scholarly journals SELF-SIMILAR BEHAVIOR IN SEMICONDUCTOR SUPERLATTICES

Fractals ◽  
2012 ◽  
Vol 20 (01) ◽  
pp. 89-95 ◽  
Author(s):  
JUAN C. CASTRO-PALACIO ◽  
FRANCISCO R. VILLATORO ◽  
OMEL MENDOZA-YERO ◽  
LUISBERIS VELÁZQUEZ-ABAD ◽  
JUAN A. MONSORIU
Keyword(s):  
Particle Energy ◽  
Self Similarity ◽  
Potential Wells ◽  
Piecewise Constant ◽  
Quantum Particles ◽  
Fractal Properties ◽  
Periodic Potentials ◽  
Constant Potential ◽  
Coefficient Versus ◽  
Self Similar

The scattering of particles in fractal superlattices has been analyzed by means of the transfer matrix method. The fractal superlattice consists of alternating layers of semiconductor materials following the rule of a Cantor set. This problem can be represented by a model of quantum particles scattering in piecewise constant potential wells. Fractal properties of the reflection coefficient versus the particle energy curves are examined comparatively to the curves when using the corresponding periodic potentials. The degree of self-similarity of the output variables has been quantified by means of the correlation function.

SELF SIMILARITY IN SWELLING SYSTEMS: FRACTAL PROPERTIES OF PEAT

Fractals ◽  
1994 ◽  
Vol 02 (01) ◽  
pp. 45-52 ◽  
Author(s):  
A. V. NEIMARK ◽  
E. ROBENS ◽  
K. K. UNGER ◽  
Yu. M. VOLFKOYICH
Keyword(s):  
Fractal Dimension ◽  
Water Adsorption ◽  
The Self ◽  
Self Similarity ◽  
Sphagnum Peat ◽  
Fractal Properties ◽  
Wide Range ◽  
Capillary Equilibrium ◽  
Scale Range ◽  
Self Similar

Sphagnum peat gives an example of a swelling system with a self-similar structure in sufficiently wide range of scales. The surface fractal dimension, dfs, has been calculated by means of thermodynamic method on the basis of water adsorption and capillary equilibrium measurements. This method makes possible the exploration of the self-similarity in the scale range over at least 4 decimal orders of magnitude from 1 nm to 10 μm. In a sample explored, two ranges of fractality have been observed: dfs ≈ 2.55 in the range 1.5–80 nm and dfs ≈ 2.42 in the range 0.25–9 µm.

scholarly journals SELF-SIMILARITY PROPERTIES OF NAFIONIZED AND FILTERED WATER AND DEFORMED COHERENT STATES

2014 ◽  
Vol 28 (03) ◽  
pp. 1450007 ◽  
Author(s):  
A. CAPOLUPO ◽  
E. DEL GIUDICE ◽  
V. ELIA ◽  
R. GERMANO ◽  
E. NAPOLI ◽  
...  
Keyword(s):  
Coherent State ◽  
Water Samples ◽  
Coherent States ◽  
Algebraic Methods ◽  
Self Similarity ◽  
Scale Free ◽  
Fractal Properties ◽  
Self Similar

By resorting to measurements of physically characterizing observables of water samples perturbed by the presence of Nafion and by iterative filtration processes, we discuss their scale free, self-similar fractal properties. By use of algebraic methods, the isomorphism is proved between such self-similarity features and the deformed coherent state formalism.

scholarly journals Conditions for realizing one-point interactions from a multi-layer structure model

2022 ◽  
Author(s):  
A V Zolotaryuk ◽  
Yaroslav Zolotaryuk
Keyword(s):  
System Parameter ◽  
Layer Structure ◽  
Dimensional Space ◽  
One Dimension ◽  
Structure Model ◽  
Point Interactions ◽  
Piecewise Constant ◽  
Quantum Particles ◽  
Constant Potential ◽  
Parameter Values

Abstract A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

scholarly journals Depressurization-Induced Nucleation in the “Polylactide-Carbon Dioxide” System: Self-Similarity of the Bubble Embryos Expansion

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1115
Author(s):  
Dmitry Zimnyakov ◽  
Marina Alonova ◽  
Ekaterina Ushakova
Keyword(s):  
Initial Rate ◽  
Initial Pressure ◽  
External Pressure ◽  
Self Similarity ◽  
Embryo Formation ◽  
Linear Behavior ◽  
Joint Influence ◽  
External Pressures ◽  
Adiabatic Cooling ◽  
Self Similar

Self-similar expansion of bubble embryos in a plasticized polymer under quasi-isothermal depressurization is examined using the experimental data on expansion rates of embryos in the CO2-plasticized d,l-polylactide and modeling the results. The CO2 initial pressure varied from 5 to 14 MPa, and the depressurization rate was 5 × 10−3 MPa/s. The constant temperature in experiments was in a range from 310 to 338 K. The initial rate of embryos expansion varied from ≈0.1 to ≈10 µm/s, with a decrease in the current external pressure. While modeling, a non-linear behavior of CO2 isotherms near the critical point was taken into account. The modeled data agree satisfactorily with the experimental results. The effect of a remarkable increase in the expansion rate at a decreasing external pressure is interpreted in terms of competing effects, including a decrease in the internal pressure, an increase in the polymer viscosity, and an increase in the embryo radius at the time of embryo formation. The vanishing probability of finding the steadily expanding embryos for external pressures around the CO2 critical pressure is interpreted in terms of a joint influence of the quasi-adiabatic cooling and high compressibility of CO2 in the embryos.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. 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 invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

scholarly journals Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Svetlana N. Khonina ◽  
Sergey G. Volotovsky ◽  
Sergey I. Kharitonov ◽  
Nikolay L. Kazanskiy
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Ground State ◽  
State Energy ◽  
Airy Functions ◽  
Piecewise Constant ◽  
Matrix Rank ◽  
The Matrix ◽  
Constant Potential ◽  
Low Dimensional

An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of theE-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.

Intermittency and related issues in 16O-Ag/Br collision at 200A GeV/c

2010 ◽  
Vol 88 (8) ◽  
pp. 575-584 ◽  
Author(s):  
M. K. Ghosh ◽  
P. K. Haldar ◽  
S. K. Manna ◽  
A. Mukhopadhyay ◽  
G. Singh
Keyword(s):  
Particle Density ◽  
Simulated Data ◽  
Space Distribution ◽  
Monte Carlo Code ◽  
Final State ◽  
Data Set ◽  
Fractal Properties ◽  
Self Similar ◽  
Singly Charged ◽  
Almost All

In this paper we present some results on the nonstatistical fluctuation in the 1-dimensional (1-d) density distribution of singly charged produced particles in the framework of the intermittency phenomenon. A set of nuclear emulsion data on 16O-Ag/Br interactions at an incident momentum of 200A GeV/c, was analyzed in terms of different statistical methods that are related to the self-similar fractal properties of the particle density function. A comparison of the present experiment with a similar experiment induced by the 32S nuclei and also with a set of results simulated by the Lund Monte Carlo code FRITIOF is presented. A similar comparison between this experiment and a pseudo-random number generated simulated data set is also made. The analysis reveals the presence of a weak intermittency in the 1-d phase space distribution of the produced particles. The results also indicate the occurrence of a nonthermal phase transition during emission of final-state hadrons. Our results on factorial correlators suggests that short-range correlations are present in the angular distribution of charged hadrons, whereas those on oscillatory moments show that such correlations are not restricted only to a few particles. In almost all cases, the simulated results fail to replicate their experimental counterparts.

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

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