Related papers: Intersection the twin dragon with rational lines
We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods.…
In some recent theories including Quantum SuperString theory we encounter duality - it arises due to a non commutative geometry which in effect adds an extra term to the Heiserberg Uncertainity Principle. The result is that the micro world…
Let $\Lambda$ be the limit set of a conformal dynamical system, i.e. a Kleinian group acting on either finite- or infinite-dimensional real Hilbert space, a conformal iterated function system, or a rational function. We give an easily…
We find clear numerical evidence for a bilinear condensate in three-dimensional QCD in the 't Hooft limit. We use a non-chiral random matrix model to extract the value of the condensate $\Sigma$ from the low-lying eigenvalues of the…
The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the…
We study quasisymmetric maps on two variants of the classical fractal percolation model: the fat and dense fractal percolations. We show that, almost surely conditioned on non-extinction, the Hausdorff dimension of the fat fractal…
Double parton scattering, occurring in high energy hadron-hadron collisions, e.g. at the LHC, is usually investigated through model dependent analyses of the so called effective cross section $\sigma_{eff}$. We present a dynamic approach to…
In Twin Higgs models which contain the minimal particle content required to address the little hierarchy problem (i.e. fraternal models), the twin tau has been identified as a promising candidate for dark matter. In this class of scenarios,…
Let $S$ and $T$ be hyperbolic endomorphisms of $\mathbb{T}^d$ with the property that the span of the subspace contracted by $S$ along with the subspace contracted by $T$ is $\mathbb{R}^d$. We show that the Hausdorff dimension of the…
Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work arXiv:1812.00309 of Dauvergne, Ortmann, and Vir\'ag, this…
In this work we reproduce the characterization of $\Gg^s$-sets from the euclidean setting [J. London Math. Soc. 49:267-280,1994] to more general metric spaces. These sets have Hausdorff dimension at least $s$ and are closed by countable…
We present an exact, closed-form expression for the Newtonian potential of the characteristic function associated with two overlapping discs in the plane. This setting naturally arises when discretising nonlocal interaction terms present in…
The growing reliance on digital twins across various industries and domains brings with it semantic interoperability challenges. Ontologies are a well-known strategy for addressing such challenges, though given the complexity of the…
For $k=1,2$, let $f_k=h_k+\overline{g_k}$ be normalized harmonic right half-plane or vertical strip mappings. We consider the convex combination $\hat{f}=\eta f_1+(1-\eta)f_2 =\eta h_1+(1-\eta)h_2 +\overline{\overline{\eta}…
This paper will extend a known relationship between the circumradius and dihedral angles of a tetrahedron in three-dimensional Euclidean space to three-dimensional affine space over a general field not of characteristic two, using only the…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
Hausdorff dimension of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections" "network" corresponding to a fractal set, $F$. This lead to the definition of the…
We study the fractal structure of space-time of two-dimensional quantum gravity coupled to c=-2 conformal matter by means of computer simulations. We find that the intrinsic Hausdorff dimension d_H = 3.58 +/- 0.04. This result supports the…
Let $K \subset {\mathbb R}^n$ be a compact definable set in an o-minimal structure over $\mathbb R$, e.g., a semi-algebraic or a subanalytic set. A definable family $\{ S_\delta|\> 0< \delta \in {\mathbb R} \}$ of compact subsets of $K$, is…
In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite-dimensional normed spaces, in the case…