The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L2-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.
A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several kinds of subsets of A,its induced equicontinuous actions on several important subsets of the dual Banach space A*,and the Lip-norm L with its induced metric space structures on the state space S(A)of A.
The trajectory of the compact torus(CT)within a tokamak discharge is crucial to fueling.In this study,we developed a penetration model with a vacuum magnetic field region to accurately determine CT trajectories in tokamak discharges.This model was used to calculate the trajectory and penetration parameters of CT injections by applying both perpendicular and tangential injection schemes in both HL-2A and ITER tokamaks.For perpendicular injection along the tokamak's major radius direction from the outboard,CTs with the same injection parameters exhibited a 0.08 reduction in relative penetration depth when injected into HL-2A and a 0.13reduction when injected into ITER geometry when considering the vacuum magnetic field region compared with cases where this region was not considered.In addition,we proposed an optimization method for determining the CT's initial injection velocity to accurately calculate the initial injection velocity of CTs for central fueling in tokamaks.Furthermore,this paper discusses schemes for the tangential injection of CT into tokamak discharges.The optimal injection angle and CT magnetic moment direction for injection into both HL-2A and ITER were determined through numerical simulations.Finally,the kinetic energy loss occurring when the CT penetrated the vacuum magnetic field region in ITER was reduced byΔEk=975.08 J by optimizing the injection angle for the CT injected into ITER.These results provide valuable insights for optimizing injection angles in fusion experiments.Our model closely represents actual experimental scenarios and can assist the design of CT parameters.
This paper studies the distributed Nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition.To keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based method.Under the assumption that the unique Nash equilibrium is the unique equilibrium of the pseudogradient system,an algorithm is proposed that is able to exponentially find the Nash equilibrium.Further,the authors also consider the distributed Nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact sets.Two examples are used to illustrate the proposed approach.
Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.
Radio frequency quadrupoles(RFQs),which are crucial components of proton injectors,significantly affect the performance of proton accelerator facilities.An RFQ with a high frequency of 714 MHz dedicated to compact proton injectors for medi-cal applications is designed in this study.The RFQ is designed to accelerate proton beams from 50 keV to 4 MeV within a short length of 2 m and can be matched closely with the downstream drift tube linac to capture more particles through a preliminary optimization.To develop an advanced RFQ,challenging techniques,including fabrication and tuning method,must be evaluated and verified using a prototype.An aluminium prototype is derived from the conceptual design of the RFQ and then redesigned to confirm the radio frequency performance,fabrication procedure,and feasibility of the tuning algorithm.Eventually,a new tuning algorithm based on the response matrix and least-squares method is developed,which yields favorable results based on the prototype,i.e.,the errors of the dipole and quadrupole components reduced to a low level after several tuning iterations.Benefiting from the conceptual design and techniques obtained from the prototype,the formal mechanical design of the 2-m RFQ is ready for the next manufacturing step.
Rice is an important food crop for human beings.Accurately distinguishing different varieties and sowing methods of rice on a large scale can provide more accurate information for rice growth monitoring,yield estimation,and phenological monitoring,which has significance for the development of modern agriculture.Compact polarimetric(CP)synthetic aperture radar(SAR)provides multichannel information and shows great potential for rice monitoring and mapping.Currently,the use of machine learning methods to build classification models is a controversial topic.In this paper,the advantages of CP SAR data,the powerful learning ability of machine learning,and the important factors of the rice growth cycle were taken into account to achieve high-precision and fine classification of rice paddies.First,CP SAR data were simulated by using the seven temporal RADARSAT-2 C-band data sets.Second,20-two CP SAR parameters were extracted from each of the seven temporal CP SAR data sets.In addition,we fully considered the change degree of CP SAR parameters on a time scale(ΔCP_(DoY)).Six machine learning methods were employed to carry out the fine classification of rice paddies.The results show that the classification methods of machine learning based on multitemporal CP SAR data can obtain better results in the fine classification of rice paddies by considering the parameters ofΔCP_(DoY).The overall accuracy is greater than 95.05%,and the Kappa coefficient is greater than 0.937.Among them,the random forest(RF)and support vector machine(SVM)achieve the best results,with an overall accuracy reaching 97.32%and 97.37%,respectively,and Kappa coefficient values reaching 0.965 and 0.966,respectively.For the two types of rice paddies,the average accuracy of the transplant hybrid(T-H)rice paddy is greater than 90.64%,and the highest accuracy is 95.95%.The average accuracy of direct-sown japonica(D-J)rice paddy is greater than 92.57%,and the highest accuracy is 96.13%.
Xianyu GUOJunjun YINKun LIJian YANGHuimin ZOUFukun YANG
The achievement of ignition at the National Ignition Facility(NIF)has prompted a global wave of further research on inertial fusion energy(IFE).However,IFE requires a target gain G of 30-100,and it is hard to achieve fusion at such high gain with the energy,configuration,and technical approach of the NIF.Here,we present a conceptual design for a next-generation laser driver that is applicable to multiple laser fusion schemes and provides 10 MJ,2-3 PW at 3ω(or 2ω,in which case the energy and power can be higher),and one shot per 30 min,with the aim of achieving G>30.It is also efficient,compact,and low in cost,and it has low susceptibility to laser-plasma instabilities.
