Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

The graphene sheet versus the 2DEG: a relativistic Fano spin-filter via STM and AFM tips

We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. To the best knowledge, our work is the first to propose the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin-filter

The type N Karlhede bound is sharp

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spacetimes are properly $CH_2$, i.e., curvature homogeneous of order 2 but non-homogeneous. This means that tetrad components of $R, \nabla R, \nabla^{(2)}R$ are constant, and that essential coordinates first appear as components of $\nabla^{(3)}R$. Covariant derivatives of orders 4,5,6 yield one additional invariant each, and $\nabla^{(7)}R$ is needed for invariant classification. Thus, our class proves that the bound of 7 on the order of the covariant derivative, first established by Karlhede, is sharp. Our finding corrects an outstanding assertion that invariant classification of four-dimensional Lorentzian manifolds requires at most $\nabla^{(6)}R$.Comment: 7 pages, typos corrected, added citation and acknowledgemen

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

Verificação, avaliação e processamento das informações do programa de melhoramento de trigo para acesso e consulta por meio de bancos de dados relacional e grafo.

Editores técnicos: Joseani Mesquita Antunes, Ana Lídia Variani Bonato, Márcia Barrocas Moreira Pimentel

Novel modeling formalisms and simulation tools in computational biosystems

Living organisms are complex systems that emerge from the fundamental building blocks of life. Systems Biology is a recent field of science that studies these complex phenomena at the cellular level (Kitano 2002). Understanding the mechanisms of the cell is essential for research and development in several areas such as drug discovery and biotechnological production. In the latter, metabolic engineering is used for building mutant microbial strains with increased productivity of compounds with industrial interest, such as biofuels (Stephanopoulos 1998). Using computational models of cellular metabolism, it is possible to systematically test and predict the optimal manipulations, such as gene knockouts, that produce the ideal phenotype for a specific application. These models are typically built in an iterative cycle of experiment and refinement, by multidisciplinary research teams that include biologists, engineers and computer scientists. The interconnection between different cellular processes, such as metabolism and genetic regulation, reflects the importance of the holistic approach claimed by the Systems Biology paradigm in replacement of traditional reductionist methods. Although most cellular components have been studied individually, the behavior of the cell emerges from the network-level interaction and requires an integrative analysis. Recent high–throughput methods have generated the so- called omics data (e.g.: genomics, transcriptomics, proteomics, metabolomics, fluxomics) that have allowed the reconstruction of biological networks (Palsson 2006). However, despite the great advances in the area, we are still far from a whole-cell computational model that is able to simulate all the components of a living cell. Due to the enormous size and complexity of intracellular biological networks, computational cell models tend to be partial and focused on the application of interest. Also, due to the multidisciplinarity of the field, these models are based on several different kinds of formalisms. Therefore, it is important to develop a framework with common modeling formalisms, analysis and simulation methods, that is able to accommodate different kinds biological networks, with different types of entities and their interactions, into genome-scale integrated models. Cells are composed by thousands of components that interact in myriad ways. Despite this intricate interconnection it is usual to divide and classify these networks according to biological function. The main types of networks are signaling, gene regulatory and metabolic. Signal transduction is a process for cellular communication where the cell receives and responds to external stimuli through signaling cascades (Gomperts et al. 2009; Albert and Wang 2009). These cascades affect gene regulation, which is the method for controlling gene expression, and consequently several cellular functions (Schlittand and Brazma 2007; Karlebach and Sgamir 2008). Many genes encode enzymes which are responsible for catalyzing biochemical reactions. The complex network of these reactions forms the cellular metabolism that sustains the cell’s growth and energy requirements (Steuer and Junker 2009; Palsson 2006). The objectives of this work, in the context of a PhD thesis, consist in re-search and selection of an appropriate modeling formalism to develop a framework for integration of different biological networks, with focus on regulatory and metabolic networks, and the implementation of suitable analysis, simulation and optimization methods. To achieve these goals, it is necessary to resolve many modeling issues, such as the integration of discrete and continuous events, representation of network topology, support for different levels of abstraction, lack of parameters and model complexity. This framework will be used for the implementation of an integrated model of E. coli, a widely used organism for industrial application

Ultrahigh energy neutrinos and non-linear QCD dynamics

The ultrahigh energy neutrino-nucleon cross sections are computed taking into account different phenomenological implementations of the non-linear QCD dynamic s. Based on the color dipole framework, the results for the saturation model supplemented by DGLAP evolution as well as for the BFKL formalism in the geometric scaling regime are presented. They are contrasted with recent calculations using NLO DGLAP and unified BFKL-DGLAP formalisms.Comment: 5 pages, 2 figures. Version to be published in Physical Review

Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors