Related papers: Power dissipation in fractal AC circuits
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
We study the transport of electrons in a Fibonacci magnetic superlattice produced on a two-dimensional electron gas modulated by parallel magnetic field stripes arranged in a Fibonacci sequence. Both the transmission coefficient and…
In this paper we deal with the notion of the effective impedance of AC networks consisting of resistances, coils and capacitors. Mathematically such a network is a locally finite graph whose edges are endowed with complex-valued weights…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
Considering diffusion in the presence of asymmetric disorder, an exact relationship between the strength of weak disorder and the electric resistance of the corresponding resistor network is revealed, which is valid in arbitrary networks.…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
A model, plane symmetric, 3-D potential, which preserves some features of galactic problems,is used in order to examine the phase space structure through the study of the properties of orbits crossing perpendicularly the plane of symmetry.…
Nonreciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that they couple, and can be used to create chiral information processing networks. We study the systematic inclusion of…
We consider a transmission problem in which the interior domain has infinitely ramified structures. Transmission between the interior and exterior domains occurs only at the fractal component of the interface between the interior and…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
In this paper we construct a self-similar fractal configured as an infinitely branched tree and equip it with a regular self-similar Dirichlet form. We show anomalous behaviour of the mean exit time with respect to typical metric balls.…
A lumped-parameter impedor-oriented and a 2-port-network-oriented circuit models for the Sierpinski gasket prefractal antenna are presented. With the former, the voltage and current patterns give a detailed understanding of the…
We characterize the existence of certain geometric configurations in the fractal percolation limit set $A$ in terms of the almost sure dimension of $A$. Some examples of the configurations we study are: homothetic copies of finite sets,…
The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with…
Electrical analogues of fracture, such as the fuse network model, are widely studied. However, the "analogy" between the electrical problem and the elastic problem is rarely established explicitly. Further, the fuse network is a discrete…
Three kinds of fractal solutions of model of reactors are presented. The first kind concerns the structure of Feigenbaum_s diagram on the limit of chaos. The second kind and the third one concern the effect of initial conditions on the…
This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…
The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years,…
Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…
The decimation map $\mathcal{D}$ for a network of admittances on an $n$-simplex lattice fractal is studied. The asymptotic behaviour of $\mathcal{D}$ for large-size fractals is examined. It is found that in the vicinity of the isotropic…