Search results for: Archimedean tilings

Authors: Yi-Hua Chen, Hsiang-Wen Tang, I-Ling Chang, Lien-Wen Chen

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The defect mode of two-dimensional phononic crystals with Archimedean tilings was explored in the present study. Finite element method and supercell method were used to obtain dispersion relation of phononic crystals. The simulations of the acoustic wave propagation within phononic crystals are demonstrated. Around the cavity which is created by removing several cylinders in the perfect Archimedean tilings, whispering-gallery mode (WGM) can be observed. The effects of the cavity geometry on the WGM modes are investigated. The WGM modes with high Q-factor and high cavity pressure can be obtained by phononic crystals with Archimedean tilings.

Keywords: defect mode, Archimedean tilings, phononic crystals, whispering-gallery modes

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Authors: Alam Ali, Ashok Kumar Pathak

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Nowadays, copulas have attracted significant attention for modeling multivariate observations, and the foremost feature of copula functions is that they give us the liberty to study the univariate marginal distributions and their joint behavior separately. The copula parameter apprehends the intrinsic dependence among the marginal variables, and it can be estimated using parametric, semiparametric, or nonparametric techniques. This work aims to compare the coverage rates between an Elliptical and an Archimedean family of copulas via a fully parametric estimation technique.

Keywords: elliptical copula, archimedean copula, estimation, coverage rate

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Authors: A. S. Mousa, R. I. Rajab, A. A. Pinto

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An envy behavioral game theoretical model with two types of homogeneous players is considered in this paper. The strategy space of each type of players is a discrete set with only two alternatives. The preferences of each type of players is given by a discrete utility function. All envy strategies that form Nash equilibria and the corresponding envy Nash domains for each type of players have been characterized. We use geometry to construct two dimensional envy tilings where the horizontal axis reflects the preference for players of type one, while the vertical axis reflects the preference for the players of type two. The influence of the envy behavior parameters on the Cartesian position of the equilibria has been studied, and in each envy tiling we determine the envy Nash equilibria. We observe that there are 1024 combinatorial classes of envy tilings generated from envy chromosomes: 256 of them are being structurally stable while 768 are with bifurcation. Finally, some conditions for the disparate envy Nash equilibria are stated.

Keywords: game theory, Nash equilibrium, envy Nash behavior, geometric tilings, bifurcation thresholds

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Authors: Catarina Cruz, Ana Breda

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Tiling problems have been capturing the attention of many mathematicians due to their real-life applications. In this study, we deal with tilings of Zⁿ by Lee spheres, where n is a positive integer number, being these tilings related with error correcting codes on the transmission of information over a noisy channel. We focus our attention on the question ‘for what values of n and r does the n-dimensional Lee sphere of radius r tile Zⁿ?’. It seems that the n-dimensional Lee sphere of radius r does not tile Zⁿ for n ≥ 3 and r ≥ 2. Here, we prove that is not possible to tile Z⁷ with Lee spheres of radius 2 presenting a proof based on a combinatorial method and faithful to the geometric idea of the problem. The non-existence of such tilings has been studied by several authors being considered the most difficult cases those in which the radius of the Lee spheres is equal to 2. The relation between these tilings and error correcting codes is established considering the center of a Lee sphere as a codeword and the other elements of the sphere as words which are decoded by the central codeword. When the Lee spheres of radius r centered at elements of a set M ⊂ Zⁿ tile Zⁿ, M is a perfect r-error correcting Lee code of word length n over Z, denoted by PL(n, r). Our strategy to prove the non-existence of PL(7, 2) codes are based on the assumption of the existence of such code M. Without loss of generality, we suppose that O ∈ M, where O = (0, ..., 0). In this sense and taking into account that we are dealing with Lee spheres of radius 2, O covers all words which are distant two or fewer units from it. By the definition of PL(7, 2) code, each word which is distant three units from O must be covered by a unique codeword of M. These words have to be covered by codewords which dist five units from O. We prove the non-existence of PL(7, 2) codes showing that it is not possible to cover all the referred words without superposition of Lee spheres whose centers are distant five units from O, contradicting the definition of PL(7, 2) code. We achieve this contradiction by combining the cardinality of particular subsets of codewords which are distant five units from O. There exists an extensive literature on codes in the Lee metric. Here, we present a new approach to prove the non-existence of PL(7, 2) codes.

Keywords: Golomb-Welch conjecture, Lee metric, perfect Lee codes, tilings

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Authors: Rahul Singha, D. Vakula

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This paper presents a corrugated antipodal vivaldi antenna with improved performance by using negative index metamaterial (NIM) of the Archimedean spiral design. A single layer NIM piece is placed perpendicular middle of the two arm of the proposed antenna. The antenna size is 30×60×0.787 mm3 operating at 8GHz. The simulated results of NIM corrugated antipodal vivaldi antenna show that the gain and directivity has increased up to 1.2dB and 1dB respectively. The HPBW is increased by 90 with the reflection coefficient less than ‒10 dB from 4.7 GHz to 11 GHz for UWB application.

Keywords: Negative Index Metamaterial (NIM), Ultra Wide Band (UWB), Half Power Beam Width (HPBW), vivaldi antenna

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Authors: El Mehdi Haily, Lahcen Bih, Mohammed Azrour, Bouchaib Manoun

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The effects of xBi₂O₃-yBaO-zP₂O₅ (BBP) glass addition on the sintering, structural, and dielectric properties of BaTiO₃ ceramic (BT) are studied. The BT ceramic was synthesized by the conventional solid-state reaction method while the glasses BaO-Bi₂O₃-P₂O₅ (BBP) were elaborated by melting and quenching process. Different composites BT-xBBP were formed by mixing the BBP glasses with BT ceramic. For each glass composition, where the ratio (x:y:z) is maintained constant, we have developed three composites with different glass weight percentage (x = 2.5, 5, and 7.5 wt %). Addition of the glass helps in better sintering at lower temperatures with the presence of liquid phase at the respective sintering temperatures. The results showed that the sintering temperature decreased from more than 1300°C to 900°C. Density measurements of the composites are performed using the standard Archimedean method with water as medium liquid. It is found that their density and molar volume decrease and increase with glass content, respectively. Raman spectroscopy is used to characterize their structural approach. This technique has allowed the identification of different structural units of phosphate and the characteristic vibration modes of the BT. The electrical properties of the composite samples are carried out by impedance spectroscopy in the frequency range of 10 Hz to 1 MHz under various temperatures from 300 to 473 K. The obtained results show that their dielectric properties depend both on the content of the glass in the composite and the Bi/P ratio in the glasses.

Keywords: phosphate, glasses, composite, Raman spectroscopy, dielectric properties

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Authors: Zeinab Gharibi, B. Stoevesandt, J. Peinke

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Long term surface erosion of wind turbine blades, especially at the leading edge, impairs aerodynamic performance; therefore, lowers efficiency of the blades mostly in the high-speed rotor tip regions. Blade protection provides significant improvements in annual energy production, reduces costly downtime, and protects the integrity of the blades. However, this protection still influences the aerodynamic behavior, and broadband noise caused by interaction between the impinging turbulence and blade’s leading edge. This paper presents an extensive numerical aeroacoustics approach by investigating the sound power spectra of the eroded and coated NACA 64-618 wind turbine airfoil and evaluates aeroacoustics improvements after the protection procedure. Using computational fluid dynamics (CFD), different quasi 2D numerical grids were implemented and special attention was paid to the refinement of the boundary layers. The noise sources were captured and decoupled with acoustic propagation via the derived formulation of Curle’s analogy implemented in OpenFOAM. Therefore, the noise spectra were compared for clean, coated and eroded profiles in the range of chord-based Reynolds number (1.6e6 ≤ Re ≤ 11.5e6). Angle of attack was zero in all cases. Verifications were conducted for the clean profile using available experimental data. Sensitivity studies for the far-field were done on different observational positions. Furthermore, beamforming studies were done simulating an Archimedean spiral microphone array for far-field noise directivity patterns. Comparing the noise spectra of the coated and eroded geometries, results show that, coating clearly improves aerodynamic and acoustic performance of the eroded airfoil.

Keywords: computational fluid dynamics, computational aeroacoustics, leading edge, OpenFOAM

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Authors: Roengchai Tansuchat, Woraphon Yamaka, Paravee Maneejuk

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From the past recent, the global financial crisis, economic instability, and large fluctuation in agricultural commodity price have led to increased concerns about the volatility transmission among them. The problem is further exacerbated by commodities volatility caused by other commodity price fluctuations, hence the decision on hedging strategy has become both costly and useless. Thus, this paper is conducted to analysis the volatility spillover effect among major agriculture including corn, soybeans, wheat and rice, to help the commodity suppliers hedge their portfolios, and manage the risk and co-volatility of them. We provide a switching regime approach to analyzing the issue of volatility spillovers in different economic conditions, namely upturn and downturn economic. In particular, we investigate relationships and volatility transmissions between these commodities in different economic conditions. We purposed a Copula-based multivariate Markov Switching GARCH model with two regimes that depend on an economic conditions and perform simulation study to check the accuracy of our proposed model. In this study, the correlation term in the cross-hedge ratio is obtained from six copula families – two elliptical copulas (Gaussian and Student-t) and four Archimedean copulas (Clayton, Gumbel, Frank, and Joe). We use one-step maximum likelihood estimation techniques to estimate our models and compare the performance of these copula using Akaike information criterion (AIC) and Bayesian information criteria (BIC). In the application study of agriculture commodities, the weekly data used are conducted from 4 January 2005 to 1 September 2016, covering 612 observations. The empirical results indicate that the volatility spillover effects among cereal futures are different, as response of different economic condition. In addition, the results of hedge effectiveness will also suggest the optimal cross hedge strategies in different economic condition especially upturn and downturn economic.

Keywords: agricultural commodity futures, cereal, cross-hedge, spillover effect, switching regime approach

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