Related papers: Gel'fand-Yaglom type equations for calculating flu…
The fluctuation determinant, the preexponential factor for the instanton transition, has been computed several years ago in the Abelian Higgs model, using a method based on integrating the Euclidean Green' function. A more elegant method…
Large deviation theory and instanton calculus for stochastic systems are widely used to gain insight into the evolution and probability of rare events. At its core lies the realization that rare events are, under the right circumstances,…
We consider the quantum tunneling phenomenon in a well-behaved triple-well potential. As required by the semiclassical approximation we take into account the quadratic fluctuations over the instanton which represents as usual the localised…
The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution…
We present a new method for sampling rare and large fluctuations in a non-equilibrium system governed by a stochastic partial differential equation (SPDE) with additive forcing. To this end, we deploy the so-called instanton formalism that…
We propose the new method for finding the non-Gaussian tails of probability distribution function (PDF) for solutions of a stochastic differential equation, such as convection equation for a passive scalar, random driven Navier-Stokes…
Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607 (2020)]. Here, we use instanton calculus to quantify the effect of extreme…
It has been shown recently that intermittency of the Gledzer Ohkitani Yamada (GOY) shell model of turbulence has to be related to singular structures whose dynamics in the inertial range includes interactions with a background of…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
We perform a detailed analytical study of the Recent Fluid Deformation (RFD) model for the onset of Lagrangian intermittency, within the context of the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. The model is…
The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. If the fluid is turbulent, the statistics of the passive scalar exhibit complex behavior. This paper is concerned with…
Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields…
Instanton calculations are performed in the context of stationary Burgers turbulence to estimate the tails of the probability density function (PDF) of velocity gradients. These results are then compared to those obtained from massive…
In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…
For many non-equilibrium dynamics driven by small noise, in physics, chemistry, biology, or economy, rare events do matter. Large deviation theory then explains that the leading order term of the main statistical quantities have an…
In the context of instanton method for stochastic system this paper purposes a modification of the arclength parametrization of the Hamilton's equations allowing for an arbitrary instanton speed. The main results of the paper are: (i) it…
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…