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Journal articles on the topic 'Geometry Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Сальков and Nikolay Sal'kov. "Geometric Simulation and Descriptive Geometry." Geometry & Graphics 4, no. 4 (2016): 31–40. http://dx.doi.org/10.12737/22841.

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Geometric simulation is creation of a geometric model, whose properties and characteristics in a varying degree determine the subject of investigation’s properties and characteristics. The geometric model is a special case of the mathematical model. The feature of the geometric model is that it will always be a geometric figure, and therefore, by its very nature, is visual. If the mathematical model is a set of equations, which says little to an ordinary engineer, the geometric model as representation of the mathematical model and as the geometric figure itself, enables to &#34;see&#34; this set. Any geometric model can be represented graphically. Graphical model of an object is a mapping of its geometric model onto a plane (or other surface). Therefore, the graphical model can be considered as a special case of the geometric model. Graphical models are very various – these are graphics, and graphical structures of immense complexity, reflecting spatial geometric figures. These are drawings of geometric figures, simulating processes of all kinds. The simulation goes on as follows. According to known geometric and differential criteria the geometric model is executed. Then a mathematical model is composed based on the geometric model, finally a computer program is compiled on the mathematical model. As a result of consideration in this paper the process of obtaining the geometric models of surface and linear forms for auto-roads it is possible to make a following conclusion. For geometric simulation and the consequent mathematical one the descriptive geometry involvement is vital. Just the descriptive geometry is used both on the initial and final stages of design.

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Isaev, Alexander, Ramil Khamzin, Artem Ershov, and Marco Leonesio. "Mathematical Models of the Geometry of Micro Milling Cutters." EPJ Web of Conferences 248 (2021): 04003. http://dx.doi.org/10.1051/epjconf/202124804003.

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Micromachining is an up-to-date technology widely used in different advanced areas like electronics, aerospace and medical industries. For manufacturing components with highest precision and lowest surface roughness, small-sized end mills with working diameter of less than 1 mm are often used. In this paper, in order to determine the functional relationships between structural strength, cutting properties and geometry of small-sized cutting tools, the mathematical models of working part of micro milling cutters were derived.

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3

Meng, Qingen, John Fisher, and Ruth Wilcox. "The effects of geometric uncertainties on computational modelling of knee biomechanics." Royal Society Open Science 4, no. 8 (2017): 170670. http://dx.doi.org/10.1098/rsos.170670.

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The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models.

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Dufresne, Emilie, Heather A. Harrington, and Dhruva V. Raman. "The geometry of Sloppiness." Journal of Algebraic Statistics 9, no. 1 (2018): 30–68. http://dx.doi.org/10.18409/jas.v9i1.64.

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The use of mathematical models in the sciences often requires the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical foundation for sloppiness and define rigorously its key concepts, such as `model manifold', in relation to concepts of structural identifiability. We redefine sloppiness conceptually as a comparison between the premetric on parameter space induced by measurement noise and a reference metric. This opens up the possibility of alternative quantification of sloppiness, beyond the standard use of the Fisher Information Matrix, which assumes that parameter space is equipped with the usual Euclidean and the measurement error is infinitesimal. Applications include parametric statistical models, explicit time dependent models, and ordinary differential equation models.

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Umulis, David M., and Hans G. Othmer. "The importance of geometry in mathematical models of developing systems." Current Opinion in Genetics & Development 22, no. 6 (2012): 547–52. http://dx.doi.org/10.1016/j.gde.2012.09.007.

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6

Ståhle, Lars. "On mathematical models of microdialysis: geometry, steady-state models, recovery and probe radius." Advanced Drug Delivery Reviews 45, no. 2-3 (2000): 149–67. http://dx.doi.org/10.1016/s0169-409x(00)00108-3.

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7

Келдибекова, Аида, Aida Keldibekova, Н. Селиванова, and N. Selivanova. "The Role and the Place of Geometry in the System of Mathematical School Olympiads." Scientific Research and Development. Socio-Humanitarian Research and Technology 8, no. 2 (2019): 72–76. http://dx.doi.org/10.12737/article_5cf5188ea59b11.06698992.

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The purpose of this article is to determine the role and place of school geometry in the subject olympiad system. For this, the authors turn to the experience of Russia in organizing and conducting geometric olympiads for schoolchildren, exploring the specifics of the olympiads named after named I.F. Sharygin, named S.A. Anischenko, named A.P. Savina, Moscow and Iran olympiads. The objectives and themes of full-time, extramural, oral geometric olympiads are defined. It is revealed that the topics of topology, projective, affine, combinatorial sections of geometry constitute the content of olympiad geometry. The study showed that the tasks of the olympiad work on geometry checked mathematical skills to perform actions with geometric figures, coordinates and vectors; build and explore simple mathematical models; apply acquired knowledge and skills in practical activities. The conclusions are made about the need to include tasks of geometric content in the block of olympiad tasks for the development of spatial thinking of schoolchildren.

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8

Vorontsova, Valeriya Leonidovna, Alfiya Gizzetdinovna Bagoutdinova, and Almaz Fernandovich Gilemzianov. "Mathematical Models of the Ocurved Spring Tubes Surfaces." Journal of Computational and Theoretical Nanoscience 16, no. 11 (2019): 4554–59. http://dx.doi.org/10.1166/jctn.2019.8353.

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One of the ways to intensify heat exchange processes is the creation of compact heat exchangers with a developed heat exchange surface. It is known that coil-type channels provide a developed heat exchange surface and belong to one of the most efficient and technological designs of heat exchange elements. In this regard, the authors proposed a small-size heat exchanger of the “pipe in pipe” type with an internal coil spring-twisted channel, and the authors of the proposed article developed mathematical models describing the heat-exchange surfaces of pipes of complex configurations, including coil spring-coiled channels. The equations of heat transfer surfaces are written in vector-parametric form based on the fundamental principles of analytical and differential geometry. In order to verify the adequacy and visualization of the written equations, surfaces were constructed using the Matlab application software package. The proposed mathematical models can be used in computer simulation of hydrodynamic processes during the flow of liquid media in curved channels, which will allow to explore and further optimize their internal geometry by changing the parameters of the equations. This work is a continuation of research on the creation of efficient heat exchangers.

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9

Mao, Jian, and Man Zhao. "Mathematical Model for Assembly Tolerance Consistence Evaluation." Applied Mechanics and Materials 401-403 (September 2013): 1610–13. http://dx.doi.org/10.4028/www.scientific.net/amm.401-403.1610.

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An assembly is described by a geometric model of its parts and their relative placement. Assembly tolerances are the result of parts of varying shape and size being put together to make the finished product. This paper considers the case where parts have tolerance geometry. Its main contribution is to use a tensor space to describe assembly features. The mathematical models are developed. The proposed approach is based on assembly feasibility analysis of shaft and hole features.

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10

Aberšek, Boris, and Jože Flašker. "Review of Experimental Models for Confirmation of Mathematical Models of Gears." Key Engineering Materials 385-387 (July 2008): 345–48. http://dx.doi.org/10.4028/www.scientific.net/kem.385-387.345.

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In order to calculate the service life as precisely and reliably as possible we need good mathematical models for describing loading, geometry, properties of materials and fracture mechanics parameters. It can be established whether a mathematical model is precise and reliable only by comparison of results of the method such as analytical methods in case of simple problems and experiment when real complex structure are deal with. Since gears and gearing belong to the second group, by correctly selected and developed test pieces and carefully planned experiments we obtained results with which we confirmed and justified the mathematical model for calculating mentioned parameters. To this end we will show in this paper series of experimental methods and test pieces used on the gears.

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11

Marotta, Vincenzo Emilio, and Richard J. Szabo. "Born sigma-models for para-Hermitian manifolds and generalized T-duality." Reviews in Mathematical Physics 33, no. 09 (2021): 2150031. http://dx.doi.org/10.1142/s0129055x21500318.

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We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely defines a worldsheet sigma-model with a para-Hermitian target space, and we describe its Lie algebroid gauging as a means of recovering the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold. Applying the Kotov–Strobl gauging leads to a generalized notion of T-duality when combined with transformations that act on Born geometries. We obtain a geometric interpretation of the self-duality constraint that halves the degrees of freedom in doubled sigma-models, and we give geometric characterizations of non-geometric string backgrounds in this setting. We illustrate our formalism with detailed worldsheet descriptions of closed string phase spaces, of doubled groups where our notion of generalized T-duality includes non-abelian T-duality, and of doubled nilmanifolds.

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12

Datta, Sambit, and David Beynon. "A Computational Approach to the Reconstruction of Surface Geometry from Early Temple Superstructures." International Journal of Architectural Computing 3, no. 4 (2005): 471–86. http://dx.doi.org/10.1260/147807705777781068.

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Recovering the control or implicit geometry underlying temple architecture requires bringing together fragments of evidence from field measurements, relating these to mathematical and geometric descriptions in canonical texts and proposing “best-fit” constructive models. While scholars in the field have traditionally used manual methods, the innovative application of niche computational techniques can help extend the study of artefact geometry. This paper demonstrates the application of a hybrid computational approach to the problem of recovering the surface geometry of early temple superstructures. The approach combines field measurements of temples, close-range architectural photogrammetry, rule-based generation and parametric modelling. The computing of surface geometry comprises a rule-based global model governing the overall form of the superstructure, several local models for individual motifs using photogrammetry and an intermediate geometry model that combines the two. To explain the technique and the different models, the paper examines an illustrative example of surface geometry reconstruction based on studies undertaken on a tenth century stone superstructure from western India. The example demonstrates that a combination of computational methods yields sophisticated models of the constructive geometry underlying temple form and that these digital artefacts can form the basis for in depth comparative analysis of temples, arising out of similar techniques, spread over geography, culture and time.

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13

Burger, William F. "One Point of View: An Active Approach to Geometry." Arithmetic Teacher 36, no. 3 (1988): 2. http://dx.doi.org/10.5951/at.36.3.0002.

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Every contemporary K–12 mathematics curriculum must contain a substantial amount of geometry. Geometry organizes and clarifies our visual experiences and provides visual models of mathematical concepts. Applications of geometry are ubiquitous—we encounter them daily. Thus, every student needs to study geometry. This idea is noncontroversial.

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14

Brody, Dorje C., and Adam Ritz. "Information geometry of finite Ising models." Journal of Geometry and Physics 47, no. 2-3 (2003): 207–20. http://dx.doi.org/10.1016/s0393-0440(02)00190-0.

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15

Ketov, S. V., K. E. Osetrin, and Ya S. Prager. "Geometry of dual two-dimensional nonlinear ? models." Theoretical and Mathematical Physics 84, no. 2 (1990): 794–99. http://dx.doi.org/10.1007/bf01017676.

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16

Legrice, I. J., P. J. Hunter, and B. H. Smaill. "Laminar structure of the heart: a mathematical model." American Journal of Physiology-Heart and Circulatory Physiology 272, no. 5 (1997): H2466—H2476. http://dx.doi.org/10.1152/ajpheart.1997.272.5.h2466.

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A mathematical description of cardiac anatomy is presented for use with finite element models of the electrical activation and mechanical function of the heart. The geometry of the heart is given in terms of prolate spheroidal coordinates defined at the nodes of a finite element mesh and interpolated within elements by a combination of linear Lagrange and cubic Hermite basis functions. Cardiac microstructure is assumed to have three axes of symmetry: one aligned with the muscle fiber orientation (the fiber axis); a second set orthogonal to the fiber direction and lying in the newly identified myocardial sheet plane (the sheet axis); and a third set orthogonal to the first two, in the sheet-normal direction. The geometry, fiber-axis direction, and sheet-axis direction of a dog heart are fitted with parameters defined at the nodes of the finite element mesh. The fiber and sheet orientation parameters are defined with respect to the ventricular geometry such that 1) they can be applied to any heart of known dimensions, and 2) they can be used for the same heart at various states of deformation, as is needed, for example, in continuum models of ventricular contraction.

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17

Fontanari, José F., and Peter F. Stadler. "Fractal geometry of spin-glass models." Journal of Physics A: Mathematical and General 35, no. 7 (2002): 1509–16. http://dx.doi.org/10.1088/0305-4470/35/7/303.

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18

McClintock, Ruth. "Animating Geometry with Flexigons." Mathematics Teacher 87, no. 8 (1994): 602–6. http://dx.doi.org/10.5951/mt.87.8.0602.

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Viewing mathematics as communication is the second standard listed for all grade levels in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This emphasis underscores the need for nurturing language skills that enable children to translate nonverbal awareness into words. One way to initiate discussion about mathematical concepts is to use physical models and manipulatives. Standard 4 of the Professional Standards for Teaching Mathematics (NCTM 1991) addresses the need for tools to enhance discourse. The flexigon is a simple and inexpensive conversation piece that helps students make geometric discoveries and find language to share their ideas.

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19

Erickson, Timothy E. "Connecting Data and Geometry." Mathematics Teacher 94, no. 8 (2001): 710–14. http://dx.doi.org/10.5951/mt.94.8.0710.

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Geometrical ideas and representations often help us understand other areas of mathematics. For example, we might use area models for multiplying polynomials, for summing series, or for conditional probability calculations. But we can also use other areas of mathematics to help us understand a geometrical situation. This article describes an activity that was adapted from Erickson (2000, pp. 111–13), in which students use data analysis and mathematical modeling to obtain insight into a geometrical question. This activity explores a simple case of what is called the isoperimetric inequality. A Web search for that term can furnish additional information.

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20

Kozubková, M., J. Krutil, and V. Nevrlý. "Experiments and mathematical models of methane flames and explosions in a complex geometry." Combustion, Explosion, and Shock Waves 50, no. 4 (2014): 374–80. http://dx.doi.org/10.1134/s0010508214040029.

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21

Pacyga, Robert. "Implementing the Curriculum and Evaluation Standards: Making Connections by Using Molecular Models in Geometry." Mathematics Teacher 87, no. 1 (1994): 43–47. http://dx.doi.org/10.5951/mt.87.1.0043.

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As instructors of mathematics, we need to demonstrate to our students the use and value of connections between mathematics and other disciplines. The authors of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) state that the mathematics curriculum should include investigations of the connections and interplay among various mathematical topics and their applications so that all students can apply mathematical thinking and modeling to solve problems that arise in other disciplines.

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22

BERGLUND, PER, BRIAN GREENE, and TRISTAN HÜBSCH. "CLASSICAL VS. LANDAU-GINZBURG GEOMETRY OF COMPACTIFICATION." Modern Physics Letters A 07, no. 20 (1992): 1855–69. http://dx.doi.org/10.1142/s0217732392001567.

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We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth) Calabi-Yau examples in which there are obstructions to parametrizing all of the complex structure cohomology by polynomial deformations thus requiring the analysis based on exact and spectral sequences. General arguments ensure that the Landau-Ginzburg chiral ring copes with such a situation by having a non-trivial contribution from twisted sectors. Beyond the expected final agreement between the mathematical and physical approaches, we find a direct correspondence between the analysis of each, thus giving a more complete mathematical understanding of twisted sectors. Furthermore, this approach shows that physical reasoning based upon spectral flow arguments for determining the spectrum of Landau-Ginzburg orbifold models finds direct mathematical justification in Koszul complex calculations and also that careful point-field analysis continues to recover surprisingly much of the stringy features.

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23

Santaella, Beatriz L., and Z. Jack Tseng. "Hole in One: an element reduction approach to modeling bone porosity in finite element analysis." PeerJ 7 (December 19, 2019): e8112. http://dx.doi.org/10.7717/peerj.8112.

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Finite element analysis has been an increasingly widely applied biomechanical modeling method in many different science and engineering fields over the last decade. In the biological sciences, there are many examples of FEA in areas such as paleontology and functional morphology. Despite this common use, the modeling of trabecular bone remains a key issue because their highly complex and porous geometries are difficult to replicate in the solid mesh format required for many simulations. A common practice is to assign uniform model material properties to whole or portions of models that represent trabecular bone. In this study we aimed to demonstrate that a physical, element reduction approach constitutes a valid protocol for addressing this problem in addition to the wholesale mathematical approach. We tested a customized script for element reduction modeling on five exemplar trabecular geometry models of carnivoran temporomandibular joints, and compared stress and strain energy results of both physical and mathematical trabecular modeling to models incorporating actual trabecular geometry. Simulation results indicate that that the physical, element reduction approach generally outperformed the mathematical approach: physical changes in the internal structure of experimental cylindrical models had a major influence on the recorded stress values throughout the model, and more closely approximates values obtained in models containing actual trabecular geometry than solid models with modified trabecular material properties. In models with both physical and mathematical adjustments for bone porosity, the physical changes exhibit more weight than material properties changes in approximating values of control models. Therefore, we conclude that maintaining or mimicking the internal porosity of a trabecular structure is a more effective method of approximating trabecular bone behavior in finite element models than modifying material properties.

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24

Marshakov, A. V. "Matrix models, complex geometry, and integrable systems: I." Theoretical and Mathematical Physics 147, no. 2 (2006): 583–636. http://dx.doi.org/10.1007/s11232-006-0065-x.

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Marshakov, A. V. "Matrix models, complex geometry, and integrable systems: II." Theoretical and Mathematical Physics 147, no. 3 (2006): 777–820. http://dx.doi.org/10.1007/s11232-006-0077-6.

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26

Chotěborský, R., M. Navrátilová, and P. Hrabě. "Effects of MIG process parameters on the geometry and dilution of the bead in the automatic surfacing." Research in Agricultural Engineering 57, No. 2 (2011): 56–62. http://dx.doi.org/10.17221/19/2010-rae.

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Automatic weld surfacing is being employed increasingly in the process, mining and power industries. Gas metal arc welding has become a natural choice for automatic surfacing due to its important properties. These include: high reliability, all positions capabilities, ease of use, low cost and high productivity. With increasing use of gas metal arc welding in its automatic mode, the use of mathematical models to predict the dimensions of the weld bead has become necessary. The development of such mathematical equations using a four factor central factorial technique to predict the geometry of the weld bead in the deposition of OK Tubrodur 15.43 electrode onto structural steel S235JR is discussed. The models developed have been checked for their adequacy and significance by using the F test and the Student&rsquo;s t test, respectively

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27

Alekseevsky, D., A. Medvedev, and J. Slovak. "Constant curvature models in sub-Riemannian geometry." Journal of Geometry and Physics 138 (April 2019): 241–56. http://dx.doi.org/10.1016/j.geomphys.2018.09.013.

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28

Chamseddine, Ali H. "Quanta of geometry and unification." Modern Physics Letters A 31, no. 40 (2016): 1630046. http://dx.doi.org/10.1142/s0217732316300469.

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This is a tribute to Abdus Salam’s memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati–Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

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Liu, Lei, Jingwen Tan, and Meijuan Fang. "Geometry and contact characteristics of torus involute gears." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 231, no. 2 (2016): 250–70. http://dx.doi.org/10.1177/0954408915591718.

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Aimed at overcoming high sensitivity to machining or mounting error of line-contact conjugate surfaces, a novel torus involute gear drive is proposed which can compensate large axial misalignments and possess good meshing characteristics without lead correction. The torus involute gear is essentially a special spur gear with continuous shifting in the second order. Based on the processing principle of the torus involute gears, their mathematical models are established according to the corresponding imaginary rack cutter. In order to provide the approach to choose proper designing parameters, geometry characteristics of the torus involute gear are investigated: condition equations of tooth undercutting for a convex torus involute gear and tooth pointing for a concave torus involute gear are formulated utilizing the developed mathematical models, and the approach to checking tooth flank interference is provided. Contact characteristics of the gear set is studied through tooth contact analysis and finite element analysis. The simulated results produce useful information about tooth contact pattern, stress distribution, and transmission errors of the gear set.

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Bormotin, Konstantin, and Win Aung. "Computation method of geometry die of stretch forming press." MATEC Web of Conferences 224 (2018): 04014. http://dx.doi.org/10.1051/matecconf/201822404014.

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Mathematical models and numerical methods for solving inverse problems of shell forming by means of stretching on a die have been developed. The algorithms implemented in MSC.Marc allow to calculate the required punch shape. The results of simulation of the stretching technology are presented.

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Mark, D. M., and A. U. Frank. "Experiential and Formal Models of Geographic Space." Environment and Planning B: Planning and Design 23, no. 1 (1996): 3–24. http://dx.doi.org/10.1068/b230003.

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In this paper human experience and perception of phenomena and relations in space are studied. This focus is in contrast to previous work where space and spatial relations were examined as objective phenomena of the world. This study leads in turn to a goal: to identify models of space that can be used both in cognitive science and in the design and implementation of geographic information systems (GISs). Experiential models of the world are based on sensorimotor and visual experiences with environments, and form in individual minds, as the associated bodies and senses experience their worlds. Formal models consist of axioms expressed in a formal language, together with mathematical rules to infer conclusions from these axioms. In this paper we will review both types of models, considering each to be an abstraction of the same ‘real world’. The review of experiential models is based primarily on recent developments in cognitive science, expounded by Rosch, Johnson, Talmy, and especially Lakoff. In these models it is suggested that perception and cognition are driven by image-schemata and other mental models, often language-based. Cross-cultural variations are admitted and even emphasized. The ways in which people interact with small-scale (‘tabletop’) spaces filled with everyday objects are in sharp contrast to the ways in which they experience geographic (large-scale) spaces during wayfinding and other spatial activities. We then address the issue of the ‘objective’ geometry of geographic space. If objectivity is defined by measurement, this leads to a surveyor's view and a near-Euclidean geometry. These models are then related to issues in the design of GISs. To be implemented on digital computers, geometric concepts and models must be formalized. The idea of a formal geometry of natural language is discussed and some aspects of it are presented. Formalizing the links between cognitive categories and models on the one hand and between geometry and computer representations on the other are key elements in the research agenda.

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Ravikumar, S. M., and P. Vijian. "Development of Mathematical Models for Prediction of Weld Bead Geometry of GTAW Stainless Steel." Applied Mechanics and Materials 867 (July 2017): 88–96. http://dx.doi.org/10.4028/www.scientific.net/amm.867.88.

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Welding input process parameters are playing a very significant role in determining the weld bead quality. The quality of the joint can be defined in terms of properties such as weld bead geometry, mechanical properties and distortion. Experiments were conducted to develop models, using a three factor, five level factorial design for 304 stainless steel as base plate with ER 308L filler wire of 1.6 mm diameter. The purpose of this study is to develop the mathematical model and compare the observed output values with predicted output values. Welding current, welding speed and nozzle to plate distance were chosen as input parameters, while depth of penetration, weld bead width, reinforcement and dilution as output parameters. The models developed have been checked for their adequacy. Confirmation experiments were also conducted and the results show that the models developed can predict the bead geometries and dilution with reasonable accuracy. The direct and interaction effect of the process parameters on bead geometry are presented in graphical form.

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Després, Bruno, and Rémy Sart. "Navier–Stokes Hierarchies of Reduced MHD Models in Tokamak Geometry." Journal of Mathematical Fluid Mechanics 20, no. 2 (2017): 329–57. http://dx.doi.org/10.1007/s00021-017-0323-8.

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Jiten, Baro. "Mathematical analysis on anisotropic Bianchi Type-III inflationary string Cosmological models in Lyra geometry." Indian Journal of Science and Technology 14, no. 1 (2021): 46–54. http://dx.doi.org/10.17485/ijst/v14i1.1705.

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Khrennikov, Andrei. "Bell Could Become the Copernicus of Probability." Open Systems & Information Dynamics 23, no. 02 (2016): 1650008. http://dx.doi.org/10.1142/s1230161216500086.

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Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.

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Mohan, B. M., and Arpita Sinha. "The simplest fuzzy PID controllers: mathematical models and stability analysis." Soft Computing 10, no. 10 (2005): 961–75. http://dx.doi.org/10.1007/s00500-005-0023-9.

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Groh, C. M., M. E. Hubbard, P. F. Jones, et al. "Mathematical and computational models of drug transport in tumours." Journal of The Royal Society Interface 11, no. 94 (2014): 20131173. http://dx.doi.org/10.1098/rsif.2013.1173.

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The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a ‘tumour cord’ geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are ‘pharmacokinetically resistant’ to chemotherapeutic strategies.

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38

GROTHAUS, MARTIN, and PATRIK STILGENBAUER. "GEOMETRIC LANGEVIN EQUATIONS ON SUBMANIFOLDS AND APPLICATIONS TO THE STOCHASTIC MELT-SPINNING PROCESS OF NONWOVENS AND BIOLOGY." Stochastics and Dynamics 13, no. 04 (2013): 1350001. http://dx.doi.org/10.1142/s0219493713500019.

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In this paper we develop geometric versions of the classical Langevin equation on regular submanifolds in Euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Lelièvre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant Euclidean norm. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jørgensen or Kolokoltsov. All our studies are strongly motivated by industrial applications in modeling the fiber lay-down dynamics in the production process of nonwovens. We light up the geometry occurring in these models and show up the connection with the spherical velocity version of the geometric Langevin process. Moreover, as a main point, we construct new smooth industrial relevant three-dimensional fiber lay-down models involving the spherical Langevin process. Finally, relations to a class of swarming models are presented and further applications of the geometric Langevin equations are given.

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Kováčová, Monika, Miloš Matúš, Peter Križan, and Juraj Beniak. "DESIGN THEORY FOR THE PRESSING CHAMBER IN THE SOLID BIOFUEL PRODUCTION PROCESS." Acta Polytechnica 54, no. 1 (2014): 28–34. http://dx.doi.org/10.14311/ap.2014.54.0028.

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The quality of a high-grade solid biofuel depends on many factors, which can be divided into three main groups - material, technological and structural. The main focus of this paper is on observing the influence of structural parameters in the biomass densification process. The main goal is to model various options for the geometry of the pressing chamber and the influence of these structural parameters on the quality of the briquettes. We will provide a mathematical description of the whole physical process of densifying a particular material and extruding it through a cylindrical chamber and through a conical chamber. We have used basic mathematical models to represent the pressure process based on the geometry of the chamber. In this paper we try to find the optimized parameters for the geometry of the chamber in order to achieve high briquette quality with minimal energy input. All these mathematical models allow us to optimize the energy input of the process, to control the final quality of the briquettes and to reduce wear to the chamber. The practical results show that reducing the diameter and the length of the chamber, and the angle of the cone, has a strong influence on the compaction process and, consequently, on the quality of the briquettes. The geometric shape of the chamber also has significant influence on its wear. We will try to offer a more precise explanation of the connections between structural parameters, geometrical shapes and the pressing process. The theory described here can help us to understand the whole process and influence every structural parameter in it.

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Cahtarevic, Rada, and Adna Proho. "Geometric modeling and complexity - a conceptual approach in architectural design and education." Spatium, no. 42 (2019): 35–40. http://dx.doi.org/10.2298/spat1942035c.

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By encompassing abstraction and patterned information, the new fields of geometry and mathematical models of complex dynamic spatial systems provide a new method for spatial modeling. Different approaches to the application of spatial modeling in architectural design are possible, taking into consideration on the one hand the theoretical background and knowledge of geometry, and on the other, advanced computational techniques. The generative principles of complex dynamic spatial formation allow parallels between the differentiated representations and directions of approach to spatial organization. The integration of conceptual, theoretical and practical methods into complex dynamic geometric models in the preliminary phase of design could support the development of cognitive capabilities, internal representations and understanding of complex dynamic formative processes. The development of nonlinear, dynamic, complex spatial imaginative thinking corresponds with trends in contemporary computational design. The application of complex geometric modeling, including sophisticated mechanisms of human perception, intelligence and creativity, provides a synthesis of artificial and human potential.

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Zhao, Hanxin, and Kornel F. Ehmann. "Topology of Spade Drills for Wood Drilling Operations, Part 1: Spade Drill Point Geometry Definition." Journal of Manufacturing Science and Engineering 127, no. 2 (2005): 298–309. http://dx.doi.org/10.1115/1.1794160.

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Spade bits, widely and routinely used in the construction industry, have not received any attention in the technical literature, yet there is a pressing need to improve the performance of these bits whose basic design has not changed for decades. To facilitate such improvements, a thorough understanding of the geometric, manufacturing, and cutting mechanics aspects of these tools is necessary. In this two-part paper, the point geometry and manufacturing issues will be discussed. To fundamentally understand the spade drill bit’s behavior, a complete mathematical model of its principal topological elements will be established. In conjunction with this model, the corresponding analytical formulations of the geometry and kinematics of the appropriate manufacturing procedures will also be formulated. In unison, these models will lay the foundation for a methodology and a software package for a detailed geometric analysis of all relevant cutting angle distributions and edge profiles of the spade bit. This will facilitate, at a later point, new point developments rooted in rigorous analytical models.

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Calderale, P. M., and G. Scelfo. "A Mathematical Model of the Locomotor Apparatus." Engineering in Medicine 16, no. 3 (1987): 147–61. http://dx.doi.org/10.1243/emed_jour_1987_016_033_02.

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This study presents a mathematical model for the musculo-skeletal system of the locomotor apparatus. Muscle forces and joint reactions are calculated for the static problem of leaning and squatting and for the dynamic problem of walking on a level surface. Muscle forces thus calculated are compared with electromyographic (EMG) patterns. The model follows previous statically indeterminate mathematical models, from which it differs chiefly in introducing intermediate constraints (in addition to the points of insertion) for the muscles, and in setting bounds on muscle tensile stress depending on system geometry, kinematics, and loading.

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Freiria Pereira, Jorge. "Dynamic modeling of trawl fishing gear components." Ciencia y tecnología de buques 6, no. 11 (2012): 57. http://dx.doi.org/10.25043/19098642.71.

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A numerical model has been developed to calculate the resistance of the different components of a trawling gear, by deduction of the drag and lift components. For this purpose, mathematical models have been considered for all the elements, such as trawl cables, floats, doors, and the net itself. The most important contribution of this numerical model is that the action of forces upon different elements permits modifying the geometric configuration of the complete set with a mutual accommodation of resistance and geometry, simulating the actual dynamics, where forces and geometry converge toward an equilibrium state. Some results obtained from actual fishing gear with data obtained from sensors during sea trials are used to compare the results of the simulator.

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CEMBRANOS, J. A. R., A. DOBADO, and A. L. MAROTO. "DARK GEOMETRY." International Journal of Modern Physics D 13, no. 10 (2004): 2275–79. http://dx.doi.org/10.1142/s0218271804006322.

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Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space–time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.

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Chekhov, L. "Matrix models with hard walls: geometry and solutions." Journal of Physics A: Mathematical and General 39, no. 28 (2006): 8857–93. http://dx.doi.org/10.1088/0305-4470/39/28/s06.

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Khramov, B. A., and A. V. Gusev. "Investigation of dynamic characteristics of three-linear flow regulator." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 1 (March 30, 2019): 91–97. http://dx.doi.org/10.38013/2542-0542-2019-1-91-97.

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The study focuses on the dynamic model of the three-linear spool flow regulator for various solutions of the spool geometry, and for two variants of mathematical description of hydraulic damping devices. The paper describes the process of small deflection linearization of the obtained mathematical models. As a result of Laplace transformation of the mathematical models, we obtained a block diagram of the spool flow regulator operation. By using Nyquist criterion, we analyzed the spool flow regulator stability. As a result, we draw conclusions on the spool flow regulator stability, and on the various types of damping devices affecting it

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Yang, Tao, Jun Xiong, Hui Chen, and Yong Chen. "Modeling of weld bead geometry for rapid manufacturing by robotic GMAW." International Journal of Modern Physics B 29, no. 10n11 (2015): 1540033. http://dx.doi.org/10.1142/s0217979215400330.

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Weld-based rapid prototyping (RP) has shown great promises for fabricating 3D complex parts. During the layered deposition of forming metallic parts with robotic gas metal arc welding, the geometry of a single weld bead has an important influence on surface finish quality, layer thickness and dimensional accuracy of the deposited layer. In order to obtain accurate, predictable and controllable bead geometry, it is essential to understand the relationships between the process variables with the bead geometry (bead width, bead height and ratio of bead width to bead height). This paper highlights an experimental study carried out to develop mathematical models to predict deposited bead geometry through the quadratic general rotary unitized design. The adequacy and significance of the models were verified via the analysis of variance. Complicated cause–effect relationships between the process parameters and the bead geometry were revealed. Results show that the developed models can be applied to predict the desired bead geometry with great accuracy in layered deposition with accordance to the slicing process of RP.

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Chekalin, V. F., and S. L. Korneev. "The analysis of principles constructions of space images geometry and mathematical models of its processing." Geodesy and Cartography 928, no. 10 (2017): 30–39. http://dx.doi.org/10.22389/0016-7126-2017-928-10-30-39.

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In this article essential principles of constructing geometry of contemporary space images with the purpose of definitions their common regularity and distinctions of generations’ inner photogrammetric relations and then – mathematical models, expedients for securing of strict processing are considered. It is significant, that scanning survey is the general case/way, but strip and panoramic surveys are particular cases. For the first time it was established, that under solving the problem of photogrammetric resection for scanner images on the basis of using dependences of well-known collinearity models the ambiguity of external orientation of images arises. The basic reason of its arising is discovered and established, by way of which it is determined poor domain the systems of initial equations’ corrections. A rigorous model of a push broom space image is introduced, which incorporates both a static a photogrammetric model and a dynamic one. The static model gives the only mean position and orientation of image, meanwhile the dynamic one makes them more exact. The table of condition numbers (cond A) of initial equations’ correction linear system is given and it confirms the fundamental idea of this article. A practical way of solving this problem is indicated for cases of using source data, both outboard measurements and control points.

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Murugan, N. "Mathematical Models for Prediction of Dilution and Bead Geometry in Single Wire Submerged Arc Surfacing." Indian Welding Journal 27, no. 3 (1994): 22. http://dx.doi.org/10.22486/iwj.v27i3.148244.

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Wang, Wen Jin, Zhi Qiang Zhang, Jing Zhang, Jian Zhao, Ling Li Zhang, and Tai Yong Wang. "Computerized Modeling and CNC Machining Simulation of Spiral Bevel Gear." Advanced Materials Research 482-484 (February 2012): 1081–84. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.1081.

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Based on the theory of gearing and differential geometry, a CNC hypoid generator mathematical model for spiral bevel has been developed. A mathematical model of a spiral bevel gear-tooth surface based on the CNC Gleason hypoid gear generator mechanism is proposed in the paper. The simulation of the spiral bevel gear is presented according to the developed machining mathematical model. A numerical example is provided to illustrate the implementation of the developed mathematic models.

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