An experimental cross-section measurement of 10B(n,α)7Li reaction on counting alpha particles track density

The present work determines the particle size based only on the number of tracks detected in a cluster created by a hot particle on the CR-39 solid state nuclear track detector and depending on the exposure time. The mathematical model of the cross section developed here gives the relationship between alpha particle emitting from the (n, α) reaction and the number of tracks created and distribution of tracks created on the surface of the track detector. In an experiment performed during this work, disc of boron compound (boric acid or sodium tetraborate) of different weights were prepared and exposed to thermal neutron from the source. Chemical etching is processes of path formation in the detector, during which a suitable etching solution attacks the detector at a sufficient speed and the damaged regions along the ion trails (latent track) are preferentially dissolved, removed and get transformed into a hollow channel. The most common etching for plastics is the aqueous solutions of NaOH and temperatures in between 50˚C - 80˚C.The program (CR-39) processing counting and calculations only take place depending on the number of tracks.

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Temperature Influence on Performance of Oxidation Ponds

Water Science & Technology ◽

10.2166/wst.1991.0115 ◽

1991 ◽

Vol 24 (5) ◽

pp. 85-96 ◽

Cited By ~ 2

Author(s):

Qingliang Zhao ◽

Zijie Zhang

Keyword(s):

Mathematical Model ◽

Temperature Influence ◽

Field Scale ◽

Experiment Data ◽

Computer Technique ◽

Oxidation Pond ◽

Optimum Model ◽

Oxidation Ponds ◽

The Mathematical Model ◽

The Relationship

By means of simulated tests of a laboratory–scale oxidation pond model, the relationship between BOD5 and temperature fluctuation was researched. Mathematical modelling for the pond's performance and K1determination were systematically described. The calculation of T–K1–CeCe/Ci) was complex but the problem was solved by utilizing computer technique in the paper, and the mathematical model which could best simulate experiment data was developed. On the basis of experiment results,the concept of plug–ratio–coefficient is also presented. Finally the optimum model recommended here was verified with the field–scale pond data.

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Numerical Simulation on Velocity Profiles of Mill Bearing Lubrication

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.145.282 ◽

2010 ◽

Vol 145 ◽

pp. 282-286

Author(s):

Qing Xue Huang ◽

Jian Mei Wang ◽

Yu Gui Li ◽

Li Feng Ma ◽

Chun Jiang Zhao

Keyword(s):

Cross Section ◽

Velocity Profiles ◽

Flow State ◽

Oil Film ◽

Velocity Gradients ◽

Oil Flow ◽

The Mathematical Model ◽

The Relationship ◽

General Velocity ◽

Oil Film Pressure

No 460 oil-film bearing oil as the dedicated lubricant is regarded as the incompressible Newtonian fluid. To comprehensively analyze the real oil flow state, the mathematical model on velocity profiles, together with its dimensionless equations, is established, and the calculating program is developed to simulate the 3D velocity profiles and velocity gradients at different oil flow layers. The relationship between velocity profiles and the oil film pressure is discussed, and the velocity tendency is consistent with the general velocity profile of wedge cross section. The conclusions are beneficial to the further study on lubricating performances of heavy contact components and to prolong their service lives.

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Development of a Mathematical Model for a Workpiece Heating and Cooling in a Protective Medium while Treatment under Pressure

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.410.115 ◽

2021 ◽

Vol 410 ◽

pp. 115-122

Author(s):

Victoria V. Devyatiarova ◽

Eugenia E. Balakhnina ◽

Lilya M. Valeeva

Keyword(s):

Mathematical Model ◽

Cross Section ◽

Arbitrary Shape ◽

Thermal Conductivity Coefficient ◽

Regression Equations ◽

Heating And Cooling ◽

Temperature Problem ◽

Protective Medium ◽

Computer Calculations ◽

The Mathematical Model

The paper reviews and develops the mathematical model of plastic flow during the hot-forming processes. A flat non-stationary temperature problem for a cross-section of a long solid (rolled product) of arbitrary shape with different heat transfer conditions along the perimeter of the cross-section was considered. Equations for calculation of the thermal conductivity coefficient and heat capacity of tungsten billets were obtained in the temperature range of 700 - 1500°C, based on the literature data. Analytical dependences in form of regression equations were obtained, allowing for computer calculations of physical specifications of 11x11 mm VA grade tungsten billets in form of temperature functions with accuracy sufficient for practical calculations.

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The mathematical model of plant diseases and insect pests and the relationship between the crop growth

Computer, Intelligent Computing and Education Technology ◽

10.1201/b16698-270 ◽

2014 ◽

pp. 1231-1233

Author(s):

Qiang Zhang

Keyword(s):

Mathematical Model ◽

Insect Pests ◽

Crop Growth ◽

Plant Diseases ◽

The Mathematical Model ◽

The Relationship

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METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

Forestry Engineering Journal ◽

10.12737/25204 ◽

2017 ◽

Vol 7 (1) ◽

pp. 137-150

Author(s):

Агапов ◽

Aleksandr Agapov

Keyword(s):

Mathematical Model ◽

Objective Function ◽

Optimization Problem ◽

Optimization Problems ◽

Target Function ◽

Cross Sectional ◽

Optimization Task ◽

Cutting Out ◽

The Mathematical Model ◽

The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

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Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.572.636 ◽

2013 ◽

Vol 572 ◽

pp. 636-639

Author(s):

Xi Chen ◽

Gang Wang

Keyword(s):

Mathematical Model ◽

Stability Analysis ◽

Stability Criterion ◽

Stability Margin ◽

Static Stability ◽

Matlab Simulation ◽

And Performance ◽

The Stability ◽

The Mathematical Model ◽

The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

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Design and Implementation of Digital Asthma Diagnosis System

International Journal of Healthcare Information Systems and Informatics ◽

10.4018/ijhisi.2019070101 ◽

2019 ◽

Vol 14 (3) ◽

pp. 1-15

Author(s):

Qinghua Yao ◽

Xiantao Yang

Keyword(s):

Mathematical Model ◽

Mutation Rate ◽

Forced Expiratory Volume ◽

Digital Signals ◽

Respiratory Parameters ◽

The Mathematical Model ◽

The Relationship ◽

Objective Indicators ◽

Signal Conditioning Circuit

In this article, the MSP430F149 is the microcontroller (MCU), and a pressure sensor, MPX5100AP, is used to measure body measurement of maximal forced expiratory volume (FEV) and peak expiratory flow rate (PEFR). The two analog signals are processed by the signal conditioning circuit, and then the corresponding digital signals are acquired by the MCU. With the related operations of multiple respiratory parameters, a built-up time of respiration signal mutation rate values and the determination of the mutation rate, a mathematical model is built among FEV, PEFR and the rate of variation. The mathematical model of the system is analyzed, and the relationship between the detection results and the degree of airway obstruction is established. Finally, the patient's condition analysis results are given directly on the LCD, which provided the objective indicators for the medical treatment of the disease.

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Bore formation, evolution and disintegration into solitons in shallow inhomogeneous channels

Nonlinear Processes in Geophysics ◽

10.5194/npg-10-407-2003 ◽

2003 ◽

Vol 10 (4/5) ◽

pp. 407-424 ◽

Cited By ~ 30

Author(s):

J.-G. Caputo ◽

Y. A. Stepanyants

Keyword(s):

Mathematical Model ◽

Cross Section ◽

Vries Equation ◽

Spatial Inhomogeneity ◽

Hydraulic Jumps ◽

Variable Depth ◽

Nonlinear Surface Waves ◽

Nonlinear Surface ◽

The Mathematical Model ◽

Riemann Waves

Abstract. The propagation of nonlinear surface waves in channels of smoothly variable in space cross section is studied theoretically and by means of numerical computations. The mathematical model describing wave evolution is based on the generalized Korteweg-de Vries equation with additional terms due to spatial inhomogeneity and energy dissipation. Specifically we consider channels of variable depth and width. The breaking of Riemann waves and the disintegration of hydraulic jumps into trains of solitons have been examined. The results obtained can be useful in particular for the understanding some peculiarities of bore (mascaret) formation, viscous evolution and disintegration into solitons in inhomogeneous channels or rivers.

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Modeling and Optimization of Bidirectional Clamping Forces in Drilling of Stacked Aluminum Alloy Plates

Materials ◽

10.3390/ma13122866 ◽

2020 ◽

Vol 13 (12) ◽

pp. 2866

Author(s):

Jintong Liu ◽

Anan Zhao ◽

Piao Wan ◽

Huiyue Dong ◽

Yunbo Bi

Keyword(s):

Mathematical Model ◽

Finite Element ◽

Aluminum Alloy ◽

Clamping Force ◽

Practical Application ◽

Element Simulation ◽

Theory Of Plates ◽

Plates And Shells ◽

The Mathematical Model ◽

The Relationship

Interlayer burrs formation during drilling of stacked plates is a common problem in the field of aircraft assembly. Burrs elimination requires extra deburring operations which is time-consuming and costly. An effective way to inhibit interlayer burrs is to reduce the interlayer gap by preloading clamping force. In this paper, based on the theory of plates and shells, a mathematical model of interlayer gap with bidirectional clamping forces was established. The relationship between the upper and lower clamping forces was investigated when the interlayer gap reaches zero. The optimization of the bidirectional clamping forces was performed to reduce the degree and non-uniformity of the deflections of the stacked plates. Then, the finite element simulation was conducted to verify the mathematical model. Finally, drilling experiments were carried out on 2024-T3 aluminum alloy stacked plates based on the dual-machine-based automatic drilling and riveting system. The experimental results show that the optimized bidirectional clamping forces can significantly reduce the burr heights. The work in this paper enables us to understand the effect of bidirectional clamping forces on the interlayer gap and paves the way for the practical application.

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