The Dyer-Roeder relation in a universe with particle production

We have obtained analytical exact solutions of the Dyer-Roeder equation in a cosmological model where creation of particles occurs at the expenses of the gravitational field. We discussed the influences of inhomogeneities in the path of a light beam on the apparent diameter of astrophysical objects and consider both redshift independent as redshift dependent distributions of the inhomogeneities.Comment: 7 pages, 4 figures. Accepted to be published in the Astronomy and Astrophysics Journa

Heterotrophy as a tool to overcome the long and costly autotrophic scale-up process for large scale production of microalgae

Industrial scale-up of microalgal cultures is often a protracted step prone to culture collapse and the occurrence of unwanted contaminants. To solve this problem, a two-stage scale-up process was developed - heterotrophically Chlorella vulgaris cells grown in fermenters (1st stage) were used to directly inoculate an outdoor industrial autotrophic microalgal production unit (2nd stage). A preliminary pilot-scale trial revealed that C. vulgaris cells grown heterotrophically adapted readily to outdoor autotrophic growth conditions (1-m3 photobioreactors) without any measurable difference as compared to conventional autotrophic inocula. Biomass concentration of 174.5 g L-1, the highest value ever reported for this microalga, was achieved in a 5-L fermenter during scale-up using the heterotrophic route. Inocula grown in 0.2- and 5-m3 industrial fermenters with mean productivity of 27.54 ± 5.07 and 31.86 ± 2.87 g L-1 d-1, respectively, were later used to seed several outdoor 100-m3 tubular photobioreactors. Overall, all photobioreactor cultures seeded from the heterotrophic route reached standard protein and chlorophyll contents of 52.18 ± 1.30% of DW and 23.98 ± 1.57 mg g-1 DW, respectively. In addition to providing reproducible, high-quality inocula, this two-stage approach led to a 5-fold and 12-fold decrease in scale-up time and occupancy area used for industrial scale-up, respectively.Agência financiadora project FERMALG 017608 Fundacao para a Ciencia e a Tecnologia (FCT) UID/Multi/04326/2019 project FERMALG (AVISO) 32/SI/2015info:eu-repo/semantics/publishedVersio

Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigonometric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in particular cases and in general, to give insight into the properties of the solution of the spectral problem. As examples, the analytical index and the eigenvalues of the Dirac operator on the torus and on the sphere are obtained and as an application of this technique, the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page

Complete Wetting of Gluons and Gluinos

Complete wetting is a universal phenomenon associated with interfaces separating coexisting phases. For example, in the pure gluon theory, at $T_c$ an interface separating two distinct high-temperature deconfined phases splits into two confined-deconfined interfaces with a complete wetting layer of confined phase between them. In supersymmetric Yang-Mills theory, distinct confined phases may coexist with a Coulomb phase at zero temperature. In that case, the Coulomb phase may completely wet a confined-confined interface. Finally, at the high-temperature phase transition of gluons and gluinos, confined-confined interfaces are completely wet by the deconfined phase, and similarly, deconfined-deconfined interfaces are completely wet by the confined phase. For these various cases, we determine the interface profiles and the corresponding complete wetting critical exponents. The exponents depend on the range of the interface interactions and agree with those of corresponding condensed matter systems.Comment: 15 pages, 5 figure

Raman-scattering study of the phonon dispersion in twisted bi-layer graphene

Bi-layer graphene with a twist angle \theta\ between the layers generates a superlattice structure known as Moir\'{e} pattern. This superlattice provides a \theta-dependent q wavevector that activates phonons in the interior of the Brillouin zone. Here we show that this superlattice-induced Raman scattering can be used to probe the phonon dispersion in twisted bi-layer graphene (tBLG). The effect reported here is different from the broadly studied double-resonance in graphene-related materials in many aspects, and despite the absence of stacking order in tBLG, layer breathing vibrations (namely ZO' phonons) are observed.Comment: 18 pages, 4 figures, research articl

Polarization tailored novel vector beams based on conical refraction

Coherent vector beams with involved states of polarization (SOP) are widespread in the literature, having applications in laser processing, super-resolution imaging and particle trapping. We report novel vector beams obtained by transforming a Gaussian beam passing through a biaxial crystal, by means of the conical refraction phenomenon. We analyze both experimentally and theoretically the SOP of the different vector beams generated and demonstrate that the SOP of the input beam can be used to control both the shape and the SOP of the transformed beam. We also identify polarization singularities of such beams for the first time and demonstrate their control by the SOP of an input beam

Error Propagation in the Hypercycle

We study analytically the steady-state regime of a network of n error-prone self-replicating templates forming an asymmetric hypercycle and its error tail. We show that the existence of a master template with a higher non-catalyzed self-replicative productivity, a, than the error tail ensures the stability of chains in which m<n-1 templates coexist with the master species. The stability of these chains against the error tail is guaranteed for catalytic coupling strengths (K) of order of a. We find that the hypercycle becomes more stable than the chains only for K of order of a2. Furthermore, we show that the minimal replication accuracy per template needed to maintain the hypercycle, the so-called error threshold, vanishes like sqrt(n/K) for large K and n<=4

Dynamics of radiating braneworlds

If the observable universe is a braneworld of Randall-Sundrum type, then particle interactions at high energies will produce 5-dimensional gravitons that escape into the bulk. As a result, the Weyl energy density on the brane does not behave like radiation in the early universe, but does so only later, in the low energy regime. Recently a simple model was proposed to describe this modification of the Randall-Sundrum cosmology. We investigate the dynamics of this model, and find the exact solution of the field equations. We use a dynamical systems approach to analyze global features of the phase space of solutions.Comment: error in figures corrected, reference adde