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O ensino de Física, inclusive no domínio da Eletrostática, demanda o desenvolvimento de competências cognitivas complexas que vão além da simples apl…

O ensino de Física, inclusive no domínio da Eletrostática, demanda o desenvolvimento de competências cognitivas complexas que vão além da simples aplicação de algoritmos. Como aponta Moreira (2021), a aplicação mecânica de equações não assegura a apreensão dos conceitos, exigindo do estudante a capacidade de modelar abstratamente cenários invisíveis ao olho humano. O domínio real de um conceito fundamenta-se em uma base invisível: o conhecimento aplicado à ação. Ele é composto pelas suposições intuitivas e pelos princípios que o indivíduo assume como verdadeiros para guiar seus padrões de comportamento e decisões. Nesse contexto, a Teoria dos Campos Conceituais (TCC), desenvolvida por Gérard Vergnaud (1996), destaca-se como um referencial cognitivista que prioriza o conteúdo do conhecimento e a análise conceitual. Para Vergnaud (1996), o conhecimento de um indivíduo é construído à medida que ele consegue estabelecer relações e conceitualizar situações ou problemas, sendo o conceito formado por um triplete de conjuntos: S (situações que dão sentido), I (invariantes operatórios) e R (representações simbólicas).

While this paper builds upon the foundation of Bob Brandenburg’s landmark 2013 Time and Tide study, it introduces critical calibrations to resolve the legacy model's unadjusted open-ocean baseli…

While this paper builds upon the foundation of Bob Brandenburg’s landmark 2013 Time and Tide study, it introduces critical calibrations to resolve the legacy model's unadjusted open-ocean baseline data and its 60-minute solar grid mismatch that graphed incorrect times for sunrise and sunset. By adjusting for localized shallow-water reef attenuation using Courtier's 0.50 Form Ratio and for true 1937 astronomical sunset times, the unified 192-hour graph in this paper restores the scientific credibility of previously marginalized radio intercepts, such as the 173°W, 5°S coordinates, and provides for a tidal height that does not require a 17-inch (0.43-meter) hoist of the airplane's vertical offset from the chart datum to rescue the airplane transmitter from submersion by salt water midway between the sequence of transmissions.

The paper asks how protected oscillations in gap-protected Hamiltonian systems fail. It distinguishes three levels: loss of a certificate, loss of the structural protection itself, and actual dynamica…

The paper asks how protected oscillations in gap-protected Hamiltonian systems fail. It distinguishes three levels: loss of a certificate, loss of the structural protection itself, and actual dynamical failure. Each stronger level implies the weaker one, but not conversely. Two failure kinds matter: escape from a neighbourhood, and exchange of action between modes. Linear instability cannot occur along a continuous family without the second-order resonance gap first tending to zero; systems with definite energy cannot exit linearly while they remain definite. At a one-to-two resonance, the outcome depends on the sign structure of the energy. In the definite case, action can exchange completely without escape. In the indefinite case, escape occurs in finite time, with smaller amplitudes taking longer. Definite systems never escape. Barrier leakage is bounded for measure-preserving maps, and near the standard map critical parameter transport is slow through a broken invariant circle. A hidden mode at a sum frequency can absorb all action even when the two-mode reduction is integrable; the extended gap detects this in advance. Resonance overlap is treated only as a heuristic. The paper proves minimality: ellipticity is implied by a uniform gap, but the two-mode gap, extended gap, and horizon are each nonredundant. Practical advice includes monitoring frequency gaps, avoiding opposite-sign energy where escape is unacceptable, keeping hidden modes away from sum and difference frequencies, and not confusing certificate expiry with failure. Limitations include truncated normal forms, cited classical results, and exclusion of noise and dissipation.  

Este trabajo utiliza herramientas de las Humanidades Digitales para comparar romances sefardíes y tradicionales con el fin de explorar la pervivencia de estructuras métricas y musicales.…

Este trabajo utiliza herramientas de las Humanidades Digitales para comparar romances sefardíes y tradicionales con el fin de explorar la pervivencia de estructuras métricas y musicales. Así pues, se emplea una metodología cuantitativa para analizar dos corpora: diez romances sefardíes de Tetuán, compilados por Manrique de Lara, y diez romances peninsulares de La Alpujarra, transcritos por Bonifacio Gil García. Tras codificar las partituras en formato **kern, el estudio analiza los elementos melódicos, rítmicos y prosódicos utilizando las herramientas Humdrum.

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This paper defines what it means for a system to be Trojan: near an operating point its dynamics reduces to an analytic Hamiltonian germ at an elliptic equilibrium whose frequencies avoid low-order re…

This paper defines what it means for a system to be Trojan: near an operating point its dynamics reduces to an analytic Hamiltonian germ at an elliptic equilibrium whose frequencies avoid low-order resonances and whose nonlinearity is small relative to that gap. The resonance gap is insensitive to signs of frequencies, scales linearly, and shrinks with order; eventually every frequency vector becomes resonant. The author introduces a dimensionless class of gap-protected germs parameterized by a scaled gap and a scaled nonlinearity. A third-order normalization yields explicit drift and confinement estimates: the certified time depends only on those class parameters, grows with the gap, and falls with nonlinearity and radius. This is called universality as uniformity, not renormalization universality. Stability for all time does not transfer across the class at third order. In two degrees of freedom, Arnold's theorem gives all-time stability under a fourth-order gap and nondegeneracy; in three or more, invariant tori cannot separate energy levels. The triangular Lagrange points illustrate the framework: classical results show instability exactly where the fourth-order gap closes. An admission test checks reduction, ellipticity, gap size, and nonlinearity. The normal form predicts that action exchange scales inversely with detuning when both modes are excited, and inversely squared when the partner starts at rest; numerical tests confirm both exponents. Practical implications include design rules, monitoring frequency drift, and transferring only certified bounds, not dynamical details. Limitations include crude constants, finite-order analysis, analytic Hamiltonian assumptions, and classical Lagrange results.

This paper argues that local chaos indicators such as positive Lyapunov exponents and positive entropy do not determine whether a system can reach a failure state. Stability should be judged relative …

This paper argues that local chaos indicators such as positive Lyapunov exponents and positive entropy do not determine whether a system can reach a failure state. Stability should be judged relative to a stability profile: a coherence projection, admissible initial set, failure region, time horizon, and possibly a probability measure. The author defines failure-reaching, confinement, and, for skew-product systems, chaos-mediated failure. A thinness ratio compares projected transport to the distance from failure. The main theorem shows that systems with identical maximal Lyapunov exponent and identical chaotic factor can be permanently confined, fail for reasons independent of chaos, or fail in a way that depends on the chaotic state. Thus chaos indicators are not sufficient statistics for functional stability. The paper then provides certificates for confinement: a scale criterion, a drift-rate bound giving a certified thinness time, a one-sided barrier, and a graph-reachability criterion for finite transition models. It emphasizes that simulation can show failure but cannot certify confinement, because sampled maxima underestimate suprema. For the Chirikov standard map, classical results are combined to show that positive topological entropy can coexist with permanent momentum confinement for small parameter values, while loss of confinement occurs near breakup of the last rotational invariant circle, not at the onset of chaos. Numerical illustrations support this picture. Finally, the paper connects the drift rate in Hamiltonian normal forms to the finite-order resonance gap, so a frequency gap acts as a transport obstruction rather than a decay rate. The contribution is a precise vocabulary and a small set of certificates separating local chaos from failure.

This repository contains the SedTrace reactive-transport models of sediment biogeochemistry and rare earth element (REE) diagenesis at site HH3000 on the northeast Pacific margin. The models quantify …

This repository contains the SedTrace reactive-transport models of sediment biogeochemistry and rare earth element (REE) diagenesis at site HH3000 on the northeast Pacific margin. The models quantify REE redistribution among pore water, Mn oxides, Fe oxides, organic matter and phosphate, and partitioning between benthic recycling and burial. Included are model configuration workbooks, Julia code, observational constraints, model outputs, sensitivity tests for Ce oxygen dependence and REE–phosphate partitioning, and numerical validation results. The README provides instructions for running the models and describes the data structure.