First Principles Calculation of the Topological Phases of the Photonic Haldane Model

Photonic topological materials with a broken time-reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge-states when enclosed by an opaque-type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed-matter systems, as it unveiled that a broken time-reversal symmetry is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of the Haldane model can be imitated in photonics with a spatially varying pseudo-Tellegen coupling. Here, we use Green’s function method to determine from “first principles” the band diagram and the topological invariants of the photonic Haldane model, implemented as a Tellegen photonic crystal. Furthermore, the topological phase diagram of the system is found, and it is shown with first principles calculations that the granular structure of the photonic crystal can create nontrivial phase transitions controlled by the amplitude of the pseudo-Tellegen parameter.

Mathematical Modelling of Canola Oil Biodegradation and Optimisation of Biosurfactant Production by an Antarctic Bacterial Consortium Using Response Surface Methodology

An Antarctic soil bacterial consortium (reference BS14) was confirmed to biodegrade canola oil, and kinetic studies on this biodegradation were carried out. The purpose of this study was to examine the ability of BS14 to produce biosurfactants during the biodegradation of canola oil. Secondary mathematical equations were chosen for kinetic analyses (Monod, Haldane, Teissier–Edwards, Aiba and Yano models). At the same time, biosurfactant production was confirmed through a preliminary screening test and further optimised using response surface methodology (RSM). Mathematical modelling demonstrated that the best-fitting model was the Haldane model for both waste (WCO) and pure canola oil (PCO) degradation. Kinetic parameters including the maximum degradation rate (μmax) and maximum concentration of substrate tolerated (Sm) were obtained. For WCO degradation these were 0.365 min−1 and 0.308%, respectively, while for PCO they were 0.307 min−1 and 0.591%, respectively. The results of all preliminary screenings for biosurfactants were positive. BS14 was able to produce biosurfactant concentrations of up to 13.44 and 14.06 mg/mL in the presence of WCO and PCO, respectively, after optimisation. The optimum values for each factor were determined using a three-dimensional contour plot generated in a central composite design, where a combination of 0.06% salinity, pH 7.30 and 1.55% initial substrate concentration led to the highest biosurfactant production when using WCO. Using PCO, the highest biosurfactant yield was obtained at 0.13% salinity, pH 7.30 and 1.25% initial substrate concentration. This study could help inform the development of large-scale bioremediation applications, not only for the degradation of canola oil but also of other hydrocarbons in the Antarctic by utilising the biosurfactants produced by BS14.

Superfluid density, Josephson relation and pairing fluctuations in a multi-component fermion superfluid

In this work, a Josephson relation is generalized to a multi-component fermion superfluid. Superfluid density is expressed through a two-particle Green function for pairing states. When the system has only one gapless collective excitation mode, the Josephson relation is simplified, which is given in terms of the superfluid order parameters and the trace of two-particle normal Green function. In addition, it is found that the matrix elements of two-particle Green function is directly related to the matrix elements of the pairing fluctuations of superfluid order parameters. Furthermore, in the presence of inversion symmetry, the superfluid density is given in terms of the pairing fluctuation matrix. The results of the superfluid density in Haldane model show that the generalized Josephson relation can be also applied to a multi-band fermion superfluid in lattice.

Superfluid density, Josephson relation and pairing fluctuations in a multi-component fermion superfluid

In this work, a Josephson relation is generalized to a multi-component fermion superfluid. Superfluid density is expressed through a two-particle Green function for pairing states. When the system has only one gapless collective excitation mode, the Josephson relation is simplified, which is given in terms of the superfluid order parameters and the trace of two-particle normal Green function. In addition, it is found that the matrix elements of two-particle Green function is directly related to the matrix elements of the pairing fluctuations of superfluid order parameters. Furthermore, in the presence of inversion symmetry, the superfluid density is given in terms of the pairing fluctuation matrix. The results of the superfluid density in Haldane model show that the generalized Josephson relation can be also applied to a multi-band fermion superfluid in lattice.

Batch and Fed-Batch Production of β-carotene by Rhodotorula Toruloides KP324973 Using Corn Steep Liquor As Sole Carbon Source

Application of agro-industrial waste in microbial fermentation is interesting in economic and environmental aspects. Carotenoids production by Rhodotorula toruloides KP324973 was investigated using corn steep liquor (CSL) as sole carbon source. Haldane model with constants µmax = 0.056 h-1, KS = 1.54 vv-1%, and KI = 58.58 vv-1% showed best describe of cell growth kinetics on CLS. A same maximum carotenoid production rate (Rp) about 2.23 μg gcell-1 h-1 was obtained at initial CSL concentration of 5 v/v% after 72 h and 21 h in batch cultivation in shaken flasks and bubble column reactor (BCR), respectively. Further improvement of carotenogenesis was followed by fed-batch cultivation in BCR where the optimal setting of factors at feed flow rate of 5 mL h-1, pH of 5.66, and temperature 14 ˚C gained a highest Rp = 8.686 μg gcell-1 h-1. Chromatographic analysis showed more than 94% of produced carotenes was β-carotene.