Related papers: Auto-Correlation Functions and Solar Cycle Predict…
Starting from a classical Budyko-Sellers-Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irradiance and the cloud cover coefficients to vary with time in…
Based on analysis of the annual averaged relative sunspot number (ASN) during 1700 -- 2009, 3 kinds of solar cycles are confirmed: the well-known 11-yr cycle (Schwabe cycle), 103-yr secular cycle (numbered as G1, G2, G3, and G4,…
Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes…
We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal…
The assumption that wave function collapse is induced by correlating interactions of the kind that constitute measurements leads to a stochastic collapse equation that does not require the introduction of any new physical constants and that…
Severity of warming predicted by climate models depends on their Transient Climate Response (TCR). Inter-model spread of TCR has persisted at ~100% of its mean for decades. Existing observational constraints of TCR are based on observed…
Filaments are very common physical phenomena on the Sun and are often taken as important proxies of solar magnetic activities. The study of filaments has become a hot topic in the space weather research. For a more comprehensive…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
We point out that by the ``smoothness means fast decay'' principle in Fourier analysis, it is possible to infer the smoothness (or nonsmoothness) of the autocorrelation function from a mere glimpse of the initial state. Specifically, for a…
The solar tachocline, located at the interface between the latitude-dependent rotation of the convection zone and the rigid radiative interior, presents high gradients of angular velocity which are of particular interest for the models of…
The precise shape of the Sun is sensitive to the influence of gravity, differential rotation, local turbulence and magnetic fields. It has been previously shown that the solar shape exhibits asphericity that evolves with the 11-year cycle.…
We develop novel methods to compute auto-correlation functions, or power spectral densities, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the…
A new approach to the correlation functions is presented for the XXZ model in the anti-ferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson…
Theoretical modeling of the driving processes of solar-like oscillations is a powerful way of understanding the properties of the convective zones of solar-type stars. In this framework, the description of the temporal correlation between…
We introduce the wavelet scattering spectra which provide non-Gaussian models of time-series having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the…
We calculate the autocorrelation function for the characteristic polynomial of a random matrix in the microscopic scaling regime. While results fitting this description have be proved before, we will cover all values of inverse temperature…
Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty…
The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in…
Solar inertial modes are quasi-toroidal modes of the Sun that are of practical interest as they allow probing the deep convection zone. Since 2010, solar images of the photospheric magnetic field are made available by HMI onboard the Solar…
Many materials quenched into their ordered phase undergo ageing and there show dynamical scaling. For any given dynamical exponent z, this can be extended to a new form of local scale-invariance which acts as a dynamical symmetry. The…