The mathematical modelling and computer simulation of wildland fire perimeter growth over a 3-dimensional surface

1999 ◽  
Vol 9 (3) ◽  
pp. 213 ◽  
Author(s):  
Gwynfor D. Richards
Keyword(s):  
Mathematical Model ◽  
Wildland Fire ◽  
Solution Technique ◽  
3 Dimensional ◽  
Variable Surface ◽  
Method Of Solution ◽  
Constant Slope ◽  
The Mathematical Model ◽  
Numerical Method Of Solution ◽  
Variable Topography

This work considers wildfire growth over variable topography. Through an analysis of fire perimeter growth for homogeneous conditions over a surface of constant slope, a mathematical model of fire growth for heterogeneous conditions and variable surface is proposed. The mathematical model is in the form of a system of partial differential equations that require a numerical method of solution. A simple numerical solution technique is described and example solutions are given for fires over a variety of complex surfaces illustrating that simulation results can be obtained in reasonable time.

A Computer Algorithm for Simulating the Spread of Wildland Fire Perimeters for Heterogeneous Fuel and Meteorological Conditions

1995 ◽  
Vol 5 (2) ◽  
pp. 73 ◽  
Author(s):  
GD Richards ◽  
RW Bryce
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Wildland Fire ◽  
Meteorological Conditions ◽  
Simple Method ◽  
Reasonable Time ◽  
Method Of Solution ◽  
Fire Scenarios ◽  
Computer Based ◽  
The Mathematical Model

This work describes a computer based technique for simulating the spread of wildland fire for heterogeneous fuel and meteorological conditions. The mathematical model is in the form of a pair of partial differential equations, and can model fuels whose fire perimeter for homogeneous conditions is any given shape, such as ellipses, double ellipses, lemniscates etc. Provided the fire does not attempt to burn into an already burnt out region, then the differential equations are easily solved and a simple method of solution is presented. To identify regions that are internal to the fire perimeter an algorithm that uses the turning number of a point in the plane relative to the fire perimeter is used. The algorithm is found to be reliable, and allows for the simulation of highly complex fire scenarios in a reasonable time. Example simulations are presented that involve variations in fuel, barriers, wind direction changes and multiple fires.

scholarly journals On the placing of synchronized vector measurements in network 110 - 330 kV for identification of the Kaliningrad region power system regime

2018 ◽  
Vol 58 ◽  
pp. 01005
Author(s):  
Magomed Gadzhiev ◽  
Eugenia Gulevich ◽  
Vyacheslav Korobka ◽  
Vladimir Ryabchenko ◽  
Yuriy Sharov
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Power System ◽  
Electric Power ◽  
Electric Power System ◽  
Phasor Measurement Unit ◽  
Measurement Unit ◽  
Method Of Solution ◽  
Kaliningrad Region ◽  
The Mathematical Model

A solution is presented for the problem of placing phasor measurement unit to identify the mathematical model of the electric power system in the state space. The criterion for complete observability of the Kalman dynamic system is taken as a basis. As a method of solution, we use the canonical genetic algorithm. The complete observability of the power system is ensured by the application of the observability rule in the form of a recursive test of observability. The proposed approach is demonstrated by the arrangement of synchronized vector meters in the Kaliningrad region power system.

scholarly journals Definition of Ship Outfitting Scheduling as a Resource Availability Cost Problem and Development of a Heuristic Solution Technique

2016 ◽  
Vol 32 (03) ◽  
pp. 154-165
Author(s):  
Christopher Rose ◽  
Jenny Coenen ◽  
Hans Hopman
Keyword(s):  
Mathematical Model ◽  
Planning Process ◽  
Computational Effort ◽  
Qualitative Description ◽  
Solution Technique ◽  
Test Case ◽  
Heuristic Solution ◽  
Resource Availability Cost ◽  
Definition Of ◽  
The Mathematical Model

The outfitting process of shipyards building complex ship types, such as offshore, passenger, and military vessels, is becoming more critical to efficient ship production as the number of components installed on these vessels continues to increase. Outfitting of such vessels is generally characterized by disorganization and rework due to a lack of coordination between the shipyard and subcontractors as well as insufficiently detailed planning. This paper presents a mathematical model for the outfitting planning process of a shipyard building complex vessels. A qualitative description is included for the constraints and objectives underlying the developed mathematical model for the Ship Outfitting Scheduling Problem (SOSP). A heuristic solution technique is also developed for solving the SOSP, and a test case of six midship sections from a recently constructed pipelaying vessel is presented to show the feasibility of both the mathematical model and heuristic. This test case shows that it is possible to find a high-quality planning for the SOSP with a reasonable computational effort. Furthermore, it was found that the greatest priority should be given to components that have the earliest deadlines or dependents with such deadlines. Components should also be scheduled in such a way to minimize the required movements of outfitting personnel between the different work sites of a shipyard.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

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