Computational and Mathematical Methods最新文献

The time-dependent neutron diffusion equation approximates the neutronic power evolution inside a nuclear reactor core. Applying a Galerkin finite element method for the spatial discretization of these equations leads to a stiff semi-discrete system of ordinary differential equations. For time discretization, an implicit scheme is used, which implies solving a large and sparse linear system of equations for each time step. The GMRES method is used to solve these systems because of its fast convergence when a suitable preconditioner is provided. This work explores several matrix-free strategies based on different updated preconditioners, which are constructed by low-rank updates of a given initial preconditioner. They are two tuned preconditioners based on the bad and good Broyden’s methods, initially developed for nonlinear equations and optimization problems, and spectral preconditioners. The efficiency of the resulting preconditioners under study is closely related to the selection of the subspace used to construct the update. Our numerical results show the effectiveness of these methodologies in terms of CPU time and storage for different nuclear benchmark transients, even if the initial preconditioner is not good enough.

Due to the specificity of the Weibull tail coefficient, most of the estimators available in the literature are based on the log excesses and are consequently quite similar to the estimators used for the estimation of a positive extreme value index. The interesting performance of estimators based on generalized means leads us to base the estimation of the Weibull tail coefficient on the power mean-of-order-p. Consistency and asymptotic normality of the estimators under study are put forward. Their performance for finite samples is illustrated through a Monte Carlo simulation. It is always possible to find a negative value of p (contrarily to what happens with the mean-of-order-p estimator for the extreme value index), such that, for adequate values of the threshold, there is a reduction in both bias and root mean square error.

We propose a discrete data classification method of scattered data in N-dimensional by solving the minimax problem for a set of points. The current research is extended from 2-dimensional and 3-dimensional to N-dimensional. The problem can be applied to artificial intelligence classification problems (machine learning, deep learning), point data analysis problems (data science problem), the optimized design of nanoscale circuits, and the location of facility problems, circle detection on 2D image, or sphere detection on depth image. We generalized the discrete data classification methodology in N-dimensional. Finally, we resolved to find an exact solution of the location of a manifold for our suggested problem in N-dimensional.

In this paper, we provide two new generalized Gauss-Seidel (NGGS) iteration methods for solving absolute value equations Ax − ∣x | = b, where A ∈ R^n×n, b ∈ Rⁿ, and x ∈ Rⁿ are unknown solution vectors. Also, convergence results are established under mild assumptions. Eventually, numerical results prove the credibility of our approaches.

Mikhlin’s integral equation is a classical integral equation for solving boundary value problems for Laplace’s equation. The kernel of the integral equation is known as the Neumann kernel. Recently, an integral equation for solving the Riemann–Hilbert problem was derived. The kernel of the new integral equation is a generalization of the Neumann kernel, and hence, it is called the generalized Neumann kernel. The objective of this paper is to present a detailed comparison between these two integral equations with emphasis on their similarities and differences. This comparison is done through applying both equations to solve Laplace’s equation with Dirichlet boundary conditions in simply connected domains with smooth and piecewise smooth boundaries.

Applied complex network theory has become an interesting research field in the last years. Many papers have appeared on this subject dealing with the topological description of real transport systems, from small networks like the Italian airport network to the worldwide air transportation network. A comprehensive topological description of those critical structures is relevant in order to understand their dynamics, capacities, and vulnerabilities. In this work, for the first time, we describe the Spanish airport network (SAN) as a complex network. Nodes are airports, and links are flight connections weighed by traffic flow. We study its topological features and traffic dynamics. Our analysis shows that SAN has complex dynamics similar to small-size air transportation networks of other developed economies. It shares properties of small-world and scale-free networks, and it is highly connected and efficient and has a disassortative pattern for high-degree nodes.

The purpose of this article is to explore different types of solutions for the Kadomtsev-Petviashvili-modified Kadomtsev-Petviashvili (KP-mKP) equation which is termed as KP-Gardner equation, extensively used to model strong nonlinear internal waves in (1 + 2)-dimensions on the stratified ocean shelf. This evolution equation is also used to describe weakly nonlinear shallow-water wave and dispersive interracial waves traveling in a mildly rotating channel with slowly varying topography. Introducing Liu’s approach regarding the complete discrimination system for polynomial and the trial equation technique, a set of new solutions to the KP-mKP equation containing Jacobi elliptic function have been derived. It is found that these analytical solutions numerically exhibit different nonlinear structures such as solitary waves, shock waves, and periodic wave profiles. The reliability and effectiveness are confirmed from the numerical graphs of the solutions. Finally, the existence and validity of the various topological structures of the solutions are confirmed from the phase portrait of the dynamical system. Based on this investigation, it is confirmed that the method is not only suited for obtaining the classification of the solutions but also for qualitative analysis, which means that it can also be extended to other fields of application.

Dengue fever is a viral mosquito-borne disease, a significant global health concern, with more than one third of the world population at risk of acquiring the disease. Caused by 4 antigenically distinct but related virus serotypes, named DENV-1, DENV-2, DENV-3, and DENV-4, infection by one serotype confers lifelong immunity to that serotype and a short period of temporary cross immunity to other related serotypes. Severe dengue is epidemiologically associated with a secondary infection caused by a heterologous serotype via the so-called antibody-dependent enhancement (ADE), an immunological process enhancing a new infection. Within-host dengue modeling is restricted to a small number of studies so far. With many open questions, the understanding of immunopathogenesis of severe disease during recurrent infections is important to evaluate the impact of newly licensed vaccines. In this paper, we revisit the modeling framework proposed by Sebayang et al. and perform a detailed sensitivity analysis of the well-known biological parameters and its possible combinations to understand the existing data sets. Using numerical simulations, we investigate features of viral replication, antibody production, and infection clearance over time for three possible scenarios: primary infection, secondary infection caused by homologous serotype, and secondary infection caused by heterologous serotype. Besides, describing well the infection dynamics as reported in the immunology literature, our results provide information on parameter combinations to best describe the differences on the immunological dynamics of secondary infections with homologous and heterologous viruses. The results presented here will be used as baseline to investigate a more complex within-host dengue model.

The Box-Cox transformations are used to make the data more suitable for statistical analysis. We know from the literature that this transformation of the data can increase the rate of convergence of the tail of the distribution to the generalized extreme value distribution, and as a byproduct, the bias of the estimation procedure is reduced. The reduction of bias of the Hill estimator has been widely addressed in the literature of extreme value theory. Several techniques have been used to achieve such reduction of bias, either by removing the main component of the bias of the Hill estimator of the extreme value index (EVI) or by constructing new estimators based on generalized means or norms that generalize the Hill estimator. We are going to study the Box-Cox Hill estimator introduced by Teugels and Vanroelen, in 2004, proving the consistency and asymptotic normality of the estimator and addressing the choice and estimation of the power and shift parameters of the Box-Cox transformation for the EVI estimation. The performance of the estimators under study will be illustrated for finite samples through small-scale Monte Carlo simulation studies.

Summary. We investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years the aquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models were initially suggested for respiartory diseases like influenza, showing complex dynamics in reasonable parameter regions when comparing to historic empirical influenza like illness data, e.g., from Ille de France. The seasonal forcing typical for respiratory diseases gives rise to the different rich dynamical scenarios with even small parameter changes. Especially the seasonality of the infection leads for small values already to period doubling bifurcations into chaos, besides additional coexisting attractors. Such models could in the future also play a role in understanding the presently experienced COVID-19 pandemic, under emerging new variants and with only limited vaccine efficacies against newly upcoming variants. From first period doubling bifurcations, we can eventually infer at which close by parameter regions complex dynamics including deterministic chaos can arise.