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Related papers: Resistance Scaling on $4N$-Carpets

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Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent $0.72 \pm 0.01$. Here, we show that, independent of the temperature, the iso-height…

Materials Science · Physics 2016-05-24 I. Giordanelli , N. Posé , M. Mendoza , H. J. Herrmann

We revisit the classical Unit Distance Problem posed by Erd\H{o}s in 1946. While the upper bound of $O(n^{4/3})$ established by Spencer, Szemer'edi, and Trotter (1984) is tight for systems of pseudo-circles, it fails to account for the…

Combinatorics · Mathematics 2026-01-28 Lucas Aloisio

Scale-invariance is a ubiquitous observation in the dynamics of large distributed complex systems. The computation of its scaling exponents, which provide clues on its origin, is often hampered by the limited available sampling data, making…

We consider the time-dependent response of a gravitationally-thinning inviscid liquid sheet (a coating curtain) leaving a vertical slot to sinusoidal ambient pressure disturbances. The theoretical investigation employs the hyperbolic…

Fluid Dynamics · Physics 2021-01-26 Bridget M. Torsey , Steven J. Weinstein , David S. Ross , Nathaniel S. Barlow

We present a unique experimental configuration that allows us to determine the interfacial forces on nearly parallel plates made from the thinnest possible mechanical structures, single and few layer graphene membranes. Our approach…

This study aims to construct a stable, high-order compact finite difference method for solving Sobolev-type equations with Dirichlet boundary conditions in one-space dimension. Approximation of higher-order mixed derivatives in some…

Numerical Analysis · Mathematics 2025-06-05 Lavanya V Salian , Samala Rathan , Rakesh Kumar

In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…

Mathematical Physics · Physics 2025-07-14 William Hoffer

In this paper, we first consider linear 2D and 3D convection-diffusion-reaction equations $-\nabla\cdot (\kappa \nabla u) + {\bm v} \cdot \nabla u + \lambda u = \phi$ and $u_t - \nabla\cdot (\kappa \nabla u) + {\bm v} \cdot \nabla u +…

Numerical Analysis · Mathematics 2026-03-18 Qiwei Feng

We prove the existence of nontrivial unbounded exceptional domains in the Euclidean space $\R^N$, $N\geq4$. These domains arise as perturbations of complements of straight cylinders in $\R^N$, and by definition they support a positive…

Analysis of PDEs · Mathematics 2023-06-21 Ignace Aristide Minlend , Tobias Weth , Jing Wu

We prove a scale-invariant boundary Harnack principle in inner uniform domains in the context of local regular Dirichlet spaces. For inner uniform Euclidean domains, our results apply to divergence form operators that are not necessarily…

Probability · Mathematics 2016-05-17 Janna Lierl , Laurent Saloff-Coste

We analyse and clarify the finite-size scaling of the weakly-coupled hierarchical $n$-component $|\varphi|^4$ model for all integers $n \ge 1$ in all dimensions $d\ge 4$, for both free and periodic boundary conditions. For $d>4$, we prove…

Mathematical Physics · Physics 2025-03-19 Emmanuel Michta , Jiwoon Park , Gordon Slade

The Landauer scattering approach to 4-probe resistance is revisited for the case of a d-dimensional disordered resistor in the presence of decoherence. Our treatment is based on an invariant-embedding equation for the evolution of the…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Dibyendu Roy , N. Kumar

We find an infinite family of $4D$ $\mathcal{N}=2$ interacting superconformal field theories which enter the description of the strong-coupling limit of $SU(2N+1)$ gauge theories with hypermultiplets in the…

High Energy Physics - Theory · Physics 2014-12-30 Oscar Chacaltana , Jacques Distler , Anderson Trimm

We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with…

Differential Geometry · Mathematics 2011-05-26 Olivier Biquard

We show how certain non-perturbative superpotentials W, which are the two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be computed via geometric engineering from 4-folds. We analyze an explicit example for which the…

High Energy Physics - Theory · Physics 2009-10-30 Wolfgang Lerche

We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system…

Statistical Mechanics · Physics 2023-02-08 Calvin Pozderac , Steven Speck , Xiaozhou Feng , David A. Huse , Brian Skinner

The main ingredient for local superconformal methods is the multiplet of gauge fields: the Weyl multiplet. We construct the transformations of this multiplet for $\mathcal{N}=3$, $D = 4$. The construction is based on a supersymmetry…

High Energy Physics - Theory · Physics 2019-01-23 Jesse van Muiden , Antoine Van Proeyen

We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as function of the correlation…

Statistical Mechanics · Physics 2018-01-03 Johannes Zierenberg , Niklas Fricke , Martin Marenz , F. P. Spitzner , Viktoria Blavatska , Wolfhard Janke

We study an effective field theory (EFT) describing the interaction of an approximate dilaton with a set of pseudo-Nambu-Goldstone bosons (pNGBs). The EFT is inspired by, and employed to analyse, recent results from lattice calculations…

High Energy Physics - Phenomenology · Physics 2020-04-22 Thomas Appelquist , James Ingoldby , Maurizio Piai

When a coherent quasi-monochromatic light is reflected from a step, a diffraction pattern is formed that can be described by Fresnel-Kirchhoff integral and visibility of the fringes depends on the height of the step. In this paper, it is…

Optics · Physics 2013-11-19 Soghra Osanloo , Ahmad Darudi
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