Related papers: Power dissipation in fractal AC circuits
This article is concerned with statistics of addition spectra for systems of identical charged particles. A classical model is suggested in order to study fluctuations of Coulomb blockade peak spacings in large two-dimensional semiconductor…
Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time…
With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
In the previous article (S. Matsutani and Y. Shimosako and Y. Wang, Physica A \bf{391} (2012) 5802-5809) we numerically investigated an electric potential problem with high contrast local conductivities ($\gamma_0$ and $\gamma_1$,…
This article shows the interfacial relation in electrodynamics shall be corrected in discrete grid form which can be seen as certain numerical dispersion beyond the usual bulk type. Furthermore we construct a lossy conductor model to…
This paper gives a (polynomial time) algorithm to decide whether a given Discrete Self-Similar Fractal Shape can be assembled in the aTAM model.In the positive case, the construction relies on a Self-Assembling System in the aTAM which…
Scattering of electrons due to fractons can result in a resistivity that {\it decreases} with temperature. Such a behavior also appears in real quasicrystals. If this is then attributed to fracton scattering, fracton-superconductivity would…
Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally…
We study the $\Gamma$-convergence of damage to fracture energy functionals in the presence of low-order nonlinear potentials that allows us to model physical phenomena such as fluid-driven fracturing, plastic slip, and the satisfaction of…
The dissipativity concept sits at the intersection of physics, systems theory, and control engineering, as a natural generalisation of passive systems that dissipate energy. It relates the external behavior of systems to their internal…
Fractional electromagnetic field theory describes electromagnetic wave propagation through the complex, nonlocal, dissipative, fractal and also recent artificially engineered materials know as fractional metamaterials. In this theory using…
This paper endeavors to show how a fractal-based approach can offer an alternative to differential equations for describing rates of interaction in complex systems. The specific example given is for combat analysis. This concerns a scenario…
We study the origin of scale invariance (SI) of the degree distribution in scale-free (SF) networks with a degree exponent $\gamma$ under coarse graining. A varying number of vertices belonging to a community or a box in a fractal analysis…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
The present paper provides a method for finding partial differential equations satisfied by the Feynman integrals for diagrams of various types, using the Griffiths theorem on the reduction of poles of rational differential forms. As an…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
An anomaly in electrical circuit theory is the disappearance of some of the energy when two capacitors, one charged and the other uncharged, are connected together through resistanceless wires. Nonstandard analysis shows that, when the…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
Similarities between models of fragmenting nuclei and disordered systems in condensed matter suggest corresponding methods. Several theoretical models of fragmentation investigated in this fashion show marked differences, indicating…