Superhydrodynamics

Nyawelo, Tino S.; Holten, J.W. van; Nibbelink, Stefan Groot

doi:10.1103/physrevd.64.021701

Cited by 13 publications

(19 citation statements)

References 7 publications

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“…We have recently proposed a supersymmetric theory of hydrodynamics in fourdimensional Minkowski space, for irrotational flow, that is, when the vorticity -the circulation in the motion of fluid around a fixed point-is zero [7]. However, general fluid motions are not irrotational.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric hydrodynamics

Nyawelo

2003

Nuclear Physics B

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We work out some properties of a recently proposed globally N = 1 supersymmetric extension of relativistic fluid mechanics in four-dimensional Minkowski space. We construct the lagrangean, discuss its symmetries and the corresponding conserved Noether charges. We reformulate the theory in hamiltonian formulation, and rederive the (supersymmetry and internal) transformations generated by these charges. Super-Poincare algebra is also realized in this formulation.Comment: 14 pages, no figure

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Section: Introductionmentioning

confidence: 99%

Supersymmetric hydrodynamics

Nyawelo

2003

Nuclear Physics B

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“…Here, the gauge field a µ is replaced by the real superfield A and therefore we have to parametrize it using a Clebsch parametrization as above. As suggested in [22] and in [24] we identify…”

Section: Clebsch Parametrization For the Supersymmetric Casementioning

confidence: 58%

Supersymmetric fluid dynamics

2012

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Recently Navier-Stokes (NS) equations have been derived from the duality between the black branes and a conformal fluid on the boundary of AdS 5 . Nevertheless, the full correspondence has to be established between solutions of supergravity in AdS 5 and supersymmetric field theories on the boundary. That prompts the construction of NS equations for a supersymmetric fluid. In the framework of rigid susy, there are several possibilities and we propose one candidate. We deduce the equations of motion in two ways: both from the divergenless condition on the energy-momentum tensor and by a suitable parametrization of the auxiliary fields. We give the complete component expansion and a very preliminary analysis of the physics of this supersymmetric fluid.

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“…24 More recently, supersymmetric generalizations of the Chaplygin gas were formulated in (1+1) and (2+1) dimensions by supplementing the Lagrangian with additional fermionic fields. 12,25,26 This latter approach was also used to build an N = 1 supersymmetric extension of polytropic gas dynamics, 27 a covariant and supersymmetric theory of relativistic hydrodynamics in four-dimensional Minkowski space, 28,29 and a Kaluza-Klein model of a relativistic fluid. 30 In the last couple of years, there has been much interest in systems of partial differential equations describing a steady, irrotational and compressible fluid flow in a plane.…”

Section: B Supersymmetric Modelsmentioning

confidence: 99%

Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

Grundland

Hariton

2008

Journal of Mathematical Physics

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In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.Running Title: Supersymmetric system in Riemann invariants PACS: primary 02.20. Sv, 12.60.Jv, 02.30.Jr, Keywords: Riemann invariants, Lie superalgebra, invariant solutions. * email address: grundlan@crm.umontreal.ca † email address: hariton@crm.umontreal.ca 1 I Introduction A Historical BackgroundThe concept of differential invariants was first introduced by B. Riemann in 1858 in his classical works 1, 2 concerning the Euler equations for an ideal fluid flow in two independent variables u t + uu x + p ′ (ρ) ρ ρ x = 0, ρ t + uρ x + ρu x = 0, ρ > 0.Here, u is the local velocity of the fluid, the pressure p is assumed to be a differentiable function of the density ρ and p ′ = dp/dρ. Riemann investigated the formulation and mathematical correctness of problems involving the propagation and superposition of waves described by equation (1). Next, he constructed rank-2 solutions corresponding to the "superposition" of two waves propagating with local velocity u = ± (p ′ Riemann studied the asymptotic behavior of initial localized disturbances (i.e. initial data with compact support) corresponding to the above-mentioned waves. Consequently, he demonstrated that even for sufficiently small initial data, after some finite time T , these waves could be separated again in such a way that waves of the same type as those assumed in the initial data could be observed. Riemann noticed that the solution for systems of hydrodynamic type (3), even with arbitrarily smooth initial data, usually(could not be continued indefinitely in time. After a certain finite time T the solutions blew 2 up (more precisely, the first derivatives of the considered solution become unbounded after some finite time T > 0). So, for times t > T , smooth solutions to the Cauchy problem do not exist. This phenomenon is known as the gradient catastrophe. 3, 4 Furthermore, Riemann was interested in extending the solution in some more generalized sense beyond the time T of the blow up. On the basis of the conservation laws for the mass, energy and momentum, Riemann 2 and later Hugoniot 5 introduced the concept of weak solutions (non-continuous) in the form of shock waves. Based on this concept he proved some laws connecting the wave front velocity and parameters of the fluid state before and behi...

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Superhydrodynamics

Abstract: We present a covariant and supersymmetric theory of relativistic hydrodynamics in four-dimensional Minkowski space.Comment: 5 pages, revte

Cited by 13 publications

References 7 publications

Supersymmetric hydrodynamics

Supersymmetric hydrodynamics

Supersymmetric fluid dynamics

Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

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