Two-dimensional Analytical Model Research Articles

Comprehensive two-dimensional analytical modeling of groundwater levels in bi-directional sloping heterogeneous aquifers under variable recharge conditions

This paper develops a comprehensive two-dimensional (2D) groundwater model that surpasses traditional one-dimensional approaches by incorporating extensive hydrological and geological data typically acquired through well drilling. The primary objective of this research is to explore and characterize the complex dynamics of groundwater flow within sloping heterogeneous aquifers subject to rainfall-induced recharge events. To achieve this, the study utilizes the 2D Boussinesq equation, which is enhanced with meticulously defined boundary conditions to more accurately reflect real-world scenarios. The Integral Transform Technique (ITT) is employed to derive an analytical solution that integrates the effects of variable rainfall recharge, aquifer inclination angles, and inherent heterogeneity. This analytical model effectively captures varying recharge dynamics, both spatially and temporally, contributing to a better understanding and management of groundwater systems. The paper presents a new analytical framework, offering deeper insights into how natural factors impact porous medium behavior, thereby providing strategic references for sustainable water resource management.

An analytical solution to ground stresses induced by tunneling considering ground surface boundary conditions and gravity

Accurately predicting the stress distribution around the tunnel is crucial for designing safe and economical support systems. The stress distribution is closely related to the ground stress release induced by tunneling, as well as the initial gravity stress and boundary conditions. In this study, a two-dimensional analytical model considering the ground surface boundary conditions and gravity is presented to investigate the stress field around the tunnel. Then, a numerical model was developed to validate the proposed analytical model. Finally, parametric analyses were conducted, and the limitations of the load calculation method of the code for design of shield tunnel in China were discussed. The results indicate that: (a) Tunnel excavation induces stress redistribution in the soil, resulting in a soil arching effect around the tunnel. This arching effect causes nonlinear load changes around the tunnel. (b) The soil mass around the tunnel can be divided into undisturbed and disturbed zones. Above the tunnel, the disturbance range is C-2D(C and D represent the burial depth and the tunnel diameter), while below and on both sides of the tunnel, the disturbance ranges are 4D and 1.5D, respectively. (c) Once the stress release rate reaches 0.6, a combined arching effect zone, consisting of both major and minor principal stresses, is formed in the disturbance zone above and below the tunnel. (d) The load distribution pattern calculated by the code for design of shield tunnel in China is gourd-shaped, and this calculation method is insufficient for accurately evaluating the load around the tunnel. The research results can provide a reference for the design of the shield tunnel.

Coupled model for liquid lithium plasma facing components

Numerical analysis provides the design choice and operating window of liquid metal Plasma Facing Components (PFC) concepts. Coupled analysis of boundary plasma together with the surrounding boundary structures is required. To achieve this goal, PPPL is developing a comprehensive multi-physics model for modeling of PFCs in fusion devices. The model includes the fluid-kinetic code SOLPS-ITER and the flow and heat transfer code CFX from ANSYS. SOLPS-ITER was augmented with a liquid metal boundary condition algorithm, allowing direct two-way coupling of the plasma analysis with the two-dimensional analytical slab flow model which includes heat convection in the liquid metal PFC. The target heat flux resulting from this coupled analysis is used as a boundary condition for detailed 3D Computational Fluid Dynamics (CFD) Magneto Hydro Dynamics (MHD) and heat transfer analysis. A new formulation of MHD equations is introduced in the numerical procedure ensuring current conservation of the discretized equations. Results of the 3D analysis are used for final validation of the coupled model. A PFC design where a porous wall is used to stabilize the liquid metal surface, while MHD drive is used to push the liquid metal flow inside the PFC, will be investigated in the regimes where vapor shielding is created for enhanced volumetric plasma heat dissipation.

Analytical model for the mitigation of VOC vapor with horizontal permeable reactive barrier in the contaminated site considering non-uniform source

Volatile organic compounds (VOCs) contamination at the groundwater may cause vapor intrusion and pose significant threats to human health. As a novel low-carbon mitigation technology, a horizontal permeable reactive barrier (HPRB) is proposed to remove the VOC vapor in the vadose zone and mitigate the vapor intrusion risk. To estimate the performance of HPRB in the contaminated site with a non-uniform source, a transient two-dimensional analytical model is developed in this study to simulate the VOC vapor migration and oxidation processes in the layered soil. The analytical model is verified against the experimental results and numerical simulation first and the parameter study is then conducted. The HPRB has good performance for the contaminated sites involving factors including deep source and local soil with low effective diffusivity. To consider the vertical heterogeneity of the local soil, the traditional equivalent homogeneity method has limitations in considering the horizontal migration of VOC vapor and is not suitable for the two-dimensional model. On the contrary, the artificial layered method based on the proposed analytical model has better accuracy and is recommended to be adopted in practice. Leading to the exponential decrease in the VOC vapor concentration at the ground surface, increasing the thickness of HPRB is an effective measure to enhance the performance of HPRB. The fitting exponential function can be applied to determine the minimum design value of the thickness of HPRB in practice.

Analytical Modeling of Steel Shielding Cylinder in Surface-Mounted Permanent Magnet Machines

Two-dimensional (2-D) analytical modeling of permanent magnet machines with shielding cylinder is a challenging task due to the saturation effect of the cylinder. This paper presents a 2-D hybrid analytical solution to model surface-mounted permanent magnet machines with a shielding cylinder attached to the exterior of the rotor body. The presented model provides an accurate representation of the motor response by accounting for the saturation effect of the shielding cylinder, as well as the stator slotting effect. For this purpose, the steel shielding cylinder is modeled by a vacuum cylinder (with the exact same size/dimension) and two inner and outer virtual surface currents. The values of the surface currents are determined by using the respective magnetic circuit model. Meanwhile, the slotting effect on the tangential flux component is modeled by injecting a virtual surface current onto a slotless stator surface. Next, the radial and tangential flux density are obtained by solving Poisson's equation via separation of variables theorem and applying relevant boundary conditions. The accuracy of the proposed model is verified by the finite element and experimental tests on the machine prototype.

A Two-dimensional Analytical Model for Volatile Organic Compound Diffusion Through the Unsaturated Soil and Horizontal Permeable Reactive Barriers

A Two-dimensional Analytical Model for Volatile Organic Compound Diffusion Through the Unsaturated Soil and Horizontal Permeable Reactive Barriers

Detailed Investigation of the Eddy Current and Core Losses in Coaxial Magnetic Gears through a Two-Dimensional Analytical Model

This work introduces a 2D model that calculates power losses in coaxial magnetic gears (CMGs). The eddy current losses of the magnets are computed analytically, whereas the core losses of the ferromagnetic segments are computed using an analytical–finite element hybrid model. The results were within 1.51% and 3.18% of those obtained from an FEA for the eddy current and core losses in the CMG for an indicative inner rotor speed of 2500 rpm. In addition, the significance of the circumferential magnet segmentation is demonstrated in the CMGs. Furthermore, a parametric investigation of the efficiency of the system for different applied external loads is carried out. Finally, a mesh sensitivity analysis is performed, along with the computation of the average power losses throughout one full period, resulting in an at least 80% reduction in computational costs with a negligible effect on accuracy. The developed model could be a valuable tool for the minimization of power losses in CMGs since it combines high accuracy with a low computational cost.

On the sediment deposition on Barugbug Situdam Weir

In this paper, we investigate the behavior of total sediment transport in the Barudbug weir, Situdam, Karawang, West Java, Indonesia, which is a crucial aspect of water management in the Citarum river basin. We utilize SESAME instrument observation data, encompassing rainfall, TSS, and depth parameters, gathered over a period of approximately three years. Additionally, we employ a two-dimensional Advection-Diffusion analytic model that takes into account settling velocity. The observation results reveal a positive correlation between TSS and depth, with TSS levels increasing following heavy rainfall. Furthermore, there exists a time delay between rainfall events and the subsequent rise in TSS concentration, suggesting an upstream source of sediment. The model outcomes demonstrate an inverse relationship between TSS concentration and the velocity of river flow, as the river flow acts as a leaching mechanism.

Two-dimensional analytical model for a non-lightly doped drain SOI MOSFET

A two-dimensional (2D) analytical model considering the effects of the gate oxide region, channel region, and buried oxide region for a non-lightly doped drain (LDD) SOI MOSFET is proposed. The top and bottom surface potential distributions have been derived on the basis of solving 2D Poisson’s equation and using an evanescent mode analysis. The potential distribution, threshold voltage, and threshold voltage roll-off have been verified by Silvaco ATLAS simulated results for the proposed device with different device parameters. The model agrees well with the simulation results under the above-mentioned conditions. Therefore, the analytical model provides the basic designing guidance for non-LDD SOI MOSFETs.

The Analytical Models of Fringe Parasitic Capacitance of FinFET - A Review

When planar MOSFET encounters its own scaling limit, FinFET was introduced and successfully replaced the traditional MOSFET. FinFET owns its privilege over the planar MOSFET for its high tolerance to short channel effect. However, due to FinFET’s 3D structure, high parasitic capacitance compared to planar MOSFET significantly degrades the transistor speed because of RC delay. This paper provides a review on the fringe capacitance of FinFET device based on the accuracy to experimental data of the two-dimensional and three-dimensional analytical models. Those models take the external and internal parasitic capacitance component into account. The three-dimensional model outperforms the two-dimensional model in levels of precision but requires more parameters and time to establish.

Analytical modeling of 2D groundwater flow in a semi-infinite heterogeneous domain with variable lateral sources

<abstract> <p>In nature, aquifers are usually composed of distinct kinds of media, i.e., heterogeneous domains rather than homogeneous domains. Groundwater level and flow changes in such domains are more complicated than those in homogeneous domains; thus, building a mathematical model for addressing groundwater flow in heterogeneous aquifers is the present research goal. In conventional research on similar topics, many one-dimensional (1D) analytical models have been presented, but it is challenging to simulate real-world scenarios. This study develops a two-dimensional (2D) analytical model for modeling groundwater flow in a conceptual sloping heterogeneous domain imposed by variable recharge. This model can consider distinct slope angles, medium heterogeneity, and any type of lateral recharge for a semi-infinite domain. The results indicate that groundwater level and flow discharge are greatly affected by the abovementioned factors. The recharge intensity significantly affects the peak of the groundwater level. For example, when the recharge rate increases by 30%, the peak water level increases by 50% as the groundwater flows from the sandy loam zone to the loam zone. The loops delineating the relationship between discharge and groundwater level for different bottom slopes cannot become close for heterogeneous aquifers. The presented 2D analytical model can simulate and better predict results of groundwater changes than previous 1D analytical models. Further, this model can simultaneously consider the effect of varying recharge over time and space on groundwater level change.</p> </abstract>

Probabilistic analysis of tunnel face seismic stability in layered rock masses using Polynomial Chaos Kriging metamodel

Face stability is an essential issue in tunnel design and construction. Layered rock masses are typical and ubiquitous; uncertainties in rock properties always exist. In view of this, a comprehensive method, which combines the Upper bound Limit analysis of Tunnel face stability, the Polynomial Chaos Kriging, the Monte-Carlo Simulation and Analysis of Covariance method (ULT-PCK-MA), is proposed to investigate the seismic stability of tunnel faces. A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis. An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects. Ten input parameters, including geological strength indices, uniaxial compressive strengths and constants for three rock formations, and the horizontal seismic coefficients, are treated as random variables. The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed. In addition, the effects of weak layer position, the middle layer thickness and quality, the tunnel diameter, the parameters correlation, and the seismic loadings are investigated, respectively. The results show that the layer distributions significantly influence the tunnel face probabilistic stability, particularly when the weak rock is present in the bottom layer. The efficiency of the proposed ULT-PCK-MA is validated, which is expected to facilitate the engineering design and construction.

Two-dimensional analytical model for fully depleted SOI MOSFETs with vertical trapezoid doping including effects of the interface trapped charges

The two-dimensional (2D) potential distribution for vertical trapezoidal doping thin-body fully depleted (FD) silicon-on-insulator (SOI) devices is derived by adopting the evanescent mode analysis method, in which the 2D effects in gate oxide region, channel region and buried oxide region are taken into account. Moreover, the effects of interface trapped charge are considered. Using this potential model, the subthreshold performance of the device including subthreshold current, and subthreshold swing under various conditions have been studied. The result shows that the analytical model is good agreement with the simulated results. Therefore, it provides a feasible way of developing new 2D models for vertical trapezoidal doping thin-body FD SOI devices. Besides offering the physical insight into device physics, the analytical model provides the basic designing guidance for vertical trapezoidal doping thin-body FD SOI devices.

Analytical Calculation and Low-Order Component Optimization of Axial Electromagnetic Force for an Axial Flux Motor

The low-order high-amplitude component of axial electromagnetic force is the leading cause of electromagnetic vibration and noise of axial flux permanent magnet (AFPM) motors. In this paper, based on the analytical calculation of the axial electromagnetic force for a 20-pole 24-slot AFPM motor, the low-order axial electromagnetic force component is weakened by optimizing the motor’s electromagnetic structure. First, the three-dimensional (3-D) structural model of the motor is equated to a two-dimensional (2-D) analytical model, which is used to calculate the magnetic field generated by each of the armature winding and permanent magnet. Then, combined with the Maxwell tensor method, the axial electromagnetic force waveform is further obtained, and the target low-order high-amplitude component is extracted by 2-D Fourier analysis. Finally, taking this axial electromagnetic force component minimization as the target function of optimization, considering the output torque and ripple as constraints, the genetic algorithm is used to search for the optimal point by varying the structural parameters of the motor. The results show that the target low-order high-amplitude component of the axial electromagnetic force of the optimized motor is effectively suppressed, and the output torque ripple decreases with slightly increased torque amplitude, which provides a practical method for vibration and noise reduction of AFPM motors.

Physics based numerical model of a nanoscale dielectric modulated step graded germanium source biotube FET sensor: modelling and simulation

This paper proposes a novel dielectric modulated step-graded germanium source biotube FET for label-free biosensing applications. Its integrated structure and unique design combine the benefits of the gate stack, germanium source, triple-gate architecture, and a step-graded biotube channel, resulting in superior performance over existing biosensors. A compact two-dimensional analytical model for channel potential, drain current, threshold voltage, and subthreshold swing has been formulated and agrees well with the simulated results. The comprehensive investigation of different device parameters, including doping and bias, offers valuable insights into optimizing the biosensor’s performance. The proposed biosensor exhibits remarkable sensitivity, achieving up to 263 mV and 1495.52 nA for certain biomolecules, which has been validated by a compact analytical model and simulations performed on the SILVACO TCAD simulator. Several parameters are employed to assess the biosensor’s effectiveness: threshold voltage, ION/IOFF ratio, subthreshold swing, off-current, peak trans-conductance, and on-current. Furthermore, the biotube channel design enables lightweight and cost-efficient biosensors, enhancing the biosensor’s practicality. This work also includes an analysis of the effect of temperature on the biosensor’s performance and characteristics, providing insights into practical applications. High sensitivity of the biosensor signifies a significant advancement in biosensing technology, suggesting a wide range of potential applications in biomedical field.

Analytical Modeling of Slotless Axial Flux Permanent Magnet Motor With Equidirectional Toroidal Winding

This study proposes a two-dimensional (2D) analytical model (AM) of slotless axial flux permanent magnet (AFPM) motor, which includes two submodels of armature winding (AW) and permanent magnet (PM) magnetic fields. It can reveal the operating mechanism of equidirectional toroidal winding (ETW) armature magnetic field in the theory and quantitatively analyze its AW and PM magnetic fields. The proposed AM is characterized in that AW magnetic field submodel is established only based on the current density distribution of the effective conductors on one side of a single toroidal coil considering its width and thickness. First, based on the proposed equivalence principle, the analytical submodels of AW and PM magnetic fields of AFPM motor with ETW are established separately, and the formulas of back EMF and torque of the motor are derived. Second, the electromagnetic performance of a slotless AFPM motor with ETW is studied by the proposed 2D AM, including the waveforms of AW and PM magnetic fields, phase back EMF and torque, which are verified by the finite element model. Finally, a prototype of AFPM motor with ETW is manufactured and tested in open-circuit and on-load conditions, which verifies the accuracy of the proposed AM.

Напружено-деформований стан клейового з’єднання, що має поздовжній дефект

In adhesive joints, one has to face the phenomenon of non-adhesive. It is known that non-adhesive reduces the strength of such joints. Analytical models known today for calculating the stress-strain state of adhesive joints have certain defects that appear as a result of simplification (one-dimensional models), and the realization of numerical methods requires a large resource of computing equipment. The subject of study in this article is a mathematical model of the stress-strain state of an adhesive joint of two plates. The purpose of this research is to study the stress-strain state of an adhesive joint with non-adhesives and to develop methods for studying the stress state of adhesive lap joints. Methods: a simplified two-dimensional analytical model of the stress state of the adhesive joint was used to construct an analytical solution to the problem of the stress state of the joint, which contains a defect in the adhesive layer along the side edge of the bonding area. The simplification of the model consists of the fact that the transverse displacements of the base layers are considered to be zero. This assumption can be interpreted as the presence of base layers of high stiffness in the transverse direction, and it allows reducing the problem of the stressed state of the joint to a system of two partial differential equations with respect to the longitudinal movements of the base layers and obtaining the solution of the problem in an analytical form. The obtained solution is written in the form of functional series. The eigenfunctions are not orthogonal. Using the least squares method, the solution of the problem is reduced to a system of linear equations. The model problem for joining two aluminum plates of the same size has been solved. The results showed that the presence of non-adhesive area can significantly increase the stress near the edge of the adhesive layer. Corner points in the adhesive layer are especially dangerous from the strength point of view. The results were compared with the results of finite element modeling. The comparison showed that the proposed mathematical model has high accuracy for engineering calculations. This model can be developed to solve similar problems, for example, to study the stress state of the joint of coaxial pipes, which has defects in the adhesive layer.

Frequency reduction and attenuation of the tire air cavity mode due to a porous lining

The tire air cavity mode is known to be a significant source of vehicle structure-borne road noise near 200 Hz. A porous lining placed on the inner surface of a tire is an effective countermeasure to attenuate that resonance. The two noticeable effects of such a lining are the sound pressure attenuation and the frequency reduction of the air cavity mode. In this paper, through both analytical and numerical methods, the mechanism of the effects of porous lining was studied. A two-dimensional duct-shaped analytical model and a tire-shaped numerical model were built to investigate the lined tire in conjunction with the Johnson-Champoux-Allard model describing the visco-inertial dissipative effects of the porous material. Design parameters of the porous lining were controlled to study their impact and optimal ranges of the design parameters were suggested. Finally, in experimental analysis, the sound attenuation and the frequency drop were observed in measurements of force, acceleration, and sound pressure. In conclusion, it was demonstrated that the suggested analytical and numerical models successfully predict the effect of porous lining and that the frequency reduction results from the decreased sound speed within the tire owing to the presence of the liner.

‘Help us better understand our changing climate’: Exploring the discourse of Citizen Science

In this article I claim that online Citizen Science projects are exemplars of a digital genre that acts as text and medium. To support this claim I apply a previously proposed two-dimensional genre analytical model and develop empirical procedures to identify how ‘communicative purpose’ is realised by functional units/links, which in turn are realised by rhetorical strategies (verbal and visual) in two dimensions, the reading mode and the navigation mode. Empirical data show that this genre fulfils a set of distinct communicative purposes, namely to build credibility and trust in scientific research, to make specialised contents accessible to audiences with different levels of scientific literacy, to convey emotion and to build and maintain citizen-volunteers’ engagement. Such multifunctionality fulfils the social exigence of the genre, that is, supporting participatory science. The study contributes to the empirical characterisation of non-linear, multimodal genres taking into account the roles of text producer and text receiver.

Calculation and Characterization of Braking Performance for Rail Eddy Current Brake With AC Excited Ring-Winding Armature

With the continuous increases of the train speed, the braking device that relies on the wheel-rail adhesion has approached its acceptable speed limit. Compared with traditional friction brakes, eddy current brakes (ECBs) have the advantages of non-wheel-rail contact, fast response, low noise, wide application range, and no pollution. This study describes an ECB with AC excitation based on Faraday's law. The two-dimensional analytical model of ECB is established by the sub-domain method. Then, the experiment system of rail ECB is designed and built to test the braking characteristics. The authenticity of mathematical model is verified by experimental results. The research indicated that braking force increased at first and reached a maximum value, then slowly decreased with the increase of speed, while normal attractive force was always reduced. This characteristic matches the requirements of high-speed trains with large braking force and low normal force, which makes it a great option for auxiliary braking mechanism in the high-speed trains.