Topologically protected swirl of the magnetic texture known as the Skyrmion has become ubiquitous in both metallic and insulating chiral magnets. Meanwhile the existence of its three-dimensional analogue, known as the magnetic monopole, has been suggested by various indirect experimental signatures in MnGe compound. Theoretically, Ginzburg-Landau arguments in favor of the formation of a three-dimensional crystal of monopoles and anti-monopoles have been put forward, however no microscopic model Hamiltonian was shown to support such a phase. Here we present strong numerical evidence from Monte Carlo simulations for the formation of a rock-salt crystal structure of monopoles and anti-monopoles in short-period chiral magnets. Real-time simulation of the spin dynamics suggests there is only one collective mode in the monopole crystal state in the frequency range of several GHz for the material parameters of MnGe.PACS numbers: 12.39. Dc, 75.10.Hk, 75.40.Mg Attempts to view building blocks of nature as topologically protected objects such as knots have been a fascinating feature of modern physical science. The knot theory of atoms advanced by Thomson (Lord Kelvin) [1] was re-incarnated by Skyrme as a topological quantum theory of hadrons in the early 60s [2]. Although the topological interpretation of quantum numbers for elementary particles may not have been universally accepted in subatomic physics, the beauty of the idea has remained well within the physics community and, quite recently, found immense physical realization in several kinds of magnetic materials ranging from B20 metallic magnetic compounds [3][4][5], atomically-thin magnetic layers [6], multiferroic insulators [7], to ferroelectrics [8]. The form of the topological matter, now called the Skyrmion lattice, bears excellent resemblance to the well-known vortex lattice in type-II superconductors [9] and shares the character of two dimensionality, extending its existence in a columnar fashion when the host material in which it is formed is three-dimensional. The topological vortex and Skyrmion lattices have both been observed successfully through the visualization technique of Lorentz microscopy [5,10].In higher dimensions one is granted the exciting opportunity to create, observe, and manipulate topological objects not permitted in lower dimensions. For example in three-dimensional Heisenberg magnets with a local unit magnetization vector n r , localized objects known as monopoles and anti-monopoles with integer topological numbers may be formed. The number characterizing the object's topology isfor an integration domain S , parameterized by (u, v), enclosing the monopole center R. Due to the high energetic cost of creating monopoles in isolation, they must be created in reality as a monopole-anti-monopole (MAM) pair, or as a crystal of such pairs forming a new kind of topological lattice unique to three dimensions. Such possibility was suggested theoretically [11] some time ago following the intriguing discovery of diffuse neutron scattering peaks i...

A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford's law (BL) of first digits, which predicts the percentages of first digits in a data collection of numbers. Both are universal in the sense that FLL only depends on the numbers of letters in the alphabet, whereas BL only depends on the number of digits in the base of the number system. The existence of these types of universal laws appears counter-intuitive. Nonetheless both describe data very well. Relations to some earlier works are given. FLL predicts that an English author on the average starts about 16 out of 100 words with the English letter 't'. This is corroborated by data, yet an author can freely write anything. Fuller implications and the applicability of FLL remain for the future.

Complex network analyses have provided clues to improve power-grid stability with the help of numerical models. The high computational cost of numerical simulations, however, has inhibited the approach, especially when it deals with the dynamic properties of power grids such as frequency synchronization. In this study, we investigate machine learning techniques to estimate the stability of power-grid synchronization. We test three different machine learning algorithms—random forest, support vector machine, and artificial neural network—training them with two different types of synthetic power grids consisting of homogeneous and heterogeneous input-power distribution, respectively. We find that the three machine learning models better predict the synchronization stability of power-grid nodes when they are trained with the heterogeneous input-power distribution rather than the homogeneous one. With the real-world power grids of Great Britain, Spain, France, and Germany, we also demonstrate that the machine learning algorithms trained on synthetic power grids are transferable to the stability prediction of the real-world power grids, which implies the prospective applicability of machine learning techniques on power-grid studies.

interacting dynamic agents can often exhibit synchronization. it has been reported that the rhythm all agents agree on in the synchronized state could be different from the average of intrinsic rhythms of individual agents. Hinted by such a real-world behavior of the interaction-driven change of the average phase velocity, we propose a modified version of the Kuramoto model, in which the ith oscillator of the phase φ i interacts with other oscillator j only when the phase difference j φ − i φ is in a limited range [−βπ, απ]. From extensive numerical investigations, we conclude that the asymmetric dynamic interaction characterized by β ≠ α leads to the shift of the synchronized frequency with respect to the original distribution of the intrinsic frequency. We also perform and report our computer-based synchronization experiment, which exhibits the expected shift of the synchronized frequency of human participants. in analogy to interacting runners, our result roughly suggests that agents tend to run faster if they are more influenced by runners ahead than behind. We verify the observation by using a simple model of interacting runners.