"Models of gliders" - Precise landing. Vocabulary work. Extra glue does not make your craft more beautiful. Glider, keel, wing, airplane, airplane, porthole. What is the name of the sport where athletes fly gliders and hang gliders? Safety rules for working with scissors and glue. Fuselage. Circle the pattern. What are the parts of a glider?
"Fashion and Model" - And only at the age of 42 he achieves success. Christian Dior. Sleep disturbance. Women suffer from disorders more, but men also have anorexia. Distorted ideas about the norm of own weight. The job of a model is to be beautiful, slim. Mini project "Fashion Now". And in the end... Gabrielle Chanel.
"Aircraft models" - Goals and objectives. Project. Yak-3 USSR 1944 Wing. French pilots of the Normandie-Niemen regiment fought on Yak-3 fighters. Keel. 4797 aircraft were produced. Fuselage. Stabilizer. Aviation Museum. Armament: 2 machine guns 12.7 mm 1 cannon 20 mm. Cabin. Cook. Magazine "Modelist-Constructor" 1972-1974 Project implementation.
"Types of models" - Non-scale: doll; children's drawing. The model may also be NOT ADEQUATE. 9. Types of models by branches of knowledge. 7. Types of models depending on the time. 6. Types of models depending on the form of presentation. Models modeling. 2. The need to create models. Insert Clip!!! Modeling is the process of creating and using models.
"Object Model" - Formalization. Representation of the object model. Answer questions on the topic. Know the definitions of modeling, formalization, the concept of visualization of models. Homework. The material model is a) a globe; b) world map; c) drawing; d) schedule. Modeling as a method of cognition. Information models play a very important role In human life.
"Model representation" - The behavior of the system can be represented as a function of time. it is recommended to use the equivalent representation scheme of the linear element. Environment model - description of the environment at the input and output. In connection with the above, brackets acquire a very important, additional role. The property of linearity is also called the principle of superposition.
"What are the hours" - What are the hours? We walk at night, we walk during the day, But we're not going anywhere. Hourglass. Atomic clock. Ancient Chinese water clock. Modern water clock. Fire watch. We beat regularly every hour, And you are friends, do not beat us, And take care of the time. World clock. Name it. The clock on the Spasskaya Tower of the Kremlin in Moscow is the main mechanical clock in our country.
"Substances of the particle body" - Bodies consist of Substances. Natural Artificial. True or not? Lomonosov Mikhail Vasilyevich (1711 - 1765). Solid liquid gaseous SALT WATER GAS. Substances. Thanks everyone for the lesson! Substances are what bodies are made of. celestial bodies; space bodies. Bodies can consist of one substance.
"Relativity of motion" - Speed of motion. The motion of the Sun relative to the Earth is analema. Traffic hot air balloon relative to the earth. The movement of the boat relative to the Earth. Speed. Movement of an artificial satellite relative to the Earth. The movement of the car relative to the trams, but wrong. Trajectory. The motion of the planets relative to the Sun.
"Object model" - The process is very slow. Full-scale models - really reproduce appearance, structure and behavior of the object. object models. The study of the object is dangerous for others. Weather map. A model is created if: Compare! What is a model? Scheme. Descriptions of the original object in information coding languages.
"Relation of objects" - Let's discuss. Looking after… Swimming… Relationships of objects. Relations. The most important. The bridge across the gorge is shorter than the bridge across the strait. Relationship - a certain relationship of two or more objects. Top left below. Below... Some relationship names change when object names are swapped. The Colosseum is located in Rome.
"Relations between objects" - Husband. Student. Relationship between objects. Boss. Family relationship. Less Expensive More Beautiful Newer. Relationship between flower and petal. The main thing that you must understand and remember! Teacher. Whole. Sister. More Stronger. Part and whole. Wife. subordinate. Part. Relationship between people. Mom Dad Girl Boy.
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Models and Simulation
A model is an object that has some properties of another object (original) and is used instead of it. Originals and models
What we can model Models of objects: small copies of buildings, ships, planes, … models of the nucleus of an atom, crystal lattices drawings … Models of processes: environmental change economic models historical models … Models of phenomena: earthquake solar eclipse tsunami
What is Modeling Modeling is the creation and use of models to study originals. When modeling is used: the original does not exist ancient Egypt the consequences of a nuclear war (N.N. Moiseev, 1966) the study of the original is life-threatening or expensive: management nuclear reactor(Chernobyl, 1986) testing of a new suit for cosmonauts development of a new aircraft or ship original difficult to study directly: Solar system, galaxy (large sizes) atom, neutron (small sizes) processes in the engine internal combustion(very fast) geological phenomena (very slow) are only interested in some properties of the original airplane fuselage paint test
The goals of modeling study of the original study of the essence of an object or phenomenon “Science is the satisfaction of one’s own curiosity at public expense” (L.A. Artsimovich) analysis (“what will happen if ...”) learn to predict the consequences of various influences on the original synthesis (“how to make …”) to learn how to manage the original by influencing it optimization (“how to do it better”) choosing the best solution under given conditions
Types of models material (physical, subject) models: information models represent information about the properties and state of an object, process, phenomenon, and its relationship with the outside world: verbal - verbal or mental sign - expressed using a formal language graphic (drawings, diagrams, cards, ...) tabular mathematical (formulas) logical (various options for choosing actions based on the analysis of conditions) special (notes, chemical formulas) educational (including simulators) experimental - when creating new technical means scientific and technical
Classification of models 1. According to the time factor, static - describe the original at a given moment of time, the forces acting on the body at rest. The results of a doctor's examination.
By the nature of the connections, the deterministic connections between the input and output values are rigidly set for the same input data, the same results are obtained each time; probabilistic (stochastic) ones take into account the randomness of events in the real world, with the same input data, each time a little is obtained. different results
By structure: tabular models (pairs of correspondence) hierarchical (multilevel) models network models(graphs)
The main stages of modeling Stage I Problem statement Stage II Model development Stage III Computer experiment Stage IV Analysis of the results The result corresponds to the goal The result does not correspond to the goal
Models and modeling © K.Yu. Polyakov, Topic 1. Models and their types
4 What can be modelled? Models of objects: reduced copies of buildings, ships, aircraft, ... models of the nucleus of an atom, crystal lattices drawings ... Models of processes: changes in the ecological situation, economic models, historical models ... Models of phenomena: earthquake, solar eclipse, tsunami ...
5 Modeling Modeling is the creation and use of models to study originals. When modeling is used: the original does not exist - ancient Egypt - the consequences of a nuclear war (N.N. Moiseev, 1966) the study of the original is life-threatening or expensive: - the control of a nuclear reactor (Chernobyl, 1986) - the testing of a new spacesuit for cosmonauts - the development of a new aircraft or a ship, the original is difficult to study directly: -Solar system, galaxy (large sizes) -atom, neutron (small sizes) -processes in an internal combustion engine (very fast) -geological phenomena (very slow) only some properties of the original are of interest -checking paint for aircraft fuselage
6 Modeling goals study of the original study of the essence of an object or phenomenon “Science is the satisfaction of one’s own curiosity at public expense” (L.A. Artsimovich) analysis (“what will happen if ...”) learn to predict the consequences of various influences on the original synthesis (“how to do, to …”) to learn how to manage the original, influencing it optimization (“how to do it better”) choosing the best solution under given conditions
9 The nature of models material (physical, subject) models: information models are information about the properties and state of an object, process, phenomenon, and its relationship with the outside world: verbal - verbal or mental sign - expressed using a formal language graphic (drawings, diagrams , maps, ...) tabular mathematical (formulas) logical (various options for choosing actions based on the analysis of conditions) special (notes, chemical formulas)
10 Models by area of application educational (including simulators) experimental - when creating new technical means scientific and technical wind tunnel tests in the experimental pool simulator of solar radiation vacuum chamber at the Institute of Space Research, a vibrating stand at NPO Energia
11 Models by time factor static - describe the original at a given moment of time the forces acting on the body at rest results of a doctor's examination photograph dynamic model of the movement of the body natural phenomena (lightning, earthquake, tsunami) case history video recording of the event
12 Models by the nature of relationships deterministic relationships between input and output values are rigidly specified with the same input data, the same results are obtained every time slightly different results Examples of body motion with regard to wind Brownian motion of particles model of ship motion in waves models of human behavior
13 Models by structure tabular models (pairs of correspondence) hierarchical (multilevel) models network models (graphs) Director Chief Engineer Vasya Petya Chief Accountant MashaDashaGlasha start finish
14 Special types simulation models - it is impossible to calculate or predict the behavior of the system in advance, but you can simulate its response to external influences; -Maximum consideration of all factors; -only numerical results; Examples: drug trials on mice, monkeys, … mathematical modeling of biological systems business model and management model of the learning process The challenge is to find the best solution by trial and error (multiple experiments)! ! !
16 Adequacy of the model Adequacy is the coincidence of the essential properties of the model and the original: the simulation results are consistent with the conclusions of the theory (conservation laws, etc.) ... are confirmed by experiment The adequacy of the model can only be proved by experiment! ! ! The model is always different from the original Any model is adequate only under certain conditions! ! !
17 System approach A system is a group of objects and links between them, isolated from the environment and considered as a whole. Examples: family ecological system computer technical system society A A B B C C D G environment The system has (due to connections!) special properties that no single object has in isolation! ! !
19 System approach A graph is a set of vertices and edges connecting them vertex edge edge weight (weighted graph) Rurik Igor Svyatoslav Vladimir Yaropolk Oleg directed graph (digraph) – edges have a direction
Models and modeling © K.Yu. Polyakov, Topic 2. Stages of modeling
22 I. Statement of the problem study of the original study of the essence of an object or phenomenon analysis (“what will happen if ...”) learn to predict the consequences of various influences on the original synthesis (“how to make ...”) learn to control the original by influencing it optimization ( “how to do it better”) choosing the best solution under given conditions Errors in setting the problem lead to the most serious consequences! ! !
23 I. Problem Statement A well-posed problem: all connections between the input data and the result are described all the input data are known the solution exists the problem has a unique solution Examples of badly posed problems: Winnie the Pooh and Piglet built a trap for a heffalump. Will he be able to catch him? The kid and Carlson decided to fraternally share two nuts - a large one and a small one. How to do it? Find the maximum value of the function y = x 2 (no solutions). Find a function that passes through the points (0,1) and (1,0) (non-unique solution).
24II. Model development select the type of model determine the essential properties of the original that need to be included in the model, discard the non-essential (for this task) build a formal model is a model written in a formal language (mathematics, logic, ...) and reflecting only the essential properties of the original develop an algorithm for the model An algorithm is a well-defined sequence of actions that must be performed to solve a problem.
25 III. Model Testing Testing is the testing of a model against simple input data with a known outcome. Examples: a device for adding multi-digit numbers - checking the model of the ship's movement on single-digit numbers - if the rudder is level, the course should not change; if the rudder is turned to the left, the ship should go to the right. model of accumulating money in the bank - at a rate of 0%, the amount should not change. The model has been tested. Does this guarantee its correctness? ? ?
26 IV. An experiment with a model An experiment is a study of a model under conditions of interest to us. Examples: number addition machine - work with multi-digit numbers - ship movement model - research in rough sea conditions - money accumulation model in a bank - calculations at a non-zero rate Can the results be 100% trustworthy? ? ?
27 V. Verification by practice, analysis of results Possible conclusions: the problem is solved, the model is adequate it is necessary to change the algorithm or modeling conditions it is necessary to change the model (for example, take into account additional properties) it is necessary to change the problem statement
29 I. Statement of the problem Assumptions: we consider a coconut and a banana as material points the distance to the palm tree is known the height of the monkey is known the height at which the banana hangs is known, the monkey is known to throw the coconut with a known initial speed, air resistance is not taken into account Under these conditions, it is required to find the initial angle at which it is necessary throw coconut. Is there always a solution? ? ?
31 III. Testing the model at zero speed the coconut falls vertically down at t=0 the coordinates are (0, h) when thrown vertically up (=90 o) the x coordinate does not change at some t the y coordinate starts to decrease (parabola branches down) Mathematical model No contradictions found! ! !
32 IV. Experiment Method I. Change the angle. For the selected angle, we build the nut's flight path. If it passes above the banana, we decrease the angle, if below, we increase it. Method II. From the first equality we express the flight time: Change the angle. For the selected angle, we consider t, and then the value of y with t. If it is greater than H, we decrease the angle, if it is less, we increase it. no need to build the entire trajectory for each
33 V. Analysis of results 1. Can a monkey always knock down a banana? 2. What will change if the monkey can throw a coconut with different strengths (with different initial speeds)? 3. What will change if coconut and bananas are not considered material points? 4. What will change if air resistance is required to be taken into account? 5. What will change if the tree sways?
Models and modeling © K.Yu. Polyakov, Topic 3. Models of biological systems (based on the textbook by A.G. Hein et al., Informatics and ICT, Grade 10, M.: Prosveshchenie, 2008)
37 Model of limited growth (P. Verhulst) L – the maximum number of animals Ideas: 1) the growth rate K L depends on the number N 2) at N=0 it should be K L =K (initial value) 3) at N=L it should be K L = 0 (limit reached) The model is adequate if the error 
Models and modeling © K.Yu. Polyakov, Topic 4. Modeling of random processes (based on the textbook by A.G. Hein et al., Informatics and ICT, grade 10, M .: Education, 2008)
45 Random numbers on a computer An electronic generator needs a special device, the results cannot be reproduced a small period (the sequence repeats after 10 6 numbers) The mid-square method (J. von Neumann) squared Pseudorandom numbers - have the properties of random numbers, but each next number is calculated according to a given formula .
46 Random numbers on a computer Linear congruential method a, c, m - integers prime number period m What period? ? ? remainder of the Mersenne Vortex division: period
48 Distribution of random numbers Features: distribution is a characteristic of the entire sequence, not just one number uniform distribution one, computer sensors of (pseudo) random numbers give a uniform distribution of uneven - many any uneven can be obtained using uniform a b a b uniform distribution
49 Area calculation (Monte Carlo method) 1. We fit a complex figure into another figure for which it is easy to calculate the area (rectangle, circle, ...). 2. Uniformly N points with random coordinates inside the rectangle. 3. We count the number of points that fell on the figure: M. 4. Calculate the area: Total N points There are M points on the figure 1. Approximate method. 2. The distribution must be uniform. 3. The more points, the more accurate. 4. Accuracy is limited by the random number generator. !
51 Brownian motion Random step: Random direction (in rad): alpha:= 2*pi*random; h:= hMax*random; Program: for i:=1 to N do begin ( find random direction and step ) x:= x + h*cos(alpha); y:= y + h*sin(alpha); end; for i:=1 to N do begin ( find random direction and step ) x:= x + h*cos(alpha); y:= y + h*sin(alpha); end;
52 Systems queuing Examples: 1) calls at a telephone exchange 2) ambulance calls 3) customer service in a bank How many crews? how many lines? how many operators? Features: 1) clients (requests for service) arrive constantly, but at random intervals of time 2) service time for each client is a random variable You need to know the characteristics (distributions) of "accidents"! ! !
Q*K then count:= count + 1; end; writeln(count/L:0:2); c" title="(!LANG:56 Bank customers (program) count:= 0; ( bad minutes counter ) for i:=1 to L do begin in:= ( random number of incoming calls ) out:= ( random number served) N:= N + in - out; if N > Q*K then count:= count + 1; end; writeln(count/L:0:2); c" class="link_thumb"> 56 !} 56 Clients in the bank (program) count:= 0; (counter of "bad" minutes) for i:=1 to L do begin in:= (random number of incoming) out:= (random number of served) N:= N + in – out; if N > Q*K then count:= count + 1; end; writeln(count/L:0:2); count:= 0; (counter of "bad" minutes) for i:=1 to L do begin in:= (random number of incoming) out:= (random number of served) N:= N + in – out; if N > Q*K then count:= count + 1; end; writeln(count/L:0:2); What is output? ? ? simulation period L minutes Q*K then count:= count + 1; end; writeln(count/L:0:2); c"> Q*K then count:= count + 1; end; writeln(count/L:0:2); count:= 0; ( bad minutes counter ) for i:=1 to L do begin in: = ( random number of incoming ) out:= ( random number of served ) N:= N + in - out; if N > Q*K then count:= count + 1; end; writeln(count/L:0:2); What is output? ??simulation period L minutes"> Q*K then count:= count + 1; end; writeln(count/L:0:2); c" title="(!LANG:56 Bank customers (program) count:= 0; ( bad minutes counter ) for i:=1 to L do begin in:= ( random number of incoming calls ) out:= ( random number served) N:= N + in - out; if N > Q*K then count:= count + 1; end; writeln(count/L:0:2); c"> title="56 Clients in the bank (program) count:= 0; (counter of "bad" minutes) for i:=1 to L do begin in:= (random number of incoming) out:= (random number of served) N:= N + in – out; if N > Q*K then count:= count + 1; end; writeln(count/L:0:2); c"> !}
4 What can be modelled? Models of objects: reduced copies of buildings, ships, aircraft, ... models of the nucleus of an atom, crystal lattices drawings ... Models of processes: changes in the ecological situation, economic models, historical models ... Models of phenomena: earthquake, solar eclipse, tsunami ...
5 Modeling Modeling is the creation and use of models to study originals. When modeling is used: the original does not exist - ancient Egypt - the consequences of a nuclear war (N.N. Moiseev, 1966) the study of the original is life-threatening or expensive: - the control of a nuclear reactor (Chernobyl, 1986) - the testing of a new spacesuit for cosmonauts - the development of a new aircraft or a ship, the original is difficult to study directly: -Solar system, galaxy (large sizes) -atom, neutron (small sizes) -processes in an internal combustion engine (very fast) -geological phenomena (very slow) only some properties of the original are of interest -checking paint for aircraft fuselage
6 Modeling goals study of the original study of the essence of an object or phenomenon “Science is the satisfaction of one’s own curiosity at public expense” (L.A. Artsimovich) analysis (“what will happen if ...”) learn to predict the consequences of various influences on the original synthesis (“how to do, to …”) to learn how to manage the original, influencing it optimization (“how to do it better”) choosing the best solution under given conditions
8 The nature of models material (physical, subject) models: information models are information about the properties and state of an object, process, phenomenon, and its relationship with the outside world: verbal - verbal or mental sign - expressed using a formal language graphic (drawings, diagrams , maps, ...) tabular mathematical (formulas) logical (various options for choosing actions based on the analysis of conditions) special (notes, chemical formulas)
9 Models by area of application educational (including simulators) experimental - when creating new technical means scientific and technical wind tunnel tests in the experimental pool simulator of solar radiation vacuum chamber at the Institute of Space Research vibration stand NPO Energia
10 Special types of game models - taking into account the actions of the enemy, models of economic situations, models of military operations sport games simulation training of personnel - it is impossible to calculate or predict the behavior of the system in advance; - you can simulate its reaction to external influences; - maximum consideration of all factors; - only numerical results; - selection of the best solution by trial and error during multiple experiments Examples: testing drugs on mice, monkeys, ... mathematical modeling of biological systems business model and management model of the learning process
11 Models by the nature of relationships deterministic relationships between input and output values are rigidly specified for the same input data, the same results are obtained every time Examples of the movement of a body thrown at an angle to the horizon calculations using known formulas model regular work probabilistic (stochastic) mechanisms take into account the randomness of events in the real world with the same input data, each time slightly different results are obtained
12 Models by the time factor static - describe the original at a given moment of time the forces acting on the body at rest results of a doctor's examination photograph dynamic model of the movement of the body natural phenomena (lightning, earthquake, tsunami) case history video recording of the event
13 Models by structure tabular models (pairs of correspondence) hierarchical (multilevel) models network models (graphs) Director Chief engineer Vasya Petya Chief accountant MashaDashaGlasha start finish
15 I. Statement of the problem study of the original study of the essence of an object or phenomenon analysis (“what will happen if ...”) learn to predict the consequences of various influences on the original synthesis (“how to make ...”) learn to control the original by influencing it optimization ( “how to do it better”) choosing the best solution under given conditions Errors in setting the problem lead to the most serious consequences! ! !
16 I. Problem statement A well-posed problem: all connections between the input data and the result are described all the input data are known the solution exists the problem has a unique solution Examples of badly posed problems: Winnie the Pooh and Piglet built a trap for a heffalump. Will he be able to catch him? The kid and Carlson decided to fraternally share two nuts - a large one and a small one. How to do it? Find the maximum value of the function y = x 2 (no solutions). Find a function that passes through the points (0,1) and (1,0) (non-unique solution).
17 II. Model development select the type of model determine the essential properties of the original that need to be included in the model, discard the non-essential (for this task) build a formal model is a model written in a formal language (mathematics, logic, ...) and reflecting only the essential properties of the original develop an algorithm for the model An algorithm is a well-defined sequence of actions that must be performed to solve a problem.
18 III. Model Testing Testing is the testing of a model against simple input data with a known outcome. Examples: a device for adding multi-digit numbers - checking the model of the ship's movement on single-digit numbers - if the rudder is level, the course should not change; if the rudder is turned to the left, the ship should go to the right. model of accumulating money in the bank - at a rate of 0%, the amount should not change. The model has been tested. Does this guarantee its correctness? ? ?
19 IV. Experiment An experiment is a study of a model under conditions of interest to us. Examples: number addition machine - work with multi-digit numbers - ship movement model - research in rough sea conditions - money accumulation model in a bank - calculations at a non-zero rate Can the results be 100% trustworthy? ? ?
22 I. Statement of the problem Assumptions: we consider a coconut and a banana as material points the distance to the palm tree is known the height of the monkey is known the height at which the banana is hanging, the monkey is known to throw a banana with a known initial speed, air resistance is not taken into account Under these conditions, it is required to find the initial angle at which it is necessary throw a nut. Is there always a solution? ? ? 24 24 III. Testing the model at zero speed the coconut falls vertically down at t=0 the coordinates are (0, h) when thrown vertically up (=90 o) the x coordinate does not change at some t the y coordinate starts to decrease (parabola branches down) Mathematical model No contradictions found ! ! !
25 IV. Experiment Method I. Change the angle. For the selected angle, we build the nut's flight path. If it passes above the banana, we decrease the angle, if below, we increase it. Method II. From the first equality we express the flight time: Change the angle. For the selected angle, we consider t, and then the value of y with t. If it is greater than H, we decrease the angle, if it is less, we increase it. no need to build the entire trajectory for each
26 V. Analysis of results 1. Can a monkey always knock down a banana? 2. What will change if the monkey can throw a coconut with different strengths (with different initial speeds)? 3. What will change if coconut and bananas are not considered material points? 4. What will change if air resistance is required to be taken into account? 5. What will change if the tree sways?
