Related papers: A Gravitational Effective Action on a Finite Trian…
The confining geometries of fermions in 2D structures exhibits interesting results that have highest symmetry. Delusion can be considered as the topological effect which is topological invariant. Topologically, genus zero surfaces needs…
The determination of the gravitational potential by the polyhedral method is revisited in the case where the surface of a body is composed of triangular facets. Based upon six test-shapes of astrophysical interest (sphere, spheroid,…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
Gravitational lensing by a spinning deflector in translational motion relative to the observer is discussed in the weak field, slow motion approximation. The effect of rotation, which generates an intrinsic gravito-magnetic field, separates…
We revisit here a fundamental result on planar triangulations, namely that the flip distance between two triangulations is upper-bounded by the number of proper intersections between their straight-segment edges. We provide a complete and…
In a previous work we showed that, in a suitable setting, one can use diffeomorphism invariance in order to derive gravitational field equations from boundary terms of the gravitational action. Standing by our results we reply here to a…
Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
We show that the trace anomaly for gravitons calculated using the usual effective action formalism depends on the choice of gauge when the background spacetime is not a solution of the classical equation of motion, that is, when off-shell.…
Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing…
The Effective Average Action is a form of effective action which depends on a cutoff scale suppressing the contribution of low momentum modes in the functional integral. It reduces to the ordinary effective action when the cutoff scale goes…
A triangulation of a surface is \emph{irreducible} if there is no edge whose contraction produces another triangulation of the surface. We prove that every irreducible triangulation of a surface with Euler genus $g\geq1$ has at most $13g-4$…
We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore…
The bending of lightrays by the gravitational field of a ``lens'' that is moving relative to the observer is calculated within the approximation of weak fields, small angles and thin lenses. Up to first order in $v/c$ -- and assuming the…
The problem of gauge independent definition of effective gravitational field is considered from the point of view of the process of measurement. Under assumption that dynamics of the measuring apparatus can be described by the ordinary…
We study the drag force on discrete objects with circular cross section moving slowly through a spherical granular medium. Variations in the geometry of the dragged object change the drag force only by a small fraction relative to shape…
We elaborate on the structure of the graviton-gauge-gauge vertex in the electroweak theory, obtained by the insertion of the complete energy-momentum tensor ($T$) on 2-point functions of neutral gauge currents ($VV'$). The vertex defines…
The image of a point situated at the center of a circularly symmetric potential is a perfect circle. The perturbative effect of non-symmetrical potential terms is to displace and break the perfect circle. These 2 effects, displacement and…
We investigate a counterintuitive geometric interaction between defects and curvature in thin layers of superfluids, superconductors and liquid crystals deposited on curved surfaces. Each defect feels a geometric potential whose functional…
We consider active nematodynamics on deformable surfaces. Based on a thermodynamically consistent surface Beris-Edwards model we add nematic activity and focus on the emerging additional coupling mechanism between the nematic field, the…