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14 pages, 7940 KB  
Article
Design, Synthesis, and Performance of Heme-Derived Carbon Towards Electrocatalytic Oxygen Reduction Reaction
by Jiatong Li, Qiming Sun, Tianyi Zhang, Jicheng Ma, Dehua Li and Shuangxi Xing
Chemistry 2026, 8(6), 83; https://doi.org/10.3390/chemistry8060083 (registering DOI) - 15 Jun 2026
Abstract
The development of highly efficient, stable, and cost-effective non-precious metal electrocatalysts to replace conventional platinum-based materials holds profound significance for accelerating the commercialization of advanced energy conversion devices, such as zinc–air batteries (ZABs). Herein, we propose a facile and highly efficient strategy to [...] Read more.
The development of highly efficient, stable, and cost-effective non-precious metal electrocatalysts to replace conventional platinum-based materials holds profound significance for accelerating the commercialization of advanced energy conversion devices, such as zinc–air batteries (ZABs). Herein, we propose a facile and highly efficient strategy to prepare a defect-rich, highly active nitrogen-doped porous carbon-based electrocatalyst (denoted U-Fe-N-C, urea-assisted iron–nitrogen–carbon material), via high-temperature co-pyrolysis of heme with urea. Our results demonstrate that urea not only serves as an excellent nitrogen source during pyrolysis, introducing abundant topological defects and heteroatom doping sites, but also induces the carbon substrate to form a hierarchical sponge-like porous structure with a high specific surface area. This unique microenvironment effectively prevents the agglomeration of iron species at high temperatures, achieving enhanced dispersion of iron species stabilized within the nitrogen-rich carbon matrix. Electrochemical evaluations reveal that under the optimal synthesis conditions (a precursor mass ratio of 1:3, calcination at 900 °C), U-Fe-N-C exhibits excellent oxygen reduction reaction (ORR) catalytic performance, delivering a half-wave potential of 0.731 V vs. RHE, and shows long-term operational durability that significantly surpasses that of commercial Pt/C. Furthermore, liquid rechargeable zinc–air batteries assembled with U-Fe-N-C as the air cathode deliver remarkable cycling stability, operating for up to 270 h of charge–discharge cycling without noticeable performance degradation. This study not only provides useful insights into the mechanisms of pore formation and assistance but also offers a practical perspective for the rational design and scalable synthesis of high-performance metal–nitrogen–carbon (M-N-C) electrocatalysts. Full article
(This article belongs to the Special Issue Catalytic Conversion of Biomass and Its Derivatives)
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29 pages, 3497 KB  
Review
Numerical Simulation for Natural Gas and Hydrogen-Blended Natural Gas Pipeline Safety: A Comprehensive Analysis of the “Leakage–Dispersion–Evolution–Consequence” Disaster Chain
by Bingyuan Hong, Ting Pan, Huizhong Xu, Fubin Wang, Xingyu Wang, Siyan Hong, Zhenglong Li, Zhanghua Yin and Zhipeng Yu
Processes 2026, 14(12), 1939; https://doi.org/10.3390/pr14121939 (registering DOI) - 13 Jun 2026
Abstract
Against the backdrop of global energy transition and the widespread adoption of Hydrogen-Blended Natural Gas (HBNG), the safety of urban gas pipeline networks faces severe challenges. This paper systematically reviews the research progress of numerical simulation in the field of natural gas pipeline [...] Read more.
Against the backdrop of global energy transition and the widespread adoption of Hydrogen-Blended Natural Gas (HBNG), the safety of urban gas pipeline networks faces severe challenges. This paper systematically reviews the research progress of numerical simulation in the field of natural gas pipeline safety, focusing on its core supporting roles throughout the “Leakage–Dispersion–Evolution–Consequence” disaster chain. First, it analyzes the kinetic modeling of high-pressure leakage holes and property corrections based on real gas equations of state, elaborating on the numerical characterization of HBNG multi-component transport. Second, it compares the dispersion mechanisms and environmental coupling modeling methods in typical scenarios such as buried porous media, confined spaces in utility tunnels, underwater environments, and urban building clusters. Third, it reviews leakage monitoring technologies based on physical field simulation and data-driven approaches (e.g., Convolutional Neural Network, Long Short-Term Memory), emphasizing the value of numerical simulation in constructing digital twin training sets. Furthermore, it explores the dynamic evolution of explosion flame–shock wave interactions and the evaluation models for secondary disaster consequences. Finally, the current research status of grid-based risk pre-warning and emergency response strategies is summarized. In conclusion, numerical simulation is not only a robust method for precisely quantifying and characterizing complex physical mechanisms but also a critical technological foundation for building smart and resilient energy cities. Future research should focus on the deep coupling of multi-physics fields, physics-informed learning, and the development of system-level integrated defense systems. Full article
17 pages, 15286 KB  
Article
Diverse Bacterial Properties Influence Dispersal Along Fungal Networks
by Roberto Regalado, Mariana Santos Craveiro Silva, Euan Price, Nai-Wen Liang, Caroline M. Grunenwald, John-Demian Sauer, David J. Beebe and Nancy P. Keller
J. Fungi 2026, 12(6), 425; https://doi.org/10.3390/jof12060425 - 11 Jun 2026
Viewed by 188
Abstract
Bacterial–fungal interactions are prevalent in microbial communities, and fungi often facilitate bacterial dispersal along networks created by fungal hyphae. Using a microfluidic device, we examined how diverse bacterial species disperse in monoculture versus travel in coculture with Aspergillus flavus. Most of the [...] Read more.
Bacterial–fungal interactions are prevalent in microbial communities, and fungi often facilitate bacterial dispersal along networks created by fungal hyphae. Using a microfluidic device, we examined how diverse bacterial species disperse in monoculture versus travel in coculture with Aspergillus flavus. Most of the bacteria traveled further when in coculture, although this was not absolute. Two bacteria showing significant dispersal rates only in coculture were the human pathogens Listeria monocytogenes and Staphylococcus aureus. Mechanistically, L. monocytogenes dispersal required flagella, with dispersal impaired in flagellar mutants but enhanced in ∆mogR strains that upregulate flagellar expression. In contrast, the non-flagellar bacterium S. aureus exhibited a unique, wave-like dispersal pattern along the hyphae, a phenomenon that was abolished in agr quorum-sensing mutants deficient in phenol-soluble modulins (PSMs). In a triculture of L. monocytogenes, S. aureus, and A. flavus, L. monocytogenes limited S. aureus dispersal along the fungal hyphae; however, this inhibition was dependent on an intact L. monocytogenes quorum system. Our findings reveal that bacterial motility on fungal networks arises from diverse, species-specific mechanisms, including flagella, transcriptional regulation, potential quorum-sensing-mediated interactions, as well as other notable dispersal phenomena that warrant further investigation. Full article
(This article belongs to the Section Fungal Genomics, Genetics and Molecular Biology)
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27 pages, 2030 KB  
Article
Waveform-Level EMT Analysis of Overhead–Cable Transition Effects in Hybrid Transmission Corridors
by Luis Salazar Fonseca, Josua Oña Aráuz, José Oscullo Lala, Nathaly Orozco Garzón, Henry Carvajal Mora, José Vega-Sánchez and Takaaki Ohishi
Energies 2026, 19(12), 2795; https://doi.org/10.3390/en19122795 - 10 Jun 2026
Viewed by 192
Abstract
Hybrid transmission corridors combining overhead lines and underground cables introduce impedance discontinuities that significantly modify electromagnetic transient behavior. These discontinuities generate traveling-wave reflections, waveform distortions, and high-frequency components at relay measurement locations during the first microseconds following disturbance inception. This paper presents a [...] Read more.
Hybrid transmission corridors combining overhead lines and underground cables introduce impedance discontinuities that significantly modify electromagnetic transient behavior. These discontinuities generate traveling-wave reflections, waveform distortions, and high-frequency components at relay measurement locations during the first microseconds following disturbance inception. This paper presents a waveform-level electromagnetic transient (EMT) analysis of overhead–cable transition effects using detailed EMTP-RV simulations including frequency-dependent line and cable models, tower representations, grounding systems, and instrument transformers within a differential protection measurement framework. The results show that overhead–cable transitions produce transient waveform modifications characterized by reflections, attenuation, dispersion, and temporary current imbalance mechanisms associated with traveling-wave propagation and cable capacitive effects. The analysis also demonstrates the transient evolution of instantaneous waveform-derived (EMT-derived) differential and restraining current quantities, defined as combinations of terminal current signals obtained directly from EMT waveforms. These quantities do not represent final phasor-domain operating values of practical numerical relays, but provide insight into the transient electromagnetic environment preceding conventional filtering and phasor estimation. The study contributes to a clearer physical interpretation of transient phenomena in hybrid transmission systems and supports EMT-based evaluation of signals relevant to differential protection applications. Full article
(This article belongs to the Special Issue Energy, Electrical and Power Engineering: 5th Edition)
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17 pages, 4213 KB  
Article
Modified Luneburg Lens: How Well Does It Focus Surface Water Waves?
by H. Pichard, A. Maurel, P. A. Martin, P. Petitjeans and V. Pagneux
Fluids 2026, 11(6), 145; https://doi.org/10.3390/fluids11060145 - 9 Jun 2026
Viewed by 190
Abstract
An optical lens focuses light and a similar device can be developed to focus surface water waves. A detailed description of such hydrodynamic lenses is given, for which the focusing is induced by shaping the bathymetry of the bottom. Classically, the Luneburg lens [...] Read more.
An optical lens focuses light and a similar device can be developed to focus surface water waves. A detailed description of such hydrodynamic lenses is given, for which the focusing is induced by shaping the bathymetry of the bottom. Classically, the Luneburg lens uses a specific radial variation of the refractive index. The modified Luneburg lens (MLL) introduces an extra degree of freedom, permitting the focal point to be tuned. It is shown how to design the MLL for water waves, and then its performance is evaluated. Compared with a simple parabolic-shaped mount, the MLL is shown to be free of spherical aberration, resulting in a focus with larger intensity and smaller size of the focal point. Moreover, the focusing properties can be tuned and enhanced thanks to the possibility of changing the position of the focal point. The focusing quality of the MLL is described in all water-depth regimes (covering dispersive and non-dispersive waves) and the focusing of linear and nonlinear waves is revealed experimentally. The option of moving the focal point outside the lens, where the water depth is constant, may be useful when locating devices for harvesting wave energy. Full article
(This article belongs to the Special Issue Multiphase Flow for Industry Applications, 2nd Edition)
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17 pages, 7461 KB  
Article
Investigation of the Formation Mechanism and Propagation Characteristics of Gliding Waves in the Coal Seam Floor
by Tianzhu Duan, Jingcun Yu and Huricha Wang
Appl. Sci. 2026, 16(12), 5798; https://doi.org/10.3390/app16125798 - 9 Jun 2026
Viewed by 205
Abstract
With the transition to deep coal mining, the transparent detection of hidden geological hazards in the floor strata is fundamental for production safety. In mine seismic exploration, gliding waves—inhomogeneous plane waves propagating along the coal–rock interface—offer a unique advantage for penetrating high-velocity floors [...] Read more.
With the transition to deep coal mining, the transparent detection of hidden geological hazards in the floor strata is fundamental for production safety. In mine seismic exploration, gliding waves—inhomogeneous plane waves propagating along the coal–rock interface—offer a unique advantage for penetrating high-velocity floors via the skin effect, overcoming the total reflection limitations of conventional in-seam waves. This study investigates the propagation laws and anomaly response characteristics of floor gliding waves using super-critical incidence theory and high-order staggered-grid finite difference simulations. The results demonstrate that the apparent velocities of gliding P and S-waves are bounded by those of the coal and host rock, exhibiting minimal dispersion. Quantitative analysis using a penetration depth model reveals that while penetration depth is frequency-dependent—with lower frequencies providing deeper reach—high-frequency components remain essential for high-resolution imaging. Crucially, the proposed method was validated through a field Case Study at the 11123 working face. By utilizing a specialized deep-hole excitation strategy to ensure super-critical incidence, the inversion successfully identified a hidden fault extending up to 60 m below the floor, which was subsequently confirmed by rock roadway excavation. These findings establish a robust physical basis for designing underground floor-detection systems and provide a significant theoretical reference for addressing detection blind spots in deep mining environments. Full article
(This article belongs to the Special Issue Exploration Geophysics and Seismic Surveying)
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18 pages, 3512 KB  
Article
Compact GCPW–SSPP Low-Pass Filter with Wide Stopband and Suppressed Radiation Using Multi-Arm Star-Shaped Slots
by Zhengzheng Ding and Lin Li
Electronics 2026, 15(12), 2513; https://doi.org/10.3390/electronics15122513 - 7 Jun 2026
Viewed by 161
Abstract
Existing ground-slotted coplanar waveguide (CPW) spoof surface plasmon polariton (SSPP) low-pass filters (LPFs) remain constrained by the difficulty of achieving a wide stopband while maintaining a compact size, as well as by undesired radiation leakage arising from their open-aperture slot configuration. To address [...] Read more.
Existing ground-slotted coplanar waveguide (CPW) spoof surface plasmon polariton (SSPP) low-pass filters (LPFs) remain constrained by the difficulty of achieving a wide stopband while maintaining a compact size, as well as by undesired radiation leakage arising from their open-aperture slot configuration. To address these issues, a grounded coplanar waveguide spoof surface plasmon polariton (GCPW-SSPP) low-pass filter based on a multi-arm star-shaped slot (MASS) loading topology is proposed. An equivalent-circuit interpretation and full-wave dispersion analysis show that the multi-arm slots introduce enhanced distributed reactive loading, thereby lowering the asymptotic frequency and enabling compact SSPP implementations. The near-field characteristics further demonstrate tighter electromagnetic confinement, as reflected by an approximately 48% reduction in the electric-field confinement width along the z-direction. To alleviate the trade-off between miniaturization and wide-stopband performance in cascaded SSPP LPFs, the single-cell S-parameters of the proposed topology are investigated. A single MASS unit exhibits a sharp cutoff and a deep transmission notch, allowing a wide stopband to be obtained with fewer cascaded cells. Radiation characteristics are subsequently quantified by a loss-decomposition method, and the MASS topology is found to suppress the radiation leakage of open-aperture ground-slotted structures, yielding a maximum radiation-loss reduction of approximately 75%. To validate the design methodology, a MASS-loaded GCPW-SSPP LPF is designed, fabricated, and measured. The measured results are in good agreement with the simulated ones, confirming the effectiveness of the proposed scheme. By simultaneously achieving a wide stopband, compact size, and suppressed radiation leakage, the proposed filter offers a promising low-interference filtering solution for highly integrated microwave and RF front-end systems. Full article
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24 pages, 475 KB  
Article
Memory-Kernel Damping in Wave Propagation from a Variational Reservoir Model: Dispersion, Stability, and Fractional Regimes
by Derik W. Gryczak, Gabriel G. da Rocha, Aloisi Somer, Luiz R. Evangelista and Ervin K. Lenzi
Fractal Fract. 2026, 10(6), 390; https://doi.org/10.3390/fractalfract10060390 - 5 Jun 2026
Viewed by 149
Abstract
Hereditary damping and fractional attenuation are widely used to model wave propagation in complex media, but the variational and spectral origin of the corresponding nonlocal-in-time operators is often left implicit. In this work, we derive such operators from a minimal conservative field–reservoir model. [...] Read more.
Hereditary damping and fractional attenuation are widely used to model wave propagation in complex media, but the variational and spectral origin of the corresponding nonlocal-in-time operators is often left implicit. In this work, we derive such operators from a minimal conservative field–reservoir model. A real scalar field is coupled locally to a continuum of harmonic reservoir modes, which are then eliminated exactly. The resulting reduced dynamics is a causal wave equation with a memory-friction term acting on the field velocity. The memory kernel is generated by the reservoir coupling spectrum through a cosine-transform relation, establishing a direct spectrum-to-kernel correspondence. This relation provides both a physical interpretation of hereditary damping and a practical admissibility criterion: macroscopic attenuation and dispersion arise from the delayed back-action of unresolved internal modes, while physically admissible kernels are constrained by the non-negativity of the underlying spectral density. The framework unifies several standard damping regimes. A broadband reservoir recovers the Markovian locally damped wave equation, reservoirs with a finite characteristic time generate finite-memory relaxation and frequency-dependent dispersion, and scale-free reservoir spectra produce power-law memory kernels. In the latter case, the hereditary damping operator reduces to a Caputo-type fractional derivative, showing that fractional wave attenuation can emerge as an effective reduced dynamics rather than being postulated phenomenologically. We further analyze dispersion, attenuation, causality, stability, and admissibility conditions in terms of the reservoir spectrum. The main contribution of the work is therefore to provide a variational and spectral derivation of hereditary and fractional wave damping, linking the structure of unresolved reservoir modes to macroscopic nonlocal wave dynamics. Full article
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21 pages, 3207 KB  
Article
Exploring Qualitative Analysis and Interaction Dynamics in a (3+1)-Dimensional Boussinesq Equation II via Hirota Bilinear Method
by Ali Danladi, Aljethi Reem Abdullah, Ejaz Hussain and Beenish
Mathematics 2026, 14(11), 1981; https://doi.org/10.3390/math14111981 - 3 Jun 2026
Viewed by 161
Abstract
In this work, we explore the nonlinear wave phenomena of the (3+1)-dimensional Boussinesq (II) equation, a significantly higher-dimensional model that describes dispersive wave propagation in fluid dynamics, plasma systems, and nonlinear optics. Using exact analytic and qualitative dynamic approaches, we study a wide [...] Read more.
In this work, we explore the nonlinear wave phenomena of the (3+1)-dimensional Boussinesq (II) equation, a significantly higher-dimensional model that describes dispersive wave propagation in fluid dynamics, plasma systems, and nonlinear optics. Using exact analytic and qualitative dynamic approaches, we study a wide range of solutions and stability characteristics of the model. Initially, we use the Hirota bilinear method to obtain a number of exact solutions, such as breather waves, two-wave interaction solutions, and other types of localized nonlinear waves. These solutions display remarkable physical properties, including periodic energy trapping, oscillatory modulations, and nonlinear wave interactions in higher dimensions. In addition, the (m+1G)-expansion method is used to derive new soliton solutions, such as bright solitary waves and W-shaped solitons, which are found to be stable and undergo pulse-shaping dynamics under certain conditions. Three-dimensional, two-dimensional, and contour plots are displayed for some of the solutions to demonstrate the physical significance of the results. The visualizations reveal the presence of localized waves, wave interactions, periodical breathing, and stable soliton profiles. Furthermore, we conduct modulation instability analysis to describe the conditions under which small perturbations of continuous wave backgrounds are unstable. The dispersion relation and the instability gain spectrum are obtained, which explain the formation of breathers, soliton trains, and other coherent structures. Furthermore, a Galilean transformation converts the governing equation into a planar nonlinear dynamical system, enabling its qualitative study. The Hamiltonian structure is revealed, and the fixed points are identified as centers, saddles, and cusps through bifurcation analysis. To investigate more complex dynamics, a periodic forcing term is introduced into the system, resulting in chaos in the forced system. The chaotic behavior is confirmed via phase portraits, three-dimensional attractors, time series, Poincaré sections, return maps, fractal dimension, and positive Lyapunov exponents. We also perform a sensitivity test to show the effect of initial condition variations on the system’s long-term dynamics. The findings greatly expand the exact solution set and dynamics of the (3+1)-dimensional Boussinesq equation (II). The analytical approach presented in this paper can also be applied to other multidimensional nonlinear evolution equations of mathematical physics. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)
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25 pages, 2644 KB  
Review
Compact Finite Difference Schemes: A Review of Fundamentals, Applications, and Practical Implementation
by Andrea Arroyo Ramo, J. Alberto Conejero, María Jezabel Perez-Quiles and Sergio Hoyas
Mathematics 2026, 14(11), 1958; https://doi.org/10.3390/math14111958 - 3 Jun 2026
Viewed by 331
Abstract
Compact finite difference schemes approximate spatial derivatives through implicit relations between neighboring grid points. Despite using compact stencils and relatively simple algebraic structures, these schemes achieve high-order accuracy and spectral-like resolution, reducing dispersion errors while maintaining low numerical dissipation. These properties make them [...] Read more.
Compact finite difference schemes approximate spatial derivatives through implicit relations between neighboring grid points. Despite using compact stencils and relatively simple algebraic structures, these schemes achieve high-order accuracy and spectral-like resolution, reducing dispersion errors while maintaining low numerical dissipation. These properties make them particularly attractive for problems requiring accurate spatial derivatives and computational efficiency, such as wave propagation, aeroacoustics, and turbulent flow simulations. This review presents the main ideas behind compact finite difference schemes, including their derivation from Taylor expansions and Padé approximations, their accuracy properties, and their resolution characteristics through modified wavenumber analysis. The manuscript is intended as a review and practical synthesis, rather than as the proposal of a new numerical scheme, and aims to connect the theoretical construction of compact schemes with their numerical behavior, practical implementation, and representative applications. To support reproducibility, we provide a fully documented open-source Python 3.11 notebook with a reference implementation of the schemes discussed in the paper. The examples include first- and second-order derivative calculations and representative one- and two-dimensional boundary-value problems, including Helmholtz-type equations. Finally, we survey applications across computational fluid dynamics, acoustics, geophysical flows, structural mechanics, biology, electromagnetism, and quantitative finance. Full article
(This article belongs to the Special Issue Differential Equations Applied in Fluid Dynamics)
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19 pages, 4289 KB  
Article
Internal Layered Reaction Front in 2.5D C/SiC Composites Under Continuous-Wave Laser Ablation: Identification and Thermal-Field Interpretation
by Chuntong Liu, Renke Wang, Yuwei Lv and Yubin Shi
Materials 2026, 19(11), 2377; https://doi.org/10.3390/ma19112377 - 3 Jun 2026
Viewed by 202
Abstract
The ablation behavior of 2.5D C/SiC composites under continuous-wave laser irradiation involves not only surface material removal but also internal structural degradation. In this study, laser ablation tests were conducted at power densities of 400, 800, and 1600 W/cm2, and the [...] Read more.
The ablation behavior of 2.5D C/SiC composites under continuous-wave laser irradiation involves not only surface material removal but also internal structural degradation. In this study, laser ablation tests were conducted at power densities of 400, 800, and 1600 W/cm2, and the ablated specimens were analyzed by macroscopic observation, infrared thermography, X-ray micro-computed tomography (micro-CT), cross-sectional scanning electron microscopy/energy-dispersive X-ray spectroscopy (SEM/EDS), depth measurement, and homogeneous thermal-field simulation. The results show that the surface morphology evolved from a transition-zone-dominated response to a typical zoned morphology consisting of a central ablation zone, transition zone, and edge zone as the power density and irradiation time increased. Under the present temperature measurement conditions, the surface transition zone corresponded to an apparent temperature window of approximately 2300–2700 K. Cross-sectional characterization further revealed a distinguishable internal reaction front beneath the external ablation surface, above which microstructural damage and Si depletion were observed. Depth measurements showed that the external ablation depth underestimated the actual degradation depth along the thickness direction. The calibrated homogeneous thermal-field model indicated that the internal front position corresponded to a relatively stable temperature range, suggesting that its formation was mainly governed by local thermal history and matrix-related reactions. The proposed internal reaction front provides a supplementary parameter for evaluating laser-induced subsurface degradation in 2.5D C/SiC composites. Full article
(This article belongs to the Section Advanced Composites)
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19 pages, 3279 KB  
Article
Exploring Bifurcation Analysis, Conservation Laws and Soliton Dynamics for the Dual-Mode Nonlinear Schrödinger Equation with Applications
by Muhammad Arshad, Naila Nasreen, Evren Hincal, Mohamed Hafez and Muhammad Farman
Math. Comput. Appl. 2026, 31(3), 97; https://doi.org/10.3390/mca31030097 - 2 Jun 2026
Viewed by 197
Abstract
This study examines the dynamical behavior of the dual-mode nonlinear Schrödinger equation (d-mNLSE), which describes the interaction, amplification, and attenuation of two coexisting wave modes in nonlinear media. The model incorporates key physical parameters including the nonlinearity coefficient, interaction phase velocity, and dispersion [...] Read more.
This study examines the dynamical behavior of the dual-mode nonlinear Schrödinger equation (d-mNLSE), which describes the interaction, amplification, and attenuation of two coexisting wave modes in nonlinear media. The model incorporates key physical parameters including the nonlinearity coefficient, interaction phase velocity, and dispersion parameter, which significantly influence the evolution of nonlinear waves. By applying the modified Sardar sub-equation method (mSS-EM), a wide spectrum of exact analytical solutions is derived. These solutions include mixed trigonometric waves, shock-type structures, singular solutions, complex dark–bright solitons, multi-peak solitons, periodic and mixed-periodic waves, as well as mixed hyperbolic structures. The analytical findings provide useful insight into nonlinear wave propagation phenomena arising in fluid mechanics, water wave dynamics, ocean engineering, and related physical systems. Moreover, the conservation laws of the d-mNLSE are established, which leads to the conserved quantities of impulse power, momentum, and energy and describes the invariant characteristics of the soliton solutions during their propagation. The bifurcation analysis of the reduced dynamical model is carried out to explore the qualitative characteristics of the obtained solutions. The equilibrium points of the considered model are calculated, and their stability properties are analyzed systematically. To demonstrate the physical characteristics of the obtained solutions, different kinds of two-dimensional, three-dimensional, and contour plots are plotted using symbolic computations software. These findings confirm that the analytical method used to obtain the soliton solutions can be used to obtain a variety of soliton solutions of nonlinear evolution equations that appear in applied sciences and engineering. Full article
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11 pages, 8471 KB  
Article
Multiparametric Ultrasound Assessment of Long-Term Liver Damage in COVID-19: Results of a Three-Year Follow-Up Study
by Maija Radzina, Davis Simanis Putrins, Ieva Vanaga, Oksana Kolesova, Arvids Buss, Aija Agera and Ludmila Viksna
Medicina 2026, 62(6), 1077; https://doi.org/10.3390/medicina62061077 - 2 Jun 2026
Viewed by 211
Abstract
Background: Liver damage in COVID-19 is multifaceted, including liver steatosis and inflammation. Multiparametric ultrasound (mpUS) is an imaging modality that has the capacity to evaluate various facets of overall liver health and is relatively accessible and thus is an excellent choice to determine [...] Read more.
Background: Liver damage in COVID-19 is multifaceted, including liver steatosis and inflammation. Multiparametric ultrasound (mpUS) is an imaging modality that has the capacity to evaluate various facets of overall liver health and is relatively accessible and thus is an excellent choice to determine parenchymal changes. Methods: A longitudinal prospective study was designed to evaluate long-term hepatic damage following COVID-19 using mpUS. Patients were assessed within a 3–6-month period after the initial episode of COVID-19 and subsequently had a follow-up after 3 years compared to a control group. Liver stiffness (2D-SWE), attenuation (ATI), and shear wave dispersion (SWD) were measured to quantify liver stiffness, steatosis, and tissue viscosity. Results: A total of 129 patients were scanned at the baseline assessment, 90 patients in research group (58 patients had a follow-up) and 39 as a clinically healthy control group, and all were included in the follow-up for evaluation after 3 years. The mpUS evaluation in research group revealed a median SWE decrease from 5.04 ± 1.74 kPa to 4.59 ± 0.81 kPa and SWD decrease from 11.88 ± 1.73 m/s/kHz to 10.83 ± 1.49 m/s/kHz (p > 0.05); in contrast, median ATI values showed slight increase over time—0.56 ± 0.09 dB/cm/MHz to 0.60 ± 0.09 dB/cm/MHz (p > 0.05). Control group was stratified according to subsequent COVID-19 status. In both the COVID-negative and -positive subgroups SWE slightly increased from initial 4.55 ± 0.78 kPa to 4.8 ± 0.88 kPa and 4.7 ± 1.29 kPa, median SWD had a slight decrease from initial 10.80 ± 1.73 m/s/kHz to 10.15 ± 1.87 m/s/kHz and 10.6 ± 1.82 m/s/kHz (p > 0.05), and ATI increased significantly from initial 0.57 ± 0.08 dB/cm/MHz to 0.62 ± 0.09 dB/cm/MHz and 0.65 ± 0.07 dB/cm/MHz (p < 0.05), respectively. Conclusions: The study found that initially COVID-19-affected patients showed stable ATI and BMI values, no hepatic steatosis, normal SWE, and reduced dispersion which suggests resolving inflammation without fibrosis. Controls showed increased ATI and mild steatosis, likely linked to BMI and metabolic changes rather than direct viral liver injury. Full article
(This article belongs to the Section Gastroenterology & Hepatology)
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16 pages, 31148 KB  
Article
Pt Catalysts Supported on Ni-N-Doped Carbon Nanotubes for Oxygen Reduction Reaction
by Shuyue Xia, Yilin Yuan, Qinghong Huang and Yuping Wu
Materials 2026, 19(11), 2331; https://doi.org/10.3390/ma19112331 - 1 Jun 2026
Viewed by 200
Abstract
This study aimed to develop high-performance, ultra-low Pt-loading 2.1 wt% vs. 20 wt% for commercial Pt/C) oxygen reduction reaction (ORR) catalysts. Utilizing carbon nanotubes (CNTs) as templates, a PANI layer was coated onto the surface to serve as a nitrogen-doped anchoring layer for [...] Read more.
This study aimed to develop high-performance, ultra-low Pt-loading 2.1 wt% vs. 20 wt% for commercial Pt/C) oxygen reduction reaction (ORR) catalysts. Utilizing carbon nanotubes (CNTs) as templates, a PANI layer was coated onto the surface to serve as a nitrogen-doped anchoring layer for metal species. Physical and structural characterizations demonstrated that the PANI-derived nitrogen-doped carbon layer uniformly encapsulates the CNT skeleton. This architecture not only achieved highly uniform Pt nanoparticle dispersion but also induced strong metal–support electronic interactions via deep-seated Ni atoms, effectively optimizing the electronic structure of the surface Pt. Electrochemical results showed that Pt/Ni-N-CNT delivers superior ORR activity in an acidic electrolyte, with a half-wave potential of 0.846 V (vs. RHE) and limiting diffusion current density outperforming commercial Pt/C (0.81 V vs. RHE), demonstrating excellent oxygen reduction kinetics. Full article
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21 pages, 2957 KB  
Article
PSO-Based Multimodal Inversion of Rayleigh-Wave Dispersion Curves for the Geotechnical Characterization of an Embankment Profile
by Meho Saša Kovačević, Mario Gazdek, Lovorka Librić and Danijela Jurić Kaćunić
Geotechnics 2026, 6(2), 54; https://doi.org/10.3390/geotechnics6020054 - 1 Jun 2026
Viewed by 154
Abstract
Reliable assessment of small-strain soil stiffness is essential for geotechnical site characterization and for analysing the behaviour of embankments and other earth structures. Surface-wave methods provide an efficient non-destructive means of estimating shear-wave velocity profiles; however, their application is limited by the non-uniqueness [...] Read more.
Reliable assessment of small-strain soil stiffness is essential for geotechnical site characterization and for analysing the behaviour of embankments and other earth structures. Surface-wave methods provide an efficient non-destructive means of estimating shear-wave velocity profiles; however, their application is limited by the non-uniqueness of the inversion process. This paper implements and evaluates a PSO-based multimodal inversion framework for Rayleigh-wave dispersion curves in the context of geotechnical characterization of layered soil profiles. The procedure involves the calculation of theoretical dispersion curves for a horizontally layered medium and their matching with experimental data through a global search scheme. The implemented framework was first evaluated using two synthetic soil profiles, and its robustness was further assessed by considering perturbations of the theoretical dispersion curve of up to 10%. Particular attention was given to the influence of higher modes on the inversion results. The results indicate that including higher modes can improve the determination of shear-wave velocity profiles for the analysed cases compared with an inversion based solely on the fundamental mode. The procedure was subsequently validated on a transverse embankment profile using an experimental dispersion curve obtained by multichannel analysis of surface waves (MASW), with comparison against seismic cone penetration test (SCPT) results. Good agreement was obtained, and the eight-layer model proved to be a good compromise between accuracy and model complexity. The results indicate that the implemented PSO-based multimodal inversion framework can support the geotechnical characterization of layered soil profiles for the analysed synthetic and field cases, particularly when modal branches are clearly identified and appropriately included in the inversion. Full article
(This article belongs to the Topic Advanced Risk Assessment in Geotechnical Engineering)
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