A three-dimensional multidimensional gas-kinetic scheme for the Navier-Stokes equations under gravitational fields

This paper extends the gas-kinetic scheme for one-dimensional inviscid shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to multidimensional gas dynamic equations under gravitational fields. Four important issues in the construction of a well-balanced scheme for gas dynamic equations are addressed. First, the inclusion of the gravitational source term into the flux function is necessary. Second, to achieve second-order accuracy of a well-balanced scheme, the Chapman-Enskog expansion of the Boltzmann equation with the inclusion of the external force term is used. Third, to avoid artificial heating in an isolated system under a gravitational field, the source term treatment inside each cell has to be evaluated consistently with the flux evaluation at the cell interface. Fourth, the multidimensional approach with the inclusion of tangential gradients in two-dimensional and three-dimensional cases becomes important in order to maintain the accuracy of the scheme. Many numerical examples are used to validate the above issues, which include the comparison between the solutions from the current scheme and the Strang splitting method. The methodology developed in this paper can also be applied to other systems, such as semi-conductor device simulations under electric fields.Comment: The name of first author was misspelled as C.T.Tian in the published paper. 35 pages,9 figure

Scattering mechanism in a step-modulated subwavelength metal slit: a multi-mode multi-reflection analysis

In this paper, the scattering/transmission inside a step-modulated subwavelength metal slit is investigated in detail. We firstly investigate the scattering in a junction structure by two types of structural changes. The variation of transmission and reflection coefficients depending on structural parameters are analyzed. Then a multi-mode multi-reflection model based on ray theory is proposed to illustrate the transmission in the step-modulated slit explicitly. The key parts of this model are the multi-mode excitation and the superposition procedure of the scatterings from all possible modes, which represent the interference and energy transfer happened at interfaces. The method we use is an improved modal expansion method (MEM), which is a more practical and efficient version compared with the previous one [Opt. Express 19, 10073 (2011)]. In addition, some commonly used methods, FDTD, scattering matrix method, and improved characteristic impedance method, are compared with MEM to highlight the preciseness of these methods.Comment: 25 pages, 9 figure

Рифма в рамках средневекового крымскотатарского силлабического стиха

В предложенной статье представлен теоретический материал, который раскрывает сущность и особенности рифмы, подкреплённый необходимым материалом из крымскотатарской литературы.У запропонованій статті представлений теоретичний матеріал, що розкриває сутність і особливості рими, підкріплений необхідним матеріалом із кримськотатарської літератури.In offered article the theoretical material which opens essence and features of the rhyme, supported by a necessary material from crimean tatars literatures is submitted

Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.Comment: 19 page

A topological optimization procedure applied to multiple region problems with embedded sources

The main objective of this work is the application of the topological optimization procedure to heat transfer problems considering multiple materials. The topological derivative (DT) is employed for evaluating the domain sensitivity when perturbed by inserting a small inclusion. Electronic components such as printed circuit boards (PCBs) are an important area for the application of topological optimization. Generally, geometrical optimization involving heat transfer in PCBs considers only isotropic behavior and/or a single material. Multiple domains with anisotropic characteristics take an important role on many industrial products, for instance when considering PCBs which are often connected to other components of different materials. In this sense, a methodology for solving topological optimization problems considering anisotropy and multiple regions with embedded heat sources is developed in this paper. A direct boundary element method (BEM) is employed for solving the proposed numerical problem.CNPQ – Brazil through the Science without Borders program and from Brunel University

Modelling the Interfacial Flow of Two Immiscible Liquids in Mixing Processes

This paper presents an interface tracking method for modelling the flow of immiscible metallic liquids in mixing processes. The methodology can provide an insight into mixing processes for studying the fundamental morphology development mechanisms for immiscible interfaces. The volume-of-fluid (VOF) method is adopted in the present study, following a review of various modelling approaches for immiscible fluid systems. The VOF method employed here utilises the piecewise linear for interface construction scheme as well as the continuum surface force algorithm for surface force modelling. A model coupling numerical and experimental data is established. The main flow features in the mixing process are investigated. It is observed that the mixing of immiscible metallic liquids is strongly influenced by the viscosity of the system, shear forces and turbulence. The numerical results show good qualitative agreement with experimental results, and are useful for optimisating the design of mixing casting processes

Correlation between centrality metrics and their application to the opinion model

In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The m order degree mass of a node is the sum of the weighted degree of the node and its neighbors no further than m hops away. We find that the B_{n}, the closeness, and the components of x_{1} are strongly correlated with the degree, the 1st-order degree mass and the 2nd-order degree mass, respectively, in both network models and real-world networks. We then theoretically prove that the Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is larger than that between x_{1} and a lower order degree mass. Finally, we investigate the effect of the inflexible antagonists selected based on different centrality metrics in helping one opinion to compete with another in the inflexible antagonists opinion model. Interestingly, we find that selecting the inflexible antagonists based on the leverage, the B_{n}, or the degree is more effective in opinion-competition than using other centrality metrics in all types of networks. This observation is supported by our previous observations, i.e., that there is a strong linear correlation between the degree and the B_{n}, as well as a high centrality similarity between the leverage and the degree.Comment: 20 page

Quasi-Periodic Releases of Streamer Blobs and Velocity Variability of the Slow Solar Wind near the Sun

We search for persistent and quasi-periodic release events of streamer blobs during 2007 with the Large Angle Spectrometric Coronagraph on the \textit{Solar and Heliospheric Observatory} and assess the velocity of the slow solar wind along the plasma sheet above the corresponding streamer by measuring the dynamic parameters of blobs. We find 10 quasi-periodic release events of streamer blobs lasting for three to four days. In each day of these events, we observe three-five blobs. The results are in line with previous studies using data observed near the last solar minimum. Using the measured blob velocity as a proxy for that of the mean flow, we suggest that the velocity of the background slow solar wind near the Sun can vary significantly within a few hours. This provides an observational manifestation of the large velocity variability of the slow solar wind near the Sun.Comment: 14 pages, 5 figures, accepted by Soalr Physic

A Measurement of the Longitudinal Acceptance of the K600 Magnetic Spectrometer

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Contributions of dry and wet depositions of polychlorinated dibenzo-p-dioxins and dibenzofurans to a contaminated site resulting from a penetachlorophenol manufacturing process

The soils at a factory for manufacturing pentachlorophenol were heavily contaminated by polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs). In order to verify the contributions of dry and wet deposition of PCDD/Fs from the ambient air, the concentration of PCDD/Fs in ambient air and soil were measured, the partition of particle- and gas-phases of atmospheric PCDD/Fs was calculated, and the annual fluxes of total dry and wet PCDD/F depositions were modeled. Average atmospheric PCDD/F concentration was 1.24 ng Nm (-aEuro parts per thousand 3) (or 0.0397 ng I-TEQ Nm (-aEuro parts per thousand 3)). Moreover, over 92.8% of total PCDD/Fs were in the particle phase, and the dominant species were high chlorinated congeners. The total PCDD/F fluxes of dry and wet deposition were 119.5 ng m (-aEuro parts per thousand 2) year (-aEuro parts per thousand 1) (1.34 ng I-TEQ m (-aEuro parts per thousand 2) year (-aEuro parts per thousand 1)) and 82.0 ng m (-aEuro parts per thousand 2) year (-aEuro parts per thousand 1) (1.07 ng I-TEQ m (-aEuro parts per thousand 2) year (-aEuro parts per thousand 1)), respectively. By scenario simulation, the total fluxes of dry and wet PCDD/F depositions were 87.1 and 68.6 ng I-TEQ, respectively. However, the estimated PCDD/F contents in the contaminated soil were 839.9 mu g I-TEQ. Hence, the contributions of total depositions of atmospheric PCDD/F were only 0.02%. The results indicated that the major sources of PCDD/F for the contaminated soil could be attributed to the pentachlorophenol manufacturing process