Tootfinder

Holographic Turbulence and the Fractal Dimension of the Turbulent Horizon
Jia Du, Yu Tian, Hongbao Zhang
https://arxiv.org/abs/2510.12198 https://arxiv.org…

Holographic Turbulence and the Fractal Dimension of the Turbulent Horizon
We study two-dimensional turbulence driven by a scalar operator within the framework of the AdS/CFT correspondence, where the external driving source is used to sustain a quasi-steady turbulent state. We numerically construct dynamical and spatially inhomogeneous turbulent black holes in the asymptotically $\mathrm{AdS}_4$ spacetime by solving the full nonlinear equations of motion in the Bondi-Sachs formalism. The inverse energy cascade and the corresponding energy spectrum of both decaying an…

Can Fractal Dimension Distinguish between Grand-design and Flocculent Spiral Arms? #galaxies

Quasisymmetric mappings on two variants of fractal percolation
Roope Anttila, Sylvester Eriksson-Bique, Aleksi Py\"or\"al\"a
https://arxiv.org/abs/2510.06900 http…

Quasisymmetric mappings on two variants of fractal percolation
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 percolation cannot be lowered with a quasisymmetry and the Hausdorff dimension of the dense fractal percolation cannot be lowered with a power quasisymmetry.

Dimension dependence of critical phenomena in long-range percolation
Tom Hutchcroft
https://arxiv.org/abs/2510.03951 https://arxiv.org/pdf/2510.03951

Dimension dependence of critical phenomena in long-range percolation
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the model is defined. Moreover, many models are conjectured to have an upper critical dimension with important quantitative and qualitative differences between critical behaviour at, above, and below the upper critical dimension. For models with long-range inter…

Hausdorff dimension of the Wedding cake type surfaces
Bal\'azs B\'ar\'any, Manuj Verma
https://arxiv.org/abs/2510.04613 https://arxiv.org/pdf/2…

Hausdorff dimension of the Wedding cake type surfaces
In this paper, we study the Hausdorff dimension of fractal interpolation surfaces (FISs) over a triangular domain. These FISs are known as `wedding cake surfaces'. These surfaces are the attractor of some deterministic self-affine iterated function systems (IFS) on $\mathbb{R}^3$ generated by a fractal interpolation algorithm. Due to the recent seminal result of Rapaport (Adv. Math. 449 (2024) 109734), the dimension theory of self-affine IFS on $\mathbb{R}^3$ is known whenever the IFS is strong…

Box dimension of the graphs of recurrent fractal interpolation functions
Lai Jiang, Xiao-Hui Li, Zhen Liang, Huo-Jun Ruan
https://arxiv.org/abs/2510.02754 https://

Box dimension of the graphs of recurrent fractal interpolation functions
Let $f$ be a generalized affine recurrent fractal interpolation function with vertical scaling functions. In this paper, by introducing underlying local iterated function systems of $f$, we define restricted vertical scaling matrices. Then we prove the monotonicity of spectral radii of these matrices without additional conditions. We also prove the irreducibility of these matrices under the assumption that vertical scaling functions are positive. With these results, we estimate the upper and lo…

Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes
Daniil Kochergin
https://arxiv.org/abs/2510.10255 https://ar…

Localization Transition on Random Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes
We studied single-particle Anderson localization in ensembles of graphs that correspond to chiral and Bogoliubov-de Gennes (BdG) symmetry classes. For a random biregular bipartite graph with chiral symmetry, the density of states was found using the cavity approach. Calculating the fractal dimension shows the effects of disordered zero modes. For Bogoliubov-de Gennes ensembles with an underlying random regular graph (RRG), the density of states was calculated both numerically and analytically. …

Bilinear spherical maximal function with fractal dilations
Surjeet Singh Choudhary, Chun-Yen Shen, Saurabh Shrivastava
https://arxiv.org/abs/2510.03094 https://

Bilinear spherical maximal function with fractal dilations
In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general dilation set $E\subset\R_+$. We quantify the range of $L^p-$boundedness in terms of a dilation-invariant notion of upper Minkowski dimension of the set $E$. A particular case of this study settles an open question of $L^p-$boundedness of the lacunary bilinear spherical maximal function at borderline cases $p_1=1$ or $p_2=1$ in dimension $d\geq4$.

Replaced article(s) found for cond-mat.str-el. https://arxiv.org/list/cond-mat.str-el/new
[1/1]:
- Fractal dimension and the counting rule of the Goldstone modes
Qian-Qian Shi, Yan-Wei Dai, Huan-Qiang Zhou, Ian P. McCulloch

Generalized Thue-Morse measures: spectral and fractal analysis
Philipp Gohlke, Marc Kesseb\"ohmer, Tanja I. Schindler
https://arxiv.org/abs/2509.22109 https://

Generalized Thue-Morse measures: spectral and fractal analysis
We investigate a family of Riesz products and show that they can be regarded as diffraction measures of generalized Thue-Morse sequences, possibly over an infinite alphabet. These measures are closely related to the dynamical system arising from the doubling map together with an observable exhibiting a logarithmic singularity. For this system, we develop a generalized thermodynamic formalism beyond the standard setting, which yields explicit formulas for Birkhoff and dimension spectra. A furthe…

Delocalization Induced by Enhanced Hyperuniformity in One-Dimensional Disordered Systems
Junmo Jeon, Harukuni Ikeda, Shiro Sakai
https://arxiv.org/abs/2509.23036 https://…

Delocalization Induced by Enhanced Hyperuniformity in One-Dimensional Disordered Systems
In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic potentials. In tight-binding chains, strong hyperuniformity induces a sharp delocalization transition and the emergence of mobility edges. The transition is identified by the generalized fractal dimension and corroborated by the scaling of localization length…