Related papers: Modeling of Solids
We provide a pedagogical introduction to some aspects of integrability, dualities and deformations of physical systems in 0+1 and in 1+1 dimensions. In particular, we concentrate on the T-duality of point particles and strings as well as on…
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
We have two basic methods of modeling matter. We can treat matter as a continuum and solve differential equations or we can treat it discretely and solve massive N-body problems. The differential equations produced by meaningful problems…
We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research,…
We present an intermediate-level course on sustainable physics, which combines lectures and student projects. Sustainable physics concepts are progressively introduced through both a global and a specialized perspective: climate change and…
Active suspensions, which consist of suspended self-propelling particles such as swimming microorganisms, often exhibit non-trivial transport properties. Continuum models are frequently employed to elucidate phenomena in active suspensions,…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
In this work, the principles of Homological Integration Theory are applied to the mathematical formulation of continuum mechanics. A central guideline in the currently acceptable formulation of continuum mechanics is that an admissible body…
We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes…
The aim in these lectures is to study singularity formation, nonuniqueness, and topological change in motion by mean curvature.
These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…
This monograph (written in 1974) is the last part of the author's study in the field of theoretical and practical mechanics of the inertless mass (or mechanics of continuous medium). The investigation enriches the theory and provides…
Physical and chemical properties of 2D material are highly sensitive to its structures whose regularity are seldom investigated, here we proposed a simple mechanical model whose covalent bonds are connected by angle springs, with which we…
We study the motion of the system, S, constituted by a rigid body, B, containing in its interior a viscous compressible fluid, and moving in absence of external forces. Our main objective is to characterize the long time behavior of the…
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.
This is a reflection on the author's experience in teaching logic at the graduate level in a computer science department. The main lesson is that model building and the process of modelling must be placed at the centre stage of logic…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
Molecular dynamics (MD) has become a powerful tool for studying biophysical systems, due to increasing computational power and availability of software. Although MD has made many contributions to better understanding these complex…