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Partha Guha

Publications and source records attributed to Partha Guha.

81 records · Page 5Linked to original sources
arXiv2007

On dynamics of velocity vector potential in incompressible fluids

An elegant quaternionic formulation is given for the Lagrangian advection equation for velocity vector potential in fluid dynamics. At first we study the topological significance of a restricted conserved quantity viz., stream-helicity and later more realistic configuration of open streamlines is figured out. Also, using Clebsch parameterisation of the velocity vector potential yet another physical significance for the stream-helicity is provided. Finally we give a Nambu-Poisson formalism of the Lagrangian advection equation for velocity vector potential.

physics.flu-dyn↗
arXiv2007

On the MHD load and the MHD metage

In analogy with the load and the metage in hydrodynamics, we define magnetohydrodynamic load and magnetohydrodynamic metage in the case of magnetofluids. They can be used to write the magnetic field in MHD in Clebsch's form. We show how these two concepts can be utilised to derive the magnetic analogue of the Ertel's theorem and also, how in the presence of non-trivial topology of the magnetic field in the magnetofluid one may associate the linking number of the magnetic field lines with the invariant MHD loads. The paper illustrates that the symmetry translation of the MHD metage in the corresponding label space generates the conservation of cross helicity.

physics.plasm-ph↗
arXiv2006

Generalized forms and vector fields

The generalized vector is defined on an $n$ dimensional manifold. Interior product, Lie derivative acting on generalized $p$-forms, $-1\le p\le n$ are introduced. Generalized commutator of two generalized vectors are defined. Adding a correction term to Cartan's formula the generalized Lie derivative's action on a generalized vector field is defined. We explore various identities of the generalized Lie derivative with respect to generalized vector fields, and discuss an application.

math-ph↗
arXiv2001

Volume preserving multidimensional integrable systems and Nambu--Poisson geometry

In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu--Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. All these dispersionless KP and dToda type equations can be studied via twistor geometry, by using the method of Gindikin's pencil of two forms. Following this approach we study the twistor construction of our volume preserving systems.

nlin.SI↗
arXiv1999

Quest for universal integrable models

In this paper we discuss a universal integrable model, given by a sum of two Wess-Zumino-Witten-Novikov (WZWN) actions, corresponding to two different orbits of the coadjoint action of a loop group on its dual, and the Polyakov-Weigmann cocycle describing their interactions. This is an effective action for free fermions on a torus with nontrivial boundary conditions. It is universal in the sense that all other known integrable models can be derived as reductions of this model. Hence our motivation is to present an unified description of different integrable models. We present a proof of this universal action from the action of the trivial dynamical system on the cotangent bundles of the loop group. We also present some examples of reductions.

nlin.SI↗
arXiv1998

Volume preserving multidimensional integrable systems and Nambu-Poisson Geometry

In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu-Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. Recently Takasaki-Takebe provided the twistor construction of dispersionless KP and dToda type equations by using the Gindikin's pencil of two forms. In this paper we generalize this twistor construction to our systems.

math-ph↗
arXiv1997

Dispersionless Hierarchies, Hamilton-Jacobi Theory and Twistor Correspondences

The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of twistor theory, such as twistor lines and twistor surfaces. A more geometric approach can be developed in a Hamilton-Jacobi formalism of Gibbons and Kodama. AMS Subject Classifiation (1991): 35Q20, 58F07,70H99

solv-int↗
arXiv1993

String Equations for the Unitary Matrix Model and the Periodic Flag Manifold

The periodic flag manifold (in the Sato Grassmannian context) description of the modified Korteweg--de Vries hierarchy is used to analyse the translational and scaling self--similar solutions of this hierarchy. These solutions are characterized by the string equations appearing in the double scaling limit of the symmetric unitary matrix model with boundary terms. The moduli space is a double covering of the moduli space in the Sato Grassmannian for the corresponding self--similar solutions of the Korteweg--de Vries hierarchy, i.e. of stable 2D quantum gravity. The potential modified Korteweg--de Vries hierarchy, which can be described in terms of a line bundle over the periodic flag manifold, and its self--similar solutions corresponds to the symmetric unitary matrix model. Now, the moduli space is in one--to--one correspondence with a subset of codimension one of the moduli space in the Sato Grassmannian corresponding to self--similar solutions of the Korteweg--de Vries hierarchy.

hep-th↗