Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
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Muhammad Zain Yousaf
,
Alina Alb Lupas
Abstract
The present research explores nematicons in liquid crystals (LCs) with quadruple power law nonlinearity utilizing the modified extended Fan sub-equation technique as an analytical tool to investigate the optical spatial soliton solutions. For the inaugural time, a novel version of nonlinearity is investigated in relation to LCs. There are distinct applications for the several wave solutions that have been created in optical handling data. The aforementioned modified extended Fan subequation approach offers novel, comprehensive solutions that are relatively easy to deploy in comparison to earlier, regular methodologies. This approach translates a coupled non-linear partial differential equation into a coupled ordinary differential equation through implementing a traveling wave conversion. This approach indicates that a large variety of traveling and solitary solutions that rely upon five parameters can be incorporated by the nematicons in LCs. In addition, the investigation yields solutions of the single and mixed non-degenerate Jacobi elliptic function form. Novel solutions, such as the periodic pattern, kink and anti-kink patterns, N-pattern, W-pattern, anti-Z-pattern, M-pattern, V-pattern, complexion pattern and anti-bell pattern, or dark soliton solutions of nematic LCs, have been constructed by means of modified extended Fan subequation technique through granting suitable values for the parameters. The computer software Mathematica 14 is used to illustrate several modulus, real and imaginary solutions visually in the form of contour, 2D, and 3D visualizations that help understand the concrete importance of the nematicons in LCs. This research additionally offers a physical comprehension of the obtained solutions and applications of model. The imposed approach is ultimately thought to be more potent and effective than alternative approaches, and the solutions found in this work could be beneficial in our understanding of soliton structures in LCs.
1 Introduction
Nonlinear partial differential equations (NLPDEs) are often involved in the basic concepts of nature. In computational physics and other applied sciences, numerous models attract influence from the following domains: nuclear physics, unbending-state physics, hydrodynamics, biological sciences, and mathematical stuff disciplines [1–8]. Non-linear (NL) wave dispersion is one of nature’s most significant phenomena, so investigation on the NL wave dynamic system has gained momentum in recent years. The analytical findings from NLPDEs accurately play a crucial part in understanding the qualitative uniqueness of various occurrences. Because NLPDEs can be analytically solved, mechanisms of many NL and complicated phenomena can be graphically and symbolically defined including variety in different environments. The majority of physical simulations have a lot of unidentified features and parameters.
These days, a lot of scholars are concentrating on gathering NLPDE solitons and other wave solutions. Many deliberate techniques, including F-expansion [9], mapping and direct algebraic method [10,11], trial equation method [12], Hirota’s bilinear scheme [13], sine-Gordon expansion method [14], Backlund transformation [15], semi-inverse variational principle [16], auxiliary equation method [17], extended tanh method [18], inverse scattering method [19],
Nematicons, a renowned phenomenon of nature in the discipline of liquid crystals (LCs) that Assanto initially presented in [23–25] and Alberucci given in [26], have caught the attention of specialists in common. Over the last few decades, a broad spectrum of research findings have been compiled about optical spatial solitons (OSSs) in nematicons in liquid crystals (NinLCs), also known as nematicons. These materials have drawn an abundance of interest. The through-depth empirical and theoretical investigation on nematicons has substantially improved our comprehension of optical distribution in nonlocal medium restructuring. The steady and adaptable light rays known as spatial solitons (SSs) are self-centered, nondifferential rays. SSs can be successfully implemented in both continuum and discontinuous conditions by using the NL behavior, nonlocality, dual refractive index, and electro-optics of NinLCs. To generate dielectric surfaces or periodic wavelength panels and regulate walk-off, anisotropy involves applying voltage. This effectively couples an external control to NL optics and light confinement in these devices. Nematicons are regarded as an instance of optics because of their possible roles in optical computation as well as their significance and prevalence in NL environments. They provide an exceptional subject since spatial optics describes diffraction rather than dispersion, radiate size rather than pulse length, and one or two crosswise dimensions rather than one in the chronological field.
Numerous scientists used various techniques to study the solitary wave (SW) solutions of NinLCs. Utilizing the generalized exponential rational function approach, certain solutions of NinLCs, including three forms of nonlinearities, are determined by Kumar et al. [27]. The extended sinh-Gordon expansion approach is utilized the study by Ismael et al. [28] to determine several solutions of NinLCs, incorporating two forms of nonlinearities. The Exp
Numerical and analytical procedures are the two major methods used to solve NLPDEs with various types of soliton solutions. The modified extended Fan subequation approach (MEFSEA) is an inexpensive and effective analytical technique that is used in this investigation. This technique relies on a widely recognized approximation. MEFSEA can be used to get precise analytical SSs that provide immediate understanding. Intensive computation, which requires an abundance of time and resources, is not necessary when employing this approach. While the MEFSEA has the previously described advantages, it also has limitations such as complexities, susceptibility to parameters, dependency on assumptions, and troubles with evaluation and generalization. When determining whether to apply the MEFSEA technique for a given application, a comprehensive evaluation of these factors is necessary. First-order derivatives problems that arise in a variety of disciplines, including fluid dynamics, biology, physics, and mechanics, are challenging to solve using MEFSEA.
Especially when it comes to solving NLPDEs and simulating intricate systems, the MEFSEA has distinct benefits over conventional analytical methods. The MEFSEA has significance since it provides superior accuracy, more flexibility, and wider applicability in contrast to alternative analytical techniques. Its versatility in handling intricate nonlinearities, adapting to changes, and offering novel perspectives makes it an invaluable resource for resolving tricky problems that conventional approaches might not be able to fully tackle. The method’s adaptability and capability for in-depth examination enable it to collaborate with other techniques, improving theoretical as well as having practical applications.
This equation explains the relationship within the direction of motion of LC molecules and their physical characteristics, which is the motivation for taking this model into consideration. The comprehension regarding the way electric fields affect LC molecules’ orientation is made possible by the equations, and it is essential for visual innovation. The current investigation uses MEFSEA, which is essential for analyzing coupled NLPDEs, to create accurate OSS solutions to the NinLCs quadruple power (QP) version of nonlinearity for the inaugural time. Reading through the literature reveals that MEFSEA has not yet been used to develop the exact OSS solutions of the NinLCs through QP version of nonlinearity. Thus, with this knowledge, we will apply the suggested technique to provide precise OSS solutions of the NinLCs using QP form of nonlinearity in this investigation. It is anticipated that this refinement will have a number of intriguing characteristics and numerous implications in the field of optics.
The subsequent layout has been developed to make this article straightforward to understand: Section 2 summarizes the strategy that will be employed in this article. The mathematical architecture of the NinLCs using QP interpretations of nonlinearity and the implementation of MEFSEA to it are particularized in Section 3. Section 4 investigates the graphical patterns of the exact OSS solutions of the NinLCs through QP version of nonlinearity by utilizing MEFSEA. The physical interpretation of solutions and applications of the partial differential equation (PDE) are specified in Section 5. A few persistent assessments are stated in Section 6.
2 Methodology of the MEFSEA
This section outlines the mechanism for the MEFSEA using the generalized elliptic equation provided in the study by Yousaf et al. [32]. A brief description of the significant stages of this approach is provided next to it. Examine the subsequent coupled NLPDE, which comprises three independent variables
where in Eq. (1)
Step 1. The process of merging the distinct spatial and temporal variables forms a single variable
where
where
Step 2. The solution to ODE (3) is predicated on a subsequent finite series pattern:
where
where
Eq. (6) is solely satisfied in the scenario that subsequent relations hold.
In specific circumstances, if
The only case in which Eq. (8) meets the criteria is when the relations that follow hold.
among
Therefore, utilizing Eq. (6) and Eq. (8), the general elliptic equation (GEE) can be simplified to yield the generalized Riccati equation. This auxiliary equation is generated through the GEE for
The elliptic equation is produced by the GEE when
There is the Riccati equation in Eq. (12),
where
Step 3. The positive integer
Step 4. With the assistance of Eq. (5), a polynomial in
Special cases
There are four cases of MEFSEA.
Case 1:
In addition, there are two additional types of first case of MEFSEA.
Type 1.
where
Type 2.
where
Case 2:
Type 1.
where
Case 3:
Type 1 When
Type 2 When
Type 3 When
Type 4 When
Type 5 When
Type 6 When
Type 7 When
where the constants
Case 4:
The single and combination nondegenerative JEFs are the frequent solutions to Eq. (12) in this particular situation. The correspondence between the parameters of
Interaction that occur between the parameters of
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The JEFs become hyperbolic functions if
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The JEFs become trigonometric functions if
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Case 5:
To give a concrete instance, the solution for the circumstance whenever Eq. (14) is satisfied is an elliptic solution of the Weierstrass double periodic type.
3 Mathematical formulation and application of the MEFSEA
The subsequently coupled set of equations governs the dimensionless dynamics of NinLCs as stated in [27]:
where the wave profile of the NinLCs is represented by
where
where prime signifies the derivative relative to
The speed of a soliton can be determined in regards of its frequency utilizing Eq. (44). For the initial instance, NinLCs investigation will be conducted in the framework of quadruple power law (QPL) nonlinearity for the functional
Examine the subsequent expression of QPL nonlinearity.
Eq. (41) can be reformulated by inserting Eq. (45) into itnto subsequent form:
Consequently, the first two components of Eq. (43) simplify to an analogous version for QPL nonlinearity:
Assuming if,
Therefore, the second part of Eq. (47) will be transform in the following manner by employing Eq. (48):
The consequences of balancing
The polynomial equation in the format of
The entire assortment of AEs can be generated via Eq. (51) having an equivalent power coefficient of
Utilizing Mathematica 13.2, the aforementioned offered grouping of AEs to determine the following:
The accurate TW solutions of Eq. (41) that appear from feeding Eq. (52) and Eqs. (15)–(40) initially within Eq. (50), and eventually Eq. (42) can be articulated as follows:
Special cases
Case 1:
Type 1.
Type 2.
Case 2:
Type 1.
where
Case 3:
Type 1. When
.
Type 2. When
Type 3. When
Type 4. When
Type 5. When
Type 6. When
Type 7. When
where the constants
Case 4:
Type 1. When
Type 2. When
Type 3. When
Type 4. When
Type 5. When
Type 6. When
Type 7. When
Type 8. When
Type 9. When
Type 10. When
Type 11. When
Type 12. When
Type 13. When
Type 14. When
where
likewise, when
where
4 Graphical depictions and discussion
This section investigates the innovative variant of nonlinearity used to create the graphical illustrations of the NinLCs. The NinLCs with an inventive nonlinearity variety can be illustrated visually through the utilization of the MEFSEA technique with multiple parametric predictions that result in TW solutions. Framework layout of NinLCs for novel version of nonlinearity mentioned in Eq. (41) with respect to altering the parameter setting constraints is analyzed using the computer software Mathematica 14. Through changing the settings of the parameters, the nematicons’ visual appearance in LC visualizations can be changed. For easy comprehension, we offered contour plots in addition to the 3D and 2D plots. It is possible to generate diverse wave patterns through setting the parameters various weights. Various solutions, including periodic pattern, kink and antikink patterns, N-pattern, W-pattern, anti-Z-pattern, M-pattern, V-pattern, complexion pattern, and anti-bell pattern or dark SW solutions, can be discovered by putting MEFSEA technique into reality.
Figure 1 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 2 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 3 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 4 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 5 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 6 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 7 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 8 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 9 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 10 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 11 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
Figure 12 signifies the contour illustrations, 2D at different intensities of
(a) A 3D plot of
5 Physical interpretation and applications
5.1 Physical interpretation
NinLCs contain extended molecules that have a tendency to arrange themselves over a common direction called the director. Their actions is dependent on the direction of view due to asymmetrical qualities resulting from this arrangement. Periodic pattern soliton depicted in Figure 1, particularly in NinLCs (and various NL mediums), is a steady, confined oscillation that travels across a medium without changing its shape. An anti-kink exhibited in Figure 2 is a change in phase that goes in the reverse way as a kink. As an instance, the anti-kink goes from a higher prospective to a fewer one if a kink travels from a smaller prospective to a greater one. Similar to kinks, anti-kinks are localized patches in which the energy density is different from that of the neighboring environment. N-shape pattern soliton shown in Figure 3 observed in NinLCs is an intriguing example of how elastic energy and molecule direction interact. An abrupt shift in the direction of each molecule in a LC is represented by the kink soliton which demonstrated in Figures 4 and 9. When contrasted to other solitons such as the N-shaped or kink solitons, the W-shaped soliton as illustrated in Figure 4 has a more complicated structure. The producer undergoes many orientational shifts, resulting in a “W”-shaped layout of the director angles. Different from conventional soliton forms, the anti-Z soliton as illustrated in Figure 6 could have intriguing topological properties. Its structure may be seen as a special state that is difficult to change into another mode absent breaking through an energy hurdle, which adds to its stability. In NinLCs, an additional intriguing kind of localized deformation in the direction region is the M-shaped soliton shown in Figure 7. As illustrated in Figure 8, another particular kind of localized deformation in the direction sector is the “V”-pattern soliton seen in nematic LCs, which is distinguished by its characteristic “V” pattern. Recognizing the form of complexion solitons as illustrated in Figures 10 and 11 holds significance for sophisticated uses in LC technologies, such as modified display innovations, visual gadgets, and detectors. The anti-bell soliton as exhibited in Figure 12 has a reversed bell-shaped center trough around by areas with greater molecular coordination.
5.2 Applications
The unique optical and electro-optical characteristics of nemalic LCs make them useful in a variety of applications. Liquid crystal displays for cell phones, computer displays, and TVs frequently employ nemalic LCs. They respond to electric fields by altering their alignment, which modulates light to produce pictures. Light signals may be controlled by the employment of LCs in optical controllers and regulators in telecommunication systems. Nematic LCs are important in laser systems and optical communications because they may be used to direct light rays. Nematic LCs are helpful in a variety of sensors because they may alter in color or transparency in response to variations in pressure or temperature. Their adaptability and distinctive qualities are spurring innovation in a range of domains.
6 Conclusion
To demonstrate the genuine tangible importance of the paired equations for NinLCs, this portion addresses the generated findings and their visual depiction. The innovative precise OSS solutions of NinLCs have been identified employing the MEFSEA technique. These solutions reflect a novel kind of nonlinearity that provides an illustration of how OSS move via particular physical frameworks. The primary advantage of this technique over competitors is that it frequently produces deeper, more original, and comprehensive solutions as well as more accurate patterns. The MEFSEA utilized the JEFs, which yield solutions in hyperbolic format when
Acknowledgments
The publication of this research was supported by the University of Oradea, Romania. The authors would like to acknowledge Deanship of Graduate Studies and Scientific Research, Taif University for funding this work.
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Funding information: The publication of this research was supported by the University of Oradea, Romania.
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Author contributions: Muhammad Zain Yousaf: formal analysis, software, investigation, visualization, writing-original draft, writing – review editing. Muhammad Abbas: formal analysis, software, supervision, investigation, visualization, writing – original draft, writing-review editing. Alina Alb Lupas: software, visualization, investigation, writing – review editing. Farah Aini Abdullah: formal analysis, investigation, writing-original draft, writing-review editing. Muhammad Kashif Iqbal: visualization, investigation, software, formal analysis, writing – review & editing. Muteb R. Alharthi: software, visualization, formal analysis, investigation, writing-review editing. Yasser S. Hamed: visualization, investigation, writing – review & editing. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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Data availability statement: All data generated or analysed during this study are included in this published article.
References
[1] Agrawal GP. Nonlinear fiber optics: its history and recent progress. JOSA B. 2011;28(12):A1–10. 10.1364/JOSAB.28.0000A1Search in Google Scholar
[2] Dianov EM, Mamyshev PV, Prokhorov AM. Nonlinear fiber optics. Soviet J. Quantum Electronics. 1988;18(1):1. 10.1070/QE1988v018n01ABEH010192Search in Google Scholar
[3] Arshad M, Seadawy AR, Lu D. Bright-dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its applications in optics. J Electromagnetic Waves Appl. 2017;31(16):1711–21. 10.1080/09205071.2017.1362361Search in Google Scholar
[4] Seadawy AR, Lu DC, Arshad M. Stability analysis of solitary wave solutions for coupled and (2. 1)-dimensional cubic Klein-Gordon equations and their applications. Commun Theoretic Phys. 2018;69(6):676. 10.1088/0253-6102/69/6/676Search in Google Scholar
[5] Najafi M, Arbabi S. Exact solutions of five complex nonlinear Schrödinger equations by semi-inverse variational principle. Commun Theoretic Phys. 2014;62(3):301. 10.1088/0253-6102/62/3/02Search in Google Scholar
[6] Arshad M, Seadawy AR, Lu D. Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications. Superlattices Microstruct. 2017;112:422–34. 10.1016/j.spmi.2017.09.054Search in Google Scholar
[7] Triki H, Biswas A. Dark solitons for a generalized nonlinear Schrödinger equation with parabolic law and dual-power law nonlinearities. Math Methods Appl Sci. 2011;34(8):958–62. 10.1002/mma.1414Search in Google Scholar
[8] Zhang LH, Si JG. New soliton and periodic solutions of (1+2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Commun Nonl Sci Numer Simulat. 2010;15(10):2747–54. 10.1016/j.cnsns.2009.10.028Search in Google Scholar
[9] Ozisik M, Secer A, Bayram M. On solitary wave solutions for the extended nonlinear Schrödinger equation via the modified F-expansion method. Opt Quantum Electron. 2023;55(3):215. 10.1007/s11082-022-04476-zSearch in Google Scholar
[10] Mohammed WW, Cesarano C. The soliton solutions for the (4+1)-dimensional stochastic Fokas equation. Math Meth Appl Sci. 2023;46(6):7589–97. 10.1002/mma.8986Search in Google Scholar
[11] Rehman HU, Ullah N, Asjad MI, Akgül A. Exact solutions of convective-diffusive Cahn-Hilliard equation using extended direct algebraic method. Numer Methods Partial Differ Equ. 2023;39(6):4517–32. 10.1002/num.22622Search in Google Scholar
[12] Pandir Y, Ekin A. New solitary wave solutions of the Korteweg-de Vries (KdV) equation by new version of the trial equation method. Electron J Appl Math. 2023;1:101–13. 10.61383/ejam.20231130Search in Google Scholar
[13] Yin T, Xing Z, Pang J. Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation. Nonl Dyn. 2023;111(11):9741–52. 10.1007/s11071-023-08356-3Search in Google Scholar
[14] Akbar MA, Akinyemi L, Yao SW, Jhangeer A, Rezazadeh H, Khater MM, et al. Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Results Phys. 2021;25:104228. 10.1016/j.rinp.2021.104228Search in Google Scholar
[15] Lu X, Lin F, Qi F. Analytical study on a two-dimensional Korteweg-de Vries model with bilinear representation, Bäcklund transformation and soliton solutions. Appl Math Model. 2015;39(12):3221–6. 10.1016/j.apm.2014.10.046Search in Google Scholar
[16] Reggab K, Gueddim A, Naas A. Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic-and perturbed Coulomb potentials. Stud Eng Exact Sci. 2023;4(1):248–67. 10.54021/sesv4n1-017Search in Google Scholar
[17] Akram G, Sadaf M, Khan MAU. Soliton solutions of the resonant nonlinear Schrödinger equation using modified auxiliary equation method with three different nonlinearities. Math Comput Simulat. 2023;206:1–20. 10.1016/j.matcom.2022.10.032Search in Google Scholar
[18] Rezazadeh H. New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. Optik. 2018;167:218–27. 10.1016/j.ijleo.2018.04.026Search in Google Scholar
[19] Ali MR, Khattab MA, Mabrouk SM. Travelling wave solution for the Landau-Ginburg-Higgs model via the inverse scattering transformation method. Nonl Dyn. 2023;111(8):7687–97. 10.1007/s11071-022-08224-6Search in Google Scholar
[20] Alam MN, Tunc C. New solitary wave structures to the (2+1)-dimensional KD and KP equations with spatio-temporal dispersion. J King Saud Univ-Sci. 2020;32(8):3400–9. 10.1016/j.jksus.2020.09.027Search in Google Scholar
[21] Islam S, Alam MN, Al-Asad MF, Tunc143 C. An analytical techinque for solving new computational solutions at the modified Zakharov-Kuznetsov equation arising on electrical engineering. J Appl Comput Mech. 2021;7(2):715–26. Search in Google Scholar
[22] Almatrafi MB, Alharbi AR, Tunç C. Constructions of the soliton solutions to the good Boussinesq equation. Adv Differ Equ. 2020;2020(1):629. 10.1186/s13662-020-03089-8Search in Google Scholar
[23] Assanto G, Peccianti M, Conti C. Nematicons: optical spatial solitons in nematic liquid crystals. Optics Photonics News. 2003;14(2):44–8. 10.1364/OPN.14.2.000044Search in Google Scholar
[24] Assanto G, Peccianti M, Conti C. Spatial optical solitons in bulk nematic liquid crystals. Acta Phys Polonica A. 2003;103(2–3):161–7. 10.12693/APhysPolA.103.161Search in Google Scholar
[25] Assanto G, Peccianti M, Brzdakiewicz KA, de Luca A, Umeton C. Nonlinear wave propagation and spatial solitons in nematic liquid crystals. J Nonl Opt Phys Materials. 2003;12(02):123–34. 10.1142/S0218863503001377Search in Google Scholar
[26] Alberucci A, Assanto G. Dissipative self-confined optical beams in doped nematic liquid crystals. J Nonl Optic Phys Materials. 2007;16(03):295–305. 10.1142/S0218863507003780Search in Google Scholar
[27] Ismael HF, Bulut H, Baskonus HM. W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws. Soft Comput. 2021;25(6):4513–24. 10.1007/s00500-020-05459-6Search in Google Scholar
[28] Kumar D, Joardar AK, Hoque A, Paul GC. Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method. Opt Quantum Electron. 2019;51:1–36. 10.1007/s11082-019-1917-6Search in Google Scholar
[29] Raza N, Afzal U, Butt AR, Rezazadeh H. Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities. Opt Quantum Electron. 2019;51:1–16. 10.1007/s11082-019-1813-0Search in Google Scholar
[30] Ilhan OA, Manafian J, Alizadeh AA, Baskonus HM. New exact solutions for nematicons in liquid crystals by the tan(ϕ⁄2)-expansion method arising in fluid mechanics. Europ Phys J Plus. 2020;135(3):1–19. 10.1140/epjp/s13360-020-00296-wSearch in Google Scholar
[31] Altawallbeh Z, Az-Zo’bi E, Alleddawi AO, Şenol M, Akinyemi L. Novel liquid crystals model and its nematicons. Opt Quantum Electron. 2022;54(12):861. 10.1007/s11082-022-04279-2Search in Google Scholar
[32] Yousaf MZ, Abbas M, Nazir T, Abdullah FA, Birhanu A, Emadifar H. Investigation of the dynamical structures of double-chain deoxyribonucleic acid model in biological sciences. Scientif Reports. 2024;14(1):6410. 10.1038/s41598-024-55786-zSearch in Google Scholar PubMed PubMed Central
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- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
- Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
- Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
- On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
- Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
- Review Article
- Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
- Special Issue on Predicting pattern alterations in nature - Part II
- A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
- On the existence and numerical simulation of Cholera epidemic model
- Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
- Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
- Prediction of COVID-19 spread with models in different patterns: A case study of Russia
- Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
- Accumulation process in the environment for a generalized mass transport system
- Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
- Special Issue on Nanomaterial utilization and structural optimization - Part II
- Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
- Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
- Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
- Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
- Special Issue on Nanofluids: Synthesis, Characterization, and Applications
- Exact solutions of a class of generalized nanofluidic models
- Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
- Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
- Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
- Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
- Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
- Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
- Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
- Comparative study of couple stress fluid flow using OHAM and NIM
- Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
- Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
- Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
- Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
- Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
- Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
- Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
- Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
- Pulsed excitation of a quantum oscillator: A model accounting for damping
- Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
- Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
- Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
- Effect of the gravitational field strength on the rate of chemical reactions
- The kinetic relativity theory – hiding in plain sight
- Special Issue on Advanced Energy Materials - Part III
- Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
Articles in the same Issue
- Regular Articles
- Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
- High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
- Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
- Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
- Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
- The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
- Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
- A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
- Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
- Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
- Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
- Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
- Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
- Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
- Chaotic control problem of BEC system based on Hartree–Fock mean field theory
- Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
- Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
- Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
- Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
- Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
- Model of conversion of flow from confined to unconfined aquifers with stochastic approach
- Study of fractional variable-order lymphatic filariasis infection model
- Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
- Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
- Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
- Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
- Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
- Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
- Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
- A two-stage framework for predicting the remaining useful life of bearings
- Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
- Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
- Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
- In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
- Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
- Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
- A comparative analysis of shielding effectiveness in glass and concrete containers
- Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
- Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
- Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
- Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
- Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
- On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
- Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
- Review Article
- Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
- Special Issue on Predicting pattern alterations in nature - Part II
- A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
- On the existence and numerical simulation of Cholera epidemic model
- Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
- Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
- Prediction of COVID-19 spread with models in different patterns: A case study of Russia
- Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
- Accumulation process in the environment for a generalized mass transport system
- Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
- Special Issue on Nanomaterial utilization and structural optimization - Part II
- Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
- Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
- Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
- Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
- Special Issue on Nanofluids: Synthesis, Characterization, and Applications
- Exact solutions of a class of generalized nanofluidic models
- Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
- Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
- Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
- Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
- Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
- Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
- Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
- Comparative study of couple stress fluid flow using OHAM and NIM
- Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
- Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
- Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
- Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
- Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
- Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
- Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
- Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
- Pulsed excitation of a quantum oscillator: A model accounting for damping
- Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
- Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
- Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
- Effect of the gravitational field strength on the rate of chemical reactions
- The kinetic relativity theory – hiding in plain sight
- Special Issue on Advanced Energy Materials - Part III
- Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
