We investigate the stability of general-relativistic boson stars by classifying singularities of differential mappings and compare our results with those of perturbation theory. Depending on the particle number, the star has the following regimes of behavior: stable, metastable, pulsation, and collapse.
The speed of silicon-based transistors has reached an impasse in the recent decade, primarily due to scaling techniques and the short-channel effect. Conversely, graphene (a revolutionary new material possessing an atomic thickness) has been shown to exhibit a promising value for electrical conductivity. Graphene would thus appear to alleviate some of the drawbacks associated with silicon-based transistors. It is for this reason why such a material is considered one of the most prominent candidates to replace silicon within nano-scale transistors. The major crux here, is that graphene is intrinsically gapless, and yet, transistors require a band-gap pertaining to a well-defined ON/OFF logical state. Therefore, exactly as to how one would create this band-gap in graphene allotropes is an intensive area of growing research. Existing methods include nano-ribbons, bilayer and multi-layer structures, carbon nanotubes, as well as the usage of the graphene substrates.Graphene transistors can generally be classified according to two working principles. The first is that a single graphene layer, nanoribbon or carbon nanotube can act as a transistor channel, with current being transported along the horizontal axis. The second mechanism is regarded as tunneling, whether this be band-to-band on a single graphene layer, or vertically between adjacent graphene layers. The high-frequency graphene amplifier is another talking point in recent research, since it does not require a clear ON/OFF state, as with logical electronics. This paper reviews both the physical properties and manufacturing methodologies of graphene, as well as graphene-based electronic devices, transistors, and high-frequency amplifiers from past to present studies. Finally, we provide possible perspectives with regards to future developments.Not long before graphene was first manufactured by the Manchester research group in 2004 [1][2][3][4], theorists still believed that such two-dimensional structures were unstable due to thermal fluctuations [4,5], famously referred to as the Landau-Peierls arguments (cf. also ). Recently, the paradox behind graphene's existence has been resolved [5,6], and that it can be stabilised by transverse lattice distortions [8]. Stable forms of various other two-dimensional crystals such as graphene, silicene and germanene have all been attained [6,9]. Graphene was the first example which is able to exist in a single atomic layer with honeycomb hierarchy [1] (cf. Figure 1). It is composed of a single layer of carbon atoms, and can be extracted from graphite with full preservation of the hexagonal honeycomb structure (also referred to as chicken wire for quantum information processing [10]). This material has astonishing properties: it is stronger than diamond, more conductive than copper and more flexible than rubber. Graphene has primarily attracted the attention of scientific and engineering communities, due to its outstanding electrical, thermal and optical properties [11][12][13][14], displaying having a strong potential for m...
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