Related papers: Power dissipation in fractal AC circuits
We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the individual impedances inside the circuit are purely imaginary.…
This paper studies the concept of power dissipation in infinite graphs and fractals associated with passive linear networks consisting of non-dissipative elements. In particular, we analyze the so-called Feynman-Sierpinski ladder, a fractal…
In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale…
We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show…
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…
We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals.…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
For a given pcf self-similar fractal, a certain network (weighted graph) is constructed whose ideal boundary is (homeomorphic to) the fractal. This construction is the first representation of a connected self-similar fractal as the boundary…
We report the statistical properties of the fluctuations of the energy flux in an electronic RC circuit driven with a stochastic voltage. The fluctuations of the power injected in the circuit are measured as a function of the damping rate…
The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of…
The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this…
Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
We study power dissipation for systems of multiple quantum wires meeting at a junction, in terms of a current splitting matrix (M) describing the junction. We present a unified framework for studying dissipation for wires with either…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
In this work we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. This…
In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation…
We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal…