Current Issue : July - September Volume : 2020 Issue Number : 3 Articles : 5 Articles
Thermodynamics being among the most synthetic theories of physics and the\nmass-energy relation E = mc2 among the most general equations of science, it\nis somewhat surprising that this latter is not explicitly present in the laws of\nthermodynamics. Coupling this observation with the conceptual difficulties\noften felt in learning thermodynamics leads to the idea that both situations\nmay have the same cause. On the basis of these clues, this paper is intended to\nprovide complementary arguments to a hypothesis already presented. It consists\nof showing the existence of an imperfect compatibility between the conventional\nformulations of the first and second laws of thermodynamics and\nsuggesting the need of the mass-energy relation to solving the problem....
It is presented and proved a version of Livschitz Theorem for hyperbolic flows pragmatically\noriented to the cohomological context. Previously, it is introduced the concept of cocycle and a natural\nnotion of symmetry for cocycles. It is discussed the fundamental relationship between the existence\nof solutions of cohomological equations and the behavior of the cocycles along periodic orbits. The\ngeneralization of this theorem to a class of suspension flows is also discussed and proved. This\ngeneralization allows giving a different proof of the Livschitz Theorem for flows based on the\nconstruction of Markov systems for hyperbolic flows....
Recent stringent experiment data of neutrino oscillations induces partial symmetries such as.......................
A three-dimensional system is presented with unknown parameters that employs\ntwo nonlinearities terms. The basic characteristics of the system are studied.\nThe stability is measured by Characteristic equation roots, Routh stability\ncriteria, Hurwitz stability criteria and Lapiynov function, all show that the system\nunstable.........................
The Sakaguchi-Kuramoto model is a modification of the well-known Kuramoto\nmodel, in which a frustration factor is added to the coupling term of\neach phase oscillator. The added frustration factor destroys the gradient\nstructure, but the modified model is more widely used in practice. In this paper,\nwe study how frustration factors influence the synchronization transition\nof coupled oscillators in the Sakaguchi-Kuramoto model with frequency\nmismatch rules. The results show that in the system of coupled oscillators, the\nfrustration factor manifests a disorder field, which restrains the explosive\nsynchronization and weakens the synchronization ability of the whole network.\nIn addition, it is found that the frequency synchronization can not be\ndetected by the common phase order parameter, so a new index is introduced\nto characterize the degree of frequency synchronization. As an example, at\nthe end of the paper, we theoretically analyze the synchronization dynamics\nof two-oscillator system, and indirectly verify the correctness of simulations\nfor the multi-body system....
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