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Journal articles on the topic 'Chemistry, Physical and theoretical – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Ah. "Theoretical and computational models for organic chemistry, NATO ASI series, mathematical and physical sciences 339." Journal of Molecular Structure: THEOCHEM 280, no. 2-3 (April 1993): 295–96. http://dx.doi.org/10.1016/0166-1280(93)80017-t.

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2

Zadoiannyi, O., and Y. Yevdokymenko. "THEORETICAL ANALYSIS OF MEMBRANE AIR DEHUMIDIFICATION IN AIR CONDITIONING SYSTEMS." Innovative Solution in Modern Science 4, no. 48 (June 30, 2021): 33. http://dx.doi.org/10.26886/2414-634x.4(48)2021.3.

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The paper presents a simulation of the process of removing moisture from the air in air conditioning systems using construction vapor-permeable membranes. The existing classical physical and mathematical models are considered and analyzed. Based on the analysis of classical models, a schematic and corresponding theoretical mathematical model of air dehumidification with a semipermeable building membrane with certain characteristics for possibilities of use in air conditioning systems is developed and presented. The data of calculations of moisture release from air for the developed model are given. As a result of analytical researches the correct data for possible use in air conditioning systems are received. Key words: air conditioning systems, air dehumidification, semipermeable membrane, permeability, membrane air dehumidification, convective flow, diffusion flow, moisture permeability.

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3

Travin, S. O., Yu I. Skurlatov, and A. V. Roshchin. "Capabilities and Limitations of Mathematical Models in Ecological Safety Forecasting." Russian Journal of Physical Chemistry B 14, no. 1 (January 2020): 86–99. http://dx.doi.org/10.1134/s1990793120010315.

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4

Li, Yalan, and Bo Deng. "A New Method to Find the Wiener Index of Hypergraphs." Discrete Dynamics in Nature and Society 2020 (June 11, 2020): 1–6. http://dx.doi.org/10.1155/2020/8138942.

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The Wiener index is defined as the summation of distances between all pairs of vertices in a graph or in a hypergraph. Both models—graph-theoretical and hypergraph-theoretical—are used in mathematical chemistry for quantitatively studying physical and chemical properties of classical and nonclassical organic compounds. In this paper, we consider relationships between hypertrees and trees and hypercycles and cycles with respect to their Wiener indices.

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5

Parrouffe, Jean-Michel, and Arun S. Mujumdar. "Bibliography on Mathematical Models of Drying and Dryers." Drying Technology 6, no. 2 (June 1988): 305. http://dx.doi.org/10.1080/07373938808916379.

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6

Chun, Changbum, and Rathinasamy Sakthivel. "New Soliton and Periodic Solutions for Two Nonlinear Physical Models." Zeitschrift für Naturforschung A 65, no. 12 (December 1, 2010): 1049–54. http://dx.doi.org/10.1515/zna-2010-1205.

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In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary and periodic solutions for the Burgers-Kadomtsev-Petviashvili and Vakhnenko equations with distinct physical structures. The results reveal that the exp-function method is very effective and powerful for solving nonlinear evolution equations in mathematical physics.

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7

Wang, Song, Shalela Mohd Mahali, Andrea McGuiness, and Xia Lou. "Mathematical models for estimating effective diffusion parameters of spherical drug delivery devices." Theoretical Chemistry Accounts 125, no. 3-6 (October 15, 2009): 659–69. http://dx.doi.org/10.1007/s00214-009-0649-2.

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8

Zielenkiewicz, W. "How do the mathematical models of calorimeters really work?" Thermochimica Acta 420, no. 1-2 (October 2004): 23–27. http://dx.doi.org/10.1016/j.tca.2003.09.037.

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9

Khawam, Ammar, and Douglas R. Flanagan. "Solid-State Kinetic Models: Basics and Mathematical Fundamentals." Journal of Physical Chemistry B 110, no. 35 (September 2006): 17315–28. http://dx.doi.org/10.1021/jp062746a.

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10

Gorskii, V. G., and S. I. Spivak. "Identifiability of parameters ? One of the most important steps in constructing mathematical models in chemistry." Journal of Structural Chemistry 29, no. 6 (1989): 924–30. http://dx.doi.org/10.1007/bf00748436.

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11

TAKATANI, Kouji. "Recent Development of the Mathematical Models of Blast Furnace." Tetsu-to-Hagane 81, no. 11 (1995): 1031–36. http://dx.doi.org/10.2355/tetsutohagane1955.81.11_1031.

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12

Simpson, William T. "GROUPING TROPICAL WOOD SPECIES FOR KILN DRYING USING MATHEMATICAL MODELS." Drying Technology 12, no. 8 (January 1994): 1877–96. http://dx.doi.org/10.1080/07373939408962211.

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13

Ginoza, Mitsuaki, and Makoto Yasutomi. "Mathematical comment on adhesive hard sphere models for fluids." Molecular Physics 87, no. 3 (February 20, 1996): 593–600. http://dx.doi.org/10.1080/00268979600100411.

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14

Dechant, Pierre-Philippe, Jess Wardman, Tom Keef, and Reidun Twarock. "Viruses and fullerenes – symmetry as a common thread?" Acta Crystallographica Section A Foundations and Advances 70, no. 2 (February 18, 2014): 162–67. http://dx.doi.org/10.1107/s2053273313034220.

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The principle of affine symmetry is applied here to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organizational principle in virus structure and assembly. This group-theoretic framework is adapted here to the physical requirements dictated by carbon chemistry, and it is shown that mathematical models for carbon onions can be derived within this affine symmetry approach. This suggests the applicability of affine symmetry in a wider context in nature, as well as offering a novel perspective on the geometric principles underpinning carbon chemistry.

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15

Radoev, B., T. Boev, and M. Avramov. "Electrostatics of heterogeneous monolayers. Constitutive equations and mathematical models." Advances in Colloid and Interface Science 114-115 (June 2005): 93–101. http://dx.doi.org/10.1016/j.cis.2004.07.010.

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16

Reshetnikov, S. I., S. I. Fadeev, and V. S. Sheplev. "Methods for finding steady-state solutions of mathematical models for chemico-technological schemes." Reaction Kinetics and Catalysis Letters 30, no. 2 (September 1986): 275–81. http://dx.doi.org/10.1007/bf02064303.

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17

Borovinskaya, Ekaterina. "Redundancy-Free Models for Mathematical Descriptions of Three-Phase Catalytic Hydrogenation of Cinnamaldehyde." Catalysts 11, no. 2 (February 4, 2021): 207. http://dx.doi.org/10.3390/catal11020207.

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A new approach on how to formulate redundancy-free models for mathematical descriptions of three-phase catalytic hydrogenation of cinnamaldehyde is presented. An automatically created redundant (generalized) model is formulated according to the complete reaction network. Models based on formal kinetics and kinetics concerning the Langmuir-Hinshelwood theory for three-phase catalytic hydrogenation of cinnamaldehyde were investigated. Redundancy-free models were obtained as a result of a step-by-step elimination of model parameters using sensitivity and interval analysis. Starting with 24 parameters in the redundant model, the redundancy-free model based on the Langmuir-Hinshelwood mechanism contains 6 parameters, while the model based on formal kinetics includes only 4 parameters. Due to less degrees of freedom of molecular rotation in the adsorbed state, the probability of a direct conversion of cinnamaldehyde to 3-phenylpropanol according to the redundancy-free model based on Langmuir-Hinshelwood approach is practically negligible compared to the model based on formal kinetics.

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18

Gani, Rafiqul, Nuria Muro-Suñé, Mauricio Sales-Cruz, Claude Leibovici, and John P. O’Connell. "Mathematical and numerical analysis of classes of property models." Fluid Phase Equilibria 250, no. 1-2 (December 2006): 1–32. http://dx.doi.org/10.1016/j.fluid.2006.09.010.

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19

Ngui, Meo O., and Surya K. Mallapragada. "Understanding isothermal semicrystalline polymer drying: Mathematical models and experimental characterization." Journal of Polymer Science Part B: Polymer Physics 36, no. 15 (November 15, 1998): 2771–80. http://dx.doi.org/10.1002/(sici)1099-0488(19981115)36:15<2771::aid-polb11>3.0.co;2-1.

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20

Stepanova, N. V., L. V. Zhorina, and E. B. Chernyaeva. "Likely Mechanism of the Hydrophobic Sensitizer Accumulation in Tumor Cells: Mathematical Models." Photochemistry and Photobiology 64, no. 5 (November 1996): 832–37. http://dx.doi.org/10.1111/j.1751-1097.1996.tb01843.x.

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21

Jiang, Zhou Hua, Jia Yu, Fu Bin Liu, Xu Chen, and Xin Geng. "Application of Mathematical Models for Different Electroslag Remelting Processes." High Temperature Materials and Processes 36, no. 4 (April 1, 2017): 411–26. http://dx.doi.org/10.1515/htmp-2016-0146.

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AbstractThe electroslag remelting (ESR) process has been effectively applied to produce high grade special steels and super alloys based on the controllable solidification and chemical refining process. Due to the difficulties of precise measurements in a high temperature environment and the excessive expenses, mathematical models have been more and more attractive in terms of investigating the transport phenomena in ESR process. In this paper, the numerical models for different ESR processes made by our lab in last decade have been introduced. The first topic deals with traditional ESR process predicting the relationship between operating parameters and metallurgical parameters of interest. The second topic is concerning the new ESR technology process including ESR with current-conductive mould (CCM), ESR hollow ingot technology, electroslag casting with liquid metal(ESC LM), and so on. Finally, the numerical simulation of solidification microstructure with multi-scale model is presented, which reveals the formation mechanism of microstructure.

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22

SHINOKURA, Tsuneki, and Koichi TAKAI. "Mathematical Models of Roll Force and Torque in Steel Bar Rolling." Tetsu-to-Hagane 72, no. 14 (1986): 1870–76. http://dx.doi.org/10.2355/tetsutohagane1955.72.14_1870.

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23

Dršata, Tomáš, and Filip Lankaš. "Theoretical models of DNA flexibility." Wiley Interdisciplinary Reviews: Computational Molecular Science 3, no. 4 (February 14, 2013): 355–63. http://dx.doi.org/10.1002/wcms.1144.

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24

ANDERSEN, N. "Statistical models for ensemble control by alloying and poisoning of catalysts I. Mathematical assumptions and derivations." Journal of Catalysis 104, no. 2 (April 1987): 454–65. http://dx.doi.org/10.1016/0021-9517(87)90377-0.

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25

Di Gesù, Giacomo, Tony Lelièvre, Dorian Le Peutrec, and Boris Nectoux. "Jump Markov models and transition state theory: the quasi-stationary distribution approach." Faraday Discussions 195 (2016): 469–95. http://dx.doi.org/10.1039/c6fd00120c.

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We are interested in the connection between a metastable continuous state space Markov process (satisfyinge.g.the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the notion of quasi-stationary distribution within a metastable state for the continuous state space Markov process to parametrize the exit event from the state. This approach is useful to analyze and justify methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques). Moreover, it is possible by this approach to quantify the error on the exit event when the parametrization of the jump Markov model is based on the Eyring–Kramers formula. This therefore provides a mathematical framework to justify the use of transition state theory and the Eyring–Kramers formula to build kinetic Monte Carlo or Markov state models.

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26

Ley, Eugene E., Christopher E. Goodyer, and Annette L. Bunge. "Mathematical models of diffusion through membranes from spatially distributed sources." Journal of Membrane Science 283, no. 1-2 (October 2006): 399–410. http://dx.doi.org/10.1016/j.memsci.2006.07.014.

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27

Fricke, Mathis, and Dieter Bothe. "Boundary conditions for dynamic wetting - A mathematical analysis." European Physical Journal Special Topics 229, no. 10 (September 2020): 1849–65. http://dx.doi.org/10.1140/epjst/e2020-900249-7.

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Abstract The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier–Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in [A.V. Lukyanov, T. Pryer, Langmuir 33, 8582 (2017)] aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model of Lukyanov and Pryer. It is found that solutions may still be singular for the latter model.

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28

Pang, S., and A. N. Haslett. "The Application of Mathematical Models to the Commercial High-Temperature Drying of Softwood Lumber." Drying Technology 13, no. 8-9 (January 1995): 1635–74. http://dx.doi.org/10.1080/07373939508917045.

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29

Ceylan, İlhan. "Determination of Drying Characteristics of Timber by Using Artificial Neural Networks and Mathematical Models." Drying Technology 26, no. 12 (November 21, 2008): 1469–76. http://dx.doi.org/10.1080/07373930802412132.

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30

Clark, Timothy, Jane S. Murray, and Peter Politzer. "A perspective on quantum mechanics and chemical concepts in describing noncovalent interactions." Physical Chemistry Chemical Physics 20, no. 48 (2018): 30076–82. http://dx.doi.org/10.1039/c8cp06786d.

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Since quantum mechanical calculations do not typically lend themselves to chemical interpretation, analyses of bonding interactions depend largely upon models (the octet rule, resonance theory, charge transfer, etc.). This sometimes leads to a blurring of the distinction between mathematical modelling and physical reality.

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31

Miranda-Quintana, Ramón Alain, and Paul W. Ayers. "Fractional electron number, temperature, and perturbations in chemical reactions." Physical Chemistry Chemical Physics 18, no. 22 (2016): 15070–80. http://dx.doi.org/10.1039/c6cp00939e.

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The mathematical framework of conceptual density functional theory is extended to use the eigenstates and eigenvalues of perturbed subsystems. This unites, justifies, and extends, several previously proposed models.

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32

Lyu, Suping, Randall Sparer, and Darrel Untereker. "Analytical solutions to mathematical models of the surface and bulk erosion of solid polymers." Journal of Polymer Science Part B: Polymer Physics 43, no. 4 (2005): 383–97. http://dx.doi.org/10.1002/polb.20340.

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33

de Oliveira, César R., and Vinícius L. Rocha. "Dirac cones for graph models of multilayer AA-stacked graphene sheets." Zeitschrift für Naturforschung A 76, no. 4 (February 15, 2021): 371–84. http://dx.doi.org/10.1515/zna-2020-0330.

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Abstract We propose an extension, of a quantum graph model for a single sheet of graphene, to multilayer AA-stacked graphene and also to a model of the bulk graphite. Spectra and Dirac cones are explicitly characterized for bilayer and trilayer graphene, as well as for graphite. For weak layer interaction (as proposed in the text), simple perturbation arguments also cover any number of layers and it mathematically recovers basic cone existences from the theoretical and experimental physics literature; its main strength is its simplicity.

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34

Szekely, Julian. "Mathematical Modeling in Materials Science and Engineering." MRS Bulletin 19, no. 1 (January 1994): 11–13. http://dx.doi.org/10.1557/s0883769400038793.

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During the past two decades, mathematical modeling has been gaining acceptance as a legitimate part of materials science and engineering. However, as common to all relatively new disciplines, we still lack a realistic perspective regarding the uses, limitations, and even the optimal methodologies of mathematical modeling techniques.The term “mathematical modeling” covers a broad range of activities, including molecular dynamics, other atomistic scale systems, continuum fluid and solid mechanics, deformation processing, systems analysis, input-output models, and lifecycle analyses. The common point is that we use algebraic expressions or differential equations to represent physical systems to varying degrees of approximation and then manipulate these equations, using computers, to obtain graphical output.While it is becoming an accepted fact that some kind of mathematical modeling will be needed to make most research programs complete, there is still considerable ambiguity as to what form this should take and what might be the actual usefulness of such an effort.Among the more seasoned and successful practitioners of this art, clear guidelines have emerged regarding the uses and limitations of the mathematical modeling approach. We seek to illustrate these uses through the successful modeling examples presented by some leading practitioners. Some general principles may be worth repeating as an introduction to this interesting collection of articles.

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35

Lortz, D. "On the Structure of the Electron." Zeitschrift für Naturforschung A 58, no. 9-10 (October 1, 2003): 491–93. http://dx.doi.org/10.1515/zna-2003-9-1002.

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Usually the electron is described as a mathematical point with charge, mass, spin angular momentum, and electromagnetic field. Because of the unbounded energies this causes mathematical difficulties [1]. These can be avoided by considering a finite radius. For a “free electron at rest” a classical relativistic model is presented where an axisymmetric torus models the electron. This configuration “differentially rotates” around its axis of symmetry with superluminal speed.

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36

Ageev, E. P., and A. V. Vershubskii. "Reversible rearrangements in the structure of polymer membranes initiated by adsorbing binary liquids. 2. Global and local mathematical models." Journal of Structural Chemistry 36, no. 5 (September 1995): 761–71. http://dx.doi.org/10.1007/bf02579667.

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37

Thakhiew, Wasina, Phatsorn Waisayawan, and Sakamon Devahastin. "Comparative Evaluation of Mathematical Models for Release of Antioxidant from Chitosan Films Prepared by Different Drying Methods." Drying Technology 29, no. 12 (September 15, 2011): 1396–403. http://dx.doi.org/10.1080/07373937.2011.588816.

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38

Babich, A., D. Senk, H. W. Gudenau, K. Mavrommatis, O. Spaniol, Y. Babich, and A. Formoso. "Visualisation of a mathematical model of blast furnace operation for distance learning purposes." Revista de Metalurgia 41, Extra (December 17, 2005): 289–93. http://dx.doi.org/10.3989/revmetalm.2005.v41.iextra.1042.

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39

Grimm, G. "Effective Boson-Fermion Dynamics for Subfermion Models." Zeitschrift für Naturforschung A 49, no. 6 (June 1, 1994): 649–62. http://dx.doi.org/10.1515/zna-1994-0601.

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Abstract Effective composite particle dynamics can be derived by weak mapping of quantum fields. This method was already applied to derive effective boson or boson-fermion coupling theories from a nonlinear subfermion field. In this paper we present an extension of those calculations to the general group theoretical treatm ent of two-fermion bound states and their coupling to (elementary) fermions within an arbitrary nonlinear spinor-isospinor field model. The resulting effective field equations are com pared with the corresponding phenomenological expressions which for example underly the standard electroweak theory. PACS 11 .10 - Field theory.PACS 12.10 - Unified field theories and models. PACS 12.35 - Composite models of particles.

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40

Legrand, N., S. Raël, B. Knosp, M. Hinaje, P. Desprez, and F. Lapicque. "Including double-layer capacitance in lithium-ion battery mathematical models." Journal of Power Sources 251 (April 2014): 370–78. http://dx.doi.org/10.1016/j.jpowsour.2013.11.044.

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41

Panfilov, Mikhail, and Alexandre Koldoba. "Kelvin’s Dissymmetric Models and Consistency Conditions of Multicomponent Gas-Liquid Equilibrium and Capillary Condensation." Journal of Thermodynamics 2016 (March 22, 2016): 1–21. http://dx.doi.org/10.1155/2016/3806364.

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To describe phase equilibrium of mixtures, we develop a nonclassical approach based on using different equations of state for gas and liquid. We show that not all the types of EOS are admissible but only those which verify some specific conditions of consistency. We developed the mathematical theory of this new approach for pure cores and for mixtures, in presence and absence of capillary forces, which leads to explicit analytical relationships for phase concentrations of chemical components. Several examples of comparison with experimental data for binary and ternary mixtures illustrate the feasibility of the suggested approach.

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42

Basterrechea, Daniel A., Javier Rocher, Mar Parra, Lorena Parra, Jose F. Marin, Pedro V. Mauri, and Jaime Lloret. "Design and Calibration of Moisture Sensor Based on Electromagnetic Field Measurement for Irrigation Monitoring." Chemosensors 9, no. 9 (September 6, 2021): 251. http://dx.doi.org/10.3390/chemosensors9090251.

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Soil moisture control is crucial to assess irrigation efficiency in green areas and agriculture. In this paper, we propose the design and calibration of a sensor based on inductive coils and electromagnetic fields. The proposed prototypes should meet a series of requirements such as low power consumption, low relative error, and a high voltage difference between the minimum and maximum moisture. We tested different prototypes based on two copper coils divided into two different sets (P1–P15 and NP1–NP4). The prototypes have different characteristics: variations in the number and distribution of spires, existence or absence of casing, and copper wires with a diameter of 0.4 or 0.6 mm. In the first set of experiments carried out in commercial soil, the results showed that the best prototypes were P5, P8, and P9. These prototypes were used in different types of soils, and P8 was selected for the subsequent tests. We carried the second set of experiments using soil from an agricultural field. Based on the data gathered, mathematical models for the calibration of prototypes were obtained and verified. In some cases, two equations were used for different moisture intervals in a single prototype. According to the verification results, NP2 is the best prototype for monitoring the moisture in agricultural lands. It presented a difference in induced voltage of 1.8 V, at 500 kHz, between wet and dry soil with a maximum voltage of 5.12 V. The verification of the calibration determined that the calibration using two mathematical models offers better results, with an average absolute error of 2.1% of moisture.

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43

Ochoa-Martinez, C. I., H. S. Ramaswamy, and A. A. Ayala-Aponte. "A Comparison of Some Mathematical Models Used for the Prediction of Mass Transfer Kinetics in Osmotic Dehydration of Fruits." Drying Technology 25, no. 10 (October 2007): 1613–20. http://dx.doi.org/10.1080/07373930701590665.

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44

Shikhmurzaev, Yulii D. "Reflections on reflections of Dieter Bothe on the ‘litmus test’ for mathematical models of dynamic wetting." European Physical Journal Special Topics 229, no. 10 (September 2020): 1989–95. http://dx.doi.org/10.1140/epjst/e2020-000148-0.

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Abstract The comments of Dieter Bothe on the ‘litmus test’ proposed in [Y.D. Shikhmurzaev, Eur. Phys. J. Special Topics 229, 1945 (2020)] as a simple way of assessing adequacy of mathematical models of dynamic wetting are examined and shown to be erroneous with regards to two of the flow configurations described in the ‘litmus test’ and missing for the remaining two. Therefore, the conclusions of Bothe’s paper [D. Bothe, Eur. Phys. J. Special Topics 229, 1979 (2020)] should be regarded as completely unfounded.

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45

Vera, Julio, Christopher Lischer, Momchil Nenov, Svetoslav Nikolov, Xin Lai, and Martin Eberhardt. "Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic." International Journal of Molecular Sciences 22, no. 2 (January 7, 2021): 547. http://dx.doi.org/10.3390/ijms22020547.

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In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today’s level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than as a powerful scientific method. This position disregards mathematical thinking as having contributed key discoveries in biology for more than a century, e.g., in the connection between genes, inheritance, and evolution or in the mechanisms of enzymatic catalysis. Here, we discuss the role of computational modelling in the arsenal of modern scientific methods in biomedicine. We list frequent misconceptions about mathematical modelling found among biomedical experimentalists and suggest some good practices that can help bridge the cognitive gap between modelers and experimental researchers in biomedicine. This manuscript was written with two readers in mind. Firstly, it is intended for mathematical modelers with a background in physics, mathematics, or engineering who want to jump into biomedicine. We provide them with ideas to motivate the use of mathematical modelling when discussing with experimental partners. Secondly, this is a text for biomedical researchers intrigued with utilizing mathematical modelling to investigate the pathophysiology of human diseases to improve their diagnostics and treatment.

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46

Vera, Julio, Christopher Lischer, Momchil Nenov, Svetoslav Nikolov, Xin Lai, and Martin Eberhardt. "Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic." International Journal of Molecular Sciences 22, no. 2 (January 7, 2021): 547. http://dx.doi.org/10.3390/ijms22020547.

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In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today’s level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than as a powerful scientific method. This position disregards mathematical thinking as having contributed key discoveries in biology for more than a century, e.g., in the connection between genes, inheritance, and evolution or in the mechanisms of enzymatic catalysis. Here, we discuss the role of computational modelling in the arsenal of modern scientific methods in biomedicine. We list frequent misconceptions about mathematical modelling found among biomedical experimentalists and suggest some good practices that can help bridge the cognitive gap between modelers and experimental researchers in biomedicine. This manuscript was written with two readers in mind. Firstly, it is intended for mathematical modelers with a background in physics, mathematics, or engineering who want to jump into biomedicine. We provide them with ideas to motivate the use of mathematical modelling when discussing with experimental partners. Secondly, this is a text for biomedical researchers intrigued with utilizing mathematical modelling to investigate the pathophysiology of human diseases to improve their diagnostics and treatment.

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47

Shikhmurzaev, Yulii D. "Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges." European Physical Journal Special Topics 229, no. 10 (September 2020): 1945–77. http://dx.doi.org/10.1140/epjst/e2020-900236-8.

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Abstract After a brief overview of the ‘moving contact-line problem’ as it emerged and evolved as a research topic, a ‘litmus test’ allowing one to assess adequacy of the mathematical models proposed as solutions to the problem is described. Its essence is in comparing the contact angle, an element inherent in every model, with what follows from a qualitative analysis of some simple flows. It is shown that, contrary to a widely held view, the dynamic contact angle is not a function of the contact-line speed as for different spontaneous spreading flows one has different paths in the contact angle-versus-speed plane. In particular, the dynamic contact angle can decrease as the contact-line speed increases. This completely undermines the search for the ‘right’ velocity-dependence of the dynamic contact angle, actual or apparent, as a direction of research. With a reference to an earlier publication, it is shown that, to date, the only mathematical model passing the ‘litmus test’ is the model of dynamic wetting as an interface formation process. The model, which was originated back in 1993, inscribes dynamic wetting into the general physical context as a particular case in a wide class of flows, which also includes coalescence, capillary breakup, free-surface cusping and some other flows, all sharing the same underlying physics. New challenges in the field of dynamic wetting are discussed.

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Wagner, Peter. "On Complexity, Grammars and the Inferring of Models." Zeitschrift für Naturforschung A 48, no. 5-6 (June 1, 1993): 651–54. http://dx.doi.org/10.1515/zna-1993-5-612.

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Abstract Various measures of the physical complexity of a dynamical system are considered. Without question, these measures introduce a new quality in the description of nonlinear complex systems, but we think that their advantages have not yet been demonstrated in a convincing manner. We show that the estimation of the complexity of a given system is related to the extraction of models from real-world data.

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Oakley, Barbara A., Darrin Hanna, Meir Shillor, and Gary Barber. "Ultrasonic Parameters as a Function of Absolute Hydrostatic Pressure. II. Mathematical Models of the Speed of Sound in Organic Liquids." Journal of Physical and Chemical Reference Data 32, no. 4 (December 2003): 1535–44. http://dx.doi.org/10.1063/1.1555589.

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Senuma, Takehide. "Preface to the Special Issue “Cutting Edge of Mathematical Models for Predicting Microstructures and Mechanical Properties of Steels”." Tetsu-to-Hagane 97, no. 4 (2011): 165. http://dx.doi.org/10.2355/tetsutohagane.97.165.

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