How the Hilbert integral theorem inspired flow lines

2017 ◽  
Author(s):  
Roland Winston ◽  
Lun Jiang
Keyword(s):  
Flow Lines ◽  
Integral Theorem ◽  
Hilbert Integral

Thermodynamic Modelling of Gas Hydrate Formation in the Presence of Inhibitors and the Consideration of their Effect

2014 ◽  
Vol 14 (1) ◽  
pp. 45
Author(s):  
Peyman Sabzi ◽  
Saheb Noroozi
Keyword(s):  
Gas Hydrates ◽  
Gas Hydrate ◽  
Low Temperatures ◽  
Hydrate Formation ◽  
Transportation Systems ◽  
Flow Lines ◽  
Main Approach ◽  
Efficient Inhibitor ◽  
System A ◽  
Gas Hydrate Formation

Gas hydrates formation is considered as one the greatest obstacles in gas transportation systems. Problems related to gas hydrate formation is more severe when dealing with transportation at low temperatures of deep water. In order to avoid formation of Gas hydrates, different inhibitors are used. Methanol is one of the most common and economically efficient inhibitor. Adding methanol to the flow lines, changes the thermodynamic equilibrium situation of the system. In order to predict these changes in thermodynamic behavior of the system, a series of modelings are performed using Matlab software in this paper. The main approach in this modeling is on the basis of Van der Waals and Plateau's thermodynamic approach. The obtained results of a system containing water, Methane and Methanol showed that hydrate formation pressure increases due to the increase of inhibitor amount in constant temperature and this increase is more in higher temperatures. Furthermore, these results were in harmony with the available empirical data.Keywords: Gas hydrates, thermodynamic inhibitor, modelling, pipeline blockage

scholarly journals Analysis of the Propagation in High-Speed Interconnects for MIMICs by Means of the Method of Analytical Preconditioning: A New Highly Efficient Evaluation of the Coefficient Matrix

2021 ◽  
Vol 11 (3) ◽  
pp. 933
Author(s):  
Mario Lucido
Keyword(s):  
Integral Equation ◽  
Integrated Circuits ◽  
High Speed ◽  
Coefficient Matrix ◽  
Single Step ◽  
Integral Theorem ◽  
Acceleration Technique ◽  
Cauchy Integral Theorem ◽  
Integral Equation Formulation ◽  
High Speed Interconnects

The method of analytical preconditioning combines the discretization and the analytical regularization of a singular integral equation in a single step. In a recent paper by the author, such a method has been applied to a spectral domain integral equation formulation devised to analyze the propagation in polygonal cross-section microstrip lines, which are widely used as high-speed interconnects in monolithic microwave and millimeter waves integrated circuits. By choosing analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges, fast convergence is achieved, and the convolution integrals are expressed in closed form. However, the coefficient matrix elements are one-dimensional improper integrals of oscillating and, in the worst cases, slowly decaying functions. In this paper, a novel technique for the efficient evaluation of such kind of integrals is proposed. By means of a procedure based on Cauchy integral theorem, the general coefficient matrix element is written as a linear combination of fast converging integrals. As shown in the numerical results section, the proposed technique always outperforms the analytical asymptotic acceleration technique, especially when highly accurate solutions are required.

scholarly journals The Effect of Flow Lines on the Mechanical Properties in Hot-Rolled Bearing Steel

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 456
Author(s):  
Dongsheng Qian ◽  
Chengfei Ma ◽  
Feng Wang
Keyword(s):  
Mechanical Characterization ◽  
Tensile Deformation ◽  
Flow Line ◽  
Plastic Property ◽  
Bearing Steel ◽  
Mechanical Anisotropy ◽  
Flow Lines ◽  
Significant Difference ◽  
Hot Rolled ◽  
Bearing Rings

Hot rolling is an essential process for the shape-forming of bearing steel. It plays a significant role in the formation and distribution of flow lines. In this work, the effect of flow lines is investigated by analyzing the microstructure and mechanical anisotropy of hot-rolled bearing steel. It was found that carbides rich with Cr and Mn elements are distributed unevenly along the flow-line direction of the hot-rolled bearing steel. Moreover, the mechanical characterization indicates that ultimate tensile strength and yield strength do not have any significant difference in two directions. Nevertheless, an ultrahigh section shrinkage of 57.51% is obtained in the 0° sample that has parallel flow lines, while 90° sample shows poor section shrinkage. The uneven distributed carbides will affect the direction and speed of crack propagation during tensile deformation. Therefore, the 0° and 90° samples exhibit great difference in plastic property. Meanwhile, after tensile deformation, a delaminated texture is observed in the flow lines, which may be caused by different degrees of deformation of grains due to the uneven distribution of carbides. The results of this work may provide guidance for controlling and optimizing flow lines in the manufacturing of bearing rings.

scholarly journals A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

A Study of Metal Flow Ahead of Tool Face With Large Negative Rake Angle

1982 ◽  
Vol 104 (3) ◽  
pp. 319-325 ◽  
Author(s):  
Y. Kita ◽  
M. Ido ◽  
N. Kawasaki
Keyword(s):  
Deformation Process ◽  
Metal Flow ◽  
Close Relation ◽  
Rake Angle ◽  
High Quality ◽  
Flow Lines ◽  
Stress Changes ◽  
Chip Formation Mechanism ◽  
Maximum Increment ◽  
Side Flow

Although the chip formation mechanism by a tool having a large negative rake angle is not well known, it is very important to make the process clear in order to get high quality in finished surfaces. In this paper, the behavior of material ahead of a tool face with a large negative rake angle is examined by means of low speed machining on lead. The deformation process of the material is investigated by the deformation study combining a finite element method with a grid line method. During cutting, the deformation process of grid lines which were drawn on the sides of testpieces was observed through a side glass which restricted the side flow of material. Cutting force was measured by a dynamometer consisting of an elongated octagonal ring with strain wire gages. As a result it was found that the shear stress on the slip line of maximum increment of shear strain is nearly constant, but the compressive stress changes along the line. It was concave near the top of cutting edge and convex near the surface of the test piece. The position of the change of polarity in the slope shifted depending on the rake angle of the tool. This phenomenon is considered to have close relation with the stagnant tip, which decides not only the size of chip, but also whether or not a chip will be formed. Flow lines of material and the deformed region ahead of tool faces with different negative rake angles were also obtained and they were compared with each other.

On the Significance of the Inlet Pressure Build-Up in the Design of Tilting-Pad Bearings

1990 ◽  
Vol 112 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Cz. M. Rodkiewicz ◽  
K. W. Kim ◽  
J. S. Kennedy
Keyword(s):  
Thrust Bearing ◽  
Ambient Pressure ◽  
Inlet Pressure ◽  
Load Carrying Capacity ◽  
Integral Theorem ◽  
Lubricating Film ◽  
Tilting Pad ◽  
Load Carrying ◽  
Momentum Integral ◽  
Entrance Pressure

An operating tilting-pad thrust bearing generates a fore-region which is responsible for maintaining, at the bearing entrance, a pressure which is higher than the ambient pressure. This entrance pressure, in the presented analysis, is obtained by applying to the fore-region the momentum integral theorem. The solution of the lubricating film region is then obtained by using this modified inlet pressure. This solution yields the pressure distribution, the load carrying capacity, the film ratio and the frictional force for several values of the modified Reynolds number and various pivot positions. The analysis shows that there is a significant influence of the fore-region pressure on the bearing performance and that to properly design efficient tilting-pad bearing this effect should be taken into consideration.

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