Related papers: A polyhedral Markov field - pushing the Arak-Surga…
We consider polygonal Markov fields originally introduced by Arak and Surgailis (1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane,…
We construct random dynamics on collections of non-intersecting planar contours, leaving invariant the distributions of length- and area-interacting polygonal Markov fields with V-shaped nodes. The first of these dynamics is based on the…
We consider the so-called length-interacting Arak-Surgailis polygonal Markov fields with V-shaped nodes - a continuum and isometry invariant process in the plane sharing a number of properties with the two-dimensional Ising model. For these…
We consider polygonal Markov fields originally introduced by Arak and Surgailis (1982,1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane,…
We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. We focus fir st on consistent polygonal fields, for which we show Markovianity and…
In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…
In this letter we describe a method of extending an existing phase field model of polycrystalline solidification from two to three dimensions (3D).
We show that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations and provide a simple equation to find how the field evolves over time. Multiple 3D fields can be realized at different times by superposing with…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and…
The As-Rigid-As-Possible (ARAP) shape deformation framework is a versatile technique for morphing, surface modelling, and mesh editing. We discuss an improvement of the ARAP framework in a few aspects: 1. Given a triangular mesh in 3D…
Across various scientific and engineering domains, a growing interest in flexible and deployable structures is becoming evident. These structures facilitate seamless transitions between distinct states of shape and find broad applicability…
The theory of Markov processes on the square lattice has been given recently by the second author a new algebraic description in terms of operads. In particular, this new approach allows for a nice description of invariant boundary…
This is a new version of the paper, which uses the same methods as in the previous version, but the model is now different. We study two complex scalar fields coupled through a quadratic interaction in 2+1 dimensions. We use the method of…
We are generalizing to higher dimensions the Bavard-Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d-dimensional polyhedra with fixed directions of facet normals has a…
Spatial Galerkin projection transfers fields between different meshes. In the area of finite element analysis of electromagnetic fields, it provides great convenience for remeshing, multi-physics, domain decomposition methods, etc. In this…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
There have been several attempts in recent years to extend the notions of symplectic and Poisson structures in order to create a suitable geometrical framework for classical field theories, trying to achieve a success similar to the use of…
A difficult task to deal with is the analytical treatment of models composed by three real scalar fields, once their equations of motion are in general coupled and hard to be integrated. In order to overcome this problem we introduce a…
Observable structures of a topological field theory of AKSZ type are analyzed. From a double (or multiple) complex structure of observable algebras, new topological invariants are constructed. Especially, Donaldson polynomial invariants and…