Reply by Les P. Beard to José Arce

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 1229-1229
Author(s):  
Les P. Beard
Keyword(s):  
Mathematical Model ◽  
Case History ◽  
Theoretical Study ◽  
Single Case ◽  
Field Measurements ◽  
Field Observations ◽  
Geological Complexity ◽  
The Mathematical Model ◽  
Theoretical Results

Jose Arce is correct in his observation that the field results of Roy and Jain (1973) are in contradiction the synthetically derived results of Beard and Tripp. I agree that field observations must ultimately take precedence over synthetic results. If careful field measurements consistently contradict theoretical results, then the mathematical model must be regarded as inadequate. However, geological complexity makes a single case history no more convincing than a single theoretical study, and few in‐field IP array comparisons have been published.

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

scholarly journals A Lot-Size Model for Deteriorating Items under Conditions of a One-Time Only Extended Credit Period

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Nita H. Shah
Keyword(s):  
Mathematical Model ◽  
Cycle Time ◽  
Deteriorating Items ◽  
Special Period ◽  
Lot Size ◽  
Credit Period ◽  
Size Model ◽  
The Mathematical Model ◽  
Special Cycle ◽  
Theoretical Results

Now-a-days, the offer of credit period to the customer for settling the account for the units purchased by the supplier is considered to be the most beneficial policy. In this article, an attempt is made to formulate the mathematical model for a customer to determine optimal special cycle time when the supplier offers the special extended credit period for one time only during a special period. A decision policy for a retailer is developed to find optimal special cycle time. The theoretical results and effects of various parameters are studied by appropriate dataset.

scholarly journals Water-In-Oil Emulsions through Porous Media and the Effect of Surfactants: Theoretical Approaches

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 620 ◽  
Author(s):  
Josue F. Perez-Sanchez ◽  
Nancy P. Diaz-Zavala ◽  
Susana Gonzalez-Santana ◽  
Elena F. Izquierdo-Kulich ◽  
Edgardo J. Suarez-Dominguez
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Theoretical Study ◽  
High Viscosity ◽  
Dispersed Phase ◽  
Interaction Energies ◽  
Theoretical Approaches ◽  
Heavy Crude ◽  
Oil Emulsions ◽  
The Mathematical Model

The most complex components in heavy crude oils tend to form aggregates that constitute the dispersed phase in these fluids, showing the high viscosity values that characterize them. Water-in-oil (W/O) emulsions are affected by the presence and concentration of this phase in crude oil. In this paper, a theoretical study based on computational chemistry was carried out to determine the molecular interaction energies between paraffin–asphaltenes–water and four surfactant molecules to predict their effect in W/O emulsions and the theoretical influence on the pressure drop behavior for fluids that move through porous media. The mathematical model determined a typical behavior of the fluid when the parameters of the system are changed (pore size, particle size, dispersed phase fraction in the fluid, and stratified fluid) and the viscosity model determined that two of the surfactant molecules are suitable for applications in the destabilization of W/O emulsions. Therefore, an experimental study must be set to determine the feasibility of the methodology and mathematical model displayed in this work.

scholarly journals EXPERIMENTAL DETERMINATION OF THE HOLE AXIS DEFLECTION WHEN WORKING WITH A COUNTERSINK WITH CARBIDE BLADES

2020 ◽  
Vol 20 (1) ◽  
pp. 55-62
Author(s):  
I. P. Deryabin ◽  
◽  
A. S. Tokarev ◽  
B. A. Lopatin ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cutting Forces ◽  
Full Scale ◽  
Shape Accuracy ◽  
Full Scale Experiment ◽  
Lateral Displacements ◽  
Scale Experiment ◽  
The Mathematical Model ◽  
Hole Axis ◽  
Theoretical Results

This article discusses the developed mathematicalmodel that takes intoaccount the errors of sharpening and assembling the cutting blades of a countersink tool with carbide blades. This allows you to determine the actual area of the cut sections of the allowance for each blade and calculate the cutting forces acting on them. The resultant cutting forces leads to lateral displacements of the axis of the tool during machining of the hole. The mathematical model makes it possible to determine the errors of processing holes (axis retraction, split and shape accuracy) with a countersink with a carbideblades. To check the adequacy of the mathematical model, fullscale experiments were performed on blanks madeof various materials. The method of conducting a full-scale experiment was developed. Recommended cutting modes and a countersink with three blades are selected. Processing was performed at the MM800 Fanuc processing center. Using modern automation tools – the Renishaw system and additive technologies using the Range Vision Spectrum 3D scanner, the drift of the hole axis was measured after processing with a vertical drill with carbide blades. This device allows you to get the desired result in a very short time. A compact sensor was used to measure the deflection of the hole axis, allowing for very accurate results. Substituting the part processing data into the mathematical model, the calculated values (theoretical) of the hole axis withdrawal during processing for the prototypes are obtained. The theoretical results and the results of the field experiment are compared. Comparing the obtained theoretical results – the results of a mathematical model, and the results of a full-scale experiment, it was concluded that the developed mathematical model is adequate and can be used in production by technologists in the development and computer debugging of technological processes.

Research on the mathematical modelling of the starting torque of self-lubricating spherical plain bearings

2021 ◽  
pp. 095440622110478
Author(s):  
Qiang Wang ◽  
Jigang Chen ◽  
Haili Zhou ◽  
Xuan Lyu ◽  
Zhanqi Hu
Keyword(s):  
Mathematical Model ◽  
Critical Load ◽  
Spherical Surface ◽  
Radial Load ◽  
Torque Generation ◽  
Allowable Range ◽  
Wrap Angle ◽  
The Mathematical Model ◽  
Theoretical Results ◽  
Starting Torque

The starting torque of self-lubricating spherical plain bearings (SSPBs) is a key parameter for evaluating the performance of bearings. Therefore, the starting torque of SSPBs should be controlled to within an allowable range. In this paper, the starting torque generation mechanism is analyzed, and the critical load for the separation of the liner from the outer spherical surface of the inner ring is determined. A mathematical model of the starting torque is established; the experimental and theoretical results of the starting torque are compared and analyzed, and then the accuracy of the mathematical model is evaluated by the deterministic coefficient R2. The research reveals that a critical load exists for the starting torque. Below the critical load, the starting torque is dependent on the outer spherical radius of the inner ring, bearing wrap angle, and liner parameters such as the compressive elastic modulus, friction coefficient, and precompression of the liner; however, the starting torque is independent of the radial load. Above the critical load, the starting torque is also dependent on the radial load. The research results provide a theoretical basis for the design and application of bearings.

Research on the Modeling of Metal Material Properties Based on Logistic Model

2014 ◽  
Vol 875-877 ◽  
pp. 1076-1082
Author(s):  
Shi Yu Zhang ◽  
Xi Ling Li
Keyword(s):  
Mathematical Model ◽  
Statistical Methods ◽  
Material Properties ◽  
Logistic Model ◽  
Theoretical Study ◽  
Metal Material ◽  
Metal Materials ◽  
The Mathematical Model ◽  
Hardenability Curve

The fact that it is difficult to establish the mathematical model of metal materials by theoretical study method means that can be done by statistical methods. Happens to, the logistic model is more suitable for this work. This paper tries to establish the model of steel hardenability curve by transforming logistic model without a large number of specimens.

The Spread-Mathematical Model of Special-Shaped Steel Wire during the Rolling

2011 ◽  
Vol 340 ◽  
pp. 56-63
Author(s):  
Bo Jian Wang ◽  
Wei Ke Sun ◽  
Yong Jie Wang
Keyword(s):  
Mathematical Model ◽  
Balance Equation ◽  
Steel Wire ◽  
Rolling Process ◽  
Force Balance ◽  
Stress Increment ◽  
Rolling Deformation ◽  
The Mathematical Model ◽  
Theoretical Results ◽  
Force Balance Equation

This article studied the rolling process of metal card wire, and established the spread formula of flat wire to special-shaped steel wire by rolling. The metal stress-increment in rolling deformation zone for the special-shaped steel wire was solved by the force-balance equation, and the mathematical model of rolling-piece spread was established according to the displacement increment function solved. By means of experiments to verify the mathematical model, the results show: the theoretical results of different materials through the model to calculate is closer the actual value after rolled , the error is less than 5%.

Theoretical Study on the Wetting Length in Triangle Wetting Region of Rectangular Microgrooves

2011 ◽  
Author(s):  
Tao Wang ◽  
Xuegong Hu ◽  
Chaohong Guo ◽  
Xuelei Nie ◽  
Ningning Xie
Keyword(s):  
Mathematical Model ◽  
Heat Flux ◽  
Theoretical Analysis ◽  
Tilt Angle ◽  
Heat Sink ◽  
Theoretical Study ◽  
Geometric Dimension ◽  
The Mathematical Model ◽  
The Relationship ◽  
Working Liquid

The mathematical model is established in this article to describe the relationship between the wetting length of working liquid in the triangular wetting region of rectangular capillary microgrooves and the geometric dimension, tilt angle, type of working liquid and heat flux when heating the back of microgrooves heat sink. The model supposes that the vapour-liquid interface of meniscus is quadratic parabola but not arc. The predictions from the theoretical analysis are successfully compared with the experimental results.

scholarly journals Capillary transport in paper porous materials at low saturation levels: normal, fast or superfast?

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200488
Author(s):  
Alex V. Lukyanov ◽  
Vladimir V. Mitkin ◽  
Tristan Pryer ◽  
Penpark Sirimark ◽  
Theo G. Theofanous
Keyword(s):  
Porous Materials ◽  
Diffusion Model ◽  
Field Measurements ◽  
Capillary Transport ◽  
Liquid Saturation ◽  
Term Evolution ◽  
Low Levels ◽  
The Mathematical Model ◽  
Theoretical Results

The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated that the process of liquid spreading in this type of porous material at low saturation can be described macroscopically by a similar super-fast, nonlinear diffusion model to that which had been previously identified in experiments and simulations in particulate porous media. The macroscopic diffusion model has been underpinned by simulations using a microscopic network model. The theoretical results have been qualitatively compared with available experimental observations within the witness card technique using persistent liquids. The long-term evolution of the wetting spots was found to be truly universal and fully in line with the mathematical model developed. The result has important repercussions for the witness card technique used in field measurements of the dissemination of various low-volatility agents in imposing severe restrictions on collection and measurement times.

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