Relevant bibliographies by topics / Coupled evolution equations

Academic literature on the topic 'Coupled evolution equations'

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Published: 14 September 2024

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Journal articles on the topic "Coupled evolution equations"

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Maruszewski, Bogdan. "Coupled evolution equations of deformable semiconductors." International Journal of Engineering Science 25, no. 2 (January 1987): 145–53. http://dx.doi.org/10.1016/0020-7225(87)90002-4.

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Yusufoğlu, Elcin, and Ahmet Bekir. "Exact solutions of coupled nonlinear evolution equations." Chaos, Solitons & Fractals 37, no. 3 (August 2008): 842–48. http://dx.doi.org/10.1016/j.chaos.2006.09.074.

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Nakagiri, Shin-ichi, and Jun-hong Ha. "COUPLED SINE-GORDON EQUATIONS AS NONLINEAR SECOND ORDER EVOLUTION EQUATIONS." Taiwanese Journal of Mathematics 5, no. 2 (June 2001): 297–315. http://dx.doi.org/10.11650/twjm/1500407338.

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Khan, K., and M. A. Akbar. "Solitary Wave Solutions of Some Coupled Nonlinear Evolution Equations." Journal of Scientific Research 6, no. 2 (April 23, 2014): 273–84. http://dx.doi.org/10.3329/jsr.v6i2.16671.

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In this article, the modified simple equation (MSE) method has been executed to find the traveling wave solutions of the coupled (1+1)-dimensional Broer-Kaup (BK) equations and the dispersive long wave (DLW) equations. The efficiency of the method for finding exact solutions has been demonstrated. It has been shown that the method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this procedure reduces the large volume of calculations. Keywords: MSE method; NLEE; BK equations; DLW equations; Solitary wave solutions. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i2.16671 J. Sci. Res. 6 (2), 273-284 (2014)
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Malfliet, W. "Travelling-wave solutions of coupled nonlinear evolution equations." Mathematics and Computers in Simulation 62, no. 1-2 (February 2003): 101–8. http://dx.doi.org/10.1016/s0378-4754(02)00182-9.

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Alabau, F., P. Cannarsa, and V. Komornik. "Indirect internal stabilization of weakly coupled evolution equations." Journal of Evolution Equations 2, no. 2 (May 1, 2002): 127–50. http://dx.doi.org/10.1007/s00028-002-8083-0.

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RYDER, E., and D. F. PARKER. "Coupled evolution equations for axially inhomogeneous optical fibres." IMA Journal of Applied Mathematics 49, no. 3 (1992): 293–309. http://dx.doi.org/10.1093/imamat/49.3.293.

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Zhao, Dan, and Zhaqilao. "Darboux transformation approach for two new coupled nonlinear evolution equations." Modern Physics Letters B 34, no. 01 (December 6, 2019): 2050004. http://dx.doi.org/10.1142/s0217984920500049.

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A new coupled Burgers equation and a new coupled KdV equation which are associated with [Formula: see text] matrix spectial problem are investigated for complete integrability and covariant property. For integrability, Lax pair and conservation laws of the two new coupled equations with four potentials are established. For covariant property, Darboux transformation (DT) is used to construct explicit solutions of the two new coupled equations.
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Khan, Kamruzzaman, and M. Ali Akbar. "Traveling Wave Solutions of Some Coupled Nonlinear Evolution Equations." ISRN Mathematical Physics 2013 (May 20, 2013): 1–8. http://dx.doi.org/10.1155/2013/685736.

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The modified simple equation (MSE) method is executed to find the traveling wave solutions for the coupled Konno-Oono equations and the variant Boussinesq equations. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It has been shown that the proposed method is direct, effective, and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this procedure reduces the large volume of calculations.
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Wan, Qian, and Ti-Jun Xiao. "Exponential Stability of Two Coupled Second-Order Evolution Equations." Advances in Difference Equations 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/879649.

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Dissertations / Theses on the topic "Coupled evolution equations"

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Pauletti, Miguel Sebastian. "Parametric AFEM for geometric evolution equations and coupled fluid-membrane interaction." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8603.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Brand, Christopher [Verfasser], and Georg [Akademischer Betreuer] Dolzmann. "Coupled Evolution Equations for Immersions of Closed Manifolds and Vector Fields / Christopher Brand ; Betreuer: Georg Dolzmann." Regensburg : Universitätsbibliothek Regensburg, 2019. http://d-nb.info/1185758143/34.

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Trad, Farah. "Stability of some hyperbolic systems with different types of controls under weak geometric conditions." Electronic Thesis or Diss., Valenciennes, Université Polytechnique Hauts-de-France, 2024. http://www.theses.fr/2024UPHF0015.

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Le but de cette thèse est d'étudier la stabilisation de certaines équations d'évolution du second ordre. Tout d’abord, nous nous concentrons sur l’étude de la stabilisation d’équations d’évolution du second ordre de type hyperbolique localement faiblement couplées, caractérisées par un amortissement direct dans une seule des deux équations. Comme de tels systèmes ne sont pas exponentiellement stables, nous souhaitons déterminer les taux de décroissance de l’énergie polynomiale. Nos principales contributions concernent les propriétés abstraites de stabilité forte et polynomiale, qui sont dérivées des propriétés de stabilité de deux problèmes auxiliaires : l'équation avec amortissement unique et l'équation avec amortissement liée à l'opérateur de couplage. La principale nouveauté est que les taux de décroissance d'énergie polynomiale sont obtenus dans plusieurs situations importantes non abordées auparavant, y compris le cas où l'opérateur de couplage n'est ni partiellement coercitif ni nécessairement limité. Les principaux outils utilisés dans notre étude sont l’approche du domaine fréquentiel combinée à une nouvelle technique de multiplicateurs basée sur les solutions des équations résolvantes des problèmes auxiliaires susmentionnés. Le cadre abstrait développé est ensuite illustré par plusieurs exemples concrets non traités auparavant. Ensuite, la stabilisation d'une équation de plaque de Kirchhoff bidimensionnelle avec des conditions aux limites acoustiques généralisées est examinée. En employant une approche spectrale combinée à un critère général d'Arendt-Batty, nous établissons d'abord la forte stabilité de notre modèle. Nous prouvons ensuite que le système ne se dégrade pas de façon exponentielle. Cependant, à condition que les coefficients des conditions aux limites acoustiques satisfassent à certaines hypothèses, nous prouvons que l'énergie satisfait à différents taux de décroissance de l'énergie polynomiale en fonction du comportement de notre système auxiliaire. Nous étudions également le taux de décroissance sur les domaines satisfaisant aux conditions aux limites du multiplicateur. De plus, nous présentons quelques exemples appropriés et montrons que nos hypothèses ont été correctement définies. Enfin, nous considérons un problème de transmission d'ondes avec des conditions aux limites acoustiques généralisées dans un espace unidimensionnel, dont nous étudions la stabilité théoriquement et numériquement. Dans la partie théorique nous prouvons que notre système est fortement stable. Nous présentons ensuite divers taux de décroissance d'énergie polynomiale, à condition que les coefficients des conditions aux limites acoustiques satisfassent certaines hypothèses, nous donnons des exemples pertinents pour montrer que nos hypothèses sont correctes. Dans la partie numérique, nous étudions une approximation numérique de notre système utilisant la discrétisation en volumes finis dans un schéma à variables spatiales et différences finies dans le temps
The purpose of this thesis is to investigate the stabilization of certain second order evolution equations. First, we focus on studying the stabilization of locally weakly coupled second order evolution equations of hyperbolic type, characterized by direct damping in only one of the two equations. As such systems are not exponentially stable , we are interested in determining polynomial energy decay rates. Our main contributions concern abstract strong and polynomial stability properties, which are derived from the stability properties of two auxiliary problems: the sole damped equation and the equation with a damping related to the coupling operator. The main novelty is thatthe polynomial energy decay rates are obtained in several important situations previously unaddressed, including the case where the coupling operator is neither partially coercive nor necessarily bounded. The main tools used in our study are the frequency domain approach combined with new multipliers technique based on the solutions of the resolvent equations of the aforementioned auxiliary problems. The abstract framework developed is then illustrated by several concrete examples not treated before. Next, the stabilization of a two-dimensional Kirchhoff plate equation with generalized acoustic boundary conditions is examined. Employing a spectrum approach combined with a general criteria of Arendt-Batty, we first establish the strong stability of our model. We then prove that the system doesn't decay exponentially. However, provided that the coefficients of the acoustic boundary conditions satisfy certain assumptions we prove that the energy satisfies varying polynomial energy decay rates depending on the behavior of our auxiliary system. We also investigate the decay rate on domains satisfying multiplier boundary conditions. Further, we present some appropriate examples and show that our assumptions have been set correctly. Finally, we consider a wave wave transmission problem with generalized acoustic boundary conditions in one dimensional space, where we investigate the stability theoretically and numerically. In the theoretical part we prove that our system is strongly stable. We then present diverse polynomial energy decay rates provided that the coefficients of the acoustic boundary conditions satisfy some assumptions. we give relevant examples to show that our assumptions are correct. In the numerical part, we study a numerical approximation of our system using finite volume discretization in a spatial variable and finite difference scheme in time
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Lienstromberg, Christina. "On Microelectromechanical Systems with General Permittivity." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLN007/document.

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Dans le cadre de la thèse des modèles physico-mathématiques pour des microsystèmes électromécaniques avec une permittivité générale sont développés et analysés par des méthodes mathématiques modernes du domaine des équations aux dérivées partielles. En particulier ces systèmes sont à frontière libre et pour conséquence difficiles à traiter. Des méthodes numériques ont été développées pour valider les résultats analytiques obtenus
In the framework of this thesis physical/mathematical models for microelectromechanical systems with general permittivity have been developed and analysed with modern mathematical methods from the domain of partial differential equations. In particular these systems are moving boundary problems and thus difficult to handle. Numerical methods have been developed in order to validate the obtained analytical results
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Petraco, Nicholas Dominick Koslap. "Benchmark open-shell coupled cluster studies and the evolution of nonvariational solutions to the Schrödinger equation." 2002. http://purl.galileo.usg.edu/uga%5Fetd/petraco%5Fnicholas%5Fd%5F200205%5Fphd.

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Thesis (Ph. D.)--University of Georgia, 2002.
Directed by Henary F. Schaefer, III. Includes articles published in, and an article submitted to The journal of chemical physics. Includes bibliographical references.
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Book chapters on the topic "Coupled evolution equations"

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Crisan, Dan, and Prince Romeo Mensah. "Blow-Up of Strong Solutions of the Thermal Quasi-Geostrophic Equation." In Mathematics of Planet Earth, 1–14. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_1.

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AbstractThe Thermal Quasi-Geostrophic (TQG) equation is a coupled system of equations that governs the evolution of the buoyancy and the potential vorticity of a fluid. It has a local in time solution as proved in Crisan et al. (Theoretical and computational analysis of the thermal quasi-geostrophic model. Preprint arXiv:2106.14850, 2021). In this paper, we give a criterion for the blow-up of solutions to the Thermal Quasi-Geostrophic equation, in the spirit of the classical Beale–Kato–Majda blow-up criterion (cf. Beale et al., Comm. Math. Phys. 94(1), 61–66, 1984) for the solution of the Euler equation.
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Saha Ray, Santanu. "New Exact Traveling Wave Solutions of the Coupled Schrödinger–Boussinesq Equations and Tzitzéica-Type Evolution Equations." In Nonlinear Differential Equations in Physics, 199–229. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-1656-6_6.

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El Allaoui, Abdelati, Said Melliani, JinRong Wang, Youssef Allaoui, and Lalla Saadia Chadli. "A Generalized Coupled System of Impulsive Integro-Differential Evolution Equations with Mutual Boundary Values." In Lecture Notes in Networks and Systems, 1–16. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-12416-7_1.

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Takabe, Hideaki. "Introduction." In Springer Series in Plasma Science and Technology, 1–14. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-45473-8_1.

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AbstractA brief overview of the fluid model to describe most of the plasmas is given. Assuming the velocity distributions of electrons and ions are shifted Maxwellian distribution, plasmas can be described with fluid approximation regardless they are collisional or collisionless. The time evolution of laser plasmas is described with the fluid model with non-ideal equation of state, non-local electron transport, radiation transport, and so on. Modeling atomic state of plasma, effective charge, spectral opacity, and emissivity are calculated to couple with the energy equation of the electron fluid. As a reference to the plasma physics explained in this book, the physics scenario of laser fusion dynamics is used to know what kinds of physics become to couple from laser absorption to the fusion energy production through the implosion dynamics.It is emphasized that the development of a physics-integrated code is important to study such laser-produced plasmas. Along with the advancement of technology for diagnostics and lasers, the analysis of the experimental data has helped the improvement of the physics models by comparing the experimental data to the corresponding simulations. Considering the technically limited number of implosion experiments with a huge laser facility, the advancement of the physics-integrated codes is becoming the main issue to increase the quality of analysis and design for better performance experiments. The progress of computer performance and advancement of experiments are now non-separable in complicated nonlinear systems such as plasma physics even within the hydrodynamic modeling of plasmas.
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Zheng, Songmu. "Decay of Solutions to Linear Evolution Equations." In Nonlinear parabolic equations and hyperbolic-parabolic coupled systems, 33–68. Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9780429154225-2.

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Nitzan, Abraham. "The quantum mechanical density operator and its time evolution." In Chemical Dynamics in Condensed Phases, 343–94. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780191947971.003.0010.

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Abstract This chapter introduces the density operator and the Liouville equation and outlines how reduced dynamical description of open quantum systems naturally leads to the appearance of relaxation processes. (1) The density operator and the quantum Liouville equation (the density matrix for a pure system, statistical mixtures, representations, coherences, thermodynamic equilibrium). (2) An example: The time evolution of a two-level system in the density matrix formalism. (3) Reduced descriptions. (4) Time evolution equations for reduced density operators: The quantum master equation (projection operators, The Nakajima–Zwanzig equation, Derivation of the quantum master equation using the thermal projector, The quantum master equation in the interaction representation, The Markovian limit—the Redfield equation, The secular approximation and the Lindblad equation). (5) The Lindblad equation in the ‘Heisenberg representation’. (6) Relaxation of a two-level system and a harmonic oscillator revisited. (7) The optically driven two-level system in a thermal environment—the Bloch equations. (8) The oscillating dipole model of a two-level molecule. (9) Analogy of a coupled two-level system to a spin ½ system in a magnetic field.
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"General Relativity Evolution of the Photons in Dielectrics." In Quantum and Optical Dynamics of Matter for Nanotechnology, 361–89. IGI Global, 2014. http://dx.doi.org/10.4018/978-1-4666-4687-2.ch010.

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Basic Einstein general relativity equations are linearized and coupled with Maxwell electromagnetic field equations to produce local gravitationally corrected Minkowsky space metrics; fundamental application on gravity action of an intense laser beam upon a weaker parallel one in dielectrics is undertaken towards evaluating of the space deviation phase shift and confirming the general equivalence principle of inertia for phonons in nanomaterials.
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Gerbeau, J. F., and C. Le Bris. "Mathematical Study of a Coupled System Arising in Magnetohydrodynamics." In Evolution Equations and Their Applications in Physical and Life Sciences, 355–67. CRC Press, 2019. http://dx.doi.org/10.1201/9780429187810-30.

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Filipovic, Nenad, Milos Radovic, Dalibor D. Nikolic, Igor Saveljic, Zarko Milosevic, Themis P. Exarchos, Gualtiero Pelosi, Dimitrios I. Fotiadis, and Oberdan Parodi. "Computer Predictive Model for Plaque Formation and Progression in the Artery." In Coronary and Cardiothoracic Critical Care, 220–45. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-8185-7.ch012.

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In this chapter we described predictive model for plaque formation and progression in the coronary and carotid artery. A full three-dimensional model for plaque formation and progression, coupled with blood flow and LDL concentration is analysed. The Navier-Stokes equations together with the Darcy law for model blood filtration and Kedem-Katchalsky equations are implemented. Additionally, the system of three additional reaction-diffusion equations for simulation of the inflammatory process is coupled with full incremental iterative procedure. We developed hybrid genetic algorithm for fitting parameters of ODE model for oxidized LDL, macrophage, smooth muscle cell and foam cell concentration evolution in time. The animal carotid and coronary artery after 2 month of high fat diet are examined. We compared with CT our computer model of the plaque size for three groups of patients: De-novo, Old-lesions and Control patients. Detailed shear stress distributions for baseline and follow-up for these patients are given. There is a good matching for plaque size and location.
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Filipovic, Nenad, Milos Radovic, Dalibor D. Nikolic, Igor Saveljic, Zarko Milosevic, Themis P. Exarchos, Gualtiero Pelosi, Dimitrios I. Fotiadis, and Oberdan Parodi. "Computer Predictive Model for Plaque Formation and Progression in the Artery." In Handbook of Research on Trends in the Diagnosis and Treatment of Chronic Conditions, 279–300. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-8828-5.ch013.

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In this chapter we described predictive model for plaque formation and progression in the coronary and carotid artery. A full three-dimensional model for plaque formation and progression, coupled with blood flow and LDL concentration is analysed. The Navier-Stokes equations together with the Darcy law for model blood filtration and Kedem-Katchalsky equations are implemented. Additionally, the system of three additional reaction-diffusion equations for simulation of the inflammatory process is coupled with full incremental iterative procedure. We developed hybrid genetic algorithm for fitting parameters of ODE model for oxidized LDL, macrophage, smooth muscle cell and foam cell concentration evolution in time. The animal carotid and coronary artery after 2 month of high fat diet are examined. We compared with CT our computer model of the plaque size for three groups of patients: De-novo, Old-lesions and Control patients. Detailed shear stress distributions for baseline and follow-up for these patients are given. There is a good matching for plaque size and location.
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Conference papers on the topic "Coupled evolution equations"

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Wang, Ya-Guang. "A new approach to study hyperbolic-parabolic coupled systems." In Evolution Equations Propagation Phenomena - Global Existence - Influence of Non-Linearities. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc60-0-18.

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Romeo, Francesco, and Achille Paolone. "Propagation Properties of Three-Coupled Periodic Mechanical Systems." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85617.

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General three-coupled periodic systems are dealt with by means of transfer matrices of single units. The solutions of the associated characteristic equation are discussed in terms of invariant quantities by exploiting the well-known reversibility of its coefficients. An exhaustive description of the free wave propagation patterns is given on the invariants’ space where propagation domains with qualitatively different character are identified. Afterwards, two three-coupled periodic mechanical models are considered: pipes and truss beams. A nonlinear mapping from the invariants’ space to the physical parameters plane provides with a concise representation of the pattern of the propagation domains. A mechanical interpretation associated with the boundaries of these regions is given. The analyzed models give rise to equations of motion where the three-coupled nature stems from the coupling between longitudinal (mono-coupled) and transversal (bi-coupled) dynamics. The evolution of the propagation properties when the coupling parameters tend to vanish is eventually discussed.
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Leftheriotis, Georgios A., and Athanassios A. Dimas. "Coupled Simulation of Oscillatory Flow, Sediment Transport and Morphology Evolution of Ripples Based on the Immersed Boundary Method." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-24006.

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In the present study, numerical simulations of oscillatory flow over a rippled bottom, coupled with bed and suspended sediment transport, as well as the resulting morphology evolution, are performed. The simulations are based on the numerical solution of the Navier-Stokes equations and the advection-diffusion equation for the suspended load, while empirical formulas are used for the bed load. The bed morphological evolution is obtained by the numerical solution of the conservation of sediment mass equation. A fractional time-step scheme is used for the temporal discretization, while finite differences are used for the spatial discretization on a Cartesian grid. The Immersed Boundary method is implemented for the imposition of fluid and sediment boundary conditions on the ripple surface. Two types of ripples are examined, i.e., ripples of parabolic shape with sharp crests and sinusoidal ripples, and cases of ripple length to orbital motion amplitude ratio of 1.6 and ripple height to orbital motion amplitude ratios of 0.16, 0.20 and 0.24, at Reynolds number equal to 5×103. The effect of ripple steepness and ripple shape on suspended sediment and ripple migration is discussed.
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Lehmann, B., D. Kraus, and A. Kummert. "Coupled curve evolution equations for ternary images in sidescan-sonar images guided by Lamé curves for object recognition." In 2012 19th IEEE International Conference on Image Processing (ICIP 2012). IEEE, 2012. http://dx.doi.org/10.1109/icip.2012.6467419.

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de Freitas Rachid, Felipe Bastos, José Henrique Carneiro de Araujo, and Renan Martins Baptista. "A Fully-Coupled Transient Model for Predicting Interface Contamination in Product Pipelines." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/htd-24180.

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Abstract This work presents a coupled fluid transient model to describe the mixing phenomenon arising in batch transfers in petroleum pipelines. The concentration evolution described by the dispersion of matter at the products’ interface is properly taken into account on the mass and momentum balance equations for the mixture as a whole. The resulting mathematical problem is formed by a system of non-linear partial differential equations which is solved by means of an operator splitting technique, combined with a Glimm’s scheme and predictor-corrector method. The influence of stopping the line during a batch transfer on the mixing volume is preliminarily analyzed for a particular batch.
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Schrade, David, Bai-Xiang Xu, Ralf Mu¨ller, and Dietmar Gross. "On Phase Field Modeling of Ferroelectrics: Parameter Identification and Verification." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-411.

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This contribution introduces a thermodynamically consistent, fully electro-mechanically coupled micro-mechanical model for ferroelectric materials. Adopting a phase field concept, in which the spontaneous polarization is used as order parameter, a Ginzburg-Landau type theory is formulated for the evolution of the order parameter. The equations are discretized within the scope of the Finite Element Method, and implicit time integration is used to solve the non-linear evolution equation. Examples illustrate the physical meaning of phase field parameters and give an application to multi-axial switching in which experimental results are used for comparison.
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Aceves, A. B., C. De Anglis, J. V. Moloney, and S. Wabnitz. "Counterpropagating waves in periodic nonlinear structures." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.mww3.

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In this paper the authors will present both numerical and analytical results on the coupled mode equations that describe the evolution of counterpropagating beams in periodic waveguides. These coupled mode equations are a generalization, by an addition of one transverse diffraction term, of the equations that describe wave trains in a fiber filter whose grating is of the order of the wavelength of light. We will first show how the well known gap soliton solutions of the fiber filter extend to the planar waveguide structure. These solutions represent beams that are cw in the transverse direction and have the soliton profile in the direction of propagation. We then numerically show whether transverse modulational instabilities arise. Finally, we numerically study the dynamics of pulses propagating along the waveguide. Here, we compare the dynamics of the coupled mode theory with that of the two dimensional nonlinear Schrodinger equation (2D NLS), which has been suggested as a good limit when the pulses are spatially broad. An interesting feature of this comparison is that for the 2D NLS in the anomalous regime, a collapse in finite time is predicted. We then want to determine if this also happens in the coupled mode analysis.
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Tao, Sha, and Benxin Wu. "Early-Stage Evolution of Electrons Emitted From Metal Target Surface During Ultrashort Laser Ablation in Vacuum." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63258.

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The early-stage evolution of electrons emitted from a metal target surface during ultrashort laser ablation in vacuum has been studied using a physics-based model. This kind of research work has been rarely reported in literature. In the model, the target heat transfer process is simulated by solving the two-temperature heat transfer equations, based on which the photoemission and thermionic emission of electrons from the target surface are calculated. The early-stage evolution of emitted electrons is described by solving the electron mass, momentum, and energy conservation equations, coupled with the Poisson’s equation that governs the developed electric field. The study shows that a relatively very high free electron density can be developed near the target surface, and the front of emitted electrons propagates very fast into the vacuum. The developed electric field strongly affects the evolution of emitted electrons. Using the physics-based model, the temporal variation and the spatial distribution of the emitted electron number density, and velocity will be studied and discussed. The early-stage evolution of the emitted electrons may affect the possible subsequent hydrodynamic motion in the target, and the resulted plasma formation and material removal (laser ablation) processes. Therefore, this study provides very useful information for the understanding of ultrashort laser-material interaction, laser-induced plasma, laser ablation (machining), and other relevant processes.
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Athanassoulis, Gerassimos A., and Konstandinos A. Belibassakis. "A Nonlinear Coupled-Mode Model for Water Waves Over a General Bathymetry." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28411.

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A non-linear coupled-mode system of horizontal equations is derived with the aid of Luke’s (1967) variational principle, which models the evolution of nonlinear water waves in intermediate depth over a general bathymetry. The vertical structure of the wave field is exactly represented by means of a local-mode series expansion of the wave potential, Athanassoulis & Belibassakis (2000). This series contains the usual propagating and evanescent modes, plus two additional modes, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The system fully accounts for the effects of non-linearity and dispersion.
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10

Krishna, C. Vamsi, and Santosh Hemchandra. "Reduced Order Modelling of Combustion Instability in a Backward Facing Step Combustor." In ASME 2013 Gas Turbine India Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gtindia2013-3559.

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This paper develops a fully coupled time domain Reduced Order Modelling (ROM) approach to model unsteady combustion dynamics in a backward facing step combustor. The acoustic field equations are projected onto the canonical acoustic eigenmodes of the systems to obtain a coupled system of modal evolution equations. The heat release response of the flame is modelled using the G-equation approach. Vortical velocity fluctuations that arise due to shear layer rollup downstream of the step are modelled using a simplified 1D-advection equation whose phase speed is determined from a linear, local, temporal stability analysis of the shear layer, just downstream of the step. The hydrodynamic stability analysis reveals a abrupt change in the value of disturbance phase speed from unity for Re < Recrit to 0.5 for Re > Recrit, where Recrit for the present geometry was found to be ≈ 10425. The results for self-excited flame response show highly wrinkled flame shapes that are qualitatively similar to those seen in prior experiments of acoustically forced flames. The effect of constructive and destructive interference between the two contributions to flame surface wrinkling results in high amplitude wrinkles for the case when Kc → 1.
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Reports on the topic "Coupled evolution equations"

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Zemach, Charles, and Susan Kurien. Notes from 1999 on computational algorithm of the Local Wave-Vector (LWV) model for the dynamical evolution of the second-rank velocity correlation tensor starting from the mean-flow-coupled Navier-Stokes equations. Office of Scientific and Technical Information (OSTI), November 2016. http://dx.doi.org/10.2172/1332214.

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