Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints

We compute the Coulomb correction $\mathcal{C}$ to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework. Arbitrary parameters stemming from differences between logarithmically divergent integrals are fixed on physical grounds exploiting only spatial $O(2)$ rotational invariance of the model which amounts to transversality of the polarization tensor. Consequently $\mathcal{C}$ is unequivocally determined to be $(19- 6\pi)/12$ within this effective model. We compare our result with explicit regularizations and discuss the origin of others results for $\mathcal{C}$ found in the literature

Subtleties in the beta function calculation of N=1 supersymmetric gauge theories

We investigate some peculiarities in the calculation of the two-loop beta-function of $N=1$ supersymmetric models which are intimately related to the so-called "Anomaly Puzzle". There is an apparent paradox when the computation is performed in the framework of the covariant derivative background field method. In this formalism, it is obtained a finite two-loop effective action, although a non-null coefficient for the beta-function is achieved by means of the renormalized two-point function in the background field. We show that if the standard background field method is used, this two-point function has a divergent part which allows for the calculation of the beta-function via the renormalization constants, as usual. Therefore, we conjecture that this paradox has its origin in the covariant supergraph formalism itself, possibly being an artifact of the rescaling anomaly.Comment: Few misprintings corrected and comments added. To meet the version to be published at European Physical Journal

A hydroinformatic tool for sustainable estuarine management

Book edited by Harry Edmar Schulz, André Luiz Andrade Simões and Raquel Jahara Lobosco• Short characterization of estuarine systems and the Mondego estuary (Portugal); • Research methods: sampling program description and mathematical integrated modelling (hydroinformatic tool presentation) • Hydrodynamic estuarine modelling, including calibration and validation procedures; • New approach for tidal prism and flow estimation in estuaries, using mathematical modelling. • Estuarine dispersion conditions, including the assessment of saline wedge propagation into the Mondego estuary. • Influence of tides and freshwater discharges on residence time spatial distribution in the Mondego estuary

Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach

Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does not apply. In the present contribution we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover we show that a new scale appears, typically an infrared scale which is completely independent of the ultraviolet one. Examples are given.Comment: 9 pages, version to appear in Mod. Phys. Lett.

Characterization of greywater by appliance: pattern of discharge along the day

To improve water resources sustainability it is imperative to consider different approaches of water management, such as water reuse strategies. Greywater decentralised reuse seems to be more advantageous than total wastewater reuse, since it is less polluted and so, it is easier and cheaper to treat. To guarantee the success of a greywater reuse strategy it is necessary to know in detail the available flow by appliance and its variation along the day, as well as its quality. The diurnal variation of activity for each major appliance is studied in this paper, as well as, the typical medium volume associated to each discharge, in order to derive volume distribution graphs per domestic device. Additionally, a range of quality parameters were determined in order to reach pollutographs per appliance. This will give important information to the greywater reuse management