Related papers: Resistance Scaling on $4N$-Carpets
We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an {\em n}-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form…
The scaling properties of self-avoiding walks on a d-dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Y. Meir and A. B.…
We use a recently proposed method [Berthier L.; Biroli G.; Bouchaud J.P.; Cipelletti L.; El Masri D.; L'Hote D.; Ladieu F.; Pierno M. Science 2005, 310, 1797.] to obtain an approximation to the 4-point dynamic correlation function from…
Using the $SO ({\cal N})$ superspace formulation for $\cal N$-extended conformal supergravity in three dimensions, we derive all maximally supersymmetric backgrounds in the ${\cal N} =4$ case. The specific feature of this choice is that the…
The Faber-Krahn inequality states that the first Dirichlet eigenvalue among all bounded domains is no less than a Euclidean ball with the same volume in $\mathbb{R}^n$ \cite{Chavel FB}. B{\i}y{\i}ko\u{g}lu and Leydold (J. Comb. Theory, Ser.…
We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragm\'en-Lindel\"of theorem and use Fourier series to obtain a discrete analog…
Singular vectors are those for which the quality of rational approximations provided by Dirichlet's Theorem can be improved by arbitrarily small multiplicative constants. We provide an upper bound on the Hausdorff dimension of singular…
Theories of anti-commuting scalar fields are non-unitary, but they are of interest both in statistical mechanics and in studies of the higher spin de Sitter/Conformal Field Theory correspondence. We consider an $Sp(N)$ invariant theory of…
We prove that any D-dimensional theory comprising gravity, an antisymmetric n-index field strength and a dilaton can be consistently reduced on S^n in a truncation in which just $n$ scalar fields and the metric are retained in…
We establish the existence of a scaling limit $\mathcal{E}_p$ of discrete $p$-energies on the graphs approximating generalized Sierpi\'{n}ski carpets for $p > \dim_{\text{ARC}}(\textsf{SC})$, where $\dim_{\text{ARC}}(\textsf{SC})$ is the…
Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes…
Effective field theories (EFTs) provide a powerful framework to parametrise unknown aspects of possible ultraviolet (UV) physics. For scalar fields in de Sitter space, however, new emergent phenomena can arise when the cut-off scale of the…
We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet…
If $U$ is a $C^{\infty}$ function with compact support in the plane, we let $u$ be its restriction to the unit circle $\mathbb{S}$, and denote by $U_i,\,U_e$ the harmonic extensions of $u$ respectively in the interior and the exterior of…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
The thermal resistivity and its scaling function in quasi-2D $^4$He systems are studied by Monte Carlo and spin-dynamics simulation. We use the classical 3D XY model on $L\times L\times H$ lattices with $L\gg H$, applying open boundary…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
The scaling of friction with the contact size $A$ and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are…
We develop a parametric approach to study the Diophantine equation $\frac{k}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$, underlying the Erd\H{o}s--Straus ($k=4$), Sierpi\'nski ($k=5$), and related generalizations. We introduce and…
Let $F$ be a Bedford-McMullen carpet defined by independent integer exponents. We prove that for every line $\ell \subseteq \mathbb{R}^2$ not parallel to the major axes, $$ \dim_H (\ell \cap F) \leq \max \left\lbrace 0,\, \frac{\dim_H…