Considering for the blanket structure scheme of HCCB DEMO

For the solid blanket concept of helium cooled ceramic breeder (HCCB) demonstration fusion power plant (DEMO), a feasible blanket structure with configuration 2×X is proposed as considering relatively low temperature limit of neutron multiplier beryllium pebbles. Based on that, preliminary design for the typical blanket module of HCCB DEMO has been carried out and verified by thermal-hydraulic analysis and structural analysis. Furthermore, the specific relationship of maximum temperature depended on the surface heating of blanket key part first wall (FW) is also analyzed.

ECONOMICAL DIFFERENCE SCHEME FOR ONE MULTI-DIMENSIONAL NONLINEAR SYSTEM

The multi-dimensional system of nonlinear partial differential equations is considered. In two-dimensional case, this system describes process of vein formation in higher plants. Variable directions finite difference scheme is constructed. The stability and convergence of that scheme are studied. Numerical experiments are carried out. The appropriate graphical illustrations and tables are given.

Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme

This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.

Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme

Computational techniques are invaluable to the continued success and development of Magnetic Resonance Imaging (MRI) and to its widespread applications. New processing methods are essential for addressing issues at each stage of MRI techniques. In this study, we present new sets of non-exponential generating functions representing the NMR transverse magnetizations and signals which are mathematically designed based on the theory and dynamics of the Bloch NMR flow equations. These signals are functions of many spinning nuclei of materials and can be used to obtain information observed in all flow systems. The Bloch NMR flow equations are solved using the Boubaker polynomial expansion scheme (BPES) and analytically connect most of the experimentally valuable NMR parameters in a simplified way for general analyses of magnetic resonance imaging with adiabatic condition.

Compact finite difference schemes for the backward fractional Feynman–Kac equation with fractional substantial derivative

The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.

Central Upwind Scheme for Solving Multivariate Cell Population Balance Models

Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-variable cell population balance models (PBMs) offer the most general way to describe the complicated phenomena associated with cell growth, substrate consumption and product formation. For that reason, solving and understanding of such models are essential to predict and control cell growth in the processes of biotechnological interest. Such models typically consist of a partial integro-differential equation for describing cell growth and an ordinary integro-differential equation for representing substrate consumption. However, the involved mathematical complexities make their numerical solutions challenging for the given numerical scheme. In this article, the central upwind scheme is applied to solve the single-variate and bivariate cell population balance models considering equal and unequal partitioning of cellular materials. The validity of the developed algorithms is verified through several case studies. It was found that the suggested scheme is more reliable and effective.

A numerical study for WENO scheme-based on different lattice Boltzmann flux solver for compressible flows

In this paper,the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows,including inviscid LBFS Ⅰ,viscous LBFS Ⅱ,hybrid LBFS Ⅲ and hybrid LBFS Ⅳ.Hybrid LBFS can automatically realize the switch between inviscid LBFS Ⅰ and viscous LBFS Ⅱ through introducing a switch function.The resultant hybrid WENO-LBFS scheme absorbs the advantages of WENO scheme and hybrid LBFS.We investigate the performance of WENO scheme based on four kinds of LBFS systematically.Numerical results indicate that the devopled hybrid WENO-LBFS scheme has high accuracy,high resolution and no oscillations.It can not only accurately calculate smooth solutions,but also can effectively capture contact discontinuities and strong shock waves.

Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs

Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and mathematical sciences. In this paper we use three finite difference schemes in order to approximate the solution of stochastic parabolic partial differential equations. The conditions of the mean square convergence of the numerical solution are studied. Some case studies are discussed.

A TIME FILTERING SCHEME FOR THE SHORT RANGE CLIMATE PREDICTION MODEL PRODUCTS AND ITS REAL CASE ANALYSIS

A filtering / extracting scheme for various timescale processes in short range climate model out-put is established by using the scale scattering method. And the climatological meanings as well as the impor-tance of the filtered series are discussed. In the latter part of work, the effectiveness of the filtering method and the performance of the prediction model are analyzed through a real case.

Numerical prediction of inner turbulent flow in conical diffuser by using a new five-point scheme and DLR k-ε turbulence model

The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.

Identification of Factors Influencing Out-of-county Hospitalizations in the New Cooperative Medical Scheme

Summary:Throughout the duration of the New Cooperative Medical Scheme(NCMS),it was found that an increasing number of rural patients were seeking out-of^county medical treatment,which posed a great burden on the NCMS fund.Our study was conducted to examine the prevalence of out-of^county hospitalizations and its related factors,and to provide a scientific basis for follow?up health insurance policies.A total of 215 counties in central and western China from 2008 to 2016 were selected.The total out-of-county hospitalization rate in nine years was 16.95%,which increased from 12.37%in 2008 to 19.21%in 2016 with an average annual growth rate of 5.66%.Its related expenses and compensations were shown to increase each year,with those in the central region being higher than those in the western region.Stepwise logistic regression reveals that the increase in out-of-county hospitalization rate was associated with region(XI),rural population(X2),per capita per year net income(X3),per capita gross domestic product(GDP)(X4),per capita funding amount of NCMS(X5),compensation ratio of out-of^county hospitalization cost(X6),per time average in-county(X7)and out-of-county hospitalization cost(X8).According to Bayesian network(BN),the marginal probability of high out-of^county hospitalization rate was as high as 81.7%.Out-of^county hospitalizations were directly related to X8,X3,X4 and X6.The probability of high out-of-county hospitalization obtained based on hospitalization expenses factors,economy factors,regional characteristics and NCMS policy factors was 95.7%,91.1%,93.0% and 88.8%,respectively.And how these factors affect out-of-county hospitalization and their interrelationships were found out.Our findings suggest that more attention should be paid to the influence mechanism of these factors on out-of-county hospitalizations,and the increase of hospitalizations outside the county should be reasonably supervised and controlled and our results will be used to help guide the formulation of proper intervention policies.

Numerical Study of Fisher’s Equation by Finite Difference Schemes

This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics. We studied accuracy in term of L∞ error norm by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations.

Velocity Projection with Upwind Scheme Based on the Discontinuous Galerkin Methods for the Two Phase Flow Problem

The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.

Proficiency of Second Derivative Schemes for the Numerical Solution of Stiff Systems

This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.

Theoretical and Numerical Study of Stress and Thermo-Optic in Photonic Crystal Fiber Laser in Different Pump Schemes

In this paper, we present a study of thermal, average power scaling, change in index of refraction and stress in photonic crystal fiber lasers with different pump schemes: forward pump scheme, backward pump scheme, forward pump scheme with reflection of 98%, backward pump scheme with reflection of 98% and bi-directional pump scheme. We show that management of thermal effects in fiber lasers will determine the efficiency and success of scaling-up efforts. In addition, we show that the most suitable scheme is the bi-directional.

LASG Global AGCM with a Two-moment Cloud Microphysics Scheme:Energy Balance and Cloud Radiative Forcing Characteristics

Cloud dominates influence factors of atmospheric radiation, while aerosol–cloud interactions are of vital importance in its spatiotemporal distribution. In this study, a two-moment(mass and number) cloud microphysics scheme, which significantly improved the treatment of the coupled processes of aerosols and clouds, was incorporated into version 1.1 of the IAP/LASG global Finite-volume Atmospheric Model(FAMIL1.1). For illustrative purposes, the characteristics of the energy balance and cloud radiative forcing(CRF) in an AMIP-type simulation with prescribed aerosols were compared with those in observational/reanalysis data. Even within the constraints of the prescribed aerosol mass, the model simulated global mean energy balance at the top of the atmosphere(TOA) and at the Earth’s surface, as well as their seasonal variation, are in good agreement with the observational data. The maximum deviation terms lie in the surface downwelling longwave radiation and surface latent heat flux, which are 3.5 W m-2(1%) and 3 W m-2(3.5%), individually. The spatial correlations of the annual TOA net radiation flux and the net CRF between simulation and observation were around 0.97 and 0.90, respectively. A major weakness is that FAMIL1.1 predicts more liquid water content and less ice water content over most oceans. Detailed comparisons are presented for a number of regions, with a focus on the Asian monsoon region(AMR). The results indicate that FAMIL1.1 well reproduces the summer–winter contrast for both the geographical distribution of the longwave CRF and shortwave CRF over the AMR. Finally, the model bias and possible solutions, as well as further works to develop FAMIL1.1 are discussed.

WEIGHTED COMPACT SCHEME FOR SHOCK CAPTURING

A new class of finite difference schemes--the weighted compact schemes are proposed. According to the idea of the WENO schemes, the weighted compact scheme is constructed by a combination of the approximations of derivatives on candidate stencils with properly assigned weights so that the non oscillatory property is achieved when discontinuities appear. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the weighted compact scheme. This new scheme not only preserves the characteristic of standard compact schemes and achieves high order accuracy and high resolution using a compact stencil, but also can accurately capture shock waves and discontinuities without oscillation. Numerical examples show that the new scheme is very promising and successful.

User Fairness Scheme with Proportional Fair Scheduling in Multi-user MIMO Limited Feedback System

In Multi-user MIMO (MU-MIMO) downlink system, suitable user selection schemes can improve spatial diversity gain. In most of previous studies, it is always assumed that the base station (BS) knows full channel state information (CSI) of each user, which does not consider the reality. However, there are only limited feedback bits in real system. Besides, user fairness is often ignored in most of current user selection schemes. To discuss the user fairness and limited feedback, in this paper, the user selection scheme with limited feedback bits is proposed. The BS utilizes codebook precoding transmitting strategy with LTE codebook. Furthermore, this paper analyzes the influence of the number of feedback bits and the number of users on user fairness and system sum capacity. Simulation results show that in order to achieve better user fairness, we can use fewer bits for feedback CSI when the number of user is small, and more feedback bits when the number of users is large.

High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids

In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.

Regulation of Queue Length in Router Based on an Optimal Scheme

Based on the proportionally fair scheme that Kelly proposed to solve the optimization problems for utility function in networks, and in order to improve the congestion control performance for the queue in router, the linear and terminal sliding active queue management (AQM) algorithms are designed. Especially in the ter-minal sliding AQM algorithm, a special nonlinear terminal sliding surface is designed in order to force queue length to reach the desired value in finite time. The upper bound of the time is also obtained. Simulation re-sults demonstrate that the proposed congestion algorithm enables the system be better transient and stable performance. At the same time, the robustness is guaranteed.