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Search Results (185)

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Keywords = non-ideal gas

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18 pages, 3098 KB  
Article
Invasiveness Study of Supersonic Gas-Curtain-Based Ionization Profile Monitor for Medical Accelerators
by William Butcher, Narender Kumar, Milaan Patel, Bharat Singh Rawat, Oliver Stringer, Farhana Thesni Mada Parambil, Hao Zhang and Carsten P. Welsch
Instruments 2026, 10(3), 35; https://doi.org/10.3390/instruments10030035 - 30 Jun 2026
Viewed by 163
Abstract
In proton beam therapy, ideally, beam monitoring should be non-invasive to provide online real-time feedback, such that the total dose delivered to the patient is not significantly affected. The invasiveness of the Supersonic Gas-Curtain-Based Ionization Profile Monitor (SGC-IPM) system was quantified by perturbation [...] Read more.
In proton beam therapy, ideally, beam monitoring should be non-invasive to provide online real-time feedback, such that the total dose delivered to the patient is not significantly affected. The invasiveness of the Supersonic Gas-Curtain-Based Ionization Profile Monitor (SGC-IPM) system was quantified by perturbation in beam current and transverse beam profile parameters induced by the supersonic gas-curtain for a 4.9–5.3 keV electron beam, representing a worst-case scenario where perturbations can be more easily observable. The experimentally measured gas-curtain effects on transverse beam parameters (≤2%), intensity (≤−1%) and beam current (≤−1%) were small in magnitude and largely below resolution limits. To confirm these effects, order-of-magnitude beam–gas interaction approximations were calculated for the experimental energy range, demonstrating negligible energy loss with minor scattering, broadly consistent with the experimental results. Clinical proton beam gas-curtain predictions (70–250 MeV) indicate a further reduction of ∼104 compared to the experimental observations. Even under the conservative electron beam conditions used in this study, the observed perturbations were minor or unresolvable and measured effects were significantly smaller than spatial and dosimetry scales relevant to proton radiotherapy. Overall, the experimental measurements and supporting order-of-magnitude estimates demonstrate that the SGC-IPM introduces negligible perturbations to beam parameters and is predicted to provide non-invasive beam profile monitoring for clinical proton beam diagnostics. Full article
(This article belongs to the Section Particle Detectors and Accelerators)
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18 pages, 3814 KB  
Article
The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics
by Alberto Robledo
Entropy 2026, 28(6), 710; https://doi.org/10.3390/e28060710 - 20 Jun 2026
Viewed by 364
Abstract
We address the paradoxical transformation of a classical-mechanical particle motion when the space and time scales of observation pass below the uncertainty principle threshold. This is analyzed in the language of classical statistical mechanics, considering specifically many-particle systems inhomogeneous along one spatial direction. [...] Read more.
We address the paradoxical transformation of a classical-mechanical particle motion when the space and time scales of observation pass below the uncertainty principle threshold. This is analyzed in the language of classical statistical mechanics, considering specifically many-particle systems inhomogeneous along one spatial direction. We employ the density functional formalism in its square-gradient form and find: (i) The macroscopic solution is analogous to the classical trajectory of a particle under a potential of force given by (minus) the free energy density. Whereas, (ii) fluctuations around the solution in (i) are equal to the quantum-mechanical wave functions of a particle under a potential given by the curvature of the free energy density. We illustrate this situation with three textbook examples: A particle in a box, the harmonic oscillator, and the hydrogen atom. We show that their time-independent Schrödinger equation wave functions describe, respectively, the fluctuations of a fluid interface, of critical point fluctuations, and of a confined ideal gas. At large scales, sharp probability distributions make fluctuations irrelevant; the vanishing of the first variation yields the macroscopically observable statistical-mechanical non-uniformity, equivalent to the classical particle trajectory. But at sufficiently small scales, with necessarily very few particles, distributions appear much wider, fluctuations dominate, and one obtains the Schrödinger equation (for the microscopic potential). Full article
(This article belongs to the Special Issue Quantum Ontology: Theory and Applications)
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30 pages, 3952 KB  
Article
A Mathematical Co-Design Framework for Synchronous Boost DC-DC Converters and PI Controllers Under Parasitic and Semiconductor Loss Effects
by Nikolay Hinov, Polya Gocheva and Valeri Gochev
Mathematics 2026, 14(12), 2086; https://doi.org/10.3390/math14122086 - 11 Jun 2026
Viewed by 214
Abstract
This paper proposes a mathematical co-design framework for synchronous Boost DC-DC converters and their PI voltage controllers. In contrast to the conventional sequential design approach, where the power stage is sized first and the controller is tuned afterward, the proposed method treats the [...] Read more.
This paper proposes a mathematical co-design framework for synchronous Boost DC-DC converters and their PI voltage controllers. In contrast to the conventional sequential design approach, where the power stage is sized first and the controller is tuned afterward, the proposed method treats the converter and the controller as a single coupled design problem. A nonlinear averaged model of the synchronous boost converter operating in continuous conduction mode is considered, explicitly incorporating the inductor series resistance, the capacitor equivalent series resistance, and the on-state resistances of the active switches. In addition, a simplified but physically interpretable loss model is included in order to capture inductor copper loss, capacitor ESR loss, semiconductor conduction loss, and switching loss. Based on this formulation, the joint design of the power stage and the PI controller is cast as a constrained multi-objective optimization problem whose decision variables include the inductance, capacitance, switching frequency, and controller gains. The optimization criteria account for output-voltage ripple, settling time, total losses, and current stress, while practical constraints related to duty cycle, current limits, ripple bounds, and closed-loop feasibility are enforced. The proposed framework makes it possible to compute Pareto-efficient designs and to reveal trade-offs that remain hidden under classical decoupled design procedures. Numerical case studies are structured to compare the proposed co-design strategy with a conventional sequential-design baseline. An optional technology-aware extension is also considered, allowing the influence of different semiconductor classes, such as Si, SiC, and GaN, to be assessed through technology-dependent loss and switching-frequency assumptions. The results indicate that the proposed framework provides a mathematically grounded and practically useful basis for integrated converter–controller synthesis in nonideal power electronic systems. Full article
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43 pages, 7533 KB  
Article
System-Level Modeling of Parabolic Solar Dish–Stirling Units with Explicit Loss Partitioning Under Variable Charge Control
by Sagi Orel Moshe and Zeev Zalevsky
Appl. Sci. 2026, 16(11), 5560; https://doi.org/10.3390/app16115560 - 2 Jun 2026
Viewed by 265
Abstract
Parabolic solar dish–Stirling (PSDS) technologies are among the most efficient solar-to-electric conversion options, but their system-level modeling remains challenging because optical losses, receiver heat losses, package leakage, and Stirling engine non-idealities are strongly coupled under variable operating conditions. This study develops a modular, [...] Read more.
Parabolic solar dish–Stirling (PSDS) technologies are among the most efficient solar-to-electric conversion options, but their system-level modeling remains challenging because optical losses, receiver heat losses, package leakage, and Stirling engine non-idealities are strongly coupled under variable operating conditions. This study develops a modular, energy-consistent system-level framework that couples dish receiver optics and thermal behavior, hot-end package losses, and a non-ideal Stirling engine under variable charge (Qu-mode) control. The key novelty is a receiver engine heat-matching formulation in which receiver temperature, useful heat, working gas charge/mean pressure, and engine output emerge from a closed energy balance rather than from prescribed hot-side temperature, fixed heat input, or prescribed mean pressure. The framework was benchmarked in stages against the Mendoza receiver formulation, GPU-3/LeRC Stirling engine data, and EuroDish dispatch-level measurements. At the integrated EuroDish level, it reproduced heat input, cooler rejection, and net electrical output with mean absolute percentage errors of 2.90%, 4.07%, and 4.28%, respectively, while preserving explicit traceability of optical, receiver, package, engine, generator, and parasitic losses. A receiver formulation comparison showed that the final receiver treatment reduced the cooler rejection MAPE from 8.11% to 4.07% relative to the Mendoza-type receiver swap baseline. A limited-input transferability study for representative pressure-controlled dish–Stirling platforms retained peak power and efficiency within a ±10% envelope for the quantitatively assessed cases. Parametric studies further showed a broad engine speed optimum, a heat exchanger sizing trade-off governed by conductance and pumping/friction losses, stronger sensitivity to ambient temperature than wind over the tested EuroDish range, and cooling boundary effects that redirect fixed thermal input from electricity to rejected heat. The resulting framework provides a compact predictive basis for loss diagnosis, design studies, and control-oriented evaluation of PSDS units. Full article
(This article belongs to the Section Energy Science and Technology)
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24 pages, 3983 KB  
Article
Effects of Soil Stratification, Anisotropy, and Spatial Heterogeneity on Methane Dispersion from Buried Pipeline Leakage: A Comparative Numerical Study
by Ting Pan, Xingyu Wang, Fei Li, Tianyu Bao, Kai Liu, Zhenglong Li, Siyan Hong, Zhanghua Yin, Zhipeng Yu and Bingyuan Hong
Appl. Sci. 2026, 16(11), 5184; https://doi.org/10.3390/app16115184 - 22 May 2026
Viewed by 193
Abstract
Accurate prediction of natural gas dispersion from buried pipelines is critical for risk assessment and emergency response. However, conventional numerical simulations often simplify soil as a homogeneous isotropic porous medium, which deviates significantly from real-world conditions characterized by stratification, anisotropy, and spatial heterogeneity. [...] Read more.
Accurate prediction of natural gas dispersion from buried pipelines is critical for risk assessment and emergency response. However, conventional numerical simulations often simplify soil as a homogeneous isotropic porous medium, which deviates significantly from real-world conditions characterized by stratification, anisotropy, and spatial heterogeneity. This study systematically investigates the effects of these non-ideal soil characteristics on methane diffusion behavior using computational fluid dynamics (CFD). Four distinct soil models—a baseline homogeneous model, a layered model, an anisotropic model, and a spatially heterogeneous model—were constructed and compared under identical leakage scenarios. Key risk indicators, including First Danger Time (FDT), Farthest Danger Range (FDR), Ground Danger Range (GDR), and leakage mass flow rate, were quantitatively evaluated. Results indicate that soil layering enhances vertical migration and expands horizontal hazard ranges, reducing FDT by approximately 8%. Anisotropy introduces a pronounced directional dependence in gas migration, with horizontal-preferred permeability leading to severe underestimation of lateral risk by homogeneous assumptions. The spatially heterogeneous model exhibits reduced hazard ranges compared to the homogeneous case but accelerates early breakthrough. Comprehensive evaluation reveals that the homogeneous model systematically underestimates lateral diffusion distances and delays alarm times. This study provides a quantitative basis for selecting appropriate soil modeling strategies, emphasizing that incorporating soil heterogeneity is essential for reliable safety assessments of buried gas pipelines. Full article
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8 pages, 2685 KB  
Proceeding Paper
Dual-Redundant Broadband Low-Noise Amplifier Module for Inter-Satellite Links at V-Band
by Peiman Parand, Hermann Barbato, Patrick Ettore Longhi, Alessandro Barigelli, Francesco Vitulli and Ernesto Limiti
Eng. Proc. 2026, 133(1), 112; https://doi.org/10.3390/engproc2026133112 - 9 May 2026
Viewed by 285
Abstract
This paper presents the design and simulation of a dual-redundant broadband low-noise amplifier (LNA) module for inter-satellite communication links operating in the V-band (59–71 GHz). The growing demand for high-capacity space communication systems requires highly reliable, low-noise front-end architectures capable of maintaining performance [...] Read more.
This paper presents the design and simulation of a dual-redundant broadband low-noise amplifier (LNA) module for inter-satellite communication links operating in the V-band (59–71 GHz). The growing demand for high-capacity space communication systems requires highly reliable, low-noise front-end architectures capable of maintaining performance over long mission lifetimes. To address these needs, a selectable dual-input receiver architecture is proposed, integrating a waveguide dual-probe, redundant switching, and a two-stage LNA within a single Gallium Arsenide (GaAs) MMIC. The design methodology accounts for the non-ideal behavior of the redundant branch and its impact on noise figure and insertion loss. The front-end is implemented using a 70 nm GaAs mHEMT technology optimized for millimeter-wave low-noise applications. Simulations show an insertion gain higher than 15 dB across the operational band, with gain ripple below 1.3 dB peak-to-peak. The simulated system noise figure is approximately 3.0 dB, closely matching the target specification. The results demonstrate that the proposed architecture provides improved reliability through redundancy while maintaining competitive noise and gain performance for future V-band inter-satellite links. Full article
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16 pages, 2959 KB  
Article
Optimization of Injection-Production Volumes in Underground Gas Storage Based on Improved Non-Dominated Sorting Genetic Algorithm II
by Xufeng Yang, Fayang Jin, Yu Fu and Chao Chen
Eng 2026, 7(5), 215; https://doi.org/10.3390/eng7050215 - 1 May 2026
Viewed by 465
Abstract
As critical infrastructure for seasonal natural gas peak-shaving, the operation of underground gas storage (UGS) must consider multiple factors including risk, economics, efficiency, and technology. Traditional UGS operation schemes are heavily dependent on subjective experience and lack intelligent methods to fully leverage historical [...] Read more.
As critical infrastructure for seasonal natural gas peak-shaving, the operation of underground gas storage (UGS) must consider multiple factors including risk, economics, efficiency, and technology. Traditional UGS operation schemes are heavily dependent on subjective experience and lack intelligent methods to fully leverage historical data. This shortcoming leads to higher risks and increased compressor energy consumption. Taking S UGS as an example, the sensitivity factors of injection-production capacity are analyzed based on geological development and multi-cycle injection-production operation data. With injection-production rates as a decision variable and while considering safety and economic factors, objective functions and constraints are defined from the formation, wellbore, and surface. The proposed injection and production cycles are both 15 days, and the total injection and production volumes are 1200 × 104 m3 and 800 × 104 m3. An optimization model was constructed using the INSGA-Ⅱ and TOPSIS to determine the optimal gas injection-production volume allocation scheme. Compared with the initial scheme, the optimal injection-production volume allocation scheme reduces compressor energy consumption by 49.19% and 49.80% and formation pressure standard deviation by 78.88% and 77.21%, respectively. This effectively lowers injection-production energy consumption while improving safety, thereby ensuring the long-term safe and efficient operation of UGS. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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34 pages, 494 KB  
Article
Area Law for the Entanglement Entropy of Free Fermions in Nonrandom Ergodic Field
by Leonid Pastur and Mira Shamis
Entropy 2026, 28(5), 509; https://doi.org/10.3390/e28050509 - 1 May 2026
Cited by 1 | Viewed by 785
Abstract
The paper deals with the asymptotic behavior of a widely used correlation characteristic in large quantum systems. The correlation is quantum entanglement, the characteristic is entanglement entropy, and the system is an ideal gas of lattice fermions. If the one-body Hamiltonian of fermions [...] Read more.
The paper deals with the asymptotic behavior of a widely used correlation characteristic in large quantum systems. The correlation is quantum entanglement, the characteristic is entanglement entropy, and the system is an ideal gas of lattice fermions. If the one-body Hamiltonian of fermions is an ergodic finite difference operator with an exponentially decaying spectral projection, then the large-block form of the entanglement entropy is the so-called area law. However, the only class of one-body Hamiltonians for which this spectral condition was verified consists of discrete Schrödinger operators with random potential. In this paper, we prove the area law for several classes of Schrödinger operators whose potentials are ergodic but not random. We begin with quasiperiodic and limit-periodic operators and then move to a highly non-trivial case of potentials generated by subshifts of finite type. These arose in the theory of dynamical systems when studying chaotic phenomena. The corresponding asymptotic study requires involved spectral analysis, which therefore constitutes the bulk of the paper. Specifically, we prove uniform localisation of the eigenfunctions for the Maryland model and exponential decay of the eigenfunction correlator for various models. We believe these properties are of significant independent interest. Full article
(This article belongs to the Section Quantum Information)
13 pages, 10825 KB  
Article
Genetic Algorithm-Optimized Volume Holographic Gratings in Ultra-Thin MiniLED Modules
by Zechao Shen, Yue Zhang, Guoqiang Lv, Zi Wang and Qibin Feng
Micromachines 2026, 17(4), 479; https://doi.org/10.3390/mi17040479 - 15 Apr 2026
Viewed by 392
Abstract
The design of volume holographic gratings (VHGs) is traditionally based on monochromatic plane waves. However, practical applications often involve light sources with broad wavelength bandwidths and certain emission areas, such as LEDs and MiniLEDs, which cause significant Bragg mismatch and degrade diffraction efficiency. [...] Read more.
The design of volume holographic gratings (VHGs) is traditionally based on monochromatic plane waves. However, practical applications often involve light sources with broad wavelength bandwidths and certain emission areas, such as LEDs and MiniLEDs, which cause significant Bragg mismatch and degrade diffraction efficiency. To address this fundamental challenge, this paper proposes a novel, to the best of our knowledge, genetic algorithm (GA)-based optimization method for VHG design. A ray-tracing analysis model that fully incorporates the spectral and spatial characteristics of extended broadband sources is established. The GA optimizes the grating fabrication angles by minimizing a fitness function defined as the residual energy after diffraction, thereby achieving optimal performance under non-ideal illumination conditions. The effectiveness of the proposed method is demonstrated through a case study: suppressing the high-intensity central beam in an ultra-thin MiniLED backlight module (BLM). Simulation and experimental results show that the GA-optimized VHG significantly reduces the peak irradiance from 5.01 W/cm2 to 4.14 W/cm2 at an optical distance (OD) of 0.5 mm. This work provides a robust and source-adaptive design methodology for VHGs, with potential applications extending beyond backlighting to areas such as augmented reality, holographic displays, and optical communications. Full article
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18 pages, 4332 KB  
Article
Skew Angle Optimization for Cogging Torque Reduction in 12-Pole/15-Slot Axial Flux PMSMs
by Ice Poonphol and Padej Pao-la-or
World Electr. Veh. J. 2026, 17(4), 192; https://doi.org/10.3390/wevj17040192 - 6 Apr 2026
Viewed by 973
Abstract
Axial Flux Permanent Magnet Synchronous Motors (AFPMSMs) are gaining increasing attention for their application in electric vehicle (EV) drive systems. Their high torque density and compact axial geometry make them attractive for high-performance EV drive systems. However, cogging torque remains a major challenge, [...] Read more.
Axial Flux Permanent Magnet Synchronous Motors (AFPMSMs) are gaining increasing attention for their application in electric vehicle (EV) drive systems. Their high torque density and compact axial geometry make them attractive for high-performance EV drive systems. However, cogging torque remains a major challenge, degrading low-speed drivability, noise performance, and control stability. This article proposes a magnet skew on rotor modulation structure using a genetic algorithm (GA) to reduce cogging torque in AFPMSMs utilizing a 12/15 non-integer pole/slot arrangement. The objective of optimization is to simultaneously reduce cogging torque under identical electromagnetic constraints. A complete three-dimensional finite element model (3D-FEM) incorporating nonlinear magnetic material properties has been developed to evaluate the electromagnetic field distribution and torque components. The results indicate that a 12/15 non-integer pole/slot arrangement improves harmonic distribution and extends the operating range with lower cogging torque compared to integer pole/slot designs. Combined with GA-optimized skew angles, this reduces peak-to-peak cogging torque to less than 50%. This design is ideally suited for the traction requirements of electric vehicles, including premium electric vehicles where smooth operation at low speeds is critical. Full article
(This article belongs to the Section Propulsion Systems and Components)
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14 pages, 318 KB  
Article
Similarity Solutions of Cylindrical Strong Shock in Self-Gravitating Medium Under the Monocromatic Radiation
by Antim Chauhan, Amit Tomar, Musrrat Ali and S. Suresh Kumar Raju
Mathematics 2026, 14(4), 705; https://doi.org/10.3390/math14040705 - 17 Feb 2026
Viewed by 415
Abstract
A class of self-similar solutions to the model of a cylindrical shock wave in non-uniform atmosphere in the presence of monochromatic radiation and gravitation in magneto gas dynamics has been obtained by using a similarity method. The propagation of a cylindrical shock wave [...] Read more.
A class of self-similar solutions to the model of a cylindrical shock wave in non-uniform atmosphere in the presence of monochromatic radiation and gravitation in magneto gas dynamics has been obtained by using a similarity method. The propagation of a cylindrical shock wave in an ideal gas with monochromatic radiation and gravitating effects has been discussed. Through applying similarity transformations to the system of equations, we obtained the symmetry generators of the system. By using the symmetry generators and the surface invariance condition, we obtained the group invariant solution and then, with the help of group invariant solution, we converted the given system of PDEs to the system of ODEs together with the boundary condition. The obtained system of ODEs together with boundary condition has been solved numerically by using Runge–Kutta method of order four. The flow variables are analyzed graphically behind the shock with respect to the variation of parameters. Full article
(This article belongs to the Special Issue Research on Applied Partial Differential Equations)
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27 pages, 1703 KB  
Review
Research on Low-Damage CO2 Foam Flooding System: Review and Outlook
by Jierui Liu, Zhen Cui, Shisheng Liang, Xinyuan Zou, Wenli Luo, Wenjuan Wang, Bo Dong and Xiaohu Xue
Molecules 2026, 31(4), 642; https://doi.org/10.3390/molecules31040642 - 12 Feb 2026
Viewed by 781
Abstract
Tight oil reservoirs are widely recognized as a critical successor in global unconventional energy development and are generally characterized by distinct geological features, including fine pore throats, pronounced heterogeneity, and a high concentration of clay minerals (e.g., montmorillonite and mixed-layer illite/smectite). Severe hydration, [...] Read more.
Tight oil reservoirs are widely recognized as a critical successor in global unconventional energy development and are generally characterized by distinct geological features, including fine pore throats, pronounced heterogeneity, and a high concentration of clay minerals (e.g., montmorillonite and mixed-layer illite/smectite). Severe hydration, swelling, and fines migration are readily induced during water injection or conventional water-based fluid operations, thereby resulting in irreversible impairment of reservoir permeability. Despite the excellent injectivity and capacity for viscosity reduction associated with CO2 flooding, sweep efficiency is severely compromised by viscous fingering and gas channeling, which are induced by the inherent low viscosity of the gas. While CO2 foam technology is widely acknowledged as a pivotal solution for addressing mobility control challenges, its implementation is hindered by a primary technical bottleneck: the incompatibility between traditional water-based foam systems and strongly water-sensitive reservoirs. A dual challenge comprising water injectivity constraints and gas channeling is presented by strongly water-sensitive tight oil reservoirs. To address these impediments, three emerging low-damage CO2 foam systems are critically evaluated in this review. First, the synergistic mechanisms of novel quaternary ammonium salts and polymers in inhibiting clay hydration and enhancing foam stability within modified water-based systems are elucidated. Next, the physical isolation strategy of substituting the water phase with a non-aqueous phase (oil/organic solvent) in organic emulsion systems is analyzed, highlighting advantages in wettability alteration and the mitigation of water blocking. Finally, the prospect of waterless operations using CO2-soluble foam systems—wherein supercritical CO2 is utilized as a surfactant carrier to generate foam or viscosify fluids via in situ formation water—is discussed. It is revealed by comparative analysis that: (1) Modified water-based systems are identified as the most economically viable option for reservoirs with moderate water sensitivity, wherein cationic stabilizers are utilized to inhibit hydration; (2) Superior wettability alteration and the elimination of aqueous phase damage are provided by organic emulsion systems, rendering them ideal for ultra-sensitive, high-value reservoirs, despite higher solvent costs; (3) CO2-soluble systems are recognized as the future direction for “waterless” flooding, specifically tailored for ultra-tight formations (<0.1 mD) where injectivity is critical. Current challenges, such as surfactant solubility, high-temperature stability, and cost control, are identified through a comparative analysis of these three systems with respect to structure-activity relationships, rheological properties, damage control capabilities, and economic feasibility. What is more, an outlook is provided on the molecular design of future environmentally sustainable, cost-effective CO2-philic materials and smart injection strategies. Consequently, theoretical foundations and technical support are established for the efficient exploitation of strongly water-sensitive tight oil reservoirs. By bridging the gap between reservoir damage control and mobility enhancement, this study identifies viable strategies for enhanced oil recovery. Crucially, it supports carbon neutrality and sustainable energy targets via CCUS integration. Full article
(This article belongs to the Special Issue Chemistry Applied to Enhanced Oil Recovery)
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16 pages, 579 KB  
Article
Thermodynamic Interpretation of the Kompanneets–Chernov–Kantowski–Sachs Solutions
by Salvador Mengual and Joan Josep Ferrando
Universe 2026, 12(2), 45; https://doi.org/10.3390/universe12020045 - 10 Feb 2026
Viewed by 418
Abstract
The spatially homogeneous perfect fluid solutions by Kompanneets–Chernov–Kantowski–Sachs are interpreted as a thermodynamic perfect fluid in isentropic evolution, namely, the isentropic limit of their non-homogeneous generalizations, the T-models. Some specific solutions that model a generic ideal gas are examined, and the associated thermodynamic [...] Read more.
The spatially homogeneous perfect fluid solutions by Kompanneets–Chernov–Kantowski–Sachs are interpreted as a thermodynamic perfect fluid in isentropic evolution, namely, the isentropic limit of their non-homogeneous generalizations, the T-models. Some specific solutions that model a generic ideal gas are examined, and the associated thermodynamic variables are obtained. We show that the necessary macroscopic conditions for physical reality are fulfilled in wide spacetime domains. The field equations for a classical ideal gas are established, and the behavior of the solution is analyzed. The models fulfilling a relativistic γ-law are also examined, and the solutions for some particular cases are obtained. Full article
(This article belongs to the Section Gravitation)
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22 pages, 3687 KB  
Article
Modelling Transdermal Permeation of Volatiles from Complex Product Formulations
by Zhihao Zhong, Guoping Lian, Tao Chen and Yuan Yu
Pharmaceutics 2026, 18(2), 221; https://doi.org/10.3390/pharmaceutics18020221 - 9 Feb 2026
Cited by 2 | Viewed by 719
Abstract
Background: The evaporation of volatile ingredients from topical formulations strongly influences transdermal permeation and overall bioavailability, yet coupled evaporation–permeation dynamics are mostly simplified or neglected in existing models. Methods: We developed a mechanistic framework that couples Fickian gas-phase evaporation and transdermal [...] Read more.
Background: The evaporation of volatile ingredients from topical formulations strongly influences transdermal permeation and overall bioavailability, yet coupled evaporation–permeation dynamics are mostly simplified or neglected in existing models. Methods: We developed a mechanistic framework that couples Fickian gas-phase evaporation and transdermal permeation, both driven by the activity coefficients of volatiles. The model equations are implemented in a hybrid MATLAB–Python architecture with the volatile activity computed on-the-fly using UNIFAC and the gas-phase diffusivity calculated by the kinetic equation of Fuller–Schettler–Giddings (FSG). Initial validation used published IVPT data for 4-Tolunitrile and Nitrobenzene. Results: For 4-Tolunitrile, the FSG-based model estimated an initial evaporation coefficient of Kevap,i = 7.9348 × 10−10 mol·cm−2·s−1, and parameter optimization converged to 8.3929 × 10−11 mol·cm−2·s−1 (≈1/10 of the FSG estimate). The optimized model predicted an accumulation amount of 19.15% versus an experimental value of 16.97% in the receptor fluid (RF) at 24 h. For Nitrobenzene, the FSG initial estimation value of Kevap,i = 6.6480 × 10−10 mol·cm−2·s−1 was optimized to 8.1174 × 10−11 mol·cm−2·s−1 (≈1/8 of the FSG value), and the predicted amount of 24 h RF is 27.61% (experimental 23.19%). Both optimized Kevap,i values are roughly one order of magnitude lower than the initial FSG estimates, but >20× larger than Stokes–Einstein (SE)-derived values. Sensitivity scans show that further tuning of internal skin parameters (e.g., diffusion coefficient (DSC,i) and partition coefficient (PSCw,i)) produced only marginal improvements in RF prediction once Kevap,i was optimized. Conclusions: The coupled evaporation–permeation framework reproduces key IVPT kinetics for volatile solutes when the effective evaporation coefficient is calibrated. The kinetic-theory estimates (FSG-based) are a reasonable starting point, but typically overestimate the evaporation rate constant under finite-dose unoccluded IVPT conditions. By implementing the on-the-fly computation of volatile activity using UNIFAC, the approach is extensible to modelling transdermal permeation of volatiles from multicomponent/non-ideal formulations. Full article
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22 pages, 3319 KB  
Article
Study, Modelling and Computing of Pressure Losses in GH2 Pipelines
by Akshay Bambore, Patrick Hendrick and Jean Philippe Ponthot
Energies 2026, 19(4), 885; https://doi.org/10.3390/en19040885 - 8 Feb 2026
Viewed by 545
Abstract
The Wallonia region of Belgium aims to transition to a modern hydrogen infrastructure. Given the relatively low density of hydrogen gas, it is important to understand its nature and behavior during transport through pipelines. This study aims to observe the pressure loss in [...] Read more.
The Wallonia region of Belgium aims to transition to a modern hydrogen infrastructure. Given the relatively low density of hydrogen gas, it is important to understand its nature and behavior during transport through pipelines. This study aims to observe the pressure loss in pipelines due to surface roughness with H2 and other singular losses to find a solution to minimize the amount of pressure loss that occurs during transportation. This study involves numerical methods and gas equation models to determine the pressure loss. This analysis includes the properties of hydrogen gas, the pipeline material used, the friction factor, pipeline efficiency, and other relevant properties of hydrogen and pipelines. To address this challenge, the study integrates numerical fluid dynamics methods with structural modelling of pipeline walls. It accounts for long-term friction effects, erosion over several years, radial pressure gradients (mixing pressure drop), acceleration effects, and gravity influences, considering the non-ideal behavior of gaseous hydrogen (GH2). This study provides a systematic comparison between AGA-based analytical models and CFD simulations using a scaled pipeline approach, enabling reliable estimation of pressure losses in long-distance hydrogen pipelines. The proposed methodology integrates scaling, numerical validation, and CFD simulation to compute pressure losses in a hydrogen pipeline. Full article
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