Related papers: Numerical Stochastic Perturbation Theory and Gradi…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
Some topological properties of stochastic flow $\varphi_t(x)$ generated by stochastic differential equation in a ${\mathbb R}^d_+$ with normal reflection at the boundary are investigated. Sobolev differentiability in initial condition is…
We propose a new strategy for the determination of the step scaling function $\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this approach the determination of $\sigma(u)$ is broken in two pieces: a change of the flow…
We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the…
We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the algorithm implementation is in principle straightforward and report on the status of the…
The Schr\"odinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the…
Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome.…
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…
We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…
A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
A few comments are made on the role of nonperturbative and perturbative power corrections. This is followed by a description of energy flow observables and correlations that may provide a flexible approach to rapidity distributions in…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
In this paper, we study the fractional harmonic gradient flow on $S^1$ taking values in $S^{n-1} \subset \mathbb{R}^n$ for every $n \geq 2$, in particular addressing uniqueness and regularity of solutions in the so-called energy class with…
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic…
Kinetic instabilities are one of the most challenging aspects in computational plasma physics. Accurately capturing their onset and evolution requires fine resolution of the high-dimensional distribution functions of each relevant species,…