from lat. modulus - measure, sample, norm) - any being in relation to any other being, having a common structure and function with it, regardless of differences in composition (content), external form, quantity (for example, size).
Excellent definition
Incomplete definition ↓
MODEL
French mod?le, from lat. modus - sample) - conventional image (image, diagram, description, etc.) k.-l. object (or system of objects). Serves to express the relationship between people. knowledge about objects and these objects; The concept of mathematics is widely used in semantics, logic, mathematics, physics, chemistry, cybernetics, linguistics, and other sciences and their (generally technical) applications in various, although closely related, senses. These different understandings can be drawn from the following. general definition. Two systems of objects A and B are called. M. each other (or modeling one another), if it is possible to establish such a homomorphic mapping of system A onto some system A? and a homomorphic mapping of B onto some system B? such that A? and B? are isomorphic to each other (see Isomorphism; the definitions given in this article should be generalized by considering relations not only between elements, but also, if necessary, between subsets of systems). A certain way attitude "to be M." there is a reflexive, symmetrical and transitive relation, i.e. relation of equivalence type (equality, identity); it, in particular (for A=A? and B=B), is satisfied by any systems isomorphic to each other. The concept of M. in science is usually associated with the use of the so-called. modeling method (see Modeling). Due to the symmetry of the relationship between c.-l., which follows from the definition of M. An object (system) and its M. any of the pairwise isomorphic systems we, in principle, with equal justification, can call the other M. For example, in painting and sculpture M. is called. depicted object; comparing among themselves k.-l. the object and its photograph, we consider M. precisely the photograph. Which of the two systems modeling each other (in the sense of the definition given above) in natural sciences. modeling will be chosen as the object of research, and which model will be chosen depends on the specific cognitive and practical problems facing the researcher. tasks. As a result of this circumstance, reflected in the grammatical text itself. structure of the term “modeling”, the latter has a certain subjective connotation (being often associated with who is “modelling”). The term “M.”, devoid of this coloring, is more natural to understand (and therefore define) independently of various possible “modelings”. In other words, if the concept of modeling characterizes the choice of research tools systems, then the concept of M. is the relationship between existing (in one sense or another) concrete and (or) abstract systems. The relationship between the model and the system being modeled depends on the totality of those properties and relationships between the objects of the systems under consideration, in relation to which their isomorphism and homomorphism are determined. Although the definition of mathematics given above is so broad that, if desired (considering the “trivial” homomorphism of each system into a set consisting of one single element), any two systems can be considered to be one another, such breadth of the concept of mathematics in no way complicates the application principle of modeling in scientific. research, since the properties and relationships that interest us can, in principle, always be fixed. Thus, the concepts of modeling and modeling, as well as the concepts of isomorphism and homomorphism, are always defined relative to a certain set of predicates (properties, relationships). Although the "be M" attitude symmetrically and systems modeling each other, according to definition, are completely equal when using the term “M.” Almost always, some kind of “modeling” is assumed (often implicitly) [for example, modeling used in theoretical research to build models using mathematical means. and logical symbolism (the so-called abstract-logical modeling), or modeling, which consists in reproducing the phenomena under study on specially designed materials in empirical terms. sciences (experimental modeling)]. Depending on which of the two systems being compared is fixed as the subject of study, and which as its M., the term “M.” understood in two different senses. In theoretical sciences (especially mathematics, physics) M. K.-L. systems are usually called another system that serves as a description of the original system in the language of a given science; e.g. differential system equations describing the passage of time over time. physical process, called M. of this process. In general, M. - in this sense - k.-l. areas of phenomena called scientific a theory designed to study phenomena in this area. Similarly, in (mathematical) logic M. k.-l. contain. theories are often called a formal system (calculus), and its interpretation is this theory. [The content we are talking about here is, of course, relative; so, the interpretation of k.-l. there may be another formal system. See Interpretation; on the other hand, and M. - in this understanding - does not necessarily have to be completely formalized (the objects that make it up can themselves be considered in a meaningful way, as having a specific meaning); The only significant thing is that the concepts (terms) “M.” are interpreted in terms of interp ret a tion. ] The use of the term "M" has the same character. in linguistics (“models of language”, which play an important role both in theoretical and linguistic. research and in tasks related to the construction of information languages, the development of machine translation, etc.; see Mathematical linguistics), theoretical. physics (for example, “nucleus models”) and in general in all those cases when the word “M.” serves as a synonym for the concepts of “theory” and “scientific description”. No less common is the use of the term “M.”, when M. is understood not as a description, but as something that is written about. When used in this way (again in mathematical logic, in axiomatic constructions of mathematics, in semantics, etc.), the term “M.” is considered as a synonym for the term "interpretation", i.e. M. k.-l. systems of relations called a set of objects that satisfy this system. More precisely, synonyms when used in this way are the expressions “build M.” and “indicate the interpretation”; in other words, the interpretation of k.-l. a system of objects is usually called not its M. itself (i.e., some other system), but a list of the so-called. semantic rules of “translation” from the “language” of the modeled system (for example, scientific theory) into the “language” of M. Thus, the interpretations of Lobachevsky’s geometry did not actually serve M. themselves, proposed by Poincaré, Italian. scientist E. Beltrami and German. scientist F. Klein, namely, the interpretation of Lobachevsky’s concepts of geometry in terms of these M. However, they contain. t.zr. selection of k.-l. M. theory as its interpretation is tantamount to indicating semantics. rules, according to which the elements of one of the M. theories are considered as an interpretation of its objects. In those cases when the main thing is not the content, but the strictly formal aspect of the concepts of mathematics and interpretation (in particular, in logical semantics), these concepts can be clarified, for example, the following. way: Let A be a formula of a certain calculus (formal system) L. The result of replacing all elements in A is illogical. constants (if any) variables respectively. types (see Type theory, Predicate calculus) will be denoted by A?. Class of objects N that fulfill formula A? (a class of objects, by definition, fulfills this formula if, with such a substitution of the names of these objects in the places of all the variables included in it, that the name of the same object is substituted in the place of different occurrences of the same variable, the formula turns into a true formula) , - subject to the requirement that the type of each object is equal to the type of the variable, it is substituted in its place, - called. M. formula A (or -?. sentence expressed by this formula). Similarly, if a class of formulas K is given, then there is a system S of classes of objects, the elements of each of which are assigned a definition. type, simultaneously performing - subject to the above instructions. conditions - all formulas of class K? (obtained from K in the same way as A? from A), called. The model of this class of formulas [bearing in mind this concept of model, some authors for the model of a separate formula (sentence) - or, similarly, a separate term (concept) - use the term “semi-model”]. A model S is considered to be the M of the entire calculus L if: 1) all axioms of the calculus L are included in K (and, therefore, are satisfied by the system S); 2) every formula from L, derived according to the rules of derivation of the calculus L from formulas of the calculus L satisfiable in S, is also fulfilled by the system S. Based on this definition, the most important semantics are easily determined. concepts: “analytical” and “synthetic” (sentences), “extensional” and “intensional” (expressions) and in general “semantic relation”. In this terminology, the relation of logical implication can easily be characterized: proposition A follows from proposition B if and only if A is satisfied by all the methods by which B is satisfied. A formal system can, generally speaking, have many different methods, as isomorphic with each other and are not isomorphic. If all M. k.-l. formal system is isomorphic, then they say that the underlying system of axioms is categorical (see Categoricality of a system of axioms), or complete (in one of the meanings of this term; see Completeness ); otherwise the system is called incomplete. (For an arbitrary system of axioms a priori, a third case is, of course, possible - the absence of any M. Then the system is called counter-verbal, or - in accordance with the terminology introduced above - not fulfilled. Conversely, the indication of the M.-K. axiomatic system serves as proof of its consistency with respect to the system by which the M. is constructed - see also Interpretation, Axiomatic Method) . In any of these cases, one of the M. systems - the so-called. allocated (implied when constructing a system or considered for certain purposes) - called. Interpretation of the system (if interpretation is identified with M. - in the last of the senses used here - then the implied interpretation is called natural). Figuratively speaking, we call any possible “translation” from the language of the modeled system into any other language, and interpretation is only that of these translations (and into that particular language) that we mean when interpreting the concepts of the system, considering it (for social reasons) the only true one. For example, the end of English. the phrase “In this way we can obtain only a 50 per cent solution” can be translated both as “only a 50 percent solution” and as “only a half solution”, and it is easy to imagine a specific text, the translation of which will require additional ( not contained in itself) indications of which of these “M. “choose as an “interpretation”. As is known, the concept of satisfiability, which appears in the just given definition of the concepts of M. and interpretation, is defined (although not necessarily explicitly) through the concept of logical truth, which in this case is taken as the original one. On the other hand, the concept of truth in formalized languages can, in turn, be defined through the concept of satisfiability. Thus, the “content” of the concepts of M. and interpretation is relative in nature - these concepts are defined in terms of (logical) “truth”, which turns out to be if not a “formal”, but in any case a formalizable concept. This circumstance justifies the view, widespread in mathematics and logic, according to which the interpretation is “formal” (and any study of any system of objects is the study of a certain Roy its M.) in the sense that the system serving for the purposes of interpretation of the M. Q.-L. system must be described in precise terms (since otherwise it makes no sense to even raise the question of its isomorphism with any was another system); Moreover, it is precisely this description itself that can be considered in this case as M. Of course, this does not remove the most important epistemological. the question of the adequacy of M. - for example, empirical. descriptions - the totality of objects of the real world described by it, but the criteria for this adequacy are already significantly extra-logical. character. The properties of interpretation models in mathematics are the subject of special study. algebraic "theory M.", which uses the concept of a "relational system, i.e. a set on which a certain set of predicates (properties, operations, relations) is defined (cf. definitions in article Isomorphism). It should be kept in mind that the nature of mathematical mathematics can be very complex and even “paradoxical” (i.e., not corresponding to established ideas, from which, however, their logical inconsistency does not follow). An example is the so-called “non-standard” mathematics. axiomatic systems, characterized by the fact that the “original” natural series of numbers (used in the theory by which mathematics is constructed) turns out to be non-isomorphic to the natural series constructed in mathematics (here we are talking about ordinary, traditional mathematics, starting from, in contrast from the so-called ultra-intuitionistic, from the assumption of the unique – up to isomorphism – definiteness of the set of natural numbers); the relation “to be M” is interpreted in this case, of course, as essentially asymmetrical. The modern stage of development of science is characterized by intensive expansion stock used in scientific. research into methods of constructing and using various M. “Cybernetic” turned out to be especially fruitful in this regard. approach to the study of systems of various natures. Applicable today scientific time M. contribute to the study of not only the structure, but also the function of very complex systems (including objects of living nature). Expanding the concept of modeling (and modeling), which involves taking into account not only structural, but also functional properties and relationships, can be achieved in at least two (related) ways. Firstly, one can demand that the description of each element of the model (and, of course, the modeled system) include a time characteristic (as is, for example, customary in certain branches of theoretical physics - see Continuum, Relativity theory) ; this path essentially means that the introduction of the time parameter would reduce the concept of functioning to the general concept of “spatio-temporal structure”. Secondly, using exact mathematical The concept of a function (the logical genesis of which, as is known, does not include the concept of a “temporary variable”) can be considered from the very beginning as elements from which a model is constructed, namely functions that describe the change in time of the elements of a “static " (i.e., "structural") M. (using for generalized definitions of isomorphism, homomorphism and M. the apparatus of predicate calculus of the second stage - see Predicate calculus). It is in this expanded sense that we speak not just about modeling systems, but also about modeling processes (chemical, physical, industrial, economic, social, biological, etc.). An example of a description of a k.-l. a process serving the purpose of its modeling can be a diagram of its algorithm; the possibility of clearly defining the concept of an algorithm has opened up, in particular, wide possibilities for modeling various processes using electronic computer programming. (digital) machines. Dr. An example of “machine” modeling is the use of the so-called. analog continuous machines [see Technology (section Computer Science)]. As often happens in the development of science, the term "M." is applied in an extensive manner and in cases where it is preliminarily. taking into account all the parameters to be reproduced when modeling (necessary for a literal understanding of the term) turns out, due to the complexity of the system being modeled, to be practically impossible. This applies in particular to time-varying so-called self-adjusting M., for example. to "learning models". But even if we remain within the framework of precise definitions, then in cybernetics (as in physics, as well as in mathematics and logic) the concept of M. used in both the senses mentioned above [the following important example is typical: the “recording” of inheritances. information in chromosomes is modeled by the parent organism (or organisms) and at the same time modeled in the offspring organism]. This apparent ambiguity of the term "M." (removed, however, by the general definition of M. proposed above, covering both meanings) actually serves as an example of the so-called. “wrapping the method”, characteristic of specific applications of many epistemological. concepts. Lit.: Kleene S.K., Introduction to Metamathematics, trans. from English, M., 1957, ch. 3, § 15; Ashby W. R., Introduction to Cybernetics, trans. from English, M., 1959, ch. 6; Lahuti D.G., ?evzin I.I., Finn V.K., On one approach to semantics, “Philosophy of Science” (Scientific reports of higher school), 1959, No. 1; Church?., Introduction to Mathematical Logic, trans. from English, [t. ] 1, M., 1960, §7; Revzin I. I., Models of language, M., 1962; Genkin L., O mathematical. induction, trans. from English, M., 1962; Modeling in biology. [Sat. Art. ], trans. from English, M., 1963; Molecular genetics. Sat. Art., trans. from English and German., M., 1963; Beer S., Cybernetics and production management, trans. from English, M., 1963; Carnap R., The logical syntax of language, L., 1937; Kemeny J. G., Models of logical systems, "J. Symbolic Logic", 1948, v. 13, No. 1; Rosser J. V., Wang H., Non-standard models of formal logics, "J. Symbolic Logic", 1950, v. 15, No. 2; Mostowaki?., On models of axiomatic systems, "Fundamenta Math.", 1953, v. 39; Tarski?., Contributions to the theory of models, 1–3, "Indagationes Math.", 1954, v. 16, 1955, v. 17; Mathematical interpretation of formal systems, Amst., 1955; Kemeny J. G., A new approach to semantics, "J. Symbolic Logic", 1956, v. 21, 1, 2; Scott D., Suppes P., Fundamental aspects of theories of measurement, "J. Symbolic Logic", 1958, v. 23, No. 2; Robinson?., Introduction to model theory and to the metamathematics of algebra, Amst., 1963; Curru H. V., Foundations of mathematical logic, N. Y., 1963. Yu. Gastev. Moscow.
Model (from Latin modulus - measure, sample, norm)
a) in the broadest sense - any mental or symbolic image of a simulated object (original). These include epistemological images (reproduction, display of a studied object or system of objects in the form of scientific descriptions, theories, formulas, systems of exercises, etc.), diagrams, drawings, graphs, plans, maps, etc.; b) a specially created or specially selected object that reproduces the characteristics of the object being studied. An important role in modern science is played by the so-called. symbolic M., allowing in the form of formulas, equations, graphs, etc. to display significant relationships between the objects, phenomena, and various processes being studied. An example of a signed equation is a differential equation in mathematics that describes (models) the flow of a class in time. physical process. Sign symbols are widely used in computer science to create appropriate computer programs; These include machines that reproduce the solution of complex problems that are specific to the activity of the human brain and are of a creative nature (M, referred to in computer science as artificial intelligence). Between the model and the object being studied (the original), which can be a very complex system, there must be similarities in some physical characteristics, or in structure, or in functions (see: Modeling).
In mathematical logic, mathematics is understood as the interpretation of a quasi-l. logical-mathematical propositions and their systems. In the theory of mathematics, developed in mathematical logic, a model is understood as an arbitrary set of elements with functions and predicates defined on it (see: Logical semantics). The concept of M. is one of the central and complex concepts of the theory of knowledge, since it is based on the concept of reflection, truth, similarity, difference, verisimilitude, etc.; its role in the methodology of science is enormous.
Dictionary of logic. - M.: Tumanit, ed. VLADOS center. A.A.Ivin, A.L.Nikiforov. 1997 .
Synonyms:See what a “model” is in other dictionaries:
model- and, f. modèle m., it. modello, German Model, floor model. 1. A sample from which a mold is removed for casting or reproduction in another material. BAS 1. Sharpen a model of dishes, make carvings, make molds 11/15/1717. Contract with Antonio Bonaveri... Historical Dictionary of Gallicisms of the Russian Language
- (model of aggregate demand and aggregate supply) macroeconomic model that considers macroeconomic equilibrium in conditions of changing prices in the short and long term... Wikipedia
1) reproduction of an object in reduced sizes; 2) a sitter who serves as a model for painting or sculpture; 3) a sample according to which any product is made. Dictionary of foreign words included in the Russian language. Pavlenkov F., 1907 ... Dictionary of foreign words of the Russian language
A model of the functioning of the human psyche used in socionics. This model hypothetically identifies eight functions in the psyche, schematically arranged in the form of a 2x4 rectangle in four horizontal levels and two vertical blocks.... ... Wikipedia
- [de], models, women. (French modele). 1. Sample, exemplary copy of some product (special). Product model. Dress model. 2. A reproduced, usually in reduced form, example of some kind of structure (technical). The model of car. 3. Type,... ... Ushakov's Explanatory Dictionary
See example... Synonym dictionary
model- A large-scale subject sample of an object or its parts, reflecting their structure and operation [Terminological dictionary of construction in 12 languages (VNIIIS Gosstroy USSR)] model Representation of a system, process, IT service, configuration item... Technical Translator's Guide
- (model) A simplified system used to simulate certain aspects of a real economy. Economic theory is forced to use simplified models: the real world economy is so large and complex that it is simply impossible... ... Economic dictionary
- (French modele, from Latin modulus measure, sample, norm), in logic and methodology of science an analogue (scheme, structure, sign system) defined. a fragment of natural or social reality, a creation of man. culture, conceptually theoretical... ... Philosophical Encyclopedia
An abstract or real representation of objects or processes that is adequate to the objects (processes) under study in relation to some specified criteria. For example, a mathematical model of layering (abstract model of the process), block diagram... ... Geological encyclopedia
- (IS LM model) A model that is often used as an extremely simple example of general equilibrium in macroeconomics. The IS curve shows the combinations of national income Y and interest rate r at which... ... Economic dictionary
Books
- Model. Vol. 3, Lee So in. Young Jay Su dreams of becoming an outstanding painter. Arriving in Europe to study, she leads the distracted life of a typical student, until one evening her friend brings her to her house...
Every modern person encounters the concepts of “object” and “model” every day. Examples of objects are both objects accessible to touch (book, earth, table, pen, pencil) and inaccessible (stars, sky, meteorites), objects of artistic creativity and mental activity (essay, poem, problem solving, painting, music and other). Moreover, each object is perceived by a person only as a single whole.
An object. Kinds. Characteristics
Based on the above, we can conclude that the object is part of the external world, which can be perceived as a single whole. Each object of perception has its own individual characteristics that distinguish it from others (shape, scope of use, color, smell, size, and so on). The most important characteristic of an object is the name, but for a complete qualitative description of it, the name alone is not enough. The more complete and detailed an object is described, the easier the process of recognizing it.
Models. Definition. Classification
In his activities (educational, scientific, artistic, technological), a person daily uses existing ones and creates new models of the external world. They allow you to form an impression of processes and objects that are inaccessible to direct perception (very small or, conversely, very large, very slow or very fast, very distant, and so on).
So, a model is an object that reflects the most important features of the phenomenon, object or process being studied. There can be several variations of models of the same object, just as several objects can be described by one single model. For example, a similar situation arises in mechanics, when different bodies with a material shell can be expressed, that is, by the same model (person, car, train, plane).
It is important to remember that no model can fully replace the depicted object, since it displays only some of its properties. But sometimes, when solving certain problems of various scientific and industrial trends, a description of the appearance of the model can be not only useful, but the only opportunity to present and study the characteristics of the object.
Scope of application of modeling items
Models play an important role in various spheres of human life: in science, education, trade, design and others. For example, without their use it is impossible to design and assemble technical devices, mechanisms, electrical circuits, machines, buildings, and so on, since without preliminary calculations and the creation of a drawing, the production of even the simplest part is impossible.
Models are often used for educational purposes. They are called visual. For example, from geography, a person gets an idea of the Earth as a planet by studying the globe. Visual models are also relevant in other sciences (chemistry, physics, mathematics, biology and others).
In turn, theoretical models are in demand in the study of natural sciences (biology, chemistry, physics, geometry). They reflect the properties, behavior and structure of the objects being studied.
Modeling as a process
Modeling is a method of cognition that includes the study of existing models and the creation of new ones. The subject of knowledge of this science is the model. are ranked according to various properties. As you know, any object has many characteristics. When creating a specific model, only the most important ones for solving the task are highlighted.
The process of creating models is artistic creativity in all its diversity. In this regard, virtually every artistic or literary work can be considered as a model of a real object. For example, paintings are models of real landscapes, still lifes, people, literary works are models of human lives, and so on. For example, when creating a model of an airplane in order to study its aerodynamic qualities, it is important to reflect in it the geometric properties of the original, but its color is absolutely unimportant.
The same objects are studied by different sciences from different points of view, and accordingly, their types of models for study will also differ. For example, physics studies the processes and results of the interaction of objects, chemistry studies the chemical composition, biology studies the behavior and structure of organisms.
Model regarding the time factor
With respect to time, models are divided into two types: static and dynamic. An example of the first type is a one-time examination of a person in a clinic. It displays a picture of his current state of health, while his medical record will be a dynamic model, reflecting changes occurring in the body over a certain period of time.
Model. Types of models relative to shape
As is already clear, models may differ in different characteristics. Thus, all currently known types of data models can be divided into two main classes: material (subject) and informational.
The first type conveys the physical, geometric and other properties of objects in material form (anatomical model, globe, building model, and so on).
The types differ in the form of implementation: symbolic and figurative. Figurative models (photos, drawings, etc.) are visual realizations of objects recorded on a specific medium (photo, film, paper or digital).
They are widely used in the educational process (posters), in the study of various sciences (botany, biology, paleontology and others). Sign models are implementations of objects in the form of symbols of one of the known language systems. They can be presented in the form of formulas, text, tables, diagrams, and so on. There are cases when, when creating a sign model (types of models convey specifically the content that is required to study certain characteristics of an object), several well-known languages are used at once. An example in this case are various graphs, diagrams, maps and the like, where both graphic symbols and symbols of one of the language systems are used.
In order to reflect information from various spheres of life, three main types of information models are used: network, hierarchical and tabular. Of these, the most popular is the last one, used to record various states of objects and their characteristic data.
Tabular implementation of the model
This type of information model, as mentioned above, is the most famous. It looks like this: it is a regular rectangular table consisting of rows and columns, the columns of which are filled with symbols of one of the famous signed languages of the world. Tabular models are used to characterize objects that have the same properties.
With their help, both dynamic and static models can be created in various scientific fields. For example, tables containing mathematical functions, various statistics, train schedules, and so on.
Mathematical model. Types of models
A separate type of information models are mathematical. All types usually consist of equations written in the language of algebra. The solution to these problems, as a rule, is based on the process of searching for equivalent transformations that contribute to the expression of a variable in the form of a formula. There are also exact solutions for some equations (quadratic, linear, trigonometric, and so on). As a result, to solve them it is necessary to use solution methods with an approximate specified accuracy, in other words, such types of mathematical data as numerical (half division method), graphic (graphing) and others. It is advisable to use the half division method only if the segment is known where the function takes on polar values at certain values.
And the method of constructing a graph is unified. It can be used both in the case described above, and in a situation where the solution can only be approximate and not exact, in the case of the so-called “rough” solution of equations.
Model - this is a material or ideal object that replaces the system under study and adequately reflects its essential aspects. The model of an object reflects its most important qualities, neglecting the secondary ones.
Computer model (English computer model), or numerical model (English computational model) is a computer program running on a separate computer, supercomputer or many interacting computers (computing nodes), implementing a representation of an object, system or concept in a form different from the real one, but close to an algorithmic description, including a set of data characterizing the properties of the system and the dynamics of their change over time.
When we talk about computer reconstruction, we mean the development of a computer model of a certain physical phenomenon or environment.
Physical phenomenon – the process of changing the position or state of a physical system. A physical phenomenon is characterized by a change in certain physical quantities interconnected. For example, physical phenomena include all known types of interaction of material particles.
Figure 1 shows a computer dynamic model of the change in the magnetic field formed by two magnets, depending on the position and orientation of the magnets relative to each other.
Picture 1- Computer dynamic model of magnetic field changes
The presented computer model reflects the dynamics of changes in magnetic field parameters using the method of graphical visualization using isolines. The construction of magnetic field isolines is carried out in accordance with physical dependencies that take into account the polarity of magnets at their specific location and orientation in the plane.
Figure 2 illustrates a computer simulation model of water flow in an open channel bounded by the walls of a long glass tray.
Figure 2- Computer simulation model of water flow in an open channel
Calculation of open flow parameters (free surface shape, water flow and pressure, etc.) in this model is performed in accordance with the laws of hydrodynamics of open flows. The calculated dependencies form the basis of the algorithm, according to which a model of water flow in a virtual three-dimensional space is built in real time. The presented computer model allows you to make geometric measurements of water surface marks at various points along the length of the stream, as well as determine water flow and other auxiliary parameters. Based on the data obtained, it is possible to study the real physical process.
The examples given consider computer simulation models with graphical visualization of a physical phenomenon. However, computer models may not contain visual or graphical information about the object of study. The same physical process or phenomenon can be represented as a set of discrete data, using the same algorithm on which the visual simulation model was built.
Thus, the main task of building computer models is a functional study of a physical phenomenon or process with obtaining comprehensive analytical data, and there can be many secondary tasks, including graphic interpretation of the model with the possibility of interactive user interaction with the computer model.
Mechanical system (or system of material points) is a collection of material points (or bodies that, according to the conditions of the problem, it turned out to be possible to consider as material points).
In technical sciences, media are divided into continuous (continuous) and discrete media. This division is to some extent an approximationor approximation, since physical matter is inherently discrete, and the concept of continuity (continuum) refers to such a quantity as time. In other words, such a “continuous” medium such as, for example, a liquid or gas consists of discrete elements - molecules, atoms, ions, etc., however, it is extremely difficult to mathematically describe the change in time of these structural elements, therefore it is quite reasonable to apply to such systems methods of continuum mechanics.
– Dvoretsky S.I., Muromtsev Yu.L., Pogonin V.A. Systems modeling. – M.: Publishing house. Center "Academy", 2009. – 320 p.
"Belov, V.V. Computer implementation of solving scientific, technical and educational problems: textbook / V.V. Belov, I.V. Obraztsov, V.K. Ivanov, E.N. Konoplev // Tver: TvSTU, 2015 . 108 s."
Modeling can be considered as replacing the object under study (the original) with its conventional image, description or other object, called a model, which provides behavior close to the original within the framework of certain assumptions and acceptable errors. Modeling is usually performed with the goal of understanding the properties of the original by examining its model, rather than the object itself. Of course, modeling is justified in the case when it is simpler than creating the original itself or when for some reason it is better not to create the original at all.
A model is understood as a physical or abstract object, the properties of which are in a certain sense similar to the properties of the object under study. In this case, the requirements for the model are determined by the problem being solved and the available means. There are a number of general requirements for models:
- Adequacy – a fairly accurate representation of the properties of an object;
- Completeness – providing the recipient with all the necessary information about the object;
- Flexibility – the ability to reproduce various situations over the entire range of changing conditions and parameters;
- The complexity of development must be acceptable for the available time and software.
Modeling is the process of constructing a model of an object and studying its properties by examining the model.
Thus, modeling involves 2 main stages:
- Model development;
- Studying the model and drawing conclusions.
At the same time, at each stage different problems are solved and essentially different methods and means are used.
In practice, various modeling methods are used. Depending on the method of implementation, all models can be divided into two large classes: physical and mathematical.
Mathematical modeling is usually considered as a means of studying processes or phenomena using their mathematical models.
Physical modeling means the study of objects and phenomena using physical models, when the process being studied is reproduced while preserving its physical nature or another physical phenomenon similar to the one being studied is used. In this case, physical models usually assume a real embodiment of those physical properties of the original that are significant in a particular situation. For example, when designing a new aircraft, a mock-up is created that has the same aerodynamic properties; When planning a development, architects prepare a model that reflects the spatial arrangement of its elements. In this regard, physical modeling is also called prototyping.
Semi-natural modeling is a study of controlled systems on modeling complexes with the inclusion of real equipment in the model. Along with real equipment, the closed model includes simulators of influences and interference, mathematical models of the external environment and processes for which a sufficiently accurate mathematical description is unknown. The inclusion of real equipment or real systems in the modeling circuit of complex processes makes it possible to reduce a priori uncertainty and explore processes for which there is no exact mathematical description. Using semi-natural modeling, studies are carried out taking into account small time constants and nonlinearities inherent in real equipment. When studying models with the inclusion of real equipment, the concept of dynamic modeling is used, when studying complex systems and phenomena - evolutionary, simulation and cybernetic modeling.
Obviously, the real benefit of modeling can only be obtained if two conditions are met:
- The model provides a correct (adequate) display of the properties of the original that are significant from the point of view of the operation under study;
- The model allows us to eliminate the problems listed above that are inherent in conducting research on real objects.