scholarly journals Mathematical Modelling of Aquatic Ecosystem

2015 ◽  
Vol 3 ◽  
pp. 92
Author(s):  
Sharif E. Guseynov ◽  
Jekaterina V. Aleksejeva
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Aquatic Ecosystem ◽  
Initial Boundary ◽  
Mathematical Physics ◽  
Evolutionary Models ◽  
Dynamic Parameters ◽  
Aqueous Systems ◽  
Boundary Problems ◽  
Qualitative Models

<p class="R-AbstractKeywords"><span lang="EN-US">In present paper we consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous systems in Latvia. All the proposed models are the evolutionary models: all they are nonstationary and continuous qualitative models having the dynamic parameters and aimed at analysis, evaluation and forecast of aqueous systems (reservoirs, lakes and seas). In constructing these mathematical models as research tools classic apparatus of differential equations (both ODE and PDE) as well as apparatus of mathematical physics were used</span><span lang="EN-US">. </span></p>

scholarly journals Complex Mathematical Models for Analysis, Evaluation and Prediction of Aqueous and Atmospheric Environment of Latvia

2012 ◽  
Vol 13 (1) ◽  
pp. 57-74
Author(s):  
Sharif Guseynov ◽  
Eugene Kopytov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Models ◽  
Environmental Pollution ◽  
Initial Boundary ◽  
Aqueous System ◽  
The Other ◽  
Atmospheric Environment ◽  
Boundary Problems ◽  
Atmospheric Systems

Complex Mathematical Models for Analysis, Evaluation and Prediction of Aqueous and Atmospheric Environment of Latvia In present paper the authors consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous (3 models) and atmospheric systems (2 models) in Latvia. All the proposed models are described in terms of differential equations theory (using both ordinary differential equations and partial differential equations) and are regarded to be the evolutional models. Two of the three aqueous system models being studied are intended to describe the natural aquatic media ecosystems while the other models are aimed at studying environmental pollution processes.

It is not evolutionary models, but models in general that social science needs

2006 ◽  
Vol 29 (4) ◽  
pp. 351-352 ◽  
Author(s):  
Bruce Bridgeman
Keyword(s):  
Social Sciences ◽  
Social Science ◽  
Mathematical Models ◽  
Cultural Models ◽  
Genetic Models ◽  
Biological Information ◽  
Evolutionary Models ◽  
Cultural Information

Mathematical models are potentially as useful for culture as for evolution, but cultural models must have different designs from genetic models. Social sciences must borrow from biology the idea of modeling, rather than the structure of models, because copying the product is fundamentally different from copying the design. Transfer of most cultural information from brains to artificial media increases the differences between cultural and biological information.

scholarly journals MODIFYING MATHEMATICAL MODELS FOR CALCULATING OPERATIONAL CHARACTERISTICS OF DIESEL ENGINES BURNING RME BIOFUELS / MATEMATINIŲ MODELIŲ PRITAIKYMAS DYZELIŲ, DIRBANČIŲ RME BIODEGALAIS, DARBO PROCESUI IR EKSPLOATACINIAMS RODIKLIAMS SKAIČIUOTI / ДОРАБОТКА МАТЕМАТИЧЕСКИХ МОДЕЛЕЙ РАСЧЕТА ПОКАЗАТЕЛЕЙ РАБОТЫ ДИЗЕЛЯ НА БИОДИЗЕЛИНАХ РРМЭ

Transport ◽  
2011 ◽  
Vol 26 (1) ◽  
pp. 50-60 ◽  
Author(s):  
Sergejus Lebedevas ◽  
Galina Lebedeva ◽  
Kristina Bereišienė
Keyword(s):  
Diesel Engine ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Diesel Engines ◽  
Fuel Injection ◽  
Internal Heat ◽  
Computer Programs ◽  
Toxic Substances ◽  
Load Range ◽  
Operational Characteristics

The article considers and solves the problems of adapting the mathematical models, used in calculating operational characteristics of diesel engines burning mineral diesel oil, to engines converted to RME biofuels. The analysis of mathematical models of calculating the main technical and economic characteristics of diesel engines as well as the parameters of the in-cylinder process and the concentration of toxic substances in the exhaust gases is performed. The need for adjusting the calculation algorithms is also demonstrated. The computer programs based on single-zone thermodynamic models are used in the research. The programs of mathematical modelling are modified, i.e. supplemented with the algorithm for calculating energy characteristics of the combustion products (e.g. specific heat capacity, internal heat, the lower calorific value, etc.). Based on the computer programs, modified for examining diesel engines burning biofuels, the computer-aided mathematical modelling experiment is carried out. The results of modelling are compared with the data obtained in testing the diesel engine 1A41. The mathematical modelling performed demonstrates the accuracy acceptable for solving practical problems: the difference between the obtained calculation results and diesel engine testing data for the load range of (1.0÷0.5) Pi nom does not exceed ± 5÷7%. Higher accuracy of modelling the characteristics of diesel engines, operating in the low- and medium-load modes, may be accounted for by the adjustment of the algorithm for calculating the induction period and the on-set phase of fuel injection. Santrauka Publikacijoje pateikti dyzelio darbo proceso ir eksploatacinių rodiklių skaičiavimo matematinių modelių tobulinimo rezultatai, siekiant matematinius modelius pritaikyti dyzeliui dirbant riebiųjų rūgščių metilesterių, taip pat RME, biodegalais. Atlikta skaičiavimo algoritmų analizė ir pagrįsti pagrindiniai jų tobulinimo aspektai. Sukurtas kompiuterinis programinis modelis, skirtas darbinio kūno dyzelio cilindre energiniams parametrams skaičiuoti (specifinei šilumai, vidinei energijai), dyzeliui dirbant plačiąja elementinės cheminės sudėties biodegalų gama. Atliktas 1A41 dyzelio techninių ir ekonominių bei ekologinių rodiklių modeliavimas kompiuteriu, naudojant patobulintus matematinius modelius. Parodytas gautų rezultatų, pakankamų praktiniams uždaviniams spręsti, tikslumas: dyzeliui dirbant artimos nominaliosios apkrovos režimais (1,0÷0,5) Pi nom skirtumas tarp skaičiavimo ir dyzelio motorinių tyrimų rezultatų neviršija ±5÷7%. Dyzeliui dirbant mažos apkrovos režimu, matematinio modeliavimo rezultatų adekvatumo didinimas susijęs su kuro įpurškimo fazės bei savaiminio užsiliepsnojimo indukcijos periodo skaičiavimo algoritmo tobulinimu. Резюме Рассмотрены и решены задачи адаптации математических моделей расчета показателей дизеля при переводе их работы с минерального дизелина на биодизелины метилового эфира рапсового масла (МЭРМ). Выполнен анализ и дано обоснование направлений доработки расчетных алгоритмов ряда однозонных термодинамических математических моделей, используемых в практике исследования эксплуатационных показателей, параметров индикаторного процесса и эмиссии токсичных компонентов в выхлопных газах дизелей. В форме программного модуля составлен алгоритм расчета энергетических параметров рабочего тела в цилиндре (удельной теплоемкости, теплоты сгорания, внутренней энергии) для топлив с широким элементарным химическим составом. С использованием доработанных компьютерных программ выполнен широкий расчетный эксперимент и сопоставлены его результаты с данными моторных стендовых испытаний одноцилиндрового отсека дизеля 1А41. Показана приемлемая для решения практических задач точность математического моделирования: для нагрузочных режимов (1÷0,5) Pmi расхождения расчетных и экспериментальных значений параметров работы дизеля не превышают ±5÷7%. Повышение качества моделирования показателей дизеля на режимах средних и малых нагрузок связано с уточнением алгоритма расчета периода индукции и фазы начала видимого горения топлива в цилиндре.

A mass-conserved tumor invasion system with quasi-variational degenerate diffusion

2021 ◽  
pp. 1-66
Author(s):  
Akio Ito
Keyword(s):  
Hilbert Space ◽  
Tumor Cells ◽  
Tumor Invasion ◽  
Real Hilbert Space ◽  
Initial Boundary ◽  
Inner Product ◽  
Boundary Problems ◽  
Theory Of Evolution ◽  
Cross Diffusion ◽  
Variational Structure

This paper deals with a nonlinear system (S) composed of three PDEs and one ODE below: [Formula: see text] The system (S) was proposed as one of the mathematical models which describe tumor invasion phenomena with chemotaxis effects. The most important and interesting point is that the diffusion coefficient of tumor cells, denoted by [Formula: see text], is influenced by both nonlocal effect of a chemical attractive substance, denoted by [Formula: see text], and the local one of extracellular matrix, denoted by [Formula: see text]. From this point, the first PDE in (S) contains a nonlinear cross diffusion. Actually, this mathematical setting gives an inner product of a suitable real Hilbert space, which governs the dynamics of the density of tumor cells [Formula: see text], a quasi-variational structure. Hence, the first purpose in this paper is to make it clear what this real Hilbert space is. After this, we show the existence of strong time local solutions to the initial-boundary problems associated with (S) when the space dimension is [Formula: see text] by applying the general theory of evolution inclusions on real Hilbert spaces with quasi-variational structures. Moreover, for the case [Formula: see text] we succeed in constructing a strong time global solution.

Mathematical modelling.

2021 ◽  
Author(s):  
Ed Rutgers Durner
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Growth And Development ◽  
Fertilizer Recommendations ◽  
Mathematical Equations

Abstract Plants are studied to understand their growth and development so that their quality and productivity can be optimised. Models are developed that can be simple and descriptive, or quite complex with numerous mathematical equations; their level of complexity is linked to their purpose. This summary serves as an introduction to mathematical models in horticulture. It is not a manual for modelling itself, but rather an overview of how important mathematical models are in horticultural production. Mathematical models are used extensively in horticulture both extrinsically, i.e. when calculating chilling hour accumulations and intrinsically, i.e. when applying fertilizer to a crop. In chilling calculations, developed models are used directly. Fertilizer recommendations were probably developed using a mathematical model. The first part of this article discusses models in general and reviews general characteristics of mathematical models. The second part outlines the major uses of mathematical modelling in modern horticultural production. Presentations of specific models are limited in order to present a general discussion of models with examples that will interest most horticulturists.

scholarly journals Air Temperature Control System in a Building on the Basis of Mathematical Modelling

2018 ◽  
Vol 155 ◽  
pp. 01041 ◽  
Author(s):  
Aleksandr Pilipenko ◽  
Sergei Petrov
Keyword(s):  
Computer Simulation ◽  
Control System ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Air Temperature ◽  
Temperature Control ◽  
Automated System ◽  
Temperature Control System ◽  
Heating Systems ◽  
The Cost

In the article the authors solve a crucial objective of reducing the cost of heating services through the introduction of a system, controlling boilers and heating devices, based on modelling of the building and predicting heating systems functioning and operation. The authors describe the method of mathematical modelling of heating systems of the building and represent the developed mathematical models, pledged and installed into the developed automated system. The authors have offered an automated system of dispatch control of the boilers with the elements of computer simulation and modelling.

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