A hierarchy of mathematical models: towards understanding the physical processes in reservoirs

1993 ◽  
pp. 93-97
Author(s):  
B. Henderson-Sellers
Keyword(s):  
Mathematical Models ◽  
Physical Processes

scholarly journals The development of scientific outlook of students when teaching inverse problems for differential equations

2019 ◽  
Vol 16 (1) ◽  
pp. 46-55
Author(s):  
Viktor Semenovich Kornilov
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Research Work ◽  
Teaching Experience ◽  
Physical Processes ◽  
Mathematical Methods ◽  
Important Place ◽  
The World ◽  
Scientific Worldview

Problem and goal. Modern achievements of the world Science of nature and the world, physical laws and laws should be disclosed at an accessible level to University students. Among the scientific methods of research of physical processes and phenomena, an important place is the method of mathematical modeling, because mathematical models have scientific and cognitive potential and versatility (see, for example, [2-4]). The use of mathematical models of inverse problems for differential equations (IPDE) allows to effectively investigate many processes and phenomena occurring in the air, earth and water environment. It is not surprising that in some Russian universities in the physical and mathematical areas of training are taught IPDE in the form of a choice of courses. The goals and objectives of such teaching are set, as a result of which students would develop creative mathematical abilities, formed fundamental knowledge in the field of physical education, developed a scientific worldview. Methodology. The development of scientific outlook of students of physical and mathematical directions of preparation, as a result of teaching IPDE, ensured the successful will be implemented in practice, such conditions as: 1. the involvement of experts in the field IPDE with teaching experience at the university; 2. development of the content of lectures and practical classes on the basis of modern achievements of the theory of inverse and incorrect problems, taking into account the professional orientation of training students; 3. the implementation of the principles, methods and means of education IPDE; 4. involvement of students in research work in scientific seminars and participation in scientific conferences devoted to IPDE; 5. implementation of methodological approaches that allow students to develop the skills and abilities of independent analysis of applied and humanitarian nature of the results of research of IPDE. Results. In practical classes on the IPDE students acquire the ability and skills to apply effective approaches and mathematical methods of finding solutions to inverse problems, followed by a logical analysis of their solutions. As a result, students gain useful experience in the analysis of new information about the studied physical processes and phenomena, form new scientific knowledge about the world on the basis of which develop a scientific worldview. Conclusion. Developed, in the process of teaching IPDE, the scientific outlook helps students to understand that mathematical models IPDE are relevant to theory, experiment and philosophy - the basic methods of knowledge researchers; to understand the humanitarian value of mathematical models IPDE.

scholarly journals Transfer of lightning optical radiation into space through the cloud layer

2019 ◽  
Vol 55 (5) ◽  
pp. 85-93
Author(s):  
V. P. Busygin ◽  
L. D. Krasnokutskaya ◽  
I. Yu. Kuzmina
Keyword(s):  
Mathematical Models ◽  
Temporal Pattern ◽  
Optical Radiation ◽  
Cloud Layer ◽  
Secondary Source ◽  
Physical Processes ◽  
Initial Impulse ◽  
Amplitude Characteristics ◽  
Upper Boundary

We have developed mathematical models and performed simulations of transfer of short optical impulses through the cloud layer into space. The main cloud layer variables chosen are its vertical optical and geometrical depths. The physical processes behind the time-amplitude characteristics of the radiative field are studied. It is shown that the presence of a cloud layer results in a formation of a secondary source at the upper boundary of a cloud and in substantial distortions in the temporal pattern of the initial impulse.

scholarly journals THE METHOD OF FINDING ADEQUATE MATHEMATICAL MODELS DESCRIBING THE CHARACTERISTICS OF RADIO ENGINEERING DEVICES

2021 ◽  
Vol 2 (336) ◽  
pp. 145-151
Author(s):  
P. V. Boikachov ◽  
A. A. Yerzhan ◽  
V. O. Isaev ◽  
I. A. Dubovik ◽  
A. Marat
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Experimental Studies ◽  
Statistical Processing ◽  
Analytical Form ◽  
Physical Processes ◽  
Technical Object ◽  
Radio Engineering ◽  
Input Action ◽  
The One

The method of finding adequate mathematical models of radio engineering devices in an analytical form is proposed. RES, as a rule, is a very complex technical object that includes a large number of components with diverse connections between them, the hierarchy of construction of which can be represented in the form of a kind of pyramid. In this regard, there is a simulation of radio-electronic devices, which can be carried out at all levels of the "pyramid". Modeling at its lower levels, including semiconductor devices, links, cascades, etc., is reduced to describing their operation using a matrix, equation, formula, graph, or table. Such a mathematical model should, on the one hand, accurately reflect the physical processes in the object under study, and on the other - be suitable for use on a PC. In some cases, the mathematical model is the result of analytical or numerical analysis of the physical model of the object, but most often-experimental studies. Processing, including statistical processing, of the available data array that characterizes the operation of the cascade or element, is carried out using a PC. The operation of an object can also be defined in the form of its response or reaction to an input action without penetrating into the essence of the physical processes occurring inside the device.

scholarly journals Bandpass Sampling – An Opportunity To Stress The Importance Of In-Depth Understanding

2010 ◽  
Vol 1 (1) ◽  
pp. 43-46
Author(s):  
Harold P. E. Stern
Keyword(s):  
Mathematical Models ◽  
Sampling Theorem ◽  
Physical Processes ◽  
Complete Understanding ◽  
Bandpass Sampling ◽  
Nyquist Rate ◽  
Shannon’S Sampling Theorem ◽  
Bandpass Signals

Many bandpass signals can be sampled at rates lower than the Nyquist rate, allowing significant practical advantages. Illustrating this phenomenon after discussing (and proving) Shannon’s sampling theorem provides a valuable opportunity for an instructor to reinforce the principle that innovation is possible when students strive to have a complete understanding of physical processes and mathematical models. 

Physical processes in hysteretic electromechanical energy converters

2016 ◽  
Author(s):  
Останин ◽  
S. Ostanin
Keyword(s):  
Mathematical Models ◽  
Power Converters ◽  
Physical Processes ◽  
Design Problems ◽  
Method Of Calculation ◽  
Electric Drives ◽  
Electromechanical Energy ◽  
Energy Converters

In «Physical processes in hysteretic electromechanical energy converters» are developed questions of account of features of physical processes in such converters, the theory of indicated processes. We consider an approach to modelling and calculations of processes, perfection of existing and formation of new mathematical models of transducers. Is held the analysis of the adequacy of the proposed method of calculation and models of hysteretic electromechanical energy converters and them adaptation for solve design problems controlled electric drives on the basis of such power converters.

scholarly journals Some modifications on RCAM for getting accurate closed-form approximate solutions of Duffing- and Lienard-type equations

2019 ◽  
Vol 16 ◽  
pp. 8213-8225 ◽  
Author(s):  
Prakash Kumar Das ◽  
Debabrata Singh ◽  
Madan Mohan Panja
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Closed Form ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Nonlinear Ordinary Differential Equations ◽  
Physical Processes ◽  
Present Scheme ◽  
Adomian Decomposition

In this work, authors propose some modifications Adomian decomposition method to get some accurate closed form approximate or exact solutions of Duffing- and Li´enard-type nonlinear ordinary differential equations.Results obtained by the revised scheme have been exploited subsequently to derive constraints among parameters to get the solutions to be bounded. The present scheme appears to be efficient and may be regarded as the confluence of apparently different methods for getting exact solutions for a variety of nonlinear ordinary differential equations appearing as mathematical models in several physical processes.

Models of Thermodynamic Properties of Prominences

1979 ◽  
Vol 44 ◽  
pp. 349-355
Author(s):  
R.W. Milkey
Keyword(s):  
Thermodynamic Properties ◽  
Mass Transport ◽  
Emission Spectrum ◽  
Thermodynamic Parameters ◽  
Working Group ◽  
Physical Processes ◽  
Theoretical Concepts ◽  
Group 3 ◽  
Observational Techniques

The focus of discussion in Working Group 3 was on the Thermodynamic Properties as determined spectroscopically, including the observational techniques and the theoretical modeling of physical processes responsible for the emission spectrum. Recent advances in observational techniques and theoretical concepts make this discussion particularly timely. It is wise to remember that the determination of thermodynamic parameters is not an end in itself and that these are interesting chiefly for what they can tell us about the energetics and mass transport in prominences.

Sampling and analysis of the air-water interface with SEM and EDS of microlayers

1989 ◽  
Vol 47 ◽  
pp. 1004-1005
Author(s):  
Randall W. Smith ◽  
John Dash
Keyword(s):  
Heavy Metals ◽  
Surface Microlayer ◽  
Surface Films ◽  
Water Interface ◽  
Physical Processes ◽  
Infrared Spectroscopic Analysis ◽  
Eds Analysis ◽  
Air Water Interface ◽  
Significant Area ◽  
Bulk Chemical

The structure of the air-water interface forms a boundary layer that involves biological ,chemical geological and physical processes in its formation. Freshwater and sea surface microlayers form at the air-water interface and include a diverse assemblage of organic matter, detritus, microorganisms, plankton and heavy metals. The sampling of microlayers and the examination of components is presently a significant area of study because of the input of anthropogenic materials and their accumulation at the air-water interface. The neustonic organisms present in this environment may be sensitive to the toxic components of these inputs. Hardy reports that over 20 different methods have been developed for sampling of microlayers, primarily for bulk chemical analysis. We report here the examination of microlayer films for the documentation of structure and composition.Baier and Gucinski reported the use of Langmuir-Blogett films obtained on germanium prisms for infrared spectroscopic analysis (IR-ATR) of components. The sampling of microlayers has been done by collecting fi1ms on glass plates and teflon drums, We found that microlayers could be collected on 11 mm glass cover slips by pulling a Langmuir-Blogett film from a surface microlayer. Comparative collections were made on methylcel1ulose filter pads. The films could be air-dried or preserved in Lugol's Iodine Several slicks or surface films were sampled in September, 1987 in Chesapeake Bay, Maryland and in August, 1988 in Sequim Bay, Washington, For glass coverslips the films were air-dried, mounted on SEM pegs, ringed with colloidal silver, and sputter coated with Au-Pd, The Langmuir-Blogett film technique maintained the structure of the microlayer intact for examination, SEM observation and EDS analysis were then used to determine organisms and relative concentrations of heavy metals, using a Link AN 10000 EDS system with an ISI SS40 SEM unit. Typical heavy microlayer films are shown in Figure 3.

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