Below are my research works, grouped by field.
Mathematical Relavitiy
2025
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A low-regularity Riemannian positive mass theorem for non-spin manifolds with distributional curvature
E. Hafemann
In preparation, 2025
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Penrose inequality for integral energy conditions
E. Hafemann and E.-A. Kontou
Classical and Quantum Gravity, 2025
The classical Penrose inequality, a relation between the ADM mass and the area of any cross section of the black hole event horizon, was introduced as a test of the weak cosmic censorship conjecture: if it fails, the trapped surface is not necessarily behind the event horizon and a naked singularity could form. Since that original derivation, a variety of proofs have developed, mainly focused on the initial data formulation on maximal spacelike slices of spacetime. Most of these proofs are applicable only for classical fields, as the energy conditions required are violated in the context of quantum field theory. In this work we provide two generalizations of the Penrose inequality for spherically symmetric spacetimes: a proof of a classical Penrose inequality using initial data and an average energy condition, and a proof of a modified Penrose inequality for evaporating black holes with a connection to the weak cosmic censorship conjecture. The latter case could also be applicable to quantum fields as it uses a condition inspired by quantum energy inequalities. Finally, we provide physically motivated examples for both.
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Hawking’s singularity theorem for Lipschitz Lorentzian metrics
M. Calisti, M. Graf, E. Hafemann, M. Kunzinger, and R. Steinbauer
Commun. Math. Phys., 2025
We prove Hawking’s singularity theorem for spacetime metrics of local Lipschitz regularity. The proof rests on (1) new estimates for the Ricci curvature of regularising smooth metrics that are based upon a quite general Friedrichs-type lemma and (2) the replacement of the usual focusing techniques for timelike geodesics—which in the absence of a classical ODE-theory for the initial value problem are no longer available—by a worldvolume estimate based on a segment-type inequality that allows one to control the volume of the set of points in a spacelike surface that possess long maximisers.
Inverse Problems
2023
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A regularization method based on level-sets for the problem of crack detection from electrical measurements
A. De Cezaro, E. Hafemann, A. Leitão, and A. Osses
Inverse Problems, 2023
We investigate regularization methods for solving the problem of crack detection in bounded planar domains from electrical measurements on the boundary. Based on the multiple level-set approach introduced in Álvarez et al (2009 J. Comput. Phys. 228 5710–21) and on the regularization strategy devised in De Cezaro et al (2009 Inverse Problems 25 035004), we propose a Tikhonov type method for stabilizing the inverse problem. Convergence and stability results for this Tikhonov method are proven. An iterative method of (multiple) level-set type is derived from the optimality conditions for the Tikhonov functional, and a relation between this method and the iterated Tikhonov method is established. The proposed level-set method is tested on the same benchmark problem considered in Álvarez et al (2009 J. Comput. Phys. 228 5710–21). The numerical experiments demonstrate its ability to identify cracks in different scenarios with high accuracy even in the presence of noise.
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A range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg–Marquardt–Kaczmarz method for solving systems of non-linear ill-posed equations: Application to EIT-CEM with real data
R. Filippozzi, E. Hafemann, J. C. Rabelo, F. Margotti, and A. Leitão
Journal of Inverse and Ill-posed Problems, 2023
In this article we propose and analyze a Levenberg–Marquardt–Kaczmarz-type (LMK) method for obtaining stable approximate solutions to systems of ill-posed equations modeled by non-linear operators acting between Hilbert spaces. We extend to the LMK iteration the strategy proposed in [A. Leitão, F. Margotti and B. F. Svaiter, Range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg–Marquardt method, IMA J. Numer. Anal. 41 2021, 4, 2962–2989] for choosing the Lagrange multipliers in the Levenberg–Marquardt (LM) method. Our main goal is to devise a simple (and easy to implement) strategy for computing the multiplier in each iterative step, such that the resulting LMK iteration is both stable and numerically efficient. Convergence analysis for the proposed LMK type method is provided, including convergence for exact data, stability and semi-convergence. Numerical experiments using real data are presented for a 2D parameter identification problem, namely the Electrical Impedance Tomography (EIT) problem. The mathematical model known as complete electrode model (EIT-CEM) is considered. The obtained numerical results validate the efficiency of the proposed LMK-type method.
2022
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Range-relaxed strategy applied to the Levenberg–Marquardt method with uniformly convex penalization term in Banach spaces
F. Margotti and E. Hafemann
Inverse Problems, 2022
In this paper we propose the employment of the so-called range-relaxed criteria Boiger et al (2020 IMA J. Numer. Anal. 40 606–627) for choosing the regularization parameters (or equivalently, the Lagrange multipliers) of the Levenberg–Marquardt method for solving nonlinear ill-posed problems in Banach spaces. The proposed algorithm employs the Bregman distance induced by a uniformly convex functional and allows the use of a penalization generated from the total variation semi-norm. We present a geometrical interpretation of the method and deliver a complete convergence analysis, including stability and regularization properties. Further, we show that our new method is competitive by testing it with real data in the complete electrode model of 2D electrical impedance tomography.
Particle Physics
2021
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Density-dependent quark mass model revisited: thermodynamic consistency, stability windows and stellar properties
B. C. Backes, E. Hafemann, I. Marzola, and D. P Menezes
Journal of Physics G: Nuclear and Particle Physics, 2021
In this work a density-dependent quark model is revisited, its thermodynamic consistency checked and the stability window for absolutely stable quark matter obtained. The hypotheses of both pure quark matter with equal quark chemical potentials and stellar matter subject to chemical stability and charge neutrality are investigated. The parameters that appear in the density-dependent mass and satisfy the Bodmer–Witten conjecture are then used to compute the masses and radii of strange stars. We show that the obtained values are compatible with the recently observed massive stars.
Chemical Engineering
2022
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RNA-seq based transcriptomic analysis of the non-conventional yeast Spathaspora passalidarum during Melle-boinot cell recycle in xylose-glucose mixtures
T. Neitzel, C. S. Lima, E. Hafemann, D. A. A. Paixão, J. M. Junior, G. F. Persinoti, L. V. Santos, and J. L. Ienczak
Renewable Energy, 2022
The Melle-Boinot is a promising process for second-generation ethanol production by xylose-fermenting yeasts. However, the impact of this process on the physiology of the non-conventional yeast Spathaspora passalidarum during second-generation ethanol production remains unclear. Therefore, we performed a transcriptomic analysis of S. passalidarum to determine the differences and global responses of differentially expressed genes (DEGs) during five fed-batch fermentations with cell recycle. A cycle-to-cycle metabolic reprogramming was observed resulting in an increase in ethanol yield (32%), volumetric productivity (33%), and titer (33%); and an expressive decrease of 94% of xylitol production. A broad set of pathways operated synergically such as fatty acid metabolism, N-glycan biosynthesis, glyoxylate and dicarboxylate metabolism, oxidative phosphorylation, glutathione metabolism and sulfur metabolism, indicating those as important mechanisms for cell recycling adaptations due to increased ethanol concentration, long-term ethanol exposure and osmotic stress. Together these results suggest that cellular energy was redirected towards the production of cell wall components enabling S. passalidarum cells to thrive on consecutive recycles. Furthermore, these results are instrumental to guide genetic-engineering efforts of xylose-fermenting yeasts to improve the productiveness and feasibility of renewable energy production from lignocellulosic biomass and hemicellulosic hydrolysates.
2019
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Valorization of royal palm tree agroindustrial waste by isolating cellulose nanocrystals
E. Hafemann, R. Battisti, C. Marangoni, and R. A. F. Machado
Carbohydrate Polymers, 2019
A considerable increase in royal palm cultivation as a result of industrialization of canned heart of palm has generated large amounts of renewable lignocellulosic waste, but reuse is still rarely practiced. In this work, for the first time, cellulose nanocrystals (CNCs) were extracted from the leaf sheath discarded from the royal palm harvest. Chlorine-free purification methods were used and strong acid hydrolysis synthesis with different times and temperatures were performed. The purification treatments removed lignin successfully, reducing its content from 10.4% to 1.0%. The formation of spherical and rod-shaped CNCs reached yields between 7.9% and 48.8%, which was confirmed by a significant increase in crystallinity from 38.9% of natural fiber to 63.6% and 79.6% of CNCs, depending on temperature and synthesis duration. The production of CNCs from this underutilized waste has the potential to add value to royal palm tree crops, in addition to significantly reducing the volume of cumulative waste in the environment.
2018
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Synthesis and characterization of cellulose acetate from royal palm tree agroindustrial waste
R. Battisti, E. Hafemann, C. A. Claumann, R. A. Francisco Machado, and C. Marangoni
Polymer Engineering and Science, 2018
This study provides a novel value-added utilization of the agroindustrial waste of royal palm tree leaf sheath to produce cellulose acetate. One of the motivations of this work was the fact that Brazil is one of the largest heart of palm producers in the world. However, as a result of extraction and processing, tons of waste are generated and discharged to the environment. Such waste is rich in lignocellulosic material, which could be reused to obtain derivatives of interest and commercial value. The synthesis of cellulose acetate was performed through a homogeneous acetylation reaction. Three different conditions were tested for delignification of the raw material, which resulted in a reduction in lignin content from 17.75 to 7.72%. The highest yield of cellulose acetate reached 99.5%, with degree of substitutions ranging between 2.08 and 2.82, which indicates satisfactory conversion. The Fourier transform infrared spectrum showed that practically all hydroxyl groups were replaced by acetate groups; this was also confirmed by nuclear magnetic resonance analysis. X-ray diffraction analysis showed that the cellulose acetate crystallinity index was 8.9%. This demonstrates the viable potential of cellulose acetate production with low cost and use of highly available agroindustrial waste.
Books
2023
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Implementação computacional da tomografia por impedância elétrica (Computational implementation of electrical impedance tomography)
F. Margotti, E. Hafemann, and L. M. Santana
2023
ISBN 978-85-244-0535-8
Master Thesis
2023
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Geometry and topology of black hole horizons
E. Hafemann
Federal University of Santa Catarina, 2023
The main motivation of this work stems from a celebrated and fundamental theorem of Hawking on the topology of black holes. The theorem states that in a 4-dimensional asymptotically flat stationary black hole spacetime satisfying the dominant energy condition, the spacelike cross sections of the event horizon are topologically 2-spheres. In this work, we explore a natural generalization of Hawking’s theorem to higher dimensions, obtained by Galloway and Schoen, with exceptional conditions, as well as more recent versions of that result, which effectively remove those exceptional conditions and recover Hawking’s result in dimension 4. In higher dimensions, we are able to show that event horizons, in the stationary case, and outermost marginally outer trapped surfaces (MOTSs), in the general case, admit a metric of positive scalar curvature. This condition imposes several well-known restrictions on the topology, and it is consistent with examples of five-dimensional stationary black hole spacetimes with horizon topology S^2 \times S^1. The proof of these results requires techniques from differential geometry, analysis, and draws its motivation from minimal surface theory. Therefore, this work aims to closely examine the intricacies of the problem and serve as a friendly introduction to the topic for readers who may not be familiar with techniques of semi-Riemannian geometry, general relativity and geometric analysis.