Non Relativistic Limit of a Model of Fermions interacting through a Chern-Simons Field

We study the non relativistic limit of a Model of Fermions interacting through a Chern-Simons Field, from a perspective that resembles the Wilson's Renormalization Group approach, instead of the more usual approach found in most texts of Field Theory. The solution of some difficulties, and a new understanding of non relativistic models is given.Comment: 16 pages (revtex), 5 figures (eps). Invited talk at the meeting ``II Trends in Theoretical Physics'', Buenos Aires, Dec. 1998. To be published by AI

Comparing a current-carrying circular wire with polygons of equal perimeter; Magnetic field versus magnetic flux

We compare the magnetic field at the center of and the self-magnetic flux through a current-carrying circular loop, with those obtained for current-carrying polygons with the same perimeter. As the magnetic field diverges at the position of the wires, we compare the self-fluxes utilizing several regularization procedures. The calculation is best performed utilizing the vector potential, thus highlighting its usefulness in practical applications. Our analysis answers some of the intuition challenges students face when they encounter a related simple textbook example. These results can be applied directly to the determination of mutual inductances in a variety of situations.Comment: 9 pages, 4 figure

The concentration-compactness principle for variable exponent spaces and applications

In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to the variable exponent case. We also give some applications to the existence problem for the $p(x)-$Laplacian with critical growth

On the finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory

Within the superfield approach, we prove the absence of UV/IR mixing in the three-dimensional noncommutative supersymmetric Maxwell-Chern-Simons theory at any loop order and demonstrate its finiteness in one, three and higher loop orders.Comment: 9 pages, 2 figures, revtex

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