American Institute of Mathematical Sciences

Advanced
September  2014, 19(7): 2297-2312. doi: 10.3934/dcdsb.2014.19.2297

q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics

Colin Rogers 1, and  Tommaso Ruggeri 2,

1. 

Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems, School of Mathematics, The University of New South Wales, Sydney, NSW2052, Australia
2. 

Department of Mathematics & Research Centre of Applied Mathematics (CIRAM), University of Bologna, Italy

Received  March 2013 Revised  March 2014 Published  August 2014

Integrable reductions in non-isothermal spatial gasdynamics are isolated corresponding to q-Gaussian density distributions. The availability of a Tsallis parameter q in the reductions permits the construction via a Madelung transformation of wave packet solutions of a class of associated q-logarithmic nonlinear Schrödinger equations involving a de Broglie-Bohm quantum potential term.
Keywords: gasdynamics., Q-Gaussian integrability, Tsallis statistical mechanics.
Mathematics Subject Classification: 37K10, 76B4.
Citation: Colin Rogers, Tommaso Ruggeri. q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2297-2312. doi: 10.3934/dcdsb.2014.19.2297
References:
[1]

Bull. Acad. Polon. Sci., 23 (1974), 461-466.  Google Scholar

[2]

Ann. Phys., 100 (1976), 62-93. doi: 10.1016/0003-4916(76)90057-9.  Google Scholar

[3]

Physica Scripta, 20 (1979), 539-544. doi: 10.1088/0031-8949/20/3-4/033.  Google Scholar

[4]

Phys. Rev., 85 (1952), 166-193. doi: 10.1103/PhysRev.85.166.  Google Scholar

[5]

Opt. Lett., 22 (1997), 1080-1082. doi: 10.1364/OL.22.001080.  Google Scholar

[6]

Physica A, 392 (2013), 2631-2642. doi: 10.1016/j.physa.2012.12.041.  Google Scholar

[7]

(1965), 244-246. Google Scholar

[8]

J. Math. Mech., 18 (1968), 91-101. doi: 10.1512/iumj.1969.18.18009.  Google Scholar

[9]

J. Fluid Mech., 325 (1996), 113-144. doi: 10.1017/S0022112096008051.  Google Scholar

[10]

J. Phys. A: Math. Theor., 43 (2010), 165207, 11pp. doi: 10.1088/1751-8113/43/16/165207.  Google Scholar

[11]

Oxford University Press, Oxford, 2004.  Google Scholar

[12]

J. Appl. Phys., 100 (2006), 073304. doi: 10.1063/1.2345460.  Google Scholar

[13]

Opt. Commun., 283 (2010), 318-322. doi: 10.1016/j.optcom.2009.09.034.  Google Scholar

[14]

Phys. Rev. E, 61 (2000), 3122-3126. Google Scholar

[15]

J. Plasma Phys., 73 (2007), 257-272. doi: 10.1017/S0022377806004648.  Google Scholar

[16]

Zeit für Phys., 40 (1926), 322-326. Google Scholar

[17]

Springer, New York, 2006.  Google Scholar

[18]

Springer-Verlag London, Ltd., London, 2011. doi: 10.1007/978-0-85729-355-8.  Google Scholar

[19]

Phys. Rev. Lett., 106 (2011), 140601. doi: 10.1103/PhysRevLett.106.140601.  Google Scholar

[20]

Europhysics Letters, 97 (2012), 41001. Google Scholar

[21]

J. Phys. A: Math. Theor., 41 (2008), 452001, 9pp. doi: 10.1088/1751-8113/41/45/452001.  Google Scholar

[22]

J. Rational Mech. Anal, 1 (1952), 425-497.  Google Scholar

[23]

Phys. Lett. A, 78 (1980), 4-6. doi: 10.1016/0375-9601(80)90789-6.  Google Scholar

[24]

J. Math. Phys., 21 (1980), 1583-1587. doi: 10.1063/1.524625.  Google Scholar

[25]

J. Phys. A. Math. & Gen., 26 (1993), 2625-2633. doi: 10.1088/0305-4470/26/11/012.  Google Scholar

[26]

J. Math. Anal. Appl., 198 (1996), 194-220. doi: 10.1006/jmaa.1996.0076.  Google Scholar

[27]

Stud. Appl. Math., 125 (2010), 275-299. doi: 10.1111/j.1467-9590.2010.00488.x.  Google Scholar

[28]

J. Phys. A: Math. Theor., 43 (2010), 455214, 15pp. doi: 10.1088/1751-8113/43/45/455214.  Google Scholar

[29]

J. Math. Phys., 52 (2011), 083701, 20pp. doi: 10.1063/1.3622595.  Google Scholar

[30]

Nonlinearity, 24 (2011), 3165-3178. doi: 10.1088/0951-7715/24/11/009.  Google Scholar

[31]

Stud. Appl. Math., 129 (2012), 389-413. doi: 10.1111/j.1467-9590.2012.00557.x.  Google Scholar

[32]

Physica Scripta, 84 (2011), 045004. Google Scholar

[33]

J. Math. Anal. Appl., 266 (2002), 55-69. doi: 10.1006/jmaa.2001.7685.  Google Scholar

[34]

J. Phys. A: Math. Gen., 29 (1996), 903-911. doi: 10.1088/0305-4470/29/4/017.  Google Scholar

[35]

Stud. Appl. Math., 130 (2013), 49-79. doi: 10.1111/j.1467-9590.2012.00559.x.  Google Scholar

[36]

Opt. Lett., 22 (1997), 16-18. doi: 10.1364/OL.22.000016.  Google Scholar

[37]

Springer, New York, 2009.  Google Scholar

[38]

Phys. Rev., 175 (1968), 256-266. doi: 10.1103/PhysRev.175.256.  Google Scholar

show all references

References:
[1]

Bull. Acad. Polon. Sci., 23 (1974), 461-466.  Google Scholar

[2]

Ann. Phys., 100 (1976), 62-93. doi: 10.1016/0003-4916(76)90057-9.  Google Scholar

[3]

Physica Scripta, 20 (1979), 539-544. doi: 10.1088/0031-8949/20/3-4/033.  Google Scholar

[4]

Phys. Rev., 85 (1952), 166-193. doi: 10.1103/PhysRev.85.166.  Google Scholar

[5]

Opt. Lett., 22 (1997), 1080-1082. doi: 10.1364/OL.22.001080.  Google Scholar

[6]

Physica A, 392 (2013), 2631-2642. doi: 10.1016/j.physa.2012.12.041.  Google Scholar

[7]

(1965), 244-246. Google Scholar

[8]

J. Math. Mech., 18 (1968), 91-101. doi: 10.1512/iumj.1969.18.18009.  Google Scholar

[9]

J. Fluid Mech., 325 (1996), 113-144. doi: 10.1017/S0022112096008051.  Google Scholar

[10]

J. Phys. A: Math. Theor., 43 (2010), 165207, 11pp. doi: 10.1088/1751-8113/43/16/165207.  Google Scholar

[11]

Oxford University Press, Oxford, 2004.  Google Scholar

[12]

J. Appl. Phys., 100 (2006), 073304. doi: 10.1063/1.2345460.  Google Scholar

[13]

Opt. Commun., 283 (2010), 318-322. doi: 10.1016/j.optcom.2009.09.034.  Google Scholar

[14]

Phys. Rev. E, 61 (2000), 3122-3126. Google Scholar

[15]

J. Plasma Phys., 73 (2007), 257-272. doi: 10.1017/S0022377806004648.  Google Scholar

[16]

Zeit für Phys., 40 (1926), 322-326. Google Scholar

[17]

Springer, New York, 2006.  Google Scholar

[18]

Springer-Verlag London, Ltd., London, 2011. doi: 10.1007/978-0-85729-355-8.  Google Scholar

[19]

Phys. Rev. Lett., 106 (2011), 140601. doi: 10.1103/PhysRevLett.106.140601.  Google Scholar

[20]

Europhysics Letters, 97 (2012), 41001. Google Scholar

[21]

J. Phys. A: Math. Theor., 41 (2008), 452001, 9pp. doi: 10.1088/1751-8113/41/45/452001.  Google Scholar

[22]

J. Rational Mech. Anal, 1 (1952), 425-497.  Google Scholar

[23]

Phys. Lett. A, 78 (1980), 4-6. doi: 10.1016/0375-9601(80)90789-6.  Google Scholar

[24]

J. Math. Phys., 21 (1980), 1583-1587. doi: 10.1063/1.524625.  Google Scholar

[25]

J. Phys. A. Math. & Gen., 26 (1993), 2625-2633. doi: 10.1088/0305-4470/26/11/012.  Google Scholar

[26]

J. Math. Anal. Appl., 198 (1996), 194-220. doi: 10.1006/jmaa.1996.0076.  Google Scholar

[27]

Stud. Appl. Math., 125 (2010), 275-299. doi: 10.1111/j.1467-9590.2010.00488.x.  Google Scholar

[28]

J. Phys. A: Math. Theor., 43 (2010), 455214, 15pp. doi: 10.1088/1751-8113/43/45/455214.  Google Scholar

[29]

J. Math. Phys., 52 (2011), 083701, 20pp. doi: 10.1063/1.3622595.  Google Scholar

[30]

Nonlinearity, 24 (2011), 3165-3178. doi: 10.1088/0951-7715/24/11/009.  Google Scholar

[31]

Stud. Appl. Math., 129 (2012), 389-413. doi: 10.1111/j.1467-9590.2012.00557.x.  Google Scholar

[32]

Physica Scripta, 84 (2011), 045004. Google Scholar

[33]

J. Math. Anal. Appl., 266 (2002), 55-69. doi: 10.1006/jmaa.2001.7685.  Google Scholar

[34]

J. Phys. A: Math. Gen., 29 (1996), 903-911. doi: 10.1088/0305-4470/29/4/017.  Google Scholar

[35]

Stud. Appl. Math., 130 (2013), 49-79. doi: 10.1111/j.1467-9590.2012.00559.x.  Google Scholar

[36]

Opt. Lett., 22 (1997), 16-18. doi: 10.1364/OL.22.000016.  Google Scholar

[37]

Springer, New York, 2009.  Google Scholar

[38]

Phys. Rev., 175 (1968), 256-266. doi: 10.1103/PhysRev.175.256.  Google Scholar

[1]

W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349
[2]

Rama Ayoub, Aziz Hamdouni, Dina Razafindralandy. A new Hodge operator in discrete exterior calculus. Application to fluid mechanics. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021062
[3]

Braxton Osting, Jérôme Darbon, Stanley Osher. Statistical ranking using the $l^{1}$-norm on graphs. Inverse Problems & Imaging, 2013, 7 (3) : 907-926. doi: 10.3934/ipi.2013.7.907
[4]

Tuvi Etzion, Alexander Vardy. On $q$-analogs of Steiner systems and covering designs. Advances in Mathematics of Communications, 2011, 5 (2) : 161-176. doi: 10.3934/amc.2011.5.161
[5]

Yuta Tanoue. Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 53-60. doi: 10.3934/puqr.2021003
[6]

Antonio De Rosa, Domenico Angelo La Manna. A non local approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021059
[7]

Yun Gao, Shilin Yang, Fang-Wei Fu. Some optimal cyclic $ \mathbb{F}_q $-linear $ \mathbb{F}_{q^t} $-codes. Advances in Mathematics of Communications, 2021, 15 (3) : 387-396. doi: 10.3934/amc.2020072
[8]

Mikhail Gilman, Semyon Tsynkov. Statistical characterization of scattering delay in synthetic aperture radar imaging. Inverse Problems & Imaging, 2020, 14 (3) : 511-533. doi: 10.3934/ipi.2020024
[9]

Suzete Maria Afonso, Vanessa Ramos, Jaqueline Siqueira. Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021045
[10]

Jennifer D. Key, Bernardo G. Rodrigues. Binary codes from $ m $-ary $ n $-cubes $ Q^m_n $. Advances in Mathematics of Communications, 2021, 15 (3) : 507-524. doi: 10.3934/amc.2020079

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (42)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences