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

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.

Download Full-text

Method of first integrals and interface, surface waves

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/32/2/310 ◽

2010 ◽

Vol 32 (2) ◽

pp. 107-120

Author(s):

Pham Chi Vinh ◽

Trinh Thi Thanh Hue ◽

Dinh Van Quang ◽

Nguyen Thi Khanh Linh ◽

Nguyen Thi Nam

Keyword(s):

Rayleigh Waves ◽

Displacement Vector ◽

Attenuation Factor ◽

Electrical Potential ◽

Polarization Vector ◽

First Integrals ◽

Dispersion Equations ◽

Interface Surface ◽

Electric Induction ◽

The One

The method of first integrals (MFI) based on the equation of motion for the displacement vector, or based on the one for the traction vector was introduced recently in order to find explicit secular equations of Rayleigh waves whose characteristic equations (i.e the equations determining the attenuation factor) are fully quartic or are of higher order (then the classical approach is not applicable). In this paper it is shown that, not only to Rayleigh waves, the MFI can be applicable also to other waves by running it on the equations for mixed vectors. In particular: (i) By applying the MFI to the equations for the displacement-traction vector we get the explicit dispersion equations of Stoneley waves in twinned crystals (ii) Running the MFI on the equations for the traction-electric induction vector and the traction-electrical potential vector provides the explicit dispersion equations of SH-waves in piezoelastic materials. The obtained dispersion equations are identical with the ones previously derived using the method of polarization vector, but the procedure of driving them is more simple.

Download Full-text

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

Download Full-text

Poisson Brackets & Angular Momentum

10.1093/oso/9780198822370.003.0017 ◽

2018 ◽

Author(s):

Peter Mann

Keyword(s):

Generating Functions ◽

First Integrals ◽

Lagrangian Mechanics ◽

Poisson Brackets ◽

Coordinate Transformations ◽

Canonical Transformations ◽

Gauge Transformations ◽

The Third ◽

Point Transformations ◽

Canonical Coordinate

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.

Download Full-text

Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case

Journal of Applied Analysis ◽

10.1515/jaa-2018-0017 ◽

2018 ◽

Vol 24 (2) ◽

pp. 175-183

Author(s):

Jean-Claude Ndogmo

Keyword(s):

Explicit Form ◽

Nonlinear Equations ◽

Variational Principles ◽

Symmetry Algebra ◽

First Integrals ◽

Maximal Symmetry ◽

General Order ◽

Linear And Nonlinear ◽

Variational Symmetries ◽

Variational Symmetry

Abstract Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. A discussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations.

Download Full-text

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.

Download Full-text

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.

Download Full-text