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

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.

Symmetries and Ambiguities in the linear sigma model with light quarks

We investigate the role of undetermined finite contributions generated by radiative corrections in a $SU(2)\times SU(2)$ linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.Comment: 9 pages. Added references through the text; an author was added due to an important contribution; corrected typos; the title also was changed. Submitted to Modern Physics Letter

Multiplicity of singularities is not a bi-Lipschitz invariant

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.Lev Birbrair: Partially supported by CNPq grant 302655/2014-0. Alexandre Fernandes: Partially supported by CNPq grant grant304221/2017-9 and by CAPES-BRASIL Finance Code 001. J. Edson Sampaio: Partially supported by CNPq-Brazil grant 303811/2018-8, by the ERCEA 615655 NMST Consolidator Grant and also by the Basque Government through the BERC 2018-2021 program and Gobierno Vasco Grant IT1094-16, by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718. Misha Verbitsky: Partially supported by the Russian Academic Excellence Project ‘5-100’, FAPERJ E-26/202.912/2018 and CNPq - Process 313608/2017-2

Effect of tidal regime on estuarine residence time spatial variation

The hydrology and the ecology of shallow estuaries are strongly influenced by the freshwater inflow and the adjacent open sea, due to tide and wind generated water exchange, creating salinity gradients, thermal stratification and assuring large transport of silt, organic material and inorganic nutrients into the estuarine waters. Nutrient enrichment is a key-factor for habitat degradation, leading to sensible structural changes in estuarine ecosystems with the consequent occurrence of episodic algal blooms. In the last two decades, the south arm of the Portuguese river Mondego estuary was stressed by an eutrophication process due to massive nutrient loading from urbanised areas and from intensively agricultural land runoff. The aim of this work is to calculate estuarine water residence time values, which are broadly recognised as important descriptors of estuarine circulation patterns and constitute key-parameters to assess estuarine eutrophication vulnerability. In fact, estuaries with nutrients residence time values, shorter than the algal cells doubling time, will inhibit algae blooms occurrence. The increase of estuarine flushing capacity can be seen as a management measure to mitigate or to invert eutrophication processes. In this work, the MONDEST model, a 2-DH water quality model, was developed and applied to calculate water residence time, at different simulated management scenarios. The results shows the effect of simulated tides on the spatial distribution of estuarine residence time values, which are related with the eutrophication gradients, observed in the Mondego estuary south arm during the last decades. This integrated model constitutes a powerful tool to support authorities’ decisions concerning the best water management practices and restoration measures for the environmental sustainable management of this complex ecosystem

Aplicação da hidroinformática na gestão sustentável de sistemas estuarinos

Os estuários são sistemas hídricos que desde sempre favoreceram o desenvolvimento de aglomerados urbanos importantes, por propiciarem actividades com grande impacto sócio-económico e sustentarem uma intensa actividade biológica, sendo autênticos viveiros e maternidades de peixes, crustáceos e bivalves A descarga excessiva e descontrolada de nutrientes, associada a várias acções antropogénicas, pode originar graves desequilíbrios na cadeia trófica destes ecossistemas e estimular a ocorrência de florescências macroalgais, conduzindo a uma significativa degradação dos habitats e redução da sua biodiversidade. Os dados recolhidos nas últimas décadas no estuário do rio Mondego confirmam que as condições hidrodinâmicas podem influenciar decisivamente os processos de eutrofização em sistemas estuarinos. O tempo de residência (da água e/ou de nutrientes) nestes sistemas, caracterizados pela alternância do sentido do escoamento, tem sido amplamente reconhecido como um parâmetro-chave na avaliação da vulnerabilidade dos estuários à eutrofização. Este trabalho teve como objectivos o desenvolvimento duma ferramenta hidroinformática (o modelo MONDEST), integrando três módulos principais: hidrodinâmico; de transporte (advecção e dispersão); e de cálculo de tempos de residência (TempResid), e a sua aplicação ao caso do estuário do rio Mondego (Portugal). Os resultados obtidos permitem avaliar a influência das condições hidrodinâmicas e o impacto das características das descargas de nutrientes na variação da distribuição espacial dos valores dos tempos de residência estuarinos, mostrando que este modelo pode ser extremamente útil na definição criteriosa de práticas de gestão adequadas à sustentabilidade destes complexos ecossistemas aquáticos, incluindo a selecção de medidas de adaptação a alterações climáticas