Optical analogue of the spin Hall effect in a photonic cavity

We observe anisotropy in the polarization flux generated in a GaAs/AlAs photonic cavity by optical illumination, equivalent to spin currents in strongly coupled microcavities. Polarization rotation of the scattered photons around the Rayleigh ring is due to the TE-TM splitting of the cavity mode. Resolving the circular polarization components of the transmission reveals a separation of the polarization flux in momentum space. These observations constitute the optical analogue of the spin Hall effect.     

Structural study of the inclusion compounds of thymol, carvacrol and eugenol in β-cyclodextrin by X-ray crystallography

The crystal structures of the inclusion compounds of thymol, carvacrol and eugenol, (components of essential oils of vegetable origin) in β-cyclodextrin have been determined. Thymol/β-CD crystallizes in the space group P1 containing two host molecules in its asymmetric unit whereas both carvacrol/β-CD and eugenol/β-CD complexes crystallize in the space group C2. In all three complexes two host molecules form head-to-head dimers their guest/host stoichiometry being: 1/2 (carvacrol/β-CD), 2/2 (thymol/β-CD) and 3/2 (eugenol/β-CD). In the cases of the thymol/β-CD and the carvacrol/β-CD complexes the β-CD dimers are arranged according to the channel packing mode. The accommodation of the geometrical isomer guests is performed solely by their hydrophobic groups revealing the leading role of the hydrophobic driving forces in the complexation process whereas the position of their hydroxyl group affects the stoichiometry of the formed dimeric complexes. In the case of the eugenol/β-CD dimeric complex one guest molecule is found lying between the β-CD groups in a sandwich fashion whereas the other two symmetry related guests protrude outwards the narrower rim of the hosts with only their hydrophobic allyl-chain located inside the hosts’ cavities. This arrangement prohibits the formation of a channel and the observed crystal packing is that of a Tetrad mode.     

A hereditarily indecomposable Banach space with rich spreading model structure

We present a reflexive Banach space \(\mathfrak{X}_{usm}\) which is Hereditarily Indecomposable and satisfies the following properties. In every subspace Y of \(\mathfrak{X}_{usm}\) there exists a weakly null normalized sequence {y _n } _n , such that every subsymmetric sequence {z _n } _n is isomorphically generated as a spreading model of a subsequence of {y _n } _n . Also, in every block subspace Y of \(\mathfrak{X}_{usm}\) there exists a seminormalized block sequence {z _n } and \(T:\mathfrak{X}_{usm} \to \mathfrak{X}_{usm}\) an isomorphism such that for every n ∈ ?, T(z _2n?1) = z _2n . Thus the space is an example of an HI space which is not tight by range in a strong sense.     

Tsallis statistics and magnetospheric self-organization

In this study we use Tsallis non-extensive statistics for a new understanding the magnetospheric dynamics and the magnetospheric self-organization during quiet and intensive superstorm periods. The _qsens$q_{sens}$, _qstat$q_{stat}$, and _qrel$q_{rel}$ indices set known as the Tsallis q$q$-triplet was estimated during both quiet and strongly active periods, as well as the correlation dimensions and Lyapunov exponents spectrum for magnetospheric bulk plasma flows data. The results obtained by our analysis clearly indicate the magnetospheric phase transition process from a high-dimensional quiet SOC state to a low-dimensional global chaotic state when superstorm events are developed. During such a phase transition process the non-extensive statistical character of the magnetospheric plasma is strengthened as the values of the q$q$-triplet indices changes obtaining higher values than their values during the quiet periods.     

Tsallis non-extensive statistics,intermittent turbulence,SOC and chaos in the solar plasma,Part one: Sunspot dynamics

In this study, the non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988, 2004, 2009) ,  and . The q$q$-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum f(a)$f\left(a\right)$, the generalized Renyi dimension spectrum D(q)$D\left(q\right)$ and the spectrum J(p)$J\left(p\right)$ of the structure function exponents were estimated experimentally and theoretically by using the q$q$-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2001, 2000)  and . Our analysis showed clearly the following: (a) a phase transition process in the solar dynamics from high dimensional non-Gaussian SOC state to a low dimensional non-Gaussian chaotic state, (b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov’s studies (Zelenyi and Milovanov (1991) [21]); Milovanov and Zelenyi (1993) [22]; Ruzmakin et al. (1996) [26]) (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of (i) non-Gaussian probability distribution function P(x)$P\left(x\right)$, (ii) multifractal scaling exponent spectrum f(a)$f\left(a\right)$ and generalized Renyi dimension spectrum _Dq$D_q$, (iii) exponent spectrum J(p)$J\left(p\right)$ of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.