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In this paper we study the problem of approximation of the $L^2$-topological invariants by their finite dimensional analogues. We obtain generalizations of the theorem of L\"uck, dealing with towers of finitely sheeted normal coverings. We…

dg-ga · Mathematics 2008-02-03 Michael Farber

A new class of truncation schemes of delta expansion on the lattice is studied. We show that the order of expansion in delta which is introduced as the dilation parameter can be taken large enough and the result gives rise to the Borel…

High Energy Physics - Lattice · Physics 2008-12-18 Hirofumi Yamada

Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth- rates of logarithmic bred vectors (which…

Chaotic Dynamics · Physics 2010-06-15 Sarah Hallerberg , Diego Pazó , Juan M. López , Miguel A. Rodríguez

We study hyperuniform properties for the square-triangle tilings. The tiling is generated by a local growth rule, where squares or triangles are iteratively attached to its boundary. The introduction of the probability $p$ in the growth…

Statistical Mechanics · Physics 2024-10-01 Akihisa Koga , Shiro Sakai , Yushu Matsushita , Tsutomu Ishimasa

To investigate the network-growth rule dependence of certain geometric aspects of percolation clusters, we propose a generalized network-growth rule introducing a generalized parameter $q$ and we study the time evolution of the network. The…

Statistical Mechanics · Physics 2013-04-24 Shu Tanaka , Ryo Tamura

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A…

Statistical Mechanics · Physics 2015-05-13 Stefan Mashkevich , Stéphane Ouvry

We consider inhomogeneous lattice walk models in a half-space and in the quarter plane. For the models in a half-space, we show by a generalization of the kernel method to linear systems of functional equations that their generating…

Combinatorics · Mathematics 2018-11-19 Manfred Buchacher , Manuel Kauers

We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…

Statistical Mechanics · Physics 2009-10-31 Supriya Krishnamurthy , Mustansir Barma

Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…

chao-dyn · Physics 2009-10-30 Awadhesh Prasad , Vishal Mehra , Ramakrishna Ramaswamy

We study numerically and theoretically the $d$-dimensional Hamiltonian motion of fast particles through a field of scatterers, modeled by bounded, localized, (time-dependent) potentials, that we refer to as (in)elastic non-dissipative…

Mathematical Physics · Physics 2015-05-19 B. Aguer , S. De Bièvre

It is well known that adding "long edges (shortcuts)" to a regularly constructed graph will make the resulted model a small world. Recently, \cite{W} indicated that, among all long edges, those edges with length proportional to the diameter…

Probability · Mathematics 2017-04-07 Xian-Yuan Wu , Rui Zhu

We investigate the quasi two-dimensional Taylor-Couette system in the regime where the radius ratio is close to unity - a transitional regime between three and two dimensions. By systematically increasing the Reynolds number we observe a…

Fluid Dynamics · Physics 2015-12-02 Sebastian Altmeyer , Younghae Do , Ying-Cheng Lai

Complex networks have certain properties that distinguish them from their respective uniform or regular counterparts. One of these properties is the variation of topological properties along different hierarchical levels. In this work, we…

Pattern Formation and Solitons · Physics 2023-06-19 Alexandre Benatti , Luciano da Fontoura Costa

We propose a growing model which interpolates between one-dimensional regular lattice and small-world networks. The model undergoes an interesting phase transition from large to small world. We investigate the structural properties by both…

Statistical Mechanics · Physics 2007-09-24 Zhongzhi Zhang , Shuigeng Zhou , Zhen Shen

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We describe the process, including a detailed shape theorem, in terms of a system of growing lilypads. As an…

Probability · Mathematics 2016-06-07 Marcel Ortgiese , Matthew I. Roberts

We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the…

Probability · Mathematics 2025-01-22 Miha Brešar , Aleksandar Mijatović , Andrew Wade

We study properties of an array of numbers, called "the triangle," in which each row is formed by rotating all the numbers in the previous row to the left by $m$ positions in cyclical fashion, then appending a number to the end of the row.…

Number Theory · Mathematics 2014-09-16 Philip Jameson Graber

We analyse a biased random walk on a 1D lattice with unequal step lengths. Such a walk was recently shown to undergo a phase transition from a state containing a single connected cluster of visited sites to one with several clusters of…

Statistical Mechanics · Physics 2010-09-13 Kabir Ramola

We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by applying round-off to planar rotations. All orbits of these maps are conjectured to be periodic. We let the angle of rotation approach pi/2, and…

Dynamical Systems · Mathematics 2014-06-02 Heather Reeve-Black

We introduce a class of cellular automata growth models on the two-dimensional integer lattice with finite cross neighborhoods. These dynamics are determined by a Young diagram $\mathcal Z$ and the radius $\rho$ of the neighborhood, which…

Probability · Mathematics 2023-07-17 Daniel Blanquicett , Janko Gravner , David Sivakoff , Luke Wilson