Explicit constructions in the classical mean squares problem in irregularities of point distribution

2002 ◽  
Vol 2002 (545) ◽  
Author(s):  
W. W. L. Chen ◽  
M.M. Skriganov
Keyword(s):  
Point Distribution ◽  
Explicit Constructions

scholarly journals Experimental Analysis of Driver Visual Characteristics in Urban Tunnels

2021 ◽  
Vol 11 (9) ◽  
pp. 4274
Author(s):  
Song Fang ◽  
Jianxiao Ma
Keyword(s):  
Traffic Safety ◽  
Clustering Algorithm ◽  
Pupil Diameter ◽  
Data Fitting ◽  
Eye Tracker ◽  
Tunnel Length ◽  
Point Distribution ◽  
Change Rate ◽  
Visual Characteristics ◽  
Diameter Change

Through an urban tunnel-driving experiment, this paper studies the changing trend of drivers’ visual characteristics in tunnels. A Tobii Pro Glasses 2 wearable eye tracker was used to measure pupil diameter, scanning time, and fixation point distribution of the driver during driving. A two-step clustering algorithm and the data-fitting method were used to analyze the experimental data. The results show that the univariate clustering analysis of the pupil diameter change rate of drivers has poor discrimination because the pupil diameter change rate of drivers in the process of “dark adaptation” is larger, while the pupil diameter change rate of drivers in the process of “bright adaptation” is relatively smooth. The univariate and bivariate clustering results of drivers’ pupil diameters were all placed into three categories, with reasonable distribution and suitable differentiation. The clustering results accurately corresponded to different locations of the tunnel. The clustering method proposed in this paper can identify similar behaviors of drivers at different locations in the transition section at the tunnel entrance, the inner section, and the outer area of the tunnel. Through data-fitting of drivers’ visual characteristic parameters in different tunnels, it was found that a short tunnel, with a length of less than 1 km, has little influence on visual characteristics when the maximum pupil diameter is small, and the percentage of saccades is relatively low. An urban tunnel with a length between 1 and 2 km has a significant influence on visual characteristics. In this range, with the increase in tunnel length, the maximum pupil diameter increases significantly, and the percentage of saccades increases rapidly. When the tunnel length exceeds 2 km, the maximum pupil diameter does not continue to increase. The longer the urban tunnel, the more discrete the distribution of drivers’ gaze points. The research results should provide a scientific basis for the design of urban tunnel traffic safety facilities and traffic organization.

scholarly journals An In-Depth Process Model for Fuel Production via Hydrothermal Liquefaction and Catalytic Hydrotreating

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1172
Author(s):  
Leonard Moser ◽  
Christina Penke ◽  
Valentin Batteiger
Keyword(s):  
Process Model ◽  
Reaction Network ◽  
Hydrothermal Liquefaction ◽  
Process Chain ◽  
Fuel Production ◽  
Model Compounds ◽  
Point Distribution ◽  
Process Step ◽  
Elemental Analyses ◽  
Made In

One of the more promising technologies for future renewable fuel production from biomass is hydrothermal liquefaction (HTL). Although enormous progress in the context of continuous experiments on demonstration plants has been made in the last years, still many research questions concerning the understanding of the HTL reaction network remain unanswered. In this study, a unique process model of an HTL process chain has been developed in Aspen Plus® for three feedstock, microalgae, sewage sludge and wheat straw. A process chain consisting of HTL, hydrotreatment (HT) and catalytic hydrothermal gasification (cHTG) build the core process steps of the model, which uses 51 model compounds representing the hydrolysis products of the different biochemical groups lipids, proteins, carbohydrates, lignin, extractives and ash for modeling the biomass. Two extensive reaction networks of 272 and 290 reactions for the HTL and HT process step, respectively, lead to the intermediate biocrude (~200 model compounds) and the final upgraded biocrude product (~130 model compounds). The model can reproduce important characteristics, such as yields, elemental analyses, boiling point distribution, product fractions, density and higher heating values of experimental results from continuous experiments as well as literature values. The model can be applied as basis for techno-economic and environmental assessments of HTL fuel production, and may be further developed into a predictive yield modeling tool.

Solution of the Pellet Equation by use of the Orthogonal Collocation and Least Squares Methods: Effects of Different Orthogonal Jacobi Polynomials

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Jannike Solsvik ◽  
Hugo Jakobsen
Keyword(s):  
Numerical Methods ◽  
Least Squares ◽  
Collocation Method ◽  
Jacobi Polynomial ◽  
Jacobi Polynomials ◽  
Least Squares Method ◽  
Condition Numbers ◽  
Orthogonal Collocation ◽  
Point Distribution ◽  
Boundary Points

Two numerical methods in the family of weighted residual methods; the orthogonal collocation and least squares methods, are used within the spectral framework to solve a linear reaction-diffusion pellet problem with slab and spherical geometries. The node points are in this work taken as the roots of orthogonal polynomials in the Jacobi family. Two Jacobi polynomial parameters, alpha and beta, can be used to tune the distribution of the roots within the domain. Further, the internal points and the boundary points of the boundary-value problem can be given according to: i) Gauss-Lobatto-Jacobi points, or ii) Gauss-Jacobi points plus the boundary points. The objective of this paper is thus to investigate the influence of the distribution of the node points within the domain adopting the orthogonal collocation and least squares methods. Moreover, the results of the two numerical methods are compared to examine whether the methods show the same sensitivity and accuracy to the node point distribution. The notifying findings are as follows: i) The Legendre polynomial, i.e., alpha=beta=0, is a very robust Jacobi polynomial giving the better condition number of the coefficient matrix and the polynomial also give good behavior of the error as a function of polynomial order. This polynomial gives good results for small and large gradients within both slab and spherical pellet geometries. This trend is observed for both of the weighted residual methods applied. ii) Applying the least squares method the error decreases faster with increasing polynomial order than observed with the orthogonal collocation method. However, the orthogonal collocation method is not so sensitive to the choice of Jacobi polynomial and the method also obtains lower error values than the least squares method due to favorable lower condition numbers of the coefficient matrices. Thus, for this particular problem, the orthogonal collocation method is recommended above the least squares method. iii) The orthogonal collocation method show minor differences between Gauss-Lobatto-Jacobi points and Gauss-Jacobi plus boundary points.

Tool Path Planning for Five-Axis U-Pass Milling of an Impeller

2021 ◽  
Author(s):  
J.Y. Feng ◽  
Z.C. Wei ◽  
M.J. Wang ◽  
X.Q. Wang ◽  
M.L. Guo
Keyword(s):  
Path Planning ◽  
Cutting Force ◽  
Tool Path ◽  
Flank Milling ◽  
Small Range ◽  
Tool Path Planning ◽  
Point Distribution ◽  
Parameter Domain ◽  
Five Axis ◽  
Tool Axis Vector

Abstract U-pass milling is a roughing method that combines the characteristics of flank milling with conventional trochoidal milling. The tool cuts in and out steadily, and the tool–workpiece wrap angle is maintained within a small range. This method can smooth the cutting force and reduce the peak cutting force while avoiding cutting heat accumulation, which can significantly improve the processing efficiency and reduce tool wear. In this study, a tool path model is established for U-pass milling, and the characteristic parameters of the path are defined. Through a comparative test of three-axis groove milling, it is demonstrated that the peak value and average value of the cutting force are reduced by 25% and 60%, respectively. An impeller runner is considered as the processing object, and the milling boundary parameters are pretreated. A tiling micro-arc mapping algorithm is proposed, which maps the three-dimensional boundary to the two-dimensional parameter domain plane with the arc length as the coordinate axis, and the dimensionally reduced tool contact point distribution form is obtained. The geometric domain tool position point and the interference-free tool axis vector are obtained by calculating the bidirectional proportional domain of the runner and the inverse mapping of any vector in the parameter domain. Finally, the calculation results are nested into the automatically programmed tool (APT) encoding form, and the feasibility of the five-axis U-pass milling tool path planning method is verified through a numerical example.

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