Related papers: 1/f noise from nonlinear stochastic differential e…
The collective behavior of a two-dimensional wet granular cluster under horizontal swirling motions is investigated experimentally. Depending on the balance between the energy injection and dissipation, the cluster evolves into various…
Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order…
The current noise in a classical one-dimensional charge density wave system is studied in the weak pinning regime by solving the overdamped equation of motion numerically. At low temperatures and just above the zero temperature depinning…
Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…
To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By…
Many simulations of stochastic processes require colored noises: I describe here an exact numerical method to simulate power-law noises: the method can be extended to more general colored noises, and is exact for all time steps, even when…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
We consider the family of stochastic partial differential equations indexed by a parameter $\eps\in(0,1]$, \begin{equation*} Lu^{\eps}(t,x) = \eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*} $(t,x)\in(0,T]\times\Rd$ with…
The power spectrum of local field potentials (LFPs) has been reported to scale as the inverse of the frequency, but the origin of this "1/f noise" is at present unclear. Macroscopic measurements in cortical tissue demonstrated that electric…
The quantum indeterminacy caused by non-commutativity of observables at different times sets a lower bound on the voltage noise power spectrum in any conducting material. This bound is calculated explicitly in the case of semiconductors…
This is a pedagogical review of the ubiquitous 1/f^\alpha noises. The sections include the representation of 1/f^\alpha noise as a superposition of many relaxation processes; a discussion of the infinitely large fluctuations in the low…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
In systems with weak ergodicity breaking, the equivalence of time averages and ensemble averages is known to be broken. We study here the computation of the power spectrum from realizations of a specific process exhibiting 1/f^beta noise,…
We propose that power-law tailed hadron spectra may be viewed as stemming from a matter in an unconventional equilibrium state typical for non-extensive thermodynamics. A non-extensive Boltzmann equation, which is able to form such spectra…
Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically; and the frequency spectrum of this chemical fluctuation carries valuable information about the mechanism and the dynamics of the intracellular…
Power spectral density scaling with frequency $f$ as $1/f^\beta$ and $\beta \approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics…
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…