Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

A MOVING WATER EQUILIBRIA PRESERVING NONSTAGGERED CENTRAL SCHEME ACHIEVED VIA FLUX GLOBALIZATION FOR THE RIPA MODEL

In this paper,we propose a second-order moving-water equilibria preserving nonstaggered central scheme to solve the Ripa model via flux globalization.To maintain the moving-water steady states,we use the discrete source terms proposed by Britton et al.(J Sci Comput,2020,82(2):Art 30)by incorporating the expression of the source terms as a whole into the flux gradient,which directly avoids the discrete complexity of the source terms in order to maintain the well-balanced properties of the scheme.In addition,since the nonstaggered central scheme requires re-projecting the updated values of the nonstaggered cells onto the staggered cells,we modify the calculation of the global variables by constructing ghost cells and alternating the values of the global variables with the water depths obtained from the solution through the nonlinear relationship between the global flux and the water depth.In order to maintain the second-order accuracy of the scheme on the time scale,we incorporate a new Runge-Kutta type time discretization in the evolution of the numerical solution for the nonstaggered cells.Meanwhile,we introduce the"draining"time step technique to ensure that the water depth is positive and that it satisfies mass conservation.Numerical experiments verify that the scheme is well-balanced,positivity-preserving and robust.

CONVERGENCE OF A QUANTUM LATTICE BOLTZMANN SCHEME TO THE NONLINEAR DIRAC EQUATION FOR GROSS-NEVEU MODEL IN 1+1 DIMENSIONS

This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.

Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

DECISION-MAKING OF SLICING SCHEME IN FUSED DEPOSITION MODELING PROCESS BASED ON ANALYTICAL HIERARCHICAL PROCESS

Based on analyzing the influences of a slicing scheme on stair-stepping effect, supporting structure, efficiency and deformation, etc. , analytical hierarchical process （AHP） combining with fuzzy synthetic evaluation is introduced to make decision in slicing schemes for a processing part. The application in determining the slicing scheme for a computer mouse during prototyping shows that the method increases the rationality during decision- making and improves quality and efficiency for the prototyping part.

Near-surface velocity model construction based on a Monte-Carlo scheme

In tomographic statics seismic data processing, it 1s crucial to cletermme an optimum base for a near-surface model. In this paper, we consider near-surface model base determination as a global optimum problem. Given information from uphole shooting and the first-arrival times from a surface seismic survey, we present a near-surface velocity model construction method based on a Monte-Carlo sampling scheme using a layered equivalent medium assumption. Compared with traditional least-squares first-arrival tomography, this scheme can delineate a clearer, weathering-layer base, resulting in a better implementation of damming correction. Examples using synthetic and field data are used to demonstrate the effectiveness of the proposed scheme.

Application of the two different salinity parameterization schemes in the sea ice model

In this study, we mainly introduce two salinity parameterization schemes used in Sea Ice Simulator （SIS）, that is, isosaline scheme and salinity profile scheme. Comparing the equation of isosaline scheme with that of salinity profile scheme, we found that there was one different term between the two schemes named the salinity different term. The thermodynamic effect of the salinity difference term on sea ice thickness and sea ice concentration showed that： in the freezing processes from November to next May, the sea ice temperature could rise on the influence of the salinity difference term and restrain sea ice freezing; at the first melting phase from June to August, the upper ice melting rate was faster than the lower ice melting rate. Then sea ice temperature could rise and accelerate the sea ice melting; at the second melting phase from September to October, the upper ice melting rate was slower than the lower ice melting rate, then sea ice temperature could decrease and restrain sea ice melting. However, the effect of the salinity difference term on the sea ice thickness and sea ice concentration was weak. To analyze the impacts of the salinity different term on Arctic sea ice thickness and sea ice concentration, we also designed several experiments by introducing the two salinity parameterizations to the ice-ocean coupled model, Modular Ocean Model （MOM4）, respectively. The simulated results confirmed the previous results of formula derivation.

Improvement of the Semi-Lagrangian Advection Scheme in the GRAPES Model:Theoretical Analysis and Idealized Tests

ABSTRACT The Global/Regional Assimilation and PrEdiction System （GRAPES） is the newgeneration numerical weather predic- tion （NWP） system developed by the China Meteorological Administration. It is a fully compressible non-hydrostatical global/regional unified model that uses a traditional semi-Lagrangian advection scheme with cubic Lagrangian interpola tion （referred to as the SL_CL scheme）. The SL_CL scheme has been used in many operational NWP models, but there are still some deficiencies, such as the damping effects due to the interpolation and the relatively low accuracy. Based on Reich＇s semi-Lagrangian advection scheme （referred to as the R2007 scheme）, the Re_R2007 scheme that uses the low- and high-order B-spline function for interpolation at the departure point, is developed in this paper. One- and two-dimensional idealized tests in the rectangular coordinate system with uniform grid cells were conducted to compare the Re..R2007 scheme and the SL_CL scheme. The numerical results showed that： （1） the damping effects were remarkably reduced with the Re_R2007 scheme; and （2） the normalized errors of the Re_R2007 scheme were about 7.5 and 3 times smaller than those of the SL_CL scheme in one- and two-dimensional tests, respectively, indicating the higher accuracy of the Re..R2007 scheme. Furthermore, two solid-body rotation tests were conducted in the latitude-longitude spherical coordinate system with non uniform grid cells, which also verified the Re_R2007 scheme＇s advantages. Finally, in comparison with other global advection schemes, the Re_R2007 scheme was competitive in terms of accuracy and flow independence. An encouraging possibility for the application of the Re_R2007 scheme to the GRAPES model is provided.

Feedback control scheme of traffic jams based on the coupled map car-following model

Based on the pioneering work of Konishi et al. [Phys. Rev. E （1999） 60 4000], a new feedback control scheme is presented to suppress traffic jams based on the coupled map car-following model under the open boundary condition. The effect of the safe headway on the traffic system is considered. According to the control theory, the condition under which traffic jams can be suppressed is analyzed. The results are compared with the previous results concerning congestion control. The simulations show that the suppression performance of our scheme on traffic jams is better than those of the previous schemes, although all the schemes can suppress traffic jams. The simulation results are consistent with theoretical analyses.

Investigation of Uncertainties of Establishment Schemes in Dynamic Global Vegetation Models

In Dynamic Global Vegetation Models （DGVMs）, the establishment of woody vegetation refers to flowering, fertiliza- tion, seed production, germination, and the growth of tree seedlings. It determines not only the population densities but also other important ecosystem structural variables. In current DGVMs, establishments of woody plant functional types （PFTs） are assumed to be either the same in the same grid cell, or largely stochastic. We investigated the uncertainties in the competition of establishment among coexisting woody PFTs from three aspects： the dependence of PFT establishments on vegetation states; background establishment; and relative establishment potentials of different PFTs. Sensitivity experi- ments showed that the dependence of establishment rate on the fractional coverage of a PFT favored the dominant PFT by increasing its share in establishment. While a small background establishment rate had little impact on equilibrium states of the ecosystem, it did change the timescale required for the establishment of alien species in pre-existing forest due to their disadvantage in seed competition during the early stage of invasion. Meanwhile, establishment purely fiom background （the scheme commonly used in current DGVMs） led to inconsistent behavior in response to the change in PFT specification （e.g., number of PFTs and their specification）. Furthermore, the results also indicated that trade-off between irtdividual growth and reproduction/colonization has significant influences on the competition of establishment. Hence, further development of es- tablishment parameterization in DGVMs is essential in reducing the uncertainties in simulations of both ecosystem structures and successions.

A STUDY OF THE INFLUENCE OF MICROPHYSICAL PROCESSES ON TYPHOON NIDA(2016) USING A NEW DOUBLE-MOMENT MICROPHYSICS SCHEME IN THE WEATHER RESEARCH AND FORECASTING MODEL

The basic structure and cloud features of Typhoon Nida(2016) are simulated using a new microphysics scheme(Liuma) within the Weather Research and Forecasting(WRF) model. Typhoon characteristics simulated with the Liuma microphysics scheme are compared with observations and those simulated with a commonly-used microphysics scheme(WSM6). Results show that using different microphysics schemes does not significantly alter the track of the typhoon but does significantly affect the intensity and the cloud structure of the typhoon. Results also show that the vertical distribution of cloud hydrometeors and the horizontal distribution of peripheral rainband are affected by the microphysics scheme. The mixing ratios of rain water and graupel correlate highly with the vertical velocity component and equivalent potential temperature at the typhoon eye-wall region. According to the simulation with WSM 6 scheme,it is likely that the very low typhoon central pressure results from the positive feedback between hydrometeors and typhoon intensity. As the ice-phase hydrometeors are mostly graupel in the Liuma microphysics scheme, further improvement in this aspect is required.

An Application of Finite Volume WENO Schemeto Numerical Modeling of Tidal Current

A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established by use of the finite volume WENO scheme which maintains both uniform high order accuracy and an essentially non-oscillatory shock transition on unstructured triangular grid. The third order TVD Range-Kutta method is used for time discretization. The model has been firstly tested against four cases： 1） tidal forcing, 2） seiche oscillation, 3） wind setup in a closed bay, and 4） onedimensional dam-break water flow. The results obtained in the present study compare well with those obtained from the corresponding analytic solutions idealized for the above four cases. The model is then applied to the simulation of tidal circulation in the Yangpu Bay, and detailed model calibration and verification have been conducted with measured tidal current in the spring tide, middle tide, and neap tide. The overall performance of the model is in qualitative agreement with the data observed in 2005, and it can be used to calculate the flow in estuaries and coastal waters.

Attribute-Based Re-Encryption Scheme in the Standard Model

In this paper, we propose a new attribute-based proxy re-encryption scheme, where a semi-trusted proxy, with some additional information, can transform a ciphertext under a set of attributes into a new ciphertext under another set of attributes on the same message, but not vice versa, furthermore, its security was proved in the standard model based on decisional bilinear Diffie-Hellman assumption. This scheme can be used to realize fine-grained selectively sharing of encrypted data, but the general proxy rencryption scheme severely can not do it, so the proposed schemecan be thought as an improvement of general traditional proxy re-encryption scheme.

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.

Intercomparison of different physics schemes in the WRF model over the Asian summer monsoon region

Enhancing the ability of the WRF model in simulating a large area covering the West Pacific Ocean, China's Mainland, and the East Indian Ocean is very important to improve prediction of the East Asian monsoon climate. The objective of this study is to identify a reasonable configuration of physical parameterization schemes to simulate the precipitation and temperature in this large area. The Mellor-Yamada-Janjic （MYJ） and Yonsei University （YSU） PBL schemes, the WSM3 and WSM5 microphysics schemes, and the Betts-Miller-Janjic （BMJ） and Tiedtke cumulus schemes are compared through simulation of the regional climate of summer 2008. All cases exhibit a similar spatial distribution of temperature as observed, and the spatial correlation coefficients are all higher than 0.95. The cases combining MY J, WSM3/WSM5, and BMJ have the smallest biases of temperature. The choice of PBL scheme has a significant effect on precipitation in such a large area. The cases with MYJ reproduce a better distribution of rain belts, while YSU strongly overestimates the precipitation intensity. The precipitation simulated using WSM3 is similar to that using WSM5. The BMJ cumulus scheme combined with the MYJ PBL scheme has a smaller bias of precipitation. However, the Tiedtke scheme reproduces the precipitation pattern better, especially over the ITCZ.

Second-order difference scheme for a nonlinear model of wood drying process

A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.

Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion

We propose a boundary scheme for addressing multi-mechanism flow in a porous medium in slip and early transition flow regimes, which is frequently encountered in shale gas reservoirs. Micro-gaseous flow in organic-rich shale involves a complex flow mechanism. A self-developed boundary scheme that combines the non-equilibrium extrapolation scheme and the combined diffusive reflection and bounce-back scheme(half-way DBB) to embed the Langmuir slip boundary into the single-relaxation-time lattice Boltzmann method(SRT-LBM) enables us to describe this process, namely, the coupling effect of micro-gaseous flow and surface diffusion in organic-rich nanoscale pores. The present LBM model comes with the careful consideration of the local Knudsen number, local pressure gradient, viscosity correction model, and regularization procedure to account for the rarefied gas flows in irregular pores. Its validity and accuracy are verified by several benchmarking cases, and the calculated results by this boundary scheme accord well with our analytical solutions.This boundary scheme shows a higher accuracy than the existing studies. Additionally, a subiteration strategy is presented to tackle the coupled micro-gaseous flow and surface diffusion, which necessitates the iteration process matching of these two mechanisms. The multi-mechanism flow in the self-developed irregular pores is also numerically investigated and analyzed over a wide range of parameters. The results indicate that the present model can effectively capture the coupling effect of micro-gaseous flow and surface diffusion in a tree-like porous medium.

A Hybrid Finite-Volume and Finite Difference Scheme for Depth- Integrated Non-Hydrostatic Model

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

A Sensitivity Study on Parameterization Scheme of Snow Internal and Interfacial Processes in Snow Model

In order to develop a seasonal snow model of land surface process as accurately as possible for climatic study. it is necessary to fully understand the effects of important snow internal processes and interaction with air and to get an insight into influence of several relevant parameterization schemes with parameters' uncertainty to some degree. Using the snow model (SAST) developed by first author and other one and some useful field observation data, this paper has conducted a series of sensitivity studies on the parameterization schemes. They are relative to compaction process, snow thermal conduction, methodology of layering snow pack and to key parameters such as snow albedo, water holding capacity. Then, based on the results from the sensitivity studies, some useful conclusions for snow cover model improvement are obtained from the analysis of the results.

Applicability of Temperature Discrete Equation to NMRF Boundary Layer Scheme in GRAPES Model

By deriving the discrete equation of the parameterized equation for the New Medium-Range Forecast(NMRF)boundary layer scheme in the GRAPES model,the adjusted discrete equation for temperature is obviously different from the original equation under the background of hydrostatic equilibrium and adiabatic hypothesis.In the present research,three discrete equations for temperature in the NMRF boundary layer scheme are applied,namely the original(hereafter NMRF),the adjustment(hereafter NMRF-gocp),and the one in the YSU boundary-layer scheme(hereafter NMRF-TZ).The results show that the deviations of height,temperature,U and V wind in the boundary layer in the NMRF-gocp and NMRF-TZ experiments are smaller than those in the NMRF experiment and the deviations in the NMRF-gocp experiment are the smallest.The deviations of humidity are complex for the different forecasting lead time in the three experiments.Moreover,there are obvious diurnal variations of deviations from these variables,where the diurnal variations of deviations from height and temperature are similar and those from U and V wind are also similar.However,the diurnal variation of humidity is relatively complicated.The root means square errors of 2m temperature(T2m)and 10m speed(V10m)from the three experiments show that the error of NMRF-gocp is the smallest and that of NMRF is the biggest.There is also a diurnal variation of T2m and V10m,where T2m has double peaks and V10m has only one peak.Comparison of the discrete equations between NMRF and NMRF-gocp experiments shows that the deviation of temperature is likely to be caused by the calculation of vertical eddy diffusive coefficients of heating,which also leads to the deviations of other elements.