Journal articles: 'Lakes – Circulation – Mathematical models'

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Larson, T. K., and R. A. Dimenna. "Preservation of Natural Circulation Similarity Criteria in Mathematical Models." Nuclear Science and Engineering 100, no. 1 (September 1988): 21–32. http://dx.doi.org/10.13182/nse88-a29011.

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Murthy, C. R., and W. M. Schertzer. "Physical Limnology and Water Quality Modelling of North American Great Lakes." Water Quality Research Journal 29, no. 2-3 (May 1, 1994): 157–84. http://dx.doi.org/10.2166/wqrj.1994.012.

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Abstract Incorporation of physical limnological processes within the water quality/contaminant modelling framework of large lake systems is fundamental for accurate simulation of transport, distribution and pathways of pollutants. Specific examples of water quality/contaminant model applications to the North American Great Lakes are presented with emphasis on models which incorporate physical processes to solve eutrophic and toxic contaminant problems. Examples of circulation and transport model application to lakes and coastal areas as well as thermocline models are briefly described. Water quality models which incorporate such physical limnological processes include eutrophication models, contaminant transport models (river plume, lake and coastal cases). Specific examples are provided primarily from applications in the lower Great Lakes.

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Guseynov, Sharif E., and Jekaterina V. Aleksejeva. "Mathematical Modelling of Aquatic Ecosystem." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 3 (June 16, 2015): 92. http://dx.doi.org/10.17770/etr2015vol3.192.

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

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Leon, L. F., D. Lam, W. Schertzer, and D. Swayne. "Lake and climate models linkage: a 3-D hydrodynamic contribution." Advances in Geosciences 4 (August 9, 2005): 57–62. http://dx.doi.org/10.5194/adgeo-4-57-2005.

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Abstract. Under a Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) project, targeted to study the feasibility to link regional climate models with lake models, one of the tasks was to consider such a coupling in large lakes. The objective is to provide detailed information on temperature and circulation distributions of the lake to take into account the spatial variability for temperature and the heat exchange through the water's surface. The major contribution of this work is focused on realistic representation of the heat fluxes and temperature distributions to and from lakes especially during the thermally stratified ice-free periods. This paper presents the detailed 3-D ELCOM model applied in Lake Erie in order to produce, at the surface layer of the lake, the spatial distribution of temperature and heat exchanges that eventually can be coupled with a regional climate model (CRCM). Preliminary results will be presented on how this lake model may improve the regional climate models, which currently do not consider such large lake circulation effects.

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Leshchinskii, L. A., I. G. Rusyak, S. B. Ponomarev, and A. G. Petrov. "Algorithm for construction of mathematical models of coronary circulation disorders." Biomedical Engineering 33, no. 4 (July 1999): 163–66. http://dx.doi.org/10.1007/bf02385333.

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Cai, Xiao, Boyun Guo, Qingfeng Guo, and Hongwei Jiang. "Mathematical Simulation of Lost Circulation in Fracture and Its Control." Geofluids 2021 (March 12, 2021): 1–14. http://dx.doi.org/10.1155/2021/6691385.

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Lost circulation has been one of the major problems that impede efficient and cost-saving drilling operations. The nature of lost circulation and its control is not yet fully understood. A method to characterize the mud loss in fracture and the plugging process of lost circulation materials is highly desired to obtain a thorough understanding of mud losses in fracture and provide reference for lost circulation control. This paper presents an easy-to-use method to identify types of lost circulation in fracture and the corresponding control. Three analytical models are presented based on three loss mechanisms, namely, seepage/filtration in a fracture, pipe flow in a fracture, and gravity displacement in a fracture. A numerical model is developed to simulate the deposition of lost circulation materials in fractures and predict the time and the volume of drilling fluid needed for lost circulation control. Case studies with these analytical models provide a deeper insight of this subject. Sensitivity analyses with the numerical model identify the major factors responsible for lost circulation control. High viscosity of drilling fluid may prevent lost circulation, while low viscosity is desired for a fast control of lost circulation. Lowering the density of drilling fluid is another way to prevent the lost circulation and facilitate the deposition of lost circulation materials. Lost circulation materials with high density could deposit faster close to the wellbore and therefore accelerating the control process. High concentration of lost circulation materials is likely to shorten the plugging time, which should be determined referring to the severity of loss. This work provides drilling engineers a practical method for simulating the lost circulation and selecting lost circulation material.

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Victorov, Alexey S., and Olga N. Trapeznikova. "Stochastic Models Of Dynamic Balance State For The Morphological Patterns Of Cryolithozone Landscapes." GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY 12, no. 3 (October 3, 2019): 6–15. http://dx.doi.org/10.24057/2071-9388-2018-68.

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The paper deals with mathematical modeling of a morphological pattern for a broad spectrum of cryolithozone landscapes in a state of a dynamic balance. The state of the dynamic balance means that all the elements of this morphological pattern are in continuous changing while its general parameters as a whole are stable. Two contradirectional processes at the same territory is a precondition for a state of dynamic balance.We developed a morphological pattern model for lacustrine thermokarst plains with fluvial erosion on the base of the mathematical morphology of landscape using the random process theory. The contra-directional processes here include thermokarst lakes appearing and increasing in size from one side and drainage of the lakes by fluvial erosion, from the other. Thus, the regularities of the structure and dynamics of each landscape morphological pattern are theoretically substantiated. The results of the mathematical modeling were empirically verified at some key sites.

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John, V. Chandy, M. G. Satish, and D. H. Waller. "Development and evaluation of numerical hydrodynamic models for small lakes and reservoirs." Canadian Journal of Civil Engineering 22, no. 2 (April 1, 1995): 270–82. http://dx.doi.org/10.1139/l95-036.

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The response of a small lake or reservoir system to wind and streamflow forcing is examined in this paper using a numerical model based on Navier–Stokes equation and a numerical hydraulic model using the segment-node approach. The main mass transport in the lake has been found to be due to wind; the circulation caused by stream inflow and outflow of the lake contributes a relatively small fraction of the total transport. The above-mentioned models have been applied to different wind regimes and constant or variable inflow–outflow conditions of Long Lake (Nova Scotia). Comparisons are made between observed data and model results by both models. The model response has also been studied for generation of seiches and wind setup in the lake; and the response of the lake to these forcing functions has been presented. The comparison of model results with in situ field data establishes model's suitability to make predictions. Drogue and water level measurements were made at a number of locations in the Long Lake to validate the numerical models. The results from the numerical simulation using the two models compare favourably with the observed data. As may be expected, the segment-node modelling scheme was found to be computationally more efficient and relatively easy to run on a personal computer. Key words: numerical model, hydrodynamics, circulation, Long Lake, temperature, dissolved oxygen, stratification, Nova Scotia.

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Ziemińska-Stolarska, Aleksandra, and Jerzy Skrzypski. "Review of Mathematical Models of Water Quality." Ecological Chemistry and Engineering S 19, no. 2 (January 1, 2012): 197–211. http://dx.doi.org/10.2478/v10216-011-0015-x.

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Review of Mathematical Models of Water Quality Water is one of the main elements of the environment which determine the existence of life on the Earth, affect the climate and limit the development of civilization. Water resources management requires constant monitoring in terms of its qualitative-quantitative values. Proper assessment of the degree of water pollution is the basis for conservation and rational utilization of water resources. Water quality in lakes and dams is undergoing continuous degradation caused by natural processes resulting from eutrophication and due to anthropogenic reasons. One of the tools that are used to solve problems of surface water pollution is modelling of changes which take place in lake waters and associated water quality changes. In the last thirty years a rapid development of mathematical modelling of water resources quality has been observed. A number of computer models have been designed which are successfully applied in practice in many countries, including Poland. This paper presents an overview of mathematical models for assessment of water quality in dam reservoirs. Description of the WASP program which will be used for modelling water quality in the Sulejow Reservoir was the focal point.

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Sudakov, I. A., and S. A. Vakulenko. "Mathematical modelling of positive carbon-climate feedback: permafrost lake methane emission case." Earth System Dynamics Discussions 3, no. 1 (April 4, 2012): 235–57. http://dx.doi.org/10.5194/esdd-3-235-2012.

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Abstract. The permafrost methane emission problem is in the focus of attention of different climate models. We present new approach to the permafrost methane emission modeling. The tundra permafrost lakes is potential source of methane emission. Typically, tundra landscape contains a number of small lakes and warming leads to lake extension. We are making use of this process by the nonlinear theory of phase transitions. We find that climate catastrophe possibility depends on a feedback coefficient connecting the methane concentration in atmosphere and temperature, and on the tundra permafrost methane pool.

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Guven, Basak, and Alan Howard. "A review and classification of the existing models of cyanobacteria." Progress in Physical Geography: Earth and Environment 30, no. 1 (January 2006): 1–24. http://dx.doi.org/10.1191/0309133306pp464ra.

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Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting bloom occurrence in lakes and rivers. In this paper existing key models of cyanobacteria are reviewed, evaluated and classified. Two major groups emerge: deterministic mathematical and artificial neural network models. Mathematical models can be further subcategorized into those models concerned with impounded water bodies and those concerned with rivers. Most existing models focus on a single aspect such as the growth of transport mechanisms, but there are a few models which couple both.

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Ojimadu, U. H., A. O. Oluwole, A. O. Olasupo, M. A. Usman, T. J. Odule, O. O. Olubanwo, O. Oyewole, and M. A. Ayodele. "MATHEMATICAL ANALYSIS OF ELECTROPHYSIOLOGICAL CARDIAC TISSUE MEMBRANE MODELS." FUDMA JOURNAL OF SCIENCES 6, no. 2 (May 11, 2022): 138–43. http://dx.doi.org/10.33003/fjs-2022-0602-931.

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This paper presents some cardiac electrophysiological models. Proper mathematical analysis was done on the proposed models. In the cause of the analysis, several assumptions were made which helped in providing a parallel platform for making qualitative solutions so as to reduce any form of bias. Graphical analysis was adopted in solving the cardiac electrophysiological models using conservation and dispersions equations. The results obtained were derived from computer simulation by observing ring lengths on a valid restitution curve. The restitution curves helps us to subject three different turns of ring lengths and certain observations were made on the behavior of the three ring lengths. An increase in ring length will cause a corresponding increase in blood circulation and vice versa. It was suggested that 2D or 3D computer simulation should be adopted for better performance and yield of the models

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Leon, Luis F., Jason P. Antenucci, Yerubandi R. Rao, and Craig McCrimmon. "Summary performance of the Estuary and Lake Computer Model (ELCOM): application in the Laurentian and other Great Lakes." Water Quality Research Journal 47, no. 3-4 (August 1, 2012): 252–67. http://dx.doi.org/10.2166/wqrjc.2012.022.

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The use of sophisticated three-dimensional (3D) hydrodynamic models is often required to simulate the spatial and temporal variability of water quality in large lakes. Recently, coupled lake–atmosphere models have also been developed to resolve the spatial distribution of the thermal behavior in lakes and to assess the feedback mechanisms at the air–water interface. In the studies summarized in this paper, the 3D Estuary and Lake Computer Model (ELCOM) acts as the hydrodynamic driver that provides temperature, salinity, and the transport fields that, if coupled with the Computational Aquatic Ecosystem Dynamics Model (CAEDYM), simulates nutrients, phytoplankton, zooplankton, and benthic habitat. This study presents a summary of the performance of ELCOM, and in an indirect form, serves as well as a corroboration of the strength or weakness of the coupled modeling and its ability to reproduce the thermal structure and circulation patterns, with examples from the Laurentian Great Lakes (Erie and Ontario), Northern Great Lakes (Great Slave Lake and Great Bear Lake), and Lake Winnipeg in Central Canada.

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Novitsky, Nikolay N. "Mathematical models and methods for analyzing flow properties in hydraulic circuits with closed circulation circuits." E3S Web of Conferences 219 (2020): 01004. http://dx.doi.org/10.1051/e3sconf/202021901004.

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The article is devoted to the problems of calculating the distribution of flow quality parameters over the elements of the hydraulic system. The main attention is paid to the problem of such a calculation in the presence of closed circulation circuits in the system, when traditional methods and algorithms become ineffective. Mathematical models of the distribution of quality parameters are given, the results of the analysis of their properties in the presence of closed circulation circuits are presented. Against the background of the analysis of the applicability of general mathematical methods for solving the problem, two new methods are proposed based on the special properties of this problem - the “iterative topological” algorithm and the “algebraic-topological” method. Both methods are universal and provide a solution in the presence of closed circulation loops, and in their absence they coincide with the traditional “topological” algorithm.

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Rzaev, E. A., S. R. Rasulov, and A. G. Rzaev. "Developing mathematical models for cardiovascular system functional assessments." Kazan medical journal 96, no. 4 (August 15, 2015): 681–85. http://dx.doi.org/10.17750/kmj2015-681.

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Aim. Development of mathematical models of circulation (considering anomaly in hemorheology) allowing to diagnose functional condition of vessels/cardiovascular system. Methods. Echocardiography, mathematical modeling, sedimentation and rheology laws, human mechanics and physiology methods were used for developing mathematical models. Results. The following mathematical models were obtained: for determination of colloid dispersive blood system viscosity, considering concentration of dispersive phase (blood cells) and blood structure formation; velocity of inconvenient blood cells sedimentation depending on flow velocity of sediment and cell concentration; parameters of blood elasticity and viscosity as a connection between the velocity change and blood viscosity, Young`s elasticity and change tension; blood filtration in vessels (modified form of Darcy`s law) considering tension and changes of destroyed and undestroyed colloid blood system structure velocity. It was shown that impairments of blood flow velocity leads to blood cells sedimentation and thrombus structure formation, which is not moving according to Newton’s law. New indicators for diagnosing functional condition of vessels and estimating the severity of vascular insufficiency are introduced. Conclusion. Developed hemorheologic models allow to adequately estimate human cardiovascular bloodflow.

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Perrone, Michela, Massimiliano Scalici, Luisa Conti, David Moravec, Jan Kropáček, Maria Sighicelli, Francesca Lecce, and Marco Malavasi. "Water Mixing Conditions Influence Sentinel-2 Monitoring of Chlorophyll Content in Monomictic Lakes." Remote Sensing 13, no. 14 (July 8, 2021): 2699. http://dx.doi.org/10.3390/rs13142699.

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Prompt estimation of phytoplankton biomass is critical in determining the ecological quality of freshwaters. Remote Sensing (RS) may provide new opportunities to integrate with situ traditional monitoring techniques. Nonetheless, wide regional and temporal variability in freshwater optical constituents makes it difficult to design universally applicable RS protocols. Here, we assessed the potential of two neural networks-based models, namely the Case 2 Regional CoastColour (C2RCC) processor and the Mixture Density Network (MDN), applied to MSI Sentinel-2 data for monitoring Chlorophyll (Chl) content in three monomictic volcanic lakes while accounting for the effect of their specific water circulation pattern on the remotely-sensed and in situ data relation. Linear mixed models were used to test the relationship between the remote sensing indices calculated through C2RCC (INN) and MDN (IMDN), and in situ Chl concentration. Both indices proved to explain a large portion of the variability in the field data and exhibited a positive and significant relationship between Chl concentration and satellite data, but only during the mixing phase. The significant effect of the water circulation period can be explained by the low responsiveness of the RS approaches applied here to the low phytoplankton biomass, typical of the stratification phase. Sentinel-2 data proved their valuable potential for the remote sensing of phytoplankton in small inland water bodies, otherwise challenging with previous sensors. However, caution should be taken, since the applicability of such an approach on certain water bodies may depend on hydrological and ecological parameters (e.g., thermal stratification and seasonal nutrient availability) potentially altering RS chlorophyll detection by neural networks-based models, despite their alleged global validity.

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Brown, Laura C., and Claude R. Duguay. "The response and role of ice cover in lake-climate interactions." Progress in Physical Geography: Earth and Environment 34, no. 5 (July 8, 2010): 671–704. http://dx.doi.org/10.1177/0309133310375653.

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This paper reviews the current state of knowledge pertaining to the interactions of lake ice and climate. Lake ice has been shown to be sensitive to climate variability through observations and modelling, and both long-term and short-term trends have been identified from ice records. Ice phenology trends have typically been associated with variations in air temperatures while ice thickness trends tend to be associated more to changes in snow cover. The role of ice cover in the regional climate is less documented and with longer ice-free seasons possible as a result of changing climate conditions, especially at higher latitudes, the effects of lakes on their surrounding climate (such as increased evaporation, lake-effect snow and thermal moderation of surrounding areas, for example) can be expected to become more prominent. The inclusion of lakes and lake ice in climate modelling is an area of increased attention in recent studies. An important step in improving predictions of ice conditions in models is the assimilation of remote sensing data in areas where in-situ data is lacking, or non-representative of the lake conditions. The ability to accurately represent ice cover on lakes will be an important step in the improvement of global circulation models, regional climate models and numerical weather forecasting.

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Reed-Andersen, Tara, Stephen R. Carpenter, Dianna K. Padilla, and Richard C. Lathrop. "Predicted impact of zebra mussel (Dreissena polymorpha) invasion on water clarity in Lake Mendota." Canadian Journal of Fisheries and Aquatic Sciences 57, no. 8 (August 1, 2000): 1617–26. http://dx.doi.org/10.1139/f00-094.

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Lake Mendota, which is plagued by periodic cyanobacterial blooms, is typical of many lakes in the Laurentian Great Lakes region that are vulnerable to zebra mussels (Dreissena polymorpha) but have yet to be invaded. We coupled removal estimates with chlorophyll production estimates in a dynamic model to predict the likely impact of mussel-mediated removal of phytoplankton on water clarity across a range of hypothetical zebra mussel densities. Models were fit to chlorophyll and temperature data collected biweekly from Lake Mendota during 1977-1993. When we assumed daily epilimnetic circulation, the percentage of days when the chlorophyll concentration exceeded 50 µg·L-1 was decreased threefold at mussel densities as low as 1000 mussels·m-2. When we assumed less frequent epilimnetic circulation, the density of mussels required to substantially improve water clarity increased dramatically. We predict that zebra mussel invasion would lead to increased water clarity in Lake Mendota. Cyanobacterial blooms would be reduced but not eliminated. Negative impacts on other lake processes following zebra mussel invasion could outweigh the benefits of lower phytoplankton concentrations.

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Moldasheva, R., A. Ismailova, and A. Zadagali. "SIGNS OF STABILITY OF AQUATIC ECOSYSTEMS IN MATHEMATICAL MODELS." Bulletin of the National Engineering Academy of the Republic of Kazakhstan 85, no. 3 (September 15, 2022): 43–48. http://dx.doi.org/10.47533/2020.1606-146x.178.

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To date, various data on water resources have been accumulated, but hydrobiological and hydrochemical indicators remain available to assess the current state of aquatic ecosystems, which can be the basis for assessing the environmental situation within the water body. Systematization of multiyear and diverse data on the lakes and rivers of the country, the use of mathematical tools for assessing and forecasting the state of the aquatic ecosystem is impossible without the use of information and communication technologies. Quality mathematical modeling of aquatic ecosystems and the development of information and analytical system for the study of aquatic ecosystems is an urgent task, including databases of various-quality data on the water body and its ecosystem, data management and processing tools, as well as a set of mathematical models for the functioning of the water body ecosystem. Research is based on information technology, statistical data processing, and mathematical modeling. Mathematical models are based on systems of differential equations, solutions are sought with the help of own computing programs and software suites (Maple, Matlab, Mathematics, etc.). When possible, modeling includes analytical studies of the properties of solutions, primarily this concerns stationary or spatially homogeneous solutions, as well as asymptotic properties of solutions. The lower trophic levels of the water body ecosystem are studied, as this determines the functioning of aquatic ecosystems. The species composition of phytoplankton is an indicator of the ecological state of the water body. Based on the quantitative characteristics of phytoplankton, the bioproductivity of the aquatic ecosystem is calculated. The physical and chemical characteristics of water allow drawing conclusions about the pollution of the water body and the composition of mineral nutrition for phytoplankton.

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Koutitas, Christopher, and Maria Gousidou-Koutita. "A comparative study of three mathematical models for wind-generated circulation in coastal areas." Coastal Engineering 10, no. 2 (July 1986): 127–38. http://dx.doi.org/10.1016/0378-3839(86)90013-x.

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Brands, Judith, Hans Vink, and Jurgen W. G. E. Van Teeffelen. "Comparison of four mathematical models to analyze indicator-dilution curves in the coronary circulation." Medical & Biological Engineering & Computing 49, no. 12 (November 18, 2011): 1471–79. http://dx.doi.org/10.1007/s11517-011-0845-9.

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Kumar, Aadesh, Dr Ram avtar, and Dr Deepti Seth. "Mathematical Modeling of Oxygen Transport in Retinal Layers." International Journal of Emerging Science and Engineering 6, no. 6 (October 25, 2019): 1–4. http://dx.doi.org/10.35940/ijese.f2304.106619.

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The retina contains maximum oxygen ( consumption making it particular valuneric to vascular in fults, diminishing oxygen and circulation of nutrients. The goel of this paper to develop a mathematical model for quantitative analysis of transportation of oxygen and consumption in each retinal layer. Such models allows us to predict the effect of qualitatative change in retinal vasculature on oxygen supply in retinal layers. A differential equation , which used in this paper describing how the oxygen transport and cosumpt by the retinal layers.

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Vieira, J. M. P., J. L. S. Pinho, N. Dias, D. Schwanenberg, and H. F. P. van den Boogaard. "Parameter estimation for eutrophication models in reservoirs." Water Science and Technology 68, no. 2 (July 1, 2013): 319–27. http://dx.doi.org/10.2166/wst.2013.248.

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Excessive eutrophication is a major water quality issue in lakes and reservoirs worldwide. This complex biological process can lead to serious water quality problems. Although it can be adequately addressed by applying sophisticated mathematical models, the application of these tools in a reservoir management context requires significant amounts of data and large computation times. This work presents a simple primary production model and a calibration procedure that can efficiently be used in operational reservoir management frameworks. It considers four state variables: herbivorous zooplankton, algae (measured as chlorophyll-a pigment), phosphorous and nitrogen. The model was applied to a set of Portuguese reservoirs. We apply the model to 23 Portuguese reservoirs in two different calibration settings. This research work presents the results of the estimation of model parameters.

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Muñoz, Ángel G., Xiaosong Yang, Gabriel A. Vecchi, Andrew W. Robertson, and William F. Cooke. "A Weather-Type-Based Cross-Time-Scale Diagnostic Framework for Coupled Circulation Models." Journal of Climate 30, no. 22 (October 17, 2017): 8951–72. http://dx.doi.org/10.1175/jcli-d-17-0115.1.

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Abstract This study proposes an integrated diagnostic framework based on atmospheric circulation regime spatial patterns and frequencies of occurrence to facilitate the identification of model systematic errors across multiple time scales. To illustrate the approach, three sets of 32-yr-long simulations are analyzed for northeastern North America and for the March–May season using the Geophysical Fluid Dynamics Laboratory’s Low Ocean–Atmosphere Resolution (LOAR) and Forecast-Oriented Low Ocean Resolution (FLOR) coupled models; the main difference between these two models is the horizontal resolution of the atmospheric model used. Regime-dependent biases are explored in the light of different atmospheric horizontal resolutions and under different nudging approaches. It is found that both models exhibit a fair representation of the observed circulation regime spatial patterns and frequencies of occurrence, although some biases are present independently of the horizontal resolution or the nudging approach and are associated with a misrepresentation of troughs centered north of the Great Lakes and deep coastal troughs. Moreover, the intraseasonal occurrence of certain model regimes is delayed with respect to observations. On the other hand, interexperiment differences in the mean frequencies of occurrence of the simulated weather types, and their variability across multiple time scales, tend to be negligible. This result suggests that low-resolution models could be of potential use to diagnose and predict physical variables via their simulated weather type characteristics.

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Fenocchi, Andrea, Gabriella Petaccia, and Stefano Sibilla. "Modelling flows in shallow (fluvial) lakes with prevailing circulations in the horizontal plane: limits of 2D compared to 3D models." Journal of Hydroinformatics 18, no. 6 (May 14, 2016): 928–45. http://dx.doi.org/10.2166/hydro.2016.033.

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The numerical modelling of circulations in shallow lakes is a relevant tool for all environmental applications in which flow advection processes are of interest, e.g. for studies on nutrients, microorganisms, pollutants and sediment dynamics. While three-dimensional (3D) models are needed to properly describe the flow fields of basins with the main circulations in the vertical plane, two-dimensional (2D) models are commonly deemed to yield adequate results for lakes with prevailing horizontal circulations. However, the depth-averaged approximation is more limiting for wind-driven flows than for gravity-driven ones, such as rivers, as the driving force is a surface rather than a volume one, distributed along the depth through turbulence. In this work, the effects of such inaccuracy on the reproduction of circulation layouts are evaluated through compared simulations between a 2D Shallow Water solver and a 3D Reynolds-Averaged Navier-Stokes one. The models are first applied to a simple enclosed elliptical test basin and then to the real case of the Superior Lake of Mantua, a shallow fluvial lake in Northern Italy, thereby also investigating the influences of the interaction of wind with a riverine current and of a complex bathymetry on the compared results.

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Bueno, Guilherme Wolff, Dominique Bureau, James Owen Skipper-Horton, Rodrigo Roubach, Flávia Tavares de Mattos, and Francisco Ernesto Moreno Bernal. "Mathematical modeling for the management of the carrying capacity of aquaculture enterprises in lakes and reservoirs." Pesquisa Agropecuária Brasileira 52, no. 9 (September 2017): 695–706. http://dx.doi.org/10.1590/s0100-204x2017000900001.

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Abstract: Flooded areas of reservoirs and artificial lakes have been increasingly used for fish production; however, the waste generated by aquaculture has become a concern for the sustainable development of this activity. One of the main strategies adopted by management and regulatory agencies is the use of hydrodynamic models that calculate the carrying or nutrient load capacity of a particular water body and the effect of fish farming. These models are precise in the development of optimal strategies for feeding and waste calculation. This review paper addresses this topic and describes the methodology developed for the analysis and simulation of the carrying capacity for fish production, based on the integration of the Fish-PrFEQ nutritional bioenergetic model and the hydrodynamic model of Dillon & Rigler. This methodology allows evaluating the real contribution of aquaculture waste and assists in the planning and management of aquaculture in these aquatic environments, besides enabling and encouraging producers and the aquaculture industry to use fish food with better nutritional quality and lower environmental impact.

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Bennington, Val, Michael Notaro, and Kathleen D. Holman. "Improving Climate Sensitivity of Deep Lakes within a Regional Climate Model and Its Impact on Simulated Climate." Journal of Climate 27, no. 8 (April 10, 2014): 2886–911. http://dx.doi.org/10.1175/jcli-d-13-00110.1.

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Abstract Regional climate models aim to improve local climate simulations by resolving topography, vegetation, and land use at a finer resolution than global climate models. Lakes, particularly large and deep lakes, are local features that significantly alter regional climate. The Hostetler lake model, a version of which is currently used in the Community Land Model, performs poorly in deep lakes when coupled to the regional climate of the International Centre for Theoretical Physics (ICTP) Regional Climate Model, version 4 (RegCM4). Within the default RegCM4 model, the lake fails to properly stratify, stifling the model’s ability to capture interannual variability in lake temperature and ice cover. Here, the authors improve modeled lake stratification and eddy diffusivity while correcting errors in the ice model. The resulting simulated lake shows improved stratification and interannual variability in lake ice and temperature. The lack of circulation and explicit mixing continues to stifle the model’s ability to simulate lake mixing events and variability in timing of stratification and destratification. The changes to modeled lake conditions alter seasonal means in sea level pressure, temperature, and low-level winds in the entire model domain, highlighting the importance of lake model selection and improvement for coupled simulations. Interestingly, changes to winter and spring snow cover and albedo impact spring warming. Unsurprisingly, regional climate variability is not significantly altered by an increase in lake temperature variability.

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Schwab, D. J., and K. W. Bedford. "Initial Implementation of the Great Lakes Forecasting System: A Real-Time System for Predicting Lake Circulation and Thermal Structure." Water Quality Research Journal 29, no. 2-3 (May 1, 1994): 203–20. http://dx.doi.org/10.2166/wqrj.1994.014.

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Abstract The Great Lakes Forecasting System is a real-time coastal prediction system for forecasting, on a daily basis, the physical state of each of the Great Lakes for the next two days. Forecast variables include the surface water level fluctuation, horizontal and vertical structure of temperature and currents, and turbulence. The system uses meteorological observations, satellite data, and forecasts from numerical weather prediction models as input. Lake circulation and thermal structure are calculated using a three-dimensional hydrodynamic prediction model. Output from the model is used to provide information on the current state of the lake and to predict changes for the next two days. This information is used by scientists, government agencies, commercial operations, and the public for enhancement of commercial and recreational activity, resource management, and hazard avoidance. This paper describes system design, data acquisition and analysis procedures, the hydrodynamic model, and sample model output. The initial implementation of the system provides daily nowcasts of system variables for one lake, Lake Erie. Requirements for implementing actual lake forecasts are discussed.

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Carley, D. W., and D. C. Shannon. "A minimal mathematical model of human periodic breathing." Journal of Applied Physiology 65, no. 3 (September 1, 1988): 1400–1409. http://dx.doi.org/10.1152/jappl.1988.65.3.1400.

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Numerous mathematical models of periodic breathing (PB) currently exist. These models suggest mechanisms that may underlie many known causes of PB. However, each model that has been shown to simulate PB under reasonable conditions contains greater than 15 physiological parameters. Because some parameters exhibit a wide range of values in a population, such simulations cannot test a model's ability to account for the breathing patterns of individuals. Furthermore it is impractical to perform a direct experimental validation study that would require the estimation of each of 15 or more parameters for each subject. A minimal model of PB is presented that is suitable for direct validation. Analytic expressions are given that define the conditions for PB in terms of the following: 1) CO2 sensitivity, 2) Cardiac output, 3) Mixed venous CO2, 4) Circulation time, and 5) Mean lung volume for CO2. This model is shown to be consistent with previous models and experimental data regarding the degree of hypoxia or congestive heart failure required to produce PB. A quantitative measure of relative stability is defined as a metric of comparison to the human studies described in the accompanying paper (J. Appl. Physiol. 65: 1389-1399, 1988).

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Run-Peng, Qiao, He Jun-Neng, Liang Qian-Chao, Yang Fan, and Fu Da-Wang. "Comparative analysis of SOFC-MGT top-level and new bottom-level system performance." E3S Web of Conferences 271 (2021): 04013. http://dx.doi.org/10.1051/e3sconf/202127104013.

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In order to make the SOFC-MGT system more widely used, the mathematical simulation models of the SOFC-MGT top-level circulatory system and the new bottom circulatory system were first established, and then the performance of the two systems was analyzed and compared using Matlab/Simulink simulation software. The research results show that the output performance of the SOFC-MGT top-level circulation system is due to the new bottom-level circulation system, and the stack output performance of the two systems is not much different.

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Charusombat, Umarporn, Ayumi Fujisaki-Manome, Andrew D. Gronewold, Brent M. Lofgren, Eric J. Anderson, Peter D. Blanken, Christopher Spence, et al. "Evaluating and improving modeled turbulent heat fluxes across the North American Great Lakes." Hydrology and Earth System Sciences 22, no. 10 (October 26, 2018): 5559–78. http://dx.doi.org/10.5194/hess-22-5559-2018.

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Abstract. Turbulent fluxes of latent and sensible heat are important physical processes that influence the energy and water budgets of the North American Great Lakes. These fluxes can be measured in situ using eddy covariance techniques and are regularly included as a component of lake–atmosphere models. To help ensure accurate projections of lake temperature, circulation, and regional meteorology, we validated the output of five algorithms used in three popular models to calculate surface heat fluxes: the Finite Volume Community Ocean Model (FVCOM, with three different options for heat flux algorithm), the Weather Research and Forecasting (WRF) model, and the Large Lake Thermodynamic Model. These models are used in research and operational environments and concentrate on different aspects of the Great Lakes' physical system. We isolated only the code for the heat flux algorithms from each model and drove them using meteorological data from four over-lake stations within the Great Lakes Evaporation Network (GLEN), where eddy covariance measurements were also made, enabling co-located comparison. All algorithms reasonably reproduced the seasonal cycle of the turbulent heat fluxes, but all of the algorithms except for the Coupled Ocean–Atmosphere Response Experiment (COARE) algorithm showed notable overestimation of the fluxes in fall and winter. Overall, COARE had the best agreement with eddy covariance measurements. The four algorithms other than COARE were altered by updating the parameterization of roughness length scales for air temperature and humidity to match those used in COARE, yielding improved agreement between modeled and observed sensible and latent heat fluxes.

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Jones, Michael L., Brian J. Shuter, Yingming Zhao, and Jason D. Stockwell. "Forecasting effects of climate change on Great Lakes fisheries: models that link habitat supply to population dynamics can help." Canadian Journal of Fisheries and Aquatic Sciences 63, no. 2 (February 1, 2006): 457–68. http://dx.doi.org/10.1139/f05-239.

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Future changes to climate in the Great Lakes may have important consequences for fisheries. Evidence suggests that Great Lakes air and water temperatures have risen and the duration of ice cover has lessened during the past century. Global circulation models (GCMs) suggest future warming and increases in precipitation in the region. We present new evidence that water temperatures have risen in Lake Erie, particularly during summer and winter in the period 19652000. GCM forecasts coupled with physical models suggest lower annual runoff, less ice cover, and lower lake levels in the future, but the certainty of these forecasts is low. Assessment of the likely effects of climate change on fish stocks will require an integrative approach that considers several components of habitat rather than water temperature alone. We recommend using mechanistic models that couple habitat conditions to population demographics to explore integrated effects of climate-caused habitat change and illustrate this approach with a model for Lake Erie walleye (Sander vitreum). We show that the combined effect on walleye populations of plausible changes in temperature, river hydrology, lake levels, and light penetration can be quite different from that which would be expected based on consideration of only a single factor.

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Uchiyama, Tadayasu, Bruce P. Finney, and Milo D. Adkison. "Effects of marine-derived nutrients on population dynamics of sockeye salmon (Oncorhynchus nerka)." Canadian Journal of Fisheries and Aquatic Sciences 65, no. 8 (August 2008): 1635–48. http://dx.doi.org/10.1139/f08-085.

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The effects of marine-derived nutrients (MDN) on the productivity of sockeye salmon ( Oncorhynchus nerka ) stocks in Alaska, USA, were examined through nitrogen stable isotope analysis of smolts and mathematical models of the sockeye stock–recruit relationship. Smolt δ15N was used to infer the degree to which smolts depend on MDN for their growth. We found that characteristics of sockeye nursery lakes and watersheds significantly affected the availability of MDN to juvenile sockeye. The magnitude of escapement and water residence time were the most important factors affecting the MDN availability to juvenile salmon. Analysis of stock–recruit models indicated that regional environmental fluctuations had a large effect on stock productivities. However, stock–recruitment data showed little evidence that increasing MDN input to nursery lakes increased stock productivities. Stock–recruitment data may be poorly suited to detection of the influence of MDN because of the multitude of factors that influence juvenile survival in the first several years of their life.

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Medvinsky, Alexander B., Alexey V. Rusakov, Boris V. Adamovich, Tamara M. Mikheyeva, and Nailya I. Nurieva. "Determinism versus randomness in plankton dynamics: The analysis of noisy time series based on the recurrence plots." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 4 (August 27, 2019): 187–96. http://dx.doi.org/10.1515/rnam-2019-0016.

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Abstract The quantitative analysis of recurrence plots while applied to mathematical models was shown to be an effective tool in recognizing a frontier between deterministic chaos and random processes. In nature, however, unlike mathematical models, deterministic processes are closely intertwined with random influences. As a result, the non-structural distributions of points on the recurrence plots, which are typical of random processes, are inevitably superimposed on the aperiodic structures characteristic of chaos. Taking into account that the stochastic impacts are an inherent feature of the dynamics of populations in the wild, we present here the results of the analysis of recurrence plots in order to reveal the extent to which irregular phytoplankton oscillations in the Naroch Lakes, Belarus, are susceptible to stochastic impacts. We demonstrate that numerical assessments of the horizon of predictability Tpr of the dynamics under study and the average number Pd of the points that belong to the diagonal segments on the recurrence plots can furnish insights into the extent to which the dynamics of both model and phytoplankton populations are affected by random components. Specifically, a comparative analysis of the values of Tpr and Pd for the time series of phytoplankton and the time series of random processes allows us to conclude that random components of the phytoplankton dynamics in the Naroch Lakes do not prevent recognition of chaotic nature of these dynamics.

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Munroe, Jeffrey S., and Benjamin J. C. Laabs. "Multiproxy lacustrine records of post-glacial environmental change from the Uinta Mountains, Utah, USA." GSA Bulletin 132, no. 1-2 (May 2, 2019): 48–64. http://dx.doi.org/10.1130/b35056.1.

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Abstract Twenty-one sediment cores were obtained from 20 lakes in the Uinta Mountains, Utah, USA. Depth-age models were developed using 14C dating, and sediments were analyzed for loss-on-ignition (LOI), carbon-nitrogen ratio (C:N), and grain size distribution. Although some of these cores have been considered individually in previous studies, here the entire set of cores is evaluated collectively to identify consistent patterns, commonalities, and trends in the post-glacial interval. All lakes accumulated substantially greater amounts of submicron-size clastic material before ca. 9.5 ka BP. This pattern is interpreted as a signal of prolonged landscape instability following deglaciation. Values of LOI and C:N exhibit a strong, positive correlation in nearly all lakes, indicating that organic matter accumulation is controlled by the influx of terrestrial material. In the six lakes exhibiting the strongest correlation, and featuring the most robust inflowing streams, median grain size and the abundance of sand increased between 10 and 6 ka BP, simultaneous with increases in LOI and C:N. This correspondence is interpreted as evidence for frequent high-intensity storms during the early Holocene, likely driven by enhanced monsoonal circulation. The early parts of five of the records contain a sharp increase in LOI. Lakes exhibiting this pattern are typically smaller and shallower, and are located in less rugged watersheds. Finally, all six cores from the western Uinta Mountains contain evidence for an environmental perturbation ca. 4.5 ka BP. Although the nature of this event is unclear, these lakes accumulated notably finer-grained sediment with less organic matter at this time. This analysis illuminates the post-glacial history of this strategically located mountain range, and underscores the value inherent in analyzing cores from multiple lakes when reconstructing paleoclimatic history.

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Quarteroni, A., A. Manzoni, and C. Vergara. "The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications." Acta Numerica 26 (May 1, 2017): 365–590. http://dx.doi.org/10.1017/s0962492917000046.

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Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. In this review article we will address the two principal components of the cardiovascular system: arterial circulation and heart function. We will systematically describe all aspects of the problem, ranging from data imaging acquisition, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, proposing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the multiscale nature of the physiological processes involved, and the need to devise computational methods that are stable, reliable and efficient. Critical issues involve filtering the data, identifying the parameters of mathematical models, devising optimal treatments and accounting for uncertainties. For this reason, we will devote the last part of the paper to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are of paramount importance when solving problems with high complexity, which would otherwise be out of reach.

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Papadimos, Dimitris, Kleoniki Demertzi, and Dimitris Papamichail. "Assessing Lake Response to Extreme Climate Change Using the Coupled MIKE SHE/MIKE 11 Model: Case Study of Lake Zazari in Greece." Water 14, no. 6 (March 15, 2022): 921. http://dx.doi.org/10.3390/w14060921.

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Lakes, either artificial or natural, are greatly important as a component in their catchments’ hydrology, but also as ecosystem service providers. However, due to climate change, they have begun to face numerous problems with their water quality and quantity. Furthermore, general circulation models (GCMs) show future climate change with a reduction in rainfall and increase in temperature. The aim of the current study is to present an application where GCMs and state-of-the-art hydrological modelling system MIKE SHE/MIKE 11 are combined for assessing the response of a Greek lake in terms of its water balance and water level under climate change. Four general circulation models (GCMs; GFDL-CM3, MIROC-ESM-CHEM, MIROC-ESM, IPSL-CM5A-LR) for the extreme climate change scenario of RCP8.5 were used in the basin of Lake Zazari in Greece as a case study. Results showed that, by keeping the irrigated demands (the main water user) unchanged in the future, the lake exhibited a lower water level for all GCMs, fluctuating from −0.70 to −1.8 m for the mean (min) water level and from −0.30 to −1.20 m for the mean (max) water level. Instead of the above and by preserving the amount of withdraw water n from the lake at a certain percentage of inflows, the irrigated area should be reduced from 54.1% to 64.05% depending on the circulation model.

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38

Grzywacz, Robert. "Continuous mathematical models of airlift bioreactors: Families, affinity, diversity and modelling for single-substrate kinetics." Chemical and Process Engineering 33, no. 2 (June 1, 2012): 291–309. http://dx.doi.org/10.2478/v10176-012-0027-9.

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Continuous mathematical models of airlift bioreactors: Families, affinity, diversity and modelling for single-substrate kinetics This paper presents a method of describing an airlift bioreactor, in which biodegradation of a carbonaceous substrate described by single-substrate kinetics takes place. Eight mathematical models based on the assumption of liquid plug flow and axial dispersion flow through the riser and the downcomer in the reactor were proposed. Additionally, the impact of degassing zone with assumed complete mixing on the obtained results was analyzed. Calculations were performed for two representative hydrodynamic regimes of reactor operation, i.e. with the presence of gas bubbles only within the riser and for complete gas circulation. The conclusions related to the apparatus design and process performance under sufficient aeration of the reaction mixture were drawn on the basis of the obtained results.

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39

Thoma, M., K. Grosfeld, C. Mayer, and F. Pattyn. "Interaction between ice sheet dynamics and subglacial lake circulation: a coupled modelling approach." Cryosphere Discussions 3, no. 3 (September 29, 2009): 805–29. http://dx.doi.org/10.5194/tcd-3-805-2009.

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Abstract. Subglacial lakes in Antarctica influence to a large extent the flow of the ice sheet. In this study we use an idealised lake geometry to study this impact. We employ a) an improved three-dimensional full Stokes ice flow model with a nonlinear rheology, b) a three-dimensional fluid dynamics model with eddy diffusion to simulate basal mass balance, and c) a newly developed coupler to exchange boundary conditions between individual models. Different boundary conditions are applied over grounded ice and floating ice. This results in significantly increased temperatures within the ice on top of the lake, compared to ice at the same depth outside the lake area. Basal melting of the ice sheet increases this lateral temperature gradient. Upstream the ice flow converges towards the lake and accelerates by about 10% whenever basal melting at the ice–lake boundary is present. Above and downstream of the lake, where the ice flow diverges, a velocity decrease of about 10% is simulated.

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40

Gendelis, Staņislavs, and Andris Jakovičs. "APPLICATION OF MATHEMATICAL MODELS FOR THE SIMULATION OF THERMAL COMFORT CONDITIONS IN A LIVING ROOM." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 1 (June 18, 2005): 11. http://dx.doi.org/10.17770/etr2005vol1.2124.

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The paper deals with the distributions of temperature and averaged turbulent airflows in living rooms in 2D and 3D approximations using Ansys/Flotran and Ansys/CFX software respectively. The distributions are calculated depending on the placement and temperature of heaters, heat transfer coefficients of the building structures and ventilation conditions. The authors analyse the influence of these factors on the air circulation and the related heat flows through building structures. The thermal balance of a room and its dependence on various external factors is also considered. As thermal comfort conditions’ parameters are analysed, the airflow velocities and indoor temperatures with its gradients. It is shown that it is possible to save heating consumption, at the same time maintaining the conditions of thermal comfort in the room.

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McBean, E., and H. Motiee. "Assessment of impact of climate change on water resources: a long term analysis of the Great Lakes of North America." Hydrology and Earth System Sciences 12, no. 1 (February 11, 2008): 239–55. http://dx.doi.org/10.5194/hess-12-239-2008.

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Abstract. In the threshold of the appearance of global warming from theory to reality, extensive research has focused on predicting the impact of potential climate change on water resources using results from Global Circulation Models (GCMs). This research carries this further by statistical analyses of long term meteorological and hydrological data. Seventy years of historical trends in precipitation, temperature, and streamflows in the Great Lakes of North America are developed using long term regression analyses and Mann-Kendall statistics. The results generated by the two statistical procedures are in agreement and demonstrate that many of these variables are experiencing statistically significant increases over a seven-decade period. The trend lines of streamflows in the three rivers of St. Clair, Niagara and St. Lawrence, and precipitation levels over four of the five Great Lakes, show statistically significant increases in flows and precipitation. Further, precipitation rates as predicted using fitted regression lines are compared with scenarios from GCMs and demonstrate similar forecast predictions for Lake Superior. Trend projections from historical data are higher than GCM predictions for Lakes Michigan/Huron. Significant variability in predictions, as developed from alternative GCMs, is noted. Given the general agreement as derived from very different procedures, predictions extrapolated from historical trends and from GCMs, there is evidence that hydrologic changes particularly for the precipitation in the Great Lakes Basin may be demonstrating influences arising from global warming and climate change.

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42

White, Ronald J. "A note regarding the mathematical treatment of a class of steady-state compartmental models of the circulation." Physiological Reports 4, no. 17 (September 2016): e12945. http://dx.doi.org/10.14814/phy2.12945.

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Durga Prasad, G. V., G. Gopa Kishor, Manmohan Pandey, and Uday S. Dixit. "Numerical Simulations and Design Optimization of the PHT Loop of Natural Circulation BWR." Science and Technology of Nuclear Installations 2008 (2008): 1–12. http://dx.doi.org/10.1155/2008/690357.

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Mathematical modeling and numerical simulation of natural circulation boiling water reactor (NCBWR) are very important in order to study its performance for different designs and various off-design conditions and for design optimization. In the present work, parametric studies of the primary heat transport loop of NCBWR have been performed using lumped parameter models and RELAP5/MOD3.4 code. The lumped parameter models are based on the drift flux model and homogeneous equilibrium mixture (HEM) model of two-phase flow. Numerical simulations are performed with both models. Compared to the results obtained from the HEM model, those obtained from the drift flux model are closer to RELAP5. The variations of critical heat flux with various geometric parameters and operating conditions are thoroughly investigated. The material required to construct the primary heat transport (PHT) loop of NCBWR has been minimized using sequential quadratic programming. The stability of NCBWR has also been verified at the optimum point.

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Kozlov, V. A., O. Yu Dmitrieva, G. P. Itkin, A. S. Ivanov, A. P. Kuleshov, E. A. Volkova, and T. N. Govorova. "The optimization of an accomodation in the thoracic cavity child the axial pump don-3 (the mathematical model research)." Russian Journal of Transplantology and Artificial Organs 20, no. 3 (September 17, 2018): 40–44. http://dx.doi.org/10.15825/1995-1191-2018-3-40-44.

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We have developed and tested a technique for constructing 3D models of the chest and thoracic cavity organs. Due to the obtained results, the mathematical model was successfully used in the development of classification of variants of placement of implantable auxiliary circulation systems, and also for building 3D models for other purposes. In particular, the patients were graded according to the variants of placing the children’s axial pump DON-3 inside the patient’s chest cavity. Based on the data, the first fitting of the DON-3 pump was performed on a patient aged 7 years.

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45

Thoma, M., K. Grosfeld, C. Mayer, and F. Pattyn. "Interaction between ice sheet dynamics and subglacial lake circulation: a coupled modelling approach." Cryosphere 4, no. 1 (January 8, 2010): 1–12. http://dx.doi.org/10.5194/tc-4-1-2010.

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Abstract. Subglacial lakes in Antarctica influence to a large extent the flow of the ice sheet. In this study we use an idealised lake geometry to study this impact. We employ a) an improved three-dimensional full-Stokes ice flow model with a nonlinear rheology, b) a three-dimensional fluid dynamics model with eddy diffusion to simulate the basal mass balance at the lake-ice interface, and c) a newly developed coupler to exchange boundary conditions between the two individual models. Different boundary conditions are applied over grounded ice and floating ice. This results in significantly increased temperatures within the ice on top of the lake, compared to ice at the same depth outside the lake area. Basal melting of the ice sheet increases this lateral temperature gradient. Upstream the ice flow converges towards the lake and accelerates by about 10% whenever basal melting at the ice-lake boundary is present. Above and downstream of the lake, where the ice flow diverges, a velocity decrease of about 10% is simulated.

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46

Belov, Alexander, Dmitry Shaforost, and Viktor Chebotarev. "Mathematical Models for Assessing the Thermal Engineering Reliability of Boiler Units of Power Complexes." Известия высших учебных заведений. Электромеханика 64, no. 6 (2021): 88–93. http://dx.doi.org/10.17213/0136-3360-2021-6-88-93.

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The analysis is carried out and the definitions of the concept of thermal engineering reliability, the determining parameter and the determining function of boiler units, are given. A classification has been developed for the determining parameters of steam and hot water boilers by level in the chain of cause-and-effect relationships in the event of a thermal failure. It is proposed to divide the determining parameters and functions of boilers according to their spatial localization into integral and local. A lot of models for defining functions with different mathematical properties (for example, the presence or absence of discontinuities of the second kind) are considered. The defining functions (reliability criteria) currently used in boiler construction have been identified. The analysis of the safety factors for overturning and stagnation in direct-flow and drum boiler units is carried out. The incorrectness of the currently used dependence is shown. A formula has been proposed for these coefficients using internal useful heads, which is especially relevant for boilers with natural circulation at ultrahigh pressure.

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Yang, Mou, Yingfeng Meng, Gao Li, Yongjie Li, Ying Chen, Xiangyang Zhao, and Hongtao Li. "Estimation of Wellbore and Formation Temperatures during the Drilling Process under Lost Circulation Conditions." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/579091.

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Significant change of wellbore and surrounding formation temperatures during the whole drilling process for oil and gas resources often leads by annulus fluid fluxes into formation and may pose a threat to operational security of drilling and completion process. Based on energy exchange mechanisms of wellbore and formation systems during circulation and shut-in stages under lost circulation conditions, a set of partial differential equations were developed to account for the transient heat exchange process between wellbore and formation. A finite difference method was used to solve the transient heat transfer models, which enables the wellbore and formation temperature profiles to be accurately predicted. Moreover, heat exchange generated by heat convection due to circulation losses to the rock surrounding a well was also considered in the mathematical model. The results indicated that the lost circulation zone and the casing programme had significant effects on the temperature distributions of wellbore and formation. The disturbance distance of formation temperature was influenced by circulation and shut-in stages. A comparative perfection theoretical basis for temperature distribution of wellbore-formation system in a deep well drilling was developed in presence of lost circulation.

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48

Samoilov, A. M., A. A. Sataev, A. A. Blokhin, and V. V. Ivanov. "Development of circuit model with natural circulation of coolant under conditions of ship motion." Vestnik IGEU, no. 6 (December 28, 2021): 19–26. http://dx.doi.org/10.17588/2072-2672.2021.6.019-026.

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Safety is the key requirement to any nuclear power installation. Various factors affect safety during operation of the nuclear power installation. These factors are difficult to study due to the high economic costs. This problem can be solved by developing prototype models to conduct the research of many complex processes. Dynamic impact on the ship installation is one of these processes. The most significant impact is the impact on the natural circulation of the coolant, that is one of the basic emergency safety systems. Also, it is a promising way to ensure movement in the main circulation circuit. The purpose of this paper is to assess the influence of external dynamic forces on the processes of natural circulation. For the study a testing bench has been developed that simulates one of the circulation loops of the reactor unit. The basic method to obtain experimental data is temperature sounding of the specific sections of the circulation route. A mathematical model has been developed that describes this process. The model is based on the equations of momentum conservation and heat balance. In accordance with the experimental data, the calculation of natural circulation for static and dynamic modes has been carried out. A mathematical model to describe this process has been developed. A comparative analysis of the results of calculating the static and dynamic modes has been carried out. It is founded out that the decrease of mass flow rate is about 10 % as compared with the static regime. It confirms the qualitative effect of ship motion on natural circulation. The practical significance of the research is the development of a model under conditions of ship motion, as well as verification of the model at the testing bench. The results show a significant effect of ship motion on the mass flow rate of the coolant in the case of natural circulation. Thus, to ensure the required safety of ship installations, it is recommended to conduct a study of natural circulation in accordance with the developed model under conditions of maximum possible ship motion.

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Reis, Renata C. dos, Ivano A. Devilla, Diego P. R. Ascheri, Ana C. O. Servulo, and Athina B. M. Souza. "Kinetics of drying of basil leaves (Ocimum basilicum L.) in the infrared." Revista Brasileira de Engenharia Agrícola e Ambiental 16, no. 12 (December 2012): 1346–52. http://dx.doi.org/10.1590/s1415-43662012001200012.

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The objective of this paper was to model the drying curves of the leaves of basil (Ocimum basilicum L.) in the infrared at temperatures of 50, 60, 70 and 80 ºC and to evaluate the influence of drying temperature on the color of dried leaves. Drying was conducted in infrared dryer with temperature and greenhouse air circulation. Experimental data were fitted to eight mathematical models. The magnitude of the coefficient of determination (R²), the mean relative error (P), the estimated mean error (SE) and chisquare test (χ2) were used to verify the degree of fitness of the models. From the study it was concluded that: a) the behavior of the drying curves of basil leaves was similar to most agricultural products, the drying times in the infrared were less than the drying times in an oven with air circulation, b) the mathematical drying model proposed by Midilli et al. (2002) was the one which best adjusted to the experimental data, c) the diffusion coefficient ranged from 9.10 x 10-12 to 2.92 x 10-11 m² s-1 and d) the color of the samples was highly influenced by drying, becoming darker due to loss of chlorophyll with increasing temperature.

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Lopes, Sarah Meier, Nicole Machuca Brassac De Arruda, and Thomaz Aurélio Pagioro. "STUDY OF THE STRATIFICATION PROCESS AT THE RESERVOIR OF THE HYDROELECTRIC POWER PLANT GOV. PEDRO VIRIATO PARIGOT DE SOUZA (CAPIVARI-CACHOEIRA), PARANÁ, BRAZIL." Eclética Química Journal 43, no. 2 (August 23, 2018): 23. http://dx.doi.org/10.26850/1678-4618eqj.v43.2.2018.p23-31.

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The study of the stratification processes in reservoirs is important because they happen along with several physical and chemical changes in the water, as in the distribution of dissolved gases and nutrients. The aim of this work was to study the stratification process of the Capivari-Waterfall Hydroelectric Power Plant, based on the data of the vertical profiles of dissolved oxygen and temperature, as well as the comparison of them with the calculation of Froude's Densimetric Number, and reservoir residence time. The data used are part of the self-monitoring program carried out by COPEL. These data were collected quarterly between 2005 and 2016. The hydraulic and operational data from the reservoir were used to calculations. According to the measurements of dissolved oxygen and temperature, it was considered to be stratified during almost all the year, with a trend of circulation in the colder months, this behavior characterizes lakes with warm monomictic circulation pattern. Therefore, the result of Froude's Densimetric Number, corresponded correctly with the observed. Regarding the residence time, this was not consistent with the results obtained, from the models. The use of different methodologies in evaluating circulation in reservoirs should be used in order to make the best management decision.

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Journal articles on the topic 'Lakes – Circulation – Mathematical models'

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