Search Results (50)

To enhance the assessment accuracy of tunnel face instability risks of active collapse during shield tunneling, this study establishes a novel unified analytical framework that couples the effects of unsaturated transient seepage induced by excavation drainage with soil stratification and heterogeneity. Grounded in unsaturated effective stress theory, the framework explicitly incorporates matric suction into the Mohr–Coulomb failure criterion via suction stress and apparent cohesion. By employing a horizontal two-layer nonhomogeneous soil model and solving the one-dimensional vertical Richards’ equation, an analytical solution for the face drainage boundary is derived to quantify the spatiotemporal evolution of suction stress and apparent cohesion. Subsequently, the critical support pressure is evaluated using the upper bound theorem of limit analysis, incorporating a horizontal layer-discretized rotational failure mechanism and the power balance equation. The validity of the proposed framework is confirmed through comparative analyses. Parametric studies reveal that in the upper hard and lower soft strata, the critical support pressure decreases and converges over time, indicating that unsaturated transient seepage exerts a significant influence in the short term that stabilizes over the long term. Additionally, sand–silt stratum exhibits lower overall stability and higher sensitivity to groundwater levels and temporal factors compared to silt–clay stratum. Conversely, silt–clay stratum displays a non-monotonic evolution with increasing cover-to-diameter ratios ($C/D$), reaching a minimum critical support pressure at approximately $C/D=1.1$. Regarding heterogeneity, the internal friction angle of the lower layer exerts dominant control over the critical support pressure compared to seepage velocity, while the influence of other strength parameters remains secondary. These findings provide a theoretical basis for the time-dependent design of tunnel face support pressure under excavation drainage conditions. Full article

Developing classical three-dimensional consolidation theories considers the small-strain assumption. This small-strain assumption is inappropriate when studying the consolidation process of soft or very soft clay layers. Instead, this study derives a novel generalized mathematical model describing a three-dimensional finite-strain consolidation process and applies the deep Galerkin method to deduce its novel numerical solution. Developing this mathematical model uses the Reynolds transport theorem to describe mass and momentum balances for clay grain and pore water phases. The governing equation is the sum of the resulting mass and momentum balance equations. Next, the deep Galerkin method is applied to train a deep neural network to minimize the loss function defined by the governing equation and available initial and boundary conditions. The unknowns are the average velocity, effective stress, and pore water pressure. Predicting consolidation settlements is implemented by updating the problem domain using the resulting average velocity. Beneficial from the deep Galerkin method, two real-world examples demonstrate that the current mathematical model provides accurate predictions of consolidation settlements caused by the self-weight of two very soft clay layers. The deep Galerkin method helps resolve ill-posed problems by fitting a family of fields constrained by sampling/regularization rather than physics if the physics is under-determined. Full article

In this paper, the vibration of a wheel running on a light rail equipped with rail dampers that use a mixed damping system (rubber–oil) is investigated under the excitation of random roughness on the rolling surfaces, to demonstrate the influence of such rail dampers on the dynamic behaviour at the wheel–rail interface. For this purpose, a model is adopted in which a rigid wheel moves at constant speed over a rail modelled as an infinite Timoshenko beam, supported by elastic foundations with an internal degree of freedom that represents the behaviour of the rail pads, sleepers, and ballast. The rail dampers are represented as two-mass oscillators, while the internal friction in the elastic components of the wheel–rail system is modelled using hysteretic damping. To obtain the time series of the rail and wheel displacements, as well as the wheel–rail contact force, the convolution theorem is applied in a heuristic manner, making use of the relationship between Green’s functions in the time and frequency domains through direct and inverse Fourier transforms. The results show that (a) rail dampers primarily affect rail dynamics and the wheel–rail contact force over a relatively wide frequency range, while having little influence on wheel motion; (b) rail dampers are highly effective in reducing rail vibration and the wheel–rail contact force when the rail pads are stiff, but considerably less effective when soft rail pads are used; and (c) they may slightly amplify the contact force at the lower edge of their effective frequency range. Full article

The soft-reset process, or a sequence of charge emissions from a floating storage node through a transistor biased in a subthreshold bias condition, is modeled by a master (Kolmogorov–Bateman) equation. The Coulomb interaction energy after each one-charge emission leads to a stepwise potential increase, giving correlated emission rates represented by Boltzmann factors. The governing probability distribution function is a hypoexponential type, and its cumulants describe characteristics of the single-charge Coulomb interaction at room temperature on a mesoscopic scale. The cumulants are further extended into a complex domain. Starting from three fundamental assumptions, i.e., the generation of non-degenerated states due to single-charge Coulomb energy, the Markovian property of each emission event, and the independence of each state, a moment function is identified as a product of mutually prime elements (algebraically termed as prime ideals) comprising the eigenvalues or the lifetimes of the emission states. Then, the algebraic structure of the moment function is found to be highly analogous to that of an integer uniquely factored into prime numbers. Treating the lifetimes as analogs of the prime numbers, two types of zeta functions are constructed. Standard analyses of the zeta functions analogous to the prime number problem or the Riemann Hypothesis are performed. For the zeta functions, the analyticity and poles are specified, and the functional equations are derived. Also, the zeta functions are found to be equivalent to the analytic extension of the cumulants. Finally, between the number of emitted charges and the lifetime, a logarithmic relation analogous to the prime number theorem is derived. Full article

Liquid crystal elastomers (LCEs) have shown great potential in the field of soft robotics due to their unique actuation capabilities. Despite the growing number of experimental studies in the soft robotics field, theoretical research remains limited. In this paper, a dynamic model of a bionic arm using an LCE fiber as artificial muscle is established, which exhibits periodic oscillation controlled by periodic illumination. Based on the assumption of linear damping and angular momentum theorem, the dynamics equation of the model oscillation is derived. Then, based on the assumption of linear elasticity model, the periodic spring force of the fiber is given. Subsequently, the evolution equations for the cis number fraction within the fiber are developed, and consequently, the analytical solution for the light-excited strain is derived. Following that, the dynamics equation is numerically solved, and the mechanism of the controllable oscillation is elucidated. Numerical calculations show that the stable oscillation period of the bionic arm depends on the illumination period. When the illumination period aligns with the natural period of the bionic arm, the resonance is formed and the amplitude is the largest. Additionally, the effects of various parameters on forced oscillation are analyzed. The results of numerical studies on the bionic arm can provide theoretical support for the design of micro-machines, bionic devices, soft robots, biomedical devices, and energy harvesters. Full article

During offshore operations of jack-up platforms, the spudcan may experience sudden punch-through failure when penetrating from an overlying stiff clay layer into the underlying soft clay, posing significant risks to platform safety. Conventional punch-through prediction methods, which rely on predetermined soil parameters, exhibit limited accuracy as they fail to account for uncertainties in seabed stratigraphy and soil properties. To address this limitation, based on a database of centrifuge model tests, a probabilistic prediction framework for the peak resistance and corresponding depth is developed by integrating empirical prediction formulas based on Bayes’ theorem. The proposed Bayesian methodology effectively refines prediction accuracy by quantifying uncertainties in soil parameters, spudcan geometry, and computational models. Specifically, it establishes prior probability distributions of peak resistance and depth through Monte Carlo simulations, then updates these distributions in real time using field monitoring data during spudcan penetration. The results demonstrate that both the recommended method specified in ISO 19905-1 and an existing deterministic model tend to yield conservative estimates. This approach can significantly improve the predicted accuracy of the peak resistance compared with deterministic methods. Additionally, it shows that the most probable failure zone converges toward the actual punch-through point as more monitoring data is incorporated. The enhanced prediction capability provides critical decision support for mitigating punch-through potential during offshore jack-up operations, thereby advancing the safety and reliability of marine engineering practices. Full article

This study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano’s theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed. Full article

A new text matching model based on dynamic gated sparse attention feature distillation with a faithful semantic preservation strategy is proposed to address the fact that text matching models are susceptible to interference from weakly relevant information and that they find it difficult to obtain key features that are faithful to the original semantics, resulting in a decrease in accuracy. Compared to the traditional attention mechanism, with its high computational complexity and difficulty in discarding weakly relevant features, this study designs a new dynamic gated sparse attention feature distillation method based on dynamic gated sparse attention, aiming to obtain key features. Weakly relevant features are obtained through the synergy of dynamic gated sparse attention, a gradient inversion layer, a SoftMax function, and projection theorem literacy. Among these, sparse attention enhances weakly correlated feature capture through multimodal dynamic fusion with adaptive compression. Then, the projection theorem is used to identify and discard the noisy features in the hidden layer information to obtain the key features. This feature distillation strategy, in which the semantic information of the original text is decomposed into key features and noise features, forms an orthogonal decomposition symmetry in the semantic space. A new variety of faithful semantic preservation strategies is designed to make the key features faithful to the original semantic information. This strategy introduces an interval loss function and calculates the angle between the key features and the original hidden layer information with the help of cosine similarity in order to ensure that the features reflect the semantics of the original text. This can further update the iterative key features and thus improve the accuracy. The strategy builds a feature fidelity verification mechanism with a symmetric core of bidirectional considerations of semantic accuracy and correspondence to the original text. The experimental results show that the accuracies are 89.10% and 95.01% in the English datasets MRPC and Scitail, respectively; 87.8% in the Chinese dataset PAWX; and 80.32% and 80.27% in the Ant Gold dataset, respectively. Meanwhile, the accuracies in the KUAKE-QTR dataset and Macro-F1 are 70.10% and 68.08%, respectively, which are better than other methods. Full article

The geometry of the coils in a magnetic link and their relative position are crucial for increasing their mutual inductance, which is important for obtaining a higher induced voltage, transferred power, and electrical efficiency. General design guidelines found in the literature point to an increase in mutual inductance by making the coils similar in shape, positioning them as close as possible, and using high-permeability soft-cores to concentrate the flux between them. But these recommendations are often difficult to follow in dynamic inductive wireless power transfer (DIWPT) configurations for vehicular applications. This is mostly due to the necessity of a mechanical clearance between the lane and the vehicle assembly, which creates an “air gap”. Also, unless tracks are used, the lateral movement of a vehicle over a primary coil potentially causes a variation in the induced voltage, which is not adequate to energize the powertrain. Considering these intrinsic problems of DIWPT applications, we developed a few theorems that might facilitate some optimum designs, in the case where rectangular secondary coils are used over oblong primary coils, for two different design targets: (i) maximum induced voltage on the secondary coil and (ii) better insensitivity to the vehicle lateral misalignment on the inductive lane. Full article

When testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, data processing is typically based on equations derived from Hertzian mechanics. To account for the finite thickness of the samples, precise extensions of Hertzian equations have been developed for both conical and parabolic indenters. However, these equations are often avoided due to the complexity of the fitting process. In this paper, the determination of Young’s modulus is significantly simplified when testing soft, thin samples on rigid substrates. Using the weighted mean value theorem for integrals, an ‘average value’ of the correction function (symbolized as g(c)) due to the substrate effect for a specific indentation depth is derived. These values (g(c)) are presented for both conical and parabolic indentations in the domain 0 < r/H ≤ 1, where r is the contact radius between the indenter and the sample, and H is the sample’s thickness. The major advantage of this approach is that it can be applied using only the area under the force–indentation curve (which represents the work performed by the indenter) and the correction factor g(c). Examples from indentation experiments on fibroblasts, along with simulated data processed using the method presented in this paper, are also included. Full article

This paper aims to introduce a novel idea of possibility multi-fuzzy soft ordered semigroups for ideals and interior ideals. Various results, formulated as theorems based on these concepts, are presented and further validated with suitable examples. This paper also explores the broad applicability of possibility multi-fuzzy soft ordered semigroups in solving modern decision-making problems. Furthermore, this paper explores various classes of ordered semigroups, such as simple, regular, and intra-regular, using this innovative method. Based on these concepts, some important conclusions are drawn with supporting examples. Moreover, it defines the possibility of multi-fuzzy soft ideals for semiprime ordered semigroups. Full article

Dimensional analysis is an effective tool for designing laboratory tests, and it is also a successful method to reasonably predict the results of large-scale or field tests, which are difficult and costly to perform, by considering the outcomes obtained from small-scale tests. This paper therefore focuses on predicting the compression load–settlement relationship of soft clay soil under a rigid foundation by dimensional analysis. For that purpose, a series of dimensionless pi (π) terms were first produced for the relevant problem by employing Buckingham’s pi (π) theorem via the MATLAB program. Secondly, the results of a small-scale physical test reported in the literature that investigated the load–settlement relationship of soft clay soil under a rigid foundation subjected to compression load were verified with the finite element method. Thereafter, the small-scale problem was scaled up several times using dimensionless terms, and the compression load–settlement relationship for the large-scale cases was investigated with both dimensional analysis and the validated finite element method. The findings indicate that dimensional analysis produces reasonably successful outcomes considering the computational ease. In addition, the MATLAB program presented in this paper is quite useful for those desiring to determine the dimensionless terms belonging to any sort of problem. Full article

Accurate knowledge of the flow rate is essential for hydraulic systems, enabling the calculation of hydraulic power when combined with pressure measurements. These data are crucial for applications such as predictive maintenance. However, most flow rate sensors in fluid power systems operate invasively, disrupting the flow and producing inaccurate results, especially under transient conditions. Utilizing pressure transducers represents a non-invasive soft sensor approach since no physical flow rate sensor is used to determine the flow rate. Usually, this approach relies on the Hagen–Poiseuille (HP) law, which is limited to steady and incompressible flow. This paper introduces a novel soft sensor with an analytical model for transient, compressible pipe flow based on two pressure signals. The model is derived by solving fundamental fluid equations in the Laplace domain and converting them back to the time domain. Using the four-pole theorem, this model contains a relationship between the pressure difference and the flow rate. Several unsteady test cases are investigated and compared to a steady soft sensor based on the HP law, highlighting our soft sensor’s promising capability. It exhibits an overall error of less than $0.15$% for the investigated test cases in a distributed-parameter simulation, whereas the HP-based sensor shows errors in the double-digit range. Full article

Battery energy storage systems based on bidirectional isolated DC-DC converters (BIDCs) have been employed to level the output power of intermittent renewable energy generators and to supply power to electric vehicles. Moreover, BIDCs use high-frequency transformers (HFTs) to achieve voltage matching and galvanic isolation. Various studies have recently been conducted using soft magnetic materials, such as nanocrystalline, amorphous solids, and ferrite, to develop more compact and effective transformers with superior power densities. The HFTs in three-phase BIDCs are composed of three magnetic cores. However, this leads to low power density and high cost. Besides, the three-phase (3P) ferrite core has not been investigated for high-power converters such as 3P-BIDCs. This paper presents the design and development of a 3P-EE ferrite magnetic core for 3P-BIDCs. The area product design method was used to determine the core and winding design. The paper also proposes the use of the superposition theorem in conducting a magnetic circuit analysis to predict the flux density and magnetising inductance of the transformer core. Moreover, the use of the superposition theorem allowed the required air-gap length for balancing the distribution of flux density and magnetizing inductance in the transformer core to be determined. The balanced flux distribution and magnetizing inductance resulted in a uniform core loss and temperature in the transformer. This paper also presents the experimental results of the designed HFT operated in a 300-V, 3-kW 3P-BIDC. The experimental results showed that the proposed HFT achieved a balanced flux density and magnetizing inductance with a high power density and low cost. Moreover, the transformer performed at a maximum efficiency of 98.67%, with a decrease of 3.33 °C in the overall temperature of the transformer as compared to the transformer without air gaps. Full article

As an extension of quasi-continuity in general topology, we define soft quasi-continuity. We show that this notion is equivalent to the known notion of soft semi-continuity. Next, we define soft weak quasi-continuity. With the help of examples, we prove that soft weak quasi-continuity is strictly weaker than both soft semi-continuity and soft weak continuity. We introduce many characterizations of soft weak quasi-continuity. Moreover, we study the relationship between soft quasi-continuity and weak quasi-continuity with their analogous notions in general topology. Furthermore, we show that soft regularity of the co-domain of a soft function is a sufficient condition for equivalence between soft semi-continuity and soft weakly quasi-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and soft graph theorems in terms of soft weak quasi-continuity. Full article