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Keywords = global monopole

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29 pages, 15419 KB  
Article
Algorithm-Driven Placement Optimization of Aircraft-Mounted VHF Antennas for Mutual Coupling Reduction
by Emre Oz, Baris Gurcan Hakanoglu, Yaser Dalveren, Ali Kara and Mohammad Derawi
Appl. Sci. 2026, 16(6), 2718; https://doi.org/10.3390/app16062718 - 12 Mar 2026
Viewed by 698
Abstract
This study investigates algorithm-driven placement optimization of two aircraft-mounted VHF monopole antennas to mitigate mutual coupling under realistic installation constraints. A parameterized 3D aircraft model inspired by general-aviation platforms is analyzed using full-wave electromagnetic simulations over the 30–100 MHz band. The optimization problem [...] Read more.
This study investigates algorithm-driven placement optimization of two aircraft-mounted VHF monopole antennas to mitigate mutual coupling under realistic installation constraints. A parameterized 3D aircraft model inspired by general-aviation platforms is analyzed using full-wave electromagnetic simulations over the 30–100 MHz band. The optimization problem is formulated to reduce inter-antenna coupling across the operating band while restricting the search space to physically installable regions on the airframe. Two global optimization methods, Genetic Algorithm and Particle Swarm Optimization, are applied and compared under the identical constraints and objective definitions. The results show that both optimizers achieve a significant reduction in coupling relative to non-optimized placements, with comparable overall performance. Installed far-field radiation characteristics are further evaluated to verify that the optimized solutions preserve, and in some cases improve, the omnidirectional coverage required for airborne VHF communication. The proposed workflow provides a practical, simulation-driven framework for electromagnetic compatibility (EMC)-oriented antenna integration on complex aircraft platforms. Full article
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66 pages, 37968 KB  
Article
Human Activity Impacts on Macrofungal Diversity: A Case Study of Grazing in Subtropical Forests
by Kun L. Yang, Xunan Xiong, Zejia Luo, Yanqun Huang, Rong Huang, Huajie Chen, Jia Y. Lin, Zhu L. Yang, Guang-Mei Li and Xiaorong Jia
J. Fungi 2025, 11(10), 749; https://doi.org/10.3390/jof11100749 - 20 Oct 2025
Cited by 9 | Viewed by 4173
Abstract
Concerns about potential negative impacts of human activity on macrofungal diversity are spreading globally, yet research on this topic remains scarce. This study focuses on forest grazing (silvopasture), a popular economic practice whose impacts on macrofungal diversity are underexplored. Through investigation and comparison [...] Read more.
Concerns about potential negative impacts of human activity on macrofungal diversity are spreading globally, yet research on this topic remains scarce. This study focuses on forest grazing (silvopasture), a popular economic practice whose impacts on macrofungal diversity are underexplored. Through investigation and comparison of macrofungal diversity and selected environmental factors in three types of subtropical forests (secondary mixed forests, dense-tree plantations and sparse-tree plantations) before and after two years of grazing at an intensity of 10 goats per hectare in South China, three key findings emerged: (1) Macrofungal alpha-diversity increased significantly after grazing, associated with an increase in large plant remains and a decrease in litterfall thickness; (2) dominance was monopolized by few taxa before grazing but became more balanced among a number of taxa after grazing; and (3) dominance of endemic taxa decreased in two of the three types of forests after grazing. Such findings suggest that grazing may create additional niches through foraging, trampling and excretion by livestock and thus recruit diverse macrofungi but may also lead to homogenization of fungal florae across regions and thus result in recessive beta-diversity loss. As this study heavily relies on taxonomy, allied updates for ambiguous taxa recognized in analyses are additionally proposed. Full article
(This article belongs to the Collection Fungal Biodiversity and Ecology)
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12 pages, 1244 KB  
Article
Evaluation of Energy Consumption for Mineral Processing of Tungsten Ore in Mongolia: Khovd Aimag and Erdene-Soum as Case Studies
by Ha Bich Trinh, Seunghyun Kim, Taehun Son, Junkun Song and Jaeryeong Lee
Minerals 2025, 15(6), 660; https://doi.org/10.3390/min15060660 - 19 Jun 2025
Cited by 1 | Viewed by 2062
Abstract
The tungsten deposits in Mongolia have the potential to be exploited as an alternative source to alleviate the risk due to the monopolization in the global production of such a critical metal. However, it is challenging to develop an efficient mineral processing method [...] Read more.
The tungsten deposits in Mongolia have the potential to be exploited as an alternative source to alleviate the risk due to the monopolization in the global production of such a critical metal. However, it is challenging to develop an efficient mineral processing method that can complement the supply based on the currently available energy resources in Mongolia. Therefore, the present study investigated the range of energy required for the beneficiation of tungsten ores, including theoretical assumptions and practical evaluation for two processes in Mongolia. The range of energy consumption was 0.12 to 2.21 kWh/t for crushing and 0.29 to 4.62 kWh/t for grinding regarding the range of Kick’s constant 0.2–0.6 kWh/t and Bond work index 7–17 kWh/t, respectively. The most dominant impact factor in the comminution was the product size. The evaluation of 18 different comminution–flotation circuits indicated a range of required energy from 362 kWh to 8298 kWh. The maximum values of energy consumption for mineral processing of Erdene-soum and Khovd Aimag tungsten ore were 6280 and 6355 kWh. An estimation regarding the energy demand (6355 kWh) and supply energy for the process of Khovd Aimag ore was conducted to propose a suitable system of renewable energy resources using the power pinch analysis method. Full article
(This article belongs to the Section Mineral Processing and Extractive Metallurgy)
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32 pages, 10802 KB  
Article
Shadow Analysis of an Approximate Rotating Black Hole Solution with Weakly Coupled Global Monopole Charge
by Mohsen Fathi
Universe 2025, 11(4), 111; https://doi.org/10.3390/universe11040111 - 27 Mar 2025
Cited by 3 | Viewed by 1127
Abstract
In this paper, we investigate the shadow properties of a rotating black hole with a weakly coupled global monopole charge using a modified Newman–Janis algorithm. This study explores how these charge and rotational effects shape the black hole’s shadow, causal structure, and ergoregions, [...] Read more.
In this paper, we investigate the shadow properties of a rotating black hole with a weakly coupled global monopole charge using a modified Newman–Janis algorithm. This study explores how these charge and rotational effects shape the black hole’s shadow, causal structure, and ergoregions, with implications for distinguishing it from Kerr-like solutions. Analysis of null geodesics reveals observable features that may constrain the global monopole charge and weak coupling parameters within nonminimal gravity frameworks. Observational data from M87* and Sgr A* constrain the global monopole charge and coupling constant to 0γ0.036 and 0.2α0, respectively. Full article
(This article belongs to the Section Gravitation)
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11 pages, 271 KB  
Article
Hydrogen and Pionic Atoms Under the Effects of Oscillations in the Global Monopole Spacetime
by R. L. L. Vitória and Kleber Anderson T. da Silva
Symmetry 2025, 17(1), 88; https://doi.org/10.3390/sym17010088 - 8 Jan 2025
Cited by 1 | Viewed by 1475
Abstract
In this analysis, we investigate hydrogen and pionic atoms subjected to Dirac and Klein-Gordon oscillators, respectively, in the global monopole spacetime. Through a purely analytical analysis, we determine solutions of bound state, in which we define the allowed energy values for the lowest [...] Read more.
In this analysis, we investigate hydrogen and pionic atoms subjected to Dirac and Klein-Gordon oscillators, respectively, in the global monopole spacetime. Through a purely analytical analysis, we determine solutions of bound state, in which we define the allowed energy values for the lowest energy state of both proposed systems. In addition to the influence of the topological defect on the results obtained, we note another quantum effect: the oscillation frequencies of both systems depend on the system quantum numbers, that is, the angular frequencies are quantized. Full article
(This article belongs to the Special Issue Symmetry in Topological Physics)
14 pages, 12082 KB  
Article
Cluster Odd-Parity Multipoles by Staggered Orbital Ordering in Locally Noncentrosymmetric Crystals
by Satoru Hayami
Crystals 2024, 14(7), 632; https://doi.org/10.3390/cryst14070632 - 9 Jul 2024
Viewed by 2001
Abstract
Odd-parity multipoles in crystals manifest themselves not only in their peculiar electronic orderings but also in unconventional parity-violating physical phenomena. We here report the emergence of odd-parity multipoles by considering staggered orbital orderings in a locally noncentrosymmetric crystal system with the global inversion [...] Read more.
Odd-parity multipoles in crystals manifest themselves not only in their peculiar electronic orderings but also in unconventional parity-violating physical phenomena. We here report the emergence of odd-parity multipoles by considering staggered orbital orderings in a locally noncentrosymmetric crystal system with the global inversion center but without the inversion center at each lattice site. We show that various odd-parity multipoles, such as the electric toroidal monopole, electric dipole, and electric toroidal quadrupole, are realized depending on the type of orbital orderings in the one-dimensional zigzag chain. Such odd-parity multipoles give rise to an antisymmetric spin splitting in the electronic band structure with the aid of the relativistic spin–orbit coupling. We also show that similar states with odd-parity multipoles are realized in other locally noncentrosymmetric crystals, such as the two-dimensional honeycomb and three-dimensional diamond structures. Full article
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21 pages, 5023 KB  
Article
Hybrid Computation of the Aerodynamic Noise Radiated by the Wake of a Subsonic Cylinder
by Benet Eiximeno, Carlos Tur-Mongé, Oriol Lehmkuhl and Ivette Rodríguez
Fluids 2023, 8(8), 236; https://doi.org/10.3390/fluids8080236 - 21 Aug 2023
Cited by 4 | Viewed by 2582
Abstract
The noise radiated by the flow around a cylinder in the subcritical regime at ReD=1×104 and at a subsonic Mach number of M=0.5 is here studied. The aerodynamic sound radiated by a cylinder has [...] Read more.
The noise radiated by the flow around a cylinder in the subcritical regime at ReD=1×104 and at a subsonic Mach number of M=0.5 is here studied. The aerodynamic sound radiated by a cylinder has been studied with a wide range of Reynolds numbers, but there are no studies about how the Mach number affects the acoustic field in the subsonic regime. The flow field is resolved by means of large-eddy simulations of the compressible Navier–Stokes equations. For the study of the noise propagation, formulation 1C of the Ffowcs Williams–Hawkings analogy is used. The fluid flow results show good agreement when comparing the surface pressure coefficient, the recirculation length, the vortex shedding frequency and the force coefficients against other studies performed under similar conditions. The dynamic mode decomposition of the pressure fluctuations is used to relate them with the far-field noise. It is shown that, in contrast to what happens for low Mach numbers, quadrupoles have a significant impact mainly in the observers located in the streamwise direction. This effect leads to a global monopole directivity pattern as the shear fluctuations compensate for the lower value of the aeolian tone away from the cross-stream direction. Full article
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26 pages, 3230 KB  
Review
Unlocking the Power of Digital Commons: Data Cooperatives as a Pathway for Data Sovereign, Innovative and Equitable Digital Communities
by Michael Max Bühler, Igor Calzada, Isabel Cane, Thorsten Jelinek, Astha Kapoor, Morshed Mannan, Sameer Mehta, Vijay Mookerje, Konrad Nübel, Alex Pentland, Trebor Scholz, Divya Siddarth, Julian Tait, Bapu Vaitla and Jianguo Zhu
Digital 2023, 3(3), 146-171; https://doi.org/10.3390/digital3030011 - 29 Jun 2023
Cited by 83 | Viewed by 14412
Abstract
Network effects, economies of scale, and lock-in-effects increasingly lead to a concentration of digital resources and capabilities, hindering the free and equitable development of digital entrepreneurship, new skills, and jobs, especially in small communities and their small and medium-sized enterprises (“SMEs”). To ensure [...] Read more.
Network effects, economies of scale, and lock-in-effects increasingly lead to a concentration of digital resources and capabilities, hindering the free and equitable development of digital entrepreneurship, new skills, and jobs, especially in small communities and their small and medium-sized enterprises (“SMEs”). To ensure the affordability and accessibility of technologies, promote digital entrepreneurship and community well-being, and protect digital rights, we propose data cooperatives as a vehicle for secure, trusted, and sovereign data exchange. In post-pandemic times, community/SME-led cooperatives can play a vital role by ensuring that supply chains to support digital commons are uninterrupted, resilient, and decentralized. Digital commons and data sovereignty provide communities with affordable and easy access to information and the ability to collectively negotiate data-related decisions. Moreover, cooperative commons (a) provide access to the infrastructure that underpins the modern economy, (b) preserve property rights, and (c) ensure that privatization and monopolization do not further erode self-determination, especially in a world increasingly mediated by AI. Thus, governance plays a significant role in accelerating communities’/SMEs’ digital transformation and addressing their challenges. Cooperatives thrive on digital governance and standards such as open trusted application programming interfaces (“APIs”) that increase the efficiency, technological capabilities, and capacities of participants and, most importantly, integrate, enable, and accelerate the digital transformation of SMEs in the overall process. This review article analyses an array of transformative use cases that underline the potential of cooperative data governance. These case studies exemplify how data and platform cooperatives, through their innovative value creation mechanisms, can elevate digital commons and value chains to a new dimension of collaboration, thereby addressing pressing societal issues. Guided by our research aim, we propose a policy framework that supports the practical implementation of digital federation platforms and data cooperatives. This policy blueprint intends to facilitate sustainable development in both the Global South and North, fostering equitable and inclusive data governance strategies. Full article
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12 pages, 2501 KB  
Communication
A Compact Size Antenna for Extended UWB with WLAN Notch Band Stub
by Syed Naheel Raza Rizvi, Wahaj Abbas Awan, Domin Choi, Niamat Hussain, Seong Gyoon Park and Nam Kim
Appl. Sci. 2023, 13(7), 4271; https://doi.org/10.3390/app13074271 - 28 Mar 2023
Cited by 15 | Viewed by 4662
Abstract
An ultra-wideband (UWB), geometrically simple, compact, and high-gain antenna with a WLAN notch band is presented for future wireless devices. The antenna is printed on the top side of the Rogers RT/Duroid 5880 substrate and has a small dimension of 10 mm × [...] Read more.
An ultra-wideband (UWB), geometrically simple, compact, and high-gain antenna with a WLAN notch band is presented for future wireless devices. The antenna is printed on the top side of the Rogers RT/Duroid 5880 substrate and has a small dimension of 10 mm × 15 mm × 0.254 mm. The primary radiator of the proposed coplanar waveguide-fed monopole antenna is comprised of a rectangular-shaped structure initially modified using a slot, and its bandwidth is further enhanced by loading a Y-shaped radiator. As a result, the antenna offers a –10 dB impedance matching bandwidth of 11.55 GHz ranging from 3–14.55 GHz, covering globally allocated C-, S-, and X-band applications. Afterward, another rectangular stub is loaded in the structure to mitigate the WLAN band from the UWB spectrum, and the final antenna offers a notched band spanning from 4.59 to 5.82 GHz. Moreover, to validate the simulated results, a hardware prototype is built and measured, which exhibits good agreement with the simulated results. Furthermore, the proposed work is compared to state-of-the-art antennas for similar applications to demonstrate its design significance, as it has a compact size, wider bandwidth, and stable gain characteristics. Full article
(This article belongs to the Special Issue Design, Analysis, and Measurement of Antennas)
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18 pages, 1041 KB  
Article
Approximate Analytical Solutions of the Schrödinger Equation with Hulthén Potential in the Global Monopole Spacetime
by Saulo S. Alves, Márcio M. Cunha, Hassan Hassanabadi and Edilberto O. Silva
Universe 2023, 9(3), 132; https://doi.org/10.3390/universe9030132 - 4 Mar 2023
Cited by 37 | Viewed by 3330
Abstract
In this paper, we studied the nonrelativistic quantum mechanics of an electron in a spacetime containing a topological defect. We also considered that the electron is influenced by the Hulthén potential. In particular, we dealt with the Schrödinger equation in the presence of [...] Read more.
In this paper, we studied the nonrelativistic quantum mechanics of an electron in a spacetime containing a topological defect. We also considered that the electron is influenced by the Hulthén potential. In particular, we dealt with the Schrödinger equation in the presence of a global monopole. We obtained approximate solutions for the problem, determined the scattering phase shift and the S-matrix, and analyzed bound states. Full article
(This article belongs to the Section Mathematical Physics)
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15 pages, 5062 KB  
Article
A Shorted Stub Loaded UWB Flexible Antenna for Small IoT Devices
by Esraa Mousa Ali, Wahaj Abbas Awan, Mohammed S. Alzaidi, Abdullah Alzahrani, Dalia H. Elkamchouchi, Francisco Falcone and Sherif S. M. Ghoneim
Sensors 2023, 23(2), 748; https://doi.org/10.3390/s23020748 - 9 Jan 2023
Cited by 41 | Viewed by 4782
Abstract
In this manuscript, a compact in size yet geometrically simple Ultra-Wideband (UWB) antenna is demonstrated. The flexible-by-nature substrate ROGERS 5880, having a thickness of 0.254 mm, is utilized to design the proposed work. The antenna configuration is an excerpt of a traditional rectangular [...] Read more.
In this manuscript, a compact in size yet geometrically simple Ultra-Wideband (UWB) antenna is demonstrated. The flexible-by-nature substrate ROGERS 5880, having a thickness of 0.254 mm, is utilized to design the proposed work. The antenna configuration is an excerpt of a traditional rectangular monopole antenna resonating at 5 GHz. Initially, a pair of triangular slots are employed to extend the impedance bandwidth of the antenna. In addition, a semi-circular-shaped, short-ended stub is connected at the upper edges of the patch to further increase the operational bandwidth. After optimization, the proposed antenna offers UWB ranging from 2.73–9.68 GHz, covering almost the entire spectrum allocated globally for UWB applications. Further, the antenna offers a compact size of 15 × 20 mm2 that can easily be integrated into small, flexible electronics. The flexibility analysis is done by bending the antenna on both the x and y axes. The antenna offers performance stability in terms of return loss, radiation pattern, and gain for both conformal and non-conformal conditions. Furthermore, the strong comparison between simulated and measured results for both rigid and bent cases of the antenna, along with the performance comparison with the state-of-the-art, makes it a potential candidate for present and future compact-sized flexible devices. Full article
(This article belongs to the Special Issue Antenna Design and Optimization for 5G, 6G, and IoT)
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15 pages, 36119 KB  
Article
A Frequency-Reconfigurable Filtenna for GSM, 4G-LTE, ISM, and 5G Sub-6 GHz Band Applications
by Wahaj Abbas Awan, Niamat Hussain, Sunggoo Kim and Nam Kim
Sensors 2022, 22(15), 5558; https://doi.org/10.3390/s22155558 - 25 Jul 2022
Cited by 37 | Viewed by 4622
Abstract
This paper presents the design and realization of a flexible and frequency-reconfigurable antenna with harmonic suppression for multiple wireless applications. The antenna structure is derived from a quarter-wave monopole by etching slots. Afterward, the high-order unwanted harmonics are eliminated by adding a filtering [...] Read more.
This paper presents the design and realization of a flexible and frequency-reconfigurable antenna with harmonic suppression for multiple wireless applications. The antenna structure is derived from a quarter-wave monopole by etching slots. Afterward, the high-order unwanted harmonics are eliminated by adding a filtering stub to the feedline to avoid signal interference. Lastly, frequency reconfigurability is achieved using pin diodes by connecting and disconnecting the stubs and the rectangular patch. The antenna is fabricated on the commercially available thin (0.254 mm) conformal substrate of Rogers RT5880. The proposed antenna resonates (|S11| < –10 dB) at five different reconfigurable bands of 3.5 GHz (3.17–3.82 GHz), 2.45 GHz (2.27–2.64 GHz), 2.1 GHz (2.02–2.29 GHz), 1.9 GHz (1.81–2.05 GHz), and 1.8 GHz (1.66–1.93 GHz), which are globally used for 5G sub-6 GHz in industrial, medical, and scientific (ISM) bands, 4G long-term evolution (LTE) bands, and global system for mobile communication (GSM) bands. The simulated and measured results show that the antenna offers excellent performance in terms of good impedance matching with controllable resonant bands, high gain (>2 dBi), stable radiation patterns, and efficiency (>87%). Moreover, the conformal analysis shows that the antenna retains its performance both in flat and bending conditions, making it suitable for flexible electronics. In addition, the antenna is compared with the state-of-the-art works for similar applications to show its potential for the targeted band spectrums. Full article
(This article belongs to the Special Issue Wearable Antennas and Wearable Wireless Communication Systems)
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6 pages, 244 KB  
Article
Deriving the Hawking Temperature of (Massive) Global Monopole Spacetime via a Topological Formula
by Junlan Xian and Jingyi Zhang
Entropy 2022, 24(5), 634; https://doi.org/10.3390/e24050634 - 30 Apr 2022
Cited by 7 | Viewed by 2267
Abstract
In this work, we study the Hawking temperature of the global monopole spacetime (non-spherical symmetrical black hole) based on the topological method proposed by Robson, Villari, and Biancalana (RVB). By connecting the Hawking temperature with the topological properties of black holes, the Hawking [...] Read more.
In this work, we study the Hawking temperature of the global monopole spacetime (non-spherical symmetrical black hole) based on the topological method proposed by Robson, Villari, and Biancalana (RVB). By connecting the Hawking temperature with the topological properties of black holes, the Hawking temperature of the global monopole spacetime can be obtained by the RVB method. We also discuss the Hawking temperature in massive gravity, and find that the effect of the mass term cannot be ignored in the calculation of the Hawking temperature; the corrected Hawking temperature in massive gravity can be derived by adding an integral constant, which can be determined by the standard definition. Full article
109 pages, 4632 KB  
Article
Notes on Confinement on R3 × S1: From Yang–Mills, Super-Yang–Mills, and QCD (adj) to QCD(F)
by Erich Poppitz
Symmetry 2022, 14(1), 180; https://doi.org/10.3390/sym14010180 - 17 Jan 2022
Cited by 31 | Viewed by 6390
Abstract
This is a pedagogical introduction to the physics of confinement on R3×S1, using SU(2) Yang–Mills with massive or massless adjoint fermions as the prime example; we also add fundamental flavours to conclude. The small- [...] Read more.
This is a pedagogical introduction to the physics of confinement on R3×S1, using SU(2) Yang–Mills with massive or massless adjoint fermions as the prime example; we also add fundamental flavours to conclude. The small-S1 limit is remarkable, allowing for controlled semiclassical determination of the nonperturbative physics in these, mostly non-supersymmetric, theories. We begin by reviewing the Polyakov confinement mechanism on R3. Moving on to R3×S1, we show how introducing adjoint fermions stabilizes center symmetry, leading to abelianization and semiclassical calculability. We explain how monopole–instantons and twisted monopole–instantons arise. We describe the role of various novel topological excitations in extending Polyakov’s confinement to the locally four-dimensional case, discuss the nature of the confining string, and the θ-angle dependence. We study the global symmetry realization and, when available, present evidence for the absence of phase transitions as a function of the S1 size. As our aim is not to cover all work on the subject, but to prepare the interested reader for its study, we also include brief descriptions of topics not covered in detail: the necessity for analytic continuation of path integrals, the study of more general theories, and the ’t Hooft anomalies involving higher-form symmetries. Full article
(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)
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17 pages, 3080 KB  
Article
Analyzing the Effects of Topological Defect (TD) on the Energy Spectra and Thermal Properties of LiH, TiC and I2 Diatomic Molecules
by Peter Nwabuzor, Collins Edet, Akpan Ndem Ikot, Uduakobong Okorie, Morris Ramantswana, Ridha Horchani, Abdel-Haleem Abdel-Aty and Gaotsiwe Rampho
Entropy 2021, 23(8), 1060; https://doi.org/10.3390/e23081060 - 17 Aug 2021
Cited by 58 | Viewed by 3721
Abstract
In this study, the impacts of TD on the energy spectra and thermal properties of LiH, TiC and I2 diatomic molecules is considered. The Schrodinger equation in cosmic string spacetime is solved with the generalized Morse potential using the well-known (NU) [...] Read more.
In this study, the impacts of TD on the energy spectra and thermal properties of LiH, TiC and I2 diatomic molecules is considered. The Schrodinger equation in cosmic string spacetime is solved with the generalized Morse potential using the well-known (NU) method. The energy spectra and eigenfunction are obtained respectively. The energy spectra is used to obtain the partition function which is then used to evaluate the thermal properties of the system is evaluated accordingly. We find that the energy spectra in the presence of the TD differ from their flat Minkowski spacetime analogue. The effects of the deformation parameter and TD on the thermal properties of the system is also analysed in detail. We observe that the specific heat capacity of the system tends to exhibit quasi-saturation as the deformation parameter and topological defect approaches unity. The results of our study can be applied in the astrophysical situation where these modifications exist in the understanding of spectroscopical data and it may be used as a probe of the presence of a cosmic string or a global monopole in the Universe. Full article
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