Fourier Techniques in the Theory of Irregularities of Point Distribution

2004 ◽  
pp. 59-82 ◽  
Author(s):  
W. W. L. Chen
Keyword(s):  
Point Distribution ◽  
Fourier Techniques

Difference Fourier Analysis of Glucose Embedded and Frozen Hydrated Purple Membrane

1982 ◽  
Vol 40 ◽  
pp. 74-75
Author(s):  
Jules S. Jaffe ◽  
Robert M. Glaeser
Keyword(s):  
Purple Membrane ◽  
Data Set ◽  
High Resolution Data ◽  
X Ray ◽  
X Ray Crystallography ◽  
Fourier Techniques ◽  
Versus Protein ◽  
The Difference ◽  
Difference Fourier ◽  
Ideal Method

Although difference Fourier techniques are standard in X-ray crystallography it has only been very recently that electron crystallographers have been able to take advantage of this method. We have combined a high resolution data set for frozen glucose embedded Purple Membrane (PM) with a data set collected from PM prepared in the frozen hydrated state in order to visualize any differences in structure due to the different methods of preparation. The increased contrast between protein-ice versus protein-glucose may prove to be an advantage of the frozen hydrated technique for visualizing those parts of bacteriorhodopsin that are embedded in glucose. In addition, surface groups of the protein may be disordered in glucose and ordered in the frozen state. The sensitivity of the difference Fourier technique to small changes in structure provides an ideal method for testing this hypothesis.

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.

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