Coquet-type formulas for the rarefied weighted Thue–Morse sequence

Newman proved for the classical Thue–Morse sequence, ((−1)^s(n))_n≥0, that for all N∈N with real constants satisfying c₂>c₁>0 and λ=log3/log4. Coquet improved this result and deduced , where F(x) is a nowhere-differentiable, continuous function with period 1 and η(N)∈{−1,0,1}. In this paper we obtain for the weighted version of the Thue–Morse sequence that for the sum a Coquet-type formula exists for every r∈{0,1,2} if and only if the sequence of weights is eventually periodic. From the specific Coquet-type formulas we derive parts of the weak Newman-type results that were recently obtained by Larcher and Zellinger.     

Feedback control variables to restrain the Babesiosis disease

In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations.     

Numerical approach to chaotic pattern formation in diffusive predator–prey system with Caputo fractional operator

This paper is primarily concern with the formulation and analysis of a reliable numerical method based on the novel alternating direction implicit finite difference scheme for the solution of the fractional reaction–diffusion system. In the work, the integer first‐order derivative in time is replaced with the Caputo fractional derivative operator. As a case study, the dynamics of predator–prey model is considered. In order to provide a good guidelines on the correct choice of parameters for the numerical simulation of full fractional reaction–diffusion system, its linear stability analysis is also examined. The resulting scheme is applied to solve both self‐diffusion and cross‐diffusion problems in two‐dimensions. We observed in the experimental results a range of spatiotemporal and chaotic structures that are related to Turing pattern. It was also discovered in the simulations that cross‐diffusive case gives rise to spatial patterns faster than the diffusive case. Apart from chaotic spiral‐like structures obtained in this work, it should also be mentioned that Turing patterns such as stationary spots and stripes are obtainable, depending on the initial and parameters choices.     

A new approximation for the generalized fractional derivative and its application to generalized fractional diffusion equation

In this paper, we derive a fourth order approximation for the generalized fractional derivative that is characterized by a scale function z(t) and a weight function w(t) . Combining the new approximation with compact finite difference method, we develop a numerical scheme for a generalized fractional diffusion problem. The stability and convergence of the numerical scheme are proved by the energy method, and it is shown that the temporal and spatial convergence orders are both 4. Several numerical experiments are provided to illustrate the efficiency of our scheme.     

Regularity for obstacle problems without structure conditions

This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions’ regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients.     

基于电缆-无线耦合的随钻测井信号传输新方法及其数值模拟研究

信号传输是随钻测井的重要组成部分, 也是随钻测井进一步发展的瓶颈.针对这个问题, 研究了由Novatek^TM提出的基于钻杆内有线传输, 钻杆间电磁耦合传输的随钻信号高速传输方法.首先, 针对钻杆间的电磁耦合结构的对称性, 采用了高效的数值模式匹配法对该耦合结构进行了电磁建模; 然后, 为了优化钻杆间耦合结构的耦合性能, 利用上述的电磁建模方法对该耦合结构进行了仿真分析, 分析了该耦合结构各个参数对耦合性能的影响, 并得出了一些有意义的结论, 该结论能够指导随钻测井信号钻杆间耦合传输的优化设计.另外, 钻杆内传输线利用矩形传输线设计, 设计出了50 Ω 特性阻抗的矩形传输线, 并计算了相关损耗.最后, 通过仿真和实验验证了优化设计的钻杆间耦合传输结构具有非常好的传输性能, 并且仿真和实验结果符合良好. 关键词： 随钻信号传输 数值模式匹配 电磁耦合 矩形传输线     

蒙卡燃耗中的氙振荡现象分析及计算研究

根据氙振荡产生的机理,按照燃耗步长来划分：在短步长条件下会产生物理氙振荡,在长步长条件下会产生数值氙振荡。研究发现,当燃耗步长增大到19 h,物理氙振荡的振幅最小,随着燃耗步长继续增大,表现为数值氙振荡,当燃耗步长27 d,数值氙振荡振幅最小。采用平衡氙方法强制使中子通量与氙浓度平衡,在堆芯物理计算程序(RMC)的输运模块中运用平衡氙方法对碘氙的浓度进行不断的迭代更新,在保证收敛的情况下抑制了氙振荡现象的发生。     

张量重正化群方法及其应用

张量重正化群方法是近年来发展起来的一种新的数值计算方法,它将经典配分函数和量子波函数的张量网络表示与重正化群方法相结合,在强关联系统的数值研究中,发挥着越来越重要的作用。文章以经典统计模型和量子格点模型为例,简要介绍了张量重正化群的一些基础知识和研究给定物理模型的一般性思路,并对张量重正化群未来可能的发展方向和亟待解决的问题进行了讨论。     

地震数值预报

地震能否预报、地震预报遇到的种种困难如何克服？在思考这一问题时,不妨借助于气象预报的经验。气象预报从经验预报发展到数值预报,虽然用了约半个世纪的时间,但获得了成功。中国地震学界,对于地震预报的发展,也必须从经验预报发展为物理预报,对此几乎没有异议;但是物理预报的基本特点就是要基于定量的物理规律,进行数值预报,却鲜被提及。文章讨论了开展地震数值预报的五个主要环节的现状,认为地震数值预报现在应该提到规划的日程上来,设计我国地震数值预报的路线图,按照它的需要部署地震台站观测工作,开展地震数值预报的理论探讨。     

反射率的数值反演

通过分析热流边界条件下的一维热传导过程,提出并实现了由后表面温度变化历史曲线反演前表面反射率变化历史曲线的数值方法。通过一维热传导的正向和反演计算过程,验证了反演程序的可靠性。对数值反演计算和实验测量两种方式得到的反射率曲线进行了对比,结果显示,两条反射率曲线在变化趋势上符合较好,初步验证了一维温度场中数值反演方法的可行性。