scholarly journals Investigation of iceberg towing processes based on finite-dimensional models of continuous media

2020 ◽  
pp. 82-88
Author(s):  
В.А. Коршунов ◽  
Р.С. Мудрик ◽  
Д.А. Пономарев ◽  
А.А. Родионов
Keyword(s):  
Numerical Modeling ◽  
Differential Equations ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Mathematical Formulation ◽  
Element Model ◽  
Dynamic Factor ◽  
System Of Differential Equations ◽  
Finite Dimensional ◽  
Simplified Algorithm

В работе рассмотрена проблема управления ледовой обстановкой при освоении участков на морской шельфе. Отмечено, что наиболее эффективным способом управления движения айсбергов и их осколков является использование буксировочных систем. В зависимости от размера айсберга в качестве буксировочной системы может использоваться либо одиночный канат, либо ледовая сетка. Описана технология осуществления буксировки. Рассмотрено два варианта математической формулировки задачи буксировки. Инженерный подход основан на решении системы нелинейных дифференциальных уравнений динамики с известными начальными условиями. Наиболее точным является аппарат механики сплошных сред, который опирается на фундаментальные законы сохранения. Он позволяет построить связанную нелинейную систему дифференциальных уравнений с минимальным количеством допущений. Использование данного подхода возможно при численном моделировании процесса буксировки. В работе создана конечно-элементная модель взаимодействия айсберга с буксировочной системой. Разработан упрощенный алгоритм учета жидкости. Получены кинематические и динамические характеристики процесса буксировки. Определен коэффициент динамичности усилий. The paper deals with the problem of ice management during the development of the sea shelf. It is noted that the most effective way to control the movement of icebergs and their fragments is to use towing systems. Depending on the size of the iceberg, either a single rope or an ice net can be used as a towing system. The technology of towing is described. Various of the mathematical formulation of the towing problem are considered. The engineering approach is based on solving a system of nonlinear differential equations of dynamics with initial conditions. More accurate approach is the computational continuum mechanics, which is based on fundamental conservation laws. It allows to build a nonlinear system of differential equations with a minimum of assumptions. This approach can be used for numerical modeling of the towing process. In the paper, a finite element model of the interaction of an iceberg with a towing system is created. To account liquid the simplified algorithm is prescribed. The kinematic and dynamic characteristics of the towing process are obtained. The dynamic factor of axial force is determined.

Volume Element Model for Modeling, Simulation, and Optimization of Parabolic Trough Solar Collectors

2017 ◽  
Author(s):  
Tugba S. Sensoy ◽  
Sam Yang ◽  
Juan C. Ordonez
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mathematical Formulation ◽  
Element Model ◽  
Volume Element ◽  
Heat Transfer Fluid ◽  
Solar Collectors ◽  
Parabolic Trough ◽  
Simulation And Optimization ◽  
Proposed Model

In this paper we present a dynamic three-dimensional volume element model (VEM) of a parabolic trough solar collector (PTC) comprising an outer glass cover, annular space, absorber tube, and heat transfer fluid. The spatial domain in the VEM is discretized with lumped control volumes (i.e., volume elements) in cylindrical coordinates according to the predefined collector geometry; therefore, the spatial dependency of the model is taken into account without the need to solve partial differential equations. The proposed model combines principles of thermodynamics and heat transfer, along with empirical heat transfer correlations, to simplify the modeling and expedite the computations. The resulting system of ordinary differential equations is integrated in time, yielding temperature fields which can be visualized and assessed with scientific visualization tools. In addition to the mathematical formulation, we present the model validation using the experimental data provided in the literature, and conduct two simple case studies to investigate the collector performance as a function of annulus pressure for different gases as well as its dynamic behavior throughout a sunny day. The proposed model also exhibits computational advantages over conventional PTC models-the model has been written in Fortran with parallel computing capabilities. In summary, we elaborate the unique features of the proposed model coupled with enhanced computational characteristics, and demonstrate its suitability for future simulation and optimization of parabolic trough solar collectors.

Multiple large-scale coherent mode interactions in a developing round jet

1993 ◽  
Vol 248 ◽  
pp. 383-401 ◽  
Author(s):  
Sang Soo Lee ◽  
J. T. C. Liu
Keyword(s):  
Differential Equations ◽  
Energy Method ◽  
Large Scale ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Wave Mode ◽  
Mean Flow ◽  
Round Jet ◽  
The Mean ◽  
Integral Energy

The integral energy method has been used to study the nonlinear interactions of the large-scale coherent structure in a spatially developing round jet. The streamwise development of a jet is obtained in terms of the mean flow shear-layer momentum thickness, the wave-mode kinetic energy and the wave-mode phase angle. With the energy method, a system of partial differential equations is reduced to a system of ordinary differential equations. The nonlinear differential equations are solved with initial conditions which are given at the nozzle exit. It is shown that the initial wave-mode energy densities as well as the initial phase angles play a significant role in the streamwise evolution of the large-scale coherent wave modes and the mean flow.

scholarly journals ESTIMATING THE INFLUENCE OF THE WIND EXPOSURE ON THE MOTION OF AN EXTINGUISHING SUBSTANCE

2020 ◽  
Vol 5 ◽  
pp. 51-59
Author(s):  
Yuriy Abramov ◽  
Oleksii Basmanov ◽  
Valentina Krivtsova ◽  
Andrii Khyzhnyak
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Wind Effect ◽  
System Of Differential Equations ◽  
Wind Action ◽  
Fire Extinguishing ◽  
Additive Component ◽  
Wind Exposure ◽  
Using Data

One of the tasks to be solved when deploying fire extinguishing systems is to determine the range of the fire extinguishing agent supply to the combustion center. This problem is solved using data on the trajectory of the fire-extinguishing agent in the combustion center. The presence of wind impact on the process of supplying a fire extinguishing agent will lead to a change in its trajectory. To take into account wind impact, it becomes necessary to assess the result of such impact. Using the basic equation of dynamics for specific forces, a system of differential equations is obtained that describes the delivery of a fire extinguishing agent to the combustion center. The system of differential equations takes into account the presence of wind impact on the movement of the extinguishing agent. The presence of wind action is taken into account by the initial conditions. To solve such a system, the integral Laplace transform was used in combination with the method of undefined coefficients. The solution is presented in parametric form, the parameter of which is time. For a particular case, an expression is obtained that describes the trajectory of the supply of the extinguishing agent into the combustion center. Nomograms are constructed, with the help of which the operative determination of the estimate of the maximum range of the fire-extinguishing agent supply is provided. Estimates are obtained for the time of delivery of a fire-extinguishing agent to the combustion center, and it is shown that for the characteristic parameters of its delivery, this value does not exceed 0.5 s. The influence of wind action on the range of supply of a fire extinguishing agent is presented in the form of an additive component, which includes the value of the wind speed and the square of the time of its delivery. To assess the effect of wind impact on the movement of the fire extinguishing agent, an analytical expression for the relative error was obtained and it was shown that the most severe conditions for supplying the fire extinguishing agent to the combustion center, the value of this error does not exceed 5.5%. Taking into account the wind effect when assessing the range of supply of a fire-extinguishing agent makes it possible to increase the efficiency of fire-extinguishing systems due to its more accurate delivery to the combustion center

CALCULATION OF THE INFLUENCE OF TEMPERATURE FIELDS ON THE QUALITY OF THE RESULTING COMPOSITE COATINGS

2021 ◽  
Vol 2 (143) ◽  
pp. 130-134
Author(s):  
Sergey Yu. Zhachkin ◽  
◽  
Marina N. Krasnova ◽  
Aleksandr V. Biryukov ◽  
Nikita A. Pen’kov ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Plasma Spraying ◽  
Performance Indicators ◽  
Plasma Torch ◽  
Initial Conditions ◽  
Composite Coatings ◽  
Nonlinear Differential Equations ◽  
Research Purpose ◽  
Mathematical Tool

Increased attention is currently being paid to improving the reliability and efficiency of power units. The use of materials with special coatings that have the necessary set of characteristics allows you to increase the service life of the restored components and assemblies. One of the ways to obtain such coatings is by plasma spraying. (Research purpose) The research purpose is in predicting the performance indicators of composite coatings using a mathematical tool that adequately describes the process of coating build-up during plasma spraying. (Materials and methods) Authors used a universal UPU-3 installation with modifications to produce coatings, which allowed controlling the heat transfer process with high accuracy. Authors used small-sized cooling water temperature sensors located at the connection point of the current-carrying hoses to the sprayer to record the enthalpy of the jet. During the coating process, the restored part remained stationary, and a plasma torch carried out the movement along the sprayed part. The advantage of this method is the independence of the mass of the recovered parts from the drive power of the plasma torch. (Results and discussion) The article presents the mathematical model, which is a system of nonlinear partial differential equations describing the process of heat transfer during the application of plasma-sputtered coatings, taking into account the initial conditions determined using the UPU-3 installation. To solve the presented system of nonlinear differential equations, the method of perturbation theory with the use of thermal potentials is used. (Conclusions) The article proposes the ways to solve the problem of heat transfer during the application of plasma-coated coatings, which allow us to predict the performance indicators of the restored parts.

scholarly journals Deterministic Chaos Theory: Basic Concepts

2016 ◽  
Vol 39 (1) ◽  
Author(s):  
Mauro Cattani ◽  
Iberê Luiz Caldas ◽  
Silvio Luiz de Souza ◽  
Kelly Cristiane Iarosz
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Deterministic Chaos ◽  
Chaotic Motions ◽  
And Mathematics ◽  
Irregular Behavior ◽  
Mathematics And Physics

This article was written to students of mathematics, physics and engineering. In general, the word chaos may refer to any state of confusion or disorder and it may also refer to mythology or philosophy. In science and mathematics it is understood as irregular behavior sensitive to initial conditions. In this article we analyze the deterministic chaos theory, a branch of mathematics and physics that deals with dynamical systems (nonlinear differential equations or mappings) with very peculiar properties. Fundamental concepts of the deterministic chaos theory are briefly analyzed and some illustrative examples of conservative and dissipative chaotic motions are introduced. Complementarily, we studied in details the chaotic motion of some dynamical systems described by differential equations and mappings. Relations between chaotic, stochastic and turbulent phenomena are also commented.

scholarly journals Construction on the Green function for Vallee-Poussin problem for nonlinear system of differential equations

2013 ◽  
Vol 5 (1) ◽  
pp. 121-128
Author(s):  
R.I. Sobkovich ◽  
A.I. Kazmerchuk
Keyword(s):  
Green Function ◽  
Nonlinear System ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Uniqueness Theorems ◽  
System Of Differential Equations ◽  
Existence And Uniqueness Theorems ◽  
Iterative Schemes ◽  
The Green Function

Existence and uniqueness theorems of solution of n-point Vallee-Poussin problem for system of nonlinear differential equations are proved. Iterative schemes for finding them are proposed.

scholarly journals Selectively caring for the most severe COVID-19 patients delays ICU bed shortages more than increasing hospital capacity

2020 ◽  
Author(s):  
Miles Roberts ◽  
Helena Duplechin Seymour ◽  
Alexander Dimitrov ◽  
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Mortality Data ◽  
System Of Differential Equations ◽  
Infection Rates ◽  
Us States ◽  
Hospital Capacity ◽  
Hospital Resources ◽  
Parameter Values ◽  
Implementing Strategies

1AbstractSARS-CoV-2, the virus responsible for COVID-19, has killed hundreds of thousands of Americans. Although physical distancing measures played a key role in slowing COVID-19 spread in early 2020, infection rates are now peaking at record levels across the country. Hospitals in several states are threatened with overwhelming numbers of patients, compounding the death toll of COVID-19. Implementing strategies to minimize COVID-19 hospitalizations will be key to controlling the toll of the disease, but non-physical distancing strategies receive relatively little attention. We present a novel system of differential equations designed to predict the relative effects of hospitalizing fewer COVID-19 patients vs increasing ICU bed availability on delaying ICU bed shortages. This model, which we call SEAHIRD, was calibrated to mortality data on two US states with different peak infection times from mid-March – mid-May 2020. It found that hospitalizing fewer COVID-19 patients generally delays ICU bed shortage more than a comparable increase in ICU bed availability. This trend was consistent across both states and across wide ranges of initial conditions and parameter values. We argue that being able to predict which patients will develop severe COVID-19 symptoms, and thus require hospitalization, should be a key objective of future COVID-19 research, as it will allow limited hospital resources to be allocated to individuals that need them most and prevent hospitals from being overwhelmed by COVID-19 cases.

Resonant Oscillations of a Beam-Pendulum System

1963 ◽  
Vol 30 (2) ◽  
pp. 181-188 ◽  
Author(s):  
R. A. Struble ◽  
J. H. Heinbockel
Keyword(s):  
Energy Transfer ◽  
Differential Equations ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Asymptotic Methods ◽  
Physical Parameters ◽  
Pendulum System ◽  
Long Period ◽  
Resonance Phenomena

The resonance phenomena and energy transfer associated with a set of coupled nonlinear differential equations are analyzed using asymptotic methods. The equations describe the motion of a beam-pendulum system which exhibits autoparametric excitation. Precise conditions under which resonant or nonresonant oscillations arise, are obtained. These conditions not only depend upon the physical parameters of the system but also upon the energy of the oscillations (i.e., initial conditions). In general, the envelopes of the resonant oscillations are periodic of long period and there is intermittent energy transfer between the pendulum and beam modes.

Application of New Homotopy Perturbation Method for Solving Partial Differential Equations

2018 ◽  
Vol 15 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Musa R. Gad-Allah ◽  
Tarig M. Elzaki
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Novel Technique ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear Differential

In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

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