We introduce a novel computational framework designed to explore the dynamic interactions between fluid and solid particles or structures immersed in a viscous fluid medium adhering to the generalized Onsager principl...
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We introduce a novel computational framework designed to explore the dynamic interactions between fluid and solid particles or structures immersed in a viscous fluid medium adhering to the generalized Onsager principle. This innovative framework harnesses the power of the phase -field -embedding method, in which each solid component, whether rigid or elastic, is characterized by a volume -preserving phase field. The unified velocity within the fluid -solid ensemble governs the movement of both solid particles and the surrounding fluid, specifically for passive particles. Active particles, however, are not only influenced by this unified velocity but are also driven by their self-propelling velocities. To capture exclusive volume interactions among particles and between particles and boundaries, we employ repulsive potential forces at a coarser scale. These forces effectively model repulsion and collision effects. Rigid particles maintain structural integrity by enforcing a zero velocity gradient tensor within their spatial domains, necessitating the introduction of a constraining stress tensor. In contrast, elastic particles are governed by a quasi -linear constitutive equation describing the elastic stress within their domains, allowing for accurate modeling of their deformations. The motion of solid particles is tracked by monitoring the dynamics of their centers of mass. This approach facilitates the development of a hybrid, thermodynamically consistent hydrodynamic model applicable to both rigid and elastic particles. To numerically solve this thermodynamically consistent model for elastic particles, we present a structure -preserving numerical algorithm. Notably, in the limit of an infinite elastic modulus, this algorithm converges to the one employed for modeling rigid particles. Finally, we substantiate the effectiveness, accuracy, and stability of our proposed scheme through a series of numerical experiments. These experiments not only validate the computati
In this paper, Particle-in-Cell algorithms for the Vlasov-Poisson system are presented based on its Poisson bracket structure. The Poisson equation is solved by finite element methods, in which the appropriate finite ...
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In this paper, Particle-in-Cell algorithms for the Vlasov-Poisson system are presented based on its Poisson bracket structure. The Poisson equation is solved by finite element methods, in which the appropriate finite element spaces are taken to guarantee that the semi-discretized system possesses a well defined discrete Poisson bracket structure. Then, splitting methods are applied to the semi-discretized system by decomposing the Hamiltonian function. The resulting discretizations are proved to be Poisson bracket preserving. Moreover, the conservative quantities of the system are also well preserved. In numerical experiments, we use the presented numerical methods to simulate various physical phenomena. Due to the huge computational effort of the practical computations, we employ the strategy of parallel computing. The numerical results verify the efficiency of the new derived numerical discretizations. (C) 2022 Elsevier Inc. All rights reserved.
A complete structure-preserving learning scheme for single-input/single-output (SISO) linear port-Hamiltonian systems is proposed. The construction is based on the solution, when possible, of the unique identification...
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A complete structure-preserving learning scheme for single-input/single-output (SISO) linear port-Hamiltonian systems is proposed. The construction is based on the solution, when possible, of the unique identification problem for these systems, in ways that reveal fundamental relationships between classical notions in control theory and crucial properties in the machine learning context, like structure-preservation and expressive power. In the canonical case, it is shown that, up to initializations, the set of uniquely identified systems can be explicitly characterized as a smooth manifold endowed with global Euclidean coordinates, which allows concluding that the parameter complexity necessary for the replication of the dynamics is only O(n) and not O(n2), as suggested by the standard parametrization of these systems. Furthermore, it is shown that linear port-Hamiltonian systems can be learned while remaining agnostic about the dimension of the underlying data-generating system. Numerical experiments show that this methodology can be used to efficiently estimate linear port-Hamiltonian systems out of input-output realizations, making the contributions in this paper the first example of a structure-preserving machine learning paradigm for linear port-Hamiltonian systems based on explicit representations of this model category.
When the matrices $A$ and $Q$ have special structure, the structure-preservingalgorithm was used to compute the stabilizing solution of the complex matrix equation $X+A^TX^{-1}A=Q.$ In this paper, we study the numeric...
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When the matrices $A$ and $Q$ have special structure, the structure-preservingalgorithm was used to compute the stabilizing solution of the complex matrix equation $X+A^TX^{-1}A=Q.$ In this paper, we study the numerical methods to solve the complex
symmetric stabilizing solution of the general matrix equation $X+A^TX^{-1}A=Q.$ We
not only establish the global convergence for the methods under an assumption, but
also show the feasibility and effectiveness of them by numerical experiments.
Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. Continuation MPC, suggested by T. Ohtsuka ...
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Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. Continuation MPC, suggested by T. Ohtsuka in 2004, uses Krylov-Newton iterations. Continuation MPC is suitable for nonlinear problems and has been recently adopted for minimum time problems. We extend the continuation MPC approach to a case where the state is implicitly constrained to a smooth manifold. We propose an algorithm for on-line controller implementation and demonstrate its numerical effectiveness for a test problem on a hemisphere.
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