Relevant bibliographies by topics / Mathematical modelling problems

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Mathematical modelling problems'

Author: Grafiati
Published: 7 June 2025
Last updated: 26 June 2025

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Journal articles on the topic "Mathematical modelling problems"

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Ural, Alattin. "A Classification of Mathematical Modeling Problems of Prospective Mathematics Teachers." Journal of Educational Issues 6, no. 1 (2020): 98. http://dx.doi.org/10.5296/jei.v6i1.16566.

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The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed using descriptive analysis. The data of the study was obtained from the mathematical modelling problem written by 59 senior mathematics teachers. They were given a 1-week period to write the problems and solutions. The participants took mathematical modelling course for one semester period prior to the research. The problems are the original problems that the participants themselves produced. The mathematical modelling problems produced are categorically as follows: “Which option is more economical” problems, “Profit-making” problems, “Future prediction” problems and “Relationship between two quantities” problems. The mathematical modelling skills used are as follows: to be able to collect appropriate data, organize the data, write dependent and independent variables, write fixed values, visualize the real situation mathematically or geometrically, use mathematical concepts. The mathematical skills used are generally; to be able to do four operations with rational numbers, draw distribution and column graph, write algebraic expression, do arithmetic operation in algebraic rational expressions, write/solve equation and inequality in 1 or 2 variables, write an appropriate mathematical function explaining the data related to the data, solve 1st degree equations in 1 variable, establish proportion, use trigonometric ratios in right triangle, use basic geometry information, draw and interpret a 1st degree inequality in 2 variables.
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Yanık, H. Bahadır, Osman Bağdat, and Murat Koparan. "Investigating Prospective Middle-School Teachers’ Perspectives of Mathematical Modelling Problems." Journal of Qualitative Research in Education 5, no. 1 (2017): 80–101. http://dx.doi.org/10.14689/issn.2148-2624.1.5c1s4m.

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Panfilov, D. A., V. V. Romanchikov, and K. N. Krupin. "Solving cross-disciplinary problems by mathematical modelling." IOP Conference Series: Materials Science and Engineering 327 (March 2018): 022080. http://dx.doi.org/10.1088/1757-899x/327/2/022080.

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BELLOMO, N., and P. K. MAINI. "PREFACE — CHALLENGING MATHEMATICAL PROBLEMS IN CANCER MODELLING." Mathematical Models and Methods in Applied Sciences 17, supp01 (2007): 1641–45. http://dx.doi.org/10.1142/s0218202507002418.

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Copeland, A. H., R. S. Segall, C. D. Ringo, and B. Moore. "Mathematical modelling of inverse problems for oceans." Applied Mathematical Modelling 15, no. 11-12 (1991): 586–95. http://dx.doi.org/10.1016/s0307-904x(09)81004-4.

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OMORI, Ryosuke. "Applications, Prospects and Problems in Mathematical Modelling." Journal of Veterinary Epidemiology 26, no. 2 (2022): 88–89. http://dx.doi.org/10.2743/jve.26.88.

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Atabekov, Ikram. "Mathematical modelling of some geo-dynamical problems." Journal of Geosciences Insights 1, no. 1 (2023): 1–8. http://dx.doi.org/10.61577/jgi.2023.100001.

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Tectonic earthquakes occur when the stress of Earth’s crust exceeds the instant shear strength. Determining the stress state of a particular area using the equations of mechanics requires knowledge of the boundary conditions, which in most cases seem impossible. This paper proposes the determination of horizontal stresses for the Central Asian territory using the well-known geodynamic hypothesis, according to which the deformation of the Earth’s crust in Central Asia is due to the interaction of the Indian, Arabian, and Eurasian plates. The unknown boundary conditions are reconstructed by solving the inverse problem of elasticity. Some known empirical stresses are used to verify the problem. The solution of the elastic problem makes it possible to set the problem of tectonic creep movements using the Stokes equations. The model is verified by means of horizontal velocity and rotation fields constructed from GPS data. The creep model makes it possible to determine the vertical velocities of the Earth’s crust and supplements the GPS data. The constructed stress state model is used to calculate the variation in the earth’s crust stresses due to earthquakes. A double dipole without a moment is taken as the source mechanism of earthquakes. The boundary element method (BEM) is used for the numerical realization of the model.
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Hacia, L. "MATHEMATICAL MODELLING IN ELECTRICAL ENGINEERING." Mathematical Modelling and Analysis 10, no. 3 (2005): 257–74. http://dx.doi.org/10.3846/13926292.2005.9637286.

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Various problems of electrical engineering lead to mathematical models being difference, differential or integral equations. In this paper some mathematical models in certain problems of electrical engineering are presented. Our considerations are restricted to the radiative heat transfer and density theory (Fredholm integral equations). Respecting time in current density problems we get integro‐differential equations or generally Volterra‐Predholm integral equations (heat‐conduction theory). The new numerical method for these equations is analysed. Daugelio elektros inžinerijos problemu sprendimui tenka sudaryti matematinius modelius, kurie dažniausiai būna aprašomi skirtuminemis, diferencialinemis ar integralinemis lygtimis. Šiame darbe apžvelgiami kai kurie modeliai, skirti konkrečiu elektros inžinerijos uždaviniu sprendimui. Apsiribojama šilumos perdavimo proceso su spinduliuote modeliavimu ir tankio pasiskirstymo teorija (Predholmo integralines lygtys) .Ivedus laika, lygtys tankiui tampa integr‐diferencialinemis arba Volteros‐Predholmo integralinemis lygtimis. Darbe pateikiamas ir nagrinejamas naujas skaitinis tokiu lygčiu sprendimo metodas.
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Lei, Jinzhi. "Viewpoints on modelling: Comments on "Achilles and the tortoise: Some caveats to mathematical modelling in biology"." Mathematics in Applied Sciences and Engineering 1, no. 1 (2020): 85–90. http://dx.doi.org/10.5206/mase/10267.

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Mathematical modelling has been proven to be useful in understanding some problems from biological science, provided that it is used properly. However, it has also attracted some criticisms as partially presented in a recent opinion article \cite{Gilbert2018} from biological community. This note intends to clarify some confusion and misunderstanding in regard to mathematically modelling by commenting on those critiques raised in \cite{Gilbert2018}, with a hope of initiating some further discussion so that both applied mathematicians and biologist can better use mathematical modelling and better understand the results from modelling.
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Herrero, Miguel A., and José M. López. "Bone Formation: Biological Aspects and Modelling Problems." Journal of Theoretical Medicine 6, no. 1 (2005): 41–55. http://dx.doi.org/10.1080/10273660412331336883.

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In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological experimentation.
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Dissertations / Theses on the topic "Mathematical modelling problems"

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Qiang, Feng. "Parallel problem generation for structured problems in mathematical programming." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/11688.

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The aim of this research is to investigate parallel problem generation for structured optimization problems. The result of this research has produced a novel parallel model generator tool, namely the Parallel Structured Model Generator (PSMG). PSMG adopts the model syntax from SML to attain backward compatibility for the models already written in SML [1]. Unlike the proof-of-concept implementation for SML in [2], PSMG does not depend on AMPL [3]. In this thesis, we firstly explain what a structured problem is using concrete real-world problems modelled in SML. Presenting those example models allows us to exhibit PSMG’s modelling syntax and techniques in detail. PSMG provides an easy to use framework for modelling large scale nested structured problems including multi-stage stochastic problems. PSMG can be used for modelling linear programming (LP), quadratic programming (QP), and nonlinear programming (NLP) problems. The second part of this thesis describes considerable thoughts on logical calling sequence and dependencies in parallel operation and algorithms in PSMG. We explain the design concept for PSMG’s solver interface. The interface follows a solver driven work assignment approach that allows the solver to decide how to distribute problem parts to processors in order to obtain better data locality and load balancing for solving problems in parallel. PSMG adopts a delayed constraint expansion design. This allows the memory allocation for computed entities to only happen on a process when it is necessary. The computed entities can be the set expansions of the indexing expressions associated with the variable, parameter and constraint declarations, or temporary values used for set and parameter constructions. We also illustrate algorithms that are important for delivering efficient implementation of PSMG, such as routines for partitioning constraints according to blocks and automatic differentiation algorithms for evaluating Jacobian and Hessian matrices and their corresponding sparsity partterns. Furthermore, PSMG implements a generic solver interface which can be linked with different structure exploiting optimization solvers such as decomposition or interior point based solvers. The work required for linking with PSMG’s solver interface is also discussed. Finally, we evaluate PSMG’s run-time performance and memory usage by generating structured problems with various sizes. The results from both serial and parallel executions are discussed. The benchmark results show that PSMG achieve good parallel efficiency on up to 96 processes. PSMG distributes memory usage among parallel processors which enables the generation of problems that are too large to be processed on a single node due to memory restriction.
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Lamper, David. "Problems in mathematical finance : market modelling and derivative pricing." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270642.

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Thornham, S. A. "The mathematical modelling of two problems in chemical engineering." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382778.

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Pope, Martin Peter. "Mathematical modelling of unsteady problems in thin aerofoil theory." Thesis, University of Southampton, 1999. https://eprints.soton.ac.uk/192771/.

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The de-icing of aircraft wings by the injection of fluid through a slot in the leading edge of the wing is analysed. A review of current de-icing methods is presented and the semi-infinite slot-injection equation derived, which is a singular partial integro-differential equation. The Stefan condition is used to close the system. A discretisation of the equation is presented and the subsequent numerical results are analysed. The model is then revised to account for the retraction of the ice layer away from the slot. An asymptotic result for the thin ice layers is also presented. The problem of describing the motion of a thin, flexible membrane fixed at both ends (a 'sail') is then considered. The steady sail is analysed for the case of an inextensible sail and previous work on this topic is extended by using a discretisation of the singular integro-differential equation that is pertinent to the later analysis of the unsteady sail. An asymptotic expression for the eigenvalues of the system, defined as the values of the tension parameter for which the sail generates zero lift, is also presented. The problem is then extended to that of an extensible sail and numerical results are presented for both the sail with excess length and the membrane without slack. The case where the angle of incidence of the sail to the free stream is a prescribed function of time is then analysed. Previous work on this subject is extended to include the extensible sail and numerical results are presented. A linear stability analysis is then undertaken for both the extensible and elastic sails; the resulting quadratic eigenvalue problem is solved numerically and is in agreement with the numerical experiments. The trailing edge of the membrane is now permitted to move freely and thus the motion of a 'flag' is analysed. The inclusion of bending stiffness is found to be crucial to the stability properties of the flag. The steady equation of motion is numerically approximated for both a hinged flag and a flag that is clamped at the leading edge. The unsteady flag equation is then discretised and numerical results are presented. A linear stability analysis is performed, the conclusions of which are consistent with the numerical approximations of the unsteady flag equation.
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Rout, Sweta. "The mathematical modelling and numerical solution of options pricing problems." Thesis, University of Greenwich, 2005. http://gala.gre.ac.uk/6285/.

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Accurate and efficient numerical solutions have been described for a selection of financial options pricing problems. The methods are based on finite difference discretisation coupled with optimal solvers of the resulting discrete systems. Regular Cartesian meshes have been combined with orthogonal co-ordinate transformations chosen for numerical accuracy rather than reduction of the differential operator to constant coefficient form. They allow detailed resolution in the regions of interest where accuracy is most desired, and grid coarsening where there is least interest. These transformations are shown to be effective in producing accurate solutions on modest computational grids. The spatial discretisation strategy is chosen to meet accuracy requirements as sell as to produce coefficient matrices with favourable sparsity and stability properties. In the case of single factor European options, a modified Crank-Nicolson, second order accurate finite difference scheme is presented, which uses adaptive upwind differences when the mesh Peclet conditions are violated. The resulting tridiagonal system of equations is solved using a direct solver. A careful study of grid refinement displays convergence towards the true solution and demonstrates a high level of accuracy can be obtained with this approach. Laplace inversion methods are also implemented as an alternative solution approach for the one-factor European option. Results are compared to those produced by the direct solver algorithm and are shown to be favourable. It is shown how Semi-Lagrange time-integration can solve the path-dependent Asian pricing problem, by integrating out the average price term and simplifying the finite difference equations into a parameterised Black-Scholes form. The implicit equations that result are unconditionally stable, second order accurate and can be solved using standard tridiagonal solvers. The Semi-Lagrange method is shown to be easily used in conjunction with co-ordinate transformations applied in both spatial directions. A variable time-stepping scheme is implemented in the algorithm. Early exercise is also easily incorporated, the resulting linear complementarity problem can be solved using a projection or penalty method (the penalty method is shown to be slightly more efficient). Second order accuracy has been confirmed for Asian options that must be held to maturity. A comparison with published results for continuous-average-rate put and call options, with and without early exercise, shows that the method achieves basis point accuracy and that Richardson extrapolation can also be applied.
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Li, Xin Kai. "Mathematical modelling and numerical approximations for two-phase flow problems." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276843.

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Alshanti, Waseem Ghazi. "Mathematical modelling and numerical simulations of various granular dynamical problems." Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/499.

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The absence of a general theory that describes the dynamical behaviour of the particulate materials makes the numerical simulations the most current powerful tool that can grasp many mechanical problems relevant to the granular materials. It provides a potential window and useful insight to answer massive questions related to the multi-state dynamical granular systems, including the prediction of internal particles behaviour within the particulate systems. In this thesis, based on a two-dimensional soft particle discrete element method (DEM), a numerical approach was developed to study three different granular dynamical problems, namely, the pulsation stress nature and the stress distribution on hopper wall during filling of granular solids into silos and discharging of granular solids from silos, the penetration of projectiles vertically into granular beds, and the stress distribution underneath granular piles. Moreover, an analytical approach based on the classical continuum mechanical theory was constructed to study the stress distributions at the base of a two-dimensional sand pile in search of the dip vertical stress directly beneath the apex of the sand pile.The granular material is assumed to be an assembly of visco-elastic discs and the motion of the particulate medium is governed by a set of nonlinear first order ordinary differential equations. This system is then solved numerically using the centred finite difference scheme. Based on the presented model, two-dimensional soft particle discrete element simulations have been developed and used to study different features of granular materials during filling and discharging processes in a silo system. The focus is on the stress pulsation mechanism developed on hopper wall and the influence of the wall and internal friction coefficients on the distribution of stresses on hopper wall throughout the static and dynamic processes of material filling and discharging from a silo.The vertical penetrations of projectiles into granular beds are simulated using a two-dimensional soft particle discrete element model to study the influence of various factors such as the impact velocity, lateral and vertical confinements, and the particle size on the projectile penetration distance. Moreover, we study the scaling of the projectile penetration distance with its impact velocity.Finally, to study the normal stress distributions along the base of a two dimensional granular pile, two different mathematical approaches are used for the investigation, including numerical simulations base on a two-dimensional soft particle discrete element model and analytical study based on the classical continuum theory. The influences of particle size and pile height on the normal force distributions beneath granular piles were investigated. Simulations results show the normal force distributions under granular pile that constructed from localised source exhibit a local minimum at the centre of the base under the pile vertex. For the continuum models, the linear elastic theory and plastic theory have been used. These continuum models include an elastic sand pile model and an elasto-plastic sand pile model with an inner plastic region and an outer elastic region. The elasto-plastic model exhibits the “M” shape stress distribution where the location of the local minimum of the vertical stress acting on a horizontal section of the sand pile is at centre.
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Lund, I. D. "Hydrodynamics and mass transfer problems in wet spinning." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370283.

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Wilmott, S. "Mathematical modelling and analysis of some problems in parasitology and ecology." Thesis, University of Oxford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382699.

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Domínguez-Ballesteros, María Belén. "The modelling and analysis of mathematical programming problems : tools and applications." Thesis, Brunel University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409843.

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Books on the topic "Mathematical modelling problems"

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Munier, Nolberto. Mathematical Modelling of Decision Problems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-82347-4.

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Bátkai, András, Petra Csomós, István Faragó, András Horányi, and Gabriella Szépszó, eds. Mathematical Problems in Meteorological Modelling. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40157-7.

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Hritonenko, Natali. Applied Mathematical Modelling of Engineering Problems. Springer US, 2003.

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Hritonenko, Natali, and Yuri Yatsenko. Applied Mathematical Modelling of Engineering Problems. Springer US, 2003. http://dx.doi.org/10.1007/978-1-4419-9160-7.

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Lindner, Ewald, Alessandra Micheletti, and Cláudia Nunes, eds. Mathematical Modelling in Real Life Problems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50388-8.

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P, I︠A︡t︠s︡enko I︠U︡, ed. Applied mathematical modelling of engineering problems. Kluwer Academic Publishers, 2003.

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Machado, J. A. Tenreiro, Necati Özdemir, and Dumitru Baleanu, eds. Mathematical Modelling and Optimization of Engineering Problems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37062-6.

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Ehrhardt, Matthias, ed. Mathematical Modelling and Numerical Simulation of Oil Pollution Problems. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16459-5.

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Dłużewski, Janusz Maciej. Numerical modelling of soil-structure interactions in consolidation problems. Wydawnictwa Politechniki Warszawskiej, 1993.

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Bielski, Jan. Wybrane problemy obliczeniowe w opisie materiałów i konstrukcji sprężysto-plastycznych: Computational problems in modeling of elastic-plastic materials and structures = Ausgewählte Berechnungsprobleme bei der Beschreibung von elastisch-plastischen Materialien und Konstruktionen. Politechnika Krakowska im. Tadeusza Kościuszki, 2013.

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Book chapters on the topic "Mathematical modelling problems"

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Serovajsky, Simon. "Mathematical problems of mathematical models." In Mathematical Modelling. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003035602-19.

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Caldwell, J., and Y. M. Ram. "Compartment Problems." In Mathematical Modelling. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-2201-8_2.

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Vauhkonen, Marko, Tanja Tarvainen, and Timo Lähivaara. "Inverse Problems." In Mathematical Modelling. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27836-0_12.

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Serovajsky, Simon. "Optimal control problems." In Mathematical Modelling. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003035602-20.

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Hofmann, Bernd. "Mathematical Modelling." In Regularization for Applied Inverse and III-Posed Problems. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-322-93034-7_2.

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Cherruault, Y. "Open Problems in Biomathematics." In Mathematical Modelling in Biomedicine. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-5492-2_13.

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Li, Tong. "Mathematical Modelling of Traffic Flows." In Hyperbolic Problems: Theory, Numerics, Applications. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55711-8_65.

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Colli, Pierluigi, Valeriano Comincioli, Giovanni Naldi, and Carlo Reggiani. "Mathematical modelling for contracting muscle." In Biomathematics and Related Computational Problems. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2975-3_54.

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Witelski, Thomas, and Mark Bowen. "Reduced Models for PDE Problems." In Methods of Mathematical Modelling. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23042-9_11.

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King, J. R., and S. J. Franks. "Mathematical Modelling of Nutrient-limited Tissue Growth." In Free Boundary Problems. Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/978-3-7643-7719-9_27.

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Conference papers on the topic "Mathematical modelling problems"

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Pasternak, Viktoriya, Artem Ruban, Oleksandr Holii, and Sergii Vavreniuk. "Mathematical Model of the Dynamics of Spherical Elements." In International Scientific Applied Conference "Problems of Emergency Situations". Trans Tech Publications Ltd, 2024. http://dx.doi.org/10.4028/p-vqm060.

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This paper presents a study in the field of modelling the dynamics of spherical elements. The results obtained indicate the successful use of the discrete element method (DEM) as a numerical tool for analysing the behaviour of the system studied with the help of spheres. The results are based on the importance of correct consideration of the boundary conditions for the spheres, which determine the key aspects of modelling with the developed three-dimensional model. The developed model solves a number of important tasks, expanding the field of scientific research. Firstly, it allows studying the main parameters of the formation of a heterogeneous medium by analysing the compaction of spherical elements in different media. Next, the three-dimensional model is used to study the process of changing the structure of a heterogeneous medium from a static to an oscillatory state, which allows for a deeper understanding of this process. By modelling the mathematical behaviour of spherical elements under the influence of external and additional factors, a detailed understanding of their dynamics and contact interaction can be obtained. The application of the developed model to analyse the contact interaction of spherical elements in heterogeneous media allows predicting the main parameters of spheres and their heterogeneous environment with a reliable accuracy of up to ±1 %. It should be noted that the results obtained on the basis of the three-dimensional model are effective and indicate a number of practical applications in various fields.
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Koshovy, George. "Mathematical Modelling of EM Wave Scattering from Electrically Narrow Strip and Coplanar Strip Systems." In 2024 IEEE 29th International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED). IEEE, 2024. http://dx.doi.org/10.1109/diped63529.2024.10706174.

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Rahman, Silvi Anggraini, Herman Mawengkang, and Sutarman. "Mathematical modelling in logistics transportation problems." In INTERNATIONAL CONFERENCE ON MATHEMATICAL ANALYSIS AND ITS APPLICATIONS 2022 (IConMAA 2022): Analysis, Uncertainty, and Optimization. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0196927.

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Sutini and Rachmat Ali. "Profile of student cognition regulations in solving mathematical problems of mathematical capabilities." In 28TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0000720.

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Murai, Daisuke, Atsushi Kawamoto, and Tsuguo Kondoh. "A Solution to Shape Optimization Problems Using Time Evolution Equations." In 9th Vienna Conference on Mathematical Modelling. ARGESIM Publisher Vienna, 2018. http://dx.doi.org/10.11128/arep.55.a55240.

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Dovgyi, S., S. Moiseienko, O. Polevoy, D. Redchyts, and S. Tarasov. "Mathematical Modelling of Vertical-Axis Wind Turbines Rotors Aerodynamics." In Topical Problems of Fluid Mechanics 2024. Institute of Thermomechanics of the Czech Academy of Sciences; CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics, 2024. http://dx.doi.org/10.14311/tpfm.2024.005.

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Numerical modeling of unsteady turbulent separated flows of incompressible fluid around vertical axis wind turbines (VAWT) with Darrieus and Savonius rotors was performed on the basis of the Reynolds-averaged Navier-Stokes equations, closed by the SpalartAllmaras turbulence model. The numerical solution was obtained using original homemade program code that implements an implicit finite volume algorithm based on the artificial compressibility method. Verification of developed CFD code has been carried out by simulation of several typical testing problems, namely: laminar and turbulent flow around steady and unsteady cylinder, subcritical and supercritical flow around steady and oscillating NACA 4412, NACA 0015 airfoils, aerodynamics of the turbulent flow around a 30P30N multi-element airfoil in cruise, takeoff and landing configurations, turbulent flow around tractor-trailer. The results of Darrieus and Savonius rotors simulation, physical and computational experiments with different number and geometry of blades are presented in the form of detailed flow visualization and reconstruction for two- and three-blade Darrieus rotor. The analysis of flow field near rotors was carried out and the main stages of vortex development were identified and analyzed. The results of three series of computational experiments on aerodynamic of two and three-bucket Savonius rotor were obtained, presented and discussed.
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Hameed, Hameed Husam, Hayder M. Al-Saedi, and Mohammed H. Al-Mayyah. "Mathematical Modelling for Cholera Epidemic in Iraq." In 2023 5th International Conference on Problems of Cybernetics and Informatics (PCI). IEEE, 2023. http://dx.doi.org/10.1109/pci60110.2023.10325918.

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Rogovchenko, Yuriy, and Svitlana Rogovchenko. "Promoting engineering students’ learning with mathematical modelling projects." In SEFI 50th Annual conference of The European Society for Engineering Education. Universitat Politècnica de Catalunya, 2022. http://dx.doi.org/10.5821/conference-9788412322262.1451.

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Mathematics constitutes a key component in engineering education. Engineering students are traditionally offered a number of mathematics courses which provide the knowledge needed at the workplace. Unfortunately, many students perceive mathematics as a discipline that teaches mostly procedures not relevant to their future careers and often view it as one of the main obstacles on their way to an engineering degree. In this paper, we discuss how introducing university students in a standard Differential Equations course to mathematical modelling (MM), a powerful strategy for solving real-life problems, contributes to the development of their mathematical competencies, motivates their interest to mathematics, promotes the use of advanced mathematical thinking, methods of applied mathematics, and digital computational tools.
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Kurbanaliev, A. Y., A. B. Turganbaeva, and A. K. Kaleeva. "Mathematical modelling of flow over the single hill." In VII INTERNATIONAL CONFERENCE “SAFETY PROBLEMS OF CIVIL ENGINEERING CRITICAL INFRASTRUCTURES” (SPCECI2021). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0125816.

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Susanah, Evangelista Lus Windyana Palupi, and Dini Kinati Fardah. "Prospective teachers’ mathematical communication profile in solving geometry proof problems." In INTERNATIONAL CONFERENCE ON MODELLING STRATEGIES IN MATHEMATICS: ICMSM 2024. AIP Publishing, 2025. https://doi.org/10.1063/5.0269207.

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Reports on the topic "Mathematical modelling problems"

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Unal, Beyza, Julia Cournoyer, Calum Inverarity, and Yasmin Afina. Uncertainty and complexity in nuclear decision-making. Royal Institute of International Affairs, 2022. http://dx.doi.org/10.55317/9781784135157.

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Complex systems modelling is already implemented in critical policy areas such as climate change and health. It could also play an important role in the nuclear weapons sphere – by opening alternative pathways that may help mitigate risks of confrontation and escalation – but such modelling has yet to be fully embraced by policymakers in this community. By applying a complexity lens, policy- and decision-makers at all stages along the nuclear chain of command might better understand how their actions could have significant consequences for international security and peace. Nuclear decision-making is shaped by, and interacts with, the ever-changing international security environment and nuclear weapons policy. Tackling problems in the nuclear weapons policy field requires the implementation of ‘system of systems’ design principles, mathematical modelling approaches and multidisciplinary analysis. This research paper presents nuclear weapons decision-making as a complex endeavour, with individual decisions being influenced by multiple factors such as reasoning, intuition (gut feeling), biases and system-level noise. At a time of crisis, these factors may combine to cause risks of escalation. The authors draw on past examples of near nuclear use to examine decision-making in the nuclear context as a ‘wicked problem’, with multi-layered, interacting and constantly fluctuating elements.
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Perdigão, Rui A. P., and Julia Hall. Spatiotemporal Causality and Predictability Beyond Recurrence Collapse in Complex Coevolutionary Systems. Meteoceanics, 2020. http://dx.doi.org/10.46337/201111.

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Causality and Predictability of Complex Systems pose fundamental challenges even under well-defined structural stochastic-dynamic conditions where the laws of motion and system symmetries are known. However, the edifice of complexity can be profoundly transformed by structural-functional coevolution and non-recurrent elusive mechanisms changing the very same invariants of motion that had been taken for granted. This leads to recurrence collapse and memory loss, precluding the ability of traditional stochastic-dynamic and information-theoretic metrics to provide reliable information about the non-recurrent emergence of fundamental new properties absent from the a priori kinematic geometric and statistical features. Unveiling causal mechanisms and eliciting system dynamic predictability under such challenging conditions is not only a fundamental problem in mathematical and statistical physics, but also one of critical importance to dynamic modelling, risk assessment and decision support e.g. regarding non-recurrent critical transitions and extreme events. In order to address these challenges, generalized metrics in non-ergodic information physics are hereby introduced for unveiling elusive dynamics, causality and predictability of complex dynamical systems undergoing far-from-equilibrium structural-functional coevolution. With these methodological developments at hand, hidden dynamic information is hereby brought out and explicitly quantified even beyond post-critical regime collapse, long after statistical information is lost. The added causal insights and operational predictive value are further highlighted by evaluating the new information metrics among statistically independent variables, where traditional techniques therefore find no information links. Notwithstanding the factorability of the distributions associated to the aforementioned independent variables, synergistic and redundant information are found to emerge from microphysical, event-scale codependencies in far-from-equilibrium nonlinear statistical mechanics. The findings are illustrated to shed light onto fundamental causal mechanisms and unveil elusive dynamic predictability of non-recurrent critical transitions and extreme events across multiscale hydro-climatic problems.
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Saptsin, Vladimir, and Володимир Миколайович Соловйов. Relativistic quantum econophysics – new paradigms in complex systems modelling. [б.в.], 2009. http://dx.doi.org/10.31812/0564/1134.

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This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system’s state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondefinable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativistic and relativistic quantum mechanics, subject to the historical, psychological and philosophical aspects and modern state of the socio-economic modeling problem. We have shown that actually and, virtually, a long time ago, new paradigms of modeling were accepted in the quantum theory, within the bounds of which the notion of the physical quantity operator becomes the primary fundamental conception(operator is a mathematical image of the procedure, the action), description of the system dynamics becomes discrete and approximate in its essence, prediction of the future, even in the rough, is actually impossible when setting aside the aftereffect i.e. the memory. In consideration of the analysis conducted in the work we suggest new paradigms of the economical-mathematical modeling.
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