Related papers: Advanced Mathematical Techniques in Renormalizatio…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Ab initio path integral Monte Carlo (PIMC) simulations constitute the gold standard for the estimation of a broad range of equilibrium properties of a host of interacting quantum many-body systems spanning conditions from ultracold atoms to…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
We illustrate how the reorganization of perturbation theory at finite temperature can be economically cast in terms of the Wilson-Polchinski renormalization methods. We take as an example the old saw of the induced thermal mass of a hot…
The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi…
An efficient numerical approach to equilibrium properties of strongly coupled systems which include a subsystem of fermionic quantum particles and a subsystem of classical particles is presented. It uses an improved path integral…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…
In this work we combine quantum renormalization group approaches with deep artificial neural networks for the description of the real-time evolution in strongly disordered quantum matter. We find that this allows us to accurately compute…
We investigate the hydrodynamic recovery of Lattice Boltzmann Method (LBM) by analyzing exact balance relations for energy and enstrophy derived from averaging the equations of motion on sub-volumes of different sizes. In the context of 2D…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
Renormalization group procedure for effective particles in the front form of Hamiltonian dynamics is applied to an elementary quantum field theory for two species of particles mixed through a mass-like interaction term. The model…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of invariant manifolds of the dynamics under…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
In this paper, we deal with the inverse problem of the shape reconstruction of inclusions in elastic bodies. The main idea of this reconstruction is based on the monotonicity property of the Neumann-to-Dirichlet operator presented in a…
We develop an asymptotically exact renormalization group (RG) approach that treats electron-electron and electron-phonon interactions on equal footing. The approach allows an unbiased study of the instabilities of Fermi liquids without the…
Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily…