Journal articles: 'Physical and mathematical model'

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Rajić, Dušan. "Mathematical-physical model of solving inventive problems." FME Transactions 49, no. 3 (2021): 726–33. http://dx.doi.org/10.5937/fme2103726r.

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The spatial-temporal LT-contradiction matrix is an inventology tool that enables exact calculations of certain parameters in an engineering system through mathematical-physical modeling. It objectifies the decision-making process and creates the preconditions to finding an adequate resource (X-element) with a higher probability, and thus to reach a higher degree of ideality solution (HDIS) of an inventive problem as well. Any engineering system that generates an inventive problem can be described using the LT-contradiction matrix. By crossing the appropriate parameters in the LT-contradiction matrix, with the help of the differential geometry of the tensor, a qualitative-quantitative analysis and calculation of relevant degree all contradictions that exist in the inventive problem can be performed. After that, the path to finding the physical characteristics of the X-element in the mathematical-physical model is facilitated, i.e. finding a real resource that will enable a HDIS of the inventive problem in an engineering system.

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Kézi, Csaba. "Teaching the Analysis of Newton’s Cooling Model to Engineering Students." International Journal of Engineering and Management Sciences 8, no. 2 (2023): 63–68. http://dx.doi.org/10.21791/ijems.2023.2.7.

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To apply mathematical methods to physical or other real life problem, we have to formulate the problem in mathematical terms. It means that, we have to construct the mathematical model for the problem. Many physical problems shows the relationships between changing quantities. The rates of change are represented mathematically by derivatives. In this case the mathematical models involve equations relating an unknown function and one or more of its derivatives. These equations are the differential equations. In this article, teaching the analysis of Newton's cooling model to engineering students is presented as one of the applications of separable differential equations.

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Gumnitsky, Jaroslav, Lubov Venger, Vira Sabadash, Dmytro Symak, Anna Hyvlud, and Zoriana Gnativ. "Physical and Mathematical Models of Target Component Extraction from Rectlinear Capillaries." Chemistry & Chemical Technology 16, no. 1 (2022): 112–17. http://dx.doi.org/10.23939/chcht16.01.112.

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The extraction of the solid component from the rectilinear capillary has been investigated. The presence of two extraction zones (convective and molecular diffusion) was confirmed. The effect of the system vacuumizing on the extraction rate has been studied. The convection zone during vacuumizing was found to be increased due to the appearance of the vapor phase bubbles. The mass transfer coefficients for the convective zone have been determined. A mathematical model of the molecular diffusion stage is given, taking into account the nonlinear change in the component concentration in the liquid due to the displacement of the extraction boundary. The molecular diffusion coefficients in the capillary have been determined.

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Kwaghkor, Lubem M., A. Mohammed, and E. V. Nyamtswam. "A MATHEMATICAL MODEL FOR DIABETES MANAGEMENT." FUDMA JOURNAL OF SCIENCES 6, no. 5 (2022): 36–40. http://dx.doi.org/10.33003/fjs-2022-0605-1091.

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Treating and controlling of diabetes is called diabetes management. The management of diabetes can be done through improvement of the patient dietary knowledge, attitudes, and practices. This research work is aimed at introducing dietary (diet restriction) to an earlier model for the detection and control of diabetes: to study the effect of physical exercise and dietary on excess glucose, insulin and epinephrine concentrations in the blood in managing diabetes. The resulting model is found to be uniformly and asymptotically stable. The result shows that when physical exercise is combined with recommended dietary in the management of diabetes, the excess glucose, insulin and epinephrine concentrations returns to their normal level faster with time compared to when only physical exercise is used as a control measure. Hence, it is recommended that in the management of diabetes, both physical exercise and dietary should be used as control measures

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Pankratova, Nataliya, and Igor Golinko. "Electric heater mathematical model for cyber-physical systems." System research and information technologies, no. 2 (September 14, 2021): 7–17. http://dx.doi.org/10.20535/srit.2308-8893.2021.2.01.

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The article discusses the heat and mass transfer dynamic model for an electric heater with lumped parameters, which allows transient processes simulation for the main influences. The proposed model is recommended to be used in cyber-physical systems for forecasting and evaluating the effectiveness of control systems integrated into a single information management system. The developed model can be used by specialists for the analysis and synthesis of control systems for balanced ventilation systems or industrial air conditioners. As an example, a numerical simulation of transient processes along the action main channels for an electric heater HE 36/2 manufactured by VTS CLIMA was carried out. The significant advantage of the proposed model is the possibility for using it for the synthesis and analysis of multidimensional control systems.

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Bergamasco, A., L. Cavaleri, and P. Sguazzero. "Physical and mathematical analysis of a wind model." Il Nuovo Cimento C 9, no. 1 (1986): 1–16. http://dx.doi.org/10.1007/bf02508048.

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Feofanova, S. S., and E. Yu Zaykova. "Territorial physical and mathematical model of stormwater management." E3S Web of Conferences 403 (2023): 04003. http://dx.doi.org/10.1051/e3sconf/202340304003.

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Climate change reduction and adaptation policies are being implemented worldwide through stormwater management in urban areas. Rational use of stormwater could influence the decrease of the "heat island" effect and "cool down" cities. The authors plan to analyze the features of green spaces in the city and demonstrate by a concrete example the opportunity to implement elements of green infrastructure. For widespread use in urban areas, the authors created physical and mathematical model of the territory and recommend variants with four main types of green structures: soil, biotope, shrub, tree. The authors' research proves that with correct analysis of the terrain from the point of view of the terrain from the point of view of urban planning, engineering and landscape, with responsible selection of plants of local flora, bio-drainage systems can work well even in regions with a cold climate, such as Russia.

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Kandic, Aleksandar. "Mathematical model of explanation of the world’s structure in Plato’s Timaeus." Theoria, Beograd 62, no. 2 (2019): 163–88. http://dx.doi.org/10.2298/theo1902163k.

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Plato?s cosmological dialogue The Timaeus initiates, among other things, the question of the status of mathematical entities: do they exist completely independently of the physical world whose structure they supposedly explain, are they present in a certain sense within the physical world, or are they, perhaps, exclusively psychological in nature. The author of the paper critically examines Johansen?s interpretation according to which the inherent structure of the human psyche, in the case of Plato?s Timaeus, is already mathematically ideal. Although Johansen?s interpretation is pervasive and well-grounded, the relationship between mathematical and sensory entities is considered mainly in the context of astronomy, disregarding Plato?s theory of micro-structures (the so-called geometric atomism). Thus, the author confronts Johansen?s interpretation with the opinions of other influential researchers of ancient philosophy, such as Cornford, Vlastos, Popper, Lloyd, Brisson, as well as the philosophers of the ancient era, Proclus, Aristotle, and others, in an effort to develop an interpretation that is as close as possible to the whole of Plato?s text. It seems that, when it comes to Plato?s Timaeus, one cannot discuss about the psychological origin of the mathematical model of explanation of natural phenomena without realizing that, in a quite complicated way, such mathematical model possesses a physical aspect as well. Plato himself, at the end of The Timaeus, claims that psychological disorders are caused by disruptions of the mathematically ideal proportions of bodily parts of the human organism (86b), which is only one of his claims that points to the psychophysical nature of mathematical entities.

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Vsevolod Horyachko, Vsevolod, Oksana Hoholyuk, Taras Ryzhyi, and Serhiy Rendzinyak. "Mathematical model of electrical activity of biological network areas." Computational Problems of Electrical Engineering 9, no. 2 (2019): 8–12. http://dx.doi.org/10.23939/jcpee2019.02.008.

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In the paper, the mathematical model describing the generation of action potential and propagation of an impulse in the neuron's filaments on the basis of the analysis of parametric electriс circuits with distributed parameters and the mathematical model of synaptic interneuron connections are proposed. Developed models allow taking into account the influence of such factors as geometric, physical and chemical parameters of the neuron's filaments and the presence of different neurotransmitters in chemical synapses on transmitting a neural impulse. Further, such models can be used for investigating the conditions of neuron firing at spatial and time integration of input signals, as well as for the simulation of neuromuscular junctions.

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Šumarac, D., Z. Perović, D. Vatić, T. Curić, I. Nurković, and M. Cao. "Preisach Mathematical Model of Hysteresis." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 15, no. 2 (2023): 61–72. http://dx.doi.org/10.46793/spsunp2302.061s.

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Hysteretic nonlinear phenomena occur in many physical processes: ferromagnetism, adsorption, cyclic plasticity in mechanics, phase transformations, economics, etc. It is characterized by the fact that the same instantaneous values of input can give different outputs depending on the history of the input applied. It means that the relationship is not only nonlinear but also multivalued making it very difficult to model and control. In this paper, accent was given to the application to mechanics i.e. to cyclic plasticity of trusses.

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Cook, D. P., and J. W. Evans. "A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part I. The mathematical model." Metallurgical and Materials Transactions B 26, no. 1 (1995): 1263–70. http://dx.doi.org/10.1007/bf02654011.

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Milyukov, V. E., and T. S. Zharikova. "HYDRODYNAMIC FUNDAMENTALS FOR PHYSICAL-MATHEMATICAL MODEL OF MYOCARDIUM CIRCULATION." Russian Journal of Cardiology, no. 8 (January 1, 2016): 92–95. http://dx.doi.org/10.15829/1560-4071-2016-8-92-95.

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Bernard, Florent, Viktor Fischer, and Boyan Valtchanov. "Mathematical model of physical RNGs based on coherent sampling." Tatra Mountains Mathematical Publications 45, no. 1 (2010): 1–14. http://dx.doi.org/10.2478/v10127-010-0001-1.

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ABSTRACT Random number generators represent one of basic cryptographic primitives used in creating cryptographic protocols. Their security evaluation represents very important part in the design, implementation and employment phase of the generator. One of important security requirements is the existence of a mathematical model describing the physical noise source and the statistical properties of the digitized noise derived from it. The aim of this paper is to propose the model of a class of generators using two jittery clocks with rationally related frequencies. The clock signals with related frequencies can be obtained using phase-locked loops, delay-locked loops or ring oscillators with adjusted oscillation periods. The proposed mathematical model is used to provide entropy per bit estimators and expected bias on the generated sequence. The model is validated by hardware experiments.

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Landberg, Lars. "A mathematical look at a physical power prediction model." Wind Energy 1, no. 1 (1998): 23–28. http://dx.doi.org/10.1002/(sici)1099-1824(199809)1:1<23::aid-we9>3.0.co;2-9.

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Cook, D. P., S. Nishioka, and J. W. Evans. "A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part II. Results from a physical model and testing of the mathematical model." Metallurgical and Materials Transactions B 26, no. 1 (1995): 1271–79. http://dx.doi.org/10.1007/bf02654012.

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Evans, J. W., B. Q. Li, and D. P. Cook. "2D and 3D mathematical models and a physical model of electromagnetic casters." ISIJ International 29, no. 12 (1989): 1048–55. http://dx.doi.org/10.2355/isijinternational.29.1048.

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Zhang, Yuman, Gang Dou, Zhao Sun, Mei Guo, and Yuxia Li. "Establishment of Physical and Mathematical Models for Sr0.95Ba0.05TiO3Memristor." International Journal of Bifurcation and Chaos 27, no. 09 (2017): 1750148. http://dx.doi.org/10.1142/s0218127417501486.

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The Sr[Formula: see text]Ba[Formula: see text]TiO3(SBT) memristor is prepared using the monolayer Sr[Formula: see text]Ba[Formula: see text]TiO3nano-film structure. In order to apply it into the nonlinear circuit design, the SBT memristor is modeled in the paper. The voltage-controlled physical model of the SBT memristor is established based on its working mechanism. Due to the difficulty in determining the accurate parameters of the voltage-controlled physical model, a flux-controlled mathematical model of the SBT memristor is proposed, and its equivalence relation with the voltage-controlled physical model is proved. Moreover, the parameters of the flux-controlled mathematical model are determined by means of the quadratic polynomial interpolation method using the experimentally measured voltage and current data of the SBT memristor. The simulated [Formula: see text]–[Formula: see text] characteristic curve using the flux-controlled mathematical model coincides well with the measured [Formula: see text]–[Formula: see text] characteristic curves. The result indicates that the flux-controlled mathematical model with the definite parameters can be used to characterize the behaviors of the physical SBT memristor and guide its application to nonlinear circuit design.

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SHESTOPALOFF, YURI K. "A MATHEMATICAL MODEL OF THE PHYSICAL GROWTH MECHANISM AND GEOMETRICAL CHARACTERIZATION OF GROWING FORMS." International Journal of Biomathematics 04, no. 01 (2011): 35–53. http://dx.doi.org/10.1142/s1793524511001180.

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The article introduces a mathematical model of the physical growth mechanism which is based on the relationships of the physical and geometrical parameters of the growing object, in particular its surface and volume. This growth mechanism works in cooperation with the biochemical and other growth factors. We use the growth equation, which mathematically describes this mechanism, and study its adequacy to real growth phenomena. The growth model very accurately fits experimental data on growth of Amoeba, Schizosaccharomyces pombe, E.coli. Study discovered a new growth suppression mechanism created by certain geometry of the growing object. This result was proved by experimental data. The existence of the growth suppression phenomenon confirms the real workings and universality of the growth mechanism and the adequacy of its mathematical description. The introduced equation is also applicable to the growth of multicellular organisms and tumors. Another important result is that the growth equation introduces mathematical characterization of geometrical forms that can biologically grow. The material is supported by software application, which is released to public domain.

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Ntaganda, Jean Marie, Froduald Minani, Wellars Banzi, et al. "Analysis of physical activity effects on plasma glucose–insulin system dynamics: A mathematical model." Transactions of the Institute of Measurement and Control 43, no. 14 (2021): 3272–81. http://dx.doi.org/10.1177/01423312211022867.

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The main objective of this paper is to understand and analyse the effect of physical activity on plasma glucose and plasma insulin levels through mathematical modelling. Energy for the human body during physical activity is provided by glucose as sugar, while insulin as hormone supports the absorption of this glucose. Furthermore, glucose and insulin are interrelated physiologically by some parameters that we estimate mathematically by using nonlinear optimization and data collected in Rwanda. Research in this direction has been done by, for example Anirban and colleagues, who developed a dynamic model of exercise effect on plasma glucose and insulin levels. As a benchmark, the results of numerical simulation obtained in this paper have been compared with those of Anirban and colleagues to test the efficiency of our mathematical model. We have concluded that the results of those two separate mathematical models are in good accordance and that the proposed mathematical model allows further investigation of the effects of physical activity on the dynamics of the glucose–insulin system. Moreover, we have implemented a particle filtering algorithm for estimation of glucose and insulin in internal parts of the body such as heart and liver by using measurements from peripheral tissues as noisy data because taking blood samples from all parts of the body is practically and clinically impossible.

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PEDYASH, Volodymyr. "INVESTIGATION OF THE MATHEMATICAL MODEL OF OPTICAL FIBER." Herald of Khmelnytskyi National University. Technical sciences 317, no. 1 (2023): 167–73. http://dx.doi.org/10.31891/2307-5732-2023-317-1-167-173.

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Fiber optic transmission systems are the main type of systems for building telecommunication networks. The transponders of modern optical transmission systems implement efficient modulation and coding methods, which can significantly increase the receiver sensitivity and increase the length of the regeneration area. The task to define the quality characteristics of optical channels occurs during the design of such systems. To solve this problem, it is necessary to develop a mathematical model of the transmission system and perform a simulation using it. One of the main blocks of the system is the propagation medium (optical fiber). The optical fiber model is based on the nonlinear Schrödinger differential equation. Several groups of modeling methods have been developed on its basis. The most widespread is the Fourier method of splitting by physical factors, as it has a simple algorithm structure, high computing speed, and high accuracy. This method is recursive, so to reduce the number of iterations, it is reasonable to use the well-known method of nonlinear phase rotation. To check the functionality of the developed program code, it is recommended to perform testing in several stages. At the first stage, it is proposed to check the accuracy of the distortion of chromatic dispersion. Single pulses of simple shape, such as Gaussian pulses, should be used as a test signal. By calculating the pulse shape using theoretical expressions and comparing them with the modeling results, the accuracy of the optical fiber modeling algorithm can be verified. The next step in verifying the fiber model is to evaluate the accuracy of the simultaneous introduction of dispersion and nonlinear distortions. For this purpose, it is proposed to analyze the propagation of pulses of optical solitons of the first and higher orders.

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Sharland, S. M., and P. W. Tasker. "A mathematical model of crevice and pitting corrosion—I. The physical model." Corrosion Science 28, no. 6 (1988): 603–20. http://dx.doi.org/10.1016/0010-938x(88)90027-3.

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Tong, T. O., M. C. Kekana, M. Y. Shatalov, and S. P. Moshokoa. "Numerical Investigation of Brusselator Chemical Model by Residual Function Using Mathematica Software." Journal of Computational and Theoretical Nanoscience 17, no. 7 (2020): 2947–54. http://dx.doi.org/10.1166/jctn.2020.9324.

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In recent years, mathematical models have been developed to illustrate some physical phenomena in science and engineering. One of those systems of nonlinear differential equations is Brusselator chemical model. A mathematical template of checking accuracy of from black-boxes has been developed and investigated. Brusselator model is used as case study as its analytical solution is non-existence. The algorithms investigated from Mathematica software includes Adams method, Backward differential formula (BDF) and Implicit Runge-Kutta method which works well on stiff systems. The graphical results are on interval of 0 ≤ t ≤ 30.

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Zeng, Yunhui, Yingxia Liu, Lubin Wu, et al. "Evaluation and Analysis Model of Wine Quality Based on Mathematical Model." Studies in Engineering and Technology 6, no. 1 (2018): 6. http://dx.doi.org/10.11114/set.v6i1.3626.

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This paper takes wine quality evaluation as the research object, establishes the analysis and evaluation model of wine quality, and explores the influence of physical with chemical indicators of wine grapes and wine on the wine quality. Firstly, the Mann-Whitney U test is used to analyze the wine evaluation results of the two wine tasters, and it is found that the significant difference between the two is small. Then this paper uses the Cronbach Alpha coefficient method to analyze the credibility of the two groups of data. It is found that the credibility of the first group of wine scores is significantly greater than that of the second group and the white wine scores are more reliable than the red wine. Therefore, the first set of data and white wine can be applied for follow-up studies. Next, the principal component analysis is used to extract the main indicators and calculate the factor coefficients as the Ward method in cluster analysis is used to classify the wine into four grades according to the quality score of the wine. Then, based on the extracted principal components that is physical with chemical indicators, this paper does the multiple linear regression analysis of wine quality, and takes the influence of aromatic substances on the aroma of wine in physical with chemical indicators as an example. Regression analysis shows that there is a positive correlation linear relationship between the scores of the aroma of wine and C2H6O, C6H12O2, C3H8O, C11H24, C7H12O2, C5H10O2 and C10H16. It can be judged that the aromatic substances in the wine such as C2H6O have a regular influence on the odor of the wine, and it is inferred that other physical and chemical properties have a similar regular relationship with the wine quality. This provides an effective reference for the analysis and evaluation of wine quality by using physical with chemical indicators such as aromatic substances in wine in the future.

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Fu, Hai Yang, Bin Hu, Xiang Dong Jia, and Hui Fang. "Study on the Physical Model and Experiments of MIMO Theory." Applied Mechanics and Materials 347-350 (August 2013): 1868–73. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.1868.

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The present researches of the MIMO theory only proved that channel capacity (CC) could be increased on the setting mathematical model in base-band by the space division multiplex (SDM) principle. But the reasonable physical model matching to that mathematical model has not been given by those researches, resulting in that the SDM could not be realized in MIMO system. So that the CC formula of MIMO system deduced by that mathematical model could not be realized physically. The infeasibility of MIMO system would be discussed in the paper in the aspects of physical characteristic of antenna, radio beam patterns of many kinds of antenna array, the un-reasonability of the MIMO physical model, the experiments of MIMO, and etc.

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Berenguer, I., P. A. Madsen, M. Rubjerg, and A. Kej. "MATHEMATICAL AND PHYSICAL WAVE DISTURBANCE MODELLING COMPLIMENTARY TOOLS." Coastal Engineering Proceedings 1, no. 20 (1986): 3. http://dx.doi.org/10.9753/icce.v20.3.

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This paper presents comparisons between physical and numerical model reproductions on the basis of comprehensive wave disturbance studies of a major Spanish port. Mathematical modelling has reached in many cases a degree of reliability comparable to that of a physical model, but it is essential that both types of modelling systems are validated against measurements.

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Okhrimenko, Viacheslav, and Maiia Zbіtnieva. "Mathematical Model of Tubular Linear Induction Motor." Mathematical Modelling of Engineering Problems 8, no. 1 (2021): 103–9. http://dx.doi.org/10.18280/mmep.080113.

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Problem of calculation of distribution of magnetic field induction in clearance of tubular linear induction motor (TLIM) is considered. Mathematical model is represented by Fredholm integral equations of second kind for complexes of electric field strength and density of coupled magnetization currents at interface of environments. Algorithm of calculation of distribution of magnetic field induction in TLIM clearance has been developed. Dependence of magnetic field induction in motor clearance on value of pole division is investigated. There is area of optimum pole pitch. Reliability of results of calculations on mathematical model is confirmed by their comparison with results obtained on physical model. Calculated dependence of induction on thickness of runner's iron circuit also has extreme character. Given model can be used at design stage of TLIM. Model allows calculating its optimal geometric dimensions based on criterion of maximum induction in motor clearance, taking into account physical properties of applied materials.

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Geiser, J., V. Buck, and M. Arab. "Model of PE-CVD Apparatus: Verification and Simulations." Mathematical Problems in Engineering 2010 (2010): 1–32. http://dx.doi.org/10.1155/2010/407561.

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In this paper, we present a simulation of chemical vapor deposition with metallic bipolar plates. In chemical vapor deposition, a delicate optimization between temperature, pressure and plasma power is important to obtain homogeneous deposition. The aim is to reduce the number of real-life experiments in a given CVD plasma reactor. Based on the large physical parameter space, there are a hugh number of possible experiments. A detailed study of the physical experiments in a CVD plasma reactor allows to reduce the problem to an approximate mathematical model, which is the underlying transport-reaction model. Significant regions of the CVD apparatus are approximated and physical parameters are transferred to the mathematical parameters. Such an approximation reduces the mathematical parameter space to a realistic number of numerical experiments. The numerical results are discussed with physical experiments to give a valid model for the assumed growth and we could reduce expensive physical experiments.

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Eremeev, V., and V. Samoilov. "MATHEMATICAL MODEL OF OSCILLATIONS IN THE CHAIN OF PHYSICAL OSCILLATORS." Modern problems of modeling 16 (February 3, 2019): 105–12. http://dx.doi.org/10.33842/2313-125x/2019/16/105/112.

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Shilova, Irina. "PHYSICAL-MATHEMATICAL MODEL OF BENDING FIBER-OPTIC SENSOR OF FORCE." Bulletin of Bryansk state technical university 2020, no. 1 (2020): 18–27. http://dx.doi.org/10.30987/1999-8775-2020-2020-1-18-27.

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There is presented a model of an explosion-proof, jam-resistant under conditions of high level electromagnetic fields fiber-optical sensor of tensile force on the basis of a fiber-optical transformer of movements in which a distinctive peculiarity is an application of loss changes in radiation spreading in sensitive elements as ring loops deformed elliptically of multi-mode fiber light-guides forming a bundle that allows using a diode as a radiation source installed without a special alignment device.  It is defined that a peculiarity of bending fiber-optical transformers of movement of a successive-parallel type is that in separate areas of rings a radius of curvature increases at the expense of deformation and the losses of radiation in these areas decrease, and in other ones this radius decreases that results in the increase of losses of the radiation spreading by light-guides. Overall losses directed at radiation in light-guides increase lineally with the increase of movement. There is carried out a choice of the optimum number of rings of a sensitive element and a choice of “source-radiation receiver” for obtaining a linear calibration characteristic of the sensor. It is shown that varying the number of coils in the bending fiber-optical transformer it is possible to change a range of movements measured ind a form of calibration characteristic of a transformer.

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Burakov, Mikhail M. "Physical and Mathematical Model of Relaxation Filtration of Undergrounds Water." Sustainability in Environment 7, no. 3 (2022): p11. http://dx.doi.org/10.22158/se.v7n3p11.

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Earlier, a number of publications presented the results of an experimental study of the free oscillations of the piezometric level of groundwater (pressure in a liquid) in wells with natural frequencies. In this case, the oscillations were initiated by a pulsed action on the aquifer through disturbing wells. The same publications proposed a theoretical interpretation of the established phenomenon. However, a critical analysis of these theoretical constructions showed their incorrectness. Accordingly, a consistent physical and mathematical model of groundwater relaxation filtration is proposed in this work, which provides a theoretical basis for the description and interpretation of the free oscillations of the piezometric level in a disturbing well with natural frequencies. Thus, the proposed physical and mathematical model made it possible to conclude that it is impossible to cause resonance during the initiation of free oscillations of the piezometric groundwater level. An analysis of the experimental data based on the model showed that the implementation of methodological developments based on the theory of relaxation filtration is possible and expedient only on fundamentally different, in comparison with existing, technical and methodological approaches to the experimental study of wave propagation in aquifers.

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Kuznetsov, V. I., V. V. Makarov, and A. Yu Shander. "Physical and mathematical model of working process of jet ejector." Omsk Scientific Bulletin. Series Aviation-Rocket and Power Engineering 5, no. 3 (2021): 75–82. http://dx.doi.org/10.25206/2588-0373-2021-5-3-75-82.

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A refined physical model of the jet ejector working process has been compiled. On the basis of the refined physical model, a mathematical model has been developed that takes into account the exchange of work and heat between the ejected and ejected gases. Based on the solution of this mathematical model, it is possible to formulate a method for calculating the optimal geometric dimensions of the jet ejector to obtain the specified thermodynamic parameters and a method for calculating the characteristics of the jet ejector with known geometric dimensions. The effect of viscosity on energy exchange is shown. The agreement between the calculated and experimental data is satisfactory.

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Popescu, Florin, Razvan Mahu, Ion V. Ion, and Eugen Rusu. "A Mathematical Model of Biomass Combustion Physical and Chemical Processes." Energies 13, no. 23 (2020): 6232. http://dx.doi.org/10.3390/en13236232.

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The numerical simulation of biomass combustion requires a model that must contain, on one hand, sub-models for biomass conversion to primary products, which involves calculations for heat transfer, biomass decomposition rate, product fractions, chemical composition, and material properties, and on the other hand, sub-models for volatile products transport inside and outside of the biomass particle, their combustion, and the char reduction/oxidation. Creating such a complete mathematical model is particularly challenging; therefore, the present study proposes a versatile alternative—an originally formulated generalized 3D biomass decomposition model designed to be efficiently integrated with existing CFD technology. The biomass decomposition model provides the chemical composition and mixture fractions of volatile products and char at the cell level, while the heat transfer, species transport, and chemical reaction calculations are to be handled by the CFD software. The combustion model has two separate units: the static modeling that produces a macro function returning source/sink terms and local material properties, and the dynamic modeling that tightly couples the first unit output with the CFD environment independently of the initial biomass composition, using main component fractions as initial data. This article introduces the generalized 3D biomass decomposition model formulation and some aspects related to the CFD framework implementation, while the numerical modeling and testing shall be presented in a second article.

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Menin, Boris M. "Preferred physical-mathematical model of the cold energy storage system." Applied Thermal Engineering 112 (February 2017): 1020–26. http://dx.doi.org/10.1016/j.applthermaleng.2016.10.128.

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Likhatsevich, A. P. "Mathematical model of agricultural crop yield." Proceedings of the National Academy of Sciences of Belarus. Agrarian Series 59, no. 3 (2021): 304–18. http://dx.doi.org/10.29235/1817-7204-2021-59-3-304-318.

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Theoretical basis for presenting research results in agricultural science is mathematical statistics and probability theory using empirical forms of generalization of experimental data. To improve the methods of planning field experiment and processing its data using digital technologies, we proposed to use mathematical modeling based on physical principle of balance of cause-and-effect interactions in a closed physical system as a priority option. When analyzing impact of environmental factors on crop yields, the initial provisions, the mathematical modeling of the crop yield is based, on are not associated with characteristics of crops and natural conditions, therefore, the model options are universal in application and are valid for any agricultural crop, regardless of the region of cultivation. To ensure statistically correct digital information, based on the established forms of mathematical model, the field experiment layout aimed at establishing the dependence of the crop yield on yield-forming factors should include at least 4 options for nutritional levels (NPK) with a research duration of at least 4 years. To check the accuracy of the developed crop yield model, the data of independent field experiments of Professor N.N. Semenenko with barley and winter triticale has been used. It has been determined that, in Belarus, yield-forming factors, as a result of their impact on the grain yield, are arranged in the following decreasing sequence: total dose of applied NPK º the amount of precipitation during the active phases of growing season → air temperature for the same period. Calculations have shown that decrease in the number of yield-forming factors taken into account in the mathematical model from three (food, moisture and heat) to two (food and moisture) reduces the accuracy of calculating the grain crop yield insignificantly.

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Akturk, Tolga, Tukur Abdulkadir Sulaiman, Haci Mehmet Baskonus, and Hasan Bulut. "Complex Acoustic Gravity Wave Behaviors to a Mathematical Model Arising in Nonlinear Mathematical Physics." ITM Web of Conferences 22 (2018): 01032. http://dx.doi.org/10.1051/itmconf/20182201032.

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In this article, we utilize the powerful sine-Gordon expansion method (SGEM) in constructing some new solutions to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation by using the Mathematica software. We successfully obtain some new travelling solutions bearing some new structures such as trigonometric function, exponential function and hyperbolic function structures. We claim that some of our results are complex in structure. All the solutions obtained verified the the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. To illustrate our results, present the numerical simulation of all the obtained solutions in this study by selecting appropriate values of the parameters. Furthermore, we give the physical interpretation of all the graphics. We also give the physical meaning to some of the obtained results in this study.

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Cardei, Petru, Gheorghe Voicu, Mihai Matache, Iulian Voicea, Vergil Muraru, and Mihai Ludig. "Nonstandard Mathematical Model for Fatigue Failure." Advanced Engineering Forum 13 (June 2015): 127–35. http://dx.doi.org/10.4028/www.scientific.net/aef.13.127.

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Tests performed under simulated regime, use simulating tools with different structures and often have a corresponding physical test to complete certain conclusions in order to explain complex phenomena that are difficult, impossible, or very costly to run physically. Computer simulations are also called virtual tests beside which there are mechanical or small scale analog simulators. Among the virtual tests for mechanical structures there are structural analysis tests that use numerical analysis methods. Sometimes, in order to understand the phenomena that occurs in the material structure, new complex theoretical models were used for explaining the material quality change. One such application is proposed, which incorporates an old author’s model, for the fatigue and quality phenomenon study of the material change.

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Bunge, H. J. "Some Remarks on Modelling and Simulation of Physical Phenomena." Textures and Microstructures 28, no. 3-4 (1997): 151–65. http://dx.doi.org/10.1155/tsm.28.151.

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Mathematical modelling and computer simulation of physical phenomena is a rapidly growing field of work in all areas of pure and applied sciences. In principle, mathematical modelling of physical phenomena has been the field of theoretical physics from the very beginning of physics although the computer has increased the potentials of this method by many orders of magnitude. Modelling and simulation are often used as synonyms. It may, however, be meaningfull to distinguish the development of a mathematical model from its use in computer simulation. Also, a mathematical model in this sense must be distinguished from mathematical expressions interpolating experimental data. In the field of textures, models of texture formation, models of materials properties, as well as the combination of the two are being used. In this connection it is important whether a texture formation model is linear or non-linear. In the first case the texture formation operator can be reduced to the orientation space whereas a non-linear operator operates in the full texture space.

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Li, B. Q., J. W. Evans, and D. P. Cook. "An improved mathematical model for electromagnetic casters and testing by a physical model." Metallurgical Transactions B 22, no. 1 (1991): 121–34. http://dx.doi.org/10.1007/bf02672533.

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Shemelova, O. "Mathematical modeling in chemical technology processes." Bulletin of Science and Practice 4, no. 12 (2018): 20–23. https://doi.org/10.5281/zenodo.2252778.

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In the practice of researching the processes of chemical technology with the help of mathematical modelling, it is relatively easy to change the parameters of the investigated object and to determine their influence on the quality of its work as a whole. This is possible because the deformation of the process model is studied not on the physical model, but directly on the mathematical model when using a computer.

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Shemyakin, Stanislav, and Evgenii Shishkin. "Physical and mathematical model of rock destruction by a milling machine cutter." Записки Горного института 251 (October 29, 2021): 639–47. http://dx.doi.org/10.31897/pmi.2021.5.3.

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As a result of the analysis of the work on rock destruction by cutters of milling of machines, it was found that the existing developments do not allow us to proceed to the derivation of calculation d dependencies for determining fracture resistance, or can be used only in preliminary calculations of the known by design parameters of milling machines. To eliminate these disadvantages, a combined physical and mathematical model of the process of interaction of a single milling cutter with a spherical tip with the rock has been developed. Consideration of the physical picture of the action of forces and stresses acting from the cutter with spherical tips on the separating rock element in the limiting condition allowed to describe analytically the components of total resistance, which are the mathematical part of the physical and mathematical model of rock destruction by cutters. Analytical dependences for determining the tangential and normal components of fracture resistance of rocks of medium hardness have been obtained. The adequacy of the physical and mathematical model to the physical process of destruction of rocks of different hardness by cutters on a universal stand was tested both in the field and in the laboratory conditions. Technical evaluation of the results of experimental studies confirms the reliability of the developed physical and mathematical model.

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McCash, Luthais B., Salman Akhtar, Sohail Nadeem, and Salman Saleem. "Entropy Analysis of the Peristaltic Flow of Hybrid Nanofluid Inside an Elliptic Duct with Sinusoidally Advancing Boundaries." Entropy 23, no. 6 (2021): 732. http://dx.doi.org/10.3390/e23060732.

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Peristaltic flow of hybrid nanofluid inside a duct having sinusoidally advancing boundaries and elliptic cross-section is mathematically investigated. The notable irreversibility effects are also examined in this mathematical research by considering a descriptive entropy analysis. In addition, this work provides a comparison analysis for two distinct nanofluid models: a hybrid model (Cu-Ag/water) and a phase flow model (Cu/water). A comprehensive graphical description is also provided to interpret the physical aspects of this mathematical analysis.

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Delort, Thierry. "Theory of Dark Matter and Dark Energy." Applied Physics Research 10, no. 5 (2018): 1. http://dx.doi.org/10.5539/apr.v10n5p1.

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In this article, we propose a new model of dark matter. According to this new model, dark matter is a substance, that is a new physical element not constituted of classical particles, called dark substance and filling the Universe. Assuming some very simple physical properties to this dark substance, we theoretically justify the flat rotation curve of galaxies and the baryonic Tully-Fisher&rsquo;s law. We then study according to our new theory of dark matter&nbsp; the different possible distributions of dark matter in galaxies and in galaxy clusters, and the velocities of galaxies in galaxy clusters.  Then using the new model of dark matter we are naturally led to propose a new geometrical model of Universe, finite, that is different from all geometrical models proposed by the Standard Cosmological Model (SCM). Despite that our Theory of dark matter is compatible with the SCM, we then expose a new Cosmological model based on this new geometrical form of the Universe and on the interpretation of the CMB Rest Frame (CRF), that has not physical interpretation on the SCM and that we will call local Cosmological frame. We then propose 2 possible mathematical models of expansion inside the new Cosmological model. The 1st mathematical model is based on General Relativity as the SCM and gives the same theoretical predictions of distances and of the Hubble&rsquo;s constant as the SCM. The 2nd mathematical model of expansion of the Universe is mathematically much simpler than the mathematical model of expansion used in the SCM, but we will see that its theoretical predictions are in agreement with astronomical observations. Moreover, this 2nd mathematical model of expansion does not need to introduce the existence of a dark energy contrary to the mathematical model of expansion of the SCM. To end we study the evolution of the temperature of dark substance in the Universe and we make appear the existence of a dark energy, due to our model of dark matter.

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SHYSHKIN, G. O. "ЦИФРОВІ ТЕХНОЛОГІЇ У ФОРМУВАННІ МОДЕЛЕЙ ПЕРЕХІДНИХ ПРОЦЕСІВ В ІНДУКТИВНОСТІ ТА ЄМНОСТІ". Scientific papers of Berdiansk State Pedagogical University Series Pedagogical sciences 1, № 2 (2021): 330–40. http://dx.doi.org/10.31494/2412-9208-2021-1-2-330-340.

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An important role in the formation of qualitative knowledge of physics in the modern education system is played by students` ability to present the processes being studied at a qualitative level. Formation of students' abilities and skills to construct figurative physical models, finding mathematical dependences between physical quantities is one of the urgent problems of physics teaching methods. Our research is devoted to the problem of the formation of high-quality imaginary models of physical processes among physics students on the basis of an educational experiment and digital technologies. To improve the quality of teaching physics, the necessity of forming physical and mathematical models of the studied processes among future specialists is substantiated. On the example of experimental study of processes occurring in DC circuits, which contain inductors and capacitors, a method of forming their imaginary and mathematical models is proposed. A digital measuring system with a personal computer was used in the research. It is proved that conducting a physical experiment with simultaneous display of research results in the form of tables and graphs contributes to the formation of a qualitative level of physical models. To form students' skills of building mathematical models of the studied processes, it is proposed to use software that allows to analyze the results of the experiment. The analysis of graphs of the studied processes allows to select mathematical dependences and to calculate necessary coefficients. The use of digital technologies and related programs provides a quick finding of mathematical models. Changing the parameters of the studied objects while finding the corresponding mathematical dependencies allows students to establish relationships between mathematical symbols and physical quantities. This approach provides students with the ability to find mathematical models of these processes or objects. The results of the implementation of the proposed method showed that the use of digital measuring systems in the educational physical experiment significantly improves the quality of students' learning of new material. Key words: physical experiment, model, digital technologies, extra current, inductance, capacitance.

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Polyanichko, Nikita. "Physical and mathematical models of ballast bed tamping via rotary device." Bulletin of scientific research results, no. 2 (August 10, 2016): 5–16. http://dx.doi.org/10.20295/2223-9987-2016-2-5-16.

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Objective: To develop a mathematical model and program for defining rational technological parameters and operation mode of a rotary device for tamping the ballast bed in the tie space area. Establish the veracity of calculations performed using the mathematical model and program developed via mathematical and physical experiments. Methods: Experimental and theoretical research conducted. Results: Established veracity of the mathematical model and program for calculating the technological parameters and operation mode of the device for tamping the ballastbed in the tie space area. Practical importance: The program developed provides the ability to select rational technological parameters and operation mode for the device. It is recommended that it be used when creating tools for ballast bed solidification in the ballast box area.

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Tao, Xin, Jianqi Cao, Jia Wang, et al. "Physical Model of Inclusions Removal at Static Steel–Slag Interface." Materials 17, no. 10 (2024): 2244. http://dx.doi.org/10.3390/ma17102244.

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Inclusions are one of the important factors affecting the cleanliness of molten steel. The current optimization of inclusion removal methods mainly focuses on promoting inclusions to float to the slag–steel interface so that the inclusions can be absorbed and removed by the refining slag. However, the research on the floating removal of inclusions cannot be carried out directly in the ladle, so methods such as mathematical models and physical models were developed. This article uses silicone oil to simulate the slag layer; polypropylene particles; and aluminum oxide particles to simulate inclusions to establish a water model experiment. By changing the viscosity of silicone oil and the diameter of particles, the factors affecting the movement of inclusions at the slag–steel interface were explored. Based on the water model, a mathematical model of the floating behavior of inclusions at the slag–steel interface was constructed, and parameters such as particle diameter and interfacial tension in the water model experiment were studied by the mathematical model for calculation. Both the mathematical model and the water model experimental results show that after the viscosity of silicone oil increases from 0.048 Pa·s to 0.096 Pa·s, the dimensionless displacement and terminal velocity of the particles decreases. When the diameter of the same particle increases, the dimensionless displacement and terminal velocity increases. The dimensionless displacement of polypropylene particles of the same diameter is larger than that of aluminum oxide particles, and the terminal velocity is smaller than that of aluminum oxide particles. This is attributed to the better overall three-phase wettability of polypropylene particle. When the liquid level increases, the dimensionless displacement and terminal velocity of particles under the same conditions show only slight differences (less than 10%).

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Areshi, Mounirah, Aly R. Seadawy, Asghar Ali, Amal F. Alharbi, and Abdulrahman F. Aljohani. "Analytical Solutions of the Predator–Prey Model with Fractional Derivative Order via Applications of Three Modified Mathematical Methods." Fractal and Fractional 7, no. 2 (2023): 128. http://dx.doi.org/10.3390/fractalfract7020128.

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We have investigated wave solutions of the Predator–Prey (PP) model with fractional derivative order by novel three modified mathematical methods with the help of the Mathematica platform. The derived solutions are in the form of distinct functions such as trigonometric, hyperbolic, exponential and rational functional. For the physical phenomena of fractional model, some solutions are plotted in 2-dimensional and 3-dimensional by inserting specific values to attached parameters under sufficient condition on each solution. Hence, proposed schemes are enormously superbly mathematical tools to review wave solutions of several fractional models in nonlinear science.

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Adoum, Adam Hassan, Mahamat Saleh Daoussa Haggar, Temga Djaokamla, and Jean Marie Ntaganda. "A MATHEMATICAL MODEL OF GLUCOSE HOMEOSTASIS IN CHAD CONTEXT." JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES 10, no. 01 (2022): 153–66. http://dx.doi.org/10.56827/jrsmms.2022.1001.13.

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During these decades, mathematical modeling has become a key domain in science, especially in biomedical sciences. It allows for an experimental and rigorous approach. Thanks to mathematical modeling, the glucose-insulin system could be materialized, which is also theoretical, in order to analyze and interpret it and to predict the results. Many of the mathematical models of the glucose-insulin system have emerged in recent years. In literature, there are models that show the role of physical activity and response of mathematical model to glucose-insulin system dynamics. We propose the mathematical model of ordinary differential equations to investigate simple homeostasis generated by the dynamics of physiological parameters of the glucose-insulin system during physical activity for a healthy subject. Model parameters are estimated using a nonlinear optimization method generally based on inverse problems. The numerical simulations show that the proposed model is adaptable to the data collected in Chad and can be used to test glucose homeostasis for glucose-insulin system.

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Cadena-Morales, J. J., C. A. López-Castro, and J. M. Alba-Maldonado. "Applications of differential equations to model the physical phenomenon of heat transfer with an internal energy source." Journal of Physics: Conference Series 2102, no. 1 (2021): 012018. http://dx.doi.org/10.1088/1742-6596/2102/1/012018.

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Abstract The mathematical modeling of the physical phenomenon of conduction in the presence of heat sources has various uses in engineering ranging from heat diffusion, pollution generation in large cities and chemical reactions. From the mathematical theory, the study of physical phenomena with the presence of heat is approached from techniques of polynomial approximation, analysis of variations and numerical methods. In this research a mathematical model is proposed to study the heat conduction in a metal bar with a heat source. In the first part of the work, by the application of the method of the parameter variation, the exact solution of the mathematical model is calculated. Subsequently, by means of a case study of the physical phenomenon of heat conduction with internal energy source, with the use of computational simulation, the convergence of the Fourier series linked to the physical phenomenon is shown. The mathematical method proposed in the paper can be applied to other physical phenomena such as wave propagation, electric potential, and chemical reactions.

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Favrie, N., and S. Gavrilyuk. "Mathematical and numerical model for nonlinear viscoplasticity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1947 (2011): 2864–80. http://dx.doi.org/10.1098/rsta.2011.0099.

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A macroscopic model describing elastic–plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In addition, Maxwell-type material behaviour is shown up: the deviatoric part of the stress tensor decays during plastic deformations. Numerical examples show the ability of this model to deal with real physical phenomena.

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Karpov, Andrey G., and Nikolay V. Egorov. "Algorithms for compiling a mathematical model of physical systems using graphs." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 20, no. 1 (2024): 10–19. http://dx.doi.org/10.21638/11701/spbu10.2024.102.

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A system of algorithms for compiling a mathematical model of physical systems, the structure of which is given using graphs of great complexity, is proposed. The proposed algorithms can be used not only to develop new systems, but also to diagnose operating equipment and troubleshooting. The resulting mathematical model of the system, presented in the form of a system of equations, allows us to obtain a unique solution. The operation of the algorithms is illustrated using the example of a mechanical system, but the results of the work can be extended to systems of a different nature using electromechanical or electroeconomic analogies.

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Journal articles on the topic 'Physical and mathematical model'

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