Quantum Gravity Phenomenology Induced in the Propagation of UHECR, a Kinematical Solution in Finsler and Generalized Finsler Spacetime

It is well-known that the universe is opaque to the propagation of Ultra-High-Energy Cosmic Rays (UHECRs) since these particles dissipate energy during their propagation interacting with the background fields present in the universe, mainly with the Cosmic Microwave Background (CMB) in the so-called GZK cut-off phenomenon. Some experimental evidence seems to hint at the possibility of a dilation of the GZK predicted opacity sphere. It is well-known that kinematical perturbations caused by supposed quantum gravity (QG) effects can modify the foreseen GZK opacity horizon. The introduction of Lorentz Invariance Violation can indeed reduce, and in some cases making negligible, the CMB-UHECRs interaction probability. In this work, we explore the effects induced by modified kinematics in the UHECR lightest component phenomenology from the QG perspective. We explore the possibility of a geometrical description of the massive fermions interaction with the supposed quantum structure of spacetime in order to introduce a Lorentz covariance modification. The kinematics are amended, modifying the dispersion relations of free particles in the context of a covariance-preserving framework. This spacetime description requires a more general geometry than the usual Riemannian one, indicating, for instance, the Finsler construction and the related generalized Finsler spacetime as ideal candidates. Finally we investigate the correlation between the magnitude of Lorentz covariance modification and the attenuation length of the photopion production process related to the GZK cut-off, demonstrating that the predicted opacity horizon can be dilated even in the context of a theory that does not require any privileged reference frame.

Reduced Multiplicative (BURA-MR) and Additive (BURA-AR) Best Uniform Rational Approximation Methods and Algorithms for Fractional Elliptic Equations

Numerical methods for spectral space-fractional elliptic equations are studied. The boundary value problem is defined in a bounded domain of general geometry, Ω⊂Rd, d∈{1,2,3}. Assuming that the finite difference method (FDM) or the finite element method (FEM) is applied for discretization in space, the approximate solution is described by the system of linear algebraic equations Aαu=f, α∈(0,1). Although matrix A∈RN×N is sparse, symmetric and positive definite (SPD), matrix Aα is dense. The recent achievements in the field are determined by methods that reduce the original non-local problem to solving k auxiliary linear systems with sparse SPD matrices that can be expressed as positive diagonal perturbations of A. The present study is in the spirit of the BURA method, based on the best uniform rational approximation rα,k(t) of degree k of tα in the interval [0,1]. The introduced additive BURA-AR and multiplicative BURA-MR methods follow the observation that the matrices of part of the auxiliary systems possess very different properties. As a result, solution methods with substantially improved computational complexity are developed. In this paper, we present new theoretical characterizations of the BURA parameters, which gives a theoretical justification for the new methods. The theoretical estimates are supported by a set of representative numerical tests. The new theoretical and experimental results raise the question of whether the almost optimal estimate of the computational complexity of the BURA method in the form O(Nlog2N) can be improved.

Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas

A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized ‘spikes’ in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that localize within bad drift curvature wells that have a critical gradient set by peak drift curvature are also observed. A case study of near-helical stellarators of increasing field period demonstrates that the critical gradient can indeed be controlled by manipulating the magnetic geometry, but underscores the need for a general framework to evaluate the critical gradient. We conclude that average curvature and global shear set the correlation length of resonant ITG modes near the absolute critical gradient, the physics of which is included through direct solution of the gyrokinetic equation. Our method, which handles the general geometry and is more efficient than conventional gyrokinetic solvers, could be applied to future studies of stellarator ITG turbulence optimization.

Integrating geological mapping and geophysical analyses in Southern Espinhaço Range, eastern edge of the São Francisco Craton, Brazil

ABSTRACT. The São Francisco Craton is one of the fundamental pieces on the evolutionary history of the Gondwana supercontinent. At its southeast edge, the Southern Espinhaço Range (SER) is built mainly by Paleo- and Mesoproterozoic units of the Espinhaço Supergroup. At its western domain, one of its major components, the Conselheiro Mata Group, occurs as a relatively narrow strip, being composed by a succession of formations related to coastal and shallow marine environments. Aiming to present and discuss an integrated research, detailed fieldwork was carried out, gamma-ray spectrometry data were reprocessed, and ground gravity data were acquired. This integration allows clarifying the regional crustal structure and the general geometry of the Espinhaço basin. The defined gamma-ray spectrometry domains fit well to the lithological types and structural framework of the stratigraphic units. Bouguer residual anomaly highlights an amplitude of 27 mGal, ranging from -12 to 15 mGal, outlining a gravity compartmentation defined by a central negative anomaly (CNA) surrounded by positive anomalies, which is approximately in conformity with the regional tectonic segments. The CNA conforms to the main axis of SER, indicating the residual metasedimentary coverage of the Espinhaço basin. Its center, positioned above the Lamarão anticline, houses the nucleus of the precursor basin of Conselheiro Mata Group.Keywords: gravimetry; Espinhaço Supergroup; Conselheiro Mata Group.Integrando mapeamento geológico e análises geofísicas na Serra do Espinhaço Meridional, borda leste do Cráton São Francisco, BrasilRESUMO. O Cráton São Francisco é uma das peças fundamentais da história evolutiva do Supercontinente Gondwana. Em sua borda sudeste, a Serra do Espinhaço Meridional é formada, principalmente, por unidades Paleo- a Mesoproterozoicas do Supergrupo Espinhaço. Um de seus principais componentes, o Grupo Conselheiro Mata, ocorre como uma faixa relativamente estreita no domínio ocidental da serra, sendo composto por uma sucessão de formações relacionadas a ambientes marinhos rasos e costeiros. Com o objetivo de apresentar e discutir uma pesquisa integrada, foram realizados trabalho de campo detalhado, processamento de dados gamaespectrométricos e aquisição de dados gravimétricos terrestres. Tal integração permite esclarecer a estrutura crustal regional e a geometria geral da bacia Espinhaço. Os domínios gamaespectrométricos definidos ajustam-se bem às litologias e ao arcabouço estrutural das unidades estratigráficas. Anomalias Bouguer residuais demonstram uma amplitude de 27 mGal, variando entre -12 a 15 mGal, concordando aproximadamente com os segmentos tectônicos regionais e esboçando uma compartimentação gravimétrica definida por uma anomalia negativa central (CNA), cercada por anomalias positivas. A CNA concorda com o eixo principal da Serra do Espinhaço Meridional, definindo a cobertura metassedimentar residual da bacia Espinhaço. Seu centro, posicionado sobre o anticlinal do Lamarão, abriga o núcleo da bacia precursora do Grupo Conselheiro Mata.Palavras-chave: gravimetria; Supergrupo Espinhaço; Grupo Conselheiro Mata.

Electron-light interaction in nonequilibrium: exact diagonalization for time-dependent Hubbard Hamiltonians

We present a straightforward implementation scheme for solving the time-dependent Schrödinger equation for systems described by the Hubbard Hamiltonian with time-dependent hoppings. The computations can be performed for clusters of up to 14 sites with, in principle, general geometry. For the time evolution, we use the exponential midpoint rule, where the exponentials are computed via a Krylov subspace method, which only uses matrix-vector multiplication. The presented implementation uses standard libraries for constructing sparse matrices and for linear algebra. Therefore, the approach is easy to use on both desktop computers and computational clusters. We apply the method to calculate time evolution of double occupation and nonequilibrium spectral function of a photo-excited Mott-insulator. The results show that not only the double occupation increases due to creation of electron-hole pairs but also the Mott gap becomes partially filled.

Integration of Additive Manufacturing, Parametric Design, and Optimization of Parts Obtained by Fused Deposition Modeling (FDM). A Methodological Approach

The use of current computer tools in both manufacturing and design stages breaks with the traditional conception of productive process, including successive stages of projection, representation, and manufacturing. Designs can be programmed as problems to be solved by using computational tools based on complex algorithms to optimize and produce more effective solutions. Additive manufacturing technologies enhance these possibilities by providing great geometric freedom to the materialization phase. This work presents a design methodology for the optimization of parts produced by additive manufacturing and explores the synergies between additive manufacturing, parametric design, and optimization processes to guide their integration into the proposed methodology. By using Grasshopper, a visual programming application, a continuous data flow for parts optimization is defined. Parametric design tools support the structural optimization of the general geometry, the infill, and the shell structure to obtain lightweight designs. Thus, the final shapes are obtained as a result of the optimization process which starts from basic geometries, not from an initial design. The infill does not correspond to pre-established patterns, and its elements are sized in a non-uniform manner throughout the piece to respond to different local loads. Mass customization and Fused Deposition Modeling (FDM) systems represent contexts of special potential for this methodology.

Influence of Fluid Properties on Intensity of Hydrodynamic Cavitation and Deactivation of Salmonella typhimurium

In this study, three microfluidic devices with different geometries are fabricated on silicon and are bonded to glass to withstand high-pressure fluid flows in order to observe bacteria deactivation effects of micro cavitating flows. The general geometry of the devices was a micro orifice with macroscopic wall roughness elements. The width of the microchannel and geometry of the roughness elements were varied in the devices. First, the thermophysical property effect (with deionized water and phosphate-buffered saline (PBS)) on flow behavior was revealed. The results showed a better performance of the device in terms of cavitation generation and intensity with PBS due to its higher density, higher saturation vapor pressure, and lower surface tension in comparison with water. Moreover, the second and third microfluidic devices were tested with water and Salmonella typhimurium bacteria suspension in PBS. Accordingly, the presence of the bacteria intensified cavitating flows. As a result, both devices performed better in terms of the intensity of cavitating flow with the presence of bacteria. Finally, the deactivation performance was assessed. A decrease in the bacteria colonies on the agar plate was detected upon the tenth cycle of cavitating flows, while a complete deactivation was achieved after the fifteenth cycle. Thus, the proposed devices can be considered as reliable hydrodynamic cavitation reactors for “water treatment on chip” applications.