Related papers: The instanton method and its numerical implementat…
How systems transit between different stable states under external perturbation is an important practical issue. We discuss here how a recently-developed energy optimization method for identifying the minimal disturbance necessary to reach…
Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the…
The Euclidean path integral is well approximated by instantons. If instantons are dynamical, then instantons are necessarily complexified. These fuzzy instantons can have various physical applications. In slow-roll inflation models, fuzzy…
We are interested in the development of an algorithmic differentiation framework for computing approximations to tangent vectors to scalar and systems of hyperbolic partial differential equations. The main difficulty of such a numerical…
Recently, a minimal kinetic model for fluid flow, known as entropic lattice Boltzmann method, has been proposed for the simulation of isothermal hydrodynamic flows. At variance with previous Lattice Boltzmann methods, the entropic version…
In fluid dynamics governed by the one dimensional inviscid Burgers equation $\partial_t u+u\partial_x(u)=0$, the stirring is explained by the sticky particles model. A Markov process $([Z^1_t,Z^2_t],\,t\geq0)$ describes the motion of random…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
The randomly driven Burgers equation with pressure is considered as a 1D model of strong turbulence of compressible fluid. It is shown that infinitely small pressure provides a finite effect on the velocity and density statistics and this…
For rare events, path probabilities often concentrate close to a predictable path, called instanton. First developed in statistical physics and field theory, instantons are action minimizers in a path integral representation. For chaotic…
Numerical simulation of turbulent fluid dynamics needs to either parameterize turbulence-which introduces large uncertainties-or explicitly resolve the smallest scales-which is prohibitively expensive. Here we provide evidence through…
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…
Identifying self-similarity is key to understanding and modelling a plethora of phenomena in fluid mechanics. Unfortunately, this is not always possible to perform formally in highly complex flows. We propose a methodology to extract the…
In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential…
In quantizing classical mechanical systems one often sums over the classical trajectories as in localization formulas, but also takes into account the contributions of the "instanton gas": a set of approximate solutions of the equations of…
The known calculations of the fermion condensate $<\bar{\psi}\psi>$ and the correlator $<\bar{\psi}\psi(x) ~\bar{\psi}\psi(0)>$ have been interpreted in terms of {\em localized} instanton solutions minimizing the {\em effective} action.…
A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the…
Using the idea of the instanton approach to quantum tunneling we try to obtain a method of calculating spontaneous fission rates for nuclei with the odd number of neutrons or protons. This problem has its origin in the failure of the…
Iterative coarse-graining procedure based on Wyld's perturbation expansion is applied to the problem of Navier-Stokes turbulence. It is shown that the low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$ (coupling…
Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…
The integral method can be used to model accurately flows down an inclined plane. Such a method consists in projecting the full 3D equations on a lower dimensional representation. The vertical velocity profiles have their functional form…