Related papers: Introduction to the method of multiple scales
Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot's model with frequency-independant coefficients. The coexistence of a propagating fast wave and a diffusive slow…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022.…
Accurate descriptions of reference systems are a central task in liquid-state theories for the study of more complex systems. Using scaled particle theory (SPT), we derive a fully analytical description of the thermodynamic properties of a…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
The paper is devoted to the study of homeomoephisms with finite distortion on the plane with use of the modulus techniques.
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding non-linear Euler--Lagrange equations, as well as connections…
This chapter is in three parts. The first presents the fundamental equations of level populations and radiative transfer which govern spectral line emission and absorption. Lines in the cm-wave band have similarities which allow us to…
This article displays a proof of concept of the mixed analytical/numerical method, presented in previous publications, to compute two-loop functions with up to five massive propagators in a scalar theory having three- and four-leg vertices…
This communication is both a pedagogical note for understanding polyatomic modelling in kinetic theory and a ''cheat sheet'' for a series of corresponding concepts and formulas. We explain, detail and relate three possible approaches for…
Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral…
The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions…
The field of partial differential equations (PDEs) is vast in size and diversity. The basic reason for this is that essentially all fundamental laws of physics are formulated in terms of PDEs. In addition, approximations to these…
Predicting ocean wave behavior is challenging due to the difficulty in choosing suitable numerical models among many with varying capabilities. This review examines the development and performance of numerical wave models in coastal…
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
This paper is the forth part of our series of work, is devoted to the analysis on the multiscales and cascade aspects of the statistical theory of isotropic turbulence based on the new Sedov-type solution. In this paper, we use the explicit…