Philosophical Transactions of the Royal Society A最新文献

The dynamical properties of periodic two-component phononic rods, whose elementary cells are generated adopting the Fibonacci substitution rules, are studied through the recently introduced method of the toroidal manifold. The method allows all band gaps and pass bands featuring the frequency spectrum to be represented in a compact form with a frequency-dependent flow line on the surface describing their ordered sequence. The flow lines on the torus can be either closed or open: in the former case, (i) the frequency spectrum is periodic and the elementary cell corresponds to a canonical configuration, (ii) the band gap density depends on the lengths of the two phases; in the latter, the flow lines cover ergodically the torus and the band gap density is independent of those lengths. It is then shown how the proposed compact description of the spectrum can be exploited (i) to find the widest band gap for a given configuration and (ii) to optimize the layout of the elementary cell in order to maximize the low-frequency band gap. The scaling property of the frequency spectrum, that is a distinctive feature of quasicrystalline-generated phononic media, is also confirmed by inspecting band-gap/pass-band regions on the torus for the elementary cells of different Fibonacci orders. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

We review here a new scenario of hot spot electroweak baryogenesis where the local energy released in the gravitational collapse to form primordial black holes (PBHs) at the quark-hadron (QCD) epoch drives over-the-barrier sphaleron transitions in a far from equilibrium environment with just the standard model CP violation. Baryons are efficiently produced in relativistic collisions around the black holes and soon redistribute to the rest of the universe, generating the observed matter-antimatter asymmetry well before primordial nucleosynthesis. Therefore, in this scenario there is a common origin of both the dark matter to baryon ratio and the photon to baryon ratio. Moreover, the sudden drop in radiation pressure of relativistic matter at H⁰/W^±/Z⁰ decoupling, the QCD transition and e⁺e^- annihilation enhances the probability of PBH formation, inducing a multi-modal broad mass distribution with characteristic peaks at 10^-6, 1, 30 and 10⁶ M_⊙, rapidly falling at smaller and larger masses, which may explain the LIGO-Virgo black hole mergers as well as the OGLE-GAIA microlensing events, while constituting all of the cold dark matter today. We predict the future detection of binary black hole (BBH) mergers in LIGO with masses between 1 and 5 M_⊙, as well as above 80 M_⊙, with very large mass ratios. Next generation gravitational wave and microlensing experiments will be able to test this scenario thoroughly. This article is part of a discussion meeting issue 'Topological avatars of new physics'.

We examine how coupling functions in the theory of dynamical systems provide a quantitative window into climate dynamics. Previously, we have shown that a one-dimensional periodic non-autonomous stochastic dynamical system can simulate the monthly statistics of surface air temperature data. Here, we expand this approach to two-dimensional dynamical systems to include interactions between two sub-systems of the climate. The relevant coupling functions are constructed from the covariance of the data from the two sub-systems. We demonstrate the method on two tropical climate indices, the El-Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), to interpret the mutual interactions between these two air-sea interaction phenomena in the Pacific and Indian Oceans. The coupling function reveals that the ENSO mainly controls the seasonal variability of the IOD during its mature phase. This demonstrates the plausibility of constructing a network model for the seasonal variability of climate systems based on such coupling functions. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

An overview is given on two representative methods of dynamical reduction known as centre-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion than the theories in the past. The target systems of reduction are coupled limit-cycle oscillators. Particular emphasis is placed on the remarkable structural similarity existing between these theories. While the two basic principles, i.e. (i) reduction of dynamical degrees of freedom and (ii) transformation of reduced evolution equation to a canonical form, are shared commonly by reduction methods in general, it is shown how these principles are incorporated into the above two reduction theories in a coherent manner. Regarding the phase reduction, a new formulation of perturbative expansion is presented for discrete populations of oscillators. The style of description is intended to be so informal that one may digest, without being bothered with technicalities, what has been done after all under the word reduction. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.