Related papers: A Gravitational Effective Action on a Finite Trian…
Surface/edge energy is typically modeled as a continuous function of orientation, $\gamma({\bf n})$. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravais lattice structure. In…
We elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations $(h)$ of the background metric, in the flat spacetime limit. For this purpose we discuss the…
The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit…
Three particles floating on a fluid surface define a triangle. The aim of this paper is to characterise the shape of the triangle, defined by two of its angles, as the three vertices are subject to a complex or turbulent motion. We consider…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the surface. A careful study of possible…
A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of…
Two exact lens equations have been recently shown to be equivalent to each other, being consistent with the gravitational deflection angle of light from a source to an observer, both of which can be within a finite distance from a lens…
Robotic motion optimization often focuses on task-specific solutions, overlooking fundamental motion principles. Building on Riemannian geometry and the calculus of variations (often appearing as indirect methods of optimal control), we…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
Given a surface $\Sigma$ equipped with a set $P$ of marked points, we consider the triangulations of $\Sigma$ with vertex set $P$. The flip-graph of $\Sigma$ whose vertices are these triangulations, and whose edges correspond to flipping…
We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…
The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including…
The classical notion of twisted product is studied in the context of partial actions, in particular, we show that the globalization of a partial action is a twisted product. In addition, we establish conditions for the metrizability of…
A procedure to measure the residual tilt angle $\tau$ between a flat surface and the azimuthal rotation axis of the sample holder is described. When the incidence angle $\theta$ and readout of the azimuthal angle $\phi$ are controlled by…
In the past perfect surfaces have been shown to yield a local critical behaviour that differs from the bulk critical behaviour. On the other hand surface defects, whether they are of natural origin or created artificially, are known to…
Using an effective one body approach we describe in detail gravitational waves from classical three body problem on a non-rotating straight line and derive their basic physical characteristics. Special attention is paid to the irregular…
We discuss a way to exploit the conformal mapping to study the response of a finite metallic element of arbitrary shape to an external electromagnetic field at finite frequencies. This provides a simple way to study different physics issues…
A number of approaches to 4D quantum gravity, such as holography and loop quantum gravity, propose areas instead of lengths as fundamental variables. The Area Regge action, which can be defined for general 4D triangulations, is a natural…
This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe…