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Depiction and analysis of a modified theta shaped double negative metamaterial for satellite application

  • Md. Jubaer Alam EMAIL logo , Mohammad Rashed Iqbal Faruque , Taya Allen , Sabirin Abdullah , Mohammad Tariqul Islam , Khairul Nizam Abdul Maulud and Eistiak Ahamed
Published/Copyright: December 26, 2018
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Open Physics
From the journal Open Physics Volume 16 Issue 1

Abstract

In this article, a modified Theta shaped, compact double negative metamaterial structure is designed and presented for satellite communication. Two oppositely faced E-shaped resonators are connected with the substantial Theta to complete the structure. A low profile dielectric substrate FR-4 is used to design the 9 × 9 mm2 unit cell which has a succinct structure where the attainment of the resonator is explored both integrally and experimentally. The proposed metamaterial has a transmission coefficient of 13 GHz (bandwidth) with a 500 MHz band gap at the middle. A correlation is made between the basic unit-cell and array structures, and a comparison is shown among 1 × 2, 2 × 2, and 4 × 4 array structures with 1 × 2, 2 × 2, and 4 × 4 unit-cell configurations to validate the performance of the proposed metamaterial. It has also been observed by the Nicolson–Ross–Weir approach at the resonating frequencies. The effective electromagnetic parameters retrieved from the simulation of the S-parameters imply that the metamaterial structure shows negative refraction bands. The structure shows negative permittivity at 2.60 to 5.16 GHz, 6.63 to 9.31 GHz and 13.03 to 16.18 GHz and negative permeability at 7.74 to 13.07 GHz and 13.88 to 16.55 GHz, respectively. It exhibits double-negative phenomena at X and Ku bands with a frequency range of about 1.17 GHz (8.14 – 9.31 GHz) and 1.42 GHz (13.80 – 15.22 GHz), respectively. Having an auspicious design and wide range double negative characteristics, this structure can be applied to satellite communication.

Keywords: Array structure; double negative; metamaterial; satellite communication
PACS: 81.05.Xj; 84.40.-x

1 Introduction

Metamaterials are the special type of materials that are usually not available in nature. They are actually engineered materials, which need to embed periodic unit cell for their formation to create naturally unavailable electromagnetic properties. Moreover, these materials have the power to control the electromagnetic wave beams to show their unorthodox characteristics. These unusual features of the metamaterials totally depend on the geometry of the atomic construction. It has been started from the year 1968, when Veselago et al. [1] observed unique properties of materials having negative permittivity (ε) and permeability (μ). But it was not appreciated until 2000, when Smith et al. [2] fortunately validated a new kind of a material with unconventional properties (both permittivity and permeability were negative), which is called left-handed metamaterial. In case of negativity, it has been categorized as single-negative (either permittivity is negative or permeability is negative), double-negative (both permittivity and permeability are negative). There is also a term called near-zero refractive index metamaterial (NZRI),where the permittivity and permeability of a material become approximately zero on a particular range of frequency. Having these captivating electromagnetic phenomena, necessary applications, like SAR reduction [3, 4], super lenses, antenna design [5, 6], filters [7, 8], invisibility cloaking [9, 10], solar cell [11], electromagnetic absorber, and electromagnetic band gaps etc. can be employed by metamaterials. In some cases, intrinsic negative permittivity is found. But it is really difficult to find the negative permeability with a natural medium. Even artificial structures can hardly obtain the negative permeability. Concurrently, it is really difficult to get the negative refractive indices. Currently, multi-band metamaterial absorbers have become an auspicious application in the detection of explosives, even in bolometers and thermal detectors. Moreover, a very few studies have been made in designing this type of materials [12, 13, 14]. Different alphabetic shapes have become popular for particular operations [15]; like, Benosman et al. [16] introduced a double S-shaped metamaterial that showed negative values of η from 15.67 to 17.43GHz. Mallik et al. proposed various U-shaped rectangular array structures left-handed aspect at approximately 5, 6 and 11GHz. A V-shaped metamaterial was presented by Ekmekci et al. - the architecture showed double-negative characteristic. Zhou et al. [17] designed an S-shaped 15 × 15 mm2 chiral metamaterial for X- and Ku-band application. Though the EMR was not higher than 4. For the purpose of application on S and C bands, Alamet al. [18] design H-shaped DNG for different unit cells and array sizes.

A metamaterial unit cell of modified theta-shaped has been proposed in this paper. The structure covers multiple bands (L, C, X, and Ku) of frequencies for the transmission coefficient. And for effective parameters, it covers the X and Ku bands with double negative characteristic.

2 Cell design

The diagram of the prospective modified Theta-shaped unit cell composition is itemized in Figure 1. Each unit cell comprises with 9mm in length and 9 mm in width. All elements have the thickness of 0.35 mm. Each Theta-shaped split resonator has the width of 0.5 mmwith a same split gap. The outer length of the resonator is 9mm where the split of each of the resonators is 0.5mm. The entire patch (made of copper) is developed on a substrate called FR-4. It has a dielectric constant of εr = 4.3, a dielectric loss-tangent of tanδε = 0.025. Sides of the substrate are L = W = 9 mm and the thickness is t = 1.6 mm. Designed parameters of the proposed metamaterial are enlisted in Table 1.

Figure 1 Metamaterial Unit cell: (a) Proposed geometry; (b) Fabricated geometry; (c) Prototype
Figure 1

Metamaterial Unit cell: (a) Proposed geometry; (b) Fabricated geometry; (c) Prototype

Table 1

Parameters of the unit cell

ParametersDimensions (mm)
L9
W9
a0.5
g0.3
b0.3

A prototype array and a unit cell are fabricated for the purpose of measurement. The area of the array is 36 × 36 mm2. Two waveguide ports are used to propagate the electromagnetic waves to excite the configuration on two opposite direction of Z-axis. PEC and PMC were used along the vertical direction of x and y axis, respectively. And for the free-space simulation purposes, a frequency domain solver was utilized. Moreover, for the analysis purpose of these configurations, a tetrahedral mesh was used with a flexible mesh. The normalized impedance was 377 Ohms and the system was performed from 1 to 18 GHz.

The area of the prototype was 9 × 9 mm2, which was fabricated for the purpose of measurements. By settling the perspective unit cell in between, the waveguides as per the Figure 2 to actuate the parameters accurately of the metamaterial unit cell. To determine the parameters, we used a vector analyzer commonly known as Agilent N5227A. To calibrate perfectly, an Agilent N4694-60001 was utilized. Figures 2(a) and 2(b) show the simulation and experimental set up of the proposed metamaterial, respectively.

Figure 2 (a) Simulation set up for measuring S parameter; (b) Experimental set up for measuring S parameter; (c) Current distribution of the unit cell at various frequencies
Figure 2

(a) Simulation set up for measuring S parameter; (b) Experimental set up for measuring S parameter; (c) Current distribution of the unit cell at various frequencies

The equation for this type of passive LC circuits of metamaterial structure is

(1)f=12πLCo

Where L represents cumulative inductance and C represents cumulative capacitance. Here Co represents the capacitance required that forms in two adjacent unit cells. Here, metal loops create inductance and splits create capacitance. When the electromagnetic waves applied through the structure, two types of coupling occurred. Electric resonances are produced due to the formation of coupling between gaps and electric field. Magnetic resonances are formed because of loops and magnetic field. Commonly, the total capacitance formed between the gaps is:

(2)C=ϵ0ϵrAd(F)

whereε0is free space permittivity and εr is relative permittivity. A infers the cross-sectional area of the gap and d refers to the gap length. Hence, the total inductance can be estimated from [19] as:

(3)L1=μ02c2w+h+(2w+h)2+l2ct

Therefore, the equivalent capacitance will be apparent as:

(4)Co≈ϵ0(2w+h)πln2ca−l

Where μ0 is 4π × 10−7 H/m, ε0 is 8.854 × 10−12 F/m, width w, height hand length l. The resonances of the proposed structure are formed because of several series and parallel inductances and capacitances. Splits maintained the capacitive effect and metal fillets are pledged to the effect of inductance.

3 Results and discussions

There are plenty of ways to find out the effective parameters of a unit cell like NRW method, DRI, etc. This paper highlights the electromagnetic properties using the real values of ε, μ, and η using S11 and S21.

3.1 Analysis of the unit cell

As the unit cell is fabricated on a Fr-4 ,which has an area of 81 mm2, it has been measured within a frequency range of 1 to 18 GHz. The simulation was done in the CST microwave studio and the result is compared with the measured one after the fabrication to measure the transmission coefficient (S21). The measured result follows the similar pattern as there is a bit shitting of frequencies in the C-band. The transmission coefficient exhibits a wide band with a coverage of L, C, X, and Ku-band. The first resonance is found in the L-band at frequency 1.63 GHz. Then a wide band from 4.68 GHz to 17.18 GHz with a little band gap of 500 MHz. The shifting is occurring due to fabrication error and the free space measurement process.

Figure 2(b) shows the current distribution of the unit cell at 6.50 GHz and 13.5 GHz. In the proposed formation, inductances are formed by the metal strip and the capacitances are formed by the splits. A homogeneous wave with polarization is an incident in the y-axis and propagation in the x-axis to the structure. Additionally, dimensional scattering consequence, the electric field in the x-direction induces a magnetic dipole in the y-direction, and the magnetic field in the y-direction induces an electric dipole in the x-direction [20]. Due to the antithetical geometry of the structure, a reverse current flow is noticed in the metal fillet of the configuration. Moreover, opposite current flows through the inner and outer surfaces of the resonator creates the stop band at this frequency [21].

Figure 3(a) shows the magnitude of the transmission coefficient (S21). By using S21and S11 parameters, the effective parameters, i.e., effective permeability and effective permittivity can be obtained [22]. Figure 3(b) and (c) show the result of effective permittivity and effective permeability respectively.

Figure 3 (a) Measured and simulated results of S21 ;Real and imaginary values of (b) effective permittivity (ε) vs frequency; (c) effective permeability (μ) vs frequency; (d) refractive index (η) vs frequency
Figure 3

(a) Measured and simulated results of S21 ;Real and imaginary values of (b) effective permittivity (ε) vs frequency; (c) effective permeability (μ) vs frequency; (d) refractive index (η) vs frequency

To differentiate the effective permittivity (εr) and permeability (μr) with S11 and S21, the NRW method is applied.

(5)ϵr=cjπfd×(1−V1)(1+V1)
(6)μr=cjπfd×1−V2(1+V2)

The effective refractive index (ηr) can also be calculated from S21 and S11 [2]:

(7)ηr=cjπfd×(S21−1)2−S112(S21+1)2−S112

The magnetic dipole moment, which is created because the electric field is subjected to generate an artificial magnetism of the resonator. Eventually, that turns out to be an effective negative permeability. On the other hand, the magnetic resonance is superimposed to the corresponding electric resonance, which correlates to the effective negative permittivity. This overlapping turns out to be the effective negative refractive index of the composite medium.

Figure 3(b) shows negative permittivity at resonating points. It shows negativity at 2.60 to 5.16 GHz, 6.63 to 9.31 GHz and 13.03 to 16.18 GHz. Figure 3 (c) exhibits the negative permeability at 7.74 to 13.07 GHz and 13.88 to 16.55 GHz. At lower frequencies, the current flow matches the applied field. But in the case of higher frequencies, it is not possible for the current to cope up with the applied field when the permeability becomes negative. In the gap, there is a charge produced of a SRR, which is regulated to a fluctuating magnetic field. Both current and applied field remain in same phase at lower frequencies, but it fails to remain in phase in higher frequencies and as a result, negative permeability is produced.

In Figure 3(d), real and imaginary parts of η are plotted as a function of frequency. The curve shows negativity at 8.13 to 12.14 GHz, 13.01 to 15.22 GHz and 16.73 to 16.95 GHz. Table 2 shows the frequency range of refractive indices with effective parameters of the unit cell at different resonating frequency bands. The refractive index

Table 2

Parameters of the unit cell

Effective parametersFrequency Range (GHz)Covered BandsValues at 8.14 and 14.01 GHz
Permittivity (ε)2.60 to 5.16, 6.63 to 9.31 & 13.03 to 16.18 GHzS, C, X & Ku-0.56 & -1.15
Permeability (μ)7.74 to 13.07 & 13.88 to 16.55 GHzC, X & Ku-292.49 & -26.21
Refractive Index (η)8.13 to 12.14, 13.01 to 15.22 & 16.73 to 16.95GHzX & Ku-18.32 &-6.99

shows negativity when the permittivity and permeability both become negative. Here η shows certain negativity at different bands of frequencies. Hence, the designed unit cell has significant portions, where all the three effective parameters become negative. Therefore, this configuration can be considered as a double-negative metamaterial as it has negative peaks at 8.14 GHz and 14.01 GHz in all the

three effective parameters, which is shown in Table 2 with bandwidths.

3.2 Array analysis

Figure 4 describes the array formation of the unit structure and unit cell structure, which are placed horizontally for 1× 2 array and both vertically and horizontally on the basic unit structure for higher degrees of arrays on the same Fr-4 substrate. The array structure is measured within the frequency range of 1 to 18 GHz. For unit structure, both the patches are placed 0.5mm apart from each other on the substrate. On the other hand, in the case of unit cell structure, the gap between the patches is 1 mm and the similar approach was used to assess the attainment of the array.

Figure 4 Unit structure (a) Different array formation; (b) S21 vs frequency; (c) Effective parameters vs frequency for the 1 × 2, 2 × 2, 4 × 4 array.
Figure 4

Unit structure (a) Different array formation; (b) S21 vs frequency; (c) Effective parameters vs frequency for the 1 × 2, 2 × 2, 4 × 4 array.

3.2.1 Unit structure analysis

Figure 4(a) shows array formation and (b) shows the transmission coefficient of the array structures. It is apparent that the resonances of the frequencies are found at the same points as the unit cell, but having higher negative magnitudes.

The S21 improves a bit as there is no band gap in between 4.68 to 17.18 GHz in case of 1 × 2 array. But it shows a little gap of about 100 MHz for 2 × 2 and 4 × 4 array. Figure 4(c) shows the real values of the permittivity, permeability and refractive index as a function of frequency of array structures.

From Figure 4(c), it is observed that the negative values for the single unit cell and the array structures are quite similar. The differences among them are the amplitudes or magnitudes and the resonating points shifted a bit to lower frequencies. The negative magnitude decreases in cases of permittivity. But in case of permeability, the negative magnitude increases at resonating points. In case of the refractive index, only the negative qualities are counted. The results of the array structures show similarity with the unit structure. All the effective parameters of these array structures are summarized in Table 3. All the arrays show double negative characteristics at 8.14 and 14.0 GHz.

Table 3

Frequency range of effective parameters of array structures

Effective parametersArray StructuresFrequency Range (GHz)Covered Bands
1 × 21.83 – 4.76, 6.55 – 9.19 & 13.92 – 16.45
Permittivity (ε)2 × 21.78 – 4.61, 6.44 – 9.19 & 12.96 – 16.27L, S, C, X & Ku
4 × 41.19 – 4.22, 6.27 – 9.12 & 12.98 – 16.20
1 × 27.71 – 13.01 & 13.92 – 16.57
Permeability (μ)2 × 27.71 – 13.01 & 13.85 – 16.58C, X & Ku
4 × 47.69 – 13.03 & 13.87 – 16.55
1 × 27.92 – 12.32, 12.98 – 15.56 & 16.63 – 17.18
Refractive Index (η)2 × 28.10 – 11.98, 12.94 – 15.24 & 16.73 – 17.11C, X & Ku
4 × 42.48 – 3.76, 8.06 – 12.03, 12.96 – 15.24 & 16.73 – 16.96

3.2.2 Unit cell structure analysis

Figure 5 shows the design of unit cell structures of 1 × 2, 2 × 2 and 4 × 4 array. Here, the total unit cell is arranged horizontally for 1 × 2 array and for higher formations, the unit cells are placed 0.5 mmapart both vertically and horizontally, based on their degree. And the structures are operated at the frequency range of 1 to 18 GHz. The same procedure is followed to evaluate the unit cell and results, whichare compared with the array structures.

Figure 5 (a) Different array formation; (b) S21 vs frequency; (c) Effective parameters vs frequency for the 1 × 2, 2 × 2, 4 × 4 array of the unit cell structure.
Figure 5

(a) Different array formation; (b) S21 vs frequency; (c) Effective parameters vs frequency for the 1 × 2, 2 × 2, 4 × 4 array of the unit cell structure.

The array formations, effective parameters and the transmission coefficient of the unit cell structures are shown in Figure 5. Array formations are shown in Figure 5(a), S-parameter is shown in Figure 5(b) and Figure 5(c) contains the real values of effective parameters.

The demonstration was done between two square unit cells. They are actually two different working cells, but the output was quite identical to the single unit cell structure. And the same procedure is repeated for a higher degree of array formations. It is evident from the figure, at lower frequencies, there is a slight deviation in the effective parameters including transmission coefficient. The resonating points shifts a bit from the basic structure. In case of S21, the effect is a bit higher. There is no resonance in the L-band except 2 × 2 formation with a negligible spike. Moreover, instead of getting the double negative at 8.14 GHz, the point shifts to 7.94 GHz to show the characteristic. But with the increase of frequencies, the unit cell structures showed good commitment to the basic unit cell. However, the unit cell still carries the double-negative characteristic at some extent.

The transmission coefficient of 13 GHz with a 500 MHz band gap in the middle is demonstrated for all of these configurations. The effective parameters of the resonators cover C, X, and Ku-band independently with double negative phenomena at X and Ku-band, which is similar to basic unit cell. All the effective parameters of these unit cell structures are summarized in Table 4.

Table 4

Frequency range of effective parameters for unit cell array structures

Effective parametersArray StructuresFrequency Range (GHz)Covered Bands
1 × 22.56 – 5.15, 6.59 – 9.28 & 13.05 – 16.41
Permittivity (ε)2 × 22.55 – 5.15, 6.60 – 9.27 & 13.06 – 16.16S, C, X & Ku
4 × 42.51 – 5.13, 6.57 – 9.26 & 13.10 – 16.09
1 × 27.73 – 13.06 & 13.92 – 16.55
Permeability (μ)2 × 27.73 – 13.01 & 13.92 – 16.54C, X & Ku
4 × 47.72 – 13.14 & 13.96 – 16.52
1 × 27.94 – 12.46, 13.01 – 15.58 & 16.61 – 17.12
Refractive Index (η)2 × 28.13 – 12.17, 13.07 – 15.25 & 16.77 – 16.86C, X & Ku
4 × 48.12 – 12.21 & 13.07 – 15.28

4 Comparative analysis of the configurations

In this paper, total observation is made on S-parameter, effective permittivity, effective permeability, and refractive index. In the proposed formation, inductances are formed by the metal strip and the capacitances are formed by the

splits. Electric resonances are produced by coupling between the gaps and electric fields, when the applied electromagnetic wave propagates along the structure. Moreover, magnetic resonances are formed by the coupling between the magnetic fields and loops [21]. The splits of the proposed metamaterial structure as capacitor as they will be storing energy in terms of an electric field. Due to electric resonance and in fact this possesses a dielectric response that provides a permittivity. The following circular structure to store its energy primarily as a magnetic field. So it has a magnetic resonance that gives rise to permeability. The magnetic dipole moment, which is created because the electric field is subjected to generate an artificial magnetic field of the resonator. And eventually that turns out to be an effective negative permeability. On other the hand, the magnetic resonance is superimposed to the corresponding electric resonance, which is correlated to effective negative permittivity. This overlapping turns out to be effective negative refractive index of the composite medium. The negative properties of the permittivity and permeability has altered a little bit due to the polarization effect on the interior construction of the interconnected array structures [23]. Different array structures with different formations vary the capacitance which has a succinct impact on the coupling of the overall circuit and the change in polarization. As a result, the variation points out to the effective parameters by changing their negative properties a bit.

All the results have shown unique, but not contradictory information throughout the methodology. Based on the comparison of 1 × 2, 2 × 2, 4 × 4 arrays and 1 × 2, 2 × 2, 4 × 4 unit structure, it is found that the metamaterial shows double negativity at X and Ku-bands. It has covered 8.13 to 9.31 GHz (bandwidth of 1.18GHz) and 13.88 to 15.22 (bandwidth of 1.34 GHz) in basic unit structure. Among these set of results, 8.14 and 14.01 GHz is the two frequencies where the double negative character of all sorts of configurations is found. Table 5 shows the covered area and relative bandwidths by the refractive index of different configurations for double negative characteristic.

Table 5

Covered area and relative bandwidths by refractive index of different configurations for double negative characteristic

StructureFrequency range (GHz)Band widthCovered BandsType of Metamaterial
Unit Cell8.14 – 9.31 13.80 – 15.221.17 1.42X & KuDNG
1 × 2 Structure7.92 – 9.19 13.92 – 15.561.27 1.64X & KuDNG
1 × 2 Unit cell Structure7.94 – 9.27 13.92 – 15.581.33 1.66X & KuDNG
2 × 2 Structure8.10 – 9.19 13.85 – 15.241.09 1.39X & KuDNG
2 × 2 Unit cell Structure8.13 – 9.27 13.92 – 15.251.14 1.33X & KuDNG
4 × 4 Structure8.06 – 9.12 13.87 – 15.241.06 1.37X & KuDNG
4 × 4 Unit Cell Structure8.12 – 9.26 13.96 – 15.271.14 1.31X & KuDNG

From the Table 5, it is evident that all the configurations show similar double negative characteristic of the respective frequency range. But more stability is found among basic unit cell, 1 × 2, 2 × 2 and 4 × 4 array with higher bandwidths. Besides 1 × 2, 2 × 2 and 4 × 4 unit cell structures shown fluctuating results with less bandwidth with respect to other configurations.

In case of array analysis, all the unit structures show similar results, where unit cell structures show similarity among themselves. The reason behind the analysis of unit cell structures was to validate the metamaterial quality with the increase in gaps among themselves, as they have to be periodic in case of application. The overall inductance in a particular unit cell was fixed. The only scope was the gap that could change the potential values of the capacitances. The impact of coupling in the structure is shown due to different array formation. Although, all the formations follow the basic metamaterial characteristics and show similar results in every effective parameters.

Table 6 illustrates the comparisons of the frequency bands and the effective medium ratio of proposed design with previous work. The proposed structure demonstrates the effective medium ratio, which is more than 10 and is applicable for X- and Ku-band applications. Islam et al. [9], proposed a unit cell with a dimension of 10 × 10 mm2, applied for invisibility cloaking but the EMR is < 4. Benosman and Hacene [16] and Rizwan et al. [24] both introduced metamaterial structures of 3 and 2 mm, respectively. Both of them have a common working range of frequency (K-band in common) with an EMR of around 6.30. Moreover, Mallik et al. [25] proposed meta-structures of 25 mm, Zhou and Yang [17] of 15 mm. All the mentioned studies with different dimensions are having different ranges of frequencies. But none of these researches have exceeded the EMR of the proposed metamaterial. However, this 9 mm Meta structure has a band coverage of X and Ku bands with an EMR of 10.19.

Table 6

Comparison the proposed unit cell with the previous unit cell

Previous WorkDimensions (mm2)Resonance FrequencyEffective Medium Ratio
10×10X-Band3.58
Benosman et al., 2012 [16]3×3Ku and K-Band6.39
Zhou et al., 2015 [17]15×15X and Ku-Band2.10
Rizwan et al., 2014 [24]2×2K and Ka-Band6.30
Malik et al., 2013 [25]25×25C and X-Band2.10
Proposed Metamaterial9×9X and Ku-Band10.19

5 Conclusions

This paper presents the framework of the modified Theta shaped unit cell and a correlation is contrived on a transmission coefficient, relative permeability, permittivity and refractive index. The analyses and the comparisons are made on unit cell, 1 × 2, 2 × 2 and 4 × 4 array structures with 1 × 2, 2 × 2 and 4 × 4 unit cell structures. The transmission coefficient (S21) is calculated and compared with different array formations. The transmission coefficient covered L, C, X and Ku bands for all the configurations. Negative effective parameters are also found in all the structures. However, unit cell, 1 × 2, 2 × 2 and 4 × 4 array structures shown good agreement to the effective parameters. Even the negative values of each of the effective parameters are found on the X and Ku bands at 8.14 and 14.01 GHz with a bandwidth of more than 1.20 and 1.32 GHz, respectively. It certainly represents the dual band double negative characteristic of the proposed compact design. Thus, these structures are valid for the application of dual bands and satellite communication. It can also be a promising choice for double negativity. The modified Theta shaped structure can be an auspicious alternative to new metamaterials, especially in utilizations where metamaterials are the only requirement.

Acknowledgement

This work was supported by the Universiti Kebangsaan Malaysia, Research University Grant, Code: DPP-2018-004.

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Received: 2018-05-01
Accepted: 2018-07-23
Published Online: 2018-12-26

© 2018 Md. Jubaer Alam et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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  13. A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions
  14. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics
  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications
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  75. Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes
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  138. Energy converting layers for thin-film flexible photovoltaic structures
  139. Effect of convection heat transfer on thermal energy storage unit
https://doi.org/10.1515/phys-2018-0105
Keywords for this article
Array structure; double negative; metamaterial; satellite communication
Creative Commons
BY-NC-ND 4.0

Articles in the same Issue

  1. Regular Articles
  2. A modified Fermi-Walker derivative for inextensible flows of binormal spherical image
  3. Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics
  4. Three-dimensional atom localization via probe absorption in a cascade four-level atomic system
  5. Determination of the energy transitions and half-lives of Rubidium nuclei
  6. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 1 - model development
  7. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 2 - model validation
  8. Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity
  9. Constructing analytic solutions on the Tricomi equation
  10. Feynman diagrams and rooted maps
  11. New type of chaos synchronization in discrete-time systems: the F-M synchronization
  12. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus
  13. A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions
  14. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics
  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications
  16. Siewert solutions of transcendental equations, generalized Lambert functions and physical applications
  17. Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction
  18. A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis
  19. Dynamics of a dry-rebounding drop: observations, simulations, and modeling
  20. Modeling the initial mechanical response and yielding behavior of gelled crude oil
  21. Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation
  22. Solitary wave solutions of two KdV-type equations
  23. Applying industrial tomography to control and optimization flow systems
  24. Reconstructing time series into a complex network to assess the evolution dynamics of the correlations among energy prices
  25. An optimal solution for software testing case generation based on particle swarm optimization
  26. Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation
  27. Alternative methods for solving nonlinear two-point boundary value problems
  28. Global model simulation of OH production in pulsed-DC atmospheric pressure helium-air plasma jets
  29. Experimental investigation on optical vortex tweezers for microbubble trapping
  30. Joint measurements of optical parameters by irradiance scintillation and angle-of-arrival fluctuations
  31. M-polynomials and topological indices of hex-derived networks
  32. Generalized convergence analysis of the fractional order systems
  33. Porous flow characteristics of solution-gas drive in tight oil reservoirs
  34. Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method
  35. A Note on Koide’s Doubly Special Parametrization of Quark Masses
  36. On right-angled spherical Artin monoid of type Dn
  37. Gas flow regimes judgement in nanoporous media by digital core analysis
  38. 4 + n-dimensional water and waves on four and eleven-dimensional manifolds
  39. Stabilization and Analytic Approximate Solutions of an Optimal Control Problem
  40. On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy
  41. New prediction method for transient productivity of fractured five-spot patterns in low permeability reservoirs at high water cut stages
  42. The collinear equilibrium points in the restricted three body problem with triaxial primaries
  43. Detection of the damage threshold of fused silica components and morphologies of repaired damage sites based on the beam deflection method
  44. On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem
  45. Ion acoustic quasi-soliton in an electron-positron-ion plasma with superthermal electrons and positrons
  46. Analysis of projectile motion in view of conformable derivative
  47. Computing multiple ABC index and multiple GA index of some grid graphs
  48. Terahertz pulse imaging: A novel denoising method by combing the ant colony algorithm with the compressive sensing
  49. Characteristics of microscopic pore-throat structure of tight oil reservoirs in Sichuan Basin measured by rate-controlled mercury injection
  50. An activity window model for social interaction structure on Twitter
  51. Transient thermal regime trough the constitutive matrix applied to asynchronous electrical machine using the cell method
  52. On the zagreb polynomials of benzenoid systems
  53. Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance
  54. The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method
  55. Quantifying the global solar radiation received in Pietermaritzburg, KwaZulu-Natal to motivate the consumption of solar technologies
  56. Sturm-Liouville difference equations having Bessel and hydrogen atom potential type
  57. Study on the response characteristics of oil wells after deep profile control in low permeability fractured reservoirs
  58. Depiction and analysis of a modified theta shaped double negative metamaterial for satellite application
  59. An attempt to geometrize electromagnetism
  60. Structure of traveling wave solutions for some nonlinear models via modified mathematical method
  61. Thermo-convective instability in a rotating ferromagnetic fluid layer with temperature modulation
  62. Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations
  63. Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel
  64. Physical cues of biomaterials guide stem cell fate of differentiation: The effect of elasticity of cell culture biomaterials
  65. Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity
  66. Rank correlation between centrality metrics in complex networks: an empirical study
  67. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  68. Modeling of electric and heat processes in spot resistance welding of cross-wire steel bars
  69. Dynamic characteristics of triaxial active control magnetic bearing with asymmetric structure
  70. Design optimization of an axial-field eddy-current magnetic coupling based on magneto-thermal analytical model
  71. Thermal constitutive matrix applied to asynchronous electrical machine using the cell method
  72. Temperature distribution around thin electroconductive layers created on composite textile substrates
  73. Model of the multipolar engine with decreased cogging torque by asymmetrical distribution of the magnets
  74. Analysis of spatial thermal field in a magnetic bearing
  75. Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes
  76. Assessment of short/long term electric field strength measurements for a pilot district
  77. Simulation study and experimental results for detection and classification of the transient capacitor inrush current using discrete wavelet transform and artificial intelligence
  78. Magnetic transmission gear finite element simulation with iron pole hysteresis
  79. Pulsed excitation terahertz tomography – multiparametric approach
  80. Low and high frequency model of three phase transformer by frequency response analysis measurement
  81. Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion
  82. Optimal design of a for middle-low-speed maglev trains
  83. Eddy current modeling in linear and nonlinear multifilamentary composite materials
  84. The visual attention saliency map for movie retrospection
  85. AC/DC current ratio in a current superimposition variable flux reluctance machine
  86. Influence of material uncertainties on the RLC parameters of wound inductors modeled using the finite element method
  87. Cogging force reduction in linear tubular flux switching permanent-magnet machines
  88. Modeling hysteresis curves of La(FeCoSi)13 compound near the transition point with the GRUCAD model
  89. Electro-magneto-hydrodynamic lubrication
  90. 3-D Electromagnetic field analysis of wireless power transfer system using K computer
  91. Simplified simulation technique of rotating, induction heated, calender rolls for study of temperature field control
  92. Design, fabrication and testing of electroadhesive interdigital electrodes
  93. A method to reduce partial discharges in motor windings fed by PWM inverter
  94. Reluctance network lumped mechanical & thermal models for the modeling and predesign of concentrated flux synchronous machine
  95. Special Issue Applications of Nonlinear Dynamics
  96. Study on dynamic characteristics of silo-stock-foundation interaction system under seismic load
  97. Microblog topic evolution computing based on LDA algorithm
  98. Modeling the creep damage effect on the creep crack growth behavior of rotor steel
  99. Neighborhood condition for all fractional (g, f, n′, m)-critical deleted graphs
  100. Chinese open information extraction based on DBMCSS in the field of national information resources
  101. 10.1515/phys-2018-0079
  102. CPW-fed circularly-polarized antenna array with high front-to-back ratio and low-profile
  103. Intelligent Monitoring Network Construction based on the utilization of the Internet of things (IoT) in the Metallurgical Coking Process
  104. Temperature detection technology of power equipment based on Fiber Bragg Grating
  105. Research on a rotational speed control strategy of the mandrel in a rotary steering system
  106. Dynamic load balancing algorithm for large data flow in distributed complex networks
  107. Super-structured photonic crystal fiber Bragg grating biosensor image model based on sparse matrix
  108. Fractal-based techniques for physiological time series: An updated approach
  109. Analysis of the Imaging Characteristics of the KB and KBA X-ray Microscopes at Non-coaxial Grazing Incidence
  110. Application of modified culture Kalman filter in bearing fault diagnosis
  111. Exact solutions and conservation laws for the modified equal width-Burgers equation
  112. On topological properties of block shift and hierarchical hypercube networks
  113. Elastic properties and plane acoustic velocity of cubic Sr2CaMoO6 and Sr2CaWO6 from first-principles calculations
  114. A note on the transmission feasibility problem in networks
  115. Ontology learning algorithm using weak functions
  116. Diagnosis of the power frequency vacuum arc shape based on 2D-PIV
  117. Parametric simulation analysis and reliability of escalator truss
  118. A new algorithm for real economy benefit evaluation based on big data analysis
  119. Synergy analysis of agricultural economic cycle fluctuation based on ant colony algorithm
  120. Multi-level encryption algorithm for user-related information across social networks
  121. Multi-target tracking algorithm in intelligent transportation based on wireless sensor network
  122. Fast recognition method of moving video images based on BP neural networks
  123. Compressed sensing image restoration algorithm based on improved SURF operator
  124. Design of load optimal control algorithm for smart grid based on demand response in different scenarios
  125. Face recognition method based on GA-BP neural network algorithm
  126. Optimal path selection algorithm for mobile beacons in sensor network under non-dense distribution
  127. Localization and recognition algorithm for fuzzy anomaly data in big data networks
  128. Urban road traffic flow control under incidental congestion as a function of accident duration
  129. Optimization design of reconfiguration algorithm for high voltage power distribution network based on ant colony algorithm
  130. Feasibility simulation of aseismic structure design for long-span bridges
  131. Construction of renewable energy supply chain model based on LCA
  132. The tribological properties study of carbon fabric/ epoxy composites reinforced by nano-TiO2 and MWNTs
  133. A text-Image feature mapping algorithm based on transfer learning
  134. Fast recognition algorithm for static traffic sign information
  135. Topical Issue: Clean Energy: Materials, Processes and Energy Generation
  136. An investigation of the melting process of RT-35 filled circular thermal energy storage system
  137. Numerical analysis on the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under various operating conditions
  138. Energy converting layers for thin-film flexible photovoltaic structures
  139. Effect of convection heat transfer on thermal energy storage unit
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