Thanh Tran
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View article: The stochastic Landau–Lifshitz–Baryakhtar equation: Global solution and invariant measure
The stochastic Landau–Lifshitz–Baryakhtar equation: Global solution and invariant measure Open
View article: A Hybrid Genetic Algorithm and Tabu Search for Construction Site Layout Planning Problem
A Hybrid Genetic Algorithm and Tabu Search for Construction Site Layout Planning Problem Open
The construction site layout is widely acknowledged as a complex challenge in the field of construction management. However, it is crucial for nearly all construction projects, as the layout of site facilities can significantly impact on t…
View article: Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth
Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth Open
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient conce…
View article: Local-in-time well-posedness for a magnetohydrodynamical model with intrinsic magnetisation
Local-in-time well-posedness for a magnetohydrodynamical model with intrinsic magnetisation Open
View article: Application of Variable Step‐Size Hybrid Methods for Solving Third‐Order Lane‐Emden Equations
Application of Variable Step‐Size Hybrid Methods for Solving Third‐Order Lane‐Emden Equations Open
This manuscript introduces a pair of variable step‐size hybrid methods (PVSHM) to efficiently solve third‐order initial value problems of Lane‐Emden‐type equations (LETE). These equations are extensively used across various disciplines, in…
View article: Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations
Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations Open
View article: Nonlinear free oscillation of tri-directional functionally graded porous skew-plates with variable thickness in high-thermal environment
Nonlinear free oscillation of tri-directional functionally graded porous skew-plates with variable thickness in high-thermal environment Open
For the first time, a finite element model was constructed based on the improved shear deformation plate theory and the von Kármán assumption to analyze the linear and nonlinear free vibration behaviour of tri-directional functionally grad…
View article: CHARACTERIZING THE COMPACTNESS OF CALDERÓN-ZYGMUND COMMUTATORS OF TYPE THETA ON GENERALIZED MORREY-LORENTZ SPACES
CHARACTERIZING THE COMPACTNESS OF CALDERÓN-ZYGMUND COMMUTATORS OF TYPE THETA ON GENERALIZED MORREY-LORENTZ SPACES Open
In this paper, we characterize the compactness of the Calderón-Zygmund commutator of type on generalized Morrey-Lorentz spaces . More precisely, we prove that if , which is the closure of , then is a compact operator on for all and .
View article: Well-Posedness for a Magnetohydrodynamical Model with Intrinsic Magnetisation
Well-Posedness for a Magnetohydrodynamical Model with Intrinsic Magnetisation Open
Ferromagnetic magnetohydrodynamics concerns the study of conducting fluids with intrinsic magnetisation under the influence of a magnetic field. It is a generalisation of the magnetohydrodynamical equations and takes into account the dynam…
View article: Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations
Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations Open
We study the long-time behaviour of solutions to some classes of fourth-order nonlinear PDEs with non-monotone nonlinearities, which include the Landau--Lifshitz--Baryakhtar (LLBar) equation (with all relevant fields and spin torques) and …
View article: Well-Posedness and Finite Element Approximation for the Landau-Lifshitz-Gilbert Equation with Spin-Torques
Well-Posedness and Finite Element Approximation for the Landau-Lifshitz-Gilbert Equation with Spin-Torques Open
Spin currents act on ferromagnets by exerting a torque on the magnetisation. This torque is modelled by appending additional terms to the Landau-Lifshitz-Gilbert equation motivating the study of the non-homogeneous Landau-Lifshitz-Gilbert …
View article: The Landau--Lifshitz--Bloch equation on polytopal domains: Unique existence and finite element approximation
The Landau--Lifshitz--Bloch equation on polytopal domains: Unique existence and finite element approximation Open
The Landau--Lifshitz--Bloch equation (LLBE) describes the evolution of the magnetic spin field in ferromagnets at high temperatures. In this paper, we study the numerical approximation of the LLBE on bounded polytopal domains in $\mathbb{R…
View article: The stochastic Landau--Lifshitz--Baryakhtar equation: Global solution and invariant measure
The stochastic Landau--Lifshitz--Baryakhtar equation: Global solution and invariant measure Open
The Landau--Lifshitz--Baryakhtar (LLBar) equation perturbed by both additive and multiplicative noises is a system of fourth order stochastic PDEs which models the evolution of magnetic spin fields in ferromagnetic materials at elevated te…
View article: High-order QMC nonconforming FEMs for nearly incompressible planar stochastic elasticity equations
High-order QMC nonconforming FEMs for nearly incompressible planar stochastic elasticity equations Open
In a recent work (Dick et al, arXiv:2310.06187), we considered a linear stochastic elasticity equation with random Lamé parameters which are parameterized by a countably infinite number of terms in separate expansions. We estimated the exp…
View article: Sparse grid approximation of nonlinear SPDEs: The Landau--Lifshitz--Gilbert equation
Sparse grid approximation of nonlinear SPDEs: The Landau--Lifshitz--Gilbert equation Open
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equation in engineering and physics, the stochastic Landau-Lif…
View article: Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties
Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties Open
We explore a linear inhomogeneous elasticity equation with random Lamé parameters. The latter are parameterized by a countably infinite number of terms in separated expansions. The main aim of this work is to estimate expected values (cons…
View article: Global solutions of the Landau–Lifshitz–Baryakhtar equation
Global solutions of the Landau–Lifshitz–Baryakhtar equation Open
The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes into account contributions from nonlocal damping and is valid at moderate temperat…
View article: A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems
A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems Open
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.
View article: Uniqueness of the Stochastic Keller--Segel Model in One Dimension
Uniqueness of the Stochastic Keller--Segel Model in One Dimension Open
View article: Global Weak Solution of the Landau–Lifshitz–Baryakhtar Equation
Global Weak Solution of the Landau–Lifshitz–Baryakhtar Equation Open
View article: Optimal control for a coupled spin-polarized current and magnetization system
Optimal control for a coupled spin-polarized current and magnetization system Open
This paper is devoted to an optimal control problem of a coupled spin drift-diffusion Landau–Lifshitz–Gilbert system describing the interplay of magnetization and spin accumulation in magnetic-nonmagnetic multilayer structures, where the c…
View article: Officers/Committee
Officers/Committee Open
View article: The one-dimensional stochastic Keller–Segel model with time-homogeneous spatial Wiener processes
The one-dimensional stochastic Keller–Segel model with time-homogeneous spatial Wiener processes Open
View article: Remarks on Sobolev norms of fractional orders
Remarks on Sobolev norms of fractional orders Open
View article: A Fully Discrete Method
A Fully Discrete Method Open
View article: Two-Level Methods: The hp-Version on Rectangular Elements
Two-Level Methods: The hp-Version on Rectangular Elements Open
View article: Multilevel Methods: The h-Version
Multilevel Methods: The h-Version Open
View article: Two-Level Methods: The h-Version
Two-Level Methods: The h-Version Open
View article: Pseudo-differential Equations with Spherical Splines
Pseudo-differential Equations with Spherical Splines Open
View article: Implementation Issues and Numerical Experiments
Implementation Issues and Numerical Experiments Open