Journal articles: 'Three-dimensional mathematical modelling'

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Volgin, Vladimir M., and Victor V. Lyubimov. "Mathematical modelling of three-dimensional electrochemical forming of complicated surfaces." Journal of Materials Processing Technology 109, no. 3 (2001): 314–19. http://dx.doi.org/10.1016/s0924-0136(00)00819-0.

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Ciarlet, Philippe G. "Mathematical modelling of linearly elastic shells." Acta Numerica 10 (May 2001): 103–214. http://dx.doi.org/10.1017/s0962492901000022.

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The objective of this article is to lay down the proper mathematical foundations of the two-dimensional theory of linearly elastic shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional linear shell theories, by means of asymptotic methods, with the thickness as the ‘small’ parameter.A major virtue of this approach is that it naturally leads to precise mathematical definitions of linearly elastic ‘membrane’ and ‘flexural’ shells. Another noteworthy feature is that it highlights in particular the role played by two fundamental tensors, each associated with a displacement field of the middle surface, the linearized change of metric and linearized change of curvature tensors.More specifically, under fundamentally distinct sets of assumptions bearing on the geometry of the middle surface, on the boundary conditions, and on the order of magnitude of the applied forces, it is shown that the three-dimensional displacements, once properly scaled, converge (in H1, or in L2, or in ad hoc completions) as the thickness approaches zero towards a ‘two-dimensional’ limit that satisfies either the linear two-dimensional equations of a ‘membrane’ shell (themselves divided into two subclasses) or the linear two-dimensional equations of a ‘flexural’ shell. Note that this asymptotic analysis automatically provides in each case the ‘limit’ two-dimensional equations, together with the function space over which they are well-posed.The linear two-dimensional shell equations that are most commonly used in numerical simulations, namely Koiter's equations, Naghdi's equations, and ‘shallow’ shell equations, are then carefully described, mathematically analysed, and likewise justified by means of asymptotic analyses.The existence and uniqueness of solutions to each one of these linear two-dimensional shell equations are also established by means of crucial inequalities of Korn's type on surfaces, which are proved in detail at the beginning of the article.This article serves as a mathematical basis for the numerically oriented companion article by Dominique Chapelle, also in this issue of Acta Numerica.

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Ang, K. C., and J. N. Mazumdar. "Mathematical modelling of three-dimensional flow through an asymmetric arterial stenosis." Mathematical and Computer Modelling 25, no. 1 (1997): 19–29. http://dx.doi.org/10.1016/s0895-7177(96)00182-3.

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Garishin, O. K., and S. N. Lebedev. "Mathematical Modelling of the Mechanical Properties of Disordered Three-Dimensional Structures." International Polymer Science and Technology 29, no. 6 (2002): 47–51. http://dx.doi.org/10.1177/0307174x0202900613.

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NOLAN, JOSHUA D., and CLIFFORD A. REITER. "COMPUTING AND VISUALIZING THREE-DIMENSIONAL QUASICRYSTALS." Fractals 26, no. 06 (2018): 1850093. http://dx.doi.org/10.1142/s0218348x18500937.

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In 1984, solid-state materials were discovered that had diffraction pattern symmetries that are forbidden for three-dimensional crystalline structures. The structures of these materials have become known as quasicrystals. A considerable literature has developed for both physical and mathematical quasicrystals. There are essentially three forms of mathematical three-dimensional quasicrystals. In this paper, we will develop computational techniques to construct these three forms of quasicrystals as point sets, and then organize those point sets in order to visualize patches of quasicrystals using parallelepipeds.

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Weihs, Daphne, Amit Gefen, and Fred J. Vermolen. "Review on experiment-based two- and three-dimensional models for wound healing." Interface Focus 6, no. 5 (2016): 20160038. http://dx.doi.org/10.1098/rsfs.2016.0038.

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Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.

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Assunção Jr, M. O., and M. Vynnycky. "MATHEMATICAL MODELLING OF MACROSEGREGATION IN INGOT CASTING." Revista de Engenharia Térmica 17, no. 2 (2018): 74. http://dx.doi.org/10.5380/reterm.v17i2.64133.

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The occurrence of macrosegregation in alloys produced by ingot casting can adversely affect the quality of the final product. Macrosegregation can be described as a severe variation on the macroscopic scale of the chemical species that compose the alloy, and the ability of computational simulations to predict such defects remains far from perfect. Therefore, this research focuses on the development of a two-dimensional mathematical model that - through computational simulations - could be applied to study and predict the formation of macrosegregation in the ingot casting of binary alloys. Once accomplished, this work can establish the framework to new studies that will tackle more advanced problems, e.g., for actual ingot geometries, three-dimensional models and industrially-important ternary alloys.

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NISHIOKA, Koki, Takayuki MAEDA, and Masakata SHIMIZU. "A Three-dimensional Mathematical Modelling of Drainage Behavior in Blast Furnace Hearth." ISIJ International 45, no. 5 (2005): 669–76. http://dx.doi.org/10.2355/isijinternational.45.669.

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Gao, Jun, and Xiao Lin. "Mathematical Interpolation and Correction of Three-Dimensional Modelling of High-Speed Railway." Intelligent Automation & Soft Computing 26, no. 5 (2020): 1023–34. http://dx.doi.org/10.32604/iasc.2020.010134.

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NISHIOKA, Koki, Takayuki MAEDA, and Masakata SHIMIZU. "A Three-dimensional Mathematical Modelling of Drainage Behavior in Blast Furnace Hearth." Tetsu-to-Hagane 92, no. 12 (2006): 967–75. http://dx.doi.org/10.2355/tetsutohagane1955.92.12_967.

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Kudryashova’, Tatiana, Sergey Polyakov, and Nikita Tarasov. "A novel parallel algorithm for 3D modelling electromagnetic purification of water." MATEC Web of Conferences 210 (2018): 04027. http://dx.doi.org/10.1051/matecconf/201821004027.

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The computational fluid dynamic research in this work has focused on the problem of full-scale three-dimensional modelling water purification processes by the electromagnetic method. Presently, this method of purification was used in the final stage of processing for the production of ultrapure water. In spite of many field experiments, detailed data on such processes can be obtained only by the mathematical modelling. This way allows us to take into account many aspects, for example: real three-dimensional geometry, physical structure of the purification system, heterogeneous composition of the impurities, etc. And also, the mathematical modelling helps to optimize many parameters in order to improve a design of the purification system. Within the framework of the modelling problem, one of the important aspects is the correct description of the three-dimensional flow inside a specific purification system. For this purpose, various mathematical models and numerical approaches are implemented. In this paper, the flow calculation was realized on basis of the Navier-Stokes equations.

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Rădan (Toader), Georgiana, Nicoleta Rădulescu, and Gheorghe Oancea. "Mathematical Modelling for Micropiles Embedded in Salt Rock." Mathematical Modelling in Civil Engineering 12, no. 1 (2016): 23–35. http://dx.doi.org/10.1515/mmce-2016-0003.

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Abstract This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.

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Oduwole, Olayinka, and Steve Sheard. "Three-dimensional mathematical modelling of magnetic bead interactions within a magnetic separation system." Applied Mathematical Modelling 45 (May 2017): 123–33. http://dx.doi.org/10.1016/j.apm.2016.12.025.

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Tu¨mer, S. T., and A. E. Engin. "Three-Dimensional Kinematic Modelling of the Human Shoulder Complex—Part II: Mathematical Modelling and Solution Via Optimization." Journal of Biomechanical Engineering 111, no. 2 (1989): 113–21. http://dx.doi.org/10.1115/1.3118775.

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In this paper, individual joint sinus cones associated with the sternoclavicular, claviscapular, and glenohumeral joints of the three-dimensional kinematic model introduced in Part I for the human shoulder complex are quantitatively determined. First, mathematical description of the humerus orientation with respect to torso is given in terms of eight joint variables. Since the system is a kinematically redundant one, solution for the joint variables satisfying a prescribed humerus orientation is possible only if additional requirements are imposed; and the “minimum joint motion” criterion is introduced for this purpose. Two methods, namely the Lagrange multipliers and flexible tolerance methods, are formulated and tested for the optimization problem. The statistical in-vivo data base for the circumductory motion of the upper arm is employed to determine a set of joint variables via optimization, which are then utilized to establish the sizes and orientations of the elliptical cones for the individual joint sinuses. The results are discussed and compared with those given on the basis of measurements made on cadaveric specimens.

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Lara, Javier L., Inigo J. Losada, Gabriel Barajas, Maria Maza, and Benedetto Di Paolo. "RECENT ADVANCES IN 3D MODELLING OF WAVE-STRUCTURE INTERACTION WITH CFD MODELS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 91. http://dx.doi.org/10.9753/icce.v36.waves.91.

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Numerical modelling of the interaction of water waves with coastal structures has continuously been among the most relevant challenges in coastal engineering research and practice. During the last years, 3D modelling based on RANS-type equations, has been the dominant methodology to address the mathematical modelling of wave and coastal structure interaction. However, the three-dimensionality of many flowstructure interactions processes demands overcoming existing modelling limitations. Under some circumstances relevant three-dimensional processes are still tackled using physical modelling. It has been shown that beyond numerical implementation of the well-known mathematical 3-D formulation of the Navier-Stokes equations, the application of 3-D codes to standard coastal engineering problems demands some additional steps to be taken. These steps could be classified into three main groups relevant to: a) the modelling of the physical processes; b) the use of the tool and c) the applicability of the codes. This work presents an analysis of the use of three-dimensional flow models to analyze wave interaction with coastal structures focusing on recent developments overcoming existing limitations. Last modelling advances, including the implementation of new physics and pre-and postprocessing tools will be shown with the aim of extending the use of three-dimensional modelling of wavestructure interaction in both coastal and offshore fields.

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Mironov, V., S. Bogomolov, A. Bondarchenko, A. Efremov, V. Loginov, and D. Pugachev. "Three-dimensional modelling of processes in Electron Cyclotron Resonance Ion Source." Journal of Instrumentation 15, no. 10 (2020): P10030. http://dx.doi.org/10.1088/1748-0221/15/10/p10030.

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Modok, Szabolcs, Philip Hyde, Howard R. Mellor, Tiina Roose, and Richard Callaghan. "Diffusivity and distribution of vinblastine in three-dimensional tumour tissue: Experimental and mathematical modelling." European Journal of Cancer 42, no. 14 (2006): 2404–13. http://dx.doi.org/10.1016/j.ejca.2006.05.020.

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Hayat, Tasawar, Taseer Muhammad, Sabir Ali Shehzad, Ahmed Alsaedi, and Falleh Al-Solamy. "Radiative Three-Dimensional Flow with Chemical Reaction." International Journal of Chemical Reactor Engineering 14, no. 1 (2016): 79–91. http://dx.doi.org/10.1515/ijcre-2014-0179.

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AbstractWe discuss the three-dimensional boundary layer flow of Maxwell nanofluid in the present article. The flow is caused due to bidirectional stretching surface. An applied magnetic field is taken into account. Heat and mass transfer characteristics are considered in the presence of thermal radiation, Brownian motion, thermophoresis and chemical reaction effects. Mathematical modelling is made under a low magnetic Reynolds number and Rosseland’s approximation. Expressions of series solutions for velocities, temperature and concentration are developed. Impacts of influential parameters on the temperature and concentration are sketched and examined. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. We found that an increase in thermophoresis and Brownian motion parameters enhanced the temperature field and thermal boundary layer thickness. The concentration field reduced gradually when we enhance the values of Lewis number and chemical reaction parameter. The values of local Nusselt number are higher for a larger radiation parameter.

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Skob, Yurii, Mykhaylo Ugryumov, and Yuriy Dreval. "Numerical Modelling of Gas Explosion Overpressure Mitigation Effects." Materials Science Forum 1006 (August 2020): 117–22. http://dx.doi.org/10.4028/www.scientific.net/msf.1006.117.

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The main aims of this study are to assess numerically the mitigation effects caused by the solid wall installed at the fueling station in order to protect personnel from the consequences of the emergent gas explosion, evaluate the optimal location of the wall and choose the appropriate material the wall have to be made of in order not to be destructed. A three-dimensional mathematical model of an explosion of hydrogen-air cloud is used. A computer technology how to define the personnel damage probability fields on the basis of probit analysis of the explosion wave is developed. The mathematical model takes into account the complex terrain and three-dimensional non-stationary nature of the shock wave propagation process. The model allows obtaining time-spatial distribution of damaging factors (overpressure in the shock wave front and the compression phase impulse) required to determine the three-dimensional non-stationary damage probability fields based on probit analysis. The developed computer technology allows to carry out an automated analysis of the safety situation at the fueling station and to conduct a comparative analysis of the effectiveness of different types of material the protective facilities made of.

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Seo, S.-J., K.-Y. Kim, and S.-H. Kang. "Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 217, no. 3 (2003): 287–97. http://dx.doi.org/10.1243/095765003322066510.

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A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

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Khoshmanesh, S., and M. Mirzaei. "Performance evaluation of a direct methanol fuel cell: combination of three-dimensional computational fluid dynamic modelling and one-dimensional diffusion layer mathematical modelling." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 225, no. 6 (2011): 718–33. http://dx.doi.org/10.1177/0957650911407316.

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RAPPAZ, JACQUES, and ADRIAN REIST. "MATHEMATICAL AND NUMERICAL ANALYSIS OF A THREE-DIMENSIONAL FLUID FLOW MODEL IN GLACIOLOGY." Mathematical Models and Methods in Applied Sciences 15, no. 01 (2005): 37–52. http://dx.doi.org/10.1142/s0218202505003897.

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The main goal of this article is to analyze a three-dimensional model for stress and velocity fields in grounded glaciers and ice sheets including the role of normal deviatoric stress gradients. This model leads to a nonlinear system of stationary partial differential equations for the velocity with a viscosity depending on the stress–tensor but which is not explicitly depending on the velocity. The existence and uniqueness of a weak solution corresponding to this model is established by using the calculus of variations. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1 on a tetrahedral mesh and error analysis is performed. Numerical solutions show that the theoretical results we have obtained are almost optimal.

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Janda, S., and Dj Kalić. "Mathematical modelling of three-phase electrode salt-bath furnace with the two-dimensional electric field." Archiv für Elektrotechnik 71, no. 1 (1988): 19–25. http://dx.doi.org/10.1007/bf01574380.

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Kolev, Spas D., Willem E. van der Linden, Wouter Olthuis, and Piet Bergveld. "Mathematical modelling and optimisation of a coulometric sensor—actuator system based on three-dimensional diffusion." Analytica Chimica Acta 285, no. 3 (1994): 247–63. http://dx.doi.org/10.1016/0003-2670(94)80063-4.

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Elkotb, M. M., O. M. F. Elbahar, T. A. Abdou Ahmed, and T. W. Abou-Arab. "Mathematical Modelling and Field Measurements of Nitrogen Oxides in Metropolitan Areas." Energy & Environment 3, no. 2 (1992): 133–47. http://dx.doi.org/10.1177/0958305x9200300203.

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A mathematical model for the prediction of pollutant emissions from motor vehicles is presented. The model is based on the numerical solution of the three-dimensional equation representing the mass conservation of dilute diffusing species. The variation of wind speed and eddy diffusivity with height is taken into consideration. The three-dimensional diffusion equation is solved numerically. The numerical procedure involves the discretization of the partial differential equation using the finite volume approach. The resulting set of discretization equation is solved iteratively using a fully implicit solution procedure. Furthermore, field measurements of the concentrations of nitrogen oxide in the downtown area of Cairo were conducted. For this purpose, a mobile air pollution laboratory fitted with gas analyzers, particulate matter sampler and equipment for the measurement of wind speed and direction has been used. This laboratory is also fitted with data recording and monitoring facility. The mathematical model is tested by comparing the computed pollutant concentrations with the experimental data obtained from the field measurements in the Cairo Metropolitan Area.

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Issakhov, Alibek. "Mathematical Modelling of Thermal Process to Aquatic Environment with Different Hydrometeorological Conditions." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/678095.

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This paper presents the mathematical model of the thermal process from thermal power plant to aquatic environment of the reservoir-cooler, which is located in the Pavlodar region, 17 Km to the north-east of Ekibastuz town. The thermal process in reservoir-cooler with different hydrometeorological conditions is considered, which is solved by three-dimensional Navier-Stokes equations and temperature equation for an incompressible flow in a stratified medium. A numerical method based on the projection method, divides the problem into three stages. At the first stage, it is assumed that the transfer of momentum occurs only by convection and diffusion. Intermediate velocity field is solved by fractional steps method. At the second stage, three-dimensional Poisson equation is solved by the Fourier method in combination with tridiagonal matrix method (Thomas algorithm). Finally, at the third stage, it is expected that the transfer is only due to the pressure gradient. Numerical method determines the basic laws of the hydrothermal processes that qualitatively and quantitatively are approximated depending on different hydrometeorological conditions.

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Jo, Kichun, Minchul Lee, Chansoo Kim, and Myoungho Sunwoo. "Construction process of a three-dimensional roadway geometry map for autonomous driving." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 231, no. 10 (2016): 1414–34. http://dx.doi.org/10.1177/0954407016675060.

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This paper presents a construction process of the three-dimensional roadway geometry map for an autonomous driving system. The presented process focuses on the post-processing and the three-dimensional roadway geometry modelling algorithms. The post-processing algorithm refines the raw Global Positioning System position data by combining the novel three-dimensional roadway geometry model which originated from the construction engineering of roadways and vehicle motion data from onboard sensors using a Rauch–Tung–Striebel smoother. The three-dimensional geometry modelling algorithm approximates the road geometry information described in three-dimensional point clouds into a mathematical curve model based on the B-spline. An adaptive curve refinement method using dominant points was applied to the road modelling algorithm. This dominant-point-based refinement method can reduce the number of knots and the number of control points of the B-spline road model while maintaining the desired accuracy of the roadway map. Also, since the dominant-point refinement method considers a road shape factor, such as the curvature and the arc length, for the road modelling, it is more efficient than the previous B-spline road modelling algorithms. The proposed map generation algorithm was verified and evaluated through experiments in various test conditions. The experimental results show that the presented construction process of the three-dimensional roadway geometry map can provide sufficient accuracy, reliability and efficiency for applications of autonomous driving systems in comparison with those of other roadway map construction processes.

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Mehta, P. S., and A. K. Gupta. "Modelling of Spray–Swirl Interaction in Direct Injection Diesel Engine Combustion Chambers." Proceedings of the Institution of Mechanical Engineers, Part D: Transport Engineering 199, no. 3 (1985): 187–98. http://dx.doi.org/10.1243/pime_proc_1985_199_156_01.

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A mathematical model for predicting spray–swirl interaction in a direct injection diesel engine combustion chamber is developed using centre-line velocity vector/continuum approach. The model has three-dimensional features in fuel spray motion. The present model responds to the various air swirl, fuel injection and cylinder charge conditions. The predicted results are compared with the analytical and experimental data available from various sources in the two-dimensional case. Very good agreement is achieved over a wide range of data. The three-dimensional predictions are directly possible without any alteration in the computation scheme.

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TRACQUI, PHILIPPE, and MAHIDINE MENDJELI. "MODELLING THREE-DIMENSIONAL GROWTH OF BRAIN TUMOURS FROM TIME SERIES OF SCANS." Mathematical Models and Methods in Applied Sciences 09, no. 04 (1999): 581–98. http://dx.doi.org/10.1142/s0218202599000300.

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The development of brain tumours, after diagnosis, is routinely recorded by different medical imaging techniques like computerised tomography (CT) or magnetic resonance imaging (MRI). However, it is only through the formulation of mathematical models that an analysis of the spatio-temporal tumour growth revealed on each patient serial scans can lead to a quantification of parameters characterising the proliferative and expensive dynamic of the brain tumour. This paper reviews some of the results and limitations encountered in modelling the different stages of a brain tumour growth, namely before and after diagnosis and therapy. It extends an original two-dimensional approach by considering three-dimensional growth of brain tumours submitted to the spatial constraints exerted by the skull and ventricles boundaries. Considering the dynamic of both the pre- and post-diagnosis stages, the tumour growth patterns obtained with various combinations of nonlinear growth rates and cellular diffusion laws are considered and compared to real MRI scans taken in a patient with a glioblastoma and having undergone radiotherapy. From these simulations, we characterise the effects of different therapies on survival durations, with special attention to the effect of cell diffusion inside the resected brain region when surgical resection of the tumour is carried out.

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Arkhipov, Vladimir, Alexander Nee, and Lily Valieva. "Numerical Simulation of Heat Transfer in a Closed Two-Phase Thermosiphon." Key Engineering Materials 743 (July 2017): 449–53. http://dx.doi.org/10.4028/www.scientific.net/kem.743.449.

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This paper presents the results of mathematical modelling of three–dimensional heat transfer in a closed two-phase thermosyphon taking into account phase transitions. Three-dimensional conduction equation was solved by means of the finite difference method (FDM). Locally one-dimensional scheme of Samarskiy was used to approximate the differential equations. The effect of the thermosyphon height and temperature of its bottom lid on the temperature difference in the vapor section was shown.

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Shilnikov, Leonid. "Mathematical Problems of Nonlinear Dynamics: A Tutorial." International Journal of Bifurcation and Chaos 07, no. 09 (1997): 1953–2001. http://dx.doi.org/10.1142/s0218127497001527.

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We review the theory of nonlinear systems, especially that of strange attractors, and give its perspectives. Of a special attention are the recent results concerning hyperbolic attractors and features of high-dimensional systems in the Newhouse regions. We present an example of a "wild" strange attractor of the topological dimension three.

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Nickerson, David P., Jonna R. Terkildsen, Kirk L. Hamilton, and Peter J. Hunter. "A tool for multi-scale modelling of the renal nephron." Interface Focus 1, no. 3 (2011): 417–25. http://dx.doi.org/10.1098/rsfs.2010.0032.

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We present the development of a tool, which provides users with the ability to visualize and interact with a comprehensive description of a multi-scale model of the renal nephron. A one-dimensional anatomical model of the nephron has been created and is used for visualization and modelling of tubule transport in various nephron anatomical segments. Mathematical models of nephron segments are embedded in the one-dimensional model. At the cellular level, these segment models use models encoded in CellML to describe cellular and subcellular transport kinetics. A web-based presentation environment has been developed that allows the user to visualize and navigate through the multi-scale nephron model, including simulation results, at the different spatial scales encompassed by the model description. The Zinc extension to Firefox is used to provide an interactive three-dimensional view of the tubule model and the native Firefox rendering of scalable vector graphics is used to present schematic diagrams for cellular and subcellular scale models. The model viewer is embedded in a web page that dynamically presents content based on user input. For example, when viewing the whole nephron model, the user might be presented with information on the various embedded segment models as they select them in the three-dimensional model view. Alternatively, the user chooses to focus the model viewer on a cellular model located in a particular nephron segment in order to view the various membrane transport proteins. Selecting a specific protein may then present the user with a description of the mathematical model governing the behaviour of that protein—including the mathematical model itself and various simulation experiments used to validate the model against the literature.

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García-Peñarrubia, Pilar, Juan J. Gálvez, and Jesús Gálvez. "Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor–ligand interactions in signalling response mechanisms." Journal of Mathematical Biology 69, no. 3 (2013): 553–82. http://dx.doi.org/10.1007/s00285-013-0712-4.

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GRACHEV, SERGEJ, DENIS SMAGIN, ROMAN SAVELEV, KONSTANTIN NAPREENKO, and ANNA ZININA. "THE CONCEPT OF FUEL SYSTEM’S MATHEMATICAL MODELING BASED ON CERTIFICATION REQUIREMENTS." Computational nanotechnology 7, no. 3 (2020): 45–51. http://dx.doi.org/10.33693/2313-223x-2020-7-3-45-51.

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The article discusses the concept of fuel system’s mathematical modeling based on certification requirements. A detailed description of the safety of aircraft operation, taking into account the standard of airworthiness, and methods for conformity assessment of certification has also been presented. The development concept modeling is not possible to without a methodology to construct an integrated mathematical model which presents a solution using a one-dimensional and three-dimensional functioning model. The combined calculation in a one-dimensional and three-dimensional setting allows the modulating of the refuelling process with drainage system, signaling and centralized fuelling management process. Also as the calculation results of simulation of fuel flow from tanks when one pump fails are shown. Dynamic simulation of fuel production from tanks for calculation of static change fuel static moment and geometric modelling of non-working and non-poured remainder also presented. The article analysed fuel system requirements. This conformity can be met using a complex of mathematical modeling tools.

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KRASUCKI, FRANCOISE, ARNAUD MÜNCH, and YVES OUSSET. "MATHEMATICAL ANALYSIS OF NONLINEAR BONDED JOINT MODELS." Mathematical Models and Methods in Applied Sciences 14, no. 04 (2004): 535–56. http://dx.doi.org/10.1142/s0218202504003349.

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Within the framework of nonlinear elasticity, we consider the problem of two adherents joined along their common surface by a thin soft adhesive. Two stored energy functions are considered: the stored energy function of Saint Venant–Kirchhoff and the stored energy function of Ciarlet–Geymonat. Using the asymptotic expansion method, the limit energy associated to each of these stored energy functions is obtained. The aim of this paper is to give a rigorous mathematical analysis of the formally derived limit problem. We show that the limit problem associated to the Saint Venant–Kirchhoff case admits at least one solution and the limit problem associated to the Ciarlet–Geymonat case admits exactly one solution. An analytical comparison in the one-dimensional case and a three-dimensional numerical application are also presented.

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Xylouris, Konstantinos, Gillian Queisser, and Gabriel Wittum. "A three-dimensional mathematical model of active signal processing in axons." Computing and Visualization in Science 13, no. 8 (2010): 409–18. http://dx.doi.org/10.1007/s00791-011-0155-7.

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Garus, Jerzy. "Control-Oriented Modelling of Spatial Motion of Autonomous Underwater Vehicle." Solid State Phenomena 196 (February 2013): 109–16. http://dx.doi.org/10.4028/www.scientific.net/ssp.196.109.

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Modelling of three-dimensional motion of an underwater vehicle along a time-varying reference trajectory with predefined speed profiles is presented in the paper. A nonlinear mathematical model with unknown nonlinearities describes the vehicle’s dynamics. Command signals are generated by an adaptive autopilot consisting of three independent controllers with a parameter adaptation law implemented. A control performance is guaranteed by suitably choosing design parameters. Selected results of computer simulations are inserted to demonstrate quality and effectiveness of the approach.

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Pincevičius, Albertas, Romualdas Baušys, and Pranas Jankauskas. "APPLICATION OF GEOGRAPHICAL INFORMATION SYSTEMS IN MODELLING OF MILITARY OPERATIONS." Aviation 9, no. 3 (2005): 36–42. http://dx.doi.org/10.3846/16487788.2005.9635909.

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The algorithm of the stochastic model of combat is given in article. Random functions describing the basic processes of combat (movement of military personnel, detection of the enemy, firing and its results, etc.) are recorded. Corresponding mathematical expressions and numerical evaluations are given. Application of Geographical Information Systems (GIS) technologies and three‐dimensional map in planning battle tactics are discussed.

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Taher, S. E.-D., and A. A. Almusallam. "A three-dimensional graphical method for shear strain analysis." Journal of Strain Analysis for Engineering Design 29, no. 4 (1994): 263–66. http://dx.doi.org/10.1243/03093247v294263.

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The efficiency of graphical methods for strain analysis depends merely on its simplicity and accuracy. For most strain definitions, the Mohr circle has proved to be the most powerful graphical technique. Unfortunately, its three-dimensional form has limitations concerning the determination of the shearing strain components on a general oblique plane. In this paper, the various deformation quantifiers and the existing extensions to Mohr's method which account for its drawbacks are briefly reviewed. A novel proposal to be appended to Mohr's original construction, allowing its complete generality, is given. It has the form of a simplified complementary triangular construction. A mathematical formulation of the suggested graphical techniques on the basis of Cauchy's formula and vector analysis is carried out.

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Barink, M., A. van Kampen, M. de Waal Malefijt, and N. Verdonschot. "A Three-Dimensional Dynamic Finite Element Model of the Prosthetic Knee Joint: Simulation of Joint Laxity and Kinematics." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 219, no. 6 (2005): 415–24. http://dx.doi.org/10.1243/095441105x34437.

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For testing purposes of prostheses at a preclinical stage, it is very valuable to have a generic modelling tool, which can be used to optimize implant features and to avoid poor designs being launched on to the market. The modelling tool should be fast, efficient, and multipurpose in nature; a finite element model is well suited to the purpose. The question posed in this study was whether it was possible to develop a mathematically fast and stable dynamic finite element model of a knee joint after total knee arthroplasty that would predict data comparable with published data in terms of (a) laxities and ligament behaviour, and (b) joint kinematics. The soft tissue structures were modelled using a relatively simple, but very stable, composite model consisting of a band reinforced with fibres. Ligament recruitment and balancing was tested with laxity simulations. The tibial and patellar kinematics were simulated during flexion-extension. An implicit mathematical formulation was used. Joint kinematics, joint laxities, and ligament recruitment patterns were predicted realistically. The kinematics were very reproducible and stable during consecutive flexion-extension cycles. Hence, the model is suitable for the evaluation of prosthesis design, prosthesis alignment, ligament behaviour, and surgical parameters with respect to the biomechanical behaviour of the knee.

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Issakhov, Alibek, and Bakytzan Zhumagulov. "Numerical Modelling of the Thermal Process in the Aquatic Environment." Advanced Materials Research 787 (September 2013): 669–74. http://dx.doi.org/10.4028/www.scientific.net/amr.787.669.

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This paper presents the mathematical model of the thermal influence to the aquatic environment of thermal power plant, which is solved by the Navier-Stokes and temperature equations for an incompressible fluid in a stratified medium. Numerical algorithm based on the projection method which solved with fractional step method. Three dimensional Poisson equation solved with Fourier method with combination of tridiagonal matrix method (Thomas algorithm).

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Smith, D. J., E. A. Gaffney, and J. R. Blake. "Mathematical modelling of cilia-driven transport of biological fluids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2108 (2009): 2417–39. http://dx.doi.org/10.1098/rspa.2009.0018.

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Cilia-driven flow occurs in the airway surface liquid, in the female and male reproductive tracts and enables symmetry-breaking in the embryonic node. Viscoelastic rheology is found in healthy states in some systems, whereas in others may characterise disease, motivating the development of mathematical models that take this effect into account. We derive the fundamental solution for linear viscoelastic flow, which is subsequently used as a basis for slender-body theory. Our numerical algorithm allows efficient computation of three-dimensional time-dependent flow, bending moments, power and particle transport. We apply the model to the large-amplitude motion of a single cilium in a linear Maxwell liquid. A relatively short relaxation time of just 0.032 times the beat period significantly reduces forces, bending moments, power and particle transport, the last variable exhibiting exponential decay with relaxation time. A test particle is propelled approximately one-fifth as quickly along the direction of cilia beating for scaled relaxation time 0.032 as in the Newtonian case, and mean volume flow is abolished, emphasizing the sensitivity of cilia function to fluid rheology. These results may have implications for flow in the airways, where the transition from Newtonian to viscoelastic rheology in the peri-ciliary fluid may reduce clearance.

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Разумова, Ганна Вікторівна. "ЗОНУВАННЯ ТРИВИМІРНОЇ МАТРИЦІ УПРАВЛІННЯ ЗМІНАМИ РЕГУЛЯТОРНОЇ ПОЛІТИКИ РОЗВИТКУ НАЦІОНАЛЬНОЇ ЕКОНОМІКИ". Bulletin of the Kyiv National University of Technologies and Design. Series: Economic sciences 135, № 3 (2019): 90–99. http://dx.doi.org/10.30857/2413-0117.2019.3.9.

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The article attempts to work out the relevant methodology that will allow an integrated approach to find solutions to current economic challenges, given the fact that the national economy is a complex multicomponent system. It is emphasized that mathematical methods and models are widely used as effective tools to handle a range of problems in various areas of research and, in particular, in economic studies. However, despite the availability of numerous research endeavors, the issues of modelling the relationships between national economic development and regulatory policy have not been sufficiently studied. The purpose of this study is to build a three-dimensional matrix of regulatory change management in the frameworks of the national economic development. The methodological research background relies on modelling of regulatory policy effects on national economic development by using economic mathematical methods and models. A three-dimensional matrix of managing change in regulatory policy has been proposed which is based on the assessment of the current state of regulatory policy and modelling of the relationships between national economic development and regulatory policy with regard to the obtained values of the aggregate development index calculated by sectors of the national economy, generalized index of the regulatory policy in industries and the indicator of the regulatory policy effects on development, the zoning of which allows to distribute its impact sector by sector along with identifying the nature and the priority areas for further regulatory actions to be applied to a particular industry or sector of the economy. The three-dimensional matrix zoning has been performed according to certain parameters: vertical zoning (zones of passive and active changes), transverse horizontal zoning (zone of fixation and transformation) and horizontal longitudinal zoning (zones adjustment and protection). It is argued that economic mathematical modelling is an important tool in managing business processes. Modelling is used to build reliability models with reference to aggregated development indices by sectors of the national economy and the generalized indices of regulatory policy, and identify specific regulatory policy changes needed to enhance the national economic development.

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Zhang, Zhenjiu, Mingjun Liu, Jiaji Jiang, et al. "Modelling and optimization of a modified sequential multilateration method for three-dimensional coordinate collection." Advances in Mechanical Engineering 11, no. 11 (2019): 168781401988979. http://dx.doi.org/10.1177/1687814019889790.

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This article proposes a modified sequential multilateration method for measuring three-dimensional coordinates. The measuring system consists of a single laser tracker and four relay targets whose relative positions have been pre-calibrated by the multilateration method. The laser tracker is fixed on three prescribed positions successively, and these positions can be calibrated by using the distances between the laser tracker and the four relay targets based on the multilateration principle. Subsequently, the three-dimensional coordinates of each under-test point can be determined by the three laser trackers’ positions based on the trilateration principle. This method is more flexible than previous multilateration methods for three-dimensional coordinate collection, especially if the measurement space is partially covered by other objects. The mathematical model of this method is established. Based on the Monte Carlo method, a series of computer simulations are performed to optimize the system arrangement by investigating the performances of the measuring system with different system arrangement, and an optimal system arrangement is finally obtained. Practical measurement is also conducted to demonstrate the validity of the proposed method by comparing with a reference coordinate measuring machine.

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Gui, Nan, Xingtuan Yang, Jiyuan Tu, and Shengyao Jiang. "An extension of hard-particle model for three-dimensional non-spherical particles: Mathematical formulation and validation." Applied Mathematical Modelling 40, no. 4 (2016): 2485–99. http://dx.doi.org/10.1016/j.apm.2015.09.111.

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Yao, L., J. S. Dai, and H. Li. "Mathematical modelling and manufacturing of the internal toroidal tooth profile." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 218, no. 9 (2004): 1043–51. http://dx.doi.org/10.1243/0954406041991224.

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This paper investigates the toroidal tooth profile of an epicyclic gear train based on the analysis of the integrated motion from both sun-worm and planet worm-gears and develops a mathematical model based on the coordinate transformation between the coordinate system of the stationary internal gear and that of the planet worm-gear. The model is derived from the geometrical analysis of the meshing system and is used to model the meshing surface which is produced as a result from the enveloping surface. This is further extended to model the internal toroidal tooth profile in the stationary gear, the normal tooth profile and the helix trajectory. Based on these models, the shape of normal tooth section of the stationary toroidal tooth profile is obtained and the three-dimensional modelling of this tooth profile is completed. The paper further examines the case of manufacturing by developing a fly-blade for the machining process and develops a manufacturing procedure which successfully produced a stationary internal toroidal tooth profile manufactured by a fly-blade on a hob machine.

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Ren, Lei, David Howard, and Richard K. Jones. "Mathematical Modelling of Biomechanical Interactions between Backpack and Bearer during Load Carriage." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/349638.

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This paper proposes a three-dimensional mathematical model of the biomechanical interactions between backpack and bearer during load carriage. The model considers both the coupled pack motions, which follow the torso, and also the longitudinal compliance and damping in the backpack suspension. The pack interaction forces and moments, acting on the bearer, are determined from kinematic relationships, equations of motion, and a dynamic pack suspension model. The parameters of the pack suspension model were identified from test data obtained using a load carriage test rig. Output from the load carriage mathematical model has been compared with measurement data during human gait and conclusions drawn with regard to the validity of the proposed approach.

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Xiang, Jin Zong, Yin Zhang, Wen Jun Fan, and You Duo He. "Numerical Modelling of Shape Evolution of Tubular Preform in Spray Forming Process." Advanced Materials Research 189-193 (February 2011): 2426–33. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.2426.

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A three-dimensional mathematical model of growth, integrated with a new and effective algorithm for visibility checking, has been established based on a spray forming equipment with three different fixed atomizers in this paper. The model was used to predict the geometrical shape and the thickness profiles of the tubular deposit under various situations. By investigating and discussing the effects of different mandrel movement parameters and spray heights, the optimal atomizer of the equipment to fabricate a tubular preform was identified numerically.

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Good, Stephen P., I. Rodriguez-Iturbe, and K. K. Caylor. "Analytical expressions of variability in ecosystem structure and function obtained from three-dimensional stochastic vegetation modelling." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2155 (2013): 20130003. http://dx.doi.org/10.1098/rspa.2013.0003.

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Whole ecosystem exchange of water, carbon and energy is predominately determined by complex leaf-level processes occurring at individual plants. Interaction between individuals results in a distribution of environmental conditions that drive a variety of nonlinear response functions such as transpiration and photosynthesis. The nonlinearity of biophysical processes requires higher-order statistical descriptions of micro-environment distributions in order to accurately determine the landscape-scale mean functional response. We present a mathematical framework for describing vegetation structure based on the density, dispersion, size distribution and allometry of individuals within a landscape. Using three-dimensional stochastic vegetation modelling, we develop analytic expressions of the second-order statistics of vegetation canopies, namely the mean and variance of leaf area density and leaf area index with height. These expressions also allow for the approximation of the distribution of beam penetration and sunfleck statistics through the canopy as a function of height. Finally, we demonstrate how landscape-scale fluxes are strongly affected by the variability in canopy micro-environments, and how stochastic vegetation modelling improves flux estimates relative to traditional homogeneous canopy models.

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Kempthorne, Daryl M., Ian W. Turner, John A. Belward, et al. "Surface reconstruction of wheat leaf morphology from three-dimensional scanned data." Functional Plant Biology 42, no. 5 (2015): 444. http://dx.doi.org/10.1071/fp14058.

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Realistic virtual models of leaf surfaces are important for several applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be smooth enough to facilitate the use of the mathematical equations that govern the motion of the droplet. Although an effective approach is to apply discrete smoothing D2-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat (Triticum aestivum L.) leaves, which tend to twist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D2-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D2-spline techniques, produces realistic virtual representations of wheat leaves.

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Journal articles on the topic 'Three-dimensional mathematical modelling'

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