scholarly journals Stability of synchronous modes of the system of two connected self-oscillators

2021 ◽  
Vol 2140 (1) ◽  
pp. 012021
Author(s):  
S S Novikov ◽  
V S Kosterova
Keyword(s):  
Computational Experiment ◽  
Dynamic Instability ◽  
Initial Conditions ◽  
Resonant Coupling ◽  
Resonance Properties ◽  
The Given

Abstract In this paper investigate the dynamic instability of a system of two self-oscillators with a strong resonant coupling. The analysis of influence of resonance properties of coupling on stability of synchronous modes was carried out. In the course of the computational experiment, it was possible to observe the different behavior of the system depending on the given initial conditions. The boundaries of destruction of coherent modes are determined.

scholarly journals A Mathematical Model for Nipah Virus Infection

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Assefa Denekew Zewdie ◽  
Sunita Gakkhar
Keyword(s):  
Virus Infection ◽  
Reproduction Number ◽  
Initial Conditions ◽  
Nipah Virus ◽  
Virus Transmission ◽  
Globally Asymptotically Stable ◽  
Dead Bodies ◽  
Manifold Theory ◽  
The Impact ◽  
The Given

It has been reported that unprotected contact with the dead bodies of infected individuals is a plausible way of Nipah virus transmission. An SIRD model is proposed in this paper to investigate the impact of unprotected contact with dead bodies of infected individuals before burial or cremation and their disposal rate on the dynamics of Nipah virus infection. The model is analyzed, and the reproduction number is computed. It is established that the disease-free state is globally asymptotically stable when the reproduction number is less than unity and unstable if it is greater than unity. By using the central manifold theory, we observe that the endemic equilibrium is locally stable near to unity. It is concluded that minimizing unsafe contact with the infected dead body and/or burial or cremation as fast as possible contributes positively. Further, the numerical simulations for the given choice of data and initial conditions illustrate that the endemic state is stable and the disease persists in the community when the reproduction number is greater than one.

scholarly journals A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Alvaro H. Salas S ◽  
Jairo E. Castillo H ◽  
Darin J. Mosquera P
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Initial Conditions ◽  
Negative Ions ◽  
Nonlinear Problems ◽  
New Approach ◽  
Weierstrass Elliptic Function ◽  
Electronegative Plasma ◽  
The Given

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

Learning solutions to the source inverse problem of wave equations using LS-SVM

2019 ◽  
Vol 27 (5) ◽  
pp. 657-669 ◽  
Author(s):  
Ziku Wu ◽  
Chang Ding ◽  
Guofeng Li ◽  
Xiaoming Han ◽  
Juan Li
Keyword(s):  
Inverse Problem ◽  
Approximate Solution ◽  
Support Vector Machines ◽  
Wave Equations ◽  
Source Term ◽  
Initial Conditions ◽  
Support Vector ◽  
Vector Machines ◽  
Robustness To Noise ◽  
The Given

Abstract A method based on least squares support vector machines (LS-SVM) is proposed to solve the source inverse problem of wave equations. Contrary to the most existing methods, the proposed method provides a closed form approximate solution which satisfies the boundary conditions and the initial conditions. The proposed method can recover the unknown source term with the given additional conditions. Furthermore, it has reasonable robustness to noise. Numerical results show the proposed method can be used to solve the source inverse problem of wave equations.

Influence of the Longitudinal Excavations Layout on Stress Concentration Value in the Peripheral Rock Mass

2014 ◽  
Vol 682 ◽  
pp. 196-201 ◽  
Author(s):  
Alexander F. Revuzhenko ◽  
Anton A. Kazantsev ◽  
Yuri F. Glazkov ◽  
Andrey A. Dortman
Keyword(s):  
Rock Mass ◽  
Stress Concentration ◽  
Computational Model ◽  
Initial Conditions ◽  
Reaction Forces ◽  
The Given

The article proposes an analysis of the various longitudinal excavations layouts in tunnel walls. The excavations are required for taking reaction forces when a ‘geokhod’ works. A computational model of the peripheral rock mass is presented. Calculations showed that the X-type layout of the longitudinal excavations is most acceptable for the given initial conditions.

scholarly journals Generalized method for forming plane isotropic curves

2020 ◽  
pp. 109-115
Author(s):  
A. V. Nesvidomin ◽  
Keyword(s):  
Initial Conditions ◽  
Plane Curve ◽  
Parametric Equation ◽  
The Real ◽  
Interactive Search ◽  
Geometric Conditions ◽  
Minimal Distortion ◽  
Isotropic Vector ◽  
Real Argument ◽  
The Given

The process of modeling the temperature distribution on surfaces, applying an image to curved areas with minimal distortion requires the formation of isometric grids on the plane and on the surface. One of the common ways to form planar isometric networks is to use the functions of a complex variable and planar isotropic curves, followed by separation of the real and imaginary parts. The development of computer models for the interactive search and analysis of isometric networks according to various initial geometric conditions provides a generalized method for their formation with the possibility of varying their shape and position. It is proposed to use an isotropic vector for the formation of flat isotropic curves, which ensured a single sequence of analytical calculations according to the following initial conditions: 1) selection of an arbitrary function of a real argument; 2) a given parametric equation of a plane curve; 3) a given polar equation of a plane curve. Since the analytical calculations of the derivation of the parametric equation of a plane isotropic curve and the corresponding isometric grid are rather laborious, their execution is carried out in the environment of the Maple symbolic algebra. To this end, the corresponding software has been created, which interactively allows you to select the function of a real argument, a parametric or polar equation of a plane guide curve. All subsequent stages of analytical transformations to form an isotropic curve and the corresponding isometric grid are carried out automatically. An interactive model for the formation and analysis of plane isotropic curves with various initial conditions has been created, which has shown its effectiveness, which is confirmed by the given examples of plane isometric grids for specific functions of the real parameter, plane curves in the parametric and polar form of their job.

scholarly journals Processing and visualization of the results of parametric numerical calculations

2021 ◽  
Vol 2127 (1) ◽  
pp. 012025
Author(s):  
A E Bondarev ◽  
A E Kuvshinnikov
Keyword(s):  
Mathematical Modeling ◽  
Visual Analytics ◽  
Gas Dynamics ◽  
Computational Experiment ◽  
Visual Presentation ◽  
Key Factors ◽  
Multidimensional Arrays ◽  
Parametric Studies ◽  
The Given ◽  
Computational Technology

Abstract In modern problems of mathematical modeling in computational gas dynamics, it is increasingly necessary to implement parametric studies. In these cases, the key factors of the problem under consideration vary with the chosen step within the given ranges. Calculations of this kind can be effectively carried out by constructing a generalized computational experiment. A generalized computational experiment is a computational technology that combines the solution of mathematical modeling problems, parallel technologies, and visual analytics technologies. The results of a generalized computational experiment are multidimensional arrays, where the dimension of the arrays corresponds to the number of key factors. Processing and visual presentation of such arrays requires solving a number of separate tasks. The processing and visual presentation of the results are carried out for target functionals represented as a function of many variables. The report presents an examples of solving specific processing and visualization problems based on the implemented generalized computational experiment for 3D cone in supersonic flow.

scholarly journals PENINGKATKAN HASIL BELAJAR MATEMATIKA SISWA KELAS 4 SD MELALUI MODEL PEMBELAJARAN PROBLEM BASED LEARNING

2018 ◽  
Vol 1 (1) ◽  
pp. 120
Author(s):  
Mita Puspita ◽  
Slameto Slameto ◽  
Eunice Widyanti Setyaningtyas
Keyword(s):  
Action Research ◽  
Student Learning ◽  
Model Problem ◽  
Initial Conditions ◽  
Problem Based Learning ◽  
Average Score ◽  
Learning Mathematics ◽  
Classroom Action Research ◽  
The Given

Abstrak:  Penelitian ini merupakan Penelitian Tindakan Kelas (PTK) yang bertujuan untuk meningkatkan hasil belajar matematika dengan menggunakan model pembelajaran Problem Based Learning.  Pada kondisi awal menunjukkan nilai rata-rata secara klasikal yang diperoleh yaitu 62. Setelah diberikan tindakan dengan model pembelajaran Problem Based Learning siklus 1 menunjukkan nilai rata-rata  yang diperoleh 77,37. Pada siklus 2 rata-rata ketuntasan hasil belajar siswa meningkat 83 Hasil ini menunjukkan bahwa adanya peningkatan hasil belajar siswa dengan menggunakan model pembelajaran Problem Based Learning , sehingga dapat disimpulkan bahwa  model pembelajaran Problem Based Learning dapat meningkatkan hasil belajar matematika siswa. Abstract:  This research is classroom action research to improve the learning results of mathematics by using the model of Problem Based Learning. On initial conditions indicate the average score in classical obtained, that is 62. After the given action by the model Problem Based Learning in the cycle 1  shows average score obtained was 77,37. In cycle 2, the average of the result of student learning increased to reach 83. These results suggest that there was an increase in student learning out comes by using the model Problem Based Learning, so it can be concluded that the model of Problem Based Learning can improve the result of learning mathematics on 4 grades student.

QUANTUM TRAJECTORY CALCULATIONS FOR BIPOLAR WAVEPACKET DYNAMICS IN ONE DIMENSION: SYNTHETIC SINGLE-WAVEPACKET PROPAGATION

2010 ◽  
Vol 09 (04) ◽  
pp. 711-734 ◽  
Author(s):  
KISAM PARK ◽  
BILL POIRIER
Keyword(s):  
Initial Conditions ◽  
Technical Difficulty ◽  
One Dimension ◽  
Quantum Trajectory ◽  
One Dimensional ◽  
Trajectory Calculations ◽  
Wave Packet Dynamics ◽  
Wavepacket Dynamics ◽  
Trajectory Method ◽  
The Given

In a previous paper [Park K, Poirier B, Parlant G, J Chem Phys129:194112, 2008], a synthetic quantum trajectory method (QTM) was successfully implemented for wave-packet dynamics in a one-dimensional (1D) symmetric Eckart barrier system, utilizing a "double-wavepacket" version of the bipolar decomposition, ψ = ψ+ + ψ- = (ψ1+ + ψ2+) + (ψ1- + ψ2-), to avoid a technical difficulty involving negligible initial ψ- density. In this paper, we develop a new synthetic algorithm which overcomes this difficulty directly, utilizing the original "single-wavepacket" version of the bipolar decomposition, ψ =ψ+ + ψ-, and also show that the initial propagation of ψ- is mainly governed by probability transfer from ψ+, rather than by the given initial conditions for ψ-. The new algorithm makes it possible to apply the synthetic bipolar QTM to asymptotically asymmetric as well as symmetric potential systems. Successful application results for both symmetric and asymmetric Eckart barrier systems in 1D are presented.

scholarly journals Simulation Modeling of Competitive Strategy of Pricing

2019 ◽  
Vol 20 (2) ◽  
pp. 294-321
Author(s):  
Sergey Sorokin ◽  
Irina Varpaeva ◽  
Ol'ga Grishina
Keyword(s):  
Mathematical Model ◽  
Simulation Modeling ◽  
Computational Experiment ◽  
Initial Conditions ◽  
Market Price ◽  
Local Market ◽  
Commercial Activities ◽  
Relationship Model ◽  
The Impact ◽  
Aging Factor

Efficiency of commercial activities depends on many factors. One of the tools to study their influence is mathematical modeling. The goal of the study is to conduct a computational experiment that simulates the dynamics of the supplier’s sales volumes in a competitive environment under various initial conditions. We take into account the possibility of changing the price of products (goods), depending on changes in sales volumes. The limitation of the experiment is the conditions of the local market and the presence of the maximum value of purchasing power within it. To conduct an experiment, it is necessary to solve the following tasks: to find out the impact of sales volumes changes caused by competition on changes of the price of products (and the price of products must be calculated according to product aging factor); to consider consumers’ preferences, on which “consumer-supplier” relationships are based and to determine the relationship between the pricing models and the model of competing relations of the “supplier-suppliers” type. To achieve this goal, we employed heuristic methods of simulation modeling and the analogy method (universality). Based on simulation modeling and the method of analogies (universality), we developed a mathematical model as a part of a computational experiment. The former simulates the market price of a product and the dynamics of sales volumes of a supplier, which considers correlation between the market price for products (goods) and their aging factor, as well as consumers’ preferences and pricing model and competing relationship model. The application of the mathematical model developed by the authors allows to take into account many interrelated factors that influence the sales dynamics of market participants in real economic situations.

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