查看更多>>摘要：This paper proposes a front-tracking fixed grid method for solving Stefan problem with moving phase change materials in any arbitrary (irregular) bounded domains. To achieve this objective, the governing partial differential equations are transformed, using a curvilinear coordinate transformation, in to a fixed rectangular domain, at each time level and an alternate direction implicit (ADI) scheme is used to solve the resultant differential system. The proposed scheme is consistent, unconditionally stable and also produces second-order accurate results. Many numerical experiments are conducted, in both one and two phase environments, to validate the proposed method. All these validations confirmed the theoretical accuracy of the produced results which are presented in the form of error graphs and tables in each case. Importance is given to understand the influence of the physical parameters like Peclet number, Stefan number, material velocity, latent heat, and thermal conductivity, etc., on the rate of change of phase and observed a continuous enhancement of the same with in the chosen range of the parameters. Also noticed a faster movement of the interface with the increase in these parameters in the direction of melting or freezing. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Contact tracing is widely adopted to inhibit the epidemics in the global world, and has been proved to be very effective in reducing infections. But it is rarely investigated whether contact tracing can completely eradicate an epidemic with asymptomatic infection. This paper proposes a novel model to explore the impacts of contact tracing on the outbreak size and outbreak threshold of an epidemic with asymptomatic infection in a two-layered network structure. Based on contact tracing, three types of effects are considered simultaneously: social distancing on the close contacts, infection test on the close contacts, and arousing risk perception from the close contacts. The results indicate that contact tracing and its three effects can largely reduce the number of infections. Among the three effects, the effect of social distancing is more effective because it acts on both the susceptible nodes and the asymptomatic nodes, while the other two only act on one type of nodes. However, contact tracing and its three effects are unable to change the epidemic threshold, even if the asymptomatic nodes and symptomatic nodes are all set to be infectious. The primary reason is that the identification of close contacts is driven by the detection of infections, and is lagged behind the outbreak of epidemic. In fact, the threshold for close contacts to emerge is highly dependent on the epidemic threshold. When the epidemic size approaches 0, close contacts will also disappear. To increase the efficiency of contact tracing on the epidemic threshold, the optimal strategy should directly target the normal people besides the close-contact individuals. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Variational integrators are particularly suitable for simulation of mechanical systems, where features such as symplecticity and momentum preservation are essential. They also exhibit excellent long-time energy behavior even if external forcing is involved. Motivated by this fact, we present a new approach, that is based on the local path fitting technique, to construct variational integrators for forced mechanical systems. The core technology exploited is to fit the local trajectory as the Lagrange interpolation polynomial by requiring that the forced Euler-Lagrange equations hold at the internal interpolation nodes. This operation also yields the essential terms of the discrete forced Euler-Lagrange equations and consequently formulates the final integrator. This new approach not only avoids numerical quadrature involved in the classical construction, but also significantly improves the precision of the resulting integrator, as illustrated by the given examples. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, a new uncertainty-based approach, termed the universal grey number-based Gaussian elimination method, is presented for the analysis of large structures that require the solution of systems of linear interval algebraic equations. Although exact ranges of the solution can be found using the enumeration method, it is known to be computationally expensive as it requires a large number of analyses. Although interval analysis has been used by some researchers, it is found to lead to wider ranges of the response quantities due to the dependency problem. Hence, modified procedures such as the truncation-based interval analysis have been suggested in the literature to overcome the dependency problem. In fact, no interval analysis-based method is available in the literature for solving large number of interval linear equations accurately. The present method is expected to overcome the limitations associated with the available methods in terms of accuracy and computational effort. To demonstrate the accuracy of the proposed method, the stress analysis of several truss structures under specified interval values of input parameters is considered. It is shown that the proposed method yields accurate results more efficiently with less computational effort compared to the truncation-based interval analysis and enumeration method. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The Wiener index of a graph W (G) is a well studied topological index for graphs. An outstanding problem of Soltes is to find graphs G such that W (G) = W (G - v) for all vertices v epsilon V (G), with the only known example being G = C-11. We relax this problem by defining a notion of Wiener indices for signed graphs, which we denote by W-sigma(G), and under this relaxation we construct many signed graphs such that W-sigma(G) = W-sigma(G - v) for all v epsilon V (G). This ends up being related to a problem of independent interest, which asks when it is possible to 2-color the edges of a graph G such that there is a path between any two vertices of G which uses each color the same number of times. We briefly explore this latter problem, as well as its natural extension to r-colorings. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Reachable set estimation problem in allusion to continuous-time singularly perturbed systems that take on time-varying delays and bounded disturbances is discussed in this paper. In many singularly perturbed systems, since the perturbed parameter kappa is not available, our task is to determine an ellipsoid as small as possible which can be independent on kappa. In this case, for any admissible singularly perturbed parameters, this ellipsoid can surround the states of the system. First, in order to obtain more accurate result, the delay is unequally divided into two sub-intervals and a kappa-dependent Lyapunov-Krasocskii functional is established. Then, with the aid of reciprocally convex inequality for each sub-interval, sufficient delay-dependent conditions are established which can make the system states contained by a kappa-independent ellipsoid. Finally, a numerical example is given to verify the validity of the result. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The paper is concerned with the unconditional stability and optimal error estimates of Galerkin finite element methods (FEMs) for a class of generalized nonlinear coupled Schrodinger equations with Caputo-type derivatives. We improve the results in [1] to a higher order temporal scheme by using a type of new Gronwall inequality. By introducing a time-discrete system, the error is separated into two parts: the temporal error and the spatial error. As the result of tau-independent of the spatial error, we obtain the L-infinity-norm boundedness of the fully discrete solutions without any restrictions on the grid ratio. The unconditionally optimal L-2-norm error estimate is then obtained naturally. Furthermore, in order to numerically solve the system with nonsmooth solutions, we construct another Galerkin FEM with nonuniform temporal meshes, and corresponding fast algorithm by using sum-of-exponentials technique is also built. Finally, numerical results are reported to show the accuracy and efficiency of the proposed FEMs and the corresponding fast algorithms. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We consider a singularly perturbed elliptic problem with two parameters in two dimensions. Using linear finite element method on a Shishkin triangular mesh, we prove the uniform convergence and supercloseness in an energy norm. Some integral inequalities play an important role in our analysis. Numerical tests verify our theoretical results. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we propose a predictor-corrector type Consensus Based Optimization(CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the nonconvex function defined on a convex domain. As a practical application of the proposed algorithm, we study the portfolio optimization problem in finance. In this application, we introduce an objective function to choose the optimal weight on each asset in an assetbundle, which yields the maximal expected returns given a certain level of risks. Simulation results show that our proposed predictor-corrector type model is successful in finding the optimal value. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let r be a positive number with r >= 2 and let A = {a(i)}(i=1)(infinity), be an arbitrarily given strictly increasing sequence of positive integers. Let S-r(A).:= Sigma(infinity)(i=1)1/[a(i) + a(i+1), ... ,a(i+r-1)]. In 1978, Borwein obtained S-2(A) <= 1 with equality occurring if and only if a(i) = 2(i-1) for i >= 1. Qian and Zhao et al. obtained exact upper bounds for S-r(A) as 3 <= r <= 7 and 8 <= r <= 11 respectively in 2017 and 2019. In this paper, we give several methods to obtain the upper bounds for S-12(A) and S-13(A), with explicit sequences which reach the corresponding upper bounds. We propose a conjecture that the exact upper bounds for S-r(A) are tau(h)-r+2/h for all r >= 2, where h is a highly composite number and tau(h) denotes the number of divisors of h. In addition, we offer some sequences that reach the exact upper bounds. (C) 2021 Elsevier Inc. All rights reserved.
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