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        ISSN 2086-5317 6 Juli 2005  
 
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  Arsip publikasi :

Construction of Navier-Stokes Equation using Gauge Field Theory Approach

Albert Sulaiman

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Abstrak

The equation of motion governs fluid flows is well known as the Navier-Stokes equation. Most researches on fluid dynamics are mostly dedicated to get the solutions of this equation with particular boundary conditions, because of difficulties in obtaining exact solutions for this kind of nonlinear equation. The gauge field theory is the most popular field theory and widely accepted as a basic theory in elementary particle physics. We then attempt to reconstruct the Navier-Stokes equation in the same manner as gauge theory. Using a four vector potential \A_\mu with appropriate content describing the fluid dynamics, i.e. A_\mu = (\Phi, \av), we show that it is possible to construct the Navier-Stokes equation from a gauge invariant bosonic lagrangian \l_{NS} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + g\ja_\mu \A^\mu. The Navier-Stoke equation is obtained as its equation of motion through the Euler-Lagrange equation. Further, we present the application of the theory, i.e. the propagation Davydov soliton immersed in fluid system and the theory of turbulence. The propagation of Davidov soliton in fluid system that can be described by the Lagrange density which is similar to the quantum electrodynamics for boson particle. In the static condition, the Lagrange density is similar with the Ginzburg-Landau lagrangian. If fluid flow parallel to soliton propagation, the phenomenon is described by the variable that is a coefficient in the nonlinear Klein-Gordon equation. Behaviour of the solution in term of single solution is also given. Finally, concerning the similarity between the statistical mechanics and the fields theory we construct the theory of turbulence.

Publikasi : Tesis S2 (2005)
Tanggal masuk / revisi : 6 Juli 2005 / 6 Juli 2005
Naskah lengkap : format PDF (341.103 byte)
Kontak : Albert Sulaiman
Keterangan : teoritik
41 halaman
bahasa Inggris

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