Related papers: Fractal Patterns in Discrete Laplacians: Iterative…
In the study of pattern formation in symmetric physical systems a 3-dimensional structure in thin domains is often modelled as 2-dimensional one. We are concerned with functions in $R^3$ that are invariant under the action of a…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
We explore a deep connection between fracton order and product codes. In particular, we propose and analyze conditions on classical seed codes which lead to fracton order in the resulting quantum product codes. Depending on the properties…
Fractal structures pervade nature and are receiving increasing engineering attention towards the realization of broadband resonators and antennas. We show that fractal resonators can support the emergence of high-dimensional chaotic…
Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The…
This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials. These numbers are associated with special elliptic functions, most notably, a…
The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies.…
A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements $u$. The model is based on the biharmonic equation $\nabla^{4}u =0$ in two-dimensional isotropic defect-free media…
Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…
In this work the spontaneous symmetry breaking in certain nonlinear theories with second-class constraints is explored. Using the Dirac's method we perform an analysis of the constraints and the counting of the degrees of freedom. The…
We construct 1-parameter families of non-periodic embedded minimal surfaces of infinite genus in $T \times \mathbb{R}$, where $T$ denotes a flat 2-tori. Each of our families converges to a foliation of $T \times \mathbb{R}$ by $T$. These…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
We use various electrode layouts to tailor the profile of the electric field in a two-dimensional (2D) dielectric-barrier-discharge system, thereby creating spatial templates for the lateral distribution of discharge filaments. Our…
We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process…
A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is…
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…
When plane waves diffract through fractal-patterned apertures, the resulting far-field profiles or diffractals also exhibit iterated, self-similar features. Here we show that this specific architecture enables robust signal processing and…
Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians…