Domain decomposition methods in a geometrical multiscale domain using finite volume schemes

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.     

The application of the Lattice Boltzmann method to the one-dimensional modeling of pulse waves in elastic vessels

The one-dimensional nonlinear equations for the blood flow motion in distensible vessels are considered using the kinetic approach. It is shown that the Lattice Boltzmann (LB) model for non-ideal gas is asymptotically equivalent to the blood flow equations for compliant vessels at the limit of low Knudsen numbers. The equations of state for non-ideal gas are transformed to the pressure-luminal area response. This property allows to model arbitrary pressure-luminal area relations. Several test problems are considered: the propagation of a sole nonlinear wave in an elastic vessel, the propagation of a pulse wave in a vessel with varying mechanical properties (artery stiffening) and in an artery bifurcation, in the last problem Resistor–Capacitor–Resistor (RCR) boundary conditions are considered. The comparison with the previous results shows a good precision.     

澄清对相对论性原理和协变性的误解

近来有些文章断言,在一个惯性参考系里能量守恒的物理系统,在别的参考系看来能量也一定守恒.实际上这些作者混淆了物理方程式的协变性和相对性原理.本文将澄清这一误解.     

The Bergman kernel for the Vekua equation

The paper extends some well-known results for analytic functions onto solutions of the Vekua equation $\partial \overline{{}_z}W=aW+b\overline{W}$ regarding the existence and construction of the Bergman kernel and of the corresponding Bergman projection operator.     

Ionic liquid gating control of magnetic anisotropy in Ni0.81Fe0.19 thin films

Voltage control magnetism is one of the most energy efficient pathway towards magnetoelectric (ME) device. Ionic liquid gating (ILG) method has already shown impressive manipulation power at the IL/electrode interface to influence the structure, orbital as well as spin of the electrode materials. As key material in anisotropy magnetoresistance sensor and spin valve heterostructure, the permalloy Ni_0.81Fe_0.19 was utilized as the electrode to investigate the ILG induced magnetic anisotropy change. In this work, we realized magnetic anisotropy control in Au/[DEME]⁺[TFSI]^-/Ni_0.81Fe_0.19 (2.5 nm)/Ta heterostructure via ILG caused electrostatic doping. This is evidenced in situ reversible ferromagnetic field (H_r) shift with electron spin resonance (ESR) spectrometer. Aiming at the question whether the charge accumulation at the ionic liquid interface is the main control mechanism at low voltage, we carefully tested the relationship between the change of resonance field and the amount of surface charge. It was found that these two had a good linear relationship between −1 V and +1 V. Defining the linear parameter as A whose value is 28.7 mT m²/Col. Unlike previously reported chemical regulation of Co, this article used ionic liquids to physically regulate NiFe, which has not been studied in the previous ionic liquid regulation. And NiFe has a narrower resonance line width for easy reference to microwave devices. In addition, It also has a stronger ferromagnetic signal than Co, which can be more easily detected as a sensor device. Therefore, this system is more promising. The ILG control NiFe may lead to a new kind of magnetoelectric sensor devices and path a new way to low energy consumption spintronics.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.