Development of multi-group Monte-Carlo transport and depletion coupling calculation method and verification with metal-fueled fast reactor

The accurate modeling of depletion,intricately tied to the solution of the neutron transport equation,is crucial for the design,analysis,and licensing of nuclear reactors and their fuel cycles.This paper introduces a novel multi-group Monte-Carlo depletion calculation approach.Multi-group cross-sections(MGXS)are derived from both 3D whole-core model and 2D fuel subassembly model using the continuous-energy Monte-Carlo method.Core calculations employ the multi-group Monte-Carlo method,accommodating both homogeneous and specific local heterogeneous geometries.The proposed method has been validated against the MET-1000 metal-fueled fast reactors,using both the OECD/NEA benchmark and a new refueling benchmark introduced in this paper.Our findings suggest that microscopic MGXS,produced via the Monte-Carlo method,are viable for fast reactor depletion analyses.Furthermore,the locally heterogeneous model with angular-dependent MGXS offers robust predictions for core reactivity,control rod value,sodium void value,Doppler constants,power distribution,and concentration levels.

GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].

A modified multi-group model of angular and momentum distribution of cosmic ray muons for thickness measurement and material discrimination of slabs

Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra of cosmic ray muons and reduced the spatial resolution. We present a modified multi-group model that takes into account these effects and calibrates the model by the material of lead. Performance tests establish that the model is capable of measuring the thickness of a Pb slab and identifying the material of an unknown slab on a reasonable exposure timescale, in both cases of complete and incomplete angular data. Results show that the modified multi-group model is helpful for improvements in image resolution in real applications.

Global dynamics of a novel multi-group model for computer worms

In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR （susceptible-infected-quarantined-removed） model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.

Multi-group ant colony algorithm based on simulated annealing method

To overcome the default of single search tendency, the ants in the colony are divided into several sub-groups. The ants in different subgroups have different trail information and expectation coefficients. The simulated annealing method is introduced to the algorithm. Through setting the temperature changing with the iterations, after each turn of tours, the solution set obtained by the ants is taken as the candidate set. The update set is obtained by adding the solutions in the candidate set to the previous update set with the probability determined by the temperature. The solutions in the candidate set are used to update the trail information. In each turn of updating, the current best solution is also used to enhance the trail information on the current best route. The trail information is reset when the algorithm is in stagnation state. The computer experiments demonstrate that the proposed algorithm has higher stability and convergence speed.

DYNAMIC FOR A STOCHASTIC MULTI-GROUP AIDS MODEL WITH SATURATED INCIDENCE RATE

In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function.Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system,which greatly improves upon previous results.

Estimates of the Fast and Termal Flux in Blanket of Critical Reactors by Using Multi-Group Methods

In this study, based differential equations methods are used to solve equations because these methods are dependent on boundary value data more than other mathematical equations. We have calculated neutron flux, criticality and geometrical eigenvalue by using multi-group method and solving the neutron diffusion equation for finite and infinite cylindrical and spherical reactors in this study. For the calculation of the total neutron flux cross sections, we need the neutron diffusion equation. Thus, we have established the relationship between neuron flow and cross-section of neuron depending on neutron energy. Critical calculations have been made by comparing the results with MNCP (montecarlo n-partical) simulation methods. For necessary computer calculations, the programme, Wolfram-Matematica-7 has been used.

Spatial pattern and driving factors of biomass carbon density for natural and planted coniferous forests in mountainous terrain,eastern Loess Plateau of China

Background:Understanding the spatial pattern and driving factors of forest carbon density in mountainous terrain is of great importance for monitoring forest carbon in support of sustainable forest management for mitigating climate change.Methods:We collected the forest inventory data in 2015 in Shanxi Province,eastern Loess Plateau of China,to explore the spatial pattern and driving factors of biomass carbon density(BCD)for natural and planted coniferous forests using Anselin Local Moran’s I,Local Getis-Ord G*and semivariogram analyses,and multi-group structural equation modeling,respectively.Results:The result of spatial pattern of BCDs for natural forests showed that the BCD was generally higher in the north but lower in the south of Shanxi.The spatial pattern for planted forests was substantially different from that for natural forests.The results of multi-group SEM suggested that elevation(or temperature as the alternative factor of elevation)and stand age were important driving factors of BCD for these two forest types.Compared with other factors,the effects of latitude and elevation on BCD showed much greater difference between these two forest types.The difference in indirect effect of latitude(mainly through affecting elevation and stand age)between natural and planted forests was to some extent a reflection of the difference between the spatial patterns of BCDs for natural and planted forests in Shanxi.Conclusions:The natural coniferous forests had a higher biomass carbon density,a stronger spatial dependency of biomass carbon density relative to planted coniferous forests in Shanxi.Elevation was the most important driving factor,and the effect on biomass carbon density was stronger for natural than planted coniferous forests.Besides,latitude presented only indirect effect on it for the two forest types.

Three-dimensional arterial spin labeling and diffusion kurtosis imaging in evaluating perfusion and infarct area size in acute cerebral ischemia

BACKGROUND Early thrombolytic therapy is crucial to treat acute cerebral infarction,especially since the onset of thrombolytic therapy takes 1-6 h.Therefore,early diagnosis and evaluation of cerebral infarction is important.AIM To investigate the diagnostic value of magnetic resonance multi-delay threedimensional arterial spin labeling(3DASL)and diffusion kurtosis imaging(DKI)in evaluating the perfusion and infarct area size in patients with acute cerebral ischemia.METHODS Eighty-four patients who experienced acute cerebral ischemia from March 2019 to February 2021 were included.All patients in the acute stage underwent magnetic resonance-based examination,and the data were processed by the system’s own software.The apparent diffusion coefficient(ADC),average diffusion coefficient(MD),axial diffusion(AD),radial diffusion(RD),average kurtosis(MK),radial kurtosis(fairly RK),axial kurtosis(AK),and perfusion parameters post-labeling delays(PLD)in the focal area and its corresponding area were compared.The correlation between the lesion area of cerebral infarction under MK and MD and T2-weighted imaging(T2WI)was analyzed.RESULTS The DKI parameters of focal and control areas in the study subjects were compared.The ADC,MD,AD,and RD values in the lesion area were significantly lower than those in the control area.The MK,RK,and AK values in the lesion area were significantly higher than those in the control area.The MK/MD value in the infarct lesions was used to determine the matching situation.MK/MD<5 mm was considered matching and MK/MD≥5 mm was considered mismatching.PLD1.5s and PLD2.5s perfusion parameters in the central,peripheral,and control areas of the infarct lesions in MK/MD-matched and-unmatched patients were not significantly different.PLD1.5s and PLD2.5s perfusion parameter values in the central area of the infarct lesions in MK/MD-matched and-unmatched patients were significantly lower than those in peripheral and control areas.The MK and MD maps showed a lesion area of 20.08±5.74 cm^(2) and 22.09±5.58 cm^(2),respectively.T2WI showed a lesion area of 19.76±5.02 cm^(2).There were no significant differences in the cerebral infarction lesion areas measured using the three methods.MK,MD,and T2WI showed a good correlation.CONCLUSION DKI parameters showed significant difference between the focal and control areas in patients with acute ischemic cerebral infarction.3DASL can effectively determine the changes in perfusion levels in the lesion area.There was a high correlation between the area of the infarct lesions diagnosed by DKI and T2WI.

Solution of Multi-Delay Dynamic Systems by Using Hybrid Functions

In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced to a system of linear algebraic equations by expanding various time functions for the hybrid functions and using operational matrices. To demonstrate the validity and the applicability of the technique, some examples are presented.

Spectrum behavior for the nonlinear fractional point reactor kinetics model

The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor's formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error(local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes.

Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.

Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

Consider the heterogeneity(e.g.,heterogeneous social behaviour,heterogeneity due to different geography,contrasting contact patterns and different numbers of sexual partners etc.)of host population,in this paper,the authors propose an infection age multigroup SEIR epidemic model.The model system also incorporates the feedback variables,where the infectivity of infected individuals may depend on the infection age.In the direction of mathematical analysis of model,the basic reproduction number R_0 has been computed.The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R_(0).More precisely,for R_(0)≤1,the disease-free equilibrium is globally asymptotically stable and for R_(0)>1,they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method.By considering a numerical example,they investigate the effects of infection age and feedback on the prevalence of the disease.Their result shows that feedback parameters have different and even opposite effects on different groups.However,by choosing an appropriate value of feedback parameters,the disease could be eradicated or maintained at endemic level.Besides,the infection age of infected individuals may also change the behaviour of the disease,global stable to damped oscillations or damped oscillations to global stable.

CT Reconstruction with Priori MRI Images Through Multi-Group Datasets Expansion

Computed tomography(CT) reconstruction with a well-registered priori magnetic resonance imaging(MRI) image can improve reconstruction results with low-dose CT, because well-registered CT and MRI images have similar structures. However, in clinical settings, the CT image of patients does not always match the priori MRI image because of breathing and movement of patients during CT scanning. To improve the image quality in this case, multi-group datasets expansion is proposed in this paper. In our method, multi-group CT-MRI datasets are formed by expanding CT-MRI datasets. These expanded datasets can also be used by most existing CT-MRI algorithms and improve the reconstructed image quality when the CT image of a patient is not registered with the priori MRI image. In the experiments, we evaluate the performance of the algorithm by using multi-group CT-MRI datasets in several unregistered situations. Experiments show that when the CT and priori MRI images are not registered, the reconstruction results of using multi-group dataset expansion are better than those obtained without using the expansion.

Robust Stabilization of Interval Coefficient Non-linear Discrete Control Systems with Multi-Group Non-integer Delays

In the paper, we give the robust stabilization and estimate formulae for interval coefficient non linear discrete control systems with multi group delays. We used the comparison principles method and frequency domain method for discrete control systems with multi group non integer delays which are proposed by Liu Yongqing.

Threshold dynamics of a multi-group SEAR alcoholism model with public health education

In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-group separately. We prove that the basic reproduction number R0 plays the role of a threshold for the long-time behavior of the model. The alcohol-free equilibrium P0 of the model is globally asymptotically stable if R0≤1,while the alcohol-present equilibrium P* exists uniquely and is globally asymptotically stable if R0>1.For the proofs of main results, we use the classical method of Lyapunov functions and apply subtle grouping technique in estimating the derivatives of Lyapunov functions guided by graph theory. Our results expand the previous results which have been obtained in single-group models. Sensitivity analysis and numerical simulations are also performed to illustrate our results.

The high-energy multi-group HEST1.0 library based on ENDF/B-Ⅶ.0: development, verification and preliminary application

ENDF/B-Ⅶ.0, which was released by the USA Cross Section Evaluation Working Group （CSEWG） in December 2006, was demonstrated to perform much better than previous ENDF evaluations over a broad range of benchmark experiments. A high-energy （up to 150 MeV） multi-group library set named HEST1.0 with 253-neutron and 48-photon groups has been developed based on ENDF/B-Ⅶ.0 using the N JOY code. This paper provides a summary of the procedure to produce the library set and a detailed description of the verification of the multi-group library set by several shielding benchmark devices, in particular for high-energy neutron data. In addition, the first application of HEST1.0 to the shielding design of the China Spallation Neutron Source （CSNS） is demonstrated.

Multi-patch multi-group epidemic model with varying infectivity

This paper presents a law of large numbers result,as the size of the population tends to infinity,of SIR stochastic epidemic models,for a population distributed over distinct patches(with migrations between them)and distinct groups(possibly age groups).The limit is a set of Volterra-type integral equations,and the result shows the effects of both spatial and population heterogeneity.The novelty of the model is that the infectivity of an infected individual is infection age dependent.More precisely,to each infected individual is attached a random infection-age dependent infectivity function,such that the various random functions attached to distinct individuals are i.i.d.The proof involves a novel construction of a sequence of i.i.d.processes to invoke the law of large numbers for processes in,by using the solution of a MacKean-Vlasov type Poisson-driven stochastic equation(as in the propagation of chaos theory).We also establish an identity using the Feynman-Kac formula for an adjoint backward ODE.The advantage of this approach is that it assumes much weaker conditions on the random infectivity functions than our earlier work for the homogeneous model in[20],where standard tightness criteria for convergence of stochastic processes were employed.To illustrate this new approach,we first explain the new proof under the weak assumptions for the homogeneous model,and then describe the multipatch-multigroup model and prove the law of large numbers for that model.

Stabilizing Decomposition of neutral Linear Time－invariant Large－Scale Control Systems With Multi－group Multi－delays

By the way of Introducing some parameters εi(i = 1, 2, 3), a result for the stabilization of the linear time-invariant isolated control subeystems without the time delays imply the stabilization of the neutral linear time-invariant large-scale control systems with the multigroup multi-delaysis improved using Lyapunov decomposition equivalence method found by Liu Yongqing. These results in this paper can be expanded the stabilization region of the parameters to be 6 times of the former stable range of the parameters.

A multi-order method for predicting stability of a multi-delay milling system considering helix angle and run-out effects

In this paper, a multi-delay milling system considering helix angle and run-out effects is firstly established. An exponential cutting force model is used to model the interaction between a work-piece and a cutting tool, and a new approach is presented for accurately calibrating exponential cutting force coefficients and cutter run-out parameters. Furthermore, based on an implicit multi-step Adams formula and an improved precise time-integration algorithm, a novel stability prediction method is proposed to predict the stability of the system. The involved time delay term and periodic coefficient term are integrated as a comprehensive state term in the integral response which is approximated by the Adams formula. Then, a Floquet transition matrix with an arbitraryorder form is constructed by using a series of matrix multiplication, and the stability of the system is determined by the Floquet theory. Compared to classical semi-discretization methods and fulldiscretization methods, the developed method shows a good performance in convergence, efficiency,accuracy, and multi-order complexity. A series of cutting tests is further carried out to validate the practicability and effectiveness of the proposed method. The results show that the calibration process needs a time of less than 5 min, and the stability prediction method is effective.