Related papers: Non-perturbative VEVs from a Local Expansion
The evolution of an initial perturbation in Vlasov plasma is studied in the intrinsically nonlinear long-time limit dominated by the effects of particle trapping. After the possible transient linear exponential Landau damping, the evolution…
Covariant Lyapunov vectors or CLVs span the expanding and contracting directions of perturbations along trajectories in a chaotic dynamical system. Due to efficient algorithms to compute them that only utilize trajectory information, they…
Detailed deterministic derivation of the kinetic equations for the relativistic plasmas is given. Focus is made on the dynamic of one-coordinate distribution functions of various tensor dimensions, but the closed set of kinetic equations is…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
A nonlocal form of a two-layer fluid system is proposed by a simple symmetry reduction, then by applying multiple scale method to it a general nonlocal two place variable coefficient modified KdV (VCmKdV) equation with shifted space and…
Reduced fluid models for collisionless plasmas including electron inertia and finite Larmor radius corrections are derived for scales ranging from the ion to the electron gyroradii. Based either on pressure balance or on the…
The gyrokinetic paradigm in the long wavelength regime is reviewed from the perspective of variational averaging (VA). The VA-method represents a third pillar for averaging kinetic equations with highly-oscillatory characteristics, besides…
We present a new approach for search of coexisting classes of localised modes admitted by the repulsive (defocusing) scalar or vector nonlinear Schr\"odinger-type equations. The approach is based on the observation that generic solutions of…
We derive new limit theorems for Brownian motion, which can be seen as non-exponential analogues of the large deviation theorems of Sanov and Schilder in their Laplace principle forms. As a first application, we obtain novel scaling limits…
The variational autoencoder (VAE) is a popular deep latent variable model used to analyse high-dimensional datasets by learning a low-dimensional latent representation of the data. It simultaneously learns a generative model and an…
The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has…
This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…
Transformation-based methods have been an attractive approach in non-parametric inference for problems such as unconditional and conditional density estimation due to their unique hierarchical structure that models the data as flexible…
A long-standing open problem in harmonic analysis is: given a non-negative measure $\mu$ on $\mathbb R$, find the infimal width of frequencies needed to approximate any function in $L^2(\mu)$. We consider this problem in the "perturbative…
Twist fields emerge in a number of physical applications ranging from entanglement entropy to scattering amplitudes in four-dimensional gauge theories. In this work, their vacuum expectation values are studied in the path integral…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special…
Shockwaves provide a useful and rewarding route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear transport…
With a view toward application of the Pauli-Villars regularization method to the Casimir energy of boundaries, we calculate the expectation values of the components of the stress tensor of a confined massive field in 1+1 space-time…
We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics - cone angle, flash duration, radiation yield and spectral distribution - are computed.…