Related papers: The instanton method and its numerical implementat…
Numerical and anaytical studies of the instanton liquid model have allowed the determination of many hadronic parameters during the last 13 years. Most part of this thesis is devoted to the extension of the analytical methods. The meson…
In these lectures we describe the use of Monte Carlo simulations in understanding the role of tunneling events, instantons, in a quantum mechanical toy model. We study, in particular, a variety of methods that have been used in the QCD…
Instanton processes are present in a variety of quantum field theories relevant to high energy as well as condensed matter physics. While they have led to important theoretical insights and physical applications, their underlying features…
Building upon the intrinsic properties of Navier-Stokes dynamics, namely the prevalence of intense vortical structures and the interrelationship between vorticity and strain rate, we propose a simple framework to quantify the extreme events…
This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are…
We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of…
We show that multiscaling properties of developed turbulence in shell models, which lead to anomalous scaling exponents in the inertial range, are determined exclusively by instanton dynamics. Instantons represent correlated extreme events…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability…
Numerical and anaytical studies of the instanton liquid model have allowed the determination of many hadronic parameters during the last 13 years. Most part of this thesis is devoted to the extension of the analytical methods. The meson…
The instant Lagranian coordinator system is used to describe the fluid material motion. By this way, the instant deformation gradient (expressed by spatial velocity gradient) concept is established. Based on this geometrical understanding,…
This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
The behaviour of the turbulent Prandtl number ($Pr_t$) for buoyancy-affected flows near a vertical surface is investigated as an extension study of {Gibson \& Leslie, \emph{Int. Comm. Heat Mass Transfer}, Vol. 11, pp. 73-84 (1984)}. By…
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…
Turbulent signals are known to exhibit burst-like activities, which affect the turbulence statistics at both large and small scales of the flow. In our study, we pursue this problem from the perspective of an event-based framework, where…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
This study investigates, by means of numerical simulations, extreme mechanical force exerted by a turbulent flow impinging on a bluff body, and examines the relevance of two distinct rare-event algorithms to efficiently sample these events.…
Recently there has been increasing interest in alternate methods to compute quantum tunneling in field theory. Of particular interest is a stochastic approach which involves (i) sampling from the free theory Gaussian approximation to the…
Canonical instanton theory is a widespread approach to describe the dynamics of chemical reactions in low temperature environments when tunneling effects become dominant. It is a semiclassical theory which requires locating classical…