Related papers: Electrodynamics on the Moebius Strip
This paper describes, in the case of the unit circle, several applications of a geometrically intrinsic treatment of counterparts of classical electrostatics, previously developed in [4] and [5].
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
These lectures are intended to provide an introduction to the rich interplay between N-body simulations and stellar-kinematic observations of galaxies. The first section describes the kinematic properties of galaxies that are accessible to…
String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as…
An appropriate diagram is a required element of a solution building process in physics problem solving and it can transform a given problem into a representation that is easier to exploit for solving the problem. A major focus while helping…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
We review basic computational techniques for simulations of various magnetic properties of solids. Several applications to compute magnetic anisotropy energy, spin wave spectra, magnetic susceptibilities and temperature dependent…
We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements, and the impedance calculus, a powerful toolbox for…
The study of graph drawings on 2-surfaces is an active area of mathematical research. Our main results are criteria for integer and modulo 2 embeddability of graphs to surfaces.
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
We present TopoTB, a software package written in the Mathematica language, designed to compute electronic structures, topological properties, and phase diagrams based on tight-binding models. TopoTB is user-friendly, with an interactive…
Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via…
Inspired by Tokieda's work on mechanical insights in geometry, we explore a hydrostatic approach to classical geometric problems. Using principles of fluid statics, we derive two mathematical results regarding polygons. These results…
The so-called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2-manifold surfaces. Applications are in the fields of surface…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
In this paper we study in detail, both analytically and numerically, the dynamical properties of the triangle map, a piecewise parabolic automorphism of the two-dimensional torus, for different values of the two independent parameters…
The use of the electric curtain (EC) has been proposed for manipulation and control of particles in various applications. The EC studied in this paper is called the 2-phase EC, which consists of a series of long parallel electrodes embedded…
A particle-based model for mesoscopic fluid dynamics is used to simulate steady and unsteady flows around a circular and a square cylinder in a two-dimensional channel for a range of Reynolds number between 10 and 130. Numerical results for…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…