Driving white dwarf metal pollution through unstable eccentric periodic orbits

Context. Planetary debris is observed in the atmospheres of over 1000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with N-body simulations lasting ∼1010 yr; these long-running simulations restrict the amount of phase space that can be investigated. Aims. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as well as chaotic indicators through dynamical stability maps, as quick scale-free analytic alternatives to N-body simulations in order to locate and predict instability in white dwarf planetary systems that consist of one major and one minor planet on very long timescales. We then classify the instability according to ejection versus collisional events. Methods. We generalized our previous work by allowing eccentricity and inclination of the periodic orbits to increase, thereby adding more realism but also significantly more degrees of freedom to our architectures. We also carried out a suite of computationally expensive 10 Gyr N-body simulations to provide comparisons with chaotic indicators in a limited region of phase space. Results. We compute dynamical stability maps that are specific to white dwarf planetary systems and that can be used as tools in future studies to quickly estimate pollution prospects and timescales for one-planet architectures. We find that these maps also agree well with the outcomes of our N-body simulations. Conclusions. As observations of metal-polluted white dwarfs mount exponentially, particularly in the era of Gaia, tools such as periodic orbits can help infer dynamical histories for ensembles of systems

Driving white dwarf metal pollution through unstable eccentric periodic orbits

Context. Planetary debris is observed in the atmospheres of over 1000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with N-body simulations lasting ∼1010 yr; these long-running simulations restrict the amount of phase space that can be investigated. Aims. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as well as chaotic indicators through dynamical stability maps, as quick scale-free analytic alternatives to N-body simulations in order to locate and predict instability in white dwarf planetary systems that consist of one major and one minor planet on very long timescales. We then classify the instability according to ejection versus collisional events. Methods. We generalized our previous work by allowing eccentricity and inclination of the periodic orbits to increase, thereby adding more realism but also significantly more degrees of freedom to our architectures. We also carried out a suite of computationally expensive 10 Gyr N-body simulations to provide comparisons with chaotic indicators in a limited region of phase space. Results. We compute dynamical stability maps that are specific to white dwarf planetary systems and that can be used as tools in future studies to quickly estimate pollution prospects and timescales for one-planet architectures. We find that these maps also agree well with the outcomes of our N-body simulations. Conclusions. As observations of metal-polluted white dwarfs mount exponentially, particularly in the era of Gaia, tools such as periodic orbits can help infer dynamical histories for ensembles of systems

The Pedagogical Representation of Mass Functions with LEGO and their Origin

We promote the teaching of mass functions as an integral part of an interdisciplinary science education. Mass functions characterize the frequency distributions of objects with different masses on all cosmic scales. We intend to enhance experiential learning of this concept with a creative LEGO brick experiment for a diverse student audience. To our surprise, the LEGO mass function is not only qualitatively but also quantitatively comparable to mass functions found across the Universe. We also discuss the relation between gravitation and mass distributions as a possible explanation for the continuity of the universal mass function.Comment: This is the version of the article before peer review and submission. The published version is Kautsch, Veras, & Hansotia 2021, European Journal of Physics, 42, 035605, https://doi.org/10.1088/1361-6404/abe75

Predictions for the correlation between giant and terrestrial extrasolar planets in dynamically evolved systems

The large eccentricities of many giant extrasolar planets may represent the endpoint of gravitational scattering in initially more crowded systems. If so, the early evolution of the giant planets is likely to be more restrictive of terrestrial planet formation than would be inferred from the current, dynamically quiescent, configurations. Here, we study statistically the extent of the anti-correlation between giant planets and terrestrial planets expected in a scattering model. We use marginally stable systems of three giant planets, with a realistic range of planetary masses, as a simple model for the initial conditions prior to scattering, and show that after scattering the surviving planets reproduce well the known extrasolar planet eccentricities beyond a > 0.5 AU. By tracking the minimum periastron values of all planets during the evolution, we derive the distribution of orbital radii across which strong perturbations (from crossing orbits) are likely to affect low mass planet formation. We find that scattering affects inner planet formation at orbital separations less than 50% of the final periastron distance of the innermost massive planet in approximately 30% of the realizations, and can occasionally influence planet formation at orbital separations less than 20% of the final periastron distance of the innermost massive planet. The domain of influence of the scattering massive planets increases as the mass differential between the massive planets decreases. Observational study of the correlation between massive and terrestrial extrasolar planets in the same system has the potential to constrain the origin of planetary eccentricity.Comment: 8 pages, 8 figures, 1 table, accepted for publication in Ap

Strangelet dwarfs

If the surface tension of quark matter is low enough, quark matter is not self bound. At sufficiently low pressure and temperature, it will take the form of a crystal of positively charged strangelets in a neutralizing background of electrons. In this case there will exist, in addition to the usual family of strange stars, a family of low-mass large-radius objects analogous to white dwarfs, which we call "strangelet dwarfs". Using a generic parametrization of the equation of state of quark matter, we calculate the mass-radius relationship of these objects.Comment: 10 pages, LaTeX, added discussion of CFL phase and strangelet pollution, version to appear in journal. arXiv admin note: text overlap with arXiv:0808.067

Diabetic Foot Ulcers Classification using a fine-tuned CNNs Ensemble

Diabetic Foot Ulcers (DFU) are lesions in the foot region caused by diabetes mellitus. It is essential to define the appropriate treatment in the early stages of the disease once late treatment may result in amputation. This article proposes an ensemble approach composed of five modified convolutional neural networks (CNNs) - VGG-16, VGG-19, Resnet50, InceptionV3, and Densenet-201 - to classify DFU images. To define the parameters, we fine-tuned the CNNs, evaluated different configurations of fully connected layers, and used batch normalization and dropout operations. The modified CNNs were well suited to the problem; however, we observed that the union of the five CNNs significantly increased the success rates. We performed tests using 8,250 images with different resolution, contrast, color, and texture characteristics and included data augmentation operations to expand the training dataset. 5-fold cross-validation led to an average accuracy of 95.04%, resulting in a Kappa index greater than 91.85%, considered Excellent

Frações de N do solo cultivado com milho e plantas de cobertura.

O milho é uma cultura de relevância no país e exige quantidades elevadas de nitrogênio (N) durante o seu crescimento. A sua disponibilidade para as plantas depende tanto do teor imediatamente disponível no solo, representada pelas formas inorgânicas, quanto do N das formas orgânicas, mineralizáveis durante o seu ciclo. O objetivo deste trabalho foi avaliar as alterações de frações do nitrogênio sob cultivo de plantas de cobertura na cultura do milho. O experimento está sendo conduzido há oito anos em Latossolo Vermelho sob milho cultivado em sistema plantio direto em sucessão às seguintes plantas de cobertura: Urochloa ruziziensis, Canavalia brasiliensis, Cajanus cajan e Sorghum bicolor. O delineamento experimental foi de blocos ao acaso com parcelas subdivididas e três repetições. Nas parcelas foram semeadas as plantas de cobertura e nas subparcelas foi feita a adubação fertilização nitrogenada em cobertura (com e sem N) na cultura do milho. Em Abril de 2013, após a colheita do milho foi realizada a coleta do solo nas profundidades de 0-10 e 10-20 cm. As plantas de cobertura apresentaram comportamento diferenciado em relação às camadas de solo. O solo sob U. ruziziensis apresentou maior N total e particulado que aquele sob C. cajan