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NEW EXACT SOLUTIONS CORRESPONDING TO
STOKES’ SECOND PROBLEM FOR MAXWELL FLUIDS
BY
IMRAN SIDDIQUE, QAMMAR RUBBAB
Abstract. In this paper new exact solutions for Stokes’ second problem for Maxwell
fluids are presented by considering both sine and cosine oscillations of the plate. These new
starting solutions, obtained by means of Laplace and Fourier sine transforms, describe the
flow for low and high values of time t, and are presented as sums of steady-state solutions
and transient solutions. In our paper we determine not only the velocity field, but also the
resulting shear stress. The time values required to reach the steady flows are also determined
by means of numerical methods. The solutions corresponding to Stokes’ second problem for
Newtonian fluids, as well as the solutions corresponding to Stokes’ first problem for
Maxwell and Newtonian fluids are obtained as particular cases from our solutions.
Key words: Maxwell fluids, exact solutions, velocity field, shear stress.
SELF-DUAL GAUGE FIELDS ON
NON-COMMUTATIVE SPACE-TIME
BY
GHEORGHE ZET
Abstract. A self-dual gauge theory is developed considering U(2) as local symmetry
group. Using the gauge fields, the covariant derivative is constructed and the strength tensor
components are calculated. The self-duality equations are written and a solution for the gauge
fields is obtained in the case of commutative space-time. The results are extended to the noncommutative
space-time defined by the condition ⎡
µ ν µν
x , x ⎤
µν νµ
⎣ ⎦
= i θ , with θ = − θ as
constant (canonical) parameters of the model. The gauge fields are expanded as power series
of θ - parameters and their components are calculated order by order using the self-duality
equations. An example of non-commutative self-dual solution is given and some of its
properties are discussed.
Key word: self-dual gauge fields, non-commutative space-time