Toan Nguyen - Academia.edu (original) (raw)

Papers by Toan Nguyen

The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave... more The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectrum in weakly nonlinear and dispersive media. Such a kinetic model has been derived by physicists in the sixties, though the well-posedness theory remains open, due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution, the first such a result, to the wave turbulence equation for capillary waves.

Consider a system of N particles interacting through Newton's second law with Coulomb interac... more Consider a system of N particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a C^2 smooth potential in any dimension. We prove that in the mean field limit N → + ∞, the N particles system displays instabilities in times of order N for some configurations approximately distributed according to unstable homogeneous equilibria.

Extending investigations of Yarahmadian and Zumbrun in the strictly parabolic case, we study time... more Extending investigations of Yarahmadian and Zumbrun in the strictly parabolic case, we study time-asymptotic stability of arbitrary (possibly large) amplitude noncharacteristic boundary layers of a class of hyperbolic-parabolic systems including the Navier--Stokes equations of compressible gas- and magnetohydrodynamics, establishing that linear and nonlinear stability are both equivalent to an Evans function, or generalized spectral stability, condition. The latter is readily checkable numerically, and analytically verifiable in certain favorable cases; in particular, it has been shown by Costanzino, Humpherys, Nguyen, and Zumbrun to hold for sufficiently large-amplitude layers for isentropic ideal gas dynamics, with general adiabiatic index γ> 1. Together with these previous results, our results thus give nonlinear stability of large-amplitude isentropic boundary layers, the first such result for compressive ("shock-type") layers in other than the nearly-constant case....

Quarterly of Applied Mathematics, 2019

Archive for Rational Mechanics and Analysis, 2018

In their classical work [35, 36], Caflisch and Sammartino proved the inviscid limit of the incomp... more In their classical work [35, 36], Caflisch and Sammartino proved the inviscid limit of the incompressible Navier-Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl's boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl's boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy-Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity.

Physica D: Nonlinear Phenomena, 2018

Duke Mathematical Journal, 2016

In this paper, we construct growing modes of the linearized Navier-Stokes equations about generic... more In this paper, we construct growing modes of the linearized Navier-Stokes equations about generic stationary shear flows of the boundary layer type in a regime of sufficiently large Reynolds number: R → ∞. Notably, the shear profiles are allowed to be linearly stable at the infinite Reynolds number limit, and so the instability presented is purely due to the presence of viscosity. The formal construction of approximate modes is well-documented in physics literature, going back to the work of Heisenberg, C.C. Lin, Tollmien, Drazin and Reid, but a rigorous construction requires delicate mathematical details, involving for instance a treatment of primitive Airy functions and singular solutions. Our analysis gives exact unstable eigenvalues and eigenfunctions, showing that the solution could grow slowly at the rate of e t/ √ R. A new, operator-based approach is introduced, avoiding to deal with matching inner and outer asymptotic expansions, but instead involving a careful study of singularity in the critical layers by deriving pointwise bounds on the Green function of the corresponding Rayleigh and Airy operators.

Two areas are currently the focus of active research, namely cloud computing and high-performance... more Two areas are currently the focus of active research, namely cloud computing and high-performance computing. Their expected impact on business and scientific computing is such that most application areas are eagerly uptaking or waiting for the associated infrastructures. However, open issues still remain. Resilience and loadbalancing are examples of such areas where innovative solutions are required to face new or increasing challenges, e.g., fault-tolerance. This paper presents existing concepts and open issues related to the design, implementation and deployment of a fault-tolerant application framework on cloud computing platforms. Experiments are sketched including the support for application resilience, i.e., faulttolerance and exception-handling. They also support the transparent execution of distributed codes on remote highperformance clusters.

The Journal of Physical Chemistry, 1991

Page 1. J. Phys. Chem. 1991, 95, 3315-3322 3315 Monte Carlo Slmulations of Liquid Acetic Acld and... more Page 1. J. Phys. Chem. 1991, 95, 3315-3322 3315 Monte Carlo Slmulations of Liquid Acetic Acld and Methyl Acetate with the OPLS Potential Functions James M. Briggs, Toan B. Nguyen, and William L. Jorgensen* Department ...

X‐Ray Spectrometry, 1998

In an inter-analytical method comparison, energy-dispersive x-ray uorescence (EDXRF) (radioactiv... more In an inter-analytical method comparison, energy-dispersive x-ray uorescence (EDXRF) (radioactive source and x-ray tube based systems), inductively coupled plasma mass spectrometry (ICP-MS) and graphite furnace atomic absorption spectrometry (GF-AAS) analyses were ...

Development and Policies Research Center Working …, 2007