Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (238)

Search Parameters:
Keywords = relaxation time approximation

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
29 pages, 1146 KB  
Article
Coupled Electro-Thermal Modeling of the Temperature Field in an Aluminum Reduction Cell Using the Finite Difference Method
by I. M. Novozhilov, A. N. Ilyushina and K. V. Martirosyan
Processes 2026, 14(8), 1284; https://doi.org/10.3390/pr14081284 - 17 Apr 2026
Viewed by 160
Abstract
The energy-intensive nature of primary aluminum production necessitates advanced computational tools for process optimization. This study presents a coupled electro-thermal model of an aluminum reduction cell, developed within the framework of smart manufacturing. Using the finite difference method (FDM) implemented in MATLAB R2025b, [...] Read more.
The energy-intensive nature of primary aluminum production necessitates advanced computational tools for process optimization. This study presents a coupled electro-thermal model of an aluminum reduction cell, developed within the framework of smart manufacturing. Using the finite difference method (FDM) implemented in MATLAB R2025b, the model resolves the three-dimensional configuration of a cell with eight prebaked anodes across four distinct physical domains (electrolyte, anodes, cathode, and gas phase). The computational grid comprises approximately 45,000 nodes with refined vertical resolution (Δz = 0.025 m) in the interelectrode gap. The electrostatic solution converges within 150–200 iterations using successive over-relaxation (SOR, ω = 1.5), with a total runtime under 15 min for 30,000 s of simulated physical time on a standard desktop workstation. Simulation results reveal characteristic temperature profiles with maxima reaching 1150 °C and a thermal uniformity index of approximately 130 °C across the central cross-section. The predicted specific energy consumption of 14.0 MWh/t Al aligns with industrial benchmarks. This computationally accessible virtual testbed enables rapid assessment of design modifications and process parameters, supporting the goals of energy efficiency and enhanced operational stability in primary aluminum production. Full article
(This article belongs to the Topic Digital Manufacturing Technology)
0 pages, 11680 KB  
Article
Adjustable ON-TIME Delay TI-ADC via Dual-Slope PWM and Four-Phase Binary Up/Down Counter
by Helgi Hafnar Gestsson, Helgi Thorbergsson, Kristinn Andersen and Runar Unnthorsson
Electronics 2026, 15(8), 1634; https://doi.org/10.3390/electronics15081634 - 14 Apr 2026
Viewed by 274
Abstract
Time-interleaved analog-to-digital converters (TI-ADC) are sensitive to inter-phase timing skew, which degrades effective resolution unless mitigated by careful phase alignment or calibration. This paper presents a low-speed proof-of-concept four-phase TI-ADC based on dual-slope pulse-width modulation, incorporating an adjustable ON-TIME delay mechanism at the [...] Read more.
Time-interleaved analog-to-digital converters (TI-ADC) are sensitive to inter-phase timing skew, which degrades effective resolution unless mitigated by careful phase alignment or calibration. This paper presents a low-speed proof-of-concept four-phase TI-ADC based on dual-slope pulse-width modulation, incorporating an adjustable ON-TIME delay mechanism at the analog front end. The proposed approach enables controlled shifting of the effective sampling instant at the comparator/D-flip-flop interface without altering waveform amplitude or functional linearity. A four-phase up/down binary counter implemented using a Gray-code-based phase multiplier provides evenly spaced phases with reduced switching activity. Measurements from a breadboard prototype operating at approximately 1.5 MHz demonstrate that the adjustable ON-TIME delay can align adjacent phases and constrain observed inter-phase timing skew to the order of approximately 30 ns within the measurement resolution. The results indicate that analog front-end phase pre-alignment can complement or relax subsequent digital background calibration in time-interleaved ADC systems. Full article
(This article belongs to the Special Issue Analog/Mixed Signal Integrated Circuit Design)
Show Figures

Figure 1

25 pages, 4504 KB  
Article
Discrete Element Modelling of Thermal Evolution of Forsmark Repository for Spent Nuclear Fuel Disposal and Long-Term Response of Discrete Fracture Network
by Jeoung Seok Yoon, Haimeng Shen, Arno Zang and Flavio Lanaro
Appl. Sci. 2026, 16(7), 3592; https://doi.org/10.3390/app16073592 - 7 Apr 2026
Viewed by 433
Abstract
Long-term safety assessment of deep geological repositories for spent nuclear fuel requires explicit evaluation of thermo-mechanical (TM) processes induced by decay heat and their influence on fractured host rock. A safety-relevant, though low-probability, scenario concerns shear reactivation of fractures intersecting deposition holes, which [...] Read more.
Long-term safety assessment of deep geological repositories for spent nuclear fuel requires explicit evaluation of thermo-mechanical (TM) processes induced by decay heat and their influence on fractured host rock. A safety-relevant, though low-probability, scenario concerns shear reactivation of fractures intersecting deposition holes, which could compromise canister integrity if displacement exceeds design limits. This study presents a three-dimensional discrete element modelling approach to analyze the thermal evolution of the Forsmark repository (Sweden) and the associated long-term response of a discrete fracture network (DFN) during the post-closure phase. The model explicitly represents repository panel, deterministic deformation zones, and a stochastically generated fracture network embedded in a bonded particle assembly representing the rock for Particle Flow Code (PFC) numerical simulations. Time-dependent heat release from spent nuclear fuel canisters is implemented using a physically based decay power function. A deposition panel-scale heat-loading formulation accounts for deposition-hole and tunnel spacing. Two emplacement scenarios are analyzed: (a) a simultaneous all-panel heating scenario, used as a conservative bounding case, and (b) a sequential panel heating scenario representing staged emplacement and closure. The simulations show that temperature and thermally induced stress evolution are sensitive to the emplacement and closure sequence. Sequential heating produces a more gradual thermal build-up and lower peak temperatures than simultaneous heating, indicating that thermal and stress perturbations in the host rock can be influenced not only through repository design, but also by operational strategy. Thermally induced fracture shear displacement displays a systematic temporal response. Fractures located within the deposition panel footprint develop shear displacement rapidly during the early post-closure period, reaching peak values at approximately 200 years, followed by gradual relaxation as temperatures decline. The average peak shear displacement on fractures is on the order of 2–3 mm, while fractures outside the panel footprint show smaller early-time displacements and a more prolonged long-term response. All simulated shear displacements remain more than one order of magnitude below the commonly cited canister damage threshold for Forsmark of approximately 50 mm, even for the conservative simultaneous heating case. These results indicate that thermally induced fracture shear is unlikely to cause direct mechanical damage to canisters. At the same time, the persistence of residual shear displacement after heating implies permanent fracture dilation, which may influence long-term hydraulic properties and indirectly affect processes such as groundwater flow and canister corrosion. The modelling framework and results presented here were conducted for review purposes independently from the Swedish safety case, and provide a mechanistic basis for evaluating thermally induced fracture deformation in crystalline rock repositories and contribute to bounding the role of thermo-mechanical processes in the safety assessment of spent nuclear fuel disposal at Forsmark. Full article
(This article belongs to the Special Issue Progress and Challenges of Rock Engineering)
Show Figures

Figure 1

26 pages, 13449 KB  
Article
Pipelined Space-Time Krylov Method with Preconditioning: A Parallel-in-Time Algorithm for Biot’s Quasi-Static Poroelasticity
by Guoliang Ju, Xin Xia, Zeyuan Zhou, Yan Gao, Huipeng Gu, Jiake Tian, Longfeng Nie, Xucong Wang and Wei Xing
Mathematics 2026, 14(7), 1177; https://doi.org/10.3390/math14071177 - 1 Apr 2026
Viewed by 235
Abstract
This paper presents a preconditioner-based parallel-in-time (PinT) method for solving the quasi-static Biot’s consolidation model in poroelasticity, a problem characterized by stiff coupling and saddle-point structures. To address the computational challenges of the resulting large-scale linear systems, we design two physics-based Schur-complement approximation [...] Read more.
This paper presents a preconditioner-based parallel-in-time (PinT) method for solving the quasi-static Biot’s consolidation model in poroelasticity, a problem characterized by stiff coupling and saddle-point structures. To address the computational challenges of the resulting large-scale linear systems, we design two physics-based Schur-complement approximation preconditioners that ensure robust Krylov convergence. Crucially, the method achieves a pipelined space-time architecture by introducing an inverted time-stepping mechanism: Instead of sequential time marching, time steps are traversed in the inner loop, while the outer loop applies an iterative solve across the entire space-time trajectory. This structure relaxes the strict dependency on fully converged solutions at each time step, enabling approximate solutions to be iteratively refined in parallel. Implemented as a pipelined wavefront scheme with strictly nearest-neighbor communication, the algorithm achieves strong scalability. Algorithmic verification conducted on systems with up to 200 thousand degrees of freedom demonstrates stable convergence and sustained strong scaling with up to 128 cores. The proposed approach maintains the accuracy of the underlying finite element discretization while alleviating the “time bottleneck,” making it highly effective for large-scale, long-duration poroelastic simulations. Full article
Show Figures

Figure 1

14 pages, 3785 KB  
Article
Topology-Induced Reduction in the Order–Disorder Transition in AB Block Copolymer: A Unit-Matched Comparison of Diblock, Multiblock, Comb, and Star Architectures
by June Huh
Polymers 2026, 18(7), 869; https://doi.org/10.3390/polym18070869 - 1 Apr 2026
Viewed by 390
Abstract
Chain topology offers a chemistry-preserving route to tune block copolymer (BCP) self-assembly by modifying intrachain correlations and relaxation pathways without changing monomer interactions. Here, we perform a unit-matched comparison of four lamella-forming AB architectures reconstructed from an identical constitutive diblock unit ( [...] Read more.
Chain topology offers a chemistry-preserving route to tune block copolymer (BCP) self-assembly by modifying intrachain correlations and relaxation pathways without changing monomer interactions. Here, we perform a unit-matched comparison of four lamella-forming AB architectures reconstructed from an identical constitutive diblock unit (N0): a linear diblock (DB), a linear multiblock (MB), a comb-like architecture (CB), and a star-like architecture (SB). Using dynamical density functional theory (DDFT), we quantify topology-dependent bulk ordering thresholds and show that architectural reconfiguration systematically stabilizes the ordered phase, reducing the order–disorder transition relative to DB (MB/CB/SB 0.793/0.762/0.752 of the diblock value), in semi-quantitative agreement with random phase approximation (RPA) spinodal trends. We also compare topology-dependent directed self-assembly in a common trench geometry under matched reduced quench depth Δ(χN0)=χN0(χN0)ODT, thereby isolating kinetic differences at comparable thermodynamic distance from bulk ordering. A Fourier-based alignment order parameter α(t) reveals sigmoidal alignment kinetics over decades in time and is well captured by a logistic form in lnt, enabling compact descriptors (t50, t90, and a steepness parameter k) that separate alignment onset from late-stage defect annihilation, while selective sidewalls robustly template sidewall-parallel lamellae across all topologies, the late-stage kinetics remain strongly connectivity dependent and can exhibit long-tailed completion associated with slow late-stage defect annihilation. These results demonstrate a dual role of topology in DSA: lowering the segregation strength required for bulk ordering while reshaping defect-mediated alignment pathways under confinement. Full article
Show Figures

Figure 1

13 pages, 2381 KB  
Article
Low-Frequency Time-Domain Response of Thin-Film Lithium Niobate Electro-Optic Modulator
by Run Li, Jinye Li, Zongyu Lu, Jiayu Huang, Qianqian Jia, Zichuan Xiang, Jinlong Xiao and Jianguo Liu
Photonics 2026, 13(4), 339; https://doi.org/10.3390/photonics13040339 - 31 Mar 2026
Viewed by 400
Abstract
Thin-film lithium niobate electro-optic modulators exhibit outstanding advantages such as large bandwidth, low insertion loss, and low half-wave voltage, demonstrating broad application prospects. However, due to internal defects in lithium niobate crystals, modulators exhibit electro-optic relaxation phenomena, with the relaxation time of thin-film [...] Read more.
Thin-film lithium niobate electro-optic modulators exhibit outstanding advantages such as large bandwidth, low insertion loss, and low half-wave voltage, demonstrating broad application prospects. However, due to internal defects in lithium niobate crystals, modulators exhibit electro-optic relaxation phenomena, with the relaxation time of thin-film structures being reduced by more than two orders of magnitude compared to bulk materials. In this study, we fitted and simulated the electro-optic relaxation behavior of thin-film lithium niobate modulators based on RC circuit model, effectively explaining their time-domain response characteristics under low-frequency conditions. By comparing thin-film modulators with and without silica cladding structures, the fitting results indicate that the relaxation time of modulators with cladding is approximately 11.9 ms, showing positive DC drift, whereas the relaxation time of modulators without cladding is significantly shortened to about 88.6 μs and exhibits negative DC drift. Additionally, the enhancement of optical intensity alters the photoconductivity of the material, thereby affecting its low-frequency electro-optic response behavior. This research provides important ideas for the design and optimization of next-generation integrated lithium niobate photonic modulators with high stability and controllability. Full article
Show Figures

Figure 1

19 pages, 4936 KB  
Article
Viscoelastic Properties of Porcine Pericardium Under Biaxial Tensile Creep and Stress Relaxation: Application for Novel Aortic Valve Bioprosthesis Design
by Edward Matjeka, Alex G. Kuchumov, Harry M. Ngwangwa, Thanyani Pandelani and Fulufhelo Nemavhola
Bioengineering 2026, 13(4), 401; https://doi.org/10.3390/bioengineering13040401 - 30 Mar 2026
Viewed by 457
Abstract
To design novel heart valve bioprostheses, it is extremely important to predict leaflet failure and fatigue for 10–20 years, as the aortic valve opens and closes approximately 40 million times per year. Most studies devoted to aortic valve leaflets mechanical tests employ uniaxial [...] Read more.
To design novel heart valve bioprostheses, it is extremely important to predict leaflet failure and fatigue for 10–20 years, as the aortic valve opens and closes approximately 40 million times per year. Most studies devoted to aortic valve leaflets mechanical tests employ uniaxial or biaxial tests, which do not fully and explicitly describe the time-dependent biomechanical behavior of this tissue. The aim of this study was to evaluate the viscoelastic response of porcine pericardium using biaxial tensile tests. Biaxial creep tests were performed on a biaxial test machine to evaluate the circumferential and axial behavior of the porcine pericardium under creep testing, and biaxial stress relaxation was used to complement creep. The results showed that the creep behavior was the same in both directions after 1 s, 60 s, 300 s, 900 s, and 1800 s. After 30 min of creep, deformation in the circumferential and radial directions was 3303 × 106 and 5192.9 × 106, respectively. Stress relaxation tests showed the same behavior as creep. At stress relaxation test after 30 min, the pericardium deformation in the circumferential and radial directions was 15.28 kPa and 9.6 kPa, respectively. The Prony series with Levenberg–Marquardt as the optimizer was used to obtain material parameters to use for finite element analysis. The data obtained during such tests can be employed in numerical FSI simulations of novel aortic valve bioprosthesis long-term performance in a patient’s body. Full article
Show Figures

Figure 1

16 pages, 6088 KB  
Article
Demonstration of Alpha-Band Entrainment via Low-Field Magnetic Stimulation: A Simulation-Driven Proof of Concept
by Costin Dămășaru, Georgiana Roșu, Leontin Tuță, Alexandra Cernian and Mihaela Rus
Bioengineering 2026, 13(4), 395; https://doi.org/10.3390/bioengineering13040395 - 29 Mar 2026
Viewed by 458
Abstract
Low-field magnetic stimulation (LFMS) has been proposed as a non-invasive approach for modulating cortical oscillations through electromagnetic coupling. Frequency-aligned enhancement of alpha-band activity is of interest due to its association with cortical inhibitory balance and relaxed wakefulness. This study investigates whether a 10 [...] Read more.
Low-field magnetic stimulation (LFMS) has been proposed as a non-invasive approach for modulating cortical oscillations through electromagnetic coupling. Frequency-aligned enhancement of alpha-band activity is of interest due to its association with cortical inhibitory balance and relaxed wakefulness. This study investigates whether a 10 Hz LFMS applied to the occipital area can induce measurable alpha-band modulation. Electromagnetic simulations were performed to determine magnetic flux distributions within a simplified spherical head model with magnetic susceptibility, which was approximating the brain’s parameters. The 10 Hz stimulation waveform—a positive ramp sawtooth—was analyzed in both time and frequency domains. Electroencephalographic (EEG) recordings were obtained before and after stimulation, and spectral analyses of relevant occipital channels were used to quantify the power redistributions. Simulations indicated localized magnetic field gradients in the occipital region. Post-stimulation EEG recordings showed a redistribution of spectral power toward the alpha-band, representing approximately 50% of total occipital spectral power, with relative increases exceeding 140% across the analyzed channels. These combined modeling and electrophysiological findings provide preliminary proof-of-concept evidence that frequency-aligned LFMS is associated with a redistribution of spectral power toward the alpha-band. Full article
(This article belongs to the Special Issue Wearable Devices for Neurotechnology)
Show Figures

Figure 1

12 pages, 1091 KB  
Article
Accelerated Cobalt-Catalyzed N-Methylation via Microwave-Induced Rapid Formation of Active Species Using Methanol and Methanol-d4
by Miki Takizawa, Takahiro Yamane, Akinobu Matsumoto, Takashi Miyazawa and Satoshi Horikoshi
Molecules 2026, 31(7), 1068; https://doi.org/10.3390/molecules31071068 - 24 Mar 2026
Viewed by 355
Abstract
The development of sustainable and environmentally benign N-methylation methodologies is essential for enhancing sustainable synthetic practice in pharmaceutical manufacturing. In this study, we demonstrate that microwave heating (MWH) markedly enhanced the efficiency of cobalt-catalyzed N-methylation using methanol or methanol-d4 [...] Read more.
The development of sustainable and environmentally benign N-methylation methodologies is essential for enhancing sustainable synthetic practice in pharmaceutical manufacturing. In this study, we demonstrate that microwave heating (MWH) markedly enhanced the efficiency of cobalt-catalyzed N-methylation using methanol or methanol-d4 as green C1 sources. Compared with conventional heating (CH), MWH enabled highly efficient syntheses of key pharmaceutical intermediates—including 6-dimethylamino-1-hexanol, imipramine hydrochloride, and butenafine hydrochloride—under milder conditions and shorter reaction times and without generating hazardous halogen-containing waste. UV–vis spectroscopic analysis revealed that MWH accelerated the transformation of Co(acac)2 into catalytically active Co species by approximately four-fold, providing a mechanistic basis for the enhanced reactivity. We hypothesized that this effect was caused by the selective microwave heating of the catalyst, which in turn promoted the rapid generation of catalytically active species. Notably, MWH also significantly improved the N-trideuteromethylation of amines using methanol-d4, achieving a 95% yield for imipramine-d3 hydrochloride versus 32% under CH. Molecular dynamics simulations indicated that methanol-d4 exhibited slower dipole relaxation and enhanced cluster fragmentation under microwave fields, improving catalyst–substrate contact, while kinetic isotope effects stabilized reactive intermediates. These synergistic effects account for the pronounced microwave promotion observed in deuterated systems. Overall, the combination of MWH and cobalt catalysis offers an energy-efficient, waste-minimizing, and environmentally benign strategy for the scalable synthesis of both methylated and deuterated amines. Full article
(This article belongs to the Special Issue Microwave-Assisted Synthesis and Extraction in Green Chemistry)
Show Figures

Figure 1

34 pages, 63807 KB  
Article
Research on Path Planning Methods and Characteristics of Urban Unmanned Aerial Vehicles Under Noise Constraints
by Yaqing Chen, Yunfei Jin, Xin He and Yumei Zhang
Drones 2026, 10(3), 227; https://doi.org/10.3390/drones10030227 - 23 Mar 2026
Viewed by 513
Abstract
This study proposes TNAP-DDQN, a deep reinforcement learning method for urban low-altitude UAV path planning under residential noise threshold constraints. With time cost and safety risk as the optimization objectives, operational constraints such as collision risk and maximum AGL altitude are incorporated to [...] Read more.
This study proposes TNAP-DDQN, a deep reinforcement learning method for urban low-altitude UAV path planning under residential noise threshold constraints. With time cost and safety risk as the optimization objectives, operational constraints such as collision risk and maximum AGL altitude are incorporated to achieve coordinated optimization of noise compliance, operational safety, and efficiency. To mitigate action space contraction and training instability induced by multiple constraints, a Noise-Degradation-Mask-based Action Bias Network (NDM-ABN) is introduced at the action selection layer. A three-tier degradation scheme prevents empty candidate sets, while bias-based decision making is applied to approximately tied actions to stabilize the policy. Moreover, multi-step prioritized experience replay (PER) improves sample efficiency and long-horizon return modeling, and potential-based reward shaping (PBRS) transforms sparse constraint signals into auxiliary rewards. Simulation results indicate that: (1) NDM-ABN is the key module for stabilizing the noise-exposure process by suppressing high-noise actions; (2) the required AGL is related to the UAV source noise level and local noise limits, implying the need for differentiated AGL altitude classes; and (3) the maximum admissible UAV source noise level increases as the threshold is relaxed. The proposed method provides quantitative guidance for noise-entry and AGL altitude regulation, while future work will incorporate additional metrics (e.g., A-weighted equivalent sound level) to better capture noise fluctuations and short-term peaks. Full article
(This article belongs to the Section Innovative Urban Mobility)
Show Figures

Figure 1

15 pages, 2078 KB  
Article
Influence of Red Seaweed Polysaccharides on Gel Properties and In Vitro Antioxidants of Surimi Product Fish Balls
by Menghan Ma, Tao Hong, Zhipeng Li, Yanbing Zhu, Yuanfan Yang, Hui Ni, Zedong Jiang and Mingjing Zheng
Foods 2026, 15(6), 1018; https://doi.org/10.3390/foods15061018 - 13 Mar 2026
Viewed by 349
Abstract
The effects of red seaweed polysaccharides, e.g., carrageenan, agar gum, Porphyra haitanensis polysaccharide (PHP), and Bangia fusco-purpurea polysaccharide (BFP), on the physicochemical properties and in vitro antioxidants of silver carp surimi gels were studied. Adding appropriate concentrations of carrageenan and agar gum increased [...] Read more.
The effects of red seaweed polysaccharides, e.g., carrageenan, agar gum, Porphyra haitanensis polysaccharide (PHP), and Bangia fusco-purpurea polysaccharide (BFP), on the physicochemical properties and in vitro antioxidants of silver carp surimi gels were studied. Adding appropriate concentrations of carrageenan and agar gum increased hydrophobic interactions, resulting in a denser and more uniform gel network as observed by SEM, and shortened the relaxation time of the fish balls, thus improving the gel strength and hardness of the products. When adding 0.75% carrageenan and 0.50% agar gum, the gel strength of the fish balls reached its maximum value, increasing by approximately 28.84% and 12.08%, respectively, compared to the control group (p < 0.05). However, with the over-addition of PHP and BFP, the cross-linking of surimi proteins was inhibited, resulting in a decrease in gel strength and hardness. In addition, red seaweed polysaccharide improved the free radical scavenging activity of fish balls, especially fish balls with 0.50% and 1.00% PHP and BFP exhibited better free radical scavenging activity after digestion. These findings offer insights and actionable strategies for enhancing the gel properties and function of surimi products with seaweed polysaccharides. Full article
(This article belongs to the Section Foods of Marine Origin)
Show Figures

Figure 1

12 pages, 268 KB  
Article
On Problems Solved in a Quasi-Linear Approximation
by Leon Kos and Davy D. Tskhakaya
Mathematics 2026, 14(6), 960; https://doi.org/10.3390/math14060960 - 12 Mar 2026
Viewed by 186
Abstract
The complete analytic solution of the time-dependent Vlasov–Boltzmann kinetic equation is used to describe selected problems in plasma physics within the framework of the quasi-linear approximation. These problems usually include the relaxation of plasma oscillations and the relaxation of beam instability. Our kinetic [...] Read more.
The complete analytic solution of the time-dependent Vlasov–Boltzmann kinetic equation is used to describe selected problems in plasma physics within the framework of the quasi-linear approximation. These problems usually include the relaxation of plasma oscillations and the relaxation of beam instability. Our kinetic equation is a first-order partial differential equation. The method of characteristics allows us to solve it analytically, while fully preserving the entire time dependence. Using the obtained analytic expression for the distribution function, the paper shows that the indicated relaxation processes do not occur in the approximation considered. Full article
(This article belongs to the Section E4: Mathematical Physics)
25 pages, 981 KB  
Article
Modeling the Timing of Trade Adjustment: A Piecewise Linear Trend Approach with Financial and Labor Frictions
by Jae Wook Jung
Mathematics 2026, 14(5), 858; https://doi.org/10.3390/math14050858 - 3 Mar 2026
Viewed by 306
Abstract
This paper studies the dynamic adjustment of bilateral trade following Economic Integration Agreements (EIAs) and examines how financial development and labor market rigidity moderate the timing of trade responses. We approximate the event time adjustment path using a Piecewise Linear Trend (PLT) specification [...] Read more.
This paper studies the dynamic adjustment of bilateral trade following Economic Integration Agreements (EIAs) and examines how financial development and labor market rigidity moderate the timing of trade responses. We approximate the event time adjustment path using a Piecewise Linear Trend (PLT) specification that relaxes global linearity restrictions common in dynamic gravity models. Event study evidence reveals heterogeneous pre-entry and post-entry slopes, particularly at the product-margin level. Split joint pre-trend tests show that aggregate trade satisfies long-run parallel trends, while product-level margins exhibit significant secular restructuring prior to implementation, motivating explicit slope parameterization. Within the PLT framework, financial development is associated with short-run anticipation effects, whereas labor rigidity corresponds to delayed post-entry adjustments. Industry-level interactions indicate that these dynamics vary systematically with sectoral characteristics. The results remain robust to zero-inclusive estimators, alternative institutional proxies, and alternative event time discretizations. Overall, the findings demonstrate that institutional conditions shape the temporal profile of trade adjustment and that flexible slope modeling is essential for identifying dynamic responses to trade liberalization. Full article
Show Figures

Figure 1

32 pages, 8198 KB  
Article
Study of Jeffrey Fluid Motion Through Irregular Porous Circular Microchannel Under the Implications of Electromagnetohydrodynamic and Surface Charge-Dependent Slip
by Serdi Dio Ranandrasana, Lijun Zhang, Muhammad Mubashir Bhatti and Marin Marin
Mathematics 2026, 14(4), 722; https://doi.org/10.3390/math14040722 - 19 Feb 2026
Cited by 1 | Viewed by 374
Abstract
This work analyzes the non-Newtonian electromagnetohydrodynamic (EMHD) flow in an irregular circular porous microchannel while incorporating the consequences of surface charge-dependent slip boundary conditions. The Jeffrey fluid is employed to examine the non-Newtonian behavior, such as elasticity. The boundary walls of the channel [...] Read more.
This work analyzes the non-Newtonian electromagnetohydrodynamic (EMHD) flow in an irregular circular porous microchannel while incorporating the consequences of surface charge-dependent slip boundary conditions. The Jeffrey fluid is employed to examine the non-Newtonian behavior, such as elasticity. The boundary walls of the channel are considered in the form of periodic sinusoidal wave function. The mathematical formulation is developed using the momentum equation, modified Darcy’s law, the continuity equation, and Ohm’s law. The perturbation method is used to derive the solutions up to second-order approximation. The analytical expression for the velocity field and volumetric flow rate are explicitly presented. At the zeroth-order, a nonhomogeneous partial differential equation is solved, and the solutions are presented in terms of Bessel functions. The first-order problem defined by a homogeneous partial differential equation is solved using the method of separation of variables. At the second-order, a homogeneous partial differential equation is obtained, and the solution form is prescribed by the boundary conditions, consisting of a radially varying mean component and a second-harmonic angular contribution. Two- and three-dimensional plots are used to analyze and discuss the impacts of key parameters, namely the Reynolds, Darcy, and Hartmann numbers, channel corrugation amplitude and wave number, surface charge density, and the relaxation and retardation times on the velocity field and flow rate. It is found that elastic memory causes a proportional growth between the flow rate and the relaxation time, emphasizing the consequences of surface charge application in conjunction with corrugations. Conversely, maintaining a short retardation time mitigates changes in wave amplitude and surface charge. While prolonging it lessens the flow rate and diminishes corrugations and surface charge effects. The Darcy number dampens the velocity and the flow rate, while its enhancement reduces the impact of surface charge density and corrugations amplitude. For high Reynolds number, a ring phenomenon emerges which is attenuated by increased Darcy number, preventing the formation of trapped boluses close to the border. Ignoring surface charge amplifies the flow rate while its consideration diminishes the latter with reinforced impacts of surface charge and wall corrugations at higher Reynolds number. Full article
(This article belongs to the Special Issue Research on Applied Partial Differential Equations)
Show Figures

Figure 1

15 pages, 24087 KB  
Article
Effect of Regularization on Efficient Modeling and Simulation of Bioinspired Composites Using Cohesive Zone Method
by Md Jalal Uddin Rumi and Xiaowei Zeng
Biomimetics 2026, 11(2), 139; https://doi.org/10.3390/biomimetics11020139 - 12 Feb 2026
Viewed by 488
Abstract
Tessellation-based polyhedral microstructures derived from Voronoi and Laguerre constructions provide a realistic geometric foundation for modeling bioinspired organic–inorganic composites with interfacial fracture. However, even after extensive centroidal relaxation, such tessellations retain numerous lower-dimensional geometric degeneracies—very short edges and small or sliver-like faces—that severely [...] Read more.
Tessellation-based polyhedral microstructures derived from Voronoi and Laguerre constructions provide a realistic geometric foundation for modeling bioinspired organic–inorganic composites with interfacial fracture. However, even after extensive centroidal relaxation, such tessellations retain numerous lower-dimensional geometric degeneracies—very short edges and small or sliver-like faces—that severely hinder volumetric meshing and render large-scale cohesive-zone simulations computationally impractical. In this work, we employ a geometric regularization step that enforces a minimum admissible feature length prior to meshing and systematically quantify its impact on downstream performance in finite element discretization and cohesive fracture simulation. By eliminating geometric features below the prescribed length scale while preserving grain topology and morphology, the regularized tessellations exhibit sharply improved edge-length and face-diameter distributions and become readily meshable at practical resolutions. When applied to a 3D bioinspired organic–inorganic composite with cohesive interfaces, the regularized geometry reduces volumetric and cohesive element counts nearly fivefold and increases the explicit stable time increment by approximately four orders of magnitude, transforming an otherwise diverging analysis into a robust simulation that converges to the prescribed deformation. These results demonstrate that the prescribed geometric regularization step is not merely a preprocessing refinement but a critical enabling step for efficient and large-scale cohesive fracture simulations of tessellation-based bioinspired composites. Full article
(This article belongs to the Special Issue Biomimicry and Functional Materials: 5th Edition)
Show Figures

Figure 1

Back to TopTop