We perform 2D and 3D numerical simulations of an accretion disc in a close binary system using the simplified flux vector splitting (SFS) finite volume method. In our calculations, the gas is assumed to be ideal with γ=1.01, 1.05, 1.1 and 1.2. The mass ratio of the mass‐losing star to the mass‐accreting star is unity. Our results show that spiral shocks are formed on the accretion disc in all cases. In 2D calculations we find that the smaller γ is, the more tightly the spiral winds. We observe this trend in 3D calculations as well in a somewhat weaker sense. Mach numbers in our discs are less than 10. These values are lower than the values in observed accretion discs in close binary systems. Recently, Steeghs, Harlaftis & Horne found the first convincing evidence for spiral structure in the accretion disc of the eclipsing dwarf nova binary IP Pegasi, using the technique known as Doppler tomography. Although the Mach numbers in present calculations are rather low, we may claim that the spiral structure that we discovered in earlier numerical simulations is now found observationally.

Intermediate resolution phase-resolved spectra of WZ Sge were obtained on five consecutive nights (July 23 -27) covering the initial stage of the 2001 superoutburst. Double-peaked emission lines of HeII at 4686 A, which were absent on July 23, emerged on July 24 together with emission lines of CIII / NIII Bowen blend. Analyses of the HeII emission lines using the Doppler tomography revealed an asymmetric spiral structure on the accretion disk. This finding demonstrates that spiral shocks with a very short orbital period can arise during the initial stage of an outburst and may be present in all SU UMa stars.

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Numerical simulation of the hydrodynamic behavior of an accretion disk in a close binary system is reported. Calculations were carried out for a region including a compact star and its gas-supplying companion. The equation of state is that of an ideal gas characterized by a specific heat ratio γ. Two cases, with γ = 1.01 and γ = 1.2, are studied. Our calculations show that the gas, flowing from the companion via a Lagrangian L1 point towards the accretion disk, forms a fine gas beam (L1 stream), which penetrates into the disk. Thus, no hot spot forms in these calculations. Another result is that the gas rotating with the disk forms -upon collision with the L1 stream-a bow shock wave, which we call an 'L1 shock'. The disk becomes hot because the L1 shock heats the disk gas in the outer parts of the disk, so that the spiral shocks wind loosely, even with γ = 1.01. The L1 shock enhances axial asymmetry of the density distribution in the disk, and therefore angular momentum is transferred through the tidal torque more effectively. The maximum value of the effective α becomes ∼ 0.3. A 'hot spot' is not formed in our simulations, but our results suggest the formation of a 'hot line', which is the L1 shock elongated along the penetrating L1 stream.

We present a method for producing laser beams of nonuniform polarization where the polarization direction rotates on a trajectory about the beam propagation direction. Our method uses a Sagnac interferometer that incorporates a spatial light modulator to combine beams that possess oppositely charged phase vortices in order to achieve the desired polarization vortex. We demonstrate the utility of our method by producing polarization vortices characterized by a fractional index, and we compare the results with calculations of the expected fields.