Journal articles: 'Mixing – Mathematical models'

1

Cutler, Alan H. "Mathematical models of temporal mixing in the fossil record." Short Courses in Paleontology 6 (1993): 169–87. http://dx.doi.org/10.1017/s2475263000001100.

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In December 1969 officials from the U.S. Selective Service System conducted a draft lottery to establish the order in which nineteen-year-old men were to be called for military service. Three hundred sixty-six capsules, one for each possible birthday, were placed in a large wooden box. As the capsules for each month were added to the box, the contents of the box were mixed. Once all 366 capsules were in the box, it was shaken several times and emptied into a deep bowl. Capsules were then drawn from the bowl to determine the draft number corresponding to each date. Observers were satisfied that the capsules had been thoroughly mixed, but, as it turned out, the results were anything but random. The Spearman rank correlation between birth date and draft number was significant at the.001 level – men with December birthdays had a significantly higher probability of being called than did those with January birthdays (Fienberg, 1971).

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Moser, A., B. Mayr, W. Jury, W. Steiner, and P. Horvat. "Mathematical models for mixing in deep jet bioreactors: analysis." Bioprocess Engineering 7, no. 4 (December 1991): 171–76. http://dx.doi.org/10.1007/bf00387413.

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Ganser, G. H., I. Christie, and M. A. McCawley. "Two Mathematical Models for Predicting Dispersion of Particles in the Human Lung." Journal of Biomechanical Engineering 129, no. 1 (June 30, 2006): 51–57. http://dx.doi.org/10.1115/1.2401183.

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The dispersion of particles in the human lung is modeled as a series of virtual mixing tanks. Using the experimental results of Scherer et al. (1975, J. Appl. Physiol., 38(4), pp. 719–723) for a five-generation glass lung model, it is shown that each generation of the glass lung behaves like an independent virtual mixing tank. The corresponding resident time distribution is shown to have a variance approximately equal to the square of the average time a particle spends in the generation. By assuming that each generation of the human lung behaves as an independent virtual mixing tank, the realistic lung data provided by Weibel (1963, Morphometry of the Human Lung, Spinger-Verlag, New York) are used to validate this assumption in two ways. First, the half-width of the exhaled particle concentration profile is obtained. Second, a system of differential equations, with the concentration of particles in each mixing tank as its solution, is derived and solved numerically. This gives the exhaled concentration profile. Both techniques yield similar results to each other, and both give excellent agreement with the experimental data. The virtual mixing tank approach allows the complex mixing that occurs in the branching pathways of the lung to be more simply modeled. The model, thereby derived, is simple to change and could lead to enhancements in the understanding of the underlying processes contributing to the ventilation of the lung in health and disease.

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Romanko, D. A., and V. M. Fomichev. "On mathematical models of key mixing for iterative block encryption algorithms." Prikladnaya diskretnaya matematika. Prilozhenie, no. 10 (September 1, 2017): 93–96. http://dx.doi.org/10.17223/2226308x/10/38.

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Moser, A., B. Mayr, W. Jury, W. Steiner, and P. Horvat. "Mathematical models for mixing in deep-jet bioreactors: Calculation of parameters." Bioprocess Engineering 7, no. 4 (December 1991): 177–82. http://dx.doi.org/10.1007/bf00387414.

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Sterpu, Ancaelena Eliza, Nicoleta Teodorescu, Iuliana Marlena Prodea, Eugeniu Popescu, and Irina Nita. "MATHEMATICAL MODELS FOR POWER CONSUMPTION AT THE MIXING OF SOME LUBRICATING GREASES." Environmental Engineering and Management Journal 9, no. 8 (2010): 1063–68. http://dx.doi.org/10.30638/eemj.2010.139.

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Ma, Lian Xiang, Rong Shan Bi, Xin Shun Tan, Zhen Dong Liu, Wen Wu Chen, and Shi Qing Zheng. "Turbulent Mixing and Scale-Up of Ejectors at High Schmidt Number." Advanced Materials Research 233-235 (May 2011): 1340–44. http://dx.doi.org/10.4028/www.scientific.net/amr.233-235.1340.

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Micro- and Macro-mixing models were built and numerical investigation of turbulent mixing in ejectors was carried out. Mixture fraction and its variance presented by Fox were remodeled to demonstrate micro- and macro-mixing performance. The length needed to reach 98% micro- and macro-mixing were founded is functions of uj/umand D/d. The mathematical scale-up models were presented based on the simulation results using least square method for micro- and macro-mixing and five different cases were used to validate the models. The results showed that macro-mixing scale-up model agreed well with CFD simulations but the micro-mixing scale-up model had a less precision compared with that of macro-mixing model. This because that the mechanism of micro-mixing process is very complexity but the CFD models we used in this work are fairy simple.

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Jelenčiaková, Nina, Bojan Petrović, Sanja Kojić, Jovana Jevremov, and Stevan Hinić. "Application of Mathematical Models and Microfluidics in the Analysis of Saliva Mixing with Antiseptic Solutions." Balkan Journal of Dental Medicine 24, no. 2 (July 1, 2020): 84–90. http://dx.doi.org/10.2478/bjdm-2020-0014.

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SummaryBackground/Aim: Human saliva offers many advantages over blood-based biochemical assays, therefore, becomes the biological fluid of interest. Once antiseptic solutions react with saliva, both fluids undergo significant changes of their biophysical properties, consequently, those changes have an impact on their principal function.Material and Methods: In this study, saliva was collected and mixed with 0,1% chlorhexidine digluconate solution, fluoride mouthwash, zinc-hydroxyapatite solution and CPP-ACP paste. Microfluidic PVC/Green tape chips within the experimental setup were used to simulate solution mixing. The chip had 2 inlets and 1 outlet, and channel was designed in Y shape without any obstacles. The inlet channels were set at a 60° angle. The channel width was 600 µm and the diameter of inlets and outlet was 2 mm. For better visualization, blue food coloring was added to the saliva. The procedure was recorded with digital USB microscope camera and afterwards the percentage of mixing was obtained by MATLAB programming language.Results: Obtained results show incomplete mixing of all the solutions with saliva. The value of mixed liquid, when mixing 0,1% chlorhexidine digluconate solution with saliva was 51,11%. In case of medium concentration fluoride mouthwash, result was 84,37%. Zinc hydroxyapatite solution obtained result of 85,24%, and the fourth tested solution, CPP-ACP paste, 83,89%.Conclusions: Analyzed mouthwashes exhibit specific, non uniform behavior during mixing with saliva. Microfluidic setups could be efficiently used in simulating real clinical conditions in laboratory settings. Image processing mathematical models are applicable, accurate and useful in determination of the interaction of saliva with commonly used antiseptic solutions.

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Khvostov, Anatoly, Anatoly Khvostov, Viktor Ryazhskikh, Viktor Ryazhskikh, Gazibeg Magomedov, Gazibeg Magomedov, Aleksey Zhuravlev, and Aleksey Zhuravlev. "Matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics in Simulink." Foods and Raw Materials 6, no. 2 (December 20, 2018): 483–92. http://dx.doi.org/10.21603/2308-4057-2018-2-483-492.

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The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. A sugar syrup cooler was chosen as an object of modeling. The mathematical model of the cooler is formalized by a set of perfect reactors. The simulation results showed that the mathematical model adequately describes the main regularities of the process, the deviation of the calculated data from the regulations did not exceed 10%. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.

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Bose, S. K., P. Ray, and B. K. Dutta. "Mathematical Models for Mixing and Dispersion in Forecasting and Management of Estuarine Water Quality." Water Science and Technology 19, no. 9 (September 1, 1987): 183–93. http://dx.doi.org/10.2166/wst.1987.0079.

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The dispersion or spread of a dissolved or suspended substance in an estuarine system occurs mainly due to the non-uniformity of velocity distribution, including turbulent fluctuations, shear stress at the boundary and surface stress caused by winds. The mixing and dispersion phenomena in rivers and estuaries are extremely important in water quality management and control. The development of a dispersion model in harmony with the nature of the flow field in a river or estuary is necessary in the estimation and correlation of dispersion parameters, called dispersion coefficients, which may, in general, be anisotropic in a multidimensional transport process. The earlier one-dimensional models have gradually given way to higher dimensional models for better description of the phenomena as well as for more accurate estimation of parameters. Field studies of dispersion of tracers have been the most important method of generating data for parameter estimation. A number of correlations for mixing and dispersion coefficients in terms of flow rates and other fundamental system parameters are available. The present study incorporates the analysis, assessment and applications of various dispersion and mixing models available. Also, a critical appraisal of the validity, inherent degree of uncertainty and the range of applications of different correlations has been incorporated.

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11

Grillo, S., and H. Montani. "Integrable mixing of An−1 type vertex models." Journal of Mathematical Physics 45, no. 5 (May 2004): 2073–89. http://dx.doi.org/10.1063/1.1704846.

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Othman, N., and S. K. Kamarudin. "Radiotracer Technology in Mixing Processes for Industrial Applications." Scientific World Journal 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/768604.

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Many problems associated with the mixing process remain unsolved and result in poor mixing performance. The residence time distribution (RTD) and the mixing time are the most important parameters that determine the homogenisation that is achieved in the mixing vessel and are discussed in detail in this paper. In addition, this paper reviews the current problems associated with conventional tracers, mathematical models, and computational fluid dynamics simulations involved in radiotracer experiments and hybrid of radiotracer.

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13

Hong, Jin, Seok-Jin Kang, Tetsuji Miwa, and Robert Weston. "Mixing of ground states in vertex models." Journal of Physics A: Mathematical and General 31, no. 28 (July 17, 1998): L515—L525. http://dx.doi.org/10.1088/0305-4470/31/28/001.

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14

Weber, C., M. Wagner, and E. Sigmund. "Valency-mixing Jahn-Teller systems: extended models." Physica Scripta 38, no. 3 (September 1, 1988): 498–501. http://dx.doi.org/10.1088/0031-8949/38/3/030.

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Easterly, C. W., F. Alarid-Escudero, E. A. Enns, and S. Kulasingam. "Revisiting assumptions about age-based mixing representations in mathematical models of sexually transmitted infections." Vaccine 36, no. 37 (September 2018): 5572–79. http://dx.doi.org/10.1016/j.vaccine.2018.07.058.

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Chleboun, P., A. Faggionato, F. Martinelli, and C. Toninelli. "Mixing Length Scales of Low Temperature Spin Plaquettes Models." Journal of Statistical Physics 169, no. 3 (September 23, 2017): 441–71. http://dx.doi.org/10.1007/s10955-017-1880-1.

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17

Qiu, Shu Xia, and Ning Pang. "A Numerical Study on the Flow Characteristics of Opposed Impinging Jets." Advanced Materials Research 516-517 (May 2012): 854–57. http://dx.doi.org/10.4028/www.scientific.net/amr.516-517.854.

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Inspired by the increasing interests on mixing effectiveness of opposed impinging jets, a numerical work is carried out to study the flow characteristics. The fluid temperature is used as a passive tracer to evaluate the mixing rate in the current mathematical models. The effect of Reynolds number on the mixing performance is discussed. Furthermore, in order to enhance the mixing efficiency and reduce the energy cost, unsteady flow pulsations are induced at the jet inlets. The numerical results indicate that the mixing efficiency can be improved by the unsteady flow pulsations via adjusting the hydrodynamics characteristics in the opposed jets.

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Yoo, Donghoon, and Brian A. O'Connor. "MATHEMATICAL MODELLING OF WAVE-INDUCED NEARSHORE CIRCULATIONS." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 122. http://dx.doi.org/10.9753/icce.v20.122.

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The paper presents a mathematical model for describing wave climate and wave-induced nearshore circulations. The model accounts for current-depth refraction, diffraction, wave-induced currents, set-up and set-down, mixing processes and bottom friction effects on both waves and currents. The present model was tested against published experimental data on wave conditions within a model harbour and shown to give very good results for both wave and current fields. The importance of including processes such as advection, flooding and current-interaction in coastal models was demonstrated by comparing the numerical results without each process to the results from the complete scheme.

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TOBIN, KATY, and CATHERINE COMISKEY. "A NOVEL APPLICATION OF A CLASSICAL METHOD FOR CALCULATING THE BASIC REPRODUCTIVE NUMBER, R0 FOR A GENDER AND RISK STRUCTURED TRANSMISSION DYNAMIC MODEL OF HUMAN PAPILLOMAVIRUS INFECTION." International Journal of Biomathematics 06, no. 06 (November 2013): 1350046. http://dx.doi.org/10.1142/s1793524513500460.

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Mathematical models are increasingly being used in the evaluation of control strategies for infectious disease such as the vaccination program for the Human Papillomavirus (HPV). Here, an ordinary differential equation (ODE) transmission dynamic model for HPV is presented and analyzed. Parameter values for a gender and risk structured model are estimated by calibrating the model around the known prevalence of infection. The effect on gender and risk sub-group prevalence induced by varying the epidemiological parameters are investigated. Finally, the outcomes of this model are applied using a classical mathematical method for calculating R0 in a heterogeneous mixing population. Estimates for R0 under various gender and mixing scenarios are presented.

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Khvostov, A. A., A. A. Zhuravlev, E. A. Shipilova, R. S. Sumina, G. O. Magomedov, and I. A. Khaustov. "Simulink models of technological systems with perfect mixing and plug-flow hydrodynamics." Proceedings of the Voronezh State University of Engineering Technologies 81, no. 3 (December 20, 2019): 28–38. http://dx.doi.org/10.20914/2310-1202-2019-3-28-38.

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The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. The process of synthesis of the dynamic matrix mathematical model was considered by the example of a sugar syrup cooler, the quality indicator of the finished product are selected as sucrose crystals and their portion in the total volume of caramel mass. Taking into account the dependence of syrup viscosity on temperature, thermal effects as a result of the process of crystallization of sucrose from syrup, design features of a typical caramel machine made it possible to clarify the dynamics of the process of syrup cooling. The model developed with this approach allows to obtain real-time estimates of temperatures at the outlet of the cooler, which makes it possible to study the dynamics of the technological process and synthesize the control system. The presented approach allows to implement mathematical models of ideal reactors in Simulink system and to move to matrix ordinary differential equations, which makes it possible to convert them into Simulink blocks. The approach is also applicable to other models of ideal reactors, which allows to form libraries of typical ideal reactors of Simulink system for synthesis of heat and mass exchange equipment. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.

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De Clercq, Bob, Filip Coen, Bart Vanderhaegen, and Peter A. Vanrolleghem. "Calibrating simple models for mixing and flow propagation in waste water treatment plants." Water Science and Technology 39, no. 4 (February 1, 1999): 61–69. http://dx.doi.org/10.2166/wst.1999.0190.

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Mathematical models are useful tools in the prediction of system responses to operational changes in waste water treatment plants (WWTPs). The tanks-in-series model is one of the widespread hydraulic models in waste water treatment. This study shows the applicability of the mentioned model. Next to the mixing of substrate in a conventional activated sludge system, an oxidation ditch and a trickling filter, also the flow propagation in a waste water treatment plant was modelled. These different full-scale examples taken from waste water treatment demonstrate the relative ease of model configuration and calibration. Difficulties like experimental design, modelling the diffusion in biofilms and transients in flow rate were encountered.

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Khazaei, Soroush, and Yashar Pourrahimian. "Mathematical Programming Application in Sublevel Caving Production Scheduling." Mining 1, no. 2 (August 9, 2021): 180–91. http://dx.doi.org/10.3390/mining1020012.

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Production scheduling determines the most beneficial mining sequence over the life of a mine. Developing a schedule that meets all mining aspects can substantially reduce mining costs and increase profitability. Among all underground mining methods, the sublevel caving method is a common method with moderate development requirements, a high production rate, and a high degree of mechanization and flexibility. None of the manual planning methods and heuristic algorithms used in commercial software will lead to a truly optimal schedule. Mathematical programming models, particularly mixed-integer programming (MIP), have been applied to provide an operationally feasible multi-time-period schedule in sublevel caving. However, confined blasting conditions, chaotic material flow, and frequent mixing of ore and waste while loading broken ore at the drawpoint make the sublevel caving method unique when producing a holistic plan. This paper reviews all mathematical programming models presented in sublevel caving production scheduling, highlights the inherent characteristics of the sublevel caving that affect production, and puts forward some promising ideas for future works.

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NOVOTNY, M. A., and A. KOLAKOWSKA. "MIXING DIFFERENT RANDOM DEPOSITIONS IN NONEQUILIBRIUM SURFACE GROWTH MODELS." International Journal of Modern Physics C 20, no. 09 (September 2009): 1377–85. http://dx.doi.org/10.1142/s0129183109014448.

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An exact solution is presented for mixing two or more different types of Random Deposition (RD) nonequilibrium surface growth processes. The depositions may be made in a sequential mode, or in a random mode by first randomly choosing the lattice site for deposition. The results hold in all dimensions d. Simulations are presented in d = 1 for comparison. Furthermore, a mean-field type of approach to mixing RD with other surface growth processes is tested against the exact solution.

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Lo, Assane, and Ziad Choucair. "Analyticity and mixing properties in classical models Kac type." Physica Scripta 94, no. 6 (April 2, 2019): 065205. http://dx.doi.org/10.1088/1402-4896/ab0f83.

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Szuster – Janiaczyk, Agnieszka, Rafał Brodziak, and Jędrzej Bylka. "The use of mathematical modelling to analyse the process of mixing waters from different sources in water supply system." E3S Web of Conferences 59 (2018): 00025. http://dx.doi.org/10.1051/e3sconf/20185900025.

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One of the processes that significantly determines the quality of water to consumers is the process of mixing water from different sources in the water mains. Put to the network two or more chemically and biologically stable waters may result in the formation of water that will be deprived of these features. This article presents the german guidelines for analysing water quality for mixing waters from different sources, in various proportions. Then performed an analysis of utility the mathematical models,including quality criteria, for use in network control. An IT tool has been developed to manage selected water quality processes using mathematical modeling. The basis for implementing the tool was a network model created in Epanet integrated with the Matlab.

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Bałdyga, Jerzy, and Magdalena Jasińska. "Energetic Efficiency of Mixing and Mass Transfer in Single Phase and Two-Phase Systems." Chemical and Process Engineering 38, no. 1 (March 1, 2017): 79–96. http://dx.doi.org/10.1515/cpe-2017-0007.

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Abstract In this work a concept of energetic efficiency of mixing is presented and discussed; a classical definition of mixing efficiency is modified to include effects of the Schmidt number and the Reynolds number. Generalization to turbulent flows is presented as well. It is shown how the energetic efficiency of mixing as well as efficiencies of drop breakage and mass transfer in twophase liquid-liquid systems can be identified using mathematical models and test chemical reactions. New expressions for analyzing efficiency problem are applied to identify the energetic efficiency of mixing in a stirred tank, a rotor stator mixer and a microreactor. Published experimental data and new results obtained using new systems of test reactions are applied. It has been shown that the efficiency of mixing is small in popular types of reactors and mixers and thus there is some space for improvement.

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Sterpu, Ancaelena Eliza, Claudia Irina Koncsag, Anca Iuliana Dumitru, and Alina-Daniela Mihalcea. "Mathematical model for power consumption at mixing of industrial and domestic wastewater sludge." Analele Universitatii "Ovidius" Constanta - Seria Chimie 24, no. 2 (December 1, 2013): 115–20. http://dx.doi.org/10.2478/auoc-2013-0019.

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AbstractPhysical investigations have been carried out to characterize the power consumption in a laboratory autoclave vessel equipped with an anchor impeller (diameter d = 0.068 mm), without baffles, at 8 speed ratio, from 100 to 800 rpm. The laminar flow regime was investigated using sludge proceeding from the treatment of mixed industrial and domestic wastewater, with a view to its subsequent processing: mixing, filtration, dewatering. The mathematical modeling focused on finding an accurate equation linking the Power number (Np) and the Reynolds number (Re) at different levels (H) of sludge in the vessel. The rheological curves indicate that the sludge have non-Newtonian behaviors which are better described by the Herschel-Buckley model. The models resulted from the Np variation versus Re are power function type Np = a ×Reb , where the coefficient a is a linear functions of H/d ratio and b = -1.016 have a constant value.

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CAPASSO, VINCENZO, FRANCESCO SICURELLO, and MARCO VILLA. "MATHEMATICAL MODELS FOR HIV TRANSMISSION IN GROUPS OF INJECTING DRUG USERS VIA SHARED DRUG EQUIPMENT." Journal of Biological Systems 03, no. 03 (September 1995): 747–58. http://dx.doi.org/10.1142/s021833909500068x.

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In many western countries, including Italy, sharing drug injection equipment is one of the main causes of HIV/AIDS spread. In this paper we propose an extension of the classical one population and multiple population mathematical models for the spread of HIV, by providing explicit expressions for the force of infection in terms of a stochastic model for the behaviour of individuals in a friendship group with respect to needle sharing. For the single population model we provide a threshold theorem in terms of the basic reproductive ratio. The extension to the multiple population case is discussed in terms of mixing matrices. The qualitative behaviour for different choices of such matrices is shown by computer simulations.

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Tobo, Yohannis Mitiku, Jan Bartacek, and Ingmar Nopens. "Linking CFD and Kinetic Models in Anaerobic Digestion Using a Compartmental Model Approach." Processes 8, no. 6 (June 17, 2020): 703. http://dx.doi.org/10.3390/pr8060703.

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Understanding mixing behavior and its impact on conversion processes is essential for the operational stability and conversion efficiency of anaerobic digestion (AD). Mathematical modelling is a powerful tool to achieve this. Direct linkage of Computational Fluid Dynamics (CFD) and the kinetic model is, however, computationally expensive, given the stiffness of the kinetic model. Therefore, this paper proposes a compartmental model (CM) approach, which is derived from a converged CFD solution to understand the performance of AD under non-ideal mixing conditions and with spatial variation of substrates, biomass, pH, and specific biogas and methane production. To quantify the effect of non-uniformity on the reactor performance, the CM implements the Anaerobic Digestion Model 1 (ADM1) in each compartment. It is demonstrated that the performance and spatial variation of the biochemical process in a CM are significantly different from a continuously stirred tank reactor (CSTR) assumption. Hence, the assumption of complete mixed conditions needs attention concerning the AD performance prediction and biochemical process non-uniformities.

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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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Lim, H., Y. Yu, J. Glimm, X.-L. Li, and D. H. Sharp. "Subgrid models for mass and thermal diffusion in turbulent mixing." Physica Scripta T142 (December 1, 2010): 014062. http://dx.doi.org/10.1088/0031-8949/2010/t142/014062.

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FRYER, CHRIS L., AIMEE L. HUNGERFORD, and GABRIEL ROCKEFELLER. "SUPERNOVA EXPLOSIONS: UNDERSTANDING MIXING." International Journal of Modern Physics D 16, no. 06 (June 2007): 941–81. http://dx.doi.org/10.1142/s0218271807010523.

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It has been known since 1987 that many features of supernovae cannot be described by the spherically-symmetric picture assumed in one-dimensional explosion models. However, the study of the propagation of a supernova shock through a star in more than one spatial dimension is still in its infancy. Understanding this propagation, and the mixing associated with it, is critical for determining accurate supernova yields and correctly interpreting observations based on those yields — from gamma-rays and overall light curves produced in supernova explosions to the abundances of isotopes studied in stars. Here we review the current state-of-the-art in this field. By necessity, this problem is computational and therefore provides an ideal setting to discuss how verification and validation techniques can play an important role in taking full advantage of the results from numerical simulations. We discuss this problem using the full arsenal of verification and validation techniques currently available.

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Domingues, Natália, António Gaspar-Cunha, and José A. Covas. "Modelling of Mixing in Single Screw Extruders." Materials Science Forum 514-516 (May 2006): 1409–13. http://dx.doi.org/10.4028/www.scientific.net/msf.514-516.1409.

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Polymer extrusion is one of the most important polymer processing techniques. Modelling of the phenomena developing inside single screw extruders enabled the development of commercial software which can be used to study the performance of existing systems and to define the equipment characteristics for new applications. Although mixing is one of the most important performance measures of extrusion, it is usually disregarded in the available programs. Consequently, in this work mathematical models for quantifying mixing in single screw extruders are developed and subsequently inserted in a global computer modelling program of single screw extrusion. The mixing model quantifies distributive and dispersive mixing and coalescence mechanisms in a liquid-liquid system. This is accomplished by calculating the variation of the thickness of drops considered to be suspended in the polymeric matrix, taking into account the rate and drop break-up time and the coalescence probability. The influence of several parameters, such as viscosities, initial drop dimension, screw speed and barrel temperature, are examined

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Shu, Zheng, Shijie Zhu, Jian Zhang, Wensen Zhao, and Zhongbin Ye. "Optimization Design and Analysis of Polymer High Efficiency Mixer in Offshore Oil Field." Processes 8, no. 1 (January 15, 2020): 110. http://dx.doi.org/10.3390/pr8010110.

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The degree of polymer-water mixing in high-pressure pipelines on offshore oilfields usually influences the polymer solution’s performance. To realize efficient mixing of the polymer mother liquor with dilution water in the high-pressure pipeline, a high-efficiency mixer is designed and optimized. The designed mixer consists of four parts: a T-shaped pipe as the main body, an inlet flow-splitting plate, a stainless-steel flow-guiding tube, and an outlet flow-splitting plate. Mathematical models are built by using computational fluid dynamics (CFD) and the mixing effects are compared by using Fluent. The research results show that compared with conventional T-shaped mixers, the designed high-efficiency mixer has better mixing performance and increases the mixing rate to 80%. To optimize the mixing rate, the length of the stainless-steel tube is increased and the tube is perforated to guide the flow. The result shows that boring holes along straight lines around the tube can achieve good optimization effect and increase the mixing rate to 95%. The designed high-efficiency mixer can effectively improve the dissolving efficiency and solve problems in polymer-water mixing in the high-pressure pipeline.

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Belcher, Stephen E. "Mixing and transport in urban areas." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1837 (October 24, 2005): 2947–68. http://dx.doi.org/10.1098/rsta.2005.1673.

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Concern over terrorist releases of harmful material has generated interest in short-range air-borne dispersion in urban areas. Here, we review the important fluid dynamical processes that control dispersion in the first kilometre, the neighbourhood scale, when much of the material remains within the urban canopy. Dispersion is then controlled by turbulent mixing and mean flow transport through the network of streets. We consider mixing and transport in a long straight street, street intersections and then a network of streets connected by intersections. The mixing and transport in these systems are illustrated with results from recent fine-resolution numerical simulations and laboratory models, which then inform simpler scaling estimates and modelling schemes. Finally, we make some tentative steps to pull the process studies together to begin to understand results from full-scale observations. In particular, it is shown that the positions of ‘shear layers’ and ‘dividing streamlines’ largely control the patterns of mixing and transport. It is also shown that neighbourhood-scale dispersion follows one scaling in the near field and another in the far field after passage through many intersections. The challenge for the future is to bring these threads together into a coherent mathematical model.

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Fuentes-Aguilera, Patricio, Diego Caamaño, Hernán Alcayaga, and Andrew Tranmer. "The Influence of Pool-Riffle Morphological Features on River Mixing." Water 12, no. 4 (April 17, 2020): 1145. http://dx.doi.org/10.3390/w12041145.

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Accurate prediction of pollutant concentrations in a river course is of great importance in environmental management. Mathematical dispersion models are often used to predict the spatial distribution of substances to help achieve these objectives. In practice, these models use a dispersion coefficient as a calibration parameter that is calculated through either expensive field tracer experiments or through empirical equations available in the scientific literature. The latter are based on reach-averaged values obtained from laboratory flumes or simple river reaches, which often show great variability when applied to natural streams. These equations cannot directly account for mixing that relates specifically to spatial fluctuations of channel geometry and complex bed morphology. This study isolated the influence of mixing related to bed morphology and presented a means of calculating a predictive longitudinal mixing equation that directly accounted for pool-riffle sequences. As an example, a predictive equation was developed by means of a three-dimensional numerical model based on synthetically generated pool-riffle bathymetries. The predictive equation was validated with numerical experiments and field tracer studies. The resulting equation was shown to more accurately represent mixing across complex morphology than those relations selected from the literature.

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Racca, Laiza Marinho, Elen Beatriz Acordi Vasques Pacheco, Luiz Carlos Bertolino, Cristiane Xavier da Silva Campos, Monica Calixto de Andrade, Ana Maria Furtado de Sousa, and Ana Lúcia Nazareth da Silva. "Composites Based on Polypropylene and Talc: Processing Procedure and Prediction Behavior by Using Mathematical Models." Advances in Condensed Matter Physics 2018 (November 1, 2018): 1–8. http://dx.doi.org/10.1155/2018/6037804.

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iPP/Talc composites were produced, with different methods of filler addition in iPP matrix. Two different grades of Talc were used for comparison. The tensile tests results showed that talc particles promoted an improvement in composite rigidity, indicating the reinforcing effect of the talc particles in the iPP matrix. However, PP/talc-based composites that were prepared from a masterbatch and with talc grade with smaller particle size showed a better efficiency on dispersion/distribution of particle filler on the thermoplastic matrix, resulting in an improvement in Young’s modulus property, even with higher filler contents. SEM analyses evaluated the composite morphologies and different mathematical models were used as a tool on prediction of mechanical behaviour of the materials. It was observed that the results of Young’s modulus of the composites can be adjusted by different models, depending on the talc characteristics and the mixing procedure used.

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BARONCHELLI, ANDREA, VITTORIO LORETO, and LUC STEELS. "IN-DEPTH ANALYSIS OF THE NAMING GAME DYNAMICS: THE HOMOGENEOUS MIXING CASE." International Journal of Modern Physics C 19, no. 05 (May 2008): 785–812. http://dx.doi.org/10.1142/s0129183108012522.

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Language emergence and evolution have recently gained growing attention through multi-agent models and mathematical frameworks to study their behavior. Here we investigate further the Naming Game, a model able to account for the emergence of a shared vocabulary of form-meaning associations through social/cultural learning. Due to the simplicity of both the structure of the agents and their interaction rules, the dynamics of this model can be analyzed in great detail using numerical simulations and analytical arguments. This paper first reviews some existing results and then presents a new overall understanding.

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Korolev, Victor, and Andrey Gorshenin. "Probability Models and Statistical Tests for Extreme Precipitation Based on Generalized Negative Binomial Distributions." Mathematics 8, no. 4 (April 16, 2020): 604. http://dx.doi.org/10.3390/math8040604.

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Mathematical models are proposed for statistical regularities of maximum daily precipitation within a wet period and total precipitation volume per wet period. The proposed models are based on the generalized negative binomial (GNB) distribution of the duration of a wet period. The GNB distribution is a mixed Poisson distribution, the mixing distribution being generalized gamma (GG). The GNB distribution demonstrates excellent fit with real data of durations of wet periods measured in days. By means of limit theorems for statistics constructed from samples with random sizes having the GNB distribution, asymptotic approximations are proposed for the distributions of maximum daily precipitation volume within a wet period and total precipitation volume for a wet period. It is shown that the exponent power parameter in the mixing GG distribution matches slow global climate trends. The bounds for the accuracy of the proposed approximations are presented. Several tests for daily precipitation, total precipitation volume and precipitation intensities to be abnormally extremal are proposed and compared to the traditional PoT-method. The results of the application of this test to real data are presented.

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Sukharev, Mikhail. "Fluid Mixing Nonequilibrium Processes in Industrial Piping Flows." Energies 13, no. 23 (December 2, 2020): 6364. http://dx.doi.org/10.3390/en13236364.

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The flow of a multicomponent fluid through a pipeline system of arbitrary configuration is considered. The problem consists in determining the component composition of the fluid for each pipeline of the system based on the values of the concentration of the components throughout the entire set of measuring points, provided that there are no phase transitions. To solve the problem, mathematical models have been developed that, in principle, are suitable for pipeline systems of various functional purposes, the presentation is concretized and carried out in relation to gas transmission systems. The models are stochastic in nature due to measurement errors, which are considered random variables. The solution of the problem is reduced to the optimization of a quadratic function with constraints in the form of equalities and inequalities. The considered mixing processes do not depend on the regime parameters of the fluid flow. The processes are irreversible and non-equilibrium. A criterion is introduced that characterizes the degree of closeness of a multicomponent mixture to an equilibrium state. The criterion is analogous to entropy in thermodynamic processes. A numerical example of calculating the distribution of a three-component mixture is given. The example illustrates the feasibility of the proposed computational procedures and gives an idea of the distribution of the component composition and the change in «entropy» along the directions of pumping of the gas supply system.

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WHARTON, ANNABEL. "Doll's House/Dollhouse: Models and Agency." Journal of American Studies 53, no. 1 (June 5, 2017): 28–56. http://dx.doi.org/10.1017/s0021875817000895.

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Models – economic, mathematical, toys, manikins – are ubiquitous. This article probes one model, the Stettheimer doll's house, in order to understand all models better. The Stettheimers, three wealthy unmarried sisters living in New York in the early the twentieth century, attracted a remarkable melange of Camp artists and writers, identified by Arthur Danto as “the American Bloomsbury.” The Stettheimers were involved in many of New York's happenings, including the Harlem Renaissance and the innovative stage productions of Gertrude Stein. Androgyny, excess, racial mixing and theatricality flourished in the Stettheimer milieu. Carrie Stettheimer's doll's house, now housed in the Museum of the City of New York, captured this life. I consider this model for two related purposes. First, and more narrowly, I document the various effects this eccentric doll's house had on the artistic production of those in its vicinity, most notably on the novels of her sister Ettie and on the paintings both of her sister Florine and Marcel Duchamp. Second, I use the evidence of the doll's house's affect to discuss the agency of models in general.

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Burridge, James. "Unifying models of dialect spread and extinction using surface tension dynamics." Royal Society Open Science 5, no. 1 (January 2018): 171446. http://dx.doi.org/10.1098/rsos.171446.

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We provide a unified mathematical explanation of two classical forms of spatial linguistic spread. The wave model describes the radiation of linguistic change outwards from a central focus. Changes can also jump between population centres in a process known as hierarchical diffusion . It has recently been proposed that the spatial evolution of dialects can be understood using surface tension at linguistic boundaries. Here we show that the inclusion of long-range interactions in the surface tension model generates both wave-like spread, and hierarchical diffusion, and that it is surface tension that is the dominant effect in deciding the stable distribution of dialect patterns. We generalize the model to allow population mixing which can induce shrinkage of linguistic domains, or destroy dialect regions from within.

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Uecker, Hildegard, and Sebastian Bonhoeffer. "Antibiotic treatment protocols revisited: the challenges of a conclusive assessment by mathematical modelling." Journal of The Royal Society Interface 18, no. 181 (August 2021): 20210308. http://dx.doi.org/10.1098/rsif.2021.0308.

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Hospital-acquired bacterial infections lead to prolonged hospital stays and increased mortality. The problem is exacerbated by antibiotic-resistant strains that delay or impede effective treatment. To ensure successful therapy and to manage antibiotic resistance, treatment protocols that draw on several different antibiotics might be used. This includes the administration of drug cocktails to individual patients (combination therapy) but also the random assignment of drugs to different patients (mixing) and a regular switch in the default drug used in the hospital from drug A to drug B and back (cycling). For more than 20 years, mathematical models have been used to assess the prospects of antibiotic combination therapy, mixing and cycling. But while tendencies in their ranking across studies have emerged, the picture remains surprisingly inconclusive and incomplete. In this article, we review existing modelling studies and demonstrate by means of examples how methodological factors complicate the emergence of a consistent picture. These factors include the choice of the criterion by which the effects of the protocols are compared, the model implementation and its analysis. We thereafter discuss how progress can be made and suggest future modelling directions.

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France, J., J. H. M. Thornley, R. C. Siddons, and M. S. Dhanoa. "On incorporating diffusion and viscosity concepts into compartmental models for analysing faecal marker excretion patterns in ruminants." British Journal of Nutrition 70, no. 1 (July 1993): 369–78. http://dx.doi.org/10.1079/bjn19930129.

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Deterministic mathematical equations are derived to describe the pattern of marker excretion in the faeces of ruminants under steady-state conditions when diffusion and viscosity concepts are introduced into a simple two-compartment scheme of the gastrointestinal tract. The basic scheme comprises a pure-mixing pool obeying first-order kinetics and a second compartment exhibiting streamline flow. Introduction of a velocity gradient, longitudinal diffusion or both into the second compartment, even with various simplifying assumptions, yields analytically insoluble equations. The impact of these mechanisms is to be investigated numerically rather than analytically in future work.

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Wu, Jiann-Ming. "Natural Discriminant Analysis Using Interactive Potts Models." Neural Computation 14, no. 3 (March 1, 2002): 689–713. http://dx.doi.org/10.1162/089976602317250951.

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Natural discriminant analysis based on interactive Potts models is developed in this work. A generative model composed of piece-wise multivariate gaussian distributions is used to characterize the input space, exploring the embedded clustering and mixing structures and developing proper internal representations of input parameters. The maximization of a log-likelihood function measuring the fitness of all input parameters to the generative model, and the minimization of a design cost summing up square errors between posterior outputs and desired outputs constitutes a mathematical framework for discriminant analysis. We apply a hybrid of the mean-field annealing and the gradient-descent methods to the optimization of this framework and obtain multiple sets of interactive dynamics, which realize coupled Potts models for discriminant analysis. The new learning process is a whole process of component analysis, clustering analysis, and labeling analysis. Its major improvement compared to the radial basis function and the support vector machine is described by using some artificial examples and a real-world application to breast cancer diagnosis.

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Ohajunwa, Comfort, Kirthi Kumar, and Padmanabhan Seshaiyer. "Mathematical modeling, analysis, and simulation of the COVID-19 pandemic with explicit and implicit behavioral changes." Computational and Mathematical Biophysics 8, no. 1 (December 31, 2020): 216–32. http://dx.doi.org/10.1515/cmb-2020-0113.

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AbstractAs COVID-19 cases continue to rise globally, many researchers have developed mathematical models to help capture the dynamics of the spread of COVID-19. Specifically, the compartmental SEIR model and its variations have been widely employed. These models differ in the type of compartments included, nature of the transmission rates, seasonality, and several other factors. Yet, while the spread of COVID-19 is largely attributed to a wide range of social behaviors in the population, several of these SEIR models do not account for such behaviors. In this project, we consider novel SEIR-based models that incorporate various behaviors. We created a baseline model and explored incorporating both explicit and implicit behavioral changes. Furthermore, using the Next Generation Matrix method, we derive a basic reproduction number, which indicates the estimated number of secondary cases by a single infected individual. Numerical simulations for the various models we made were performed and user-friendly graphical user interfaces were created. In the future, we plan to expand our project to account for the use of face masks, age-based behaviors and transmission rates, and mixing patterns.

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Berezin, A. A., A. A. Sataev, O. V. Khvoynov, and A. V. Duncev. "Assessment of the influence of an external dynamic force on the mixing of non-isothermal flows in the reactor plant." Vestnik IGEU, no. 5 (2019): 5–11. http://dx.doi.org/10.17588/2072-2672.2019.5.005-011.

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Today one of the main problems to be solved is increasing the safety of nuclear power plants (NPP). Possible shortcomings of the reactor plant (RP) can be identified by creating full-scale or large-scale prototype models for testing. There is an urgent need to create models for a more detailed study of some complex processes (flow mixing, heat and mass transfer and flow mixing under the action of dynamic forces). For example, the negative impact of these processes on the switchgear makes it difficult to ensure the natural circulation of the coolant (NCC) in all modes of operation, which could significantly increase the switchgear safety. At modern NPP this condition is not achieved either and the problem is solved by large safety factors. The purpose of this work is to evaluate the influence of external dynamic forces (EDF) on the processes of mixing of non-isothermal flows in the simulator of the core, applied to the research stand «Single-loop RP model». For the research stand we have designed a swinging platform simulating EDF. The main method for obtaining experimental data is direct layer-by-layer temperature sensing. We have also constructed a simple one-dimensional mathematical model describing these processes, based on Newton's Second Law. The adequacy of model selection has been confirmed experimentally. We have plotted graphs of temperature fronts for the experimental model and made a graphic representation of the coolant temperature field at the model entrance / exit for the dynamic mode. A mathematical equation has been obtained for describing the effect of EDF on the length of the Prandtl mixing path for the one-dimensional approximation. Based on the analysis of the results obtained, we can conclude that the external dynamic force has a negative effect on the mixing of non-isothermal flows. They change the length of the mixing path in comparison with the stationary mode by an average of 5–10 %, which, when transferred to a real NPP, can significantly affect the NCC and will need to be taken into account in the form of correction factors at the design stage.

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Till, Zoltán, Bálint Molnár, Attila Egedy, and Tamás Varga. "CFD Based Qualification of Mixing Efficiency of Stirred Vessels." Periodica Polytechnica Chemical Engineering 63, no. 1 (July 10, 2018): 226–38. http://dx.doi.org/10.3311/ppch.12245.

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In this work, we focus on the most crucial units in a chemical technology, the chemical reactors. Using a commercially available CFD software package, COMSOL Multiphysics, 3D mathematical models of a batch reactor with different impeller geometries have been investigated. The reasonable agreement between the experimental and simulation results indicates the validity of the developed CFD model. The effect of the impeller design, e. g. number of blades on the mixing efficiency is evaluated based on the simulation studies. The proposed measure to determine the energy efficiency of mixing (i. e. mixing index) is based on the calculated velocity field and energy usage. The information about the homogeneity of the mixed phase in the system can be extracted from the developed velocity field. Hence, we proposed histograms of velocity fluctuations on a logarithmic scale as an efficient tool to measure the achieved homogeneity of the phase in case of different impellers and rotational speeds.

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Jumiati, Ety, and Ismail Husein. "MODEL OF SPREAD CONTENT DISEASE FOR ASSOCIATION OF VACCINE." ZERO: Jurnal Sains, Matematika dan Terapan 2, no. 2 (January 3, 2019): 75. http://dx.doi.org/10.30829/zero.v2i2.3166.

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<em>Transmission of infectious diseases in epidemiological models is usually based on the assumption that populations in random mixing. However, in reality this assumption is not fulfilled, because each individual has a limited set of contacts that they can pass through infection; the ensemble of all such contacts forms a complex network. Knowledge of network structure allows a model to calculate the dynamics of an epidemic at a population scale from individual level infection behavior. This paper discusses mathematical models to illustrate the epidemic pattern of transmission of infectious diseases in dynamic networks based on compartment systems.</em>

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MUESCHKE, NICHOLAS J., OLEG SCHILLING, DAVID L. YOUNGS, and MALCOLM J. ANDREWS. "Measurements of molecular mixing in a high-Schmidt-number Rayleigh–Taylor mixing layer." Journal of Fluid Mechanics 632 (July 27, 2009): 17–48. http://dx.doi.org/10.1017/s0022112009006132.

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Molecular mixing measurements are reported for a high-Schmidt-number (Sc~ 103), small-Atwood-number (A≈ 7.5 × 10−4) buoyancy-driven turbulent Rayleigh–Taylor (RT) mixing layer in a water channel facility. Salt was added to the top water stream to create the desired density difference. The degree of molecular mixing was measured as a function of time by monitoring a diffusion-limited chemical reaction between the two fluid streams. The pH of each stream was modified by the addition of acid or alkali such that a local neutralization reaction occurred as the two fluids molecularly mixed. The progress of this neutralization reaction was tracked by the addition of phenolphthalein – a pH-sensitive chemical indicator – to the acidic stream. Accurately calibrated backlit optical techniques were used to measure the average concentration of the coloured chemical indicator. Comparisons of chemical product formation for pre-transitional buoyancy- and shear-driven mixing layers are given. It is also shown that experiments performed at different equivalence ratios (acid/alkali concentrations) can be combined to obtain a mathematical relationship between the coloured product formed and the density variance. This relationship was used to obtain high-fidelity quantitative measures of the degree of molecular mixing which are independent of probe resolution constraints. The dependence of molecular mixing on the Schmidt and Reynolds numbers is examined by comparing the currentSc~ 103measurements with previousSc= 0.7 gas-phase andPr= 7 (wherePris the Prandtl number) liquid-phase measurements. This comparison indicates that the Schmidt number has a large effect on the quantity of mixed fluid at small Reynolds numbersReh< 103. At larger Reynolds numbers, corresponding to later times in this experiment, all mixing parameters indicated a greater degree of molecular mixing and a decreased Schmidt number dependence. Implications for the development and quantitative assessment of turbulent transport and mixing models appropriate for RT instability-induced mixing are discussed.

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Journal articles on the topic 'Mixing – Mathematical models'

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