In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional tran...In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.展开更多
This paper considers a secure multigroup multicast multiple-input single-output(MISO)communication system aided by an intelligent reflecting surface(IRS).Specifically,we aim to minimize the transmit power at Alice via...This paper considers a secure multigroup multicast multiple-input single-output(MISO)communication system aided by an intelligent reflecting surface(IRS).Specifically,we aim to minimize the transmit power at Alice via jointly optimizing the transmit beamformer,artificial noise(AN)vector and phase shifts at the IRS subject to the secrecy rate constraints as well as the unit modulus constraints of IRS phase shifts.To tackle the optimization problem,we first transform it into a semidefinite relaxation(SDR)problem,and then alternately update the transmit beamformer and AN matrix as well as the phase shifts at the IRS.In order to reduce the high computational complexity,we further propose a low-complexity algorithm based on second-order cone programming(SOCP).We decouple the optimization problem into two sub-problems and optimize the transmit beamformer,AN vector and the phase shifts alternately by solving two corresponding SOCP subproblem.Simulation results show that the proposed SDR and SOCP schemes require half or less transmit power than the scheme without IRS,which demonstrates the advantages of introducing IRS and the effectiveness of the proposed methods.展开更多
Rate-splitting multiple access(RSMA)can cope with a wide range of propagation conditions in multigroup multicast communications through rate splitting optimization.To breakthrough the grouprate limited bottleneck,reco...Rate-splitting multiple access(RSMA)can cope with a wide range of propagation conditions in multigroup multicast communications through rate splitting optimization.To breakthrough the grouprate limited bottleneck,reconfigurable intelligent surface(RIS)technique can be introduced to assist wireless communications through enhancing the channel quality.In RIS-aided RSMA multigroup multicasting,how to provide fair and high-quality multiuser service under power and spectrum constraints is essential.In this paper,we propose a max-min fair RIS-aided rate-splitting multiple access(MMF-RISRSMA)scheme for multigroup multicast communications,where the rate fairness is obtained by maximizing the minimum group-rate.In doing so,we jointly optimize the beamformers,the rate splitting vector at the transmitter,as well as the phase shifts at RIS.To solve it,we divide the original optimization problem into two subproblems and alternately optimize the variables.The beamforming and rate splitting optimization subproblem is solved by using the successive convex approximation technique.The phase shift optimization subproblem is solved through the penalty function method to achieve a rank-one locally optimal solution.Simulations demonstrate that the proposed MMF-RIS-RSMA scheme can obtain significant performance gain in terms of the minimum group-rate.展开更多
Onboard resources are limited for multibeam satellite communication systems,while differences exist in traffic demands among users.Since conventional multigroup multicast precoding methods do not take traffic demands ...Onboard resources are limited for multibeam satellite communication systems,while differences exist in traffic demands among users.Since conventional multigroup multicast precoding methods do not take traffic demands for users into consideration,it is difficult to flexibly adjust the offered throughput to users’demands.Users with higher demand may obtain lower throughput while users with lower demand may be over-satisfied,which results in the requested-offered throughput mismatch and resource waste.This paper proposes a fair multigroup multicast precoding design based on traffic demands.To obtain the precoding design,the optimization problem aimed at maximizing the minimum throughput satisfaction ratio,which is defined as the ratio of the offered throughput to the traffic demand,is formulated,so as to provide fair service for all users while satisfying per-feed power constraints and traffic demand constraints.To address this problem,an auxiliary variable is first introduced to equivalently simplify it.Then,the semidefinite relaxation and the bisection search strategies are adopted to further handle the problem.Finally,the optimal precoding vectors are obtained by employing eigenvalue decomposition or Gaussian randomization.Simulation results indicate the effectiveness of the proposed precoding algorithm and demonstrate that it can better adapt to the scenarios with different traffic demands.展开更多
In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also s...In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.展开更多
Asymptotic expansions for the finite element approximation to the eigenvalues of the mult-igroup diffusion equations on Ω(?)R^n(n=2,3)of reactor theory are given,firstly for a piecewiseuniform triangulation,then for ...Asymptotic expansions for the finite element approximation to the eigenvalues of the mult-igroup diffusion equations on Ω(?)R^n(n=2,3)of reactor theory are given,firstly for a piecewiseuniform triangulation,then for nonuniform quadrilateral meshes,and finally for nonuniformhexahedral meshes.The effect of certain classes of numerical integrations is studied.As applicationsof the expansions,several extrapolation formulas and a posteriori error estimates are obtained.展开更多
In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqu...In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.展开更多
We propose a general multigroup model for cholera dynamics that involves both direct and indirect transmission pathways and that incorporates spatial heterogeneity. Under biologically feasible conditions, we show that...We propose a general multigroup model for cholera dynamics that involves both direct and indirect transmission pathways and that incorporates spatial heterogeneity. Under biologically feasible conditions, we show that the basic reproduction number R0 remains a sharp threshold for cholera dynamics in multigroup settings. We verify the analysis by numerical simulation results. We also perform an optimal control study to explore optimal vaccination strategy for cholera outbreaks.展开更多
文摘In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.
基金supported in part by the National Natural Science Foundation of China under Grants 62071234,61901121 and 61771244in part by the Natural Science Research Project of Education Department of Anhui Province of China under Grant KJ2019A1002.
文摘This paper considers a secure multigroup multicast multiple-input single-output(MISO)communication system aided by an intelligent reflecting surface(IRS).Specifically,we aim to minimize the transmit power at Alice via jointly optimizing the transmit beamformer,artificial noise(AN)vector and phase shifts at the IRS subject to the secrecy rate constraints as well as the unit modulus constraints of IRS phase shifts.To tackle the optimization problem,we first transform it into a semidefinite relaxation(SDR)problem,and then alternately update the transmit beamformer and AN matrix as well as the phase shifts at the IRS.In order to reduce the high computational complexity,we further propose a low-complexity algorithm based on second-order cone programming(SOCP).We decouple the optimization problem into two sub-problems and optimize the transmit beamformer,AN vector and the phase shifts alternately by solving two corresponding SOCP subproblem.Simulation results show that the proposed SDR and SOCP schemes require half or less transmit power than the scheme without IRS,which demonstrates the advantages of introducing IRS and the effectiveness of the proposed methods.
基金supported in part by the Project of International Cooperation and Exchanges NSFC under Grant No.61860206005in part by the National Natural Science Foundation of China under Grant No.62201329,No.62171262in part by Shandong Provincial Natural Science Foundation under Grant ZR2021YQ47。
文摘Rate-splitting multiple access(RSMA)can cope with a wide range of propagation conditions in multigroup multicast communications through rate splitting optimization.To breakthrough the grouprate limited bottleneck,reconfigurable intelligent surface(RIS)technique can be introduced to assist wireless communications through enhancing the channel quality.In RIS-aided RSMA multigroup multicasting,how to provide fair and high-quality multiuser service under power and spectrum constraints is essential.In this paper,we propose a max-min fair RIS-aided rate-splitting multiple access(MMF-RISRSMA)scheme for multigroup multicast communications,where the rate fairness is obtained by maximizing the minimum group-rate.In doing so,we jointly optimize the beamformers,the rate splitting vector at the transmitter,as well as the phase shifts at RIS.To solve it,we divide the original optimization problem into two subproblems and alternately optimize the variables.The beamforming and rate splitting optimization subproblem is solved by using the successive convex approximation technique.The phase shift optimization subproblem is solved through the penalty function method to achieve a rank-one locally optimal solution.Simulations demonstrate that the proposed MMF-RIS-RSMA scheme can obtain significant performance gain in terms of the minimum group-rate.
基金the National Key R&D Program of China(No.2020YFB1806800).
文摘Onboard resources are limited for multibeam satellite communication systems,while differences exist in traffic demands among users.Since conventional multigroup multicast precoding methods do not take traffic demands for users into consideration,it is difficult to flexibly adjust the offered throughput to users’demands.Users with higher demand may obtain lower throughput while users with lower demand may be over-satisfied,which results in the requested-offered throughput mismatch and resource waste.This paper proposes a fair multigroup multicast precoding design based on traffic demands.To obtain the precoding design,the optimization problem aimed at maximizing the minimum throughput satisfaction ratio,which is defined as the ratio of the offered throughput to the traffic demand,is formulated,so as to provide fair service for all users while satisfying per-feed power constraints and traffic demand constraints.To address this problem,an auxiliary variable is first introduced to equivalently simplify it.Then,the semidefinite relaxation and the bisection search strategies are adopted to further handle the problem.Finally,the optimal precoding vectors are obtained by employing eigenvalue decomposition or Gaussian randomization.Simulation results indicate the effectiveness of the proposed precoding algorithm and demonstrate that it can better adapt to the scenarios with different traffic demands.
基金The authors are grateflfl to tile anonymous referees for carefully reading the manuscript and for important snggestions and comments, which led to the improvement of their manuscript. This research is supported by NSFC grant 11601043, China Postdoctoral Science Foundation （Grant No. 2016M590243）, Jiangsu Province ＂333 High-Level Personnel Training Project＂ （Grant No. BRA2017468） and Qing Lan Project of Jiangsu Province of 2016 and 2017.
文摘In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.
文摘Asymptotic expansions for the finite element approximation to the eigenvalues of the mult-igroup diffusion equations on Ω(?)R^n(n=2,3)of reactor theory are given,firstly for a piecewiseuniform triangulation,then for nonuniform quadrilateral meshes,and finally for nonuniformhexahedral meshes.The effect of certain classes of numerical integrations is studied.As applicationsof the expansions,several extrapolation formulas and a posteriori error estimates are obtained.
基金This work is supported by the National Natural Science Foundation of China(Nos.12001090 and 11871473)Shandong Provincial Natural Science Foundation(No.ZR2019MA010)the Fundamental Research Funds for the Central Universitiesof China(No.2412020QD024).
文摘In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.
文摘We propose a general multigroup model for cholera dynamics that involves both direct and indirect transmission pathways and that incorporates spatial heterogeneity. Under biologically feasible conditions, we show that the basic reproduction number R0 remains a sharp threshold for cholera dynamics in multigroup settings. We verify the analysis by numerical simulation results. We also perform an optimal control study to explore optimal vaccination strategy for cholera outbreaks.
