Time-dependent Stability Research Articles

Embolism propagation does not rely on pressure only: time-based shifts in xylem vulnerability curves of angiosperms determine the accuracy of the flow-centrifuge method.

Centrifuges provide a fast approach to quantify embolism resistance of xylem in vulnerability curves (VCs). Since embolism formation is assumingly driven by pressure only, spin time is not standardised for flow centrifuge experiments. Here, we explore to what extent embolism resistance could be spin-time dependent, and hypothesise that changes in hydraulic conductivity (Kh) would shift VCs towards higher water potential (Ψ) values over time. We quantified time-based shifts in flow-centrifuge VCs and their parameter estimations for six angiosperm species by measuring Kh over 15minutes of spinning at a particular speed, before a higher speed was applied to the same sample. We compared various VCs per sample based on cumulative spin time, and modelled the relationship between Kh, Ψ, and spin-time. Time-based changes of Kh showed considerable increases and decreases at low and high centrifuge speeds, respectively, which generally shifted VCs towards more positive Ψ values. Values corresponding to 50% loss of hydraulic conductivity (P50) became less negative by up to 0.72MPa in Acer pseudoplatanus, and on average by 8.5% for all six species compared to VCs that did not consider spin-time. By employing an asymptotic exponential model, we estimated time-stable Kh, which improved the statistical significance of VCs in 5 of the 6 species studied. This model also revealed the instability of VCs at short spin times with embolism formation in flow-centrifuges following a saturating exponential growth curve. Although pressure remains the major determinant of embolism formation, spin-time should be considered in flow-centrifuge VCs because not considering the time-dependent stability of Kh overestimates embolism resistance. This spin-time artefact is species-specific, and likely based on relatively slow gas diffusion that is associated with embolism propagation. The accuracy of VCs is improved by determining time-stable Kh values for each centrifuge speed, without considerably extending the experimental time to construct VCs.

Biogenic PAG-FeNPs from Prunus armeniaca (Gum) as robust colorimetric sensors for methyl orange detection

Biogenic synthesis of nanoparticles is an emerging research area of the scientific community holding versatile and potential applications. The nanoscaled iron nanoparticles (FeNPs) have unique chemical and physical properties. Beside the available physical and chemical methods, the aqueous extract of the Prunus armeniaca Gum (PAG) was employed to promote a green and sustainable approach for the synthesis of FeNPs. The structure and morphology of the FeNPs were characterized by SEM, FTIR, and XRD techniques. And UV–Vis spectrophotometry is employed to study optical properties, time, temperature, and pH dependent stability. Herein PAG-FeNPs has been employed as efficient and cost-effective colorimetric probe for the sensing of methyl orange (MO) for the first time displaying a color change from light orange to dark voilet on exposure to MO. The selectivity of the detection method for MO against various interferences including heavy metals, and organic dyes was examined and sensor’s signal remained unaffected by common interferences. Under ideal detection conditions, the proposed method demonstrates an excellent linear correlation (R2 = 0.992) in the concentration range of 10–350 µM methyl orange. The limits of detection and limit of quantification are 13 µM and 40 µM, respectively. Moreover, the technique has been successfully employed for detecting methyl orange in self-contaminated tape water samples.

Unraveling time-dependent roof stability dynamics in Iran's coal mines through laboratory-based rock displacement testing

Roof stability is a critical concern in coal mines, as the potential for roof collapse poses a significant risk to miners' safety and productivity. Roof stability is heavily influenced by the time-dependent properties of the rock mass above the workings. This study uses rock displacement testing to examine the effect of time-dependent properties on roof stability and resistance reduction in coal mines in Iran. The study employed laboratory-based rock displacement tests on samples collected from coal mines in Iran, subjected to varying stress levels over time, to simulate the gradual deterioration of rock mass strength in underground mining conditions. The samples were monitored for displacement under these conditions to quantify the reduction in roof resistance over time and assess its effect on roof stability. The study found that areas with high stress at equilibrium gradually fail with time, and the stress transfers from the failure zone into deeper solid rock. The results demonstrate that varying viscous parameters can lead to different relaxation behaviors and stress distribution. Furthermore, incorporating strength degradation into numerical simulation can capture the failure under creep conditions and improve the accuracy of predicting time-dependent roof failure. This research aims to enhance safety measures and reduce the risk of collapses by investigating the time-dependent properties of roof stability through rock displacement testing in Iran's coal mines. The study's innovative approach uses numerical simulation based on the viscoelastic-plastic model to simulate the time-dependent behavior of the rock and incorporate strength degradation into the simulation. The results provide valuable insights into the time-dependent behavior of rock mass in coal mines in Iran and contribute to developing strategies for improving roof stability and lessening the chance of roof collapses. The instantaneous elastic strain was 4.35 × 10–4, and creep simulation was activated to run for a time equivalent to 2 × 106 s.

Isolation, identification and characterization of neopullulanase from Thermomonas hydrothermalis GKE 08

The production of neopullulanase from thermophiles, such as Thermomonas hydrothermalis GKE 08, holds paramount significance due to the enzyme's unique thermophilic nature. Harnessing this characteristic ensures enhanced stability and functionality at elevated temperatures, a crucial aspect for industrial processes demanding efficient catalysis under extreme conditions. The investigation into pullulanase from T. hydrothermalis GKE 08 revealed significant findings. Optimal conditions for enzyme production were determined, with peak activity observed in the presence of 1.5% soluble pullulan and 0.5% peptone. The study delved into the pH and temperature dynamics, identifying an optimal pH of 7 and peak activity at 55 °C. Notably, the neopullulanase exhibited time-dependent stability, retaining 72% activity after 1 hour but declining to 50% after 2 hours. Furthermore, the enzyme displayed remarkable thermostability at 60 °C, with 88% activity after 30 minutes. Metal ion studies indicated susceptibility to inhibition by Cu2+, Mg2+, and Zn2+, while Ca2+ stimulated activity up to 138% at higher concentrations. The enzyme's response to specific reagents revealed sensitivity to SDS and EDTA, while urea surprisingly enhanced activity to 85%. The study enhances understanding of pullulanase behavior, offering valuable insights for biotechnological and industrial applications.

Rock bolt and frame support of mine workings with a compound cross-section: Collective refuge chambers for mine workers

Purpose is to study the influence of mining and geological conditions on the time-dependent stability of the collective refuge chamber for mine workers with the adjacent mine workings and develop support schemes for different conditions of construction of such mine workings. Methods. Numerical modelling methods of the connected processes of elastoplastic deformation of gas-bearing rocks and gas filtration within the area disturbed during mining operations were used to study stability of mine workings with a compound cross-section, i.e. the collective refuge chambers and its adjacent extraction gallery. The model was based on fundamental principles of solid mechanics and filtration theory. The problem was solved using a finite element method. Findings. A classification of the conditions for locating collective refuge chambers for mine workers according to the relative strength of the enclosing rocks was developed. Support schemes for the chamber and its adjacent mine working were elaborated. The schemes include basic support and provide for its strengthening with rock bolts located in the roof of the mine working and chamber, or in their walls. The compliance of these support schemes with the developed classification of location conditions was determined. A numerical study of the time-dependent stability of the chamber and its adjacent mine working, while applying the recommended support scheme, was performed. It is shown that the strengthening of rock bolting schemes reduces the multicomponent stress field and the area of the zone of inelastic deformations, forms a rock-bolt overlap in the roof of the mine workings and chambers, which helps increase their stability under the complicated mining and geological conditions. Originality. Dependence of the changes within the area of a zone of inelastic deformations around the chamber with its adjacent mine working on the relative strength of the enclosing rocks was identified; time-dependent changes within the area of the zone of inelastic deformations, when using different support types, were specified. Practical implications. Support schemes for collective rescue chambers for mine workers in terms of different construction conditions were developed along with the procedure of their selection for specific mining and geological conditions. The results of the study provide theoretical substantiation and scientific guidelines for the selection of supports for collective refuge chambers adjacent to the mine working.

Effect of swab and surge pressure on the time-dependent wellbore natural fracture development

Drilling engineers continue to grapple with the persistent challenge of maintaining wellbore stability. Throughout the drilling process, the wellbore pressure experiences fluctuations induced by various factors such as swab and surge pressure, leading to potential instability. This study employs a numerical approach, utilizing Abaqus software, to investigate the impact of swab and surge pressure on the natural fracture growth within the wellbore and the evolving pore pressure. A computational tool developed with MATLAB is then utilized to ascertain a safe operational mud window by assessing the time-dependent collapse and fracture pressures. The findings illustrated a notable increase in fracture width as a function of time in response to swab and surge pressure, with the most significant percentage increase reaching 69.92%. Notably, a 69.16% augmentation in fracture width is observed in the immediate vicinity of the wellbore following the application of swab and surge pressure. However, parameters such as fracture length, loss circulation rate, and pore fluid pressure exhibited marginal changes post-integration of swab and surge effects. The examination of the time-dependent wellbore stability after integration of swab and surge pressure indicated a narrowing of the initial mud window as a function of time, with a 14.33% increase in collapse pressure and a 13.80% decrease in fracture pressure. The numerical model verification against analytical solutions demonstrated good agreement, highlighting its potential utility in optimizing particle size for wellbore reinforcement and mitigating lost circulation through natural fracture sealing.

Biopolymer-assisted stable halloysite nanotubes dispersion in alkaline environment and their application in cementitious composite

The colloidal dispersion of biopolymer-treated HNTs in the cementitious environment was studied. Three different biopolymer treatments, namely casein (C), guar gum (GG), and xanthan gum (XG), were utilized to prepare the stable colloidal dispersions of HNTs in such environments. The examination of the dispersion and time-dependent stability of untreated HNTs in a synthetic pore solution (SPS) revealed rapid agglomeration and settling of the particles. Specifically, the stabilization of XG-treated HNTs was superior compared to those treated with GG and C biopolymers. XG-treated HNT suspension in the pH 13 environment existed as monodisperse nanoparticles centered around 20 nm, while bare HNTs existed as polydisperse across 200 nm to 7000 nm. Moreover, XG-treated HNTs boosted cement mortar samples, increasing compressive strength by 29.4 % and reducing initial and final water absorption by 15.8 % and 19.9 %, respectively, after 90 days. Furthermore, the microstructural morphology of the HNT-XG-modified mortar exhibited improved compactness and homogeneity.

Review of the creep constitutive models for rocks and the application of creep analysis in geomechanics

AbstractThe creep behavior of rocks has been broadly researched because of its extensive application in geomechanics. Since the time-dependent stability of underground constructions is a critical aspect of geotechnical engineering, a comprehensive understanding of the creep behavior of rocks plays a pivotal role in ensuring the safety of such structures. Various factors, including stress level, temperature, rock damage, water content, rock anisotropy, etc., can influence rocks’ creep characteristics. One of the main topics in the creep analysis of rocks is the constitutive models, which can be categorized into empirical, component, and mechanism-based models. In this research, the previously proposed creep models were reviewed, and their main characteristics were discussed. The effectiveness of the models in simulating the accelerated phase of rock creep was evaluated by comparing their performance with the creep test results of different types of rocks. The application of rock’s creep analysis in different engineering projects and adopting appropriate creep properties for rock mass were also examined. The primary limitation associated with empirical and classical component models lies in their challenges when it comes to modeling the tertiary phase of rock creep. The mechanism-based models have demonstrated success in effectively simulating the complete creep phases; nevertheless, additional validation is crucial to establish their broader applicability. However, further investigation is still required to develop creep models specific to rock mass. In this paper, we attempted to review and discuss the most recent studies in creep analysis of rocks that can be used by researchers conducting creep analysis in geomechanics.

Investigating the influence of excitation force on compaction behavior of gravel in granular blends through DEM simulation

During the construction of subgrades, the compaction of granular blends is typically achieved through vibrational techniques at varying the frequencies and excitation forces. This study investigates the impact of excitation forces, within the range of 300-600 kPa, on subgrade compaction by employing the discrete element method (DEM). Calibration tests were conducted to establish the contact parameters for the DEM models, and their reliability was verified via vibration compaction tests. The research further explores the evolution of settlement, particle motion, and contact interactions at both macroscopic and mesoscopic levels as influenced by the excitation forces. Furthermore, the influence of excitation force on the stability of skeleton frameworks was analyzed. The results indicated that the number of contacts in the final state increased consistently with the excitation force, leading to a more uniform distribution. This change contributes to a time-dependent stability within the skeleton framework, which effectively limits the movement of fine particles in the final stages and diminishes the sliding between the coarse particles. Conversely, in the initial phases, a rise in excitation force increases the stress concentration between the contacts, which increases the sliding damage to the skeleton frameworks and leads to greater compaction deformation.

Ligand engineering for improving the stability and optical properties of CsPbI3 perovskite nanocrystals

Inorganic lead halide perovskite nanocrystals (NCs) have recently become one of the research topics for optoelectronic applications due to their excellent photophysical properties. Despite their notable thermal stability over organic-inorganic halide perovskites, CsPbI3 NCs suffer from the phase instability of α-CsPbI3 phase at room temperature and under ambient conditions. Here, the effects of 4-Hydroxybenzoic acid (4-HBA) as an additive to standard oleic acid – oleylamine pair on the stability and optical properties of CsPbI3 perovskite NCs are discussed. 4-HBA addition into perovskite NC systems causes a compressive strain on perovskite lattice, which leads to the formation of a mixed phase α- and γ-CsPbI3 phases while pristine perovskite has α-CsPbI3 phase. Time-dependent stability of the perovskite NCs was tested under an ethanol (EtOH) medium. After EtOH exposure of the perovskite NCs, CsPbI3 NCs transformed to non-perovskite phase in 1 h while 4-HBA added CsPbI3 NCs still have perovskite phase after 48 h. In addition to the improved optical properties of the perovskite NCs, 4-HBA addition remarkably improves CsPbI3 perovskite stability.

Bovine serum albumin uptake and polypeptide disaggregation studies of hypoglycemic ruthenium(II) uracil Schiff-base complexes

Our prior studies have illustrated that the uracil ruthenium(II) diimino complex, [Ru(H3ucp)Cl(PPh3)] (1) (H4ucp = 2,6-bis-((6-amino-1,3-dimethyluracilimino)methylene)pyridine) displayed high hypoglycemic effects in diet-induced diabetic rats. To rationalize the anti-diabetic effects of 1, three new derivatives have been prepared, cis-[Ru(bpy)2(urdp)]Cl2 (2) (urdp = 2,6-bis-((uracilimino)methylene)pyridine), trans-[RuCl2(PPh3)(urdp)] (3), and cis-[Ru(bpy)2(H4ucp)](PF6)2 (4). Various physicochemical techniques were utilized to characterize the structures of the novel ruthenium compounds. Prior to biomolecular interactions or in vitro studies, the stabilities of 1–4 were monitored in anhydrous DMSO, aqueous phosphate buffer containing 2% DMSO, and dichloromethane (DCM) via UV–Vis spectrophotometry. Time-dependent stability studies showed ligand exchange between DMSO nucleophiles and chloride co-ligands of 1 and 3, which was suppressed in the presence of an excess amount of chloride ions. In addition, the metal complexes 1 and 3 are stable in both DCM and an aqueous phosphate buffer containing 2% DMSO. In the case of compounds 2 and 4 with no chloride co-ligands within their coordination spheres, high stability in aqueous phosphate buffer containing 2% DMSO was observed. Fluorescence emission titrations of the individual ruthenium compounds with bovine serum albumin (BSA) showed that the metal compounds interact non-discriminately within the protein's hydrophobic cavities as moderate to strong binders. The metal complexes were capable of disintegrating mature amylin amyloid fibrils. In vivo glucose metabolism studies in liver (Chang) cell lines confirmed enhanced glucose metabolism as evidenced by the increased glucose utilization and glycogen synthesis in liver cell lines in the presence of complexes 2–4.

Development and Characterization of Plant-derived Aristatoside C and Davisianoside B Saponin-loaded Phytosomes with Suppressed Hemolytic Activity.

Saponins are glycosides widely distributed in the plant kingdom and have many pharmacological activities. However, their tendency to bind to cell membranes can cause cell rupture, limiting their clinical use. In the previous study, aristatoside C and davisianoside B were isolated from Cephalaria species. Cytotoxicity assays showed that they are more active on A-549 cell lines than doxorubicin but caused hemolysis. In the current research, aristatoside C and davisianoside B were loaded to phytosomes called ALPs and DLPs respectively, and characterized for particle size, zeta potential, encapsulation efficiency, release kinetic, hemolytic activity, and cytotoxicity on A-549 cell line. DLPs maintained the cytotoxic activity of the free saponins against A-549 cells with IC50 of 9,64±0,02 μg/ml but dramatically reduced their hemolytic activity. Furthermore, temperature and time-dependent stability studies based on the size and zeta potential of ALPs and DLPs revealed that the phytosomes have sustained release properties over 2 weeks. Overall, DLPs displayed cytotoxicity against A-549 cells with minimal hemolysis and sustained release, highlighting their potential as nanotherapeutics for clinical applications.

Development of a Space Grease Lubricant with Long-Term-Storage Properties

Controlled vacuum environments as in space applications represent a challenge for the lubrication of tribological components. In addition to common space lubricant requirements like, e.g., low evaporation, a broad operational temperature range and a high stability during operation, long-term-storage (LTS) properties have gained increasing attention recently. The term addresses the time-dependent stability of a lubricant under static conditions, which can mean chemical degradation processes such as oxidation on the one hand, but also the physical separation of oil and thickener in heterogeneous lubricants like greases. Due to the extended storage periods of lubricated components on-ground but also during a space mission for several years, it has to be ensured that a lubricant is still functional after LTS. This article depicts the development of a space lubricant grease with LTS properties. Firstly, LTS requirements and methods for their assessment are discussed. In the following, a systematic approach towards the design of a grease formulation compatible with LTS is described. Finally, the manufacturing of prototype formulations and their broad characterization by means of LTS behaviour, outgassing, and tribological performance is presented.

Gold-Deposited Graphene Nanosheets for Self-Cleaning Graphene Surface-Enhanced Raman Spectroscopy with Superior Charge-Transfer Contribution.

The interaction of graphene with metals initiates charge-transfer interaction-induced chemical enhancements, which critically depend on the doping effect from deposited metallic configurations. In this paper, we have explored the gold nanoparticle-decorated monolayer graphene nanosheets for the large graphene-induced Raman enhancement of adsorbed analytes, indicating the surface-enhanced Raman spectroscopy (SERS) capabilities of metal-doped graphene (G-SERS). Here, the systematically sputtered Au thickness optimization procedure revealed noticeable modifications in the graphene Raman spectra and photoluminescence (PL) background quenching, which indicated favorable charge transfer through n-type doping of chemical vapor deposition-grown graphene nanosheets. The highly consistent, individually distributed morphology of the gold nanoislands over graphene nanosheets depicted a reproducibly uniform G-SERS signal with excellent relative standard deviation values (<5%), resulting in the strongest Raman intensity enhancement factors of ∼108 (MB) (methylene blue) and 107 (DPA) (2,6-pyridinedicarboxylic acid) composed of the weakest PL background. The combined charge-transfer-induced chemical enhancement and electromagnetic enhancement from individual Au nanoislands result in a lowering of detectability down to 10-16 M (MB) and 10-11 M (DPA) concentrations with efficient time-dependent signal stability. Additionally, the GAu demonstrated its effective (∼94.4%) photocatalytic degradation capabilities by decomposing MB dye molecules from a concentration of 1 μM to 2.52 fM within 60 min. Therefore, the prominent charge-transfer contribution through controlled Au decoration over graphene nanosheets provides a potential strategy for fabricating superior SERS sensors and photocatalysts exhibiting adequate signal consistency, stability, and photodegradation efficiency through overcoming the limitations of the traditional sensing platforms.

Experimental switching between coexisting attractors in the yoke-bell-clapper system.

This paper presents experimental switching between two attractors in the swinging bell. In the considered yoke-bell-clapper system, two coexisting solutions appear. In the first one, we observe a single impact between the bell and the clapper per one period of motion, and in the second solution, no impacts occur-no sound is produced. Based on the time-dependent stability margin method, we numerically detect parts of the trajectories where the system is most prone to perturbations. Using this knowledge, we experimentally investigate switching between attractors by applying the perturbation to the clapper. We show that we can easily enforce the change of attractor by properly timing the perturbation. The results prove that, based on the results from the time-dependent stability margin numerical method, we are able to effectively alter the wrong operation of the bell (lack of impact) to the correct operation (solution with impact). The analysis is conducted on the real-world mechanical system rather than paradigmatic examples. Therefore, it contributes to the subject of multistability and nonlinearity in engineering design. Novel, recently developed methods for analyzing multistable systems are successfully employed during the investigation. The paper shows that a complex phenomenon of multistability observed in the system, which is considered simple and undemanding from an engineering design point of view.

Gradient and Lie Bracket Estimation of Extremum Seeking Systems: A Novel Geometric-based Kalman Filter and Relaxed Time-dependent Stability Condition

Gradient and Lie Bracket Estimation of Extremum Seeking Systems: A Novel Geometric-based Kalman Filter and Relaxed Time-dependent Stability Condition

Strength degradation of argillaceous sandstone induced by relaxation behaviour

The underground engineering time-dependent stability is affected by the surrounding rock combination behaviors of creep and relaxation. A series of triaxial relaxation tests under 10–30 MPa confining pressure was conducted on argillaceous sandstone to investigate the relaxation-induced strength degradation. Based on tested data, an empirical equation is proposed to describe the rock strength degradation quantitatively. The rock strength after relaxation is approximately 67–83 % of the instant strength. While the rock strength after the creep process is only about 40 ∼ 60 % of its instant strength, the results indicate the rock strength degradation induced by relaxation is much lower than that of creep behavior.

Arrhenius activation energy effect in thermally viscous dissipative flow of micropolar material with gyrotactic microorganisms

The rheology of micropolar material with heat energy transport features is fully progressive, which allows considerable industrial and engineering applications. In this study, numerical analysis is presented to examine the micro-rotation characteristics of magnetized micropolar fluid flow towards the stagnation point region on a porous shrinking surface with gyrotactic microorganisms. To describe the convective energy transport features, Arrehenius activation energy, thermal radiation, Ohmic, and viscous dissipation effects are taken into consideration. The governing equations are converted into ordinary differential equations using appropriate similarity variables. The physical features of flow constraints are displayed and explained for velocity, thermal and solutal distributions, microorganism profile, as well as friction drag, couple stress, and energy transport rate. The results revealed that suction strength contributes to the increment of friction drag, couple stress, and energy transport rate, but the boosted values of the micropolar parameter lower the values of these physical quantities. For a specific range of the shrinking parameter, analysis confirmed the persistence of non-uniqueness solutions. Further, the microorganism profile declines as the bioconvection Lewis number and the bioconvection Peclet number increases. Additionally, according to time-dependent stability analysis, only the upper branch of solutions is physically stable, while the lower branch is not physically.

Investigation of carrot/squid blends as edible inks for extrusion 3D printing: Effect of hydrocolloids incorporation

Extrusion-based food printing is an emerging technology that enables the creation of personalized food products in terms of shapes and designs while satisfying individual nutritional and sensory requirements. The present study focused on the optimization of carrot- and squid-based ink formulations for extrusion-based three-dimensional (3D) printing while systematically investigating the impacts of varying hydrocolloids on the water retention, rheological characteristics, and printing performance of the inks. Of the ten food hydrocolloids, xanthan gum (XG) and alginate had the greatest effect on preventing water syneresis in the inks. Moreover, the inks supplemented with hydrocolloids exhibited proper shear-thinning behavior, softer network strength, and lower yield stress than the control ink. Three-interval thixotropy (3ITT) test results also revealed an enhanced solid-like character after nonlinear deformation in the inks with XG, alginate, or high-methoxyl (HM) pectin addition. Finally, 3D printing assessment showed that only the addition of XG or alginate allowed smooth extrusion and precise filament stacking into the predefined geometry, which was attributed to the homogeneity of the inks resulting from their superior water-holding capacity. 3D constructs fabricated using XG-added ink achieved time-dependent structural stability, whereas alginate addition caused slight filament sagging owing to insufficient self-supporting ability. Collectively, XG was found to be the best additive for carrot/squid-based printing, providing useful suggestions for future investigations on determining the 3D/4D printing and post-printing processes of carrot or squid powder-based nutritious inks.

Investigation of the time dependent gate dielectric stability in SiC MOSFETs with planar and trench gate structures

In this work, the time-dependent dielectric breakdown (TDDB) analysis is performed to understand the gate oxide reliability in SiC MOSFETs with two different structures, i.e., planar and trench gate structures. We have discovered different gate leakage current behaviors between the SiC MOSFETs with planar gate (Sample A) and trench gate (Sample B) during the forward gate bias stress. Notably, the slight increase of the gate current during the stress and the negative activation energy (Ea = −0.07 eV) observed in Sample A suggest that the hole generation caused by the impact ionization can be occurred during the forward gate TDDB tests. Furthermore, the SiC MOSFETs with trench gate structure (Sample B) exhibit the operation voltage of 55.7 V (exponential law) and 57.3 V (power law) for the 0.001 % failure of 30 years under 175 °C, indicating that SiC trench gate MOSFETs with enough thick gate dielectric (87.1 nm (bottom) and 77.9 nm (sidewall)) can have the promising forward gate TDDB stability.