Related papers: The Geometry of Point Particles
Postulating that spacetime is discrete, we assume that physical space is described by a 3-dimensional cubic lattice.The corresponding symmetry group of rotations has order 24 and motivates the introduction of a cubic shaped graph with 27…
Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free energy landscape of such…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
Euclidean field theory on 4-dimensional sphere is suggested for the study of high energy multiparticle production. The singular classical field configurations are found in scalar and SU(2)-gauge theories and the cross section of 2->n…
In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space. The geometric contributions can result from the…
We have discovered that two significant quantities within hard particle systems: the probability of successfully inserting an additional particle at random and the scale distribution function, can be connected by a concise relation. We…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
A cohomological study is made of an equivariant map betwen the configuration space of n points in space and the flag manifold of U(n).
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
This paper investigates minimal $n$-dimensional submanifolds in the Euclidean space that are $(n-2)$-umbilic, meaning they carry an umbilical distribution of rank $n-2$. We establish a correspondence between the class of minimal…
We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs (x,x') of points in R^n which satisfy d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of n)…
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space $\mathbb{R}^3$ are easier to feel by human's intuition. We give the maximum order of finite group actions on $(\mathbb{R}^3, \Sigma)$…
It is quite an interesting phenomenon in Topology that configuration spaces on a manifold M are intrinsically related to certain mapping spaces from M. In this paper we interpret and greatly expand on this relationship. Building (mainly) on…
The basic principles of self-organization of one-component charged particles, confined in disk and circular parabolic potentials, are proposed. A system of equations is derived, that allows us to determine equilibrium configurations for an…
We report on a study of a finite system of classical confined particles in two-dimensions in the presence of a uniform magnetic field and interacting via a two-body repulsive potential. We develop a simple analytical method of analysis to…
We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the…
We investigate asymmetric nuclear matter with two- and three-nucleon interactions based on chiral effective field theory, where three-body forces are fit only to light nuclei. Focusing on neutron-rich matter, we calculate the energy for…
We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for…