Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites

2014 ◽  
pp. 217-262 ◽  
Author(s):  
Leonid Filshtinsky ◽  
Vladimir Mityushev
Keyword(s):  
Mathematical Models ◽  
Two Dimensional ◽  
Piezoelectric Fields

Three-Dimensional Dynamic Modeling of the Human Knee to Include Tibio-Femoral and Patello-Femoral Joints

2001 ◽  
Author(s):  
Dumitru Caruntu ◽  
Mohamed Samir Hefzy
Keyword(s):  
Knee Joint ◽  
Mathematical Models ◽  
Dynamic Modeling ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Human Knee ◽  
Two Dimensional Model ◽  
Rigid Contact ◽  
Locomotor Activities

Abstract Most of the anatomical mathematical models that have been developed to study the human knee are either for the tibio-femoral joint (TFJ) or patello-femoral joint (PFJ). Also, most of these models are static or quasistatic, and therefore do not predict the effects of dynamic inertial loads, which occur in many locomotor activities. The only dynamic anatomical model that includes both joints is a two-dimensional model by Tumer and Engin [1]. The model by Abdel-Rahman and Hefzy [2] is the only three dimensional dynamic model for the knee joint available in the literature; yet, it includes only the TFJ and allows only for rigid contact.

scholarly journals On the correctness of mathematical models of time-of-flight cathodoluminescence of direct-gap semiconductors

2019 ◽  
Vol 30 ◽  
pp. 07014
Author(s):  
Mikhail A. Stepovich ◽  
Dmitry V. Turtin ◽  
Elena V. Seregina ◽  
Veronika V. Kalmanovich
Keyword(s):  
Electron Beam ◽  
Gallium Nitride ◽  
Initial Data ◽  
Mathematical Models ◽  
Single Crystal ◽  
Three Dimensional ◽  
Time Of Flight ◽  
Semiconductor Material ◽  
Two Dimensional ◽  
Cathodoluminescence Intensity

Two-dimensional and three-dimensional mathematical models of diffusion and cathodoluminescence of excitons in single-crystal gallium nitride excited by a pulsating sharply focused electron beam in a homogeneous semiconductor material are compared. The correctness of these models has been carried out, estimates have been obtained to evaluate the effect of errors in the initial data on the distribution of the diffusing excitons and the cathodoluminescence intensity.

scholarly journals Analysis of spatial thermal field in a magnetic bearing

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 52-56
Author(s):  
Dawid Wajnert ◽  
Bronisław Tomczuk
Keyword(s):  
Temperature Field ◽  
Mathematical Models ◽  
Computer Simulations ◽  
Thermal Field ◽  
Three Dimensional ◽  
Magnetic Bearing ◽  
Field Analysis ◽  
Two Dimensional ◽  
Temperature Distributions ◽  
Dimensional Simulation

AbstractThis paper presents two mathematical models for temperature field analysis in a new hybrid magnetic bearing. Temperature distributions have been calculated using a three dimensional simulation and a two dimensional one. A physical model for temperature testing in the magnetic bearing has been developed. Some results obtained from computer simulations were compared with measurements.

The Kinematic Basis for an Improved Friction Wedge Model

2003 ◽  
Author(s):  
A. D. McKisic
Keyword(s):  
Mathematical Models ◽  
North American ◽  
Two Dimensional ◽  
The North ◽  
Rail Industry ◽  
Dominant Design

One of the reasons the three-piece truck is the dominant design in the North American freight rail industry is the efficiency of the friction wedge damping system. Even with the proliferation of the system there is a limited understanding of the mechanics of its operation and an absence of mathematical models capable of accurately simulating systems employing friction wedges. This paper presents the kinematic basis for an improved two-dimensional friction wedge model that is capable of more accurately simulating the system.

GENERATION OF SYMMETRICAL COLORED IMAGES VIA SOLUTION OF THE INVERSE PROBLEM OF CHEMICAL REACTIONS DISCRETE CHAOTIC DYNAMICS

2006 ◽  
Vol 16 (05) ◽  
pp. 1419-1434 ◽  
Author(s):  
V. GONTAR ◽  
O. GRECHKO
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Inverse Problem ◽  
Mathematical Models ◽  
Chemical Reactions ◽  
Chaotic Dynamics ◽  
Two Dimensional

An automatic procedure for generating colored two-dimensional symmetrical images based on the chemical reactions discrete chaotic dynamics (CRDCD) is proposed. The inverse problem of derivation of symmetrical images from CRDCD mathematical models was formulated and solved using a special type of genetic algorithm. Different symmetrical images corresponding to the solutions of a CRDCD mathematical model for which the parameters were obtained automatically by the proposed method are presented.

scholarly journals Dynamical Behaviors of Coupled Memristor-Based Oscillators with Identical and Different Nonlinearities

2018 ◽  
Vol 2018 ◽  
pp. 1-20
Author(s):  
A. Elsonbaty ◽  
A. Abdelkhalek ◽  
A. Elsaid
Keyword(s):  
Mathematical Models ◽  
Coupled Oscillators ◽  
Perturbation Methods ◽  
Normal Forms ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Ring Configuration ◽  
Dynamical Behaviors

In this work, the interesting dynamics of coupled nonlinear memristor-based oscillators in ring configuration are explored. The mathematical models are derived to describe the possible cases of employing identical or different nonlinearities. Analytical and numerical techniques, involving perturbation methods, normal forms, phase portraits, and Lyapunov exponents are used to investigate various types of dynamical behaviors along with their stability regions in parameters space. The effects of time-delayed coupling on the proposed system are numerically studied. It is demonstrated that the coupled oscillators show rich dynamics including periodic orbits, quasiperiodicity, two-dimensional, and three-dimensional tori.

scholarly journals Simulation of Unsteady Movement in the Downstream of a Hydroelectric Complex During the Destruction of a Soil Dam

2021 ◽  
Vol 64 (6) ◽  
pp. 554-567
Author(s):  
V. V. Veremenyuk ◽  
V. V. Ivashechkin ◽  
O. V. Nemeravets
Keyword(s):  
Mathematical Models ◽  
Flow Rate ◽  
Hydraulic Structure ◽  
Two Dimensional ◽  
Hydrodynamic Models ◽  
Earthen Dam ◽  
Hydrodynamic Parameters ◽  
Wave Parameters ◽  
Flooding Zone ◽  
The Republic

153 reservoirs have been created in the Republic of Belarus. During the period of passing catastrophic floods and high waters along the river, there is a risk of overflowing reservoirs, overflow of water masses through the crest of an earthen dam and flooding of significantly large areas. The destruction of the dam is accompanied by the formation of a breach and the outflow through it of an unsteady flow of water in the form of a breakthrough wave into the downstream. A breakthrough wave and catastrophic flooding of the area are the main destructive factors of hydrodynamic accidents. Calculations to determine parameters of the wave and to assess the possible consequences of flooding are necessary when drawing up operational-and-tactical plans for the prevention and elimination of emergencies in case of accidents at retaining structures, determining the probable damage from flooding of the territory in the downstream of a hydraulic structure as a result of the passage of a breakthrough wave. It is necessary to assess the flooding zone and the hydrodynamic parameters of the flow, viz. the maximum values of the depth and velocity of the flow in the zone of catastrophic flooding, the time from the beginning of the accident to the arrival of a breakthrough wave at the particular point of the terrain, the duration of flooding, the boundaries of the zone of catastrophic flooding, the hydrographic flow rate in the section of the eroded dam and the graph of the fall headwater level. The degree of reliability of predictive calculations is determined by the accuracy of the two applied mathematical models, viz.: 1) erosion of the dam; 2) the movement of the breakout wave. The analysis of the applied mathematical models shows that in all cases the hydrodynamic models based on the oneand two-dimensional equations of Boussinesq – Saint-Venant are used to calculate the movement of the breakthrough wave. Wave parameters, i. e. wave height and speed of its propagation, completely depend on the hydrograph of the discharge in the section of the eroded dam, which, in its turn, is determined by the dynamics of its erosion. The aim of the work is to develop a methodology for calculating the flooding of the downstream as a result of the destruction of a soil dam.

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