasov-Maxwell system, linearized around a spatially homogeneous equilibrium, set in the whole space $$\mathbb{R}^3 \times \mathbb{R}^3$$ . The equilibrium is assumed to belong to a class of radial, smooth, rapidly decaying functions. Under appropriate conditions on the initial data, we prove algebraic decay (of dispersive nature) for the electromagnetic field. For the electric scalar potential, the leading behavior is driven by a dispersive wave packet with non-degenerate phase and compactly supported amplitude, while for the magnetic vector potential, it is driven by a wave packet whose phase behaves globally like the one of Klein-Gordon and the amplitude has unbounded support.

  PublisherOA PDFDOI

• Plasmons for the Hartree equations with Coulomb interaction

  Probability and Mathematical Physics · 2025-06-21 · 1 citations

  articleOpen access1st authorCorresponding
  PublisherDOI

• Modified Scattering for Long-Range Hartree Equations of Infinite Rank Near Vacuum

  SIAM Journal on Mathematical Analysis · 2025-11-10

  article1st authorCorresponding
  PublisherDOI

• Landau damping below survival threshold

  arXiv (Cornell University) · 2024-12-16

  preprintOpen access1st authorCorresponding

  In this paper, we establish nonlinear Landau damping below survival threshold for collisionless charged particles following the meanfield Vlasov theory near general radial equilibria. In absence of collisions, the long-range Coulomb pair interaction between particles self-consistently gives rise to oscillations, known in the physical literature as plasma oscillations or Langmuir's oscillatory waves, that disperse in space like a Klein-Gordon's dispersive wave. As a matter of fact, there is a non-trivial survival threshold of wave numbers that characterizes the large time dynamics of a plasma: {\em phase mixing} above the threshold driven by the free transport dynamics and {\em plasma oscillations} below the threshold driven by the collective meanfield interaction. The former mechanism provides exponential damping, while the latter is much slower and dictated by Klein-Gordon's dispersion which gives decay of the electric field precisely at rate of order $t^{-3/2}$. Up to date, all the works in the mathematical literature on nonlinear Landau damping fall into the phase mixing regime, in which plasma oscillations were absent. The present work resolves the problem in the plasma oscillation regime. Our nonlinear analysis includes (1) establishing the existence and dispersion of Langmuir's waves, (2) decoupling oscillations from phase mixing in different time regimes, (3) detailing the oscillatory structure of particle trajectories in the phase space, (4) treating plasma echoes via a detailed analysis of particle-particle, particle-wave, and wave-wave interaction, and (5) designing a nonlinear iterative scheme in the physical space that captures both phase mixing and dispersion in low norms and allows growth in time in high norms. As a result, we establish nonlinear plasma oscillations and Landau damping below survival threshold for data with finite Sobolev regularity.

  PublisherOA PDFDOI

• A new framework for particle-wave interaction

  arXiv (Cornell University) · 2024-10-17

  preprintOpen access1st authorCorresponding

  In plasma physics, collisionless charged particles are transported following the dynamics of a meanfield Vlasov equation with a self-consistent electric field generated by the charge density. Due to the long range interaction between particles, the generating electric field oscillates and disperses like a Klein-Gordon dispersive wave, known in the physical literature as plasma oscillations or Langmuir's oscillatory waves. The oscillatory electric field then in turn drives particles. Despite its great physical importance, the question of whether such a nonlinear particle-wave interaction would remain regular globally and be damped in the large time has been an outstanding open problem. In this paper, we propose a new framework to resolve this exact nonlinear interaction. Specifically, we employ the framework to establish the large time behavior and scattering of solutions to the nonlinear Vlasov-Klein-Gordon system in the small initial data regime. The novelty of this work is to provide a detailed physical space description of particles moving in an oscillatory field and to resolve oscillations for the electric field generated by the collective interacting particles. This appears to be the first such a result analyzing oscillations in the physical phase space $\mathbb{R}^3_x\times \mathbb{R}_v^3$.

  PublisherOA PDFDOI

• On nonlinear instability of Prandtl's boundary layers: The case of Rayleigh's stable shear flows

  Journal de Mathématiques Pures et Appliquées · 2024-03-01 · 22 citations

  articleSenior authorCorresponding
  PublisherDOI

• The Inviscid Limit of Navier–Stokes Equations for Locally Near Boundary Analytic Data on an Exterior Circular Domain

  Communications in Mathematical Physics · 2024-02-01 · 3 citations

  article1st author
  PublisherDOI

• Linear Landau damping in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ℝ</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:math>

  Journées Équations aux dérivées partielles · 2024-07-22

  articleOpen access1st authorCorresponding

  This article gives an overview on linear Landau damping for collisionless kinetic models such as the non-relativistic Vlasov–Poisson and relativistic Vlasov–Maxwell systems near spatially homogenous radial steady states on the phase space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>ℝ</mml:mi> <mml:mi>x</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msubsup> <mml:mi>ℝ</mml:mi> <mml:mi>v</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> .

  PublisherOA PDFDOI

Recent grants

• Mathematical Questions in Kinetic Theory

  NSF · $300k · 2021–2024

• Dynamics of Wave Structures in Fluid Dynamics, Oscillatory Media, and Plasma Physics

  NSF · $90k · 2014–2018

• The Inviscid Limit and Large Time Behavior of Fluid Flows

  NSF · $210k · 2018–2022

• Stability and Dynamics of Traveling Waves, and Boundary Layer Theory

  NSF · $114k · 2011–2013

• Stability and Dynamics of Traveling Waves, and Boundary Layer Theory

  NSF · $49k · 2013–2014

Frequent coauthors

• Emmanuel Grenier

  Unité de Mathématiques Pures et Appliquées

  64 shared

• Frédéric Rousset

  21 shared

• Yan Guo

  19 shared

• Daniel Han-Kwan

  18 shared

• Kevin Zumbrun

  Indiana University Bloomington

  13 shared

• Claude Bardos

  Laboratoire Jacques-Louis Lions

  12 shared

• David Gérard‐Varet

  Cambridge University Press

  12 shared

• Harpinder Saini

  10 shared

Awards & honors

• Early Career Award