American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Bifurcation and bursting in Morris-Lecar model for class I and class II excitability
  • PROC Home
  • This Issue
  • Next Article
    About maximum principles for one of the components of solution vector and stability for systems of linear delay differential equations
2011, 2011(Special): 381-390. doi: 10.3934/proc.2011.2011.381

Dispersion relations for supersonic multiple virtual jets

Joshua Du 1, and  Liancheng Wang 2,

1. 

Department of Mathematics, Kennesaw State University, 1000 Chastain Rd, P.O. Box 1204, Kennesaw, GA 30144
2. 

Department of Mathematics & Statistics, Kennesaw State University, Kennesaw, GA 30144

Received  July 2010 Revised  April 2011 Published  October 2011

In this paper, a special type of circulant matrices, circulant trinity matrices, are first introduced and some properties of these matrices are investigated. Then, in studying a supersonic circular N-jet vortex sheet model, circulant trinity matrices are used to classify the general solutions of the $N$-jet model into 2$N$ families. Finally, the dispersion relations of $N$-jets for each family are derived by using Graf’s Addition Theorem.
Keywords: dispersion relations, Circulant trinity matrix, classification of solutions.
Mathematics Subject Classification: 76J20, 76E99.
Citation: Joshua Du, Liancheng Wang. Dispersion relations for supersonic multiple virtual jets. Conference Publications, 2011, 2011 (Special) : 381-390. doi: 10.3934/proc.2011.2011.381
[1]

Christophe Cheverry, Adrien Fontaine. Dispersion relations in cold magnetized plasmas. Kinetic & Related Models, 2017, 10 (2) : 373-421. doi: 10.3934/krm.2017015
[2]

Adrian Constantin. Dispersion relations for periodic traveling water waves in flows with discontinuous vorticity. Communications on Pure & Applied Analysis, 2012, 11 (4) : 1397-1406. doi: 10.3934/cpaa.2012.11.1397
[3]

Calin Iulian Martin. Dispersion relations for periodic water waves with surface tension and discontinuous vorticity. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3109-3123. doi: 10.3934/dcds.2014.34.3109
[4]

Houduo Qi, ZHonghang Xia, Guangming Xing. An application of the nearest correlation matrix on web document classification. Journal of Industrial & Management Optimization, 2007, 3 (4) : 701-713. doi: 10.3934/jimo.2007.3.701
[5]

Calin Iulian Martin, Adrián Rodríguez-Sanjurjo. Dispersion relations for steady periodic water waves of fixed mean-depth with two rotational layers. Discrete & Continuous Dynamical Systems, 2019, 39 (9) : 5149-5169. doi: 10.3934/dcds.2019209
[6]

Delia Ionescu-Kruse, Anca-Voichita Matioc. Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3045-3060. doi: 10.3934/dcds.2014.34.3045
[7]

Shengfu Deng. Periodic solutions and homoclinic solutions for a Swift-Hohenberg equation with dispersion. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1647-1662. doi: 10.3934/dcdss.2016068
[8]

Haiyun Deng, Hairong Liu, Long Tian. Classification of singular sets of solutions to elliptic equations. Communications on Pure & Applied Analysis, 2020, 19 (6) : 2949-2964. doi: 10.3934/cpaa.2020129
[9]

Yuxia Guo, Jianjun Nie. Classification for positive solutions of degenerate elliptic system. Discrete & Continuous Dynamical Systems, 2019, 39 (3) : 1457-1475. doi: 10.3934/dcds.2018130
[10]

Mustafa Hasanbulli, Yuri V. Rogovchenko. Classification of nonoscillatory solutions of nonlinear neutral differential equations. Conference Publications, 2009, 2009 (Special) : 340-348. doi: 10.3934/proc.2009.2009.340
[11]

Xia Huang, Liping Wang. Classification to the positive radial solutions with weighted biharmonic equation. Discrete & Continuous Dynamical Systems, 2020, 40 (8) : 4821-4837. doi: 10.3934/dcds.2020203
[12]

Chang-Shou Lin, Lei Zhang. Classification of radial solutions to Liouville systems with singularities. Discrete & Continuous Dynamical Systems, 2014, 34 (6) : 2617-2637. doi: 10.3934/dcds.2014.34.2617
[13]

Lei Zhang, Anfu Zhu, Aiguo Wu, Lingling Lv. Parametric solutions to the regulator-conjugate matrix equations. Journal of Industrial & Management Optimization, 2017, 13 (2) : 623-631. doi: 10.3934/jimo.2016036
[14]

A. Cibotarica, Jiu Ding, J. Kolibal, Noah H. Rhee. Solutions of the Yang-Baxter matrix equation for an idempotent. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 347-352. doi: 10.3934/naco.2013.3.347
[15]

Yangyang Xu, Wotao Yin, Stanley Osher. Learning circulant sensing kernels. Inverse Problems & Imaging, 2014, 8 (3) : 901-923. doi: 10.3934/ipi.2014.8.901
[16]

Phuong Le. Classification of nonnegative solutions to an equation involving the Laplacian of arbitrary order. Discrete & Continuous Dynamical Systems, 2021, 41 (4) : 1605-1626. doi: 10.3934/dcds.2020333
[17]

Kuan-Ju Huang, Yi-Jung Lee, Tzung-Shin Yeh. Classification of bifurcation curves of positive solutions for a nonpositone problem with a quartic polynomial. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1497-1514. doi: 10.3934/cpaa.2016.15.1497
[18]

Soohyun Bae. Classification of positive solutions of semilinear elliptic equations with Hardy term. Conference Publications, 2013, 2013 (special) : 31-39. doi: 10.3934/proc.2013.2013.31
[19]

Veronica Felli, Ana Primo. Classification of local asymptotics for solutions to heat equations with inverse-square potentials. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 65-107. doi: 10.3934/dcds.2011.31.65
[20]

Lidan Wang, Lihe Wang, Chunqin Zhou. Classification of positive solutions for fully nonlinear elliptic equations in unbounded cylinders. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1241-1261. doi: 10.3934/cpaa.2021019

 Impact Factor: 

Tools

Metrics

  • PDF downloads (54)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences