查看更多>>摘要：The extension from the planar case to three dimensions of the clothoid curve (Euler spiral) is herein presented, that is, a curve parametrised by arc length, whose curvature and torsion are linear (affine) functions of the arc length. The problem is modelled as a linear time variant system and its stability is studied with Lyapunov techniques. Closed form solutions in terms of the standard Fresnel integrals are for the first time presented and they are valid for a wide family of clothoids; for the remaining cases, numerical methods of order four, based on Lie algebra, Magnus Expansions and Commutator-Free Expansions are provided. These geometric integrators have been optimised to be easily implemented with few lines of code and require only matrix-vector products (avoiding explicit matrix exponentials at each iteration). The achieved computational efficiency has a dramatic impact for several real-time applications, especially for designing trajectories for flying vehicles, as previous approaches were fully numeric and could not take advantage of the present closed form solutions, which render the computation of the 3D clothoid as computationally expensive as its planar companion.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity . Four different types of travelling wave solutions are identified which represent polarisation and depolarisation waves resulting from either colliding or departing cell sheets as observed in model wound experiments. We study the linear stability of the travelling wave solutions numerically and using spectral theory. This involves the computation of the Evans function most of which we are able to carry out explicitly, with one final step left to numerical simulation.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper investigates the adaptive tracking control problem for a class of p-normal nonlinear time-delay systems with actuator failures via a dynamic event-triggered strategy. To deal with the time-varying delay, a modified Lyapunov-Krasovskii functional (LKF) with the system powers is constructed. By using radial basis function neural networks and hyperbolic tangent function, the residual terms caused by the derivative of LKF can be handled. Then, to achieve better communication efficiency, a dynamic event-triggered strategy is proposed, in which the threshold parameter is dynamically adjusted with the change of the virtual control signal. With the help of the proposed adaptive controller, all states of the closed-loop system are bounded and a favorable tracking performance is ensured. Finally, two examples are given to demonstrate the effectiveness of the proposed method. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper addresses problem of two collinear cracks in an infinity orthotropic solid subject to combined thermal and mechanical loads. Based on a model called ' improved partially conductive crack model', the Fourier transform and superposition theorem, the analytical solutions to some physical quantities and fracture parameters are given. It is revealed that the dimensionless thermal resistance (Rc) between the upper and below crack regions and the proposed coefficient (epsilon) exert a great influence on some physical quantities and fracture parameters, i.e., the mode-II stress intensity factors (K-II) by numerical results. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we propose a novel convex model to recover the sparse signal through the proposed model in the framework of restricted isometry property without the knowledge of the noise type of the measurement model. In addition, several reliable numerical experiments are given to show that the new model has better recovery performance for signals with different noise compared with classical methods such as basis pursuit and Dantzig selector. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we investigate projection-based intrusive and data-driven model order reduction in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form. Discretization of the RTSWE in space with centered finite differences leads to Hamiltonian system of ordinary differential equations with linear and quadratic terms. The full-order model (FOM) is obtained by applying linearly implicit Kahan's method in time. Applying proper orthogonal decomposition with Galerkin projection (POD-G), we construct the intrusive reduced-order model (ROM). We apply operator inference (OpInf) with re-projection as data-driven ROM. In the parametric case, we make use of the parameter dependency at the level of the PDE without interpolating between the reduced operators. The least-squares problem of the OpInf is regularized with the minimum norm solution. Both ROMs behave similarly and are able to accurately predict the in the test and training data and capture system behaviour in the prediction phase with several orders of magnitude in computational speed-up over the FOM. The preservation of system physics such as the conserved quantities of the RTSWE by both ROMs enable that the models fit better to data and stable solutions are obtained in long-term predictions which are robust to parameter changes. (C) 2022 Elsevier Inc. All rights reserved.
Chan, Eunice Y. S.Corless, Robert M.Sendra, J. RafaelSendra, Juana...
13页
查看更多>>摘要：In this paper, for certain type of structured {0, 1, -1}-matrices, we give a complete description of the inner Bohemian inverses over any population containing the set {0, 1, -1}. In addition, when the population is exactly {0, 1, -1 }, we provide explicit formulas for the number of inner Bohemian inverses of these type of matrices. (c)& nbsp;2022 The Authors. Published by Elsevier Inc.& nbsp;
查看更多>>摘要：In this paper we develop a PDE-based mathematical model for valuing real options on the expansion of an investment project whose underlying commodity price and its volatility follow their respective geometric Brownian motions. This mathematical model is of the form of a 2-dimensional Black-Scholes equation whose payoff condition is determined also by a PDE system. A novel 9-point finite difference scheme is proposed for the discretiza-tion of the spatial derivatives and the fully implicit time-stepping scheme is used for the time discretization of the PDE systems. We show that the coefficient matrix of the fully discretized system is an M-matrix and prove that the solution generated by this finite dif-ference scheme converges to the exact one when the mesh sizes approach zero. To demon-strate the usefulness and effectiveness of the mathematical model and numerical method, we present a case study on a real option pricing problem in the iron-ore mining industry. Numerical experiments show that our model and methods are able to produce numerical results which are financially meaningful.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, a novel incremental Newton's iterative algorithm for investigating the optimal control problem of Ito stochastic systems is presented. Newton's method is employed under the Frechet derivative framework to iteratively solve a stochastic algebraic Riccati equation. Under moderate conditions, the convergence and even quadratic convergence of the proposed incremental Newton's iterative algorithm are discussed, respectively. In addition, the Newton's method is extended to the one with linear search. In the end, numerical results are given to demonstrate the effectiveness and superiority of the proposed algorithms. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we carry out the error analysis for a totally decoupled, linear and unconditionally energy stable finite element method to solve the Cahn-Hilliard-Navier-Stokes equations. The fully finite element scheme is based on a stabilization for Cahn-Hilliard equation and projection method for Navier-Stokes equation, as well as the first order Euler method for time discretization. A priori error analysis for phase field, velocity field and pressure variable are derived for the fully discrete scheme.(c) 2022 Elsevier Inc. All rights reserved.
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