Large granulation cells on the surface of the giant star π1 Gruis.

Convection plays a major part in many astrophysical processes, including energy transport, pulsation, dynamos and winds on evolved stars, in dust clouds and on brown dwarfs. Most of our knowledge about stellar convection has come from studying the Sun: about two million convective cells with typical sizes of around 2,000 kilometres across are present on the surface of the Sun-a phenomenon known as granulation. But on the surfaces of giant and supergiant stars there should be only a few large (several tens of thousands of times larger than those on the Sun) convective cells, owing to low surface gravity. Deriving the characteristic properties of convection (such as granule size and contrast) for the most evolved giant and supergiant stars is challenging because their photospheres are obscured by dust, which partially masks the convective patterns. These properties can be inferred from geometric model fitting, but this indirect method does not provide information about the physical origin of the convective cells. Here we report interferometric images of the surface of the evolved giant star π1 Gruis, of spectral type S5,7. Our images show a nearly circular, dust-free atmosphere, which is very compact and only weakly affected by molecular opacity. We find that the stellar surface has a complex convective pattern with an average intensity contrast of 12 per cent, which increases towards shorter wavelengths. We derive a characteristic horizontal granule size of about 1.2 × 1011 metres, which corresponds to 27 per cent of the diameter of the star. Our measurements fall along the scaling relations between granule size, effective temperature and surface gravity that are predicted by simulations of stellar surface convection.

Family of fuzzy J-K flip-flops based on bounded product, bounded sum and complementation.

This paper presents a concept of new fuzzy J-K flip-flops based on bounded product, bounded sum and fuzzy complementation operations. Relationships between various types of the J-K flip-flops are given and characteristics of them are graphically shown by computer simulation. Two examples of circuits able to memorize and fuzzy information processing using the proposed fuzzy J-K flip-flops are presented.