Complete classification of discrete resonant Rossby/drift wave triads on periodic domains

We consider the set of Diophantine equations that arise in the context of the barotropic vorticity equation on periodic domains, when nonlinear wave interactions are studied to leading order in the amplitudes. The solutions to this set of Diophantine equations are of interest in atmosphere (Rossby waves) and Tokamak plasmas (drift waves), because they provide the values of the spectral wavevectors that interact resonantly via three-wave interactions. These come in "triads", i.e., groups of three wavevectors. We provide the full solution to the Diophantine equations in the case of infinite Rossby deformation radius. The method is completely new, and relies on mapping the unknown variables to rational points on quadratic forms of "Minkowski" type. Classical methods invented centuries ago by Fermat, Euler, Lagrange and Minkowski, are used to classify all solutions to our original Diophantine equations, thus providing a computational method to generate numerically all the resonant triads in the system. Our method has a clear computational advantage over brute-force numerical search: on a 10000^2 grid, the brute-force search would take 15 years using optimised C++ codes, whereas our method takes about 40 minutes. The method is extended to generate quasi-resonant triads, which are defined by relaxing the resonant condition on the frequencies, allowing for a small mismatch. Quasi-resonances are robust with respect to physical perturbations, unlike exact resonances. Therefore, the new method is really valuable in practical terms. We show that the set of quasi-resonances form an intricate network of clusters of connected triads, whose structure depends on the value of the allowed mismatch. We provide some quantitative comparison between the clusters' structure and the onset of fully nonlinear turbulence in the barotropic vorticity equation, and provide perspectives for new research.Comment: Improved version, accepted in Commun. Nonlinear Sci. Numer. Simula

Image Encryption Using Elliptic Curves and Rossby/Drift Wave Triads

We propose an image encryption scheme based on quasi-resonant Rossby/drift wave triads (related to elliptic surfaces) and Mordell elliptic curves (MECs). By defining a total order on quasi-resonant triads, at a first stage we construct quasi-resonant triads using auxiliary parameters of elliptic surfaces in order to generate pseudo-random numbers. At a second stage, we employ an MEC to construct a dynamic substitution box (S-box) for the plain image. The generated pseudo-random numbers and S-box are used to provide diffusion and confusion, respectively, in the tested image. We test the proposed scheme against well-known attacks by encrypting all gray images taken from the USC-SIPI image database. Our experimental results indicate the high security of the newly developed scheme. Finally, via extensive comparisons we show that the new scheme outperforms other popular schemes.Comment: Accepted and published version (Entropy 2020, 22, 454

Counting of discrete Rossby/drift wave resonant triads (again)

The purpose of our earlier note (arXiv:1309.0405 [physics.flu-dyn]) was to remove the confusion over counting of resonant wave triads for Rossby and drift waves in the context of the Charney-Hasegawa-Mima equation. A comment by Kartashov and Kartashova (arXiv:1309.0992v1 [physics.flu-dyn]) on that note has further confused the situation. The present note aims to remove this obfuscation

Reaktualisasi Pendidikan Islam Dalam Pengembangan Pola Asuh Anak Sebagai Konsep Revolusi Mental

Kehidupan masyarakat sudah masuk dalam situasi yang mengkhawatirkan. Kriminalisasi, kejahatan, pertikaian, kesenjangan dan berbagai aspek kehidupan gelap (kemaksiatan) sudah merajalela. Baik di pedesaan, terutama di kehidupan perkotaan. Keberadaan ini ditentukan oleh masyarakat itu sendiri yang dibangun melalui individu masing-masing, terutama pola asuh hidup keluarga. Remaja masa kini menjadi penentu utama dalam regenerasi pola hidup masyarakat. Pemuda menjadi penentu masa depan bangsa dan masyarakat, remaja menjadi tumpuan utama dalam kehidupan bermasyarakat. Masa muda adalah masa dimana harapan bangsa, negara dan agama dipangkuannya. Menjadi masalah, ketika pola hidup remaja tidak sesuai dengan tuntutan adat, etika, estetika maupun karakter yang bersifat baik karena hal itu akan berdampak terhadap lingkungan sekitar. Hal ini tidak terlepas dari pola asuh di dalam kehidupan keluarga. Anak sebagai aset penting dan berharga dalam keluarga, menjadi tumpuan utama dalam kebahagiaan keluarganya. Pola asuh yang salah terhadap anak, akan berdampak kepada mental dan karakter anak ketika sudah remaja kelak. Mindset dan paradigma pendidikan yang diberikan orang tua kepada anak, akan membentuk pola hidup, mental dan karakternya. Untuk mencegah “kebrutalan” masa remaja dan mencegah menularnya “penyakit” mentalitas yang cenderung negatif maka dibutuhkan sebuah revolusi mental dalam pola asuh anak dalam kehidupan keluarga, yaitu dengan melakukan reaktualisasi pendidikan Islam sebagai pembentukan karakter. Society life has been in a situation that is worrying. Criminalization, crime, conflict, inequality, and the various aspects of disobedience have been rampant. Both in the countryside, especially in urban life. This existence is determined by the community itself, which was built by the individual, especially family life parenting. Teens today be a major determinant in the regeneration of the life style of the people. Youth determine the future of the nation and society, teenagers become the main focus of public life, youth is the period in which the hope of the nation, the state, and religion. Becomes a problem, when the pattern of teenage life with the demands of custom, ethics, aesthetics and character that is good, because it will have an impact on the surrounding environment. It is not independent of parenting in family life. Children as an important and valuable asset in the family became the main focus in the happiness of his family. Wrong up bringing of children, will have an impact on children's mental and character as a teenager later. Mindset and paradigms of education provided to children's parents will form a pattern of life, mental and character. To prevent the ”brutality” of adolescence and prevent the spread of the ”disease” mentality that tends to negative, then it takes a mental revolution in parenting a child in family life, by doing education renewal of Islam as the character buliding

Connected to Give: Faith Communities

This is the third report in the "Connected to Give" series, and compares the relationship between the charitable giving behavior of American's from a variety of backgrounds, including their key demographics; an examination their motivations for giving; and the types of organizations to which they contribute

On design of robust fault detection filter in finite-frequency domain with regional pole assignment

This brief is concerned with the fault detection (FD) filter design problem for an uncertain linear discrete-time system in the finite-frequency domain with regional pole assignment. An optimized FD filter is designed such that: 1) the FD dynamics is quadratically D-stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H∞-norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized H--norm. With the aid of the generalized Kalman-Yakubovich-Popov lemma, the mixed H--/H∞ performance and the D-stability requirement are guaranteed by solving a convex optimization problem. An iterative algorithm for designing the desired FD filter is proposed by evaluating the threshold on the generated residual function. A simulation result is exploited to illustrate the effectiveness of the proposed design technique.This work was supported in part by the Deanship of Scientific Research (DSR) at King Abdulaziz University in Saudi Arabia under Grant 16-135- 35-HiCi, the National Natural Science Foundation of China under Grants 61134009 and 61203139, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany