Article
Meteorology & Atmospheric Sciences
Rudiger Brecht, Long Li, Werner Bauer, Etienne Memin
Summary: A physically relevant stochastic representation of the rotating shallow water equations is introduced using stochastic transport principle and decomposition of fluid flow. The model conserves global energy of any realization and allows for generation of physically relevant random simulations with a good balance between model error representation and ensemble spread.
JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS
(2021)
Article
Computer Science, Interdisciplinary Applications
Andrea Brugnoli, Ramy Rashad, Stefano Stramigioli
Summary: In this paper, a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure is proposed. The method utilizes a finite element exterior calculus formulation to represent conservation laws and handle mixed open boundary conditions. By employing a dual-field representation of the physical system, the need to mimic the Hodge star operator at the discrete level is eliminated. Numerical experiments validate the effectiveness of the method and the preservation of energy balance.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Francis Filbet, Luis Miguel Rodrigues
Summary: We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. Our approach is based on higher-order semi-implicit numerical schemes that have been validated on dissipative systems and for magnetic fields pointing in a fixed direction. This scheme provides a consistent approximation of the guiding-center system when the magnitude of the external magnetic field is large.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Sergey Smirnov
Summary: This study discusses different methods of discretizing integrable systems, and considers the semi-discrete analog of two-dimensional Toda lattices associated to the Cartan matrices of simple Lie algebras proposed by Habibullin in 2011. This discretization is based on the notion of Darboux integrability. It is proven that the semi-discrete analogs of Toda lattices associated to the Cartan matrices of all simple Lie algebras are Darboux integrable. The properties of Habibullin's discretization are examined to show that characteristic integrals in the continuous case are also characteristic integrals in the semi-discrete case.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics, Applied
Qianru Zhang, Bin Tu, Qiaojun Fang, Benzhuo Lu
Summary: The study presents a structure-preserving finite element discretization approach for solving the time-dependent Nernst-Planck equation, ensuring the properties of nonnegativity, total mass conservation, and energy dissipation of the solution. The method is validated through numerical experiments, showing better performance in preserving physical properties compared to traditional methods even with dominant convection and coarse grids.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics
Inwon Kim, Dohyun Kwon, Norbert Pozar
Summary: In this work, we investigate the global existence of volume-preserving crystalline curvature flow in a non-convex setting, demonstrating that a natural geometric property related to the reflection symmetries of the Wulff shape is preserved during the flow. By utilizing this geometric property, we analyze the global existence and regularity of the flow for smooth anisotropies, as well as establish global existence results for non-smooth cases involving well-posed anisotropies.
MATHEMATISCHE ANNALEN
(2022)
Article
Mechanics
Rudiger Brecht, Werner Bauer, Alexander Bihlo, Francois Gay-Balmaz, Scott MacLachlan
Summary: A variational integrator is developed to conserve energy while dissipating potential enstrophy in the shallow water equations, improving the quality of approximate solutions and allowing for long-term integrations.
Article
Computer Science, Interdisciplinary Applications
H. Egger, M. Sabouri
Summary: The systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium is discussed, with inf-sup stable finite elements found suitable to avoid oscillations in pressure. The role of the inf-sup condition for well-posedness, choice of initial conditions, and high-order time discretization schemes are clarified. The study aims to provide high-order Galerkin approximations with optimal convergence rates for both space and time.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics
Vesa Julin, Massimiliano Morini, Marcello Ponsiglione, Emanuele Spadaro
Summary: This article provides the first general result for the asymptotics of the area preserving mean curvature flow in two dimensions. It demonstrates that flat flow solutions, starting from any bounded set of finite perimeter, converge with exponential rate to a finite union of equally sized disjoint disks. A similar result is also established for the periodic two-phase Mullins-Sekerka flow.
MATHEMATISCHE ANNALEN
(2023)
Article
Computer Science, Interdisciplinary Applications
Quercus Hernandez, Alberto Badias, David Gonzalez, Francisco Chinesta, Elias Cueto
Summary: The method developed uses feedforward neural networks to learn physical systems from data while ensuring compliance with the first and second principles of thermodynamics. By enforcing the metriplectic structure of dissipative Hamiltonian systems, it minimizes the amount of data required and naturally achieves conservation of energy and dissipation of entropy in its predictions. No prior knowledge of the system is necessary, and the method can handle both conservative and dissipative, discrete and continuous systems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Automation & Control Systems
Flavio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefevre
Summary: This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems, focusing on hyperbolic systems with two conservation laws. The method, derived based on integration by parts of weak form conservation laws, is investigated on nonlinear one-dimensional and two-dimensional shallow-water equations with numerical experiments. Extensions to curvilinear coordinate systems, space-varying coefficients, and higher-order port-Hamiltonian systems are also provided.
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
(2021)
Article
Engineering, Manufacturing
Yanan Wang, Xiang Li
Summary: This study develops a novel programming control strategy to achieve arbitrary 3D shape deformation using four-dimensional printing technology. The experimental results confirm the effectiveness and accuracy of the approach. This strategy is of great importance for the development of shape-morphing systems in the manufacturing field.
ADDITIVE MANUFACTURING
(2022)
Article
Computer Science, Artificial Intelligence
Hongjie Jia, Dongxia Zhu, Longxia Huang, Qirong Mao, Liangjun Wang, Heping Song
Summary: This research proposes a global and local structure preserving nonnegative subspace clustering method, which learns data similarities and cluster indicators in a mutually enhanced way within a unified framework. The model is extended to kernel space to strengthen its capability of dealing with nonlinear data structures. Abundant experiments have shown that the proposed model is better than many advanced clustering methods in most cases.
PATTERN RECOGNITION
(2023)
Article
Automation & Control Systems
Nidhish Raj, Leonardo J. Colombo, Ashutosh Simha
Summary: A reduced attitude controller was designed within a geometric control framework to reorient the spin axis of a gyroscope, preserving gyroscopic stability and achieving almost-global asymptotic stability of the desired equilibrium in the closed loop. Experimental validation demonstrated that the proposed controller outperformed a conventional reduced attitude geometric controller in performance comparison.
Article
Computer Science, Information Systems
Mingxiu Cai, Minghua Wan, Guowei Yang, Zhangjing Yang, Hao Zheng, Hai Tan, Mingwei Tang
Summary: The proposed method aims to address the common defects of subspace mapping methods by introducing a novel structure preserving projections learning via low-rank embedding (SPPL-LRE) algorithm. It achieves this by extracting principal component information, regressing it to classwise block-diagonal structure, and imposing a strong L2 norm constraint on the projection. The method is shown to be more robust and effective than other state-of-the-art methods through extensive experiments.
INFORMATION SCIENCES
(2023)
