A critical stochastic heat equation with long-range noise

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We study the singular stochastic wave equation on T 2 , with a cubic nonlinearity and Gaussian rough 'Matérn' forcing (a Fourier multiplier of order α > 0 applied to space-time white noise) and establish local well-posedness for α < 3 8. This extends [GKO18] beyond white noise and strengthens the quadratic-case result [OO21] (α < 1 2). Our argument develops new trilinear estimates in Bourgain spaces together with case-specific cubic counting estimates.

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A methodology to perform a rigorous verification of Particle-in-Cell (PIC) simulations is presented, both for assessing the correct implementation of the model equations (code verification), and evaluating the numerical uncertainty affecting the simulation results (solution verification). The proposed code verification methodology is a generalization of the procedure developed for plasma simulation codes based on finite difference schemes that is described by Riva in [Riva et al, Physics of Plasmas, Volume

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Chaotic synchronization is treated within the framework of information theory. It is shown that information theory implies fundamental limits to chaotic synchronization in the presence of channel noise. With regard for these limits, a scheme is suggested for the synchronization of two-dimensional chaotic maps. The central idea is that the communication channel should convey a symbolic sequence that contains information about the drive signal. It is established by computer simulations that the scheme enables

A critical stochastic heat equation with long-range noise

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