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14 pages, 3665 KiB

Open AccessArticle

Dry Friction Analysis in Doped Surface by Network Simulation Method

by Joaquín Solano, Francisco Balibrea, José Andrés Moreno and Fulgencio Marín

Mathematics 2023, 11(6), 1341; https://doi.org/10.3390/math11061341 - 9 Mar 2023

Cited by 1 | Viewed by 1392

Dry friction cannot be understood on a macroscopic scale without knowing what happens at the contact of sliding surfaces on an atomic scale. Tests on this scale are very expensive and very sensitive to the effects of contamination or inaccurate fittings. On the [...] Read more.

Dry friction cannot be understood on a macroscopic scale without knowing what happens at the contact of sliding surfaces on an atomic scale. Tests on this scale are very expensive and very sensitive to the effects of contamination or inaccurate fittings. On the other hand, the sample dimensions are small because of the requirements of the test equipment, which makes it difficult to generalise the conclusions drawn. This work reviews the models used to analyse friction processes, and proposes the application of one of the models, the Frenkel–Kontorova–Tomlinson (FKT) model, to study the dry frictional behaviour of doped surfaces. The study shows that for concreted types of doped pattern, the behaviour can change from chaotic to periodic depending on the stiffness, which in turn are associated with temperature. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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49 pages, 598 KiB

Open AccessFeature PaperArticle

Flows in Infinite-Dimensional Phase Space Equipped with a Finitely-Additive Invariant Measure

by Vsevolod Zh. Sakbaev

Mathematics 2023, 11(5), 1161; https://doi.org/10.3390/math11051161 - 26 Feb 2023

Cited by 3 | Viewed by 2584

Abstract

Finitely-additive measures invariant to the action of some groups on a separable infinitedimensional real Hilbert space are constructed. The invariantness of a measure is studied with respect to the group of shifts on a vector of Hilbert space, the orthogonal group and some [...] Read more.

Finitely-additive measures invariant to the action of some groups on a separable infinitedimensional real Hilbert space are constructed. The invariantness of a measure is studied with respect to the group of shifts on a vector of Hilbert space, the orthogonal group and some groups of symplectomorphisms of the Hilbert space equipped with the shift-invariant symplectic form. A considered invariant measure is locally finite, σ finite, but it is not countably additive. The analog of the ergodic decomposition of invariant finitely additivemeasures with respect to some groups are obtained. The set of measures that are invariant with respect to a group is parametrized using the obtained decomposition. The paper describes the spaces of complex-valued functions which are quadratically integrable with respect to constructed invariant measures. This space is used to define the Koopman unitary representation of the group of transformations of the Hilbert space. To define the strong continuity subspaces of a Koopman group, we analyze the spectral properties of its generator. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

14 pages, 298 KiB

Open AccessArticle

Introduction to Completely Geometrically Integrable Maps in High Dimensions

by Lyudmila S. Efremova

Mathematics 2023, 11(4), 926; https://doi.org/10.3390/math11040926 - 12 Feb 2023

Cited by 3 | Viewed by 2633

Abstract

We introduce here the concept of completely geometrically integrable self-maps of n-dimensional (

n \geq 2

) cells, cylinders and tori. This concept is the extension of the geometric integrability concept previously introduced for the self-maps of a rectangle in the plane. [...] Read more.

We introduce here the concept of completely geometrically integrable self-maps of n-dimensional (

n \geq 2

) cells, cylinders and tori. This concept is the extension of the geometric integrability concept previously introduced for the self-maps of a rectangle in the plane. We formulate and prove here the criteria for the complete geometric integrability of maps on the cells, cylinders and tori of high dimensions. As a corollary of these results, we obtain, in particular, the generalization of the famous Sharkovsky’s Theorem for the set of periods of periodic points of completely geometrically integrable self-maps of multidimensional cells. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

24 pages, 4942 KiB

Open AccessArticle

Hybrid Nanofluid Radiative Mixed Convection Stagnation Point Flow Past a Vertical Flat Plate with Dufour and Soret Effects

by Nur Syahirah Wahid, Norihan Md Arifin, Najiyah Safwa Khashi’ie, Ioan Pop, Norfifah Bachok and Mohd Ezad Hafidz Hafidzuddin

Mathematics 2022, 10(16), 2966; https://doi.org/10.3390/math10162966 - 17 Aug 2022

Cited by 11 | Viewed by 1758

Abstract

The widespread application of hybrid nanofluid in real applications has been accompanied by a large increase in computational and experimental research. Due to the unique characteristics of hybrid nanofluid, this study aspires to examine the steady two-dimensional mixed convection stagnation point flow of [...] Read more.

The widespread application of hybrid nanofluid in real applications has been accompanied by a large increase in computational and experimental research. Due to the unique characteristics of hybrid nanofluid, this study aspires to examine the steady two-dimensional mixed convection stagnation point flow of a hybrid nanofluid past a vertical plate with radiation, Dufour, and Soret effects, numerically. The formulations of the specific flow model are presented in this study. The model of fluid flow that is expressed in the form of partial differential equations is simplified into ordinary differential equations via the transformation of similarity, and then solved numerically by using the boundary value problem solver known as bvp4c in MATLAB, which implements the finite difference scheme with the Lobatto IIIa formula. Two possible numerical solutions can be executed, but only the first solution is stable and meaningful from a physical perspective when being evaluated via a stability analysis. According to the findings, it is sufficient to prevent the boundary layer separation by using 2% copper nanoparticles and considering the lesser amount of Dufour and Soret effects. The heat transfer rate was effectively upgraded by minimizing the volume fraction of copper and diminishing the Dufour effect. Stronger mixed convection would lead to maximum skin friction, mass transfer, and heat transfer rates. This important preliminary research will give engineers and scientists the insight to properly control the flow of fluids in optimizing the related complicated systems. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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17 pages, 6789 KiB

Open AccessArticle

Frequency Analysis of the Railway Track under Loads Caused by the Hunting Phenomenon

by Gerardo Hurtado-Hurtado, Luis Morales-Velazquez, Martín Valtierra-Rodríguez, Frank Otremba and Juan C. Jáuregui-Correa

Mathematics 2022, 10(13), 2286; https://doi.org/10.3390/math10132286 - 30 Jun 2022

Cited by 3 | Viewed by 2484

Abstract

Hunting is a potentially dangerous phenomenon related to the lateral oscillation of the wheels that impacts the rails and causes the wear of the infrastructure’s components. Therefore, the analysis and timely detection of hunting can lead to the application of corrective maintenance tasks, [...] Read more.

Hunting is a potentially dangerous phenomenon related to the lateral oscillation of the wheels that impacts the rails and causes the wear of the infrastructure’s components. Therefore, the analysis and timely detection of hunting can lead to the application of corrective maintenance tasks, reducing damages, and costs and even derailments as a result. In this work, the vibration response of a finite element model of a rail with hunting-induced loads by a single wheel is analyzed in three directions: longitudinal, lateral, and vertical. The contact patch forces are calculated by means of Simpack^® using the Kalker linear theory and the contact Hertz theory. The system is solved by using the Newmark-β approach. The results of the deflection and vibration analysis, following the proposed methodology, show how the different characteristics of the loads impact the rail. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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17 pages, 3640 KiB

Open AccessArticle

Calculating Column Separation in Liquid Pipelines Using a 1D-CFD Coupled Model

by David Khani, Yeo Howe Lim and Ahmad Malekpour

Mathematics 2022, 10(12), 1960; https://doi.org/10.3390/math10121960 - 7 Jun 2022

Cited by 4 | Viewed by 2600

Abstract

This paper proposes a coupled 1D-CFD model for calculating column separation in liquid pipelines. ANSYS Fluent is utilized to calculate two-phase flow analysis. Method of Characteristics and Discrete Gas Cavity Model (DGCM) are both employed to conduct 1D transient analysis. The results show [...] Read more.

This paper proposes a coupled 1D-CFD model for calculating column separation in liquid pipelines. ANSYS Fluent is utilized to calculate two-phase flow analysis. Method of Characteristics and Discrete Gas Cavity Model (DGCM) are both employed to conduct 1D transient analysis. The results show that the proposed model, with both 2D and 3D CFD analysis, captures the transient responses of the system that have nearly identical accuracy and are both consistent with the results of a physical experiment. The results of a pure CFD analysis are employed to evaluate the performance of the proposed model in capturing the shape of the vapor cavity. The comparison shows that the results are generally consistent. However, the vapor cavity in the pure CFD model is established and grown on top of a film of liquid, while the cavity in some places fills the whole pipe cross-section in the proposed model. In addition, the results obtained from using Modified Two-Component Pressure Approach (MTPA), an open-channel based model proposed by the authors, also confirm the results obtained from the pure CFD analysis. Some minor discrepancies are found, which may be attributed to the uniform velocity distribution considered at the interface between 1D and CFD zones. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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32 pages, 826 KiB

Open AccessFeature PaperArticle

On Periods of Interval Exchange Transformations

by Jose S. Cánovas, Antonio Linero Bas and Gabriel Soler López

Mathematics 2022, 10(9), 1487; https://doi.org/10.3390/math10091487 - 29 Apr 2022

Viewed by 1511

Abstract

In this paper, we study the periods of interval exchange transformations. First, we characterize the periods of interval exchange transformations with one discontinuity. In particular, we prove that there is no forcing between periods of maps with two branches of continuity. This characterization [...] Read more.

In this paper, we study the periods of interval exchange transformations. First, we characterize the periods of interval exchange transformations with one discontinuity. In particular, we prove that there is no forcing between periods of maps with two branches of continuity. This characterization is a partial solution to a problem by Misiurewicz. In particular, a periodic structure is not possible for a family of the maps with one point of discontinuity in which the monotonicity changes. Second, we study a similar problem for interval exchange transformations with two discontinuities. Here we classify these maps in several classes such that two maps in the same class have the same periods. Finally, we study the set of periods for two categories, obtaining partial results that prove that the characterization of the periods in each class is not an easy problem. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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46 pages, 18525 KiB

Open AccessArticle

Study of the Angular Positioning of a Rotating Object Based on Some Computational Intelligence Methods

by Constantin Volosencu

Mathematics 2022, 10(7), 1157; https://doi.org/10.3390/math10071157 - 3 Apr 2022

Viewed by 1779

Abstract

The paper presents the result of a study that can be included in the broader field of research aimed at increasing the performance of automatic motion control systems. The main contribution of the article is the comparative study of three control methods from [...] Read more.

The paper presents the result of a study that can be included in the broader field of research aimed at increasing the performance of automatic motion control systems. The main contribution of the article is the comparative study of three control methods from the domain of computational intelligence—state feedback fuzzy control, neural predictive control, and neural model reference control—and three linear control methods—error feedback control, digital control, and state feedback control, in the case of positioning a rotating object around a central axis. The developed control structures were modeled and simulated using MATLAB/Simulink. The paper presents the chosen control structures; how to dimension them; the parameters of the linear, fuzzy, and neural regulators; the training parameters of the neural networks; and the characteristics of the variables of the control systems in the transient regime and the steady-state regime. Transient characteristics obtained for the six control structures are compared from the point of view of their control efficiency criteria. The differences in performance criteria between the control methods studied are small. All these studied methods make the regulated system to be carried on various state trajectories, short response times are obtained with aperiodic and asymptotic behavior, and the differences between the values of the efficiency indicators are small. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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14 pages, 367 KiB

Open AccessArticle

Chaos for the Dynamics of Toeplitz Operators

by Salud Bartoll, Ronald Richard Jiménez-Munguía, Rubén Alejandro Martínez-Avendaño and Alfred Peris

Mathematics 2022, 10(3), 425; https://doi.org/10.3390/math10030425 - 28 Jan 2022

Cited by 2 | Viewed by 1671

Abstract

Chaotic properties in the dynamics of Toeplitz operators on the Hardy–Hilbert space

H^{2} (D)

are studied. Based on previous results of Shkarin and Baranov and Lishanskii, a characterization of different versions of chaos formulated in terms of the coefficients of [...] Read more.

Chaotic properties in the dynamics of Toeplitz operators on the Hardy–Hilbert space

H^{2} (D)

are studied. Based on previous results of Shkarin and Baranov and Lishanskii, a characterization of different versions of chaos formulated in terms of the coefficients of the symbol for the tridiagonal case are obtained. In addition, easily computable sufficient conditions that depend on the coefficients are found for the chaotic behavior of certain Toeplitz operators. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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24 pages, 2691 KiB

Open AccessFeature PaperArticle

Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms

by Jaroslav Haslinger, Radek Kučera, Kristina Motyčková and Václav Šátek

Mathematics 2021, 9(22), 2906; https://doi.org/10.3390/math9222906 - 15 Nov 2021

Cited by 1 | Viewed by 1704

Abstract

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is [...] Read more.

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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15 pages, 3449 KiB

Open AccessArticle

Motion of an Unbalanced Impact Body Colliding with a Moving Belt

by Marek Lampart and Jaroslav Zapoměl

Mathematics 2021, 9(9), 1071; https://doi.org/10.3390/math9091071 - 10 May 2021

Cited by 2 | Viewed by 2127

Abstract

In the field of mechanical engineering, conveyors and moving belts are frequently used machine parts. In many working regimes, they are subjected to sudden loading, which can be a source of irregular motion in the impacting bodies and undesirable behavior in the working [...] Read more.

In the field of mechanical engineering, conveyors and moving belts are frequently used machine parts. In many working regimes, they are subjected to sudden loading, which can be a source of irregular motion in the impacting bodies and undesirable behavior in the working machine. This paper deals with a mechanical model where colisions between an impact body and a moving belt take place. The impact body is constrained by a flexible rope, the upper end of which is excited by a slider in the vertical direction. The behavior of the system was investigated in terms of its dependence on the amplitude and frequency of excitation given by the movement of the slider, and the eccentricity of the center of gravity of the impact body. Outputs of the computations indicate that different combinations of the analyzed parameters lead to high complexity of the system’s movement. The bifurcation analysis shows multiple periodic areas changed by chaotic regions. The research carried out provides more details about the behavior and properties of strongly nonlinear mechanical systems resulting from impacts and dry friction. The obtained information will enable designers to propose parameters for industrial machines that make it possible to avoid their working at undesirable operating levels. Full article

(This article belongs to the Special Issue Theory and Application of Dynamical Systems in Mechanics)

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