Related papers: Examples of geometric transition in low dimensions
In this paper, a lot of examples of four-dimensional manifolds with an almost hypercomplex pseudo-Hermitian structure are constructed in several explicit ways. The received 4-manifolds are characterized by their linear invariants in the…
This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a…
Waveguide geometries combining bent asymmetric coupled structures and adiabatic transitions shaped as partial Euler bends are put forward and theoretically analyzed in this work. Designs aiming to reduce the radiation loss, with application…
In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector…
Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…
Following notation introduced in the recent paper \cite{Rdef}, this paper is aimed to present in detail an example of a "small" geometric transition which is not a "simple" one i.e. a deformation of a conifold transition. This is realized…
A geometric analysis of the $sdg$ interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole ($\beta_2$), axial hexadecapole ($\beta_4$) and triaxial ($\gamma_2$). The…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
We study phase structures of Lorentzian Dyonic Taub-NUT-AdS spacetimes for different horizon geometries, which are spherical, flat, and hyperbolic. We check the consistency of our extended thermodynamics approach through satisfying the…
This paper investigates several distinct attempts to generalize in higher dimension the standard 2-dimensional phyllotaxy set construction. We first recall known contructions for these sets on $2D$ manifolds of constant curvature (the…
One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how…
This thesis details the results of four interrelated projects. The first of these presents a new proof of the theorem of Cooper, Danciger and Wienhard classifying the limits under conjugacy of the orthogonal groups in GL(n; R). The second…
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…
In this note we give simple examples of a one-dimensional mixing subshift with positive topological entropy which have two distinct measures of maximal entropy. We also give examples of subshifts which have two mutually singular equilibrium…
Changes of type transitions for the two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 X 2 Jordan block) on the transition line with hodograph equations becoming…
We give the first example of a transitive quadratic map whose real and complex geometric pressure functions have a high-order phase transition. In fact, near the phase transition these functions behave as $x \mapsto \exp (- 1 / x^2)$ near…
We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets of full topological entropy and full Hausdorff dimension. The examples include some partially hyperbolic systems and geometric Lorenz flows. We…
We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function. This implies that several dimension spectra and large deviation rate functions associated to this map are not…
The purpose of this article is to review some recent results on the geometry of neutral signature metrics in dimension four and their twistor spaces. The following topics are considered: Neutral K\"ahler and hyperk\"ahler surfaces, Walker…
We study a simplified two-dimensional model for a cubic-to-orthorhombic phase transition occuring in certain shape-memory-alloys. In the low temperature regime the linear theory of elasticity predicts various possible patterns of martensite…