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Higher-order topological states, as emergent topological phases of matter, originating from condensed matter physics, have sparked a vibrant exploration of topological insulators. Their topologically protected multidimensional localized states are typically associated with nontrivial bulk band topology, and the significant impact of lattice geometry is unconsciously overlooked. Here, we construct coupled acoustic cavities on a two-dimensional honeycomb lattice to investigate the sensitivity of higher-order topological modes to the variations of edge contour. Fractional charge is utilized to accurately predict topological modes with distinct topological orders, in spite of the minimal bulk bandgaps inherent in the honeycomb lattice and bound states in the continuum. It is found that the presence and absence of the first-order and higher-order topological modes in the same topological phase are tightly linked to the sample boundaries, which can be demonstrated by both theoretical analysis and numerical calculation. Our study also discusses potential physical realization of geometry-dependent topological states across different platforms, providing inspiration for the prospective application of topological devices in acoustics. [ABSTRACT FROM AUTHOR]

Thermal activation of a particle from a deep potential trap follows the Arrhenius law. Recently, this result has been generalized for interacting diffusive particles in the trap, revealing two universality classes—the Arrhenius class and the excluded volume class. The result was demonstrated with the aid of numerical analysis. Here, we present a perturbative hydrodynamic approach to analytically validate the existence and range of validity for the two universality classes. [ABSTRACT FROM AUTHOR]

In this work, we investigate the possibilities of performing charge and spin current rectifications using graphene nano-ribbon in the presence of Rashba spin–orbit (SO) interaction. More specifically, we explore the specific role of mechanical strain on these two different types of current rectifications. The system is simulated by a tight-binding framework, where all the results are worked out based on the standard Green's function formalism. In order to have current rectification, an asymmetry is required, which is incorporated through uncorrelated disorder among the constituent lattice points. From our extensive numerical analysis, we find that reasonably large charge and spin current rectifications can be obtained under strained conditions, and all the physical pictures are valid for a broad range of tight-binding parameters. The rectification properties are studied mostly for zigzag graphene nano-ribbons; however, an armchair ribbon is also taken into account for a clear comparison. Our work may provide a new direction of getting strain-controlled current rectifications in similar kinds of other physical systems as well. [ABSTRACT FROM AUTHOR]

The excitation and tuning of multiple resonances with narrow spectral width based on Brewster's effect is possible in an ultrathin dual-band terahertz absorber. The angular variation establishes a monotonic relation with the frequency of some generated resonances offering tunability. Moreover, burying a graphene ring resonator beneath the metallic ring splits the resonance for providing the triple narrow absorption windows. The electrical modulation offers the feature of independent tunability in the generated third absorption band. Thus, the frequency ratio of the upper to lower spectral absorption peak can be modulated by the electrically tunable Fermi energy of graphene. Engraving the graphene resonator also enhances the incident angle based tunability by affecting a greater number of Brewster generated resonance peaks. The narrow line shape of the triple band absorption can enable refractive index sensing and the detection of extraneous elements in localized analyte samples. The detection of imidacloprid pesticide in wheat flour is performed by the implemented sensor. The numerical analysis is done for the design and analysis of the absorber structures to report the above facts. [ABSTRACT FROM AUTHOR]

The Unitary Group Adaptation (UGA) offers a very compact and efficient spin adaptation strategy for any spin-free Hamiltonian in a many body framework. Our use of UGA in the context of state-specific (SS) Jeziorski–Monkhorst Ansatz based multireference coupled cluster (MRCC) theory obviates the non-commutativity between the spin-free cluster operators via a normal ordered exponential parametrization in the wave operator. A previous formulation of UGA-SSMRCC by us [R. Maitra, D. Sinha, and D. Mukherjee, J. Chem. Phys. 137, 024105 (2012)], using the same ansatz, employed certain sufficiency conditions to reach the final working equations, which cannot be improved systematically. In this article, we will present a more rigorous formulation that follows from an exact factorization of the unlinked terms of the Bloch equation, resulting in equations on which a hierarchy of approximations can be systematically performed on the emergent additional terms. This derivation was shown in our recent article [D. Chakravarti, S. Sen, and D. Mukherjee, Mol. Phys. 119, e1979676 (2021)] in the context of a single open shell CC formalism and was applied to spectroscopic energy differences where the contribution of the new terms was found to be of the order of ∼0.001 eV for ionization potential, electron affinity, and excitation energy. In the current work, we will present a comparison between the earlier and current formulations via both a theoretical analysis and a numerical demonstration of the dramatic effect of the additional terms brought in by the factorization on potential energy curves. The contribution of such terms was found to gain importance with an increase in the number of singly occupied active orbitals in the model space functions. [ABSTRACT FROM AUTHOR]

The kernel polynomial method (KPM) is a powerful numerical method for approximating spectral densities. Typical implementations of the KPM require an a prior estimate for an interval containing the support of the target spectral density, and while such estimates can be obtained by classical techniques, this incurs addition computational costs. We propose a spectrum adaptive KPM based on the Lanczos algorithm without reorthogonalization, which allows the selection of KPM parameters to be deferred to after the expensive computation is finished. Theoretical results from numerical analysis are given to justify the suitability of the Lanczos algorithm for our approach, even in finite precision arithmetic. While conceptually simple, the paradigm of decoupling computation from approximation has a number of practical and pedagogical benefits, which we highlight with numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the influence of saturable absorber parameters, namely, modulation depth, recovery time, and saturation energy, on the performance of an ultrafast fiber laser that is mode-locked by a hybrid scheme of a saturation absorber (SA) and a nonlinear polarization rotation (NPR). Maps of mode-locked states related to intracavity wave-plates are created to evaluate the operation of hybrid mode-locking under different modulation depths of the SA. Along with the improvement of modulation depth of the SA, the mode-locked pulse results from a combination effect of the SA and NPR. The numerical analysis reveals that the SA parameters can significantly impact the pulse profile, peak power, and operation state. Moreover, they can also impact the selection of NPR mode-locked points, resulting in variation in stable single pulse output. A higher modulation depth can suppress the unstable multiple pulses' operation and convert them into harmonic mode-locked pulses. The obtained results indicate that the selection of appropriate SA parameters can effectively improve the output characteristics of hybrid mode-locked fiber lasers. [ABSTRACT FROM AUTHOR]

A computationally efficient model is proposed to analyze plasma-assisted combustion using nanosecond repetitive pulsed (NRP) plasmas. The NRP plasma discharge is placed in the oxidizer stream of a counter-flow diffusion flame. The effect of changing the flow rate and the pulse repetition frequency (PRF) of a continuous NRP plasma discharge on the temperature and species profiles of a counter-flow diffusion flame is investigated numerically. The results confirm that oxygen atom and nitrogen vibrational states are the most important species to enhance combustion. The results also show that kinetic effects are much more significant for higher PRF and lower pulse voltage. In addition, when steady plasma profiles are used instead of unsteady plasma profiles, the extinction strain rates increase by 25.8%, 21.1%, and 10.8% for PRF equal to 1, 2, and 4 kHz, respectively. [ABSTRACT FROM AUTHOR]

Drilling glass fiber reinforced polymer matrix (GFRP) composites typically causes burrs, splintering, and microcracks within the GFRP structure, as well as delamination, fiber pull‐out, and thermal degradation of the polymer matrix. Designing and manufacturing molded‐hole GFRP components, as opposed to drilling, has recently been proposed as a promising method for overcoming the issues associated with drilling, for which there is limited research. Specifically, the mechanical response of molded‐hole GFRP has not been fully addressed in the literature. In the present study, molded and drilled GFRP composites with epoxy matrix were fabricated by hand lay‐up, and then the samples were analyzed utilizing experimental and numerical analysis techniques. Stress and strain analyses of GFRP samples were performed in Ansys Transient Structural Analysis. Although the fiber orientations of the layer geometries [0°/90°] and 3D models were the same, an additional layer was defined in the direction of the fiber orientation [45°/−45°] of molded‐hole composites to simulate the fiber accumulation effect. Experimental findings revealed that the flexural strength of molded composites was 12% greater than that of drilled composites. According to the numerical analysis, 98.7% proximity was achieved between the experimental and numerical results. Thus, the present study has provided numerical modeling to understand the flexural strength of molded composites for the first time, which will contribute to the increased use of molded composites in numerous applications in the fields of aerospace, automotive, and marine. Highlights: Drilled‐ and molded‐hole GFRP composites were produced by hand lay‐up.Flexural properties of the composites were examined via 4P bending tests.Flexural strength of molded composites was higher than that of drilled ones.98.7% proximity was achieved between the experimental and FEM results.A unified FEM method is proposed for the molded‐hole composites. [ABSTRACT FROM AUTHOR]

Let { X n , n ≥ 1 } be a sequence of independent random variables with common general error distribution GED (v) with shape parameter v > 0 , and denote M n and m n the partial maximum and minimum of { X n , n ≥ 1 } . With different normalizing constants, the distributional expansions of normalized sample range M n − m n are established in this article. A byproduct is to deduce the convergence rates of distributions of normalized sample range to their limits, which shows that the optimal convergence rate is proportional to 1 / log n as v ∈ (0 , 1) ∪ (1 , ∞) contrary to the case of v = 1 , which is proportional to 1 / n . Furthermore, numerical analysis is provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

We investigate a robust equilibrium investment-reinsurance problem for n ambiguity-averse competitive insurers, n ≥ 2 . Each insurer is allowed to purchase proportional reinsurance and invest in a risk-free asset and a risky asset. Each insurer aims to maximize the expected utility of a weighted relative terminal wealth with respect to the other competitors. In this article, the risky asset is assumed to follow a general and flexible model: the square root factor process. Following the game theory approach, we derive the closed solutions of the robust equilibrium investment-reinsurance strategies. Moreover, the verification theorem is provided in this article. Finally, we demonstrate some numerical analyses and give the economic explanations as well. [ABSTRACT FROM AUTHOR]

Studies to increase the joint strength of adhesively bonded joints used in the aerospace and automotive sectors are met with interest in the field of engineering. Many different methods are used to increase the strength of the bonded joint, and one of these methods is to change the joint geometry. This study aims to increase the joint strength by changing the geometry of the joint with the same adhesive area condition. In the study, the DP460 structural adhesive was used as the adhesive, the AA2024-T3 aluminum alloy was used as the adherend, and the One Step-Lap Joint (OSLJ), Double-Strap Joint (DSJ), and Stepped Double-Strap Joint (SDSJ) was used as the joint types. The joint strengths of the joints obtained by using different step lengths and different patch lengths for these three types of joints with the same adhesive area were investigated experimentally and numerically. Firstly, the strengths of the SLJ type obtained by using four different step lengths and the DSJ type obtained by using patches of four different lengths were investigated. In the light of these investigations, the mechanical properties of the joints obtained by changing the step length and patch length in the SDSJ type, a new joint type with the same adhesive area, were obtained. As a result, compared to the OSLJ type with the same adhesive area, the joint strength of the DSJ type increases by approximately 45% to 67%. In addition, while the strength of the new type of joint (SDSJ) obtained in the presented study increases between 7% and 35% according to the DSJ type, it increases between 56% and 126% according to the OSLJ type. These increases in the joint strength vary according to the bonding area. Additionally, in the presented study, experimental data were compared with numerical analysis, and it was observed that the data were quite consistent with each other. [ABSTRACT FROM AUTHOR]

In order to develop a vaccination system that have no contact with healthcare workers during highly transmissible epidemics, a portable modular vaccine injection system (PMVIS) composed of YT-type modules (YTM), winding modules (WM) and an active injector (AI) actuated by shape memory alloy (SMA) wires are proposed in this article. By series layout of WMs, YTMs and AI, the multi-posture requirements of PMVIS can be realized. Then, the thermodynamic model of SMA together with kinematic and dynamic models of structure for each module are established, and studied the output stroke of each module through numerical analysis and experiments. The results show that the designed YTM achieves a maximum output of 1.84 mm displacement or 1.9° angle under the given size parameters. After connecting 1-WM in series, the output displacement and rotation angle are enlarged to 12.12 mm and 10.8°, which are increased by 558.7% and 468.4%, respectively. PMVIS can realize multi-postures through different functional modules to play the role of position adjustment. It provides theoretical and technical support for future contactless injection systems. [ABSTRACT FROM AUTHOR]

Highlights Computational methods provide effective tools for the prediction of the curing behavior of composites, especially for large‐scale complex composite structures. The flow‐compaction analysis during curing receives insufficient attention in current studies. In this work, an integrated framework considering the heat transfer, the cross‐linking reaction, the flow and compaction, and the stress–strain module is established. A comprehensive resin flow termination criterion is proposed. L‐shaped composites with a stacking layer of [45/90/−45/0]s were fabricated, and the good agreement between the experimentally measured and the numerically predicted contour data validated the current model. Compared with Hubert's model, the prediction accuracy of the thickness and fiber volume content increases by 4.24% and 3.92%, respectively. Correlation analysis between the fiber volume ratio predicted by numerical methods and experimental results (94% for this method, −41% for Hubert's model) demonstrates the well‐capture of nonuniform fiber distribution in curved composites for the current strategy. The overall framework provides an accurate and promising tool for the prediction of the curing behavior of complex composite components. An integrated numerical methodology is proposed considering the resin flow and compaction. The viscosity‐temperature coupled feature of resin is considered in the permeability coefficients. A comprehensive resin flow termination criterion is proposed for an accurate prediction. The resin content, thickness, and spring‐in angle of L‐shaped laminates are characterized. The good correlation between the experimental and numerical results validates this method. Compared with the model proposed by Hubert, the prediction accuracy improves. [ABSTRACT FROM AUTHOR]

Presently, due to its extraordinary mechanical, thermal, electrical and biomedical facets nanofluids deliver several prospects to exaggerate the propensity of isothermal systems by augmenting the conductivity features of the host fluids. In various areas of the energy partition, nanoparticles show a remarkable measure in energy storage, energy variation, and energy convertible, i.e. thermoelectric plans, petroleum cells, supercapacitors, stellar cells, rechargeable batteries, light-radiating diode and carbon-based light-radiating diode, smart coatings. In this current conversation, we anticipated an unsteady 3D flow of the Sutterby nanofluid consequence of a bidirectional extended surface. To envision the thermophoresis and Brownian motion properties in Sutterby's nanofluid, the Buongiorno association is utilized in an additional refined technique. Variable thermal conductivity with heat source/sink property occurred deliberated considering heat transmission techniques. The appropriate transformation is applied for transposing the PDEs into nonlinear ODEs. For numerical results, the bvp4c programmed is prerequisite for elucidating the subsequent Ordinary differential equations. The distinct performance of the Sutterby nanofluid temperature and the concentration field are designated and discussed in the physical parameter's aspect. It is clear that the temperature of the Sutterby fluid decreases with respect to the ratio of stretching rates parameter and similar developments are observed for the thermophoresis and Brownian motion parameters. Furthermore, the concentration profile declines for sophisticated estimates of the Lewis number and thermophoresis parameters. [ABSTRACT FROM AUTHOR]

This document introduces a novel concept involving an Omni-Directional Guided Vane (ODGV) encompassing a vertical axis wind turbine (VAWT) with the goal of improving its overall performance. Extensive three-dimensional computational analysis of the airfoils used in this novel ODGV structure is conducted to investigate the impact of various geometric parameters. Diverse geometric configurations of the ODGV are explored to analyze wind flow behavior across the turbine utilizing a well-validated computational fluid dynamics (CFD) model. The numerical investigations employ the Reynolds Averaged Navier–Stokes (RANS) modeling approach with the k-epsilon turbulence model. The steady state governing equations are solved using the validated CFD solver STAR CCM+. The study considers three distinct inlet velocities: 3, 6, and 9 m/s, with the aim of improving flow behavior and velocity through the ODGV. Four different modifications of the ODGV are examined, and the accuracy of the CFD model is affirmed through comparison with NACA airfoil data. Integration of the ODGV results in an enhanced self-starting behavior of the VAWT, leading to a reduction in the cut-in speed. Validation results demonstrate a strong agreement with the data obtained from CFD simulations. These results suggest that most shape ratios, except for 0.3 and 0.4 at Tip Speed Ratio (TSR) of 1.3 and 3, contribute to enhancing power and torque coefficients. Furthermore, the findings indicate that with a Sharpe ratio of 0.56, both torque and power coefficients could be improved by up to 48% and 58%, respectively. [ABSTRACT FROM AUTHOR]

Process of transportation of heat in ferrofluids has innumerable applications in the fields of electronics and automobile industry. By tracing the materials, the ferrofluid got popularity among researchers and engineers, also most ferrofluids are non-Newtonian in nature so here the non-Newtonian fluid is under consideration. In this study, the influences of viscous dissipation and magnetic parameter in the flow of ferromagnetic Carraeu fluid for a stretching surface are examined. Suitable similarity transformations in the system that consists of nonlinear form of Partial Differential Equations (PDEs) are transformed into a system of nonlinear form of ODEs, then the resulting Ordinary Differential Equations (ODEs) are resolved by use of a mathematical technique known as bvp4c. Effects of ferromagnetic interaction factor, Curie temperature, viscous dissipation and material parameter are examined for temperature profile as well as velocity fields. Moreover, the variations in velocity and thermal gradients are analyzed and described with the help of graphs. An upsurge in the values of magnetic interaction parameter and Weissenberg number causes a decline in the velocity field while the thermal gradient shows opposite behavior. It is detected that the temperature of Carreau fluid intensifies for larger and  λ. [ABSTRACT FROM AUTHOR]

Strain localization simulation of overconsolidated soils with high overconsolidation ratio (OCR) has been a long‐standing challenge. Some critical state soil models, including the modified Cam‐clay (MCC) model, have been widely applied, but they may not predict the shear dilatancy of overconsolidated soils well in some cases. Hence, the unified hardening (UH) model, which may be viewed as a generalized version of the MCC model, is implemented. It has been recognized, nonetheless, that without resorting to the regularization mechanism, the standard finite element method (FEM) or the second‐order cone programming optimized finite element method (FEM‐SOCP) often experiences instability or interruption of calculating the hardening‐softening responses of overconsolidated soils. To resolve the aforementioned difficulty, the UH model is developed and implemented in the framework of FEM‐SOCP based on the micropolar continuum (mpcFEM‐SOCP) to predict strain localizations of overconsolidated soils. Furthermore, to obviate non‐convexity of mpcFEM‐SOCP induced by material softening, an effective composite update scheme of hardening variable pc, which refers to the implicit variable (IV) scheme for the hardening stage and then refers to the explicit variable (EV) scheme for the softening stage, is proposed. Based on one biaxial compression problem and one rigid strip footing problem, numerical analyses disclose that by applying mpcFEM‐SOCP in conjunction with the composite update scheme of pc, the UH model of micropolar continuum can effectively predict the strain localization behavior of overconsolidated soil during its failure stage, and the stable hardening‐softening responses of overconsolidated soils can be readily attained. [ABSTRACT FROM AUTHOR]

We evaluated topological protection for edge and higher-order corner states in topological diffusion systems based on the breathing kagome lattice. In the kagome lattice, the corner states appear at the corner boundary where all three Wannier centers in nontrivial unit cells are located. The three Wannier centers in a unit cell can be placed on the obtuse- and acute-corner boundaries utilizing the armchair boundary, generating topological acute- and obtuse-corner states. For another representative zigzag boundary, only the acute-corner unit cell has three Wannier centers located at the boundary; hence, only the acute-corner state appears. Our band analysis and numerical studies show that the topologically protected decay behavior for armchair boundaries is as robust as that for zigzag boundaries, unlike wave phenomena with space and time periodicities. Our findings can guide the flexible design of topological diffusion applications such as heat localization and recovery systems. [ABSTRACT FROM AUTHOR]

This study examines the thermodynamic and numerical analyses of a methane-fed solid oxide fuel cell (SOFC) over a temperature range varying between 873 K and 1273 K. These analyses were conducted to investigate and compare the performance of the SOFC under various operating conditions in detail. As part of the thermodynamic analysis, important parameters such as cell voltage, power density, exergy destruction, entropy generation, thermal efficiency, and exergy efficiency were calculated. These calculations were used to conduct energy and exergy analyses of the cell. According to the findings, an increase in operating temperature led to a significant improvement in performance. At the initial conditions where the SOFC operated at a temperature of 1073 K and a current density of 9000 A/m2, it was observed that when the temperature increased by 200 K while keeping the current density constant, the power density increased by a factor of 1.90 compared to the initial state, and the thermal efficiency increased by a factor of 1.45. Under a constant current density, the voltage and power density values were 1.0081 V, 1.0543 V, 2337.13 W/m2, and 2554.72 W/m2 at operating temperatures of 1073 K and 1273 K, respectively. Under a current density of 4500 A/m2, the entropy generation in the cell was determined to be 29.48 kW/K at 973 K and 23.68 kW/K at 1173 K operating temperatures. The maximum exergy efficiency of the SOFC was calculated to be 41.67% at a working temperature of 1273 K and a current density of 1500 A/m2. This study is anticipated to be highly significant, as it examines the impact of temperature variation on exergy analysis in SOFC, validating both numerical and theoretical results, thus providing a crucial roadmap for determining optimized operating conditions. [ABSTRACT FROM AUTHOR]

Utilizing broadband low Earth orbit satellite signals in an opportunistic manner for navigation is becoming increasingly popular. This paper deals with a particularly useful approach for navigation based on satellite signals of opportunity, which uses carrier Doppler-shift observables. We provide analytically derived and simplified formulas for the Jacobian involved in the numerical computation of the navigation solution and derive a global navigation satellite system-like dilution-of-precision metric that can be used to assess accuracy. A numerical study provides preliminary computational results. [ABSTRACT FROM AUTHOR]

The pseudo-differential operator with symbol | k |α has been widely used in seismic modelling and imaging when involving attenuation, anisotropy and one-way wave equation, which is usually calculated using the pseudo-spectral method. For large-scale problems, applying high-dimensional Fourier transforms to solve the wave equation that includes pseudo-differential operators is much more expensive than finite-difference approaches, and it is not suitable for parallel computing with domain decomposition. To mitigate this difficulty, we present a truncated space-domain convolution method to efficiently compute the pseudo-differential operator |$\sqrt{-\nabla ^2}$|⁠ , and then apply it to viscoacoustic reverse-time migration. Although |$\sqrt{-\nabla ^2}$| is theoretically non-local in the space domain, we take the limited frequency band of seismic data into account, and constrain the approximated convolution stencil to a finite length. The convolution coefficients are computed by solving a least-squares inverse problem in the wavenumber domain. In addition, we exploit the symmetry of the resulting convolution stencil and develop a fast spatial convolution algorithm. The applications of the proposed method in Q -compensated reverse-time migration demonstrate that it is a good alternative to the pseudo-spectral method for computing the pseudo-differential operator |$\sqrt{-\nabla ^2}$|⁠ , with almost the same accuracy but much higher efficiency. [ABSTRACT FROM AUTHOR]

The nanofluids became much of interest due to their superior heat mechanism over the conventional fluids. The addition of nanoparticles in the host solvent enhances the internal ability of the liquid to store and transmit heat. Therefore, these fluids are widely used in biomedical engineering, detergents, medication, applied thermal engineering, mechanical, and chemical engineering and so forth. Keeping in mind the significance of nanofluids, this study is conducted to investigate the comparative heat transmission in γAl2O3−H2O${\mathrm{\gamma Al}}_2{{\mathrm{O}}}_3 - {{\mathrm{H}}}_2{\mathrm{O}}$ and γAl2O3−C2H6O2${\mathrm{\gamma Al}}_2{{\mathrm{O}}}_3 - {{\mathrm{C}}}_2{{\mathrm{H}}}_6{{\mathrm{O}}}_2$ under the Effective Prandtl Number Model (EPNM) effects over a vertical permeable cylinder. Formulation of the model is carried out over a vertical cylinder about the stagnation point and the heat transport model is achieved after the successful implementation of the cylindrical stream function, nanofluids effective characteristics, and cylindrical similarity equations. The mathematical treatment was done via RK technique and furnished the results. The nanofluids have the capacity to control the fluid motion more effectively than ordinary fluid and combined convection is better where rapid fluid movement is desired. In the existence of EPNM, higher heat transmission is achieved and is prominent for γAl2O3−C2H6O2${\mathrm{\gamma Al}}_2{{\mathrm{O}}}_3 - {{\mathrm{C}}}_2{{\mathrm{H}}}_6{{\mathrm{O}}}_2$ based on their thermophysical values. Further, the skin friction and Nusselt number are optimum for γAl2O3−C2H6O2${\mathrm{\gamma Al}}_2{{\mathrm{O}}}_3 - {{\mathrm{C}}}_2{{\mathrm{H}}}_6{{\mathrm{O}}}_2$ against α1${\alpha }_1$. [ABSTRACT FROM AUTHOR]

The report of the 20th National Congress of the Communist Party of China pointed out that it is necessary to accelerate the construction of digital China, and actively develop equipment intelligence, digitalization, and high‐end equipment manufacturing. With the construction of a new round of digital China, the safety of digital technology and high‐end equipment is particularly important for power grid. Transformer is an important link of power grid operation. The destructive thermal failure of transformer has become a hot research issue in the power industry. At the same time, there are more and more power electronic equipment in the power grid, which makes the regulation and control more and more complicated. Taking a 1000 kVA oil‐immersed transformer as an example, the magnetic, current, and thermal multi field coupling numerical analysis method is first used to simulate and analyse the operation status of the transformer. By comparing the simulation results with the monitoring data results, the error of the results is controlled within 5%. Finally, the multi‐state characteristic parameters of the transformer are monitored through sensors, and the numerical simulation analysis results are integrated with the state monitoring results to build a transformer thermal life loss assessment system. The method in this paper can evaluate and analyse the running state of transformer in real time, which is of great significance for the power company to formulate the treatment measures. [ABSTRACT FROM AUTHOR]

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In this paper, we detail a three-pronged lesson introducing differential equations using analytical, numerical and experimental approaches in a large first-year differential calculus course. Presenting the three approaches in succession allows students to evaluate advantages and disadvantages. The lesson incorporates software and programming and provides opportunities for active, experiential, team-based learning. [ABSTRACT FROM AUTHOR]

We present an innovative approach to deep learning server infrastructure, emphasizing the importance of continuous service availability and efficiency. The model features a single server managing two distinct service phases: model training and model inference, each with separate queues. In the event of a server failure, a standby server seamlessly takes over, ensuring uninterrupted service. We also incorporate structured maintenance cycles which is mentioned as single vacation state, to optimize system reliability through server maintenance and enhancements. The research mainly focuses on transient numerical results, presenting a solution to the challenge of continuous service availability in the fast-evolving field of deep learning. [ABSTRACT FROM AUTHOR]

This study investigated the performance of screw piles under uplift. The screw piles were installed in sand in the laboratory and uplifted to evaluate the effects of the screw thread pitch and relative density of sand on the pile uplift capacity. The uplift capacity was compared with that of the shaft pile using the digital image correlation technique. Discrete element modelling was used to further examine the load-sharing characteristics, axial force, and shaft friction of the screw pile. The results suggest that the screw pile outperformed the shaft pile in terms of uplift capacity, pile–sand interactions, and load transfer. The improved uplift performance is attributed to the screw threads reaching out to a larger volume of sand particles to resist the uplift. An equation was also proposed to determine the uplift capacity. [ABSTRACT FROM AUTHOR]

The possibility of capturing and releasing cosmic masses is considered within the framework of a plane hyperbolic three-body problem, as well as within the framework of a plane parabolic three-body problem. A mathematical model is proposed that allows us to explain the formation of nonspherical satellites of planets, similar to the Martian satellites Phobos and Deimos, due to the interception or exchange of cosmic masses, and also allows us to understand why there is no space debris of extraterrestrial origin in near-Earth and lunar space. The effect of accumulation of artificial debris in the Earth–Moon system is being studied. The present study is based on a numerical and analytical analysis of certain Chazy classification schemes for final motions in the three-body problem. The three-body boundary value problem is considered, the possibility of the existence of a solution to this problem is shown, and the conditions for the final hyperbolic-ellipticity of motion are obtained. The analytical results are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This study investigates the effectiveness of a vertical trench in mitigating the hazards associated with reverse faulting on shallow foundations and assesses the accuracy of analytical relations for estimating the required trench depth through numerical analyses. Results show that a trench near a foundation diverts the fault rupture away from the building. Increasing the trench depth and width, positioning it closer to the foundation, and increasing the structure weight significantly increase the fault rupture diversion probability, reducing foundation damage level. Moving the foundation towards the hanging wall decreases rupture diversion probability. Trenches are more effective at smaller fault-dip angles. Narrower foundations with deeper alluvium require shallower trenches to minimize foundation damage. Existing analytical relations estimate trench depth with reasonable accuracy to divert fault rupture and minimize structural damage. [ABSTRACT FROM AUTHOR]

In this work, we use two newly powerful and efficient techniques, the unified method and the unified Riccati equation expansion (UREE) method, to derive solitary wave solutions for the (1 + 1)-dimensional longitudinal wave equation (LWE), presenting a systematic approach to reveal the underlying dynamics. By incorporating mathematical analysis and numerical simulations, we investigate the behavior and properties of these solitary wave solutions in various fields of science. The derived solutions are entirely new, and these findings show the essential complexities of the longitudinal wave equation. These obtained solutions shed light on the fundamental mechanisms governing solitary waves in the longitudinal wave equation, contributing to a deeper understanding of nonlinear wave phenomena. We present effective visualizations of the dynamical wave structures using various graphs, such as 3D, 2D, and contour plots in the obtained solutions to improve our comprehensive understanding. Consequently, numerous types of wave profiles, including periodic wave, interaction between periodic wave and kink wave, W-shape wave, kink wave, interaction between breather wave and kink wave, traveling wave, mixed periodic, singular soliton, and some new types of soliton profiles were found. Consequently, this work presents a comprehensive study of solitary wave solutions using the unified method and UREE method for the (1 + 1)-dimensional LWE equation. The outcomes of the current study manifest that the considered methods are significant and systematic in solving nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

Positive semidefinite kernels on spheres cross time are on demand in spatial statistics, machine learning and numerical analysis, motivated by applications in the climate, environmental and earth sciences. Most of the recent literature has focused on kernels that are isotropic on the sphere and stationary in time, but this assumption is often overly limited in quantifying spatial dependence properly. A broader class of kernels can be obtained by trading isotropy for axial symmetry, i.e., stationarity with respect to longitudes only. This paper challenges theoretical aspects by providing a spectral representation that uniquely characterizes space-time positive semidefinite kernels that are axially symmetric on the sphere and stationary in time. We also address the problem of partial Fourier inversion and show that it is feasible under mild technical conditions. The second part of the paper focuses on constructive methods to build nonseparable kernels having axial symmetry on the sphere and stationarity over time. [ABSTRACT FROM AUTHOR]