Related papers: Advanced Mathematical Techniques in Renormalizatio…
Experimental High Energy Physics has entered an era of precision measurements. However, measurements of many of the accessible processes assume that the final states' underlying kinematic distribution is the same as the Standard Model…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
Quantitative characterization of tissue properties, known as elasticity imaging, can be cast as solving an ill-posed inverse problem. The finite element methods (FEMs) in magnetic resonance elastography (MRE) imaging are based on solving a…
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the…
This is the second part of the notes to the course on quantum theory of large systems of non-relativistic matter taught by J. Fr\"{o}hlich at the 1994 Les Houches summer school. It is devoted to a sketchy exposition of some of the beautiful…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer…
Understanding the intricate properties of one-dimensional quantum systems coupled to multiple reservoirs poses a challenge to both analytical approaches and simulation techniques. Fortunately, density matrix renormalization group-based…
From sand piles to electrons in metals, one of the greatest challenges in modern physics is to understand the behavior of an ensemble of strongly interacting particles. A class of quantum many-body systems such as neutron matter and cold…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…
These lectures serve as an introduction to the renormalization group approach to effective field theories, with emphasis on systems with a Fermi surface. For such systems, demanding appropriate scaling with respect to the renormalization…
The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages such as density, linear momentum, and energy were previously…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
I apply a two-step density-matrix renormalization group method to the anisotropic two-dimensional tight-binding model. This study, which is a prelude to the study of models of quasi-one dimensional materials, shows the potential power of…
Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the non-interacting) Hamiltonian. We describe such a renormalized…
We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…