Relevant bibliographies by topics / Cyclostationary waves – Mathematical models

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

Academic literature on the topic 'Cyclostationary waves – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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

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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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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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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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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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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 of different character and, as shown by numerous examples, other methods are then used for the analysis. It is also shown that propagating instabilities possess wave properties and in this case the modeling of energy redistribution has a great importance. Finally, some new directions in the theory and applications are indicated.
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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 inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh–Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al . kinetics.
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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 occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction–diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.
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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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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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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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Dissertations / Theses on the topic "Cyclostationary waves – Mathematical models"

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Hanson, David Mechanical &amp Manufacturing Engineering Faculty of Engineering UNSW. "Operational modal analysis and model updating with a cyclostationary input." Awarded by:University of New South Wales. School of Mechanical and Manufacturing Engineering, 2006. http://handle.unsw.edu.au/1959.4/31199.

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This thesis addresses the problem of identifying the modal properties of a system based only on measurements of the system responses. This situation is frequently encountered in structural dynamics and is particularly relevant for systems where the in-service excitation is not artificially reproducible. The inherent non-linearities in these systems mean that the modal properties estimated using traditional input/output techniques will be different to those exhibited in operation. A common example from the literature is an aircraft in flight where the modal properties are heavily influenced by the operating point, i.e. the combination of load, speed, altitude etc., at which the aircraft is travelling. The process of identifying the modal properties of systems in-service is called Operational Modal Analysis (OMA). Not knowing the input complicates the analysis. Most of the techniques in the literature overcome the lack of knowledge about the unmeasured excitations by assuming they are both spatially and frequentially white, i.e. of equal magnitude and with a flat autospectrum. This thesis presents a new technique for OMA which relaxes these constraints, requiring only that the system is excited by a so called cyclostationary input with a unique cyclic frequency, and that the log spectrum of the second order component of this input is frequentially smooth, as will be explained. Such systems include vehicles with internal combustion engines as the vibration from such an engine exhibits cyclostationary statistics. In this thesis, the technique is applied to a laboratory test rig and a passenger train both using an artificial input, and to a race car using the engine as the excitation. By combining cyclostationary signal processing and the concept of the cepstrum, the technique identifies the resonances and anti-resonances in the transfer functions between each response and the cyclostationary source. These resonances and antiresonances can be used to regenerate Frequency Response Functions (FRFs) and it is shown how the unknown scaling of the system can be recovered by employing finite element model updating in conjunction with this regeneration. In addition, the contribution made to model updating by the anti-resonances is also investigated. Finally, the potential of OMA to inform a model updating process is demonstrated using an experimental case study on a diesel railcar.
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Button, Peter. "Models for ocean waves." Master's thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/14299.

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Includes bibliography.<br>Ocean waves represent an important design factor in many coastal engineering applications. Although extreme wave height is usually considered the single most important of these factors there are other important aspects that require consideration. These include the probability distribution of wave heights, the seasonal variation and the persistence, or duration, of calm and storm periods. If one is primarily interested in extreme wave height then it is possible to restrict one's attention to events which are sufficiently separated in time to be effectively independently (and possibly even identically) distributed. However the independence assumption is not tenable for the description of many other aspects of wave height behaviour, such as the persistence of calm periods. For this one has to take account of the serial correlation structure of observed wave heights, the seasonal behaviour of the important statistics, such as mean and standard deviation, and in fact the entire seasonal probability distribution of wave heights. In other words the observations have to be regarded as a time series.
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Chan, Johnson Lap-Kay. "Numerical procedure for potential flow problems with a free surface." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/28637.

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A numerical procedure based upon a boundary integral method for gravity wave making problems is studied in the time domain. The free-surface boundary conditions are combined and expressed in a Lagrangian notation to follow the free-surface particle's motion in time. The corresponding material derivative term is approximated by a finite difference expression, and the velocity terms are extrapolated in time for the completion of the formulations. The fluid-body intersection position at the free surface is predicted by an interpolation function that requires information from both the free surface and the submerged surface conditions. Solutions corresponding to a linear free-surface condition and to a non-linear free-surface condition are obtained at small time increment values. Numerical modelling of surface wave problems is studied in two dimensions and in three dimensions. Comparisons are made to linear analytical solutions as well as to published experimental results. Good agreement between the numerical solutions and measured values is found. For the modelling of a three dimensional wave diffraction problem, results at high wave amplitude are restricted because of the use of quadrilateral elements. The near cylinder region of the free surface is not considered to be well represented because of the coarse element size. Wave forces calculated on the vertical cylinder are found to be affected by the modelled tank length. When the simulated wave length is comparable to the wave tank's dimension, numerical results are found to be less than the experimental measurements. However, when the wave length is shorter than the tank's length, solutions are obtained with very good precision.<br>Applied Science, Faculty of<br>Mechanical Engineering, Department of<br>Graduate
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Bleach, Gordon Phillip. "Acceleration waves in constrained thermoelastic materials." Doctoral thesis, University of Cape Town, 1989. http://hdl.handle.net/11427/15850.

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Bibliography: pages 242-249.<br>We study the propagation and growth of acceleration waves in isotropic thermoelastic media subject to a broad class of thermomechanical constraints. The work is based on an existing thermodynamic theory of constrained thermoelastic materials presented by Reddy (1984) for both definite and non- conductors, but we differ by adopting a new definition of a constrained non-conductor and by investigating the consequences of isotropy. The set of constraints considered is not arbitrary but is large enough to include most constraints commonly found in practice. We also extend Reddy's (1984) work by including consideration of sets of constraints for which a set of vectors associated with the constraints is linearly dependent. These vectors play a significant role in the propagation conditions and in the growth equations described below. Propagation conditions (of Fresnel-Hadamard type) are derived for both homothermal and homentropic waves, and solutions for longitudinal and transverse principal waves are discussed. The derivations involve the determination of jumps in the time derivative of constraint multipliers which are required in the solution of the corresponding growth equations, and it is found that these multipliers cannot be separately determined if the set of constraint vectors mentioned above is linearly dependent. This difficulty forces us to restrict the constraint set for which the growth equations for homothermal and homentropic waves can be derived. The growth of plane, cylindrical and spherical waves is considered and solutions are discussed, concentrating on the influence of the constraints on the results.
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Marchant, Timothy Robert. "On short-crested water waves." Title page, contents and introduction only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phm3151.pdf.

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Zink, Florian. "Gravity waves and turbulence in the lower atmosphere /." Title page, contents and abstract only, 2000. http://web4.library.adelaide.edu.au/theses/09PH/09phz778.pdf.

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Mercer, Geoffry Norman. "On standing waves and models of shear dispersion /." Title page, contents and summary only, 1992. http://web4.library.adelaide.edu.au/theses/09PH/09phm5541.pdf.

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朱書堂 and Shutang Zhu. "Interaction between waves and porous seawalls." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31239869.

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Frankel, Jay Irwin. "A theoretical investigation of thermal waves." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/76212.

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A unified and systematic study of one-dimensional heat conduction based on thermal relaxation is presented. Thermal relaxation is introduced through the constitutive equation (modified Fourier's law) which relates this heat flux and temperature. The resulting temperature and flux field equations become hyperbolic rather than the usual classical parabolic equations encountered in heat conduction. In this formulation, heat propagates at a finite speed and removes one of the anomalies associated to parabolic heat conduction, i.e., heat propagating at an infinite speed. In situations involving very short times, high heat fluxes, and cryogenic temperatures, a more exact constitutive relation must be introduced to preserve a finite speed to a thermal disturbance. The general one-dimensional temperature and flux formulations for the three standard orthogonal coordinate systems are presented. The general solution, in the temperature domain, is developed by the finite integral transform technique. The basic physics and mathematics are demonstrated by reviewing Taitel's problem. Then attention is turned to the effects of radially dependent systems, such as the case of a cylinder and sphere. Various thermal disturbances are studied showing the unusual physics associated with dissipative wave equations. The flux formulation is shown to be a viable alternative domain to develop the flux distribution. Once the flux distribution has been established, the temperature distribution may be obtained through the conservation of energy. Linear one-dimensional composite regions are then investigated in detail. The general temperature and flux formulations are developed for the three standard orthogonal coordinate systems. The general solution for the flux and temperature distributions are obtained in the flux domain using a generalized integral transform technique. Additional features associated with hyperbolic heat conduction are displayed through examples with various thermal disturbances. A generalized expression for temperature dependent thermal conductivity is introduced and incorporated into the one-dimensional hyperbolic heat equation. An approximate analytical solution is obtained and compared with a standard numerical method. Finally, recommendations for future analytical and experimental investigations are suggested.<br>Ph. D.
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Zhang, Wenjun. "Waves in mathematical models of intracellular calcium and other excitable systems." Thesis, University of Auckland, 2011. http://hdl.handle.net/2292/14482.

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Oscillations in cytoplasmic calcium concentration are a crucial control mechanism in almost every cell type. Two important classes of oscillation are of particular interest: solitary and periodic waves. Both types of waves are commonly observed in physical experiments and found in mathematical models of calcium dynamics and other excitable systems. In this thesis, we try to understand these two classes of wave solutions. We first investigate wave solutions of the canonical excitable model, the FitzHugh-Nagumo (FHN) equations. We analyze the FHN equations using geometric singular perturbation theory and numerical integration, and find some new codimension-two organizing centres of the overall dynamics. Many analytical results about the FHN model in its classical form have already been established. We devise a transformation to change the form of the FHN equations we study into the classical form to make use of the results. This enables us to show how basic features of the bifurcation structure of the FHN equations arise from the singular limit. We then study waves of a representative calcium model. We analyze the dynamics of the calcium model in the singular limit, and show how homoclinic and Hopf bifurcations of the full system arise as perturbations of singular homoclinic and Hopf bifurcations. We compare the wave solutions in the FHN model and the calcium model, and show that the dynamics of the two models differ in some respects (most importantly, in the way in which diffusion enters the equations). We conclude that the FHN model should not uniformly be used as a prototypical model for calcium dynamics. Motivated by phenomena seen in the FHN and calcium models, we then investigate reduction techniques for excitable systems, including the quasi-steady state approximation and geometric singular perturbation theory, and show that criticality of Hopf bifurcations may be changed when applying these reduction methods to slow-fast biophysical systems. This suggests that great care should be taken when using reduction techniques such as these, to ensure that spurious conclusions about the dynamics of a model are not drawn from the dynamics of a reduced version of the model. Finally, we describe the class of numerical algorithms used to compute features of the detailed bifurcation sets for the FHN and calcium models, and show how these were used to locate a non-structurally stable heteroclinic connection between periodic orbits in a calcium model; this is the first time such a global bifurcation has been computed.
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Books on the topic "Cyclostationary waves – Mathematical models"

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Lin, Pengzhi. Numerical modeling of water waves. Taylor & Francis, 2008.

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Lin, Pengzhi. Numerical modeling of water waves. Taylor & Francis, 2008.

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Won, Y. S. Spectral Boussinesq modelling of random waves. Delft University of Technology, Dept. of Civil Engineering, Fluid Mechanics Group, 1992.

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Numerical modeling of water waves. 2nd ed. CRC Press, 2004.

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The water waves problem: Mathematical analysis and asymptotics. American Mathematical Society, 2013.

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Mayumi, Shōji, ed. The mathematical theory of permanent progressive water-waves. World Scientific, 2001.

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Wind-waves in oceans: Dynamics and numerical simulations. Springer, 2003.

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Vengayil, Padmaraj. Similarity relations of wind waves in finite depth. Woods Hole Oceanographic Institution, 1988.

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Operational analysis and prediction of ocean wind waves. Springer-Verlag, 1989.

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Miyazaki, Takeshi. Vortices, waves and turbulence in a rotating stratified fluid. Center for Global Environmental Research, National Institute for Environmental Studies, Japan, 2004.

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Book chapters on the topic "Cyclostationary waves – Mathematical models"

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Murray, James D. "Biological Waves: Single Species Models." In Mathematical Biology. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4_11.

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Murray, James D. "Biological Waves: Single Species Models." In Mathematical Biology. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-08542-4_11.

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Murray, James D. "Biological Waves: Multi-species Reaction Diffusion Models." In Mathematical Biology. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4_12.

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Murray, James D. "Biological Waves: Multi-Species Reaction Diffusion Models." In Mathematical Biology. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-08542-4_12.

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Sentis, Rémi. "Coupling Electron Waves and Laser Waves." In Mathematical Models and Methods for Plasma Physics, Volume 1. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03804-9_5.

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Matsumoto, Y., M. Kameda, F. Takemura, H. Ohashi, and A. Ivandaev. "Wave dynamics of bubbly liquids mathematical models and numerical simulation." In Shock Waves. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-77648-9_84.

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Maugin, G. A. "Physical and Mathematical Models of Nonlinear Waves in Solids." In Nonlinear Waves in Solids. Springer Vienna, 1994. http://dx.doi.org/10.1007/978-3-7091-2444-4_3.

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Kedrinskiy, V. "Explosive eruptions of volcanos: simulation shock tube methods and multi-phase mathematical models." In Shock Waves. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85168-4_3.

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Kistovich, Anatoly. "The Exact Mathematical Models of Nonlinear Surface Waves." In Springer Geology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77788-7_32.

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Sentis, Rémi. "Langmuir Waves and Zakharov Equations." In Mathematical Models and Methods for Plasma Physics, Volume 1. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03804-9_4.

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Conference papers on the topic "Cyclostationary waves – Mathematical models"

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COLIZZA, V., F. GARGIULO, J. J. RAMASCO, A. BARRAT, and A. VESPIGNANI. "NETWORK STRUCTURE AND EPIDEMIC WAVES IN METAPOPULATION MODELS." In International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814271820_0005.

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Watanabe, Akira, and Mohammad Dibajnia. "Mathematical Models for Waves and Beach Profiles in Surf and Swash Zones." In 25th International Conference on Coastal Engineering. American Society of Civil Engineers, 1997. http://dx.doi.org/10.1061/9780784402429.240.

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Kononenko, O., and I. Mitina. "Mathematical models to study rectangular and smooth gyrotron resonators." In 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics (IRMMW-THz). IEEE, 2007. http://dx.doi.org/10.1109/icimw.2007.4516572.

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Nazarov, Ravshanjon, Mikhail K. Khodzitskiy, and Tianmiao Zhang. "Comparison of Mathematical Models for the Calculation of Optical Properties of Composite Medium in the Terahertz Regime." In 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz). IEEE, 2019. http://dx.doi.org/10.1109/irmmw-thz.2019.8874268.

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Kumar Mulimani, Mahesh, Jaya Kumar Alageshan, and Rahul Pandit. "Detection and Termination of Broken-Spiral-Waves in Mathematical Models for Cardiac Tissue: A Deep-Learning Approach." In 2019 Computing in Cardiology Conference. Computing in Cardiology, 2019. http://dx.doi.org/10.22489/cinc.2019.142.

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Taghipour, Reza, Tristan Perez, and Torgeir Moan. "Time Domain Hydroelastic Analysis of a Flexible Marine Structure Using State-Space Models." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29272.

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This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms in the mathematical model are replaced by their alternative state-space representations whose parameters are obtained by using the realization theory. The mathematical model is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.
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Nelli, Filippo, David M. Skene, Luke G. Bennetts, Micheal H. Meylan, Jason P. Monty, and Alessandro Toffoli. "Experimental and Numerical Models of Wave Reflection and Transmission by an Ice Floe." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61248.

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The marginal ice zone (MIZ) is the outer part of the sea-ice covered ocean, where ice can be found in the form of large floating chucks better known as floes. Since it is the area where the most part of the interaction between ice cover and ocean waves takes place, it requires careful modelling. However existing mathematical models, based on the traditional thin-plate theory, underestimate waves attenuation for the most energetic waves, since the energy dissipation occurring during the process is not taken into account. New laboratory experimental and direct numerical models are presented here. In the experimental model a thin plastic plate is tested under the action of incident waves with varying amplitudes and periods. The same experimental set-up was reproduced using a numerical model, which was developed by coupling a High Order Spectral Numerical Wave Tank with the Navier-Stokes solver IHFOAM. Data from the experiments and numerical models confirm that non-linear effects lead to a decrease of wave transmission.
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Takács, Dénes, and Gábor Stépan. "Regenerative Effect of Tire Carcass in Simple Shimmy Models." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13158.

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A simple mechanical model of the towed elastic wheel is constructed and analyzed. The lateral deformation of the tire is described by the time delayed tire model, which considers the memory effect of the contact patch. The deformation outside the contact patch is also modeled with the help of the brush model in order to take into account the effect of the deformation waves that propagate along the circumference of the tire. The mathematical model for small oscillations is composed in the form of a functional differential equation of the neutral type. The linear stability of the towed wheel is analyzed via the construction of stability charts in the plane of the relevant engineering parameters. Simulations are also presented to illustrate the regenerative effect of the tire carcass.
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Ellermann, Katrin. "The Motion of Floating Systems: Nonlinear Dynamics in Periodic and Random Waves." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92037.

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Floating systems, such as ships, barges or semi-submersibles, show a dynamical behavior which is determined by their internal structure and the operating conditions caused by external forces e.g. due to waves and wind. Due to the complexity of the system which commonly includes coupling of multiple components or nonlinear restoring forces, the response can exhibit inherently nonlinear characteristics. In this paper different models of floating systems are considered. For the idealized case of purely harmonic forcing they all show nonlinear behavior such as subharmonic motion or different steady state responses at constant operating conditions. The introduction of random disturbances leads to deviations from the idealized case which may change the overall response significantly. Advantages and limitations of the different mathematical models and the applied numerical techniques are discussed.
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Khichar, Mayank, Romir Moza, and Supreet Singh Bahga. "Effect of Surface Conduction on Propagation of Ion-Concentration Shock Waves in Isotachophoresis." In ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/icnmm2015-48089.

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Isotachophoresis (ITP) is a widely used nonlinear electrophoretic technique for preconcentration and separation of ionic species. Typically, ITP is performed in microchannels where the effect of surface conduction due to electric double layer (EDL) at channel walls is negligible compared to bulk conduction. However, when electrophoretic techniques such as ITP are integrated in nanochannels or shallow microchannels, surface conduction can alter bulk electrophoretic transport. The existing mathematical models for multispecies electrophoretic transport do not account for the competing effects of surface and bulk conduction. We present a mathematical model for multispecies electrophoretic transport incorporating the effects of surface conduction on bulk ion-transport. Our one-dimensional model is capable of describing electrophoretic systems consisting of arbitrarily large number of co-ions, having same charge polarity as the wall charge, and a single counter-ion. Based on numerical solutions of the governing equations, we show that unlike in conventional ITP where surface conduction is negligible, the zone concentrations do not obey the Kohlrausch regulating function when surface conduction is prominent. Moreover, our simulations show that surface conduction alters the propagation speeds of ion-concentration shock waves in ITP. In addition, surface conduction results in additional shock and expansion waves in ITP which are otherwise not present in conventional ITP.
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