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Journal articles on the topic 'Cyclostationary waves – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Cassier, Maxence, Patrick Joly, and Maryna Kachanovska. "Mathematical models for dispersive electromagnetic waves: An overview." Computers & Mathematics with Applications 74, no. 11 (2017): 2792–830. http://dx.doi.org/10.1016/j.camwa.2017.07.025.

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2

Shakhin, Victor M., and Tatiana V. Shakhina. "Waves on the Water Surface — Mathematical Models — Part 1." International Journal of Ocean and Climate Systems 6, no. 3 (2015): 113–35. http://dx.doi.org/10.1260/1759-3131.6.3.113.

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3

Shakhin, Victor M., and Tatiana V. Shakhina. "Waves on the Water Surface — Mathematical Models — Part 2." International Journal of Ocean and Climate Systems 6, no. 3 (2015): 137–57. http://dx.doi.org/10.1260/1759-3131.6.3.137.

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4

Turner, R. E. L. "Traveling Waves in Neural Models." Journal of Mathematical Fluid Mechanics 7, S2 (2005): S289—S298. http://dx.doi.org/10.1007/s00021-005-0160-z.

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5

Engelbrecht, Jüri. "Waves, Solids, and Nonlinearities." Shock and Vibration 2, no. 2 (1995): 173–90. http://dx.doi.org/10.1155/1995/640974.

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In this article nonlinearity is taken as a basic property of continua or any other wave-bearing system. The analysis includes the conventional wave propagation problems and also the wave phenomena that are not described by traditional hyperbolic mathematical models. The basic concepts of continuum mechanics and the possible sources of nonlinearities are briefly discussed. It is shown that the technique of evolution equations leads to physically well-explained results provided the basic models are hyperbolic. Complicated constitutive behavior and complicated geometry lead to mathematical models

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6

Biktasheva, I. V., R. D. Simitev, R. Suckley, and V. N. Biktashev. "Asymptotic properties of mathematical models of excitability." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1842 (2006): 1283–98. http://dx.doi.org/10.1098/rsta.2006.1770.

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We analyse small parameters in selected models of biological excitability, including Hodgkin–Huxley (Hodgkin & Huxley 1952 J. Physiol. 117 , 500–544) model of nerve axon, Noble (Noble 1962 J. Physiol. 160 , 317–352) model of heart Purkinje fibres and Courtemanche et al . (Courtemanche et al . 1998 Am. J. Physiol. 275 , H301–H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches ina

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7

Sherratt, Jonathan A., and Matthew J. Smith. "Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models." Journal of The Royal Society Interface 5, no. 22 (2008): 483–505. http://dx.doi.org/10.1098/rsif.2007.1327.

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Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction–diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves oc

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Engelbrecht, Jüri, and Arkadi Berezovski. "Reflections on mathematical models of deformation waves in elastic microstructured solids." Mathematics and Mechanics of Complex Systems 3, no. 1 (2015): 43–82. http://dx.doi.org/10.2140/memocs.2015.3.43.

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9

FERNANDO BARBERO G., J., GUILLERMO A. MENA MARUGÁN, and EDUARDO J. S. VILLASEÑOR. "QUANTUM CYLINDRICAL WAVES AND SIGMA MODELS." International Journal of Modern Physics D 13, no. 06 (2004): 1119–27. http://dx.doi.org/10.1142/s0218271804004554.

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We analyze cylindrical gravitational waves in vacuo with general polarization and develop a viewpoint complementary to that presented recently by Niedermaier showing that the auxiliary sigma model associated with this family of waves is not renormalizable in the standard perturbative sense.

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10

Gaeta, Giuseppe, and Laura Venier. "Solitary waves in helicoidal models of DNA dynamics." Journal of Nonlinear Mathematical Physics 15, no. 2 (2008): 186–204. http://dx.doi.org/10.2991/jnmp.2008.15.2.6.

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11

Wang, Lihui, Min Cao, Qingchan Liu, Guangjin Wei, Bo Li, and Cong Lin. "Mathematical models of light waves in Brillouin-scattering fiber-optic gyroscope resonator." Optik 126, no. 21 (2015): 2937–40. http://dx.doi.org/10.1016/j.ijleo.2015.07.017.

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12

TAKAHASHI, L., N. MAIDANA, W. FERREIRAJR, P. PULINO, and H. YANG. "Mathematical models for the dispersal dynamics: travelling waves by wing and wind." Bulletin of Mathematical Biology 67, no. 3 (2005): 509–28. http://dx.doi.org/10.1016/j.bulm.2004.08.005.

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13

Bikbaev, R. F. "Shock waves in one-dimensional models with cubic nonlinearity." Theoretical and Mathematical Physics 97, no. 2 (1993): 1236–49. http://dx.doi.org/10.1007/bf01016869.

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14

Lipton, Alex, and Artur Sepp. "Stochastic volatility models and Kelvin waves." Journal of Physics A: Mathematical and Theoretical 41, no. 34 (2008): 344012. http://dx.doi.org/10.1088/1751-8113/41/34/344012.

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15

ZHANG, FEN-FEN, GANG HUO, QUAN-XING LIU, GUI-QUAN SUN, and ZHEN JIN. "EXISTENCE OF TRAVELLING WAVES IN NONLINEAR SI EPIDEMIC MODELS." Journal of Biological Systems 17, no. 04 (2009): 643–57. http://dx.doi.org/10.1142/s0218339009003101.

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In this paper, we investigate a spatially extended SI epidemic system with a nonlinear incidence rate. Using mathematical analysis, we study the existence of a heteroclinic orbit connecting two equilibrium points in R3 which corresponds to a travelling wave solution connecting the disease-free and endemic equilibria for the reaction-diffusion system. In other words, the travelling wave solutions of the model are studied to determine the speed of disease dissemination, form the biological point of view. Moreover, this wave speed is obtained as a function of the model's parameters, in order to a

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16

Shin, Sang-Ik, Prashant D. Sardeshmukh, Matthew Newman, Cecile Penland, and Michael A. Alexander. "Impact of Annual Cycle on ENSO Variability and Predictability." Journal of Climate 34, no. 1 (2021): 171–93. http://dx.doi.org/10.1175/jcli-d-20-0291.1.

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AbstractLow-order linear inverse models (LIMs) have been shown to be competitive with comprehensive coupled atmosphere–ocean models at reproducing many aspects of tropical oceanic variability and predictability. This paper presents an extended cyclostationary linear inverse model (CS-LIM) that includes the annual cycles of the background state and stochastic forcing of tropical sea surface temperature (SST) and sea surface height (SSH) anomalies. Compared to a traditional stationary LIM that ignores such annual cycles, the CS-LIM is better at representing the seasonal modulation of ENSO-relate

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17

Zdravkovic, Slobodan. "Microtubules: A network for solitary waves." Journal of the Serbian Chemical Society 82, no. 5 (2017): 469–81. http://dx.doi.org/10.2298/jsc161118020z.

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In the present paper we deal with nonlinear dynamics of microtubules. The structure and role of microtubules in cells are explained as well as one of models explaining their dynamics. Solutions of the crucial nonlinear differential equation depend on used mathematical methods. Two commonly used procedures, continuum and semi-discrete approximations, are explained. These solutions are solitary waves usually called as kink solitons, breathers and bell-type solitons.

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18

Li, Ming. "The Modeling and Rendering of the Waves." Advanced Materials Research 756-759 (September 2013): 1766–68. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.1766.

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The article analyzes the mathematical and physical models of the waves. Base on the oceanography existing statistical observations and spectrum function formula. This article puts forward the method of making waves modeling, and using mesh model and texture mapping techniques to achieve a photorealistic rendering of the waves. The methods have achieved good results in realistic and real-time.

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19

Alverez, Jorge Calderon, and Adolfo Maron Loureiro. "MAXIMUM ENTROPY SPECTRAL ESTIMATION FOR WIND WAVES." Coastal Engineering Proceedings 1, no. 20 (1986): 1. http://dx.doi.org/10.9753/icce.v20.1.

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Some results are presented on the application of new spectral estimation techniques using AR and ARMA models, also known as Maximum Entropy- Methods, to wind wave spectral analysis. The results are compared with those obtained with conventional FFT methods. The application of some mathematical methods for model order selection is included. The relation between the optimum order and different spectral parameters is investigated.

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20

Kichenassamy, Satyanad. "Existence of solitary waves for water-wave models." Nonlinearity 10, no. 1 (1997): 133–51. http://dx.doi.org/10.1088/0951-7715/10/1/009.

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21

Bayly, P. V., and S. K. Dutcher. "Steady dynein forces induce flutter instability and propagating waves in mathematical models of flagella." Journal of The Royal Society Interface 13, no. 123 (2016): 20160523. http://dx.doi.org/10.1098/rsif.2016.0523.

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Cilia and flagella are highly conserved organelles that beat rhythmically with propulsive, oscillatory waveforms. The mechanism that produces these autonomous oscillations remains a mystery. It is widely believed that dynein activity must be dynamically regulated (switched on and off, or modulated) on opposite sides of the axoneme to produce oscillations. A variety of regulation mechanisms have been proposed based on feedback from mechanical deformation to dynein force. In this paper, we show that a much simpler interaction between dynein and the passive components of the axoneme can produce c

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22

Madeiro, J. P. V., E. M. B. Santos, P. C. Cortez, J. H. S. Felix, and F. S. Schlindwein. "Evaluating Gaussian and Rayleigh-Based Mathematical Models for T and P-waves in ECG." IEEE Latin America Transactions 15, no. 5 (2017): 843–53. http://dx.doi.org/10.1109/tla.2017.7910197.

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23

Ishanov, S. A., E. I. Levanov, V. V. Medvedev, V. A. Zalesskaya, and K. I. Novikova. "Use of mathematical models of the ionosphere for studying the propagation of electromagnetic waves." Journal of Engineering Physics and Thermophysics 81, no. 6 (2008): 1242–46. http://dx.doi.org/10.1007/s10891-009-0143-7.

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24

Hadadifard, Fazel, and Atanas G. Stefanov. "Sharp relaxation rates for plane waves of general reaction-diffusion models." Journal of Mathematical Physics 61, no. 4 (2020): 041502. http://dx.doi.org/10.1063/5.0004762.

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25

Figotin, Alexander, and Abel Klein. "Localization of electromagnetic and acoustic waves in random media. Lattice models." Journal of Statistical Physics 76, no. 3-4 (1994): 985–1003. http://dx.doi.org/10.1007/bf02188695.

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26

Cornille, H. "Shock waves for discrete velocity nonconservative (except mass) models." Journal of Physics A: Mathematical and General 32, no. 37 (1999): 6479–501. http://dx.doi.org/10.1088/0305-4470/32/37/301.

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27

Bose, S. K. "Dynamical algebra of spin waves in localised-spin models." Journal of Physics A: Mathematical and General 18, no. 6 (1985): 903–22. http://dx.doi.org/10.1088/0305-4470/18/6/014.

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28

Engelbrecht, J., and M. Braun. "Nonlinear Waves in Nonlocal Media." Applied Mechanics Reviews 51, no. 8 (1998): 475–88. http://dx.doi.org/10.1115/1.3099016.

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This review article gives a brief overview on nonlocal theories in solid mechanics from the viewpoint of wave motion. The influence of two essential qualities of solids—nonlocality and nonlinearity—is discussed. The effects of microstructure are analyzed in order to understand their role in nonlocal theories. The various models are specified on the level of one-dimensional unidirectional motion in order to achieve mathematical clarity of interpreting physical phenomena. Three main types of evolution equations are shown to govern deformation waves under such assumptions. Based on the dispersion

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29

Dudko, Olga V., Victoria E. Ragozina, and Anastasia A. Lapteva. "Mathematical Modeling the Nonlinear 1D Dynamics of Elastic Heteromodular and Porous Materials." Materials Science Forum 945 (February 2019): 899–905. http://dx.doi.org/10.4028/www.scientific.net/msf.945.899.

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Approaches to mathematical modeling of nonlinear strain dynamics in heteromodular and porous materials are discussed; the mechanical properties of media are described in terms of the simple piecewise linear elastic models. Several nonstationary 1D boundary value problems show that the singularity of model relationships gives rise to shock waves and centered Riemann waves in generalized solutions. Nonstationary load modes leading to the listed nonlinear effects are indicated separately for heteromodular and porous media.

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30

Seadawy, Aly R., Asghar Ali, and Dianchen Lu. "Applications of modified mathematical method on some nonlinear water wave dynamical models." Modern Physics Letters A 33, no. 35 (2018): 1850204. http://dx.doi.org/10.1142/s0217732318502048.

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The extended simple equation method is applied to construct solitary wave solutions of (3 + 1)-dimensional Kadomtsev–Petviashvili-Benjamin–Bona–Mahony (KP-BBM), Korteweg–de Vries Benjamin–Bona–Mahony (KdV-BBM), Breaking soliton (BS) and (2 + 1) Maccari system waves system of equations. These models have prevalent usage in modern science. This technique can also be functional to solve different kinds of nonlinear evolution problems in contemporary areas of research. It is an effective and powerful mathematical tool in finding solitary wave solutions of nonlinear evolution equations (NLEEs) in m

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31

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

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32

Li, Qinjun, Danyal Soybaş, Onur Alp Ilhan, Gurpreet Singh, and Jalil Manafian. "Pure Traveling Wave Solutions for Three Nonlinear Fractional Models." Advances in Mathematical Physics 2021 (April 9, 2021): 1–18. http://dx.doi.org/10.1155/2021/6680874.

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Three nonlinear fractional models, videlicet, the space-time fractional 1 + 1 Boussinesq equation, 2 + 1 -dimensional breaking soliton equations, and SRLW equation, are the important mathematical approaches to elucidate the gravitational water wave mechanics, the fractional quantum mechanics, the theoretical Huygens’ principle, the movement of turbulent flows, the ion osculate waves in plasma physics, the wave of leading fluid flow, etc. This paper is devoted to studying the dynamics of the traveling wave with fractional conformable nonlinear evaluation equations (NLEEs) arising in nonlinear w

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33

Lu, Dianchen, Aly R.Seadawy, and Asghar Ali. "Structure of traveling wave solutions for some nonlinear models via modified mathematical method." Open Physics 16, no. 1 (2018): 854–60. http://dx.doi.org/10.1515/phys-2018-0107.

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Abstract We have employed the exp(-φ(ξ))-expansion method to derive traveling waves solutions of breaking solition (BS), Zakharov-Kuznetsov-Burgers (ZKB), Ablowitz-Kaup-Newell-Segur (AKNS) water wave, Unstable nonlinear Schrödinger (UNLS) and Dodd-Bullough-Mikhailov (DBM) equations. These models have valuable applications in mathematical physics. The results of the constructed model, along with some graphical representations provide the basic knowlegde about these models. The derived results have various applications in applied science.

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34

Calini, Annalisa, and Constance M. Schober. "Dynamical criteria for rogue waves in nonlinear Schrödinger models." Nonlinearity 25, no. 12 (2012): R99—R116. http://dx.doi.org/10.1088/0951-7715/25/12/r99.

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35

Lu, Dianchen, Aly R. Seadawy, and Asghar Ali. "Dispersive analytical wave solutions of three nonlinear dynamical water waves models via modified mathematical method." Results in Physics 13 (June 2019): 102177. http://dx.doi.org/10.1016/j.rinp.2019.102177.

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36

Pyatkov, S. G., and S. N. Shergin. "Inverse Problems for Mathematical Models of Quasistationary Electromagnetic Waves in Anisotropic Nonmetallic Media with Dispersion." Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 11, no. 1 (2018): 44–59. http://dx.doi.org/10.14529/mmp180105.

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37

Mornev, O. A., O. V. Aslanidi, and I. M. Tsyganov. "Soliton-like regimes, echo and concave spiral waves in mathematical models of biological excitable media." Macromolecular Symposia 160, no. 1 (2000): 115–22. http://dx.doi.org/10.1002/1521-3900(200010)160:1<115::aid-masy115>3.0.co;2-h.

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38

Tenkam, H. M., M. Shatalov, I. Fedotov, and R. Anguelov. "Mathematical Models for the Propagation of Stress Waves in Elastic Rods: Exact Solutions and Numerical Simulation." Advances in Applied Mathematics and Mechanics 8, no. 2 (2016): 257–70. http://dx.doi.org/10.4208/aamm.2013.m383.

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AbstractIn this work, the Bishop and Love models for longitudinal vibrations are adopted to study the dynamics of isotropic rods with conical and exponential cross-sections. Exact solutions of both models are derived, using appropriate transformations. The analytical solutions of these two models are obtained in terms of generalised hypergeometric functions and Legendre spherical functions respectively. The exact solution of Love model for a rod with exponential cross-section is expressed as a sum of Gauss hypergeometric functions. The models are solved numerically by using the method of lines

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39

Królicka, Agnieszka. "State equations in the mathematical model of dynamic behaviour of multihull floating unit." Polish Maritime Research 17, no. 1 (2010): 33–38. http://dx.doi.org/10.2478/v10012-010-0003-6.

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State equations in the mathematical model of dynamic behaviour of multihull floating unit This paper concerns dynamic behaviour of multihull floating unit of catamaran type exposed to excitations due to irregular sea waves. Dynamic analysis of multihull floating unit necessitates, in its initial stage, to determine physical model of the unit and next to assume an identified mathematical model. Correctly elaborated physical models should contain information on the basis of which a mathematical model could be built. Mathematical models describe mutual relations between crucial quantities which c

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40

Burke, W. C., P. S. Crooke, T. W. Marcy, A. B. Adams, and J. J. Marini. "Comparison of mathematical and mechanical models of pressure-controlled ventilation." Journal of Applied Physiology 74, no. 2 (1993): 922–33. http://dx.doi.org/10.1152/jappl.1993.74.2.922.

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Recent evidence that volume-cycled mechanical ventilation may itself produce lung injury has focused clinical attention on the pressure waveform applied to the respiratory system. There has been an increasing use of pressure-controlled ventilation (PCV), because it limits peak cycling pressure and provides a decelerating flow profile that may improve gas exchange. In this mode, however, the relationships are of machine adjustments to ventilation and alveolar pressure are not straightforward. Consequently, setting selection remains largely an empirical process. In previous work, we developed a

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41

Yoo, Donghoon, and Brian A. O'Connor. "MATHEMATICAL MODELLING OF WAVE-INDUCED NEARSHORE CIRCULATIONS." Coastal Engineering Proceedings 1, no. 20 (1986): 122. http://dx.doi.org/10.9753/icce.v20.122.

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The paper presents a mathematical model for describing wave climate and wave-induced nearshore circulations. The model accounts for current-depth refraction, diffraction, wave-induced currents, set-up and set-down, mixing processes and bottom friction effects on both waves and currents. The present model was tested against published experimental data on wave conditions within a model harbour and shown to give very good results for both wave and current fields. The importance of including processes such as advection, flooding and current-interaction in coastal models was demonstrated by compari

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42

Rudenko, O. V., and C. M. Hedberg. "Single shock and periodic sawtooth-shaped waves in media with non-analytic nonlinearities." Mathematical Modelling of Natural Phenomena 13, no. 2 (2018): 18. http://dx.doi.org/10.1051/mmnp/2018028.

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The review of new mathematical models containing non-analytic nonlinearities is given. These equations have been proposed recently, over the past few years. The models describe strongly nonlinear waves of the first type, according to the classification introduced earlier by the authors. These models are interesting because of two reasons: (i) equations admit exact analytic solutions, and (ii) solutions describe the real physical phenomena. Among these models are modular and quadratically cubic equations of Hopf, Burgers, Korteveg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko type. Me

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43

Andrukhiv, Andrij, Bohdan Sokil, and Mariia Sokil. "Wave concept of motion in mathematical models of the dynamics of two-dimensional media studying." Ukrainian journal of mechanical engineering and materials science 5, no. 3-4 (2019): 8–15. http://dx.doi.org/10.23939/ujmems2019.03-04.008.

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The methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement. The value determining the impact of nonlinear forces on the basic parameters of the waves for the dist

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44

Nechayev, Yu I. "Concerning the Goodness of Fit of Mathematical Models of the Dynamics of a Ship in Waves." International Journal of Fluid Mechanics Research 26, no. 3 (1999): 348–56. http://dx.doi.org/10.1615/interjfluidmechres.v26.i3.60.

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45

Mazurov, Mikhail. "Nonlinear Concave Spiral Waves in Active Media Transferring Energy." EPJ Web of Conferences 224 (2019): 02011. http://dx.doi.org/10.1051/epjconf/201922402011.

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Spiral concave autowaves are widely implemented in physics, chemistry, hydrodynamics, meteorology and other fields. A mathematical model of spiral concave autowaves based on the Fitzhugh-Nagumo equation and modified axiomatic models are presented. The existence of spiral concave autowaves transferring energy was predicted via computational experiments. Applications of spiral concave autowaves carrying energy in hydrodynamics, generation of tornadoes, breaking waves, and tsunamis and examples of such autowaves in biology and medicine are reviewed and the importance of concave spiral autowaves t

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46

Fiorot, G. H., G. F. Maciel, and C. Kitano. "MATHEMATICAL MODEL AND EXPERIMENTAL PROCEEDINGS TO DETERMINE ROLL WAVES IN OPEN CHANNELS." Revista de Engenharia Térmica 10, no. 1-2 (2011): 55. http://dx.doi.org/10.5380/reterm.v10i1-2.61953.

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The goal of this paper is consolidate a representative model previously developed by RMVP team (Rheological Studies on Viscous and Viscousplastic Materials) from UNESP - Ilha Solteira, for a typical phenomenonthat occurs on spillways, river's bed, landslides, mudflows, blood flows, for Newtonian and non-Newtonian fluids, known as roll waves. Another goal of this paper is present an experimental project designed for capturing measurements (amplitude and wavelength) of these instabilities. From a mathematical perspective, a first-order analytical model is showed, based on Cauchy's equations syst

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47

Hong, Woo-Pyo. "Dynamics of Combined Solitary-waves in the General Shallow Water Wave Models." Zeitschrift für Naturforschung A 58, no. 9-10 (2003): 520–28. http://dx.doi.org/10.1515/zna-2003-9-1008.

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We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the general fifth-order shallow water wave models using the hyperbolic function ansatz method. We study the dynamical properties of the solutions in the combined form of a bright and a dark solitary-wave by using numerical simulations. It is shown that the solitary-waves can be stable or marginally stable, depending on the coefficients of the model.We study the interaction dynamics by using the combined solitary-waves as the initial profiles to show the formation of sech2-type solitary-waves in the presen

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48

Sarrico, C. O. R., and A. Paiva. "Creation, Annihilation, and Interaction of Delta-Waves in Nonlinear Models: a Distributional Product Approach." Russian Journal of Mathematical Physics 27, no. 1 (2020): 111–25. http://dx.doi.org/10.1134/s1061920820010112.

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49

Muratov, Maxim V., Polina V. Stognii, Igor B. Petrov, Alexey A. Anisimov, and Nazim A. Karaev. "The study of dynamical processes in problems of mesofracture layers exploration seismology by methods of mathematical and physical simulation." Radioelectronics. Nanosystems. Information Technologies. 13, no. 1 (2021): 71–78. http://dx.doi.org/10.17725/rensit.2021.13.071.

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The article is devoted to the study of the propagation of elastic waves in a fractured seismic medium by methods of mathematical modeling. The results obtained during it are compared with the results of physical modeling on similar models. For mathematical modeling, the grid-characteristic method with hybrid schemes of 1-3 orders with approximation on structural rectangular grids is used. The ability to specify inhomogeneities (fractures) of various complex shapes and spatial orientations has been implemented. The description of the developed mathematical models of fractures, which can be used

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Lin, Ray-Qing, Weijia Kuang, and Arthur M. Reed. "Numerical Modeling of Nonlinear Interactions Between Ships and Surface Gravity Waves, Part 1: Ship Waves in Calm Water." Journal of Ship Research 49, no. 01 (2005): 1–11. http://dx.doi.org/10.5957/jsr.2005.49.1.1.

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Abstract:

This paper presents a pseudo-spectral model for nonlinear ship-surface wave interactions. The algorithm used in the model is a combination of spectral and boundary element methods: the boundary element method is used to translate physical quantities between the nonuniform ship surface and the regular grid of the spectral representation; the spectral method is used throughout the remainder of the fluid domain. All possible wave-wave interactions are included in the model (up to N-wave interactions for the truncation order N of the spectral expansions). This paper focuses on the mathematical the

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