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Search Results (652)

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Keywords = nonlinear crystals

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16 pages, 5778 KB  
Article
Influence of Dry Density and Salt Content on Hydraulic Conductivity and Drying Shrinkage
by Xuejun Liu, Lifeng Zeng, Zejun Song, Bo Yao, Wuping Ran, Yanjun Li and Tiande Wen
Geosciences 2026, 16(6), 242; https://doi.org/10.3390/geosciences16060242 (registering DOI) - 22 Jun 2026
Viewed by 113
Abstract
Soil is prone to structural degradation under water infiltration, and the combined effects of dry density and salinity further complicate its hydraulic conductivity and drying shrinkage behavior. However, previous studies have primarily focused on single factors, and the interactive mechanisms between compaction state [...] Read more.
Soil is prone to structural degradation under water infiltration, and the combined effects of dry density and salinity further complicate its hydraulic conductivity and drying shrinkage behavior. However, previous studies have primarily focused on single factors, and the interactive mechanisms between compaction state and salinity remain poorly understood. To investigate the hydraulic conductivity and drying shrinkage behavior of soil under different dry densities and salinity levels, this study examined three dry densities (1.30, 1.35, 1.45 g/cm3) and four NaCl contents (0, 0.5%, 2%, 6%). Saturated hydraulic conductivity (ks) and drying shrinkage were systematically measured. The results indicate that dry density is the primary factor controlling pore structure evolution, ks and drying shrinkage behavior. Increasing dry density markedly reduced porosity (up to 15.95%), ks (by 57.14–92.91%), and drying shrinkage. In contrast, salinity exhibited non-monotonic, density-dependent effects. Salts increased porosity through electrochemical interactions and crystallization-induced pore support, but their effects on ks and drying shrinkage displayed threshold and reversal behavior. These coupled effects demonstrate strong nonlinearity and density dependence, providing a mechanistic basis for compaction optimization and the stability assessment of soil under saline conditions. Full article
(This article belongs to the Section Geomechanics)
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25 pages, 10661 KB  
Article
Nonlinear Optical Material for Generating and Converting Laser Radiation: Structure and Optical Properties of LiNbO3:Mg:Er Single Crystals
by Irina Biryukova, Mikhail Palatnikov, Diana Manukovskaya, Sofja Masloboeva, Roman Titov, Olga Palatnikova, Alexandra Kadetova, Olga Tokko, Natalya Teplyakova, Il’ya Efremov and Nikolay Sidorov
Technologies 2026, 14(6), 348; https://doi.org/10.3390/technologies14060348 - 10 Jun 2026
Viewed by 241
Abstract
A series of co-doped LiNbO3:Mg:Er crystals were grown in a single technological cycle and under the same technological conditions by Czochralski. In each subsequent step of the growth cycle, the content of Mg and Er dopants decreased. The initial concentration of [...] Read more.
A series of co-doped LiNbO3:Mg:Er crystals were grown in a single technological cycle and under the same technological conditions by Czochralski. In each subsequent step of the growth cycle, the content of Mg and Er dopants decreased. The initial concentration of dopants in the melt was [Mg] = 4.0 mol% and [Er] = 0.78 mol%. The melt was obtained from a homogeneously doped batch. The batch included the Nb2O5:Mg:Er precursor synthesized by the liquid-phase method. The physicochemical features of crystallization were studied. The optical properties of the crystals were investigated using laser conoscopy and photoinduced light scattering. Macro- and microdefect structures were studied by optical microscopy. Quantitative phase analysis was performed for single-crystal samples. The defect structures of powdered LiNbO3:Mg:Er samples were determined by refining XRD patterns by Rietveld. The optical quality of doubly doped crystals corresponds to that of singly doped LiNbO3:Er crystals. Mg significantly reduces the transparency of LiNbO3:Mg:Er crystals in the ultraviolet and violet spectral ranges. The optimal dopant concentration in the melt was [Er] = 0.63 mol% and [Mg] = 3.0 mol%, and [Er] = 0.47 mol% and [Mg] = 3.07 mol% in crystal. The optical properties of LiNbO3:Mg:Er crystals make them promising active nonlinear optical materials for generating and converting laser radiation. Full article
(This article belongs to the Section Innovations in Materials Science and Materials Processing)
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19 pages, 10120 KB  
Article
Noise-Robust Loop-Based Deep Optical Convolutional Neural Network
by Maryam Dehbashizadeh Chehreghan and Ripalta Stabile
Photonics 2026, 13(6), 552; https://doi.org/10.3390/photonics13060552 - 4 Jun 2026
Viewed by 359
Abstract
We demonstrate a loop-based deep optical convolutional neural network that reuses a single free-space optical hardware to realize network depth through repeated passes. Convolution is implemented with programmable SLM with Fourier plane kernels, nonlinearity is provided by the photorefractive phase-only response of a [...] Read more.
We demonstrate a loop-based deep optical convolutional neural network that reuses a single free-space optical hardware to realize network depth through repeated passes. Convolution is implemented with programmable SLM with Fourier plane kernels, nonlinearity is provided by the photorefractive phase-only response of a BSO crystal and converted to an effective intensity activation via spatial filtering, and pooling is performed optically using demagnified imaging with an iris. On MNIST, the BSO-based nonlinearity improves test accuracy from 90.8% (linear) to 95.7%, with optimal operation. We model realistic optical noises (laser fluctuation, aberration, detector misalignment, and dust) and compare them using an SSIM-normalized severity metric. Under noise at (s = 0.35) on Fashion-MNIST, accuracy drops from 88.53% (clean) to 79.5% (noisy inference); a feature-level noise-aware training strategy recovers performance to 86.87%. Together, these advances demonstrate that a compact, loop-based hybrid DOCNN, completed with simple optical nonlinearities, simplified pooling, and noise-aware learning, can improve accuracy under realistic conditions. Full article
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15 pages, 16008 KB  
Article
Nonlinear Electrical Conductivity and Thermal Conductivity of g-C3N4/Liquid Silicone Rubber Field Grading Composites
by Peng Han, Jiayang Li, Peng Hu, Zheng Zhang, Chen Zhao and Dongli Zhang
Materials 2026, 19(11), 2367; https://doi.org/10.3390/ma19112367 - 2 Jun 2026
Cited by 1 | Viewed by 290
Abstract
The uneven electric field in cable accessory insulation can be optimized by field grading composite (FGC). We explored graphitic carbon nitride (g-C3N4) as a filler in liquid silicone rubber (LSR) matrices. Oxygen-doped g-C3N4 (O-g-C3N [...] Read more.
The uneven electric field in cable accessory insulation can be optimized by field grading composite (FGC). We explored graphitic carbon nitride (g-C3N4) as a filler in liquid silicone rubber (LSR) matrices. Oxygen-doped g-C3N4 (O-g-C3N4) was prepared via calcination of g-C3N4 with ascorbic acid. Composites of g-C3N4/LSR and O-g-C3N4/LSR with different filler contents were fabricated. Microstructural and optical characterizations demonstrate that O-g-C3N4 retains the crystal structure of pristine g-C3N4 but exhibits thinner layers, modified elemental composition, and a 27.8% reduction in band gap; fillers are uniformly dispersed in the LSR matrix. Experimental measurements reveal that both composites exhibit nonlinear conductivity, while O-g-C3N4/LSR shows more pronounced nonlinearity at lower filler contents, accompanied by a faster decline in dielectric breakdown strength. There is little difference in thermal conductivity between g-C3N4/LSR and O-g-C3N4/LSR composites with the same filler content, which indicates that the change in band gap width has no significant influence on thermal conductivity. The low-cost synthesis and simple bandgap tuning method of g-C3N4 provide certain advantages for its use as a nonlinear filler in the preparation of FGC, broadening the application fields of g-C3N4, and verifying the possibility of reducing FGC filler usage through bandgap tuning. Full article
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22 pages, 334 KB  
Article
Global Strong Solutions to the Vacuum Free Boundary Problem for 1D Liquid Crystal Flow with Degenerate Viscosity
by Tong Li, Junhan Wang and Pan Shi
Axioms 2026, 15(6), 412; https://doi.org/10.3390/axioms15060412 - 1 Jun 2026
Viewed by 162
Abstract
In this paper, we consider the one-dimensional liquid crystal flow with a vacuum free boundary and a degenerate viscosity coefficient. The global existence and long-time dynamics of strong solutions are established under a smallness condition on the initial energy at the basic level. [...] Read more.
In this paper, we consider the one-dimensional liquid crystal flow with a vacuum free boundary and a degenerate viscosity coefficient. The global existence and long-time dynamics of strong solutions are established under a smallness condition on the initial energy at the basic level. The main challenges come from the degeneracy near the moving boundary and the strong nonlinear coupling between the velocity and the director field. To overcome these, we obtain uniform-in-time and space point-wise bounds of the deformation variable, and we construct uniform-in-time weighted energy estimates via singular multiplier techniques. Unlike previous works, the density is allowed to vanish and the viscosity coefficient is taken to be density-dependent rather than constant. Full article
(This article belongs to the Section Mathematical Physics)
12 pages, 8377 KB  
Article
Molecular Beam Epitaxial Growth and Nonlinear Optical Signatures of Single-Domain Bi2Se3
by Eunice Y. Paik, George J. de Coster, Brandi Wooten, Greg Meissner, Blair C. Connelly and Patrick Taylor
Photonics 2026, 13(6), 529; https://doi.org/10.3390/photonics13060529 - 29 May 2026
Viewed by 282
Abstract
We report a new approach to enhance the photonic response of thin-film topological insulator Bi2Se3 by significantly reducing twin domains and antiphase disorder. The strategy employs closely lattice-matched trigonal substrates combined with surface structuring to preferentially seed a single rotational [...] Read more.
We report a new approach to enhance the photonic response of thin-film topological insulator Bi2Se3 by significantly reducing twin domains and antiphase disorder. The strategy employs closely lattice-matched trigonal substrates combined with surface structuring to preferentially seed a single rotational domain before epitaxy. Characterization using optical second harmonic generation (SHG), nonlinear optical tensor analysis, X-ray diffraction, and atomic force microscopy confirms the near-single crystal Bi2Se3 heteroepitaxial layers. These results show a clear six-fold symmetric sin2(3ϕ) SHG pattern at normal incidence, and a vanishingly small 100-to-1 peak-height ratio from X-ray pole-scans showing negligible twinning. These results show that this approach can yield near perfect single crystal heteroepitaxial Bi2Se3 whose photonic properties converge to those of bulk-grown single crystals. Full article
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20 pages, 11510 KB  
Article
Minimization of Intrinsic Impurity Concentration in ZnGeP2 Single Crystals via Directional Recrystallization
by Alexander Gribenyukov, Alexey Lysenko, Nikolay Yudin, Elena Slyunko, Sergey Podzyvalov, Mikhail Zinovev, Vladimir Kuznetsov, Andrey Kalsin, Andrei Khudoley, Houssain Baalbaki, Maxim Kulesh and Alexey Olshukov
Int. J. Mol. Sci. 2026, 27(11), 4890; https://doi.org/10.3390/ijms27114890 - 28 May 2026
Viewed by 275
Abstract
Zinc germanium phosphide (ZnGeP2) is an important nonlinear crystal for mid-infrared conversion, but its performance is limited by residual absorption and intrinsic impurity phases. In this study, polycrystalline ZnGeP2 was synthesized by a modified two-temperature method, purified by inclined directional [...] Read more.
Zinc germanium phosphide (ZnGeP2) is an important nonlinear crystal for mid-infrared conversion, but its performance is limited by residual absorption and intrinsic impurity phases. In this study, polycrystalline ZnGeP2 was synthesized by a modified two-temperature method, purified by inclined directional recrystallization for up to three cycles, and then grown into single crystals by the vertical Bridgman method. The resulting material was examined by shadow-projection imaging, transmission spectroscopy in the 650–2500 nm range, absorption measurements at 2.097 µm, laser-induced damage threshold (LIDT) testing, and powder X-ray diffraction. Repeated purification improved optical homogeneity and near-infrared transparency, while the absorption coefficient at 2.097 µm decreased from 0.45 to 0.30 cm−1 after three purification cycles. Semi-quantitative PXRD analysis showed progressive suppression of intrinsic impurity phosphides, with phase purity increasing from 86.31% after the first cycle to 95.995% after the second and reaching 100% after the third within the detection limit of the method. However, the LIDT decreased with increasing purification number, indicating a trade-off between lower optical losses and damage resistance. These results demonstrate that inclined directional recrystallization is an effective pre-growth purification route for ZnGeP2 and that the optimal number of purification cycles should be selected according to the intended application. Full article
(This article belongs to the Section Materials Science)
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10 pages, 3212 KB  
Communication
Teaching Chaos Through Electro-Optics in Nematic Liquid Crystals and AI
by Grazia Giuseppina Politano
Optics 2026, 7(3), 34; https://doi.org/10.3390/opt7030034 - 25 May 2026
Viewed by 206
Abstract
The teaching of chaos and nonlinear dynamics remains a significant challenge in physics education, as these concepts are often introduced through abstract mathematical models that are difficult to visualize. In this work, we propose an experimental approach based on electro-optics in nematic liquid [...] Read more.
The teaching of chaos and nonlinear dynamics remains a significant challenge in physics education, as these concepts are often introduced through abstract mathematical models that are difficult to visualize. In this work, we propose an experimental approach based on electro-optics in nematic liquid crystals as an effective and accessible platform for teaching these phenomena. In particular, the system exhibits a transition from ordered convective patterns to strongly disordered turbulent regimes, which can be directly observed in real time using simple optical techniques. This experimental framework enables students to explore key concepts of nonlinear physics, including instability thresholds, pattern formation, and the emergence of complex dynamical behavior. The transition occurs through the nucleation and growth of turbulent domains, facilitating the understanding of nonequilibrium dynamics. From a pedagogical perspective, the proposed experiment combines strong visual impact with experimental controllability and accessibility, making it suitable for undergraduate students in physics, mathematics, and engineering. Furthermore, the integration of AI-assisted analysis provides students with an accessible framework to process experimental data, identify dynamical regimes, and explore complex systems through novel data-driven methodologies. Full article
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13 pages, 24076 KB  
Article
Persistent Near-Linear Relationship Between Global Stress and Mean Atomic Bond Strain in Metallic Glasses Despite Significant Local Nonaffine Displacements
by Tittaya Thaiyanurak and Donghua Xu
Materials 2026, 19(10), 2176; https://doi.org/10.3390/ma19102176 - 21 May 2026
Viewed by 445
Abstract
Mean atomic bond strain (MABS), based on the globally averaged bond length, has recently emerged as a new strain metric that retains clear physical meaning even as severe atomic neighborhood reconstruction occurs. It has been shown to exhibit a nearly perfect linear relationship [...] Read more.
Mean atomic bond strain (MABS), based on the globally averaged bond length, has recently emerged as a new strain metric that retains clear physical meaning even as severe atomic neighborhood reconstruction occurs. It has been shown to exhibit a nearly perfect linear relationship with global stress throughout the elastic and plastic deformation in single-crystal face-centered cubic (FCC) metals, contradicting conventional expectations based on nonlinear dislocation activity. Whether this near-linear relationship holds in other materials stands out as an important and intriguing question. In this study, we examine the MABS–stress relationship in representative unary, binary, and ternary metallic glasses (MGs), where neither a crystal structure nor dislocations are present. Large-scale molecular dynamics simulations of uniaxial tensile tests and statistical analysis of millions of atomic bonds are performed. Irrespective of their differing compositions, all the MGs exhibit a persistent near-linear relationship between total MABS (all bonds included) and global stress up to fracture, even in the presence of significant local nonaffine displacements (shear transformation zones and shear bands), with the Pearson correlation coefficient consistently exceeding 0.99. Unlike the nonaffine displacements, the spatial distribution of individual atomic bond strain does not localize under the uniaxial loading. In the MGs containing more than one element, MABS computed for a single bond type may not correlate as linearly with global stress as total MABS. The results demonstrate that the persistent near-linear total MABS–stress relationship over the entire deformation process, recently discovered in single-crystal FCC metals, also applies to MGs despite their vastly different atomic structures. This strengthens the candidacy of total MABS as a universal stress descriptor across materials classes and deformation regimes. With further development and implementation in atomistic simulations and constitutive modeling, the MABS concept has the potential to reshape our understanding of materials mechanics and generate new insights into the design of stronger, tougher, and more thermally and chemically stable materials. Full article
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11 pages, 9899 KB  
Communication
Gel-Grown Kebab-like KDP Crystal Formation Mechanisms
by Fugui Cai, Jie Ren, Yuqing Yao and Hanying Li
Molecules 2026, 31(10), 1744; https://doi.org/10.3390/molecules31101744 - 20 May 2026
Viewed by 279
Abstract
Using the gel-grown method to control the morphology of crystals attracts extensive attention. Potassium dihydrogen phosphate (KDP) is a nonlinear optical crystal with a high laser damage threshold. Here, we studied the crystallization of KDP in silica gel. The kebab-like KDP crystals (multiple [...] Read more.
Using the gel-grown method to control the morphology of crystals attracts extensive attention. Potassium dihydrogen phosphate (KDP) is a nonlinear optical crystal with a high laser damage threshold. Here, we studied the crystallization of KDP in silica gel. The kebab-like KDP crystals (multiple KDP crystals aligning along a straight line) were prepared in the silica gel. In situ observation revealed that the kebab-like crystals were obtained through secondary nucleations on preformed needle-like crystals. Further investigation revealed that the hydroxyl groups on the gel network have an important influence on the formation of kebab-like KDP crystals. The hydroxyl groups on the gel networks can form hydrogen bonds with the phosphoric acid group of the KDP crystal and hinder the growth of the prismatic KDP faces, which leads to the preformation of needle-like crystals. Additionally, the influence of the acetic acid concentration and antisolvent on morphology was also studied. Full article
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14 pages, 1923 KB  
Article
Prediction of Removal Function in Ion Beam Polishing of Potassium Dihydrogen Phosphate Crystals Using a Back-Propagation Neural Network
by Hailin Guo, Dasen Wang, Shiyan Zhao, Chaoxiang Xia and Ning Pei
Appl. Sci. 2026, 16(10), 4845; https://doi.org/10.3390/app16104845 - 13 May 2026
Viewed by 362
Abstract
To overcome the challenges of processing soft-brittle potassium dihydrogen phosphate (KDP) crystals, this study proposes a back-propagation (BP) neural network model for the rapid prediction of the ion beam removal function using Faraday cup scanning data (a method that measures the spatial distribution [...] Read more.
To overcome the challenges of processing soft-brittle potassium dihydrogen phosphate (KDP) crystals, this study proposes a back-propagation (BP) neural network model for the rapid prediction of the ion beam removal function using Faraday cup scanning data (a method that measures the spatial distribution of ion beam current density). By correlating current density measurements with point etching experiment results, the model accurately maps both the linear relationship (R2 = 0.98) between peak removal rate and peak current density, and the non-linear relationship between the full width at half maximum (FWHM) of the beam and the removal function. The predicted removal function demonstrates high accuracy, with a volume removal rate error of just 2.56% compared to experimental results. Furthermore, this method drastically reduces calculation time from approximately 2 h (required by the conventional point-etching experiment, which involves iterative vacuum cycling, etching, and ex situ interferometry) to just 2 min, significantly improving efficiency. Applied to the ion beam polishing of a 50 mm × 50 mm × 10 mm KDP crystal, the model proved highly effective. The surface figure error was corrected from an initial 0.298λ peak-to-valley (PV) and 0.0496λ root-mean-square (RMS) to 0.167λ PV and 0.036λ RMS, where λ (632.8 nm) is the wavelength of the He-Ne laser used for interferometric surface measurement, achieving a convergence ratio (defined as the ratio of initial PV to final PV) of 1.78. This research provides a high-efficiency, high-precision technical solution for manufacturing KDP components for inertial confinement fusion (ICF) applications. Full article
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33 pages, 3593 KB  
Review
Fiber-Optic Gyroscopes in Modern Navigation Systems: A Comprehensive Review
by Nurzhigit Smailov, Yerlan Tashtay, Pawel Komada, Yerzhan Nussupov, Kanat Zhunussov, Askhat Batyrgaliyev, Daulet Naubetov, Aziskhan Amir, Beibarys Sekenov and Darkhan Yerezhep
Network 2026, 6(2), 28; https://doi.org/10.3390/network6020028 - 29 Apr 2026
Viewed by 1825
Abstract
This paper provides a comprehensive overview of the progress in fiber-optic gyroscope technology, covering 260 key studies of the last ten years. A critical comparative analysis of fiber-optic gyroscope with alternative inertial sensors (Micro-Electro-Mechanical Systems, Hemispherical Resonator Gyroscope, Ring Laser Gyroscope) has been [...] Read more.
This paper provides a comprehensive overview of the progress in fiber-optic gyroscope technology, covering 260 key studies of the last ten years. A critical comparative analysis of fiber-optic gyroscope with alternative inertial sensors (Micro-Electro-Mechanical Systems, Hemispherical Resonator Gyroscope, Ring Laser Gyroscope) has been carried out. Confirming the unique advantages of fiber-optic gyroscope for autonomous navigation. Fundamental limitations of accuracy are considered in detail: temperature drifts, polarization noise, and Rayleigh backscattering. Modern hardware methods for suppressing these errors, including the use of photonic crystal and hollow fibers (Air-Core/Hollow-Core), are also considered in this work. The central place in the review is occupied by the analysis of the technological paradigm shift from bulky discrete circuits to hybrid integrated photonics (Indium Phosphide, Silicon Nitride, Lithium Niobate) and hybrid architectures to reduce weight and size characteristics. The role of artificial intelligence (Deep Learning, Long Short-Term Memory) methods in nonlinear drift compensation and calibration is discussed. The usage of the Brillouin effect and optomechanics promising areas are outlined, necessary to create a new generation of navigation systems operating in the absence of Global Navigation Satellite Systems signals. Full article
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15 pages, 2434 KB  
Article
Linear and Nonlinear Dynamics of Crystals with B2 (CsCl) Structure
by Dina U. Abdullina, Sergey V. Dmitriev, Ilya S. Sugonyako, Arseny M. Kazakov and Elena A. Korznikova
Crystals 2026, 16(5), 286; https://doi.org/10.3390/cryst16050286 - 25 Apr 2026
Cited by 1 | Viewed by 598
Abstract
This study investigates the phenomenon of supratransmission in three-dimensional crystals with a B2 (CsCl) structure, employing classical molecular dynamics with β-Fermi–Pasta–Ulam–Tsingou potentials up to fourth-nearest neighbors. We analyze energy transfer from a harmonically driven surface into the crystal bulk across various frequency regimes [...] Read more.
This study investigates the phenomenon of supratransmission in three-dimensional crystals with a B2 (CsCl) structure, employing classical molecular dynamics with β-Fermi–Pasta–Ulam–Tsingou potentials up to fourth-nearest neighbors. We analyze energy transfer from a harmonically driven surface into the crystal bulk across various frequency regimes relative to the phonon spectrum. While low-amplitude excitation results in energy transmission only within the phononic bands, high-amplitude driving triggers supratransmission in the phononic gap and above the optical band. Our results demonstrate that in these nonlinear regimes, energy is transported not by linear phonon waves but by discrete breathers (DBs) emitted quasi-periodically from the surface. A key finding is the distinct sublattice selectivity of these excitations: gap DBs propagate primarily along the heavy atom sublattice, whereas above-spectrum DBs travel along the light atom sublattice. We quantify the velocities and oscillation periods of these localized modes, revealing their critical role in bypassing linear spectral restrictions. These findings provide new insights into nonlinear energy transport in binary alloys and suggest potential applications for controlling heat flow and signal processing in crystals. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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30 pages, 977 KB  
Article
Field-Theoretic Derivation of the Constructal Law from Non-Equilibrium Thermodynamics
by Antonio F. Miguel
Symmetry 2026, 18(5), 732; https://doi.org/10.3390/sym18050732 - 24 Apr 2026
Cited by 1 | Viewed by 403
Abstract
Traditional analyses of transport phenomena rely on prescribed geometric boundaries, yet natural flow systems dynamically evolve their architecture to maximize access to currents. To address this disparity, we propose a field-theoretic framework for the constructal law that treats physical geometry as a dynamic [...] Read more.
Traditional analyses of transport phenomena rely on prescribed geometric boundaries, yet natural flow systems dynamically evolve their architecture to maximize access to currents. To address this disparity, we propose a field-theoretic framework for the constructal law that treats physical geometry as a dynamic state variable, represented by a time-dependent conductivity tensor. Using a variational approach grounded in non-equilibrium thermodynamics, we derive a general tensor evolution equation. Within this framework, macroscopic flow architecture emerges deterministically from the continuous competition between non-linear flux-induced accretion, linear entropic relaxation, and spatial smoothing. Scaling analysis reduces this dynamic to a tri-parameter dimensionless phase space: a morphogenic number driving structural growth, a structural diffusion number governing spatial coherence, and a stochastic intensity number providing the microscopic seeds for symmetry breaking. Our principal result is the analytical prediction of a critical bifurcation. When the local morphogenic number strictly exceeds unity, the system escapes its stable, isotropic configuration and branches into highly conductive, anisotropic architectures. We demonstrate the predictive validity and trans-scalar applicability of this continuum theory by mapping it to highly diverse phase transitions, successfully capturing phenomena ranging from microscopic aerosol agglomeration and microbial resistance, to macroscopic coral plasticity and crystal growth instabilities, and finally to the astrophysical launching of relativistic jets from black holes. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2026)
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18 pages, 3285 KB  
Article
Research on the Preparation of Red Mud High-Performance Cement Mortar and the Corresponding Resistance to Dry–Wet Alternation Cycles of Exposure to Chloride and Sulfate Solutions
by Ligai Bai, Chunying Zhu, Jian Zhang, Jiameng Wan, Junzhe Liu, Kangshuo Xia, Feiting Shi and Huihui Tong
Coatings 2026, 16(4), 484; https://doi.org/10.3390/coatings16040484 - 17 Apr 2026
Viewed by 928
Abstract
The accumulation of highly alkaline red mud poses serious environmental risks due to land occupation and potential soil/groundwater contamination. Recycling red mud as a secondary resource offers an eco-friendly solution, yet its influence on the performance of high-performance mortar (HPM) remains incompletely understood, [...] Read more.
The accumulation of highly alkaline red mud poses serious environmental risks due to land occupation and potential soil/groundwater contamination. Recycling red mud as a secondary resource offers an eco-friendly solution, yet its influence on the performance of high-performance mortar (HPM) remains incompletely understood, particularly in aggressive environments. This study aims to systematically evaluate the effects of red mud on the fresh and hardened properties of HPM, including rheological parameters, setting time, mechanical strength, drying shrinkage, and sulfate dry–wet erosion resistance. The novelty lies in (1) quantifying the nonlinear relationships between red mud content and rheological/setting behaviors, (2) revealing the dual effect of red mud with curing age, and (3) using XRD/SEM-EDS to elucidate the micro-mechanisms related to hydration products and elemental changes (Al and Fe). The results show that increasing red mud content reduces slump flow (max 76.03%), plastic viscosity (46.7%), and yield stress (42.3%) while also shortening initial/final setting times (67.91% and 76.18% max reductions). At curing ages below 7 days, flexural and compressive strength increase (up to 64.53% and 33.35%, respectively), following cubic functions; however, at 7 and 28 days, both strength values decrease (max reductions of 13.43% and 12.98%). Red mud increases drying shrinkage and delays sulfate-induced degradation. Microstructural analysis reveals improved compactness of hydration products at early ages but reduced compactness at later ages, accompanied by increased Al/Fe content and enhanced SiO2/calcium silicate hydrate crystals. These findings provide valuable insights for applying red mud HPM in marine environments. Full article
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