Matrix logarithmic wave equation and multi-channel systems in fluid mechanics
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Durban University of Technology, Institute of Systems Science, Durban
Submission date: 2018-12-04
Acceptance date: 2019-04-16
Online publication date: 2019-10-15
Publication date: 2019-10-15
Journal of Theoretical and Applied Mechanics 2019;57(4):843-852
We formulate the mapping between a large class of nonlinear wave equations and flow equations for a barotropic fluid with internal surface tension and capillary effects. Motivated by statistical mechanics and multi-channel physics arguments, we focus on wave equations with logarithmic nonlinearity, and further generalize them to matrix equations. We map the resulting equation to flow equations of multi-channel or multi-component Korteweg-type materials. For some special cases, we analytically derive Gaussian-type matrix solutions and study them in the context of fluid mechanics.
Acton F.S., 1997, Numerical Methods that Work, Mathematical Association of America, Washington.
Anderson D.M., Mc Fadden G.B., Wheeler A.A., 1998, Diffuse-interface methods in fluid mechanics, Annual Review of Fluid Mechanics, 30, 139-165.
Antanovskii L.K., 1996, Microscale theory of surface tension, Physical Review, E, 54, 6285-6290.
Avdeenkov A.V., Zloshchastiev K.G., 2011, Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent, Zeitschrift f¨ur Naturforschung, 44, 195303.
Bialynicki-Birula I., Mycielski J., 1976, Nonlinear wave mechanics, Annals of Physics, 100, 62-93.
Bialynicki-Birula I., Mycielski J., 1979, Gaussons: solitons of the logarithmic Schrödinger equation, Physica Scripta, 20, 539-544.
Bouharia B., 2015, Stability of logarithmic Bose-Einstein condensate in harmonic trap, Modern Physics Letters B, 29, 1450260.
Brasher J.D., 1991, Nonlinear wave mechanics, information theory, and thermodynamics, International Journal of Theoretical Physics, 30, 979-984.
Čížek J., 1966, On the correlation problem in atomic and molecular systems: Calculation of wavefunction components in Ursell-type expansion using quantum-field theoretical methods, Journal of Chemical Physics, 45, 4256-4266.
De Martino S., Falanga M., Godano C., Lauro G., 2003, Logarithmic Schrödinger-like equation as a model for magma transport, Europhysics Letters (EPL), 63, 472-475.
Dell’Isola F., Kosiński W., 1993, Deduction of thermodynamic balance laws for bidimensional nonmaterial directed continua modelling interphase layer, Archives of Mechanics, 45, 333-359.
Dunn J.E., Serrin J.B., 1985, On the thermomechanics of interstitial working, Archive for Rational Mechanics and Analysis, 88, 95-133.
Hagen G., Hjorth-Jensen M., Jansen G.R., Papenbrock T., 2016, Emergent properties of nuclei from ab initio coupled-cluster calculations, Physica Scripta, 91, 063006.
Lauro G., 2008, A note on a Korteweg fluid and the hydrodynamic form of the logarithmic Schrödinger equation, Geophysical and Astrophysical Fluid Dynamics, 102, 373-380.
McClain J., Lischner J., Watson T., Matthews D.A., Ronca E., Louie S.G., Berkelbach T.C., Chan G.K.L, 2016, Spectral functions of the uniform electron gas via coupled-cluster theory and comparison to the GW and related approximations, Physical Review, B, 93, 235139
Rosen G., 1968, Particlelike solutions to nonlinear complex scalar field theories with positivedefinite energy densities, Journal of Mathematical Physics, 9, 996-998.
Rosen G., 1969, Dilatation covariance and exact solutions in local relativistic field theories, Physical Review, 183, 1186-1188.
Rylov Yu.A., 1999, Spin and wave function as attributes of ideal fluid, Journal of Mathematical Physics, 40, 256-278.
Scott T.C., Zhang X., Mann R.B., Fee G.J., 2016, Canonical reduction for dilatonic gravity in 3+1 dimensions, Physical Review, D, 93, 084017.
Yasue K., 1978, Quantum mechanics of nonconservative systems, Annals of Physics, 114, 479-496.
Zloshchastiev K.G., 2010, Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational consequences, Gravitation and Cosmology, 16, 288-297.
Zloshchastiev K.G., 2011, Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory, Acta Physica Polonica B, 42, 261-292.
Zloshchastiev K.G., 2012, Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation, European Physical Journal, B, 85, 273.
Zloshchastiev K.G., 2017, Stability and metastability of trapless Bose-Einstein condensates and quantum liquids, Zeitschrift f¨ur Naturforschung, A, 72, 677-687.
Zloshchastiev K.G., 2018a, On the dynamical nature of nonlinear coupling of logarithmic quantum wave equation, Everett-Hirschman entropy and temperature, , Zeitschrift für Naturforschung, A, 73, 619-628.
Zloshchastiev K.G., 2018b, Nonlinear wave-mechanical effects in Korteweg fluid magma transport, Europhysics Letters (EPL), 122, 39001.
Znojil M., Růžička F., Zloshchastiev K.G., 2017, Schrödinger equations with logarithmic self-interactions: from antilinear PT-symmetry to the nonlinear coupling of channels, Symmetry, 9, 165
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