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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
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2

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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3

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 reali
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4

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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5

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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6

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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7

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
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8

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 sim
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9

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 elemen
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10

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
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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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12

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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15

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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16

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 th
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18

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 compari
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19

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 c
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20

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 elemen
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21

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 configura
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22

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
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23

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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24

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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25

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 m
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26

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
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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
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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 discuss
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29

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 su
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30

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 f
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31

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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32

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 st
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33

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 glob
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34

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 Fl
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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 system
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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 vari
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37

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,
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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 over
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39

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 dist
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40

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. T
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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 flou
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42

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
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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 bac
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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
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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
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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-bas
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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
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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. m
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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 infecti
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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 prog
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