Matching soil grid unit resolutions with polygon unit map scales is important to minimize the uncertainty of regional soil organic carbon(SOC) pool simulation due to their strong influences on the modeling.A series of...Matching soil grid unit resolutions with polygon unit map scales is important to minimize the uncertainty of regional soil organic carbon(SOC) pool simulation due to their strong influences on the modeling.A series of soil grid units at varying cell sizes was derived from soil polygon units at six map scales,namely,1:50 000(C5),1:200 000(D2),1:500 000(P5),1:1 000 000(N1),1:4 000 000(N4) and 1:14 000 000(N14),in the Taihu Region of China.Both soil unit formats were used for regional SOC pool simulation with a De Nitrification-DeC omposition(DNDC) process-based model,which spans the time period from 1982 to 2000 at the six map scales.Four indices,namely,soil type number(STN),area(AREA),average SOC density(ASOCD) and total SOC stocks(SOCS) of surface paddy soils that were simulated by the DNDC,were distinguished from all these soil polygon and grid units.Subjecting to the four index values(IV) from the parent polygon units,the variations in an index value(VIV,%) from the grid units were used to assess its dataset accuracy and redundancy,which reflects the uncertainty in the simulation of SOC pools.Optimal soil grid unit resolutions were generated and suggested for the DNDC simulation of regional SOC pools,matching their respective soil polygon unit map scales.With these optimal raster resolutions,the soil grid units datasets can have the same accuracy as their parent polygon units datasets without any redundancy,when VIV < 1% was assumed to be a criterion for all four indices.A quadratic curve regression model,namely,y = – 0.80 × 10^(–6)x^2 + 0.0228 x + 0.0211(R^2 = 0.9994,P < 0.05),and a power function model R? = 10.394?^(0.2153)(R^2 = 0.9759,P < 0.05) were revealed,which describe the relationship between the optimal soil grid unit resolution(y,km) and soil polygon unit map scale(1:10 000x),the ratio(R?,%) of the optimal soil grid size to average polygon patch size(?,km^2) and the ?,with the highest R^2 among different mathematical regressions,respectively.This knowledge may facilitate the grid partitioning of regions during the investigation and simulation of SOC pool dynamics at a certain map scale,and be referenced to other landscape polygon patches' mesh partition.展开更多
Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which...Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which increases the programming complexity of and limits the parallelizability of the whole simulation.In this paper,a new adaptive preconditioned Jacobian-free Newton-GMRES(m)method is proposed to be applied to dynamic simulations of power systems.This new method has totally Jacobian-free characteristics,which saves calculations and storages of Jacobian matrixes and features strong parallelizability.Moreover,several speedup strategies are introduced to enhance efficiency and parallelizability of overall computations.Numerical tests are carried out on IEEE standard test systems and results show that in series computing environment,simulations based on the proposed method have comparable speed to those based on classical Newton-Raphson methods.展开更多
The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications ...The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications have sprung up recently.The prediction of wave competitions is also very important and quite useful in these fields.This paper considers the behaviors of wave competitions in simple,inhomogeneous media which is modeled by Brusselator equations.We present a simple rule to judge the results of wave competitions utilizing the dispersion relation curves and the waves coming from different wave sources.Moreover,this rule can also be used to predict the results of wave propagation.It provides methods of obtaining the desired waves with given frequencies in inhomogeneous media.All our results are concluded and verified by computer simulations.展开更多
基金Under the auspices of Special Project of National Key Research and Development Program(No.2016YFD0200301)National Natural Science Foundation of China(No.41571206)Special Project of National Science and Technology Basic Work(No.2015FY110700-S2)
文摘Matching soil grid unit resolutions with polygon unit map scales is important to minimize the uncertainty of regional soil organic carbon(SOC) pool simulation due to their strong influences on the modeling.A series of soil grid units at varying cell sizes was derived from soil polygon units at six map scales,namely,1:50 000(C5),1:200 000(D2),1:500 000(P5),1:1 000 000(N1),1:4 000 000(N4) and 1:14 000 000(N14),in the Taihu Region of China.Both soil unit formats were used for regional SOC pool simulation with a De Nitrification-DeC omposition(DNDC) process-based model,which spans the time period from 1982 to 2000 at the six map scales.Four indices,namely,soil type number(STN),area(AREA),average SOC density(ASOCD) and total SOC stocks(SOCS) of surface paddy soils that were simulated by the DNDC,were distinguished from all these soil polygon and grid units.Subjecting to the four index values(IV) from the parent polygon units,the variations in an index value(VIV,%) from the grid units were used to assess its dataset accuracy and redundancy,which reflects the uncertainty in the simulation of SOC pools.Optimal soil grid unit resolutions were generated and suggested for the DNDC simulation of regional SOC pools,matching their respective soil polygon unit map scales.With these optimal raster resolutions,the soil grid units datasets can have the same accuracy as their parent polygon units datasets without any redundancy,when VIV < 1% was assumed to be a criterion for all four indices.A quadratic curve regression model,namely,y = – 0.80 × 10^(–6)x^2 + 0.0228 x + 0.0211(R^2 = 0.9994,P < 0.05),and a power function model R? = 10.394?^(0.2153)(R^2 = 0.9759,P < 0.05) were revealed,which describe the relationship between the optimal soil grid unit resolution(y,km) and soil polygon unit map scale(1:10 000x),the ratio(R?,%) of the optimal soil grid size to average polygon patch size(?,km^2) and the ?,with the highest R^2 among different mathematical regressions,respectively.This knowledge may facilitate the grid partitioning of regions during the investigation and simulation of SOC pool dynamics at a certain map scale,and be referenced to other landscape polygon patches' mesh partition.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51277104 and 51207076)the National High-Tech Research & Development Program of China ("863" Program) (Grant No.2012AA050217)+1 种基金the Postdoctoral Science Foundation of China (Grant No.2012M510441)Tsinghua University Initiative Scientific Research Program (Grant No. 20121087926)
文摘Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which increases the programming complexity of and limits the parallelizability of the whole simulation.In this paper,a new adaptive preconditioned Jacobian-free Newton-GMRES(m)method is proposed to be applied to dynamic simulations of power systems.This new method has totally Jacobian-free characteristics,which saves calculations and storages of Jacobian matrixes and features strong parallelizability.Moreover,several speedup strategies are introduced to enhance efficiency and parallelizability of overall computations.Numerical tests are carried out on IEEE standard test systems and results show that in series computing environment,simulations based on the proposed method have comparable speed to those based on classical Newton-Raphson methods.
基金Supported by National Natural Science Foundation of China under Grant Nos.11105051,11104071,11247272Fundamental Research Funds for Central Universities,Beijing Higher Education Elite Young Teacher ProjectYouth Scholars Program of Beijing Normal University
文摘The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications have sprung up recently.The prediction of wave competitions is also very important and quite useful in these fields.This paper considers the behaviors of wave competitions in simple,inhomogeneous media which is modeled by Brusselator equations.We present a simple rule to judge the results of wave competitions utilizing the dispersion relation curves and the waves coming from different wave sources.Moreover,this rule can also be used to predict the results of wave propagation.It provides methods of obtaining the desired waves with given frequencies in inhomogeneous media.All our results are concluded and verified by computer simulations.
