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Examination of the gamma radiation shielding properties of different clay and sand materials in the Adrar region

  • Abbane Sara , Boussaid Mohammed EMAIL logo and Dib Anis Sami Amine
Published/Copyright: June 2, 2025
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Open Physics
From the journal Open Physics Volume 23 Issue 1

Abstract

Four samples of natural sand and clay materials from the Adrar region in southern Algeria were studied for their shielding parameters at three chosen energies in this work (0.662, 1.172,1.333 MeV). There was only a small difference between the outcomes demonstrated by Géant 4 and WinXcom. Due to the nearly equal density of the materials examined, the shielding coefficients were likewise similar. But the green clay was the best, as the value of the linear attenuation coefficient (LAC) is equal to 0.117 cm−1 at photon energy was 1.172 MeV and it required a small thickness half-value layer equal to 5.903 cm. Subsequently, sand, red clay, and white clay follow green clay in a sequential manner.

Keywords: clay; attenuation coefficient; WinXCom program; Geant 4

1 Introduction

The wide range of uses of ionizing radiation is in nuclear research centers, in health and medical physics, in industries, and even in the agricultural field. This prompts us to take caution in dealing with radiation and enhance protection, especially in buildings and facilities where radiation is present. It must have high shielding ability [1,2,3,4].

We investigate the attenuation coefficient of the materials, which is the total of the attenuation coefficients of the interactions that occur with the photon (photoelectric interaction, Compton scattering, binary creation), to acquire an adequate shielding capacity. The attenuation coefficient of a substance is related to the photon energy, atomic number, and density of the substance [5,6,7,8,9,10,11,12,13].

Because of this, lead and concrete are among the most frequently utilized materials and have proven high shielding performance in several studies and research projects. Nevertheless, because it is costly to create big buildings and toxic to the environment, it still has a negative effect [14].

This is the reason behind research efforts to create and enhance shielding coefficients for safe and environmentally friendly materials. For example, despite having low chemical properties and being susceptible to weather and climate, the mixture of sand and clay used in ancient buildings has a high melting point, indicating that it will remain thermally stable when exposed to radiation over a long period of time [15,16].

According to the research [17] on four clay samples collected from various locations in Egypt and compared to ordinary concrete, it has a shielding capacity comparable to other commonly used radiation shields.

Researchers [16] conducted a study on four different types of clay from different parts of Nigeria. They compared the attenuation coefficients of clay materials were measured for gamma photon energies ranging from 100 to 2,000, using known shielding materials such as iron and concrete. They found that spherical clay is superior to ordinary concrete at low photon energies and extremely similar at high photon energies.

The attenuation coefficient values can be calculated using the WinXcom software, which has demonstrated results in numerous research that are closely comparable to the theoretical results [18]. However, when the software’s results are compared to those of the Genat4 simulator, they are extremely accurate and nearly match the experimental results [19].

Our current investigation uses both WinXcom and Genat4 simulators to discuss the attenuation coefficients and shielding properties of clay materials found in southern Algeria. It then compares these findings to studies from Egypt and Nigeria as well as other common shielding materials.

2 Theory

If a photon beam of intensity I goes through a barrier with thickness x , it interacts with matter atoms through a variety of processes. Scattering, absorption, and path change are some of these interactions. This is shown by the attenuation coefficient [20], which can be calculated using the equation below:

(1) d I d x = μ I ,

(2) I = I 0 exp ( − μ x ) .

The total attenuation coefficient ( μ or μ total ) for a specific gamma radiation energy is determined by adding together the attenuation coefficients for photoelectric absorption, Compton scattering, and any other significant mechanisms [21]

(3) μ total = μ photo + μ compton + μ pair − production .

The attenuation coefficient in conjunction with the material’s density can be used to determine the quantity of gamma radiation that passes through a certain thickness of shielding material. The following equation allows us to express the attenuation coefficient in terms of the mass attenuation coefficient [5]:

(4) μ = ( μ / ρ ) ρ = μ s ρ .

By substituting this into the Eq. (1), we can write the following:

(5) I = I 0 exp ( − μ s d ) .

In linear form, we can write the following:

(6) ln I = − μ s d + ln I 0 .

The mass attenuation coefficient of a compound or mixture is equal to the sum of the individual contributions of all the constituent parts. Therefore, according to the mixture rule, we write the following:

(7) μ s = μ ρ mix = ∑ i ω i μ ρ i ,

where ω i is the proportion by weight.

A material’s thickness that is necessary to attenuate radiation to half its initial intensity (50%) is referred to as half-value layer (HVL) [22]. It can be calculated as follows:

(8) HVL = ln 2 μ .

The term tenth value layer (TVL) refers to the thickness of material needed to attenuate radiation to 90% of its initial intensity, and it can be calculated as follows [22]:

(9) TVL = ln 10 μ .

Mean free path (MFP) refers to the thickness of the material needed to attenuate radiation to 63.2% of its initial intensity and can be calculated using the following equation [22]:

(10) MFP = 1 μ .

3 Materials and methods

3.1 Preparation and analysis of samples

The Adrar region is located 1,500 km south of Algeria and is famous for its traditional construction method using clay and sand [23,24]. Four samples were taken from different locations in the Adrar region; the first region, the Reggane region, which was a field for French nuclear tests [25]. We collected a sample of red clay, some sand, and some green clay from the Adrar region, the center of the state, and some white clay from the Buda region. Figure 1 shows the location of these areas. We use the following symbols to identify the samples: S1 = red clay, S2 = green clay, S3 = white clay, S4 = sand. Figure 2 displays photos of the studied samples. After removing all impurities from each sample, we grind it, let it dry in the sun, and then bake it at a high temperature 100°C [26].

Figure 1 An image depicting the specific locations from where samples were collected.
Figure 1

An image depicting the specific locations from where samples were collected.

Figure 2 Photos showing the studied samples ) S1 = red clay, S2 = green clay, S3 = white clay, S4= sand).
Figure 2

Photos showing the studied samples ) S1 = red clay, S2 = green clay, S3 = white clay, S4= sand).

Our scanning electron microscope (SEM) is equipped with an energy-dispersive X-ray spectroscopy (EDX) pre-probe for quantitative chemical analysis of samples of interest [27]. To illustrate the particle distribution within each clay type, as shown in Figure 3, and analyze the elemental compositions of these clay types. The compositions are listed in Table 1.

Figure 3 Photos of the studied samples captured with an SEM.
Figure 3

Photos of the studied samples captured with an SEM.

Table 1

Composition of the samples’ elements

Element Sample S1 Density = 1.97 g cm−3 Sample S2 Density = 1.99 g cm−3 Sample S3 Density = 1.98 g cm−3 Sample S4 Density = 1.99 g cm−3
O 58.35 45.69 42.77 53.40
Fe 0.21 1.91 0.71 3.55
Co 0.03 1.10 0.58 0.62
Al 6.70 9.38 18.53 6.48
Si 27.78 28.44 26.44 28.53
K 4.65 7.64 4.85 4.09
Ca 2.29 2.47 0.43 3.33
Mg — 3.36 — —
Na — — 5.69 —

3.2 Calculate the mass attenuation coefficient using WinXCom

WinXCom is an online program that computes photon interaction mass attenuation coefficients (µm) or cross-sections for elements, compounds, and mixtures. The data can be presented as attenuation coefficients (µ), total cross-sections, and partial cross-sections for various processes including incoherent and coherent scatterings, photoelectric absorption, and pair production within the atomic nucleus and electrons. The elemental compositions obtained from EDX of clay samples were utilized. The computation relies on Eqs. (5) and (6) [18].

3.3 Calculate the mass attenuation coefficient using Geant 4

Geant 4 is a widely used toolset for simulating the movement of particles through materials using the Monte Carlo method. The software is based on object-oriented programming and allows users to create classes that define the geometry of the detector, the generator of primary particles, and models of physics processes related to electromagnetic, hadronic, and decay physics. These models can be based on theoretical frameworks, experimental data, or parameterizations. Physics process models usually include various phenomena such as multiple scattering, ionization, Bremsstrahlung, positron annihilation, photoelectric effect, Compton and Rayleigh scattering, pair production, synchrotron and transition radiation, Cherenkov effect, refraction, reflection, absorption, scintillation, fluorescence, and Auger electron emission [28,29,30,31]. We also used the elemental compositions obtained from EDX of used clay samples.

4 Results and discussion

4.1 Analysis of elements

Table 1 presents the results of the elemental analysis (SEM/EDX) of the materials under study. The results showed that oxygen is the dominant element in all samples, confirming its position as the most widespread element in the Earth’s crust. It was followed by Si, which showed constant percentages in all samples, with a maximum percentage of 28.44 in green clay and a minimum of 26.44 in white clay. The remainder consists of alkali and alkaline earth metals and elements (Fe, Co, Al, Si, K, Ca). The green clay contains Mg at a concentration of 3.36, a characteristic not found in other samples. On the contrary, white clay alone has an Na concentration of 5.69.

SEM/EDX was utilized to demonstrate the distribution of grains [32] in each type of clay: S1 = red clay, S2 = green clay, S3 = white clay, S4 = sand, as depicted in Figure 3. We observe variations in the morphology and dimensions of the grains among the samples. The particles in A and B were clearly defined and greater in size.

4.2 Calculation of μ s , μ , HVL , TVL , MFP

Tables 2–6 illustrate the theoretical results for the mass attenuation coefficients, linear attenuation coefficient, HVL, TVL, and MFP, respectively. These results were derived from the XCOM software and the Géant 4 program. The study examines four different varieties of clay with three specific energies (energy released Cs-137 and Co-60).

Table 2

Mass attenuation coefficients ( μ s ) of the samples

Samples Energy (MeV) μ s (cm2 g−1)
XCOM Geant 4
S1 0.060 0.241 0.240
0.662 0.077 0.077
1.172 0.059 0.058
1.333 0.055 0.055
S2 0.060 0.261 0.261
0.662 0.077 0.078
1.172 0.059 0.059
1.333 0.055 0.055
S3 0.060 0.247 0.247
0.662 0.077 0.077
1.172 0.058 0.058
1.333 0.054 0.055
S4 0.060 0.249 0.251
0.662 0.077 0.077
1.172 0.058 0.059
1.333 0.055 0.056
Table 3

Linear attenuation coefficient ( μ ) of the samples

Samples Energy (MeV) µ (cm−1)
XCOM Geant 4
S1 0.060 0.475 0.473
0.662 0.152 0.155
1.172 0.115 0.117
1.333 0.108 0.111
S2 0.060 0.519 0.519
0.662 0.153 0.155
1.172 0.117 0.117
1.333 0.109 0.109
S3 0.060 0.489 0.489
0.662 0.152 0.154
1.172 0.114 0.116
1.333 0.106 0.110
S4 0.060 0.496 0.499
0.662 0.153 0.153
1.172 0.115 0.117
1.333 0.109 0.111
Table 4

HVL of the samples

Samples Energy (MeV) HVL (cm)
XCOM Geant 4
S1 0.662 4.560 4.471
1.172 5.975 5.924
1.333 6.418 6.245
S2 0.662 4.523 4.472
1.172 5.903 5.924
1.333 6.333 6.359
S3 0.662 4.560 4.501
1.172 6.080 5.975
1.333 6.539 6.301
S4 0.662 4.523 4.530
1.172 6.005 5.924
1.333 6.333 6.245
Table 5

TVL of the samples

Samples Energy (MeV) TVL (cm)
XCOM Geant 4
S1 0.662 15.146 14.855
1.172 19.849 19.680
1.333 21.320 20.744
S2 0.662 15.026 14.855
1.172 19.611 19.680
1.333 21.037 21.125
S3 0.662 15.149 14.951
1.172 20.198 19.845
1.333 21.723 20.933
S4 0.662 15.026 15.049
1.172 19.949 19.680
1.333 21.037 20.744
Table 6

MFP of the samples

Samples Energy (MeV) MFP (cm)
XCOM Geant 4
S1 0.662 6.579 6.452
1.172 8.621 8.547
1.333 9.259 9.009
S2 0.662 6.526 6.452
1.172 8.517 8.547
1.333 9.136 9.174
S3 0.662 6.579 6.493
1.172 8.772 8.621
1.333 9.434 9.091
S4 0.662 6.536 6.461
1.172 8.664 8.589
1.333 9.136 9.174

It is interesting to note that the findings acquired from both XCOM and Géant 4 programs in all tables are highly similar, to the extent of being nearly identical.

According to the data in Table 2, we observe that the mass attenuation coefficients drop as the energy increases. This holds for all four samples (S1, S2, S3, S4). At the minimum energy level of 0.662 MeV, the mass attenuation coefficients were identical in all four samples 0.077 cm2 g−1, with a minor variation observed at higher energy levels.

Table 3, along with Figure 4, displays the linear attenuation coefficients of the samples and their variations with gamma radiation energy. All samples exhibit nearly identical values at the specified gamma radiation energy. This can be attributed to the fact that the samples possess similar densities and chemical compositions, as explained in Eqs. (1)–(7). Samples S2 and S4, in particular, are enriched with metals and contain the highest proportions of (Si, Ca, Co, Fe). As a consequence, they display higher values of the linear attenuation coefficient, which makes them the most efficient materials for shielding.

Figure 4 Comparison of linear attenuation coefficient (LAC) values calculated by Geant 4.
Figure 4

Comparison of linear attenuation coefficient (LAC) values calculated by Geant 4.

By examining Tables 4 and 5, it is clear that the values of the HVL and the TVL show an upward trend with increasing energy levels. The results indicated that a small sample of clay was sufficient to effectively absorb radiation at low energies, while thicker samples are required at higher energy levels. As an illustration, in the given sample S2 with an energy of 0.662 MeV, the length of the HVL is precisely 4.523 cm. The HVL has a length of 6.333 cm when the energy is 1.333 MeV.

In a similar way, according to Table 6, the MFP also increases when the energy of gamma radiation increases. It is observed that the thickness of the material required to attenuate 63.2% of the initial radiation was best in sample S2, followed by S4, S1, and S3.

Table 7 shows the effectiveness of the samples under study [S1, S2, S3, S4] where LAC, HVL, and MFP at high energies 1.172 and 1.333 MeV were compared with previous studies [17,16] of the same nature of clay materials, and their results showed satisfactory values when compared to normal concrete and steel concrete. Upon careful analysis of the table, it is evident that bentonite clay demonstrates superior reading shielding parameters. The greatest LAC value is 0.224 cm−1 at a photon energy level of 1.172 MeV and 0.114 cm−1 at a photon energy level of 1.333 MeV. The HVL and MFP have the lowest values (5.664, 6.047 cm) and (8.172, 8.725 cm) are read at the energies (1.172, 1.333 MeV), respectively. The green clay sample S2 from our current investigation came next, and it also had good shielding coefficients. At photon energy 1.172 MeV and photon energy 1.333 MeV, the LAC values were equivalent to 0.117 and 0.109 cm−1, respectively. The remaining samples are S4, Ball Clay, Kaolin Clay, and S3, which are in that order.

Table 7

Shielding parameters of four different clay types were compared to previously published data

Shielding parameters Energy (MeV) This work [16] [17]
S1 S2 S3 S4 Ball clay Kaolin clay Bentonite clay Red clay
LAC 1.172 0.116 0.117 0.114 0.115 0.115 0.115 0.224 0.117
1.333 0.108 0.109 0.106 0.109 0.108 0.108 0.114 0.110
HVL 1.172 5.975 5.903 6.080 6.005 6.025 6.015 5.664 5.899
1.333 6.418 6.333 6.539 6.333 6.425 6.413 6.047 6.297
M FP 1.172 8.621 8.517 8.772 8.664 8.694 8.679 8.172 8.510
1.333 9.259 9.136 9.434 9.136 9.271 9.254 8.725 9.085

Table 8 presents a juxtaposition of the experimentally derived MAC values with the WinXCOM results obtained from the study [17]. These results are then compared with the Geant 4 result estimated in this investigation. Upon examining the table, it is evident that the outcomes obtained from Geant 4 were highly consistent with the experimental results across various energy levels and clay kinds. Furthermore, the results from Geant 4 were found to be more closely aligned with the experimental data compared to the results generated by WinXOM, albeit with a minor discrepancy.

Table 8

Shielding parameters of four different clay types were compared to previously published data [17]

Clay type Energy (MeV) MAC (cm2 g−1)
XCOM Experimental Geant 4 (This work)
Red clay 0.06 0.352 0.346 0.351
0.662 0.076 0.077 0.076
1.172 0.058 0.056 0.057
1.333 0.054 0.053 0.054
Ball clay 0.06 0.287 0.282 0.286
0.662 0.077 0.076 0.076
1.172 0.058 0.058 0.058
1.333 0.276 0.270 0.271
Kalion clay 0.06 0.276 0.270 0.274
0.662 0.077 0.075 0.076
1.172 0.058 0.059 0.058
1.333 0.055 0.054 0.054
Bentonite clay 0.06 0.372 0.383 0.379
0.662 0.077 0.078 0.077
1.172 0.058 0.057 0.058
1.333 0.055 0.054 0.054

5 Conclusion

Geant 4 simulation serves as a viable substitute for experimentation when its components are unavailable. Moreover, engaging in pre-experiment work enables the opportunity to meticulously design the experiment and thoroughly analyze all the factors associated with it.

The photoelectric process dominates at low-energy gamma radiation. As the energy increases to a medium level, the Compton interaction process and scattering effect become more prevalent. At high energies, the cogeneration process takes over as the dominant interaction. Materials with high atomic numbers and effective atomic numbers are necessary for this purpose. Consequently, the researched material is particularly useful for low-energy protection. Considering its accessibility, autonomy, and resistance to heat and chemicals, it can be employed in fortified structures for safeguarding purposes.

The investigated samples can be organized in descending order of shielding efficiency as follows: S2, S4, S1, S3.

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2025-01-25
Revised: 2025-03-23
Accepted: 2025-04-15
Published Online: 2025-06-02

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  21. Study on the duration of laser-induced air plasma flash near thin film surface
  22. Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique
  23. The mechanism of carbon monoxide fluorescence inside a femtosecond laser-induced plasma
  24. Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
  25. Numerical examination of the chemically reactive MHD flow of hybrid nanofluids over a two-dimensional stretching surface with the Cattaneo–Christov model and slip conditions
  26. Impacts of sinusoidal heat flux and embraced heated rectangular cavity on natural convection within a square enclosure partially filled with porous medium and Casson-hybrid nanofluid
  27. Stability analysis of unsteady ternary nanofluid flow past a stretching/shrinking wedge
  28. Solitonic wave solutions of a Hamiltonian nonlinear atom chain model through the Hirota bilinear transformation method
  29. Bilinear form and soltion solutions for (3+1)-dimensional negative-order KdV-CBS equation
  30. Solitary chirp pulses and soliton control for variable coefficients cubic–quintic nonlinear Schrödinger equation in nonuniform management system
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  32. Dissipative disorder optimization in the radiative thin film flow of partially ionized non-Newtonian hybrid nanofluid with second-order slip condition
  33. Bifurcation, chaotic behavior, and traveling wave solutions for the fractional (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili model
  34. New investigation on soliton solutions of two nonlinear PDEs in mathematical physics with a dynamical property: Bifurcation analysis
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  38. Chaotic dynamics and some solutions for the (n + 1)-dimensional modified Zakharov–Kuznetsov equation in plasma physics
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  48. Decoherence of steerability and coherence dynamics induced by nonlinear qubit–cavity interactions
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  51. Statistical inference of constant-stress partially accelerated life tests under type II generalized hybrid censored data from Burr III distribution
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  58. Investigation of solar radiation effects on the energy performance of the (Al2O3–CuO–Cu)/H2O ternary nanofluidic system through a convectively heated cylinder
  59. Quantum resources for a system of two atoms interacting with a deformed field in the presence of intensity-dependent coupling
  60. Studying bifurcations and chaotic dynamics in the generalized hyperelastic-rod wave equation through Hamiltonian mechanics
  61. A new numerical technique for the solution of time-fractional nonlinear Klein–Gordon equation involving Atangana–Baleanu derivative using cubic B-spline functions
  62. Interaction solutions of high-order breathers and lumps for a (3+1)-dimensional conformable fractional potential-YTSF-like model
  63. Hydraulic fracturing radioactive source tracing technology based on hydraulic fracturing tracing mechanics model
  64. Numerical solution and stability analysis of non-Newtonian hybrid nanofluid flow subject to exponential heat source/sink over a Riga sheet
  65. Numerical investigation of mixed convection and viscous dissipation in couple stress nanofluid flow: A merged Adomian decomposition method and Mohand transform
  66. Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves
  67. Analysis of MHD hybrid nanofluid flow over cone and wedge with exponential and thermal heat source and activation energy
  68. Solitons and travelling waves structure for M-fractional Kairat-II equation using three explicit methods
  69. Impact of nanoparticle shapes on the heat transfer properties of Cu and CuO nanofluids flowing over a stretching surface with slip effects: A computational study
  70. Computational simulation of heat transfer and nanofluid flow for two-sided lid-driven square cavity under the influence of magnetic field
  71. Irreversibility analysis of a bioconvective two-phase nanofluid in a Maxwell (non-Newtonian) flow induced by a rotating disk with thermal radiation
  72. Hydrodynamic and sensitivity analysis of a polymeric calendering process for non-Newtonian fluids with temperature-dependent viscosity
  73. Exploring the peakon solitons molecules and solitary wave structure to the nonlinear damped Kortewege–de Vries equation through efficient technique
  74. Modeling and heat transfer analysis of magnetized hybrid micropolar blood-based nanofluid flow in Darcy–Forchheimer porous stenosis narrow arteries
  75. Activation energy and cross-diffusion effects on 3D rotating nanofluid flow in a Darcy–Forchheimer porous medium with radiation and convective heating
  76. Insights into chemical reactions occurring in generalized nanomaterials due to spinning surface with melting constraints
  77. Review Article
  78. Examination of the gamma radiation shielding properties of different clay and sand materials in the Adrar region
  79. Special Issue on Fundamental Physics from Atoms to Cosmos - Part II
  80. Possible explanation for the neutron lifetime puzzle
  81. Special Issue on Nanomaterial utilization and structural optimization - Part III
  82. Numerical investigation on fluid-thermal-electric performance of a thermoelectric-integrated helically coiled tube heat exchanger for coal mine air cooling
  83. Special Issue on Nonlinear Dynamics and Chaos in Physical Systems
  84. Analysis of the fractional relativistic isothermal gas sphere with application to neutron stars
  85. Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique
  86. Successive midpoint method for fractional differential equations with nonlocal kernels: Error analysis, stability, and applications
https://doi.org/10.1515/phys-2025-0156
Keywords for this article
clay; attenuation coefficient; WinXCom program; Geant 4
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BY 4.0

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  23. The mechanism of carbon monoxide fluorescence inside a femtosecond laser-induced plasma
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  25. Numerical examination of the chemically reactive MHD flow of hybrid nanofluids over a two-dimensional stretching surface with the Cattaneo–Christov model and slip conditions
  26. Impacts of sinusoidal heat flux and embraced heated rectangular cavity on natural convection within a square enclosure partially filled with porous medium and Casson-hybrid nanofluid
  27. Stability analysis of unsteady ternary nanofluid flow past a stretching/shrinking wedge
  28. Solitonic wave solutions of a Hamiltonian nonlinear atom chain model through the Hirota bilinear transformation method
  29. Bilinear form and soltion solutions for (3+1)-dimensional negative-order KdV-CBS equation
  30. Solitary chirp pulses and soliton control for variable coefficients cubic–quintic nonlinear Schrödinger equation in nonuniform management system
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  33. Bifurcation, chaotic behavior, and traveling wave solutions for the fractional (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili model
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  37. Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber
  38. Chaotic dynamics and some solutions for the (n + 1)-dimensional modified Zakharov–Kuznetsov equation in plasma physics
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  42. Tavis–Cummings model in the presence of a deformed field and time-dependent coupling
  43. Spinning dynamics of stress-dependent viscosity of generalized Cross-nonlinear materials affected by gravitationally swirling disk
  44. Design and prediction of high optical density photovoltaic polymers using machine learning-DFT studies
  45. Robust control and preservation of quantum steering, nonlocality, and coherence in open atomic systems
  46. Coating thickness and process efficiency of reverse roll coating using a magnetized hybrid nanomaterial flow
  47. Dynamic analysis, circuit realization, and its synchronization of a new chaotic hyperjerk system
  48. Decoherence of steerability and coherence dynamics induced by nonlinear qubit–cavity interactions
  49. Finite element analysis of turbulent thermal enhancement in grooved channels with flat- and plus-shaped fins
  50. Modulational instability and associated ion-acoustic modulated envelope solitons in a quantum plasma having ion beams
  51. Statistical inference of constant-stress partially accelerated life tests under type II generalized hybrid censored data from Burr III distribution
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  54. Stability analysis, circuit simulation, and color image encryption of a novel four-dimensional hyperchaotic model with hidden and self-excited attractors
  55. A high-accuracy exponential time integration scheme for the Darcy–Forchheimer Williamson fluid flow with temperature-dependent conductivity
  56. Novel analysis of fractional regularized long-wave equation in plasma dynamics
  57. Development of a photoelectrode based on a bismuth(iii) oxyiodide/intercalated iodide-poly(1H-pyrrole) rough spherical nanocomposite for green hydrogen generation
  58. Investigation of solar radiation effects on the energy performance of the (Al2O3–CuO–Cu)/H2O ternary nanofluidic system through a convectively heated cylinder
  59. Quantum resources for a system of two atoms interacting with a deformed field in the presence of intensity-dependent coupling
  60. Studying bifurcations and chaotic dynamics in the generalized hyperelastic-rod wave equation through Hamiltonian mechanics
  61. A new numerical technique for the solution of time-fractional nonlinear Klein–Gordon equation involving Atangana–Baleanu derivative using cubic B-spline functions
  62. Interaction solutions of high-order breathers and lumps for a (3+1)-dimensional conformable fractional potential-YTSF-like model
  63. Hydraulic fracturing radioactive source tracing technology based on hydraulic fracturing tracing mechanics model
  64. Numerical solution and stability analysis of non-Newtonian hybrid nanofluid flow subject to exponential heat source/sink over a Riga sheet
  65. Numerical investigation of mixed convection and viscous dissipation in couple stress nanofluid flow: A merged Adomian decomposition method and Mohand transform
  66. Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves
  67. Analysis of MHD hybrid nanofluid flow over cone and wedge with exponential and thermal heat source and activation energy
  68. Solitons and travelling waves structure for M-fractional Kairat-II equation using three explicit methods
  69. Impact of nanoparticle shapes on the heat transfer properties of Cu and CuO nanofluids flowing over a stretching surface with slip effects: A computational study
  70. Computational simulation of heat transfer and nanofluid flow for two-sided lid-driven square cavity under the influence of magnetic field
  71. Irreversibility analysis of a bioconvective two-phase nanofluid in a Maxwell (non-Newtonian) flow induced by a rotating disk with thermal radiation
  72. Hydrodynamic and sensitivity analysis of a polymeric calendering process for non-Newtonian fluids with temperature-dependent viscosity
  73. Exploring the peakon solitons molecules and solitary wave structure to the nonlinear damped Kortewege–de Vries equation through efficient technique
  74. Modeling and heat transfer analysis of magnetized hybrid micropolar blood-based nanofluid flow in Darcy–Forchheimer porous stenosis narrow arteries
  75. Activation energy and cross-diffusion effects on 3D rotating nanofluid flow in a Darcy–Forchheimer porous medium with radiation and convective heating
  76. Insights into chemical reactions occurring in generalized nanomaterials due to spinning surface with melting constraints
  77. Review Article
  78. Examination of the gamma radiation shielding properties of different clay and sand materials in the Adrar region
  79. Special Issue on Fundamental Physics from Atoms to Cosmos - Part II
  80. Possible explanation for the neutron lifetime puzzle
  81. Special Issue on Nanomaterial utilization and structural optimization - Part III
  82. Numerical investigation on fluid-thermal-electric performance of a thermoelectric-integrated helically coiled tube heat exchanger for coal mine air cooling
  83. Special Issue on Nonlinear Dynamics and Chaos in Physical Systems
  84. Analysis of the fractional relativistic isothermal gas sphere with application to neutron stars
  85. Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique
  86. Successive midpoint method for fractional differential equations with nonlocal kernels: Error analysis, stability, and applications
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