Solution for Accurate Calculations in Complicated Coordination Equilibrium System with Excel Iteration Program

This paper discusses the kinematic characteristics of lapping process and the main parameters of the process. It was determined that the influencing degree of technological parameters to the forming surface and processes. It was projected the construction of the lapping head for processing of internal cylindrical surfaces, scheme of the lapping operation and graphic description of the forces influencing. The relationships between the axial, radial and tangential cutting forces and the effect of the combined force thereof are determined in order to ensure the necessary surface pressure. During the analysis geometric and mathematical relationships were obtained. The extracted analytical expressions can be realized by further experimental researches and can be used in engineering calculations of technological parameters of processing by lapping. Angular velocity, friction force, linear velocity, also the length of the tactile curve and the radius of the part can be considered the main kinematic and dynamic parameters of the process that the formation of the surface, also the course of the process depends on these parameters. Depending on the kinematic parameters, the wear nature of the tool changes and this changes the linear and angular velocities, which have a significant impact on the accuracy, quality and productivity of processing. When examining the technological capabilities of the process, the nature of the movement between the part and the grinding tool, also changes in cutting speed are often considered as a main factor. Analytical expressions were obtained to determine the main parameters of the process, taking into account the kinematic characteristics of the friction process. These expressions can be used in engineering calculations and allow to determine the optimal values of the processing mode. In order to obtain the required micrometric surface cleanliness and measurement accuracy, correlation relationships were established between the main parameters of the process, equations of the equilibrium system of shear forces were compiled and analytical expressions were obtained based on the analysis of kinematic and dynamic properties of the system.

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Application of Genetic Algorithms (GA) and Threshold Acceptance (TA) to a Ternary Liquid-Liquid Equilibrium System

International Review on Modelling and Simulations (IREMOS) ◽

10.15866/iremos.v9i1.8029 ◽

2016 ◽

Vol 9 (1) ◽

pp. 29 ◽

Cited By ~ 3

Author(s):

Ayache Boultif ◽

Azeddine Kabouche ◽

Segni Ladjel

Keyword(s):

Genetic Algorithms ◽

Equilibrium System ◽

Liquid Equilibrium ◽

Threshold Acceptance

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Crystallization of Polymers under the Influence of an External Force Field

Polymers ◽

10.3390/polym13132078 ◽

2021 ◽

Vol 13 (13) ◽

pp. 2078

Author(s):

Rajdeep Singh Payal ◽

Jens-Uwe Sommer

Keyword(s):

External Force ◽

Melting Behavior ◽

Mechanical Work ◽

Stem Length ◽

Heat Of Fusion ◽

Strong Increase ◽

Lamellar Thickness ◽

Equilibrium System ◽

External Force Field ◽

Work Done

We simulated the crystallization and melting behavior of entangled polymer melts using molecular dynamics where each chain is subject to a force dipole acting on its ends. This mimics the deformation of chains in a flow field but represents a well-defined equilibrium system in the melt state. Under weak extension within the linear response of the chains, the mechanical work done on the system is about two orders of magnitude smaller as compared with the heat of fusion. As a consequence, thermodynamic and simple arguments following the secondary nucleation model predict only small changes of the crystalline phase. By contrast, an increase of the stem length up to a factor of two is observed in our simulations. On the other hand, the lamellar thickening induced by the external force is proportional to the increase of the entanglement length in the melt prior to crystallization as measured by the primitive path method. While the mechanical work done on the system is only a small perturbation for thermodynamics of polymer crystallization, the change of the primitive path is large. This suggests that a strong increase in the lamellar thickness induced, by external deformation, a topological rather than a thermodynamic origin.

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An iterative algorithm for the system of split mixed equilibrium problem

Demonstratio Mathematica ◽

10.1515/dema-2020-0027 ◽

2020 ◽

Vol 53 (1) ◽

pp. 309-324

Author(s):

Ibrahim Karahan ◽

Lateef Olakunle Jolaoso

Keyword(s):

Variational Inequality ◽

Iterative Algorithm ◽

Equilibrium Problems ◽

Nonexpansive Mappings ◽

Equilibrium System ◽

Convergence Conditions ◽

Mixed Equilibrium Problems ◽

Split Variational Inequality ◽

Mixed Equilibrium ◽

Split Mixed Equilibrium Problem

AbstractIn this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

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Cordon-based congestion pricing in a continuum traffic equilibrium system

Transportation Research Part A Policy and Practice ◽

10.1016/j.tra.2005.02.017 ◽

2005 ◽

Vol 39 (7-9) ◽

pp. 813-834 ◽

Cited By ~ 12

Author(s):

H.W. Ho ◽

S.C. Wong ◽

Hai Yang ◽

Becky P.Y. Loo

Keyword(s):

Congestion Pricing ◽

Traffic Equilibrium ◽

Equilibrium System

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The Klein first integrals in an equilibrium system with electromagnetic, weak, strong and gravitational interactions

Nuclear Physics A ◽

10.1016/j.nuclphysa.2011.09.005 ◽

2011 ◽

Vol 872 (1) ◽

pp. 286-295 ◽

Cited By ~ 32

Author(s):

Jorge A. Rueda ◽

R. Ruffini ◽

S.-S. Xue

Keyword(s):

First Integrals ◽

Equilibrium System

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Effect of sodium silicate on the solubility of zinc oxide of the Na2O–ZnO–H2O equilibrium system

Hydrometallurgy ◽

10.1016/j.hydromet.2012.12.002 ◽

2013 ◽

Vol 136 ◽

pp. 46-50 ◽

Cited By ~ 6

Author(s):

Ailiang Chen ◽

Zhongwei Zhao ◽

Dong Xu ◽

Xuheng Liu ◽

Xingyu Chen

Keyword(s):

Zinc Oxide ◽

Sodium Silicate ◽

Equilibrium System

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Membrane extraction of 1-phenylethanol from fermentation solution

Chemical Papers ◽

10.2478/s11696-010-0096-5 ◽

2011 ◽

Vol 65 (2) ◽

Cited By ~ 8

Author(s):

Mário Mihaľ ◽

Jozef Markoš ◽

Vladimír Štefuca

Keyword(s):

Mathematical Model ◽

Organic Solvents ◽

Hollow Fiber ◽

Hollow Fiber Membrane ◽

Membrane Extraction ◽

Equilibrium System ◽

Extraction Kinetics ◽

Hollow Fiber Contactor ◽

Experimental Values ◽

Fermentation Solution

Abstract1-Phenylethanol can be produced by biotransformation of acetophenone using microorganisms. The next step is the separation of biomass from the fermentation solution (e.g. using microfiltration) and then the separation of the product. Membrane extraction was studied in the presented work for this purpose. Equilibria of acetophenone and 1-phenylethanol in the equilibrium system solute-organic solvent-water were investigated for three different organic solvents (heptane, toluene, ethyl acetate). On the basis of this investigation, extraction kinetics of both solutes from the model aqueous solution to the heptane organic phase, using a hollow fiber membrane module, were studied. To simulate the extraction kinetics, mathematical model of an experimental parallel flow hollow fiber contactor is presented and verified using experimental values with good agreement. Extraction kinetics for the investigated organic solvents were simulated and compared using the verified mathematical model and the chosen membrane extraction parameters.

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