Related papers: Higher Order Spectra in Avalanche Models
We present a novel analytic calculation of the Haar power spectra, and various higher order spectra, of mean field avalanche models. We also compute these spectra from a simulation of the zero-temperature mean field RFIM and infinite range…
We analyze the statistics of gaps ($\Delta H$) between successive avalanches in one dimensional random field Ising models (RFIMs) in an external field $H$ at zero temperature. In the first part of the paper we study the nearest-neighbour…
To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems.…
The spectra of, e.g. open quantum systems are typically given as the superposition of resonances with a Lorentzian line shape, where each resonance is related to a simple pole in the complex energy domain. However, at exceptional points two…
Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
Modern cosmological surveys cover extremely large volumes and map fluctuations on scales reaching gigaparsecs. As a result, it is no longer a valid assumption to ignore cosmological evolution along the line of sight from one end of the…
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two…
In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…
One of the primitive aims of the two-dimensional BTW model had been to explain the $1/f^{\alpha}$ noise which is widely seen in the natural systems. In this paper we study some time signals, namely the activity inside an avalanche ($x(t)$),…
Within the framework of the random first-order transition theory of glasses, we discuss the statistics of thermal avalanches, the large scale rearrangements in driven amorphous systems near their instability. Stringy excitations yield…
We demonstrate that the present superaccurate measurements of transition processes between atomic states in hydrogen atom reached the limit of accuracy when transition frequency cannot be defined anymore in a unique way. This was predicted…
In Part I we have developed a theory for fitting p-mode Fourier spectra assuming that these spectra have a multi-normal distribution. We showed, using Monte-Carlo simulations, how one can obtain p-mode parameters using 'Maximum Likelihood…
The NMR spectra of paramagnetic substances can feature shifts over thousands of ppm. In high magnetic field instruments, this corresponds to extreme offsets, which make it challenging or impossible to achieve uniform excitation without…
Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the…
An exact generalization of the Ramsey transition probability is derived to improve ultra-high precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The…
We consider the contribution of 3rd and 4th order terms to the power spectrum of 21 cm brightness temperature fluctuations during the epoch of reionization, which arise because the 21 cm brightness temperature involves a product of the…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
The Hamiltonian Mean Field (HMF) model is a prototype for systems with long-range interactions. It describes the motion of $N$ particles moving on a ring, coupled through an infinite-range potential. The model has a second order phase…