Scale effect removal and range migration correction for hypersonic target coherent detection

The detection of hypersonic targets usually confronts range migration(RM)issue before coherent integration(CI).The traditional methods aiming at correcting RM to obtain CI mainly considers the narrow-band radar condition.However,with the increasing requirement of far-range detection,the time bandwidth product,which is corresponding to radar’s mean power,should be promoted in actual application.Thus,the echo signal generates the scale effect(SE)at large time bandwidth product situation,influencing the intra and inter pulse integration performance.To eliminate SE and correct RM,this paper proposes an effective algorithm,i.e.,scaled location rotation transform(ScLRT).The ScLRT can remove SE to obtain the matching pulse compression(PC)as well as correct RM to complete CI via the location rotation transform,being implemented by seeking the actual rotation angle.Compared to the traditional coherent detection algorithms,Sc LRT can address the SE problem to achieve better detection/estimation capabilities.At last,this paper gives several simulations to assess the viability of ScLRT.

Precipitation scale effect of the TRMM satellite in Tianshan,China

High-resolution precipitation data is conducive to objectively describe the spatial-temporal variability of regional precipitation,and the study of downscaling techniques and spatial scale effects can provide technical and theoretical support to improve the spatial resolution and accuracy of satellite precipitation data.In this study,we used a machine learning algorithm combined with a regression algorithm RF-PLS(Random Forest-Partial Least Squares)to construct a downscaling model to obtain three types of high-resolution TRMM(Tropical Rainfall Measuring Mission)downscaled precipitation data for the years 2000-2017 at 250 m,500 m,and 1km.The scale effects with topographic and geomorphological features in the study area were analysed.Finally,we described the spatial and temporal variation of precipitation based on the optimal TRMM downscaled precipitation data.The results showed that:1)The linear relationships between the TRMM downscaled precipitation data obtained by each of the three downscaled models(PLS,RF,and RF-PLS)and the precipitation at the observation stations were improved compared to the linear relationships between the original TRMM data and the precipitation at the observation stations.The accuracy of the RF-PLS model was better than the other two models.2)Based on the RF-PLS model,the resolution of the TRMM data was increased to three different scales(250 m,500 m,and 1 km),considering the scale effects with topographic and geomorphological features.The precipitation simulation effect with a spatial resolution of 500 m was better than the other two scales.3)The annual precipitation was the highest in the areas with extremely high mountains,followed by the mediumhigh mountain,high mountain,medium mountain,medium-low mountain,plain,low mountain,and basin.

Scale dependence of forest fragmentation and its climate sensitivity in a semi-arid mountain:Comparing Landsat,Sentinel and Google Earth data

Landscape fragmentation is generally viewed as an indicator of environmental stresses or risks,but the fragmentation intensity assessment also depends on the scale of data and the definition of spatial unit.This study aimed to explore the scale-dependence of forest fragmentation intensity along a moisture gradient in Yinshan Mountain of North China,and to estimate environmental sensitivity of forest fragmentation in this semi-arid landscape.We developed an automatic classification algorithm using simple linear iterative clustering(SLIC)and Gaussian mixture model(GMM),and extracted tree canopy patches from Google Earth images(GEI),with an accuracy of 89.2%in the study area.Then we convert the tree canopy patches to forest category according to definition of forest that tree density greater than 10%,and compared it with forest categories from global land use datasets,FROM-GLC10 and GlobeLand30,with spatial resolutions of 10 m and 30 m,respectively.We found that the FROM-GLC10 and GlobeLand30 datasets underestimated the forest area in Yinshan Mountain by 16.88%and 21.06%,respectively;and the ratio of open forest(OF,10%<tree coverage<40%)to closed forest(CF,tree coverage>40%)areas in the underestimated part was 2:1.The underestimations concentrated in warmer and drier areas occupied mostly by large coverage of OFs with severely fragmented canopies.Fragmentation intensity of canopies positively correlated with spring temperature while negatively correlated with summer precipitation and terrain slope.When summer precipitation was less than 300 mm or spring temperature higher than 4°C,canopy fragmentation intensity rose drastically,while the forest area percentage kept stable.Our study suggested that the spatial configuration,e.g.,sparseness,is more sensitive to drought stress than area percentage.This highlights the importance of data resolution and proper fragmentation measurements for forest patterns and environmental interpretation,which is the base of reliable ecosystem predictions with regard to the future climate scenarios.

Scale Effects on Propeller Cavitating Hydrodynamic and Hydroacoustic Performances with Non-uniform Inflow

Considering the lack of theoretical models and ingredients necessary to explain the scaling of the results of propeller cavitation inception and cavitating hydroacoustics from model tests to full scale currently, and the insufficient reflection of the nuclei effects on cavitation in the numerical methods, the cavitating hydrodynamics and cavitation low frequency noise spectrum of three geometrically similar 7-bladed highly skewed propellers with non-uniform inflow are addressed. In this process, a numerical bridge from the multiphase viscous simulation of propeller cavitation hydrodynamics to its hydro-acoustics is built, and the scale effects on performances and the applicability of exist scaling law are analyzed. The effects of non-condensable gas（NCG） on cavitation inception are involved explicitly in the improved Sauer＇s cavitation model, and the cavity volume acceleration related to its characteristic length is used to produce the noise spectrum. Results show that, with the same cavitation number, the cavity extension on propeller blades increases with diameter associated with an earlier shift of the beginning point of thrust decline induced by cavitation, while the three decline slopes of thrust breakdown curves are found to be nearly the same. The power of the scaling law based on local Reynolds number around 0.9R section is determined as 0.11. As for the smallest propeller, the predominant tonal noise is located at blade passing frequency（BPF）, whereas 2BPF for the middle and both 2BPF and 3BPF for the largest, which shows the cavitating line spectrum is fully related to the interaction between non-uniform inflow and fluctuated cavity volume. The predicted spectrum level exceedance from the middle to the large propeller is 6.65 dB at BPF and 5.94 dB at 2BPF. Since it just differs less than 2 dB to the increment obtained by empirical scaling law, it is inferred that the scale effects on them are acceptable with a sufficient model scale, and so do the scaling law. The numerical implementation of cavitating hydrodynamics and hydro-acoustics prediction of propeller in big scale in wake has been completed.

Numerical Study on Scale Effect of Form Factor for DTMB5415, KCS,KVLCC2, and 4000TEU Container Ship

Four ships,a twin-propeller naval ship,two single-propeller container ships,and a single-propeller very large crude carrier(VLCC),were studied to investigate the scale effect of the form factor.The viscous flow fields of the ships at different scales were solved numerically via the Reynolds-averaged Navier–Stokes method combined with the shear stress transport k–ωturbulence model.The numerical method was validated through comparisons with experimental data,and numerical uncertainty analysis was carried out based on the ITTC recommended procedure.On this basis,scale effects of the form factor were analyzed using different friction lines,and scale effects of flow fields and the mean axial wake fractions were further analyzed in details.The results showed that the form factor exhibited scale effects when adopting the ITTC-1957 line,and it increased with the increase in the Reynolds number.The scale effect of the form factor reduces the prediction precision of the full-scale ship resistance.The friction line has a significant effect on the form factor.The form factor exhibits little dependence on the Reynolds number when using the numerical friction line or the Katsui line,which is useful for full-scale ship resistance predictions.With the increasing Reynolds number,the boundary layer thickness becomes thinner and the axial velocity contour contracts toward the center plane,and there is nearly a linear relationship between the reciprocal of mean axial wake fraction on propeller disc and Reynolds number in logarithmic scale for the three types of ship forms.

Hazard degree identification of goafs based on scale effect of structure by RS-TOPSIS method

In order to precisely predict the hazard degree of goaf(HDG), the RS-TOPSIS model was built based on the results of expert investigation. To evaluate the HDG in the underground mine, five structure size factors, i.e. goaf span, exposed area, goaf height, goaf depth, and pillar width, were selected as the evaluation indexes. And based on rough dependability in rough set(RS)theory, the weights of evaluation indexes were identified by calculating rough dependability between evaluation indexes and evaluation results. Fourty goafs in some mines of western China, whose indexes parameters were measured by cavity monitoring system(CMS), were taken as evaluation objects. In addition, the characteristic parameters of five grades' typical goafs were built according to the interval limits value of single index evaluation. Then, using the technique for order preference by similarity to ideal solution(TOPSIS), five-category classification of HDG was realized based on closeness degree, and the HDG was also identified.Results show that the five-category identification of mine goafs could be realized by RS-TOPSIS method, based on the structure-scale-effect. The classification results are consistent with those of numerical simulation based on stress and displacement,while the coincidence rate is up to 92.5%. Furthermore, the results are more conservative to safety evaluation than numerical simulation, thus demonstrating that the proposed method is more easier, reasonable and more definite for HDG identification.

Numerical Analysis of a Spiral-groove Dry-gas Seal Considering Micro-scale Effects

A dry-gas seal system is a non-contact seal technology that is widely used in different industrial applications.Spiral-groove dry-gas seal utilizes fluid dynamic pressure effects to realize the seal and lubrication processes,while forming a high pressure gas film between two sealing faces due to the deceleration of the gas pumped in or out.There is little research into the effects and the influence on seal performance,if the grooves and the gas film are at the micro-scale.This paper investigates the micro-scale effects on spiral-groove dry-gas seal performance in a numerical solution of a corrected Reynolds equation.The Reynolds equation is discretized by means of the finite difference method with the second order scheme and solved by the successive-over-relaxation（SOR） iterative method.The Knudsen number of the flow in the sealing gas film is changed from 0.005 to 0.120 with a variation of film depth and sealing pressure.The numerical results show that the average pressure in the gas film and the sealed gas leakage increase due to micro-scale effects.The open force is enlarged,while the gas film stiffness is significantly decreased due to micro-scale effects.The friction torque and power consumption remain constant,even in low sealing pressure and spin speed conditions.In this paper,the seal performance at different rotor face spin speeds is also described.The proposed research clarifies the micro-scale effects in a spiral-groove dry-gas seal and their influence on seal performance,which is expected to be useful for the improvement of the design of dry-gas seal systems operating in the slip flow regime.

Model of Polysilicon Electro-thermal Micro Actuator and Research of Micro Scale Effect

A type of crank beam electro-thermal micro actuator was prescribed. Mechanical model of the actuator was established, and the static characteristic was analyzed.Comparing the theoretical analysis with experimental data, it is found that the thermodynamic character of material in micro actuator has a different variable regularity contrasted to that used in macro scale machines. It is the micro scale effect that results in the deviation between the simulating result and experimental results. The thermodynamic expression of polysilicon, which was fitted by means of the experimental data concerned, was used to modify the mechanical model. The modified model, in which the micro scale thermodynamic characteristic was considered, was more reasonable and could make the optimal design and control strategies analyzing the straight-line micro actuator more feasible.

Delineation and Scale Effect of Precision Agriculture Management Zones Using Yield Monitor Data Over Four Years

In this study, precision agriculture management zones were delineated using yield data over four years from the combine harvester equipped with yield monitor and DGPS receiver. Relative yields measured during each year were interpolated to 4 m2 grid size using ordinary kriging. The resultant interpolated yield maps were averaged across years to create a map of the mean relative yield, which was then used for cluster analysis. The mean yield map of post-classification was processed by applying majority filtering with window sizes that were equivalent to the grid sizes of 12, 20, 28, 36, 44, 52 and 60 m. The scale effect of management zones was evaluated using relative variance reduction, test of significant differences of the means of yield zones, spatial fragmentation, and spatial agreement. The results showed that the post-classification majority filtering （PCMF） eliminated lots of isolated cells or patches caused by random variation while preserving yield means, high variance reduction, general yield patterns, and high spatial agreement. The zoned result can be used as yield goal map for preplant or in-season fertilizer recommendation in precision agriculture.

Experimental, Numerical and Simplified Theoretical Model Study for Internal Solitary Wave Load on FPSO with Emphasis on Scale Effect

Scale effect of ISWs loads on Floating Production Storage and Offloading(FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depthaveraged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model.The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension.Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.

Scale effects of eroded sediment transport in Wujiang River Basin, Guizhou Province, China

In recent years, research on spatial scale and scale transformation of eroded sediment transport has become a forefront field in current soil erosion research, but there are very few studies on the scale effect problem in Karst regions of China. Here we quantitatively extracted five main factors influencing soil erosion, namely rainfall erosivity, soil erodibility, vegetative cover and management, soil and water conservation, and slope length and steepness. Regression relations were built between these factors and also the sediment transport modulus and drainage area, so as to initially analyze and discuss scale effects on sediment transport in the Wujiang River Basin(WRB). The size and extent of soil erosion influencing factors in the WRB were gauged from: Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model(ASTER GDEM), precipitation data, land use, soil type and Normalized Difference Vegetation Index(NDVI) data from Global Inventory Modeling and Mapping Studies(GIMMS) or Advanced Very High Resolution Radiometer(AVHRR), and observed data from hydrometric stations. We find that scaling effects exist between the sediment transport modulus and the drainage area. Scaling effects are expressed after logarithmic transformation by a quadratic function regression relationship where the sediment transport modulus increases before decreasing, alongside changes in the drainage area. Among the five factors influencing soil erosion, slope length and steepness increases first and then decreases, alongside changes in the drainage area, and are the main factors determining the relationship between sediment transport modulus and drainage area. To eliminate the influence of scale effects on our results, we mapped the sediment yield modulus of the entire WRB, adopting a 1 000 km^2 standard area with a smaller fitting error for all sub-basins, and using the common Kriging interpolation method.

Physical modelling and scale effects of air-water flows on stepped spillways

During the last three decades, the introduction of new construction materials (e.g. RCC (Roller Compacted Concrete), strengthened gabions) has increased the interest for stepped channels and spillways. However stepped chute hydraulics is not simple, because of different flow regimes and importantly because of very-strong interactions between entrained air and turbu- lence. In this study, new air-water flow measurements were conducted in two large-size stepped chute facilities with two step heights in each facility to study experimental distortion caused by scale effects and the soundness of result extrapolation to pro- totypes. Experimental data included distributions of air concentration, air-water flow velocity, bubble frequency, bubble chord length and air-water flow turbulence intensity. For a Froude similitude, the results implied that scale effects were observed in both facilities, although the geometric scaling ratio was only Lr=2 in each case. The selection of the criterion for scale effects is a critical issue. For example, major differences (i.e. scale effects) were observed in terms of bubble chord sizes and turbulence levels al- though little scale effects were seen in terms of void fraction and velocity distributions. Overall the findings emphasize that physical modelling of stepped chutes based upon a Froude similitude is more sensitive to scale effects than classical smooth-invert chute studies, and this is consistent with basic dimensional analysis developed herein.

Evaluation of Spectral Scale Effects in Estimation of Vegetation Leaf Area Index Using Spectral Indices Methods

Spectral index methodology has been widely used in Leaf Area Index(LAI) retrieval at different spatial scales. There are differences in the spectral response of different remote sensors and thus spectral scale effect generated during the use of spectral indices to retrieve LAI. In this study, PROSPECT, leaf optical properties model and Scattering by Arbitrarily Inclined Layers(SAIL) model, were used to simulate canopy spectral reflectance with a bandwidth of 5 nm and a Gaussian spectral response function was employed to simulate the spectral data at six bandwidths ranging from 10 to 35 nm. Additionally, for bandwidths from 5 to 35 nm, the correlation between the spectral index and LAI, and the sensitivities of the spectral index to changes in LAI and bandwidth were analyzed. Finally, the reflectance data at six bandwidths ranging from 40 to 65 nm were used to verify the spectral scale effect generated during the use of the spectral index to retrieve LAI. Results indicate that Vegetation Index of the Universal Pattern Decomposition(VIUPD) had the highest accuracy during LAI retrieval. Followed by Normalized Difference Vegetation Index(NDVI), Modified Simple Ratio Indices(MSRI) and Triangle Vegetation Index(TVI), although the coefficient of determination R^2 was higher than 0.96, the retrieved LAI values were less than the actual value and thus lacked validity. Other spectral indices were significantly affected by the spectral scale effect with poor retrieval results. In this study, VIUPD, which exhibited a relatively good correlation and sensitivity to LAI, was less affected by the spectral scale effect and had a relatively good retrieval capability. This conclusion supports a purported feature independent of the sensor of this model and also confirms the great potential of VIUPD for retrieval of physicochemical parameters of vegetation using multi-source remote sensing data.

Discussion and prediction on decreasing flow stress scale effect

Based on crystal plasticity theory and surface layer model, relation of flow stress to billet dimension and grain size was built, and rationality of derived relation was verified with tensile tests of different size billets. With derived expressions, relation of decreasing flow stress scale effect to billet dimension, grain size as well as billet shape was discussed and predicted. The results show that flow stress is proportional to billet size; with decrease of grain size, flow stress is less influenced by billet dimension. When both cross section area and grain size are same, flow stress decrease of rectangular section billet or sheet is larger than that of circular section billet.

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses dueto their relatively lower stiffness and shear strength than those of the rock matrix. Understanding theeffects of fracture geometrical distribution, such as length, spacing, persistence and orientation, isimportant for quantifying the mechanical behavior of fractured rock masses. The relation betweenfracture geometry and the mechanical characteristics of the fractured rock mass is complicated due tothe fact that the fracture geometry and mechanical behaviors of fractured rock mass are stronglydependent on the length scale. In this paper, a comprehensive study was conducted to determine theeffects of fracture distribution on the equivalent continuum elastic compliance of fractured rock massesover a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, threedifferent simulation techniques involving Oda＇s elastic compliance tensor, Monte Carlo simulation （MCS）,and suitable probability density functions （PDFs） were employed to represent the elastic compliance offractured rock masses. To yield geologically realistic results, parameters for defining fracture distributionswere obtained from different geological fields. The influence of the key fracture parameters andtheir relations to the overall elastic behavior of the fractured rock mass were studied and discussed. Adetailed study was also carried out to investigate the validity of the use of a representative elementvolume （REV） in the equivalent continuum representation of fractured rock masses. A criterion was alsoproposed to determine the appropriate REV given the fracture distribution of the rock mass.

Analysis of Spatial Scale Effect on Urban Resilience:A Case Study of Shenyang,China

Based on urban physical space and theory of landscape ecology,a triune assessment framework—‘size-densitymorphology’—was constructed in order to analyze the spatial pattern and the scale effect of urban resilience in Shenyang of China in 2015,and to explore the main impact factors of landscape under different spatial scale backgrounds.The results show that:1)Urban resilience is an optimal combination of the resilience of size,density,and morphology.The urban resilience of Shenyang displays scale effect;the overall resilience level increases with the increase in scale,while the spatial difference and spatial similarity tend to decrease resilience.2)As 2 km,1 km and 2 km are scale inflection points of average value curves for size resilience,density resilience and morphology resilience,respectively in an urban setting;the optimal scale unit of comprehensive resilience is 1 km.Choosing 1 km–2 km as the basic spatial scale better depicts overall pattern and detailed characteristics of resilience in Shenyang.The spatial amplitudes of 0.5 km and 1 km are sensitive points for spatial autocorrelation of morphology and density resilience,size,and comprehensive resilience to scale effect.3)The major landscape factors of urban size and morphology resilience transform with scale expansion.Aggregation index(AI)has a significant impact on urban resilience at different scales;its influence increases significantly with the increase in scale.4)The high-level area of comprehensive resilience in Shenyang is the eastern ecological corridor area,while the low value area is the peripheral extension area of the city.To promote the overall level of resilience in Shenyang,this paper argues that the construction of ecological infrastructure should be strengthened in the peripheral extension area in a balanced manner.In the city center,population and building density should be controlled;the intensity of human activities should be reduced;impetus should be placed on landscape heterogeneity;and the homogeneous expansion of the area of construction should be prevented.In the eastern ecological corridors,the exploitation of ecosystem lands should be strictly controlled,and the integrity of the green landscape patches should be maintained.

Investigation of acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure

In this paper, the acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure are investigated. The similitude conditions and relations between the similitude model and its prototype were studied in the references. This paper investigates the acoustic scale effects for the similitude model, which are influenced by loss factor, shear and rotatory inertia. At the same time, the boundary effects which are influenced by surface sound reflection are investigated in the experiment of similitude model. The results show that the acoustic scale effects may be controlled with model designing, the boundary effects can be controlled with experimental designing between the similitude model and its prototype.

LAI scale effect research based on compact airborne spectrographic imager data in the Heihe Oasis

As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.

Spatial Scale Effects of Water Erosion Dynamics:Complexities, Variabilities, and Uncertainties

Severe water erosion is notorious for its harmful effects on land-water resources as well as local societies. The scale effects of water erosion, however, greatly exacerbate the difficulties of accurate erosion evaluation and hazard control in the real world. Analyzing the related scale issues is thus urgent for a better understanding of erosion variations as well as reducing such erosion. In this review article, water erosion dynamics across three spatial scales including plot, watershed, and regional scales were selected and discussed. For the study purposes and objectives, the advantages and disadvantages of these scales all demonstrate clear spatial-scale dependence. Plot scale studies are primarily focused on abundant data collection and mechanism discrimination of erosion generation, while watershed scale studies provide valuable information for watershed management and hazard control as well as the development of quantitatively distributed models. Regional studies concentrate more on large-scale erosion assessment, and serve policymakers and stakeholders in achieving the basis for regulatory policy for comprehensive land uses. The results of this study show that the driving forces and mechanisms of water erosion variations among the scales are quite different. As a result, several major aspects contributing to variations in water erosion across the scales are stressed: differences in the methodologies across various scales, different sink-source roles on water erosion processes, and diverse climatic zones and morphological regions. This variability becomes more complex in the context of accelerated global change. The changing climatic factors and earth surface features are considered the fourth key reason responsible for the increased variability of water erosion across spatial scales.

Simulation study on fluctuant flow stress scale effect

Crystal plasticity theory was used to simulate upsetting tests of different dimensions and grain size micro copper cylinders in this study on the fluctuant flow stress scale effect. Results showed that with the decrease of billet grain quantity, flow stress fluctuation is not always increased, but there is a maximum. Through this study, the fluctuant flow stress scale effect can be understood deeper, and relevant necessary information was obtained for further prediction and control of this scale effect and to design the microforming process and die.