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Journal articles on the topic 'Mathematical model of a vacuum'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Du, Guizhen, Xianshan Dong, Xinglong Huang, Wei Su, and Peng Zhang. "Reliability Evaluation Based on Mathematical Degradation Model for Vacuum Packaged MEMS Sensor." Micromachines 13, no. 10 (2022): 1713. http://dx.doi.org/10.3390/mi13101713.

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Vacuum packaging is used extensively in MEMS sensors for improving performance. However, the vacuum in the MEMS chamber gradually degenerates over time, which adversely affects the long-term performance of the MEMS sensor. A mathematical model for vacuum degradation is presented in this article for evaluating the degradation of vacuum packaged MEMS sensors, and a temperature-accelerated test of MEMS gyroscope with different vacuums is performed. A mathematical degradation model is developed to fit the parameters of the degradation of Q-factor over time at three different temperatures. The resu

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2

Dostal, M., and K. Petera. "Vacuum cooling of liquids: mathematical model." Journal of Food Engineering 61, no. 4 (2004): 533–39. http://dx.doi.org/10.1016/s0260-8774(03)00223-1.

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3

Sadig Mehdiyev, Mahiyaddin. "An empirical model expressing the dependence of the boiling temperature on pressure." NATURE AND SCIENCE 03, no. 04 (2020): 26–28. http://dx.doi.org/10.36719/2707-1146/04/26-28.

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Large sp empiric rules, "When atmospheric pressure drops by half, the boiling point drops by about 15 " has been replaced by a mathematical formula. The proposed mathematical formula is correct for the interval 1≤ <760 mm.Hg. Key words: distillation, vacuum, temperature, empirical, formula

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4

Laskin, A. A., R. R. Yakupov, A. A. Raykov, T. N. Mustafin, S. I. Salikeev, and A. V. Burmistrov. "Mathematical Model of Screw Vacuum Pump Working Process." Proceedings of Higher Educational Institutions. Маchine Building, no. 8 (749) (August 2022): 65–73. http://dx.doi.org/10.18698/0536-1044-2022-8-65-73.

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The screw vacuum pump combines high performance, low ultimate pressure and ability to create an oil-free vacuum. The calculation of the pump characteristics can be performed using mathematical modeling. The article considers main stages of creating a mathematical model: constructing the geometry of the rotors, calculating the dependence of the working cavity volume and the area of the suction and discharge windows on the angle of rotor rotation, determining the main directions of gas flows, calculating the dependence of pressure and temperature on the angle of rotor rotation. The thermodynamic

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5

Hous̆ka, M., S̆ Podloucký, R. Z̆itný, et al. "Mathematical model of the vacuum cooling of liquids." Journal of Food Engineering 29, no. 3-4 (1996): 339–48. http://dx.doi.org/10.1016/0260-8774(96)00003-9.

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6

Raykov, A., S. Salikeev, A. Burmistrov, and M. Fomina. "Non‐contact vacuum pumps." Vakuum in Forschung und Praxis 35, no. 4 (2023): 34–37. http://dx.doi.org/10.1002/vipr.202300804.

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SummaryAn overview of the main methods for mathematical modeling of the working process of non‐contact vacuum pumps is given. The specifics and the main stages of mathematical model development for screw, scroll, claw and Roots vacuum pumps are considered. The results of mathematical modeling of pump characteristics are presented and compared with experimental data. The mathematical modeling technique presented here can be recommended for analyzing the influence of pump geometry and operating conditions on the pump characteristics of non‐contact oil‐free vacuum pumps.

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7

Aygun, Safarova Agamirza, and İslamzade Nigar. "THE PROBLEM OF İDENTİFİCATİON OF A VACUUM DİSTİLLATİON COLUMN." Annali d'Italia 66 (April 29, 2025): 98–101. https://doi.org/10.5281/zenodo.15303151.

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Development of scientific bases of the automated control system allowing to increase economic efficiency of operation modes of vacuum block of oil refineries, which is one of the main technological processes of the fuel and energy complex, is an urgent problem of great national economic importanceIn the presented paper the main technological parameters characterizing the vacuum column have been determined. A deterministic linear mathematical model capable of adequately reflecting the current technological state of the main apparatuses of the vacuum block of the technological complex of primary

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8

Zhang, Shi Wei, Zhuo Wang, and Zhi Jun Zhang. "Study on Evacuating Process of Vacuum Glazing." Applied Mechanics and Materials 71-78 (July 2011): 1204–8. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.1204.

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Vacuum glazing is a very choice in building energy efficiency. Therefore, it is necessary to study on evacuating process of vacuum glazing. Based on fundamental pumping equation of vacuum technique and simplified the existing pumping system for vacuum glazing, a mathematical model, which is described evacuating process of vacuum glazing, is established. An exact mathematical solution is obtained by solving the model. According to the solution, an example from a practical evacuating system is solved and analyzed, and two conclusions are summed up as follows: First, the evacuating time needed fo

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9

Zhang, Fan, Yu, Zhang, Lv, and Xu. "Study on the Mathematical Model of Vacuum Breaker Valve for Large Air Mass Conditions." Water 11, no. 7 (2019): 1358. http://dx.doi.org/10.3390/w11071358.

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The mathematical model of vacuum breaker valve is significant to the protection scheme. The more accurate the vacuum breaker valve model, the more reliable the calculation results. In this study, the application conditions of the air valve model are analyzed according to the assumptions used in the derivation, and the contradictions between these assumptions are proposed. Then, according to the different working characteristics between the vacuum breaker valve on the siphon outlet pipe and the air valve, the vacuum breaker valve model is deduced based on the modified assumptions. In the deriva

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10

Lesnyak, I. Y., A. V. Panichkin, and V. A. Urbansky. "MATHEMATICAL MODELING OF THE PROCESS OF DRYING WHEAT GRAIN UNDER ACOUSTIC-VACUUM EXPOSURE." DYNAMICS OF SYSTEMS, MECHANISMS AND MACHINES 11, no. 1 (2023): 10–15. http://dx.doi.org/10.25206/2310-9793-2023-11-1-10-15.

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To investigate the process of drying wheat grain under conditions of combined acousticvacuum exposure, a mathematical model of the process under consideration was developed based on differential equations. Preliminary numerical experiments were carried out using the developed mathematical model. The results of mathematical modeling were obtained in the form of dependencies of changes in mass, temperature and humidity of wheat grain both under separate acoustic and vacuum exposure, and under combined acoustic-vacuum exposure. The drying rate of wheat grain was determined, which is 0.01 g/min un

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11

Arkenova, Saniia B., Elena N. Ivashkina, and Elizaveta F. Gritsenko. "Forecasting the operation of an industrial vacuum distillate hydrotreating unit using a mathematical model." Bulletin of the Tomsk Polytechnic University Geo Assets Engineering 336, no. 3 (2025): 183–92. https://doi.org/10.18799/24131830/2025/3/4895.

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Relevance. Current trends in processing heavy oil with high sulfur content and tightening environmental fuel requirements necessitate hydrocarbon feedstock purification from harmful components such as sulfur. One of the processes for upgrading medium and heavy oil fractions is hydrotreating. Due to the high importance of the hydrotreating in modern oil refining, the use of mathematical models is critically important in the design of new units, optimization of existing ones, and development of catalysts. Aim. This work is devoted to forecasting the operation of an industrial vacuum gas oil hydr

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12

Vorob’ev, A. M., N. S. Belinskaya, D. A. Afanasieva, et al. "Mathematical Modeling of the Vacuum Gas Oil Hydrotreatment." Kataliz v promyshlennosti 22, no. 5 (2022): 40–52. http://dx.doi.org/10.18412/1816-0387-2022-5-40-52.

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Thermochemical properties of molecules and thermodynamic characteristics of vacuum distillate hydrotreatment were calculated by quantumchemical methods. A kinetic model of the hydrotreatment process was developed using a formalized transformation scheme of hydrocarbons. The developed kinetic model was employed in numerical studies aimed to estimate the effect of the feedstock composition on the residual content of heteroatomic components in the product of vacuum gas oil hydrotreatment, the effect of temperature on the content of aromatic hydrocarbons, nitrogen and sulfur in the hydrotreatment

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13

Li, Hua, Lihua Li, Xingli Jiao, and Xueli Qin. "Mathematical model of vacuum freeze-drying in the secondary drying." JOURNAL OF ADVANCES IN CHEMISTRY 3, no. 2 (2007): 192–96. http://dx.doi.org/10.24297/jac.v3i2.931.

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The freeze-drying process is a complex heat and mass transfer process virtually. The drying process of freeze-drying is not only the key stage which decides the success of freeze-drying, but also the most difficult stage to control. There are lots of papers about heat and mass transfer in vacuum freeze drying at home and abroad. The present status of research on heat and mass transfer during vacuum freeze drying in the secondary drying is summed up and analyzed, and the trend of research in this field is discussed in this paper.

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14

Jin, Wen Zhong, Su Fang Li, and Wei Zhang. "Feeding Mathematical Modeling of Superalloy Vacuum-Electromagnetic Casting and its Application." Advanced Materials Research 629 (December 2012): 171–75. http://dx.doi.org/10.4028/www.scientific.net/amr.629.171.

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The new technology of superalloy vacuum-electromagnetic casting was developed and the feeding mathematical model melt in vacuum-electromagnetic casting was established. The availability of mathematical model was approved by the experiments of the IN100 superalloy. The experimental results indicate that the feeding capacity of melt in vacuum casting can be greatly increased by imposing the 50Hz, 60A rotating electromagnetic stirring, which can decrease the central shrinkage cavity in superalloy ingots, so the quality of the superalloy ingots can be wide-range improved.

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15

Tertychny-Dauri, V. Yu. "Nuclear Electromagnetic Generator: Mathematical Model on Toroidal Vacuum Scheme." OALib 05, no. 04 (2018): 1–8. http://dx.doi.org/10.4236/oalib.1104524.

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16

Derevyanov, M. Yu, M. Yu Livshits, and E. A. Yakubovich. "Vacuum Carburizing Process: Identification of Mathematical Model and Optimization." IOP Conference Series: Materials Science and Engineering 327 (March 2018): 022022. http://dx.doi.org/10.1088/1757-899x/327/2/022022.

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17

Korsun, A. G., E. M. Tverdokhlebova, and F. F. Gabdullin. "Mathematical model of hypersonic plasma flows expanding in vacuum." Computer Physics Communications 164, no. 1-3 (2004): 434–41. http://dx.doi.org/10.1016/j.cpc.2004.06.078.

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18

Koumoutsakos, Anastasios, Stavros Avramidis, and Savvas G. Hatzikiriakos. "RADIO FREQUENCY VACUUM DRYING OF WOOD. I. MATHEMATICAL MODEL." Drying Technology 19, no. 1 (2001): 65–84. http://dx.doi.org/10.1081/drt-100001352.

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19

Kozak, Oleksandr, and Volodymyr Telychkun. "Mathematical model of vacuum cooling process for wheat bread." Ukrainian Food Journal 13, no. 4 (2024): 780–93. https://doi.org/10.24263/2304-974x-2024-13-4-11.

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20

Maamar, Mouhcine Ibn, Mohamed Badraoui, Mohamed Mazouzi, and Laila Mouakkir. "Mathematical Modeling on Vacuum Drying of Olive Pomace." Trends in Sciences 20, no. 2 (2022): 3822. http://dx.doi.org/10.48048/tis.2023.3822.

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Abstract: The thin-layer olive pomace vacuum drying behavior was experimentally investigated for 3 gauge pressures; −130, −200, −250 mbar, and for various sample thicknesses 5, 10 and 15 mm. Nine thin layer mathematical models were used to fit olive cake vacuum drying. Olive pomace vacuum drying took place in the falling rate period at all pressures and for all thicknesses, no constant rate period was observed. Among the selected models, the Diffusion Approach was found to be the most appropriate model better describing the olive pomace drying behavior. The drying rate is correlated to the dep

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21

Gaidash, Andrey A., Roman K. Goncharov, Anton V. Kozubov, and Pavel V. Yakovlev. "Mathematical model of random number generator based on vacuum fluctuations." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 20, no. 2 (2024): 136–53. http://dx.doi.org/10.21638/spbu10.2024.202.

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A mathematical model of quantum random number generator based on vacuum fluctuations is considered. A mathematical justification for the “randomness” of the generated sequence is given under the assumption of the truth of the basic postulates of quantum theory and the validity of the Poisson probability distribution for the photon flux. The results of experiments and the obtained estimates of the minimum entropy are presented.

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22

Safarova, A. A. "Development of a Mathematical Model and Solution to the Problem of Optimizing the Vacuum Block of Oil Distillation Unit." Herald of Azerbaijan Engineering Academy 16, no. 3 (2024): 105–11. https://doi.org/10.52171/2076-0515_2024_16_03_105_111.

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As it is known, one of the initial and important stages in the creation of optimal control systems ofoil refining technological units is the development of a mathematical model that can adequately record theprocesses at any time. Studies have shown that the lack of information about the state of complex oilrefining processes in many cases reduces their efficiency and effectiveness. On the other hand, the widerange of both quality and quantity of raw materials for processing makes their efficiency even moreunsatisfactory. Under these conditions, it is difficult to develop mathematical models th

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23

A. Shirkin, L., O. G. Selivanov, T. A. Trifonova, S. I. Roshchina, and M. E. Ilina. "Mathematical Model of Vacuum Evaporation Using Apparatus with Mechanical Water Vapor Recompression." International Journal of Engineering & Technology 7, no. 4.38 (2018): 1222. http://dx.doi.org/10.14419/ijet.v7i4.38.27768.

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This article presents mathematical model of evaporation of aqueous solutions of mineral salts on apparatus with mechanical recompression of water vapor and process intensification upon vacuuming. The developed mathematical model is an engineering prediction where all calculations are associated with technological flowchart of evaporator. Predictions according to the mathematical model for evaporator are exemplified for the case of 2% aqueous solution of sodium chloride evaporated to 15 wt % at distillation capacity of 30 kg/h. Engineering predictions were performed consecutively in 5 stages in

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24

Sevostianov, I. B., V. E. Verijenko, C. J. von Klemperer, and B. Chevallereau. "Mathematical model of stress formation during vacuum resin infusion process." Composites Part B: Engineering 30, no. 5 (1999): 513–21. http://dx.doi.org/10.1016/s1359-8368(99)00012-8.

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25

MORAIS, C. W., and A. L. MOTA. "MOMENTUM SPACE REGULARIZATIONS AND THE INDETERMINACY IN THE SCHWINGER MODEL." International Journal of Modern Physics A 26, no. 12 (2011): 1991–2006. http://dx.doi.org/10.1142/s0217751x11053067.

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We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an ansatz in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their v

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26

Zheng, D., K. Wei, W. Ma, Z. Sheng, and Y. Dai. "A mathematical model for distribution of calcium in silicon by vacuum directional solidification." Journal of Mining and Metallurgy, Section B: Metallurgy 52, no. 2 (2016): 157–62. http://dx.doi.org/10.2298/jmmb141203012z.

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Calcium is one of the main impurity elements in silicon. The removal of calcium strongly affects the quality of the polycrystalline silicon ingot produced by a vacuum directional solidification method. Based on the considerations of the theory of segregation, mass transfer and evaporation during vacuum directional solidification process, a mathematical model for calcium distribution in silicon was proposed and it can be used to explain the removal mechanism. In order to confirm the mathematical model, an industrial scale experiment on UMG-Si with an initial purity of 99.98 wt. % was performed.

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27

Ovsyannikov, B. L., V. V. Vasilevsky, and E. K. Kulomzin. "Hardening of chromium steels in vacuum." Izvestiya MGTU MAMI 8, no. 2-2 (2014): 67–72. http://dx.doi.org/10.17816/2074-0530-67682.

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The experience and results of research of hardening modes of steel products 40H13 in a vacuum, in a single-unit and small-scale production is described. There is shown the effectiveness of high-temperature hardening with outdoors cooling of vacuum chamber. The mathematical model of the cooling of the vacuum chamber is developed. It allows the investigation of cooling modes and options for the construction of the vacuum chamber.

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28

Aliiev, Elchyn, Andriy Paliy, Viktor Kis, et al. "Establishing the influence of technical and technological parameters of milking equipment on the efficiency of machine milking." Eastern-European Journal of Enterprise Technologies 1, no. 1 (115) (2022): 44–55. http://dx.doi.org/10.15587/1729-4061.2022.251172.

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One of the tasks that imply increasing the milk productivity of cows is to create optimal maintenance conditions that ensure the increased use of the genetic potential of cattle based on the implementation of engineering and technological solutions. A mathematical model has been built that links the technical and technological parameters of the vacuum system of milking equipment, namely, the value of the working vacuum P, the pulsation frequency n, the ratio of pulsation cycles, and the tension strength of milking rubber FH to cows’ milk yield rate V. The range of milking plant operating param

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29

Li, Gang, Bao Ren Li, and Jing Min Du. "Nonlinear Model-Based Control for Vacuum Altitude Simulator." Applied Mechanics and Materials 470 (December 2013): 663–67. http://dx.doi.org/10.4028/www.scientific.net/amm.470.663.

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Vacuum altitude simulator (VAS) is the key component of the hardware in the loop simulation (HILS) of the aircraft control system. Due to the compressibility of the air and the nonlinearity of the exhaust capacity of the vacuum pump, it is difficult to get a good performance with normal linear controller. In this paper, the nonlinear mathematical model of the system is established. A feedback linearization controller is developed based on the model. To handle the uncertain nonlinear dynamics, the integral control is introduced. Experiments indicate that the proposed controller can effectively

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30

Kitamura, Toshihiro, Kenichiro Miyamoto, Ryouji Tsujino, Shozo Mizoguchi, and Katsuhiko Kato. "Mathematical Model for Nitrogen Desorption and Decarburization Reaction in Vacuum Degasser." ISIJ International 36, no. 4 (1996): 395–401. http://dx.doi.org/10.2355/isijinternational.36.395.

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31

Afify, M. T., Z. A. El-Haddad, G. E. Hassan, and YA Shaaban. "MATHEMATICAL MODEL FOR PREDICTING VACUUM PRESSURE OF ONION SEEDS PRECISION SEEDER." Misr Journal of Agricultural Engineering 26, no. 4 (2009): 1776–99. http://dx.doi.org/10.21608/mjae.2009.107382.

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32

Liu, Yunhong, Wenxue Zhu, Lei Luo, Xin Li, and Huichun Yu. "A Mathematical Model for Vacuum Far-Infrared Drying of Potato Slices." Drying Technology 32, no. 2 (2013): 180–89. http://dx.doi.org/10.1080/07373937.2013.811687.

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33

Sun, Da-Wen, and Lijun Wang. "Development of a mathematical model for vacuum cooling of cooked meats." Journal of Food Engineering 77, no. 3 (2006): 379–85. http://dx.doi.org/10.1016/j.jfoodeng.2005.07.002.

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34

Burmistrov, A., S. Salikeev, A. Raykov, and M. Fomina. "Mathematical model of working process of oil free scroll vacuum pump." Vakuum in Forschung und Praxis 29, no. 6 (2017): 28–31. http://dx.doi.org/10.1002/vipr.201700663.

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35

Ion, Sorin Mihai, Constantin Gheorghe Opran, and Giuseppe Lamanna. "Mathematical Model of Vacuum–Resin Transfer Molding for Polymeric Composites Products." Macromolecular Symposia 389, no. 1 (2020): 1900108. http://dx.doi.org/10.1002/masy.201900108.

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36

Kudělka, Jan, Jiří Fryč, Vlastimil Slaný, Robert Rouš, Akshaya Raj, and Radek Martínek. "Parameters setting of Frequency Converter PI regulation to ensure the vacuum of the milking process." PLOS ONE 16, no. 7 (2021): e0253427. http://dx.doi.org/10.1371/journal.pone.0253427.

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This paper presents regulation of an asynchronous induction motor so as to create a stable vacuum milk pump using Variable Frequency Drive (VFD). Contribution includes providing information about the usage of the VFD, which regulates the activity of an asynchronous induction motor so that the vacuum pump milking machine creates stable vacuum. The paper describes the functional and time dependence of input values and output parameters of frequency converters at changing electric motor speed. For simulation and verification the milking process a mathematical model of the milking machine was crea

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37

Saberian, Hamed, Mojtaba Amooi, and Zohreh Hamidi-Esfahani. "Modeling of vacuum drying of loquat fruit." Nutrition & Food Science 44, no. 1 (2014): 24–31. http://dx.doi.org/10.1108/nfs-08-2012-0087.

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Purpose – The aim of the present research was to study and model drying of loquat fruit under vacuum conditions at three temperatures to select the best mathematical model for predicting drying rate of loquat during times which is used in designing of vacuum dryer. The dried product may be used in the preparation of soups, jam, premixed foods, snacks, etc. Design/methodology/approach – Loquat samples were dried by vacuum oven (52 cm Hg) at three temperatures, 60, 70 and 80°C. First, moisture content was plotted against time for each treatment and after that moisture ratio curves were plotted.

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38

Mitrevski, Vangelce, Aleksandar Dedinac, Cvetanka Mitrevska, Slobodan Bundalevski, Tale Geramitcioski, and Vladimir Mijakovski. "Mathematical modelling of far-infrared vacuum drying of apple slices." Thermal Science 23, no. 1 (2019): 393–400. http://dx.doi.org/10.2298/tsci180205143m.

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In this study, a mathematical model of far-infrared vacuum drying of shrinkage body is presented. The system of two coupled PDE for heat and mass transfer with appropriate initial and boundary conditions are solved numerically with used of the finite difference method. On the basis of the numerical solutions a computer program for calculation of temperature profiles, transient moisture content, mid-plane temperature, and the volume averaged moisture content changes for different drying regime was developed. For verification of a mathematical model a series of numerical calculations were carrie

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39

Smyksy, K., R. Wrona, M. Brzeziński, and E. Ziółkowski. "Analysis and Assessment of Measurements Results of Electric Power Demand in a Model Vacuum-assisted Moulding Installation." Archives of Foundry Engineering 12, no. 4 (2012): 135–40. http://dx.doi.org/10.2478/v10266-012-0121-y.

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Abstract In this article the main problems related with the proper choice of the design and operation parameters of vacuum installation in vacuum moulding system have been discussed. In such system a vacuum are generated using electric-driven vacuum pumps. The aim of the experiment is to evaluate the performance of a vacuum system basing on registered plots of selected electric power parameters of the power-supplying system of the pumps with parallel measurements instantaneous values of pressure in selected points of model stand. The measurements system for power-supply unit has incorporated t

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40

Elchyn, Aliiev, Paliy Andriy, Kis Viktor, et al. "Establishing the influence of technical and technological parameters of milking equipment on the efficiency of machine milking." Eastern-European Journal of Enterprise Technologies 1, no. 1 (115) (2022): 44–55. https://doi.org/10.15587/1729-4061.2022.251172.

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Abstract:

One of the tasks that imply increasing the milk productivity of cows is to create optimal maintenance conditions that ensure the increased use of the genetic potential of cattle based on the implementation of engineering and technological solutions. A mathematical model has been built that links the technical and technological parameters of the vacuum system of milking equipment, namely, the value of the working vacuum P, the pulsation frequency n, the ratio of pulsation cycles, and the tension strength of milking rubber F<sub>H</sub> to cows’ milk yield rate V. The range of milking

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41

Tkach, V. V., G. O. Magomedov, and A. A. Shevtsov. "Numerical and analytical solution of temperature distribution in foamed soy suspension during vacuum microwave drying." Herald of Dagestan State Technical University. Technical Sciences 50, no. 4 (2024): 129–38. http://dx.doi.org/10.21822/2073-6185-2023-50-4-129-138.

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Objective. Technologies of vacuum dehydration of solutions in the microwave field are constantly developing in the direction of increasing the energy efficiency of the drying process and reducing the cost of target products. This scientific direction fully applies to vacuum microwave drying of soy suspension in a foamed state. In this regard, the most important task is to improve mathematical modeling, which provides significant assistance in the study of heat and mass transfer processes occurring in vacuum dryers with microwave power supply; in the design of new installations and the developm

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42

Huifen, Zou, Ye Sheng, Wang Dexi, Li Huixing, Cao Xiaozhen, and Yan Lijun. "Model of Mass and Heat Transfer during Vacuum Freeze-Drying for Cornea." Mathematical Problems in Engineering 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/941609.

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Cornea is the important apparatus of organism, which has complex cell structure. Heat and mass transfer and thermal parameters during vacuum freeze-drying of keeping corneal activity are studied. The freeze-drying cornea experiments were operated in the homemade vacuum freeze dryer. Pressure of the freeze-drying box was about 50 Pa and temperature was about −10°C by controlled, and operating like this could guarantee survival ratio of the corneal endothelium over the grafting normal. Theory analyzing of corneal freeze-drying, mathematical model of describing heat and mass transfer during vacuu

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43

Shvydia, V. O. "To the mathematical model of the process of contact heating of seeds in vacuum." Mehanization and electrification of agricultural, no. 14(113) (2021): 98–104. http://dx.doi.org/10.37204/0131-2189-2021-14-10.

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Annotation Purpose. To increase the degree of adequacy of the mathematical model of contact heating of seeds in a vacuum due to the refinement of the overall coefficient of thermal conductivity. Methods. The study of the mathematical model of the process of contact heating of seeds in vacuum was carried out using the methods of optical physics, planimetry, thermal physics. Mathematical dependencies were developed using algebraic transformations. The analysis of the obtained mathematical dependencies was carried out by the methods of technical analysis and graphic-analytical methods by comparin

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Fiscaletti, Davide. "Dynamic Quantum Vacuum and Relativity." Annales Universitatis Mariae Curie-Sklodowska, sectio AAA – Physica 71 (February 23, 2017): 11. http://dx.doi.org/10.17951/aaa.2016.71.11.

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<p>A model of a three-dimensional dynamic quantum vacuum with variable energy density is proposed. In this model, time we measure with clocks is only a mathematical parameter of changes running in quantum vacuum. Mass and gravity are carried by the variable energy density of quantum vacuum. Each elementary particle is a structure of quantum vacuum and diminishes the quantum vacuum energy density. Symmetry “particle – diminished energy density of quantum vacuum” is the fundamental symmetry of the universe which gives origin to the inertial and gravitational mass. Special relativity’s Sagn

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Da Costa, Eudulino, and Arzu Yazgi. "Mathematical Modelling and Optimization of Seed Metering Unit Performance in Precision Peanut Seeding." Applied Sciences 14, no. 17 (2024): 7525. http://dx.doi.org/10.3390/app14177525.

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The objective of this study was to determine, develop mathematical models, and optimize the in-row seed distribution uniformity performance of a vacuum-type seed metering unit in peanut seeding under different operating conditions. The greased belt stand trials based on the Central Composite Design (CCD) were. Quality of feed index, multiple index, miss index, precision, and coefficient of precision were examined as dependent variables, while the peripheral speed of the seed plate, hole diameter of the seed plate, and vacuum pressure were selected as independent variables. Based on the analysi

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Adamchuk, V. V., and V. О. Shvidia. "Mathematical model of heating seeds with stirring in a drying drum of vacuum drying of seeds." Mehanization and electrification of agricultural, no. 13(112) (2021): 89–96. http://dx.doi.org/10.37204/0131-2189-2021-13-9.

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Annotation Purpose. To increase the uniformity of seed heating by substantiating the transitional modes of a vacuum drum dryer through a mathematical model of heating seeds with mixing in a drying drum. Methods. The solutions of the heat equation were used with the use of the Fourier method for parabolic partial differential equations and the analysis of the motion of a material point on a rough surface. The adequacy of the mathematical model was verified on the basis of statistical methods. Results. Based on the solution of the heat conductivity equation and the analysis of the movement of se

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Londer, Yakov I., and Konstantin N. Ulyanov. "Mathematical Model of the Vacuum Arc in an External Axial Magnetic Field." IEEE Transactions on Plasma Science 35, no. 4 (2007): 897–904. http://dx.doi.org/10.1109/tps.2007.902121.

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Nastaj, J. F. "A MATHEMATICAL MODEL FOR THE CONTINUOUS VACUUM DRYING OF HIGHLY VISCOUS FOODSTUFFS." Drying Technology 7, no. 1 (1989): 47–58. http://dx.doi.org/10.1080/07373938908916574.

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Shi, Xian Quan, and Pedro Fito Maupoey. "Mass Transfer in Vacuum Osmotic Dehydration of Fruits: A Mathematical Model Approach." LWT - Food Science and Technology 27, no. 1 (1994): 67–72. http://dx.doi.org/10.1006/fstl.1994.1014.

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Novruz Aliyeva, Yegana, and Sakina Mammad Abbasova. "MATHEMATİCAL MODEL OF VORTEX VACUUM ROBOT GRİPPER TO DETERMİNE İTS CARRYİNG CAPACİTY." Elmi Əsərlər 3, no. 2 (2024): 5–12. https://doi.org/10.61413/yavx2451.

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Analysis of the quality and reliability of the results of boundary layer formation depending on the parameters of gas flow calculation, separation of the device connection model into finite elements was carried out in ANSYS FLUENT environment using the finite element method. The results of calculations on the obtained analytical dependencies show high convergence with the calculations obtained by more complex modeling in the Ansys Fluent environment. They also include items with different surface shapes to provide gripping of items with different surface shapes while generating the technologic

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