scholarly journals Self-Similarity Properties of Complex Quasi-Periodic Fibonacci and Cantor Photonic Crystals

Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 558
Author(s):  
Aleksander Augustyniak ◽  
Mariusz Zdanowicz ◽  
Tomasz Osuch
Keyword(s):  
Photonic Crystals ◽  
Spectral Response ◽  
Photonic Devices ◽  
The Self ◽  
Mirror Reflection ◽  
Self Similarity ◽  
Simple Modification ◽  
Structural Modifications ◽  
Self Similar ◽  
First Time

In this paper, the influence of structural modifications on basic quasi-periodic (QP) photonic crystals (PhC’s) on self-similarity feature in their spectral responses is examined. Investigated crystals are chosen based on a present knowledge on the QP crystals, and are classified according to their structure. One of the QP crystals considered for the calculations is a concatenation, Fibonacci structure. It characterizes with a self-similar spectra for its different orders, which means, that the spectral shape repeats itself and can be partially identical for a different orders of the Fibonacci QP crystal. The calculations were also performed for the fractal structure, based on a Cantor QP crystal. Just as for the case of the Fibonacci structure, it characterizes with a self-similar spectra for different orders of the structure. Considered photonic devices are next put through simple modification operations by multiplication, conjugation or mirror reflection. Resulting, modified structures are used for the calculations of their spectral response. Results show, that the self-similarity of the spectra is not affected by performed modifications, and thus spectral response of QP PhC can be designed without losing this feature. Moreover the regular expansion of the repeated central part of the spectrum that appears in higher-order Fibonacci QP PhC spectra (due to the self-similarity) with the increase Fibonacci crystal order is presented here for the first time.

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.

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.

A self-assembly based on a hydrogel interface: facile, rapid, and large-scale preparation of colloidal photonic crystals

2020 ◽  
Vol 4 (8) ◽  
pp. 2409-2417
Author(s):  
Mengfan Wu ◽  
Chuyan Zhang ◽  
Fujing Wei ◽  
Huifang An ◽  
Xiaqing Wang ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Self Assembly ◽  
Large Scale ◽  
The Self ◽  
Colloidal Photonic Crystals ◽  
Large Scale Preparation ◽  
Scale Preparation ◽  
First Time

This is the first time that a hydrogel interface has been used as an assembly interface for the self-assembly of photonic crystals with excellent performances.

scholarly journals Sodium Alginate Cross-Linkable Planar 1D Photonic Crystals as a Promising Tool for Pb2+ Detection in Water

Chemosensors ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 37 ◽  
Author(s):  
Andrea Dodero ◽  
Paola Lova ◽  
Silvia Vicini ◽  
Maila Castellano ◽  
Davide Comoretto
Keyword(s):  
Refractive Index ◽  
Photonic Crystals ◽  
Sodium Alginate ◽  
Spectral Response ◽  
High Refractive Index ◽  
Polluted Water ◽  
Ionic Exchange ◽  
Promising Tool ◽  
Rural Environments ◽  
First Time

Due to its high toxicity, Pb2+ pollution is a serious threat for human health and environments. However, in situ real-time detection of Pb2+ pollution is difficult and laboratory instruments are usually required. Then, the possibility to monitor water quality without laboratory instruments could lead to the extensive assessment of polluted water sources, especially in rural environments and developing countries where large lead concentrations are often found in surface water. Consequently, new simple colorimetric sensors are highly interesting in the field. In this work we report for the first time disposable polymer planar 1D photonic crystals made of poly (N-vinylcarbazole) as high refractive index medium and sodium alginate as low refractive index and active medium for the detection of Pb2+ in water. The detection relies on the ionic exchange occurring into the alginate matrix. This process effectively induces a physical cross-linking phenomenon, which inhibits water solubilization of the polymer. In turn, this affects the spectral response of the planar 1D photonic crystals modifying its color.

ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950016 ◽  
Author(s):  
JIN CHEN ◽  
LONG HE ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Complex Networks ◽  
Sierpinski Gasket ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of self-similar measure on the Sierpiński gasket and use the self-similarity of distance and measure to obtain the exact value of this integral.

Identification of Chaos-Periodic Transitions, Band Merging, and Internal Crisis Using Wavelet-DFA Method

2016 ◽  
Vol 26 (04) ◽  
pp. 1650065 ◽  
Author(s):  
Mahsa Vaghefi ◽  
Ali Motie Nasrabadi ◽  
Seyed Mohammad Reza Hashemi Golpayegani ◽  
Mohammad Reza Mohammadi ◽  
Shahriar Gharibzadeh
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Period Doubling ◽  
Nonstationary Time Series ◽  
The Self ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Analysis Method ◽  
Self Similarity ◽  
Self Similar ◽  
Detrended Fluctuation

Detrended Fluctuation Analysis (DFA) is a scaling analysis method that can identify intrinsic self-similarity in any nonstationary time series. In contrast, Wavelet Transform (WT) method is widely used to investigate the self-similar processes, as the self-similarity properties exist within the subbands. Therefore, a combination of these two approaches, DFA and WPT, is promising for rigorous investigation of such a system. In this paper a new methodology, so-called wavelet DFA, is introduced and interpreted to evaluate this idea. This approach, further than identifying self-similarity properties, enable us to detect and capture the chaos-periodic transitions, band merging, and internal crisis in systems that become chaotic through period-doubling phenomena. Changes of wavelet DFA exponent have been compared with that of Lyapunov and DFA through Logistic, Sine, Gaussian, Cubic, and Quartic Maps. Furthermore, the potential capabilities of this new exponent have been presented.

Direct numerical simulation of axisymmetric wakes embedded in turbulence

2012 ◽  
Vol 710 ◽  
pp. 482-504 ◽  
Author(s):  
Elad Rind ◽  
Ian P. Castro
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Decay Rate ◽  
Relative Strength ◽  
Decay Rates ◽  
The Self ◽  
Self Similarity ◽  
Self Similar ◽  
External Turbulence ◽  
Different Levels

AbstractDirect numerical simulation has been used to study the effects of external turbulence on axisymmetric wakes. In the absence of such turbulence, the time-developing axially homogeneous wake is found to have the self-similar properties expected whereas, in the absence of the wake, the turbulence fields had properties similar to Saffman-type turbulence. Merging of the two flows was undertaken for three different levels of external turbulence (relative to the wake strength) and it is shown that the presence of the external turbulence enhances the decay rate of the wake, with the new decay rates increasing with the relative strength of the initial external turbulence. The external turbulence is found to destroy any possibility of self-similarity within the developing wake, causing a significant transformation in the latter as it gradually evolves towards the former.

scholarly journals On the self-similarity of wind turbine wakes in complex terrain using large-eddy simulation

2019 ◽  
Author(s):  
Arslan Salim Dar ◽  
Jacob Berg ◽  
Niels Troldborg ◽  
Edward G. Patton
Keyword(s):  
Large Eddy Simulation ◽  
Complex Terrain ◽  
The Self ◽  
Self Similarity ◽  
Flat Terrain ◽  
Eddy Simulation ◽  
Atmospheric Stratification ◽  
Large Eddy ◽  
Self Similar ◽  
Turbine Wake

Abstract. We perform large-eddy simulation of flow in complex terrain under neutral atmospheric stratification. We study the self-similar behavior of a turbine wake as a function of varying terrain complexity and perform comparison with a flat terrain. By plotting normalized velocity deficit profiles in different complex terrain cases, we verify that self-similarity is preserved as we move downstream from the turbine. We find that this preservation is valid for a shorter distance downstream compared to what is observed in flat terrain. A larger spread of the profiles toward the tails due to varying levels of shear is also observed.

scholarly journals Self-similar cosmological solutions in f(R,T) gravity theory

2021 ◽  
pp. 2150206
Author(s):  
José Antonio Belinchón ◽  
Carlos González ◽  
Sami Dib
Keyword(s):  
Exact Solutions ◽  
The Self ◽  
Exact Form ◽  
Field Equations ◽  
Self Similarity ◽  
Similarity Hypothesis ◽  
Geometrical Quantity ◽  
Cosmological Solutions ◽  
Self Similar ◽  
Matter Collineation

We study the [Formula: see text] cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case[Formula: see text] and the case [Formula: see text]. In each case, we state general theorems which determine completely the form of the unknown functions [Formula: see text] such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric[Formula: see text] In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

Coherent Structures and Correlation Fields in the Mixing Transition of a Turbulent Round Free Jet

2018 ◽  
Author(s):  
Benedikt Krohn ◽  
Sunming Qin ◽  
Victor Petrov ◽  
Annalisa Manera
Keyword(s):  
Coherent Structures ◽  
High Speed ◽  
Near Field ◽  
The Self ◽  
Turbulent Shear ◽  
Past Century ◽  
Self Similarity ◽  
Free Jet ◽  
Similar Region ◽  
Self Similar

Turbulent free jets attracted the focus of many scientists within the past century regarding the understanding of mass- and momentum transport in the turbulent shear field, especially in the near-field and the self-similar region. Recent investigations attempt to understand the intermediate fields, called the mixing transition or ‘the route to self-similarity’. An apparent gap is recognized in light of this mixing transition, with two main conjectures being put forth. Firstly the flow will always asymptotically reach a fully self-similar state if boundary conditions permit. The second proposes partial and local self-similarity within the mixing transition. We address the later with an experimental investigation of the intermediate field turbulence dynamics in a non-confined free jet with a nozzle diameter of 12.7 mm and an outer scale Reynolds number of 15,000. High speed Particle Image Velocimetry (PIV) is used to record the velocity fields with a final spatial resolution of 194 × 194 μm2. The analysis focuses on higher order moments and two-point correlations of velocity variances in space and time. We observed local self-similarity in the measured correlation fields. Coherent structures are present within the near-field where the turbulent energy spectrum cascades along a dissipative slope. Towards the transition region, the spectrum smoothly transforms to a viscous cascade, as it is commonly observed in the self-similar region.

Sign in / Sign up

Export Citation Format

Share Document