查看更多>>摘要：In this paper, a split-step balanced theta-method (SSBT) has been presented for solving stochastic differential equations (SDEs) under non-global Lipschitz conditions, where theta is an element of[0, 1] is a parameter of the scheme. The moment boundedness and strong convergence of the numerical solution have been studied, and the convergence rate is 0.5. Moreover, under some conditions it is proved that the SSBT scheme can preserve the exponential mean-square stability of the exact solution when theta is an element of(1/2, 1] for every step size h > 0. Numerical examples verify the theoretical findings. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper deals with the network-based robust distributed state estimation problem of a class of discrete-time positive systems with bounded parameter perturbation and bounded disturbance. The system outputs are measured by multiple groups of sensors and transmitted to observers through communication networks suffering from deception attacks. To attain real-time monitoring and interval estimation of the system state and achieve a satisfactory estimation accuracy, a distributed secure interval observation approach is presented, where the interval observer is composed of an upper-bounding observer and a lower-bounding observer. The construction of each interval observer is based on the system positivity and the bounds of parameter perturbation, disturbance input and attack signals. Using the stochastic finite-time boundedness and l(1)-gain analysis method together with the linear programming technique, some sufficient conditions on analysis, design and optimization of the distributed interval observers for the uncertain positive system against deception attacks are established. The practicability and advantage of the proposed approach is checked by a numerical example, which comes from the remote monitoring of power distribution in smart grid. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this study we investigate a novel approach to stochastically perturb the disease transmission coefficient, which is a key parameter in susceptible-infected-susceptible (SIS) models. Motivated by the papers [5] and [2], we perturb the disease transmission coefficient with a Gaussian white noise, formally modelled as the time derivative of a mean reverting Ornstein-Uhlenbeck process. We remark that, thanks to a suitable representation of the solution to the deterministic SIS model, this perturbation is rigorous and supported by a Wong-Zakai approximation argument that consists in smoothing the singular Gaussian white noise and then taking limit of the solution from the approximated model. We prove that the stochastic version of the classic SIS model obtained this way preserves a crucial feature of the deterministic equation: the reproduction number dictating the two possible asymptotic regimes for the infection, i.e. extinction and persistence, remains unchanged. We then identify the class of perturbing noises for which this property holds and propose simple sufficient conditions for that. All the theoretical discoveries are illustrated and discussed with the help of several numerical simulations. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A higher-order compact (HOC) discretization of generalized 3D convection-diffusion equation (CDE) in nonuniform grid is presented. Even in the presence of cross-derivative terms, the discretization uses only nineteen point stencil. Extension of this newly proposed discretization to semi-linear and convection-diffusion-reaction problems is seen to be straightforward and this inherent advantage is thoroughly exploited. The scheme being designed on a transformation free coordinate system is found to be efficient in capturing boundary layers and preserve the nonoscillatory property of the solution. The proposed method is tested using several benchmark linear and nonlinear problems from the literature. Additionally, problems with sharp gradients are solved. These diverse numerical examples demonstrate the accuracy and efficiency of the scheme proposed. Further, the numerical rate of convergence is seen to approach four confirming theoretical estimation. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A conserved high-order traffic flow model (CHO model) is extended to the case with discontinuous fluxes which is called the CHO model with discontinuous fluxes. Based on the independence of its homogeneous subsystem and the property of Riemann invariants, Riemann solvers to the homogeneous CHO model with discontinuous fluxes are discussed. Moreover, we design the first-order Godunov scheme based on the Riemann solvers to solve the extended model, and prove the invariant region principle of numerical solutions. Two numerical examples are given to illustrate the effectiveness of the extended model and the designed scheme. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We investigated the gravitational settling of a single semi-torus shaped particle immersed in a viscous, incompressible fluid in two dimensions. To study the problem, numerical simulations were done using Immersed boundary (IB) method. Parametric studies were conducted to investigate the effect of varying parameters namely, density of the particle (for a fixed fluid density), fluid's dynamic viscosity and particle's size on the settling velocity of the particle considered. We also considered the particles in different orientations to investigate its effect on the dynamics of the settling particle. The results obtained were physically justified. The convergence studies done validated IB method's spatial accuracy of first order. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The primary goal of this paper is to model and study the behavior of ellipsoidal microplastic particles in a 3D lid-driven cavity. An Eulerian equation for the hydrodynamics is solved toward stationarity under the Reynolds number 1000 and coupled with a Lagrangian system governing the particle dynamics. The key points of departure in the modeling are laminar flow and small particle Reynolds number under which the drag force has extensively been studied. We then address the question, what would be the behavior of prolate and oblate particles under extreme conditions, where the aspect ratio tends to either 8 (thin needle) or 0 (thin disk). The corresponding tool, Singular Perturbation Theory, not only settles the analysis of the critical manifold but also underlies a quasi-steady state approximation (QSSA) of the particle velocity around the manifold. We show that in a certain range of particle aspect ratio, the QSSA gives quite good approximations of the particle positions yet more computational efficiency. Sedimentation is shown to highly be dependent on the particle's initial position, aspect ratio, and size. Meanwhile initial position determines to which direction the fluid stream drifts the particles, larger size and aspect ratio closer to 1 increase the likelihood of sedimenting. We also show that neutrally buoyant particles prefer to deposit on the cavity base as well as on vorticity-dominating regions. Generally, buoyant particles with aspect ratios between 1/20 and 20 spin faster than tumble, and they spin even faster as the aspect ratio gets smaller. (C) 2021 Elsevier Inc. All rights reserved.
Kaltenbacher, StefanSteinberger, MartinHorn, Martin
27页
查看更多>>摘要：The identification of pipe roughnesses in a water distribution network is formulated as a nonlinear system of algebraic equations which turns out to be demanding to solve under real-world circumstances. This paper proposes an enhanced technique to numerically solve this identification problem, extending the conventional Newton-Raphson approach with second-order derivatives in the determination of the search direction. Despite the requirement to solve a nonlinear equation to obtain a search direction, the application of the Hadamard/Schur product operator enables the resulting formulation to be represented compactly and thus facilitates the development of an efficient and more robust solving-technique. Algorithms on the basis of this more enhanced solving method are then compared to a customized Newton-Raphson approach in simulation examples. (C) 2021 Published by Elsevier Inc.
查看更多>>摘要：In this article we mainly extend to a multi-currency setting some previous works in the literature concerning total value adjustments in a single currency framework. The motivation comes from the fact that financial institutions operate in global markets, so that the financial derivatives in their portfolios involve different currencies. More precisely, in this multi-currency setting we pose the PDE formulations for pricing the total adjustment and the financial derivative with counterparty risk. Moreover, we also formulate the problem in terms of expectations, which allows the use of suitable Monte Carlo techniques that overcome the curse of dimensionality associated to the numerical solution of PDE formulation, when a high number of stochastic factors are involved. Finally, we present some examples to illustrate the performance of the formulations and the proposed numerical techniques. (C) 2021 The Authors. Published by Elsevier Inc.
查看更多>>摘要：This article presents a study of nanofluid and hybrid nanofluid near a parabolic surface under the influence of heat generation and MHD. AA7072 and AA7075 are treated as nano particles while mathanol is used as a base fluid. We incorporated aluminum alloy of AA7072 in a base fluid for nanofluid and AA7072+AA7075 in base fluid for hybrid nanofluid. AA7072 and AA7075 manipulated in this study are uniquely manufactured to possess high heat transfer features. AA7072 alloy is a combined mixture of zinc and aluminium with some metallic elements such as copper, silicon, and ferrous. Similarly AA7075 is a compounded mixture of zinc, magnesium, ferrous, and silicon. By using similarity transformations, the PDEs are transmuted into ODEs. Furthermore, the transmuted equations are than interpreted numerically in MATLAB using Bvp4c. The graphical analysis is performed for different parameters to check the behaviour of velocity and temperature profiles. Velocity field attains increasing behaviour by an accretion in volume fraction phi(1) for both methanol+AA7072(nanofluid) and methanol+AA7072+AA7075(hybrid nanofluid). The velocity profile for methanol+AA7072 is higher than methanol+AA7072+AA7075. By increasing magnetic field parameter M, the velocity component f ' (psi) proceeds diminish trend for both methanol+AA7072 and methanol+AA7072+AA7075. But velocity field for methanol+AA7072 is moderate than methanol+AA7072+AA7075. The influence of heat generation parameter gamma shows rising trend in temperature profile for both fluids. But heat generation parameter gamma is more effective for hybrid nanofluid. Moreover, an entropy generation rate is also evaluated. (C) 2021 Elsevier Inc. All rights reserved.
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