Response to de Groot et al.

Armstrong, Erika S.; Reynolds, Jenny; Carroll, Sandra; Suterwala, Mustafa S.

doi:10.1038/s41372-021-00971-5

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…The harmonic approximation has been also successfully applied to study chains of cold dipoles in tubes and layers [49][50][51]. One can show, however, that the harmonic approximation obtained from a two-body dipole-dipole potential does not describe accurately more complicated structures, e.g., with more than one dipole per tube, and should be modified [52]. To this end, one might first calculate energies and structural properties of few-body structures (e.g., from ref.…”

Section: Discussionmentioning

confidence: 99%

A solvable model for decoupling of interacting clusters

Volosniev¹,

Jensen²,

Harshman³

et al. 2019

EPL

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We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This paper derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.

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Section: Discussionmentioning

confidence: 99%

A solvable model for decoupling of interacting clusters

Volosniev¹,

Jensen²,

Harshman³

et al. 2019

EPL

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“…Ref: [1] Hadden & Lithwick ( 2014 All of the 500 simulations we perform survive the 2 Myr integration without experiencing instability. We explore each simulation for resonance, looking for libration of the critical resonant angles ϕ…”

Section: Constraining the Masses Of Kepler-305mentioning

confidence: 99%

“…We define the critical resonant angle for two bodies as: Θ b,c = j 1 λ b + j 2 λ c + j 3 ω b + j 4 ω c + j 5 Ω b + j 6 Ω c (1) where λ p is the mean longitude of planet p, ω p is the argument of periapsis, Ω p is the longitude of the ascending node, j i are coefficients which sum to zero, and planet b orbits interior to planet c.…”

Section: Introductionmentioning

confidence: 99%

exoMMR: A New Python Package to Confirm and Characterize Mean Motion Resonances

MacDonald,

Polania Vivas,

D’Angiolillo

et al. 2023

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The study of orbital resonances allows for the constraint of planetary properties of compact systems. We can predict a system’s resonances by observing the orbital periods of the planets, as planets in or near mean motion resonance (MMR) have period ratios that reduce to a ratio of small numbers. However, a period ratio near commensurability does not guarantee a resonance; we must study the system’s dynamics and resonant angles to confirm resonance. Because resonances require in-depth study to confirm, and because two-body resonances require a measurement of the eccentricity vector which is quite challenging, very few resonant pairs or chains have been confirmed. We thus remain in the era of small-number statistics, not yet able to perform large population synthesis or informatics studies. To address this problem, we build a python package to find, confirm, and analyze MMRs, primarily through N-body simulations. We then analyze all near-resonant planets in the Kepler/K2 and TESS catalogs, confirming over 60 new resonant pairs and various new resonant chains. We additionally demonstrate the package’s functionality and potential by characterizing the mass–eccentricity degeneracy of Kepler-80g, exploring the likelihood of an exterior giant planet in Kepler-80, and constraining the masses of planets in Kepler-305. We find that our methods overestimate the libration amplitudes of the resonant angles and struggle to confirm resonances in systems with more than three planets. We identify various systems that are likely resonant chains but that we are unable to confirm, and highlight next steps for exoplanetary resonances.

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“…These intervals are called the atmospheric windows (cf. Armstrong et al, 2021). The atmosphere itself emits thermal radiation I atm toward space and Earth, since in general a body emits heat in all directions equally.…”

Section: Ejemplo 61 Possible Solutionmentioning

confidence: 99%

Compartment models to study human impact on climate change

Hattebuhr

Frank

2022

Model. Sci. Educ. Learn.

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El cambio climático es objeto de animados debates públicos. Especialmente la cuestión de si el cambio climático está provocado por el hombre es un punto central de controversia. Dado que los procesos climáticos están entrelazados y son complejos, es difícil evaluar las las declaraciones públicas, políticas o científicas. En este trabajo, examinamos los modelos matemáticos que subyacen a los procesos climáticos a un nivel simplificado. Presentamos un modelo sencillo del brote energético de la Tierra desarrollado por los propios estudiantes de secundaria durante una semana de proyectos. El modelo permite calcular la temperatura global de la superficie de la Tierra y los efectos de la variación de la actividad solar y los cambios en la superficie terrestre. Más concretamente, el modelo que describe el balance energético de la Tierra forma un sistema de ecuaciones diferenciales parciales y puede vincularse a modelos de compartimentos. Mostramos cómo esta cuestión matemáticamente difícil puede reducirse didácticamente de manera que los estudiantes puedan desarrollar, resolver y ampliar los modelos de compartimentos de forma independiente sin que se les haya enseñado la base teórica. Implementamos este curso como un taller interactivo en línea y presentamos nuestras experiencias con grupos de estudiantes superdotados. Creemos que nuestro material presenta una oportunidad para demostrar el poder de la modelización matemática, para comprender los fenómenos naturales y reflexionar críticamente sobre los debates.

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Response to de Groot et al.

Cited by 3 publications

References 5 publications

A solvable model for decoupling of interacting clusters

A solvable model for decoupling of interacting clusters

exoMMR: A New Python Package to Confirm and Characterize Mean Motion Resonances

Compartment models to study human impact on climate change

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