Semi-analytical Approach Research Articles

Surface parameterisation and spectral synthesis of rapidly rotating stars. Vega as a testbed

Spectral synthesis is a powerful tool with which to find the fundamental parameters of stars. Models are usually restricted to single values of temperature and gravity, and assume spherical symmetry. This approximation breaks down for rapidly rotating stars. This paper presents a joint formalism to allow a computation of the stellar structure — namely, the photospheric radius, $R$, the effective temperature, $T_ eff $, and gravity, $g_ eff $ — as a function of the colatitude, theta , for rapid rotators with radiative envelopes, and a subsequent method to build the corresponding synthetic spectrum. The structure of the star is computed using a semi-analytical approach, which is easy to implement from a computational point of view and which reproduces very accurately the results of much more complex codes. Once $R( eff and eff are computed, the suite of codes atlas and synthe by R. Kurucz are used to synthesise spectra for a mesh of cells in which the star is divided. The appropriate limb-darkening coefficients are also computed, and the final output spectrum is built for a given inclination of the rotation axis with respect to the line of sight. All the geometrical transformations required are described in detail. The combined formalism has been applied to Vega, a rapidly rotating star almost seen pole-on, as a testbed. The structure reproduces the results from interferometric studies and the synthetic spectrum matches the peculiar shape of the spectral lines well. Contexts where this formalism can be applied are outlined in the final sections.

Semi-analytical approach to study wave interaction with a pair of obliquely submerged heterogeneous flexible structures

ABSTRACT Analyzing inclined flexible plates of varying thickness is crucial for optimising and attaining precise control over wave reflection and transmission. This is particularly significant in the context of breakwater construction. In contrast to horizontal breakwaters, inclined barriers can penetrate multiple layers of fluid with varying particle velocities, facilitating interactions and causing wave breaking, which results in the dissipation of wave energy. Moreover, compared to vertical structures, inclined ones demonstrate more effective wave attenuation. In the context of the present study, we investigate the interaction of water waves with a pair of obliquely submerged flexible thin plates characterised by non-uniform thickness. In order to model this complex physical scenario, we employ the principles of linear water wave theory in conjunction with Kirchhoff's thin plate theory. By employing repeated integration and Green's integral theorem, we reduce the boundary value problem to a system of coupled integral equations. Through appropriate approximations, we solve this system and obtain numerical values for various hydrodynamic quantities. This model provides comprehensive results for both horizontal and vertical plates, making it highly versatile. We examine the impact of varying thickness and the inclination of the two flexible plates to understand their roles in the wave scattering process and the associated physical parameters. The results obtained from this study shed light on the intricate dynamics involved in wave-structure interactions and can inform the design and optimisation of breakwater systems.

A new semi-analytical approach for nonlinear electro-thermo-mechanical dynamic responses of FG-GPLRC shallow spherical caps and circular plates with porous core

A new semi-analytical approach for nonlinear electro-thermo-mechanical dynamic responses of FG-GPLRC shallow spherical caps and circular plates with porous core

A Mean Field to Capture Asynchronous Irregular Dynamics of Conductance-Based Networks of Adaptive Quadratic Integrate-and-Fire Neuron Models.

Mean-field models are a class of models used in computational neuroscience to study the behavior of large populations of neurons. These models are based on the idea of representing the activity of a large number of neurons as the average behavior of mean-field variables. This abstraction allows the study of large-scale neural dynamics in a computationally efficient and mathematically tractable manner. One of these methods, based on a semianalytical approach, has previously been applied to different types of singleneuron models, but never to models based on a quadratic form. In this work, we adapted this method to quadratic integrate-and-fire neuron models with adaptation and conductance-based synaptic interactions. We validated the mean-field model by comparing it to the spiking network model. This mean-field model should be useful to model large-scale activity based on quadratic neurons interacting with conductance-based synapses.

Unsteady Dean flow between concentric circular cylinders in the presence of a uniform axial magnetic field

An analysis is carried out on the unsteady Dean flow of an incompressible electrically conducting viscous fluid between two concentric, stationary permeable circular cylinders in the presence of magnetic field of low intensity. The flow phenomenon is important in view of its biological as well as industrial applications, particularly in polymer industries for designing flows in cylindrical shaped pipes/tubes. The novelty of the study is to analyze the effect of electromagnetic body force which comes into play due to interaction of magnetic field with conducting fluid in flow. The cross flow due to suction/injection, azimuthal pressure gradient, and the Lorentz force (electromagnetic body force) are considered in the momentum transport equation. The mathematical model and the corresponding governing equations are solved in two methods; one is analytical using special function and another one is semi analytical approach, i.e. Laplace transform in conjuction with Riemann–Sum approximation for inversion. The study reveals the effects of magnetic parameter, suction/injection parameter and radii ratio of two concentric cylinders forming annular region. The striking outcomes which fulfills the design requirements are as follows. The applied radial magnetic field resulting electromagnetic body force on the flow, accelerates the circumferential velocity which energizes the industrial setup (flow model) to enhance faster productivity. Moreover, the curves of skin friction at R = λ posses critical points serving as benchmark for engendering flow instability.

Seismic wave amplification in a weakly nonlinear two-layered soil deposit

Based on numerous observations, local soil site conditions can significantly affect the formation of seismic responses. In this paper, we examine seismic responses caused by shear waves propagating through a two-layered soil deposit. The aim of the research is to study the phenomenon of amplification of shear waves due to the resonant properties of the soil deposit and the nonlinear characteristics of partial layers, which are assumed to be the cubically nonlinear continuous media. The target problem relates to a nonlinear boundary value problem, the solution of which is carried out using a semi-analytical approach. According to the approach, the problem’s solution is sought using the method of separation of variables, while the solution to the corresponding spectral problem is derived in the form of a power series. Additionally, good agreement is shown between theoretical studies and numerical simulations. The developed approach allows one to evaluate the amplification factor for a nonlinear two-layered soil deposit and to detect changes in the shape of amplification factor profiles when the frequency of an incident wave on a rigid bedrock is varied.

A novel semi-analytical method for fillet foundation deflection calculation in presence of a tooth crack propagating into the rim of a spur gear

Existing analytical approaches for calculating fillet foundation deflections in spur gear struggle to adequately address the complexities introduced by tooth cracks, particularly as cracks propagate into the gear body. The finite element methods are accurate but computationally expensive. In response to these challenges, the paper introduces a novel semi-analytical method based on elastic circular ring theory that is capable of calculating the fillet foundation deflection for both healthy and cracked conditions. To establish the usefulness of the method, the fillet foundation deflections obtained are further used to obtain the time-varying mesh stiffness. A methodology centered on compatibility conditions is employed to achieve load distribution during double tooth engagement. The results are verified using two three-dimensional finite element models. In addition, the effect of different hub hole radii, crack lengths and orientations on the fillet foundation deflections and TVMS are investigated. The outcomes suggest that the proposed semi-analytical approach demonstrates superior accuracy in the calculation of spur gear mesh stiffness compared to alternative methods.

A computationally efficient thermo-mechanical model with temporal acceleration for prediction of residual stresses and deformations in WAAM

ABSTRACT The present paper introduces a novel temporal acceleration strategy for computationally efficient prediction of residual stresses and deformations in wire arc additive manufacturing (WAAM) components. It employs a semi-analytical approach, dividing temperature into the analytical and the complementary fields. The analytical field is obtained by a closed-form solution, and the complementary field is employed to solve the boundary conditions. A temporal acceleration factor for the heating period is applied. Meanwhile, the diffusion time in the analytical field is manipulated to guarantee accurate temperature prediction. Validation via WAAM experiments, including both a thin-wall structure and a practical engineering component with characteristic dimensions on the order of metres, indicates that the predicted stresses is 50 MPa lower than the experimental values. Moreover, the discrepancy of between the predicted deformations and the experimental measurements is less than 10%, demonstrating reasonable accuracy can be achieved with attractive computational efficiency.

Analytical insights into the behavior of finite amplitude waves in plasma fluid dynamics

This study introduces innovative analytical solutions for the [Formula: see text]-dimensional nonlinear Jaulent–Miodek ([Formula: see text]) equation, a governing model elucidating the propagation characteristics of nonlinear shallow water waves with finite amplitude. Employing analytical methodologies such as the Khater II and unified methods, alongside the Adomian decomposition method as a semi-analytical approach, series solutions are derived with the primary aim of elucidating the fundamental physics dictating the evolution of [Formula: see text] waves. Within the realm of nonlinear fluid dynamics, the [Formula: see text] equation encapsulates the behavior of irrotational, inviscid, and incompressible fluid flow, wherein nonlinear effects and dispersion intricately balance to yield stable propagating waves. This equation encompasses terms representing nonlinear convection, dispersion, and nonlinearity effects. The analytical methodologies employed in this investigation yield solutions for various instances of the [Formula: see text] equation, demonstrating convergence, accuracy, and computational efficiency. The outcomes reveal that the Adomian decomposition method yields solutions congruent with those obtained through analytical techniques, thereby affirming the precision of the derived solutions. Furthermore, this study advances the comprehension of the physical implications inherent in the [Formula: see text] equation, serving as a benchmark for evaluating alternative methodologies. The analytical approaches elucidated in this research furnish accessible tools for addressing a diverse array of nonlinear wave equations in mathematical physics and engineering domains. In summary, the introduction of novel exact and approximate solutions significantly contributes to the advancement of knowledge pertaining to the [Formula: see text]-dimensional [Formula: see text] equation. The ramifications of this research extend to the modeling of shallow water waves, offering invaluable insights for researchers and practitioners engaged in the field.

Control-inspired design and power optimization of an active mechanical motion rectifier based power takeoff for wave energy converters

Ocean waves have high energy density and are persistent and predictable. Yet, converting wave energy to a useable form remains challenging. A significant hurdle is the oscillatory nature of waves resulting in the alternating loads, which necessitate the use of rectification at some stage of the energy conversion. This research effort presents a novel design of active mechanical motion rectifier (AMMR) for the power takeoff (PTO), which provides enhanced controllability and better power performance when compared to passive mechanical motion rectifiers (MMR). Inspired by transistors used in synchronous electrical rectifiers, the proposed design uses controllable electromagnetic clutches in the mechanical transmission to allow active engagement-disengagement control; thus, rectifying the oscillatory motion into a unidirectional rotation for high energy conversion efficiency and allowing the generator in unidirectional rotation to control the bidirectional wave capture structure for maximizing the power output. A semi-analytical computational approach is developed to efficiently evaluate the optimal power achieved using the proposed AMMR-based PTO and active control. It is found that the AMMR-based PTO design yields a higher optimal power than the previous passive MMR design across the wave spectrum. The influences of generator inertia and reactive power are discussed. The effects of control parameters on the power output and the optimal trajectories are analyzed. Wave tank tests with the AMMR prototype demonstrated the effectiveness of AMMR based PTO design and validated the numerical analysis.

Oscillations of coaxial hydrophobic spherical colloidal particles in a micropolar fluid

The microstructured flow field of a micropolar model around a straight chain of multiple hydrophobic spherical particles oscillating rectilinearly along their line of centers is studied under the conditions of low Reynolds numbers. In general, the particles can exhibit variations in both radius and amplitude of oscillations, and they are allowed to be unevenly spaced. The amplitudes are required to be small in comparison with a characteristic length, which can be considered as the radius of the larger particle. The concepts of slip length and spin slip length are introduced to characterize the partial slip and spin slip boundary conditions at the hydrophobic surfaces of the colloidal particles. The differential equations that govern the system are solved through a semi-analytical approach in combination with boundary collocation techniques. The interaction effects between the particles are assessed through the in-phase and out-of-phase drag force coefficients acting on each particle for various values of geometrical and physical parameters. The numerical schemes are carried for the case of two oscillating spherical particles. The results of this investigation indicate that the drag coefficients are notably influenced by the presence of the second particle, micropolarity, frequency, and slip parameters. The current study reveals that the impact of the micropolarity parameter is not significant on the in-phase force coefficient for slippage parameter values less than one. However, it becomes significant for slippage parameter values exceeding one. Typically, when particles oscillate in opposing modes, in-phase coefficient values surpass 1, whereas they fall below 1 when oscillating in the same mode. The present study is driven by the necessity to gain a deeper comprehension of the fluid tapping mode employed in atomic force microscope devices, especially when this mode pertains to microstructures in the vicinity of a curved surface.

Estimating turbidity concentrations in highly dynamic rivers using Sentinel-2 imagery in Google Earth Engine: Case study of the Godavari River, India.

Turbidity is an essential biogeochemical parameter for water quality management because it shapes the physical landscape and regulates ecological systems. It varies spatially and temporally across large water bodies, but monitoring based on point-source field observations remains a difficult task in developing countries due to the need for logistics and costs. In this study, we present a novel semi-analytical approach for estimating turbidity from remote sensing reflectance in moderate to highly turbid waters in the lower part of the Godavari River (i.e., locations near Rajahmundry). The proposed method includes two sub-algorithms-Normalized Difference Turbidity Index (NDTI) and semi-empirical single-band turbidity ( ) algorithm-to retrieve spectral reflectance information corresponding to the study locations for turbidity modeling. Sentinel-2 Multi-Spectral Imager data have been used to quantify the turbidity in the Google Earth Engine (GEE) platform. The correlation analysis was observed between spectral reflectance values and in situ turbidity data using cubic polynomial regression equations. The results indicated that the , which uses the only red-edge wavelength, identified turbidity as the most accurate across all locations (highest R2 = 0.91, lowest RMSE = 0.003), followed by NDTI (highest R2 = 0.85, lowest RMSE = 0.05), respectively. The remote sensing data application provides a better way to monitor turbidity at large spatio-temporal scales in attaining the water quality standards of the Godavari River.

A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads

This paper presents a novel semi-analytical simulation approach for analysing the behaviour of bi-directional functionally graded cantilever beams subjected to arbitrary static loads, such as concentrated moments, concentrated forces, distributed force and their combinations applied at any location along the beam. The fundamental equations governing the cantilever beam’s response are derived, on the basis of which the proposed semi-analytical method is implemented using MATLAB programming language. The simulation results include field variables as well as stress contours, providing a compressive understanding of the beam’s behaviour. To validate the accuracy and reliability of the proposed method, a convergence study is conducted in comparison with the graded finite element method (GFEM) and analytical solutions. In the end, the developed method is applied to simulate the bending behaviour of bi-directional functionally graded cantilever beams under various loads individually and their combinations. The stress contours and deflection curves obtained from the simulation are compared with the solutions obtained using GFEM, revealing that the developed method possesses excellent capability in accurately simulating the bending behaviour of cantilever beams.

Robust and efficient implementation of finite strain generalized continuum models for material failure: Analytical, numerical, and automatic differentiation with hyper-dual numbers

Generalized continuum models for representing nonlinear material behavior including material failure in the finite strain regime are commonly formulated based on scalar elastic and dissipation potential functions. The evolution of stresses and internal variables, i.e., the material state, is governed by partial derivatives of the potential functions with respect to deformation and stress measures. Furthermore, for application of such models in implicit nonlinear finite element analysis tangent operators, consistent with the numerical integration algorithm, are required. In this work, we study analytical, numerical and automatic differentiation schemes for the implementation of coupled, generalized continuum models considering finite inelastic deformations and fracture. This includes the application of finite difference approximations, complex-step derivative approximations and automatic differentiation based on hyper-dual numbers. For the use of automatic differentiation, a semi-analytical split approach is introduced for increasing the computational efficiency. Based on a comprehensive 2D and 3D finite element study, we demonstrate the superior properties of automatic differentiation compared to numerical differentiation methods with regards to accuracy and robustness. Furthermore, the additional computational cost for automatic differentiation using the proposed split approach becomes negligible for large problems.

Perturbative and semi-analytical solutions to Teukolsky equations for massive fermions

In this work, we aim at solving the Teukolsky equations for a fermion with mass m e ≠ 0 in the presence of a rotating black hole with mass M. We consider two different regimes: m˜e=M−1me≪1 and a ω ≪ 1; m˜e≪1 and a ω ≳ 1. We treat each of these two regimes in different ways: we use a perturbative approach for the first, similar to the usual one employed for spin 0, 1, 2 and mass-less 1/2 fields, but with two small parameters (aω and m˜e ); as we shall see, the second can be treated with a semi-analytical approach. In a forthcoming paper we shall study the remaining two cases in which m˜e≳1 , while a ω ≪ 1 or a ω ≳ 1. The regime with m˜e≪1 , but a ω ≳ 1 is probably the most interesting from the astrophysics point of view, but this last two cases might be of some interest for the study of the interaction of fermions with very small black holes, which may be formed, for example, in the last stages of the Hawking evaporation.

Semi-Analytical Assessment of Multiple Gravity-Assist Opportunities Based on Feasibility Domains

This paper proposes a semi-analytical method for multiple gravity-assist (MGA) opportunity assessment, which can judge the feasibility of MGA sequences and predict corresponding opportunities in terms of the relative phases between flyby planets. The proposed method features the feasible domains of gravity-assist states and the phase differences in MGA rather than focusing on a limited number of optimal solutions. First, the planet flyby departure and arrival conditions for successive gravity assist are analytically derived based on the planar circular model. Second, the feasible domain of gravity assist described by flyby parameters is established and pruned based on the conditions, and the corresponding relative phases between planets are calculated. Third, a MGA opportunity search algorithm via feasible domain is formulated to match the phase differences in the ephemeris. Lastly, the method is examined in two types of MGA missions: the rendezvous and flyby missions. The results from the semi-analytical approach can cover all optimized opportunities in the rendezvous mission and 94.44% optimized opportunities in the flyby mission under the accurate three-dimensional model. The results of the proposed semi-analytical method can serve as a good initial guess for further accurate trajectory optimization and provide reference for future MGA mission design.

Investigating the Response Variability of Statically Determined Sandwich Beams considering two Random Fields of Elastic Modulus

In this paper, the displacement variation in sandwich beams is determined by employing a semi-analytical approach. The classical displacement is calculated by integration using Mohr’s equation, although the integration is complicated due to the inclusion of random fields in the inertial moment term. Using the trapezoidal rule to compute these integrals, the random fields are discretized into random variables at the nodal point of the beam segments. Thus, the expected displacement, standard deviation, and coefficient of variation can be computed. To validate the results, the random fields are simulated using a previously described spectral method. The results of numerical examples were compared with the semi-analytical method and the Monte Carlo simulation demonstrating the high accuracy of the proposed method. The results also illustrate the influence of the parameters of the random fields of elastic modulus on the variability of displacement.

Uncertainties in regularized long-wave equation and its modified form: A triangular fuzzy-based approach

This article explores the solution of the regularized long-wave equation (RLWE) and modified RLWE (MRLWE) using a semi-analytical approach known as the homotopy perturbation transform method (HPTM), revealing the characteristics of shallow water waves and ion-acoustic plasma waves. The effectiveness and accuracy of the technique are demonstrated by solving scenarios involving a single solitary wave (SSW) and two solitary waves (TSW) presented and compared with the exact solution of the RLWE. Furthermore, we introduced a fuzzy model for both RLWE and MRLWE, considering uncertainties in the coefficients related to the wave amplitude, and to understand the behavior of both fuzzy RLWE (FRLWE) and fuzzy MRLWE (FMRLWE) in the SSW by examining various numerical results using MATLAB.

Modeling of 3D-printed composite filaments using X-ray computer tomography images segmented by neural networks

This study introduces a novel semi-analytical two-scale approach to model 3D-printed composite filament where both fibers and voids are present. The proposed approach utilizes micro computer tomography (micro-CT) images to visualize fibers and voids. Then, a novel segmentation process based on neural network algorithms (specifically the YOLO v7 algorithm) is employed to segment the distinct fiber and void phases. The volume fractions and the geometries of the phases are then used in the first scale (the micro-scale) of the approach and the effective elastic properties of internal regions of the filament are obtained using the Mori–Tanaka effective field method. These regions are then joined together to form the second scale (the macro-scale), for which the elastic properties are evaluated using the finite element method. The two-scale approach is applied for 3D-printed nylon reinforced with continuous carbon fibers and the predictions of the elastic properties are compared to tensile tests conducted on the single filament. A great agreement is observed for Young’s modulus along the fiber direction of the single printed filament.

Chirped Managed Laser for Multilevel Modulation Formats: A Semi-Analytical Approach for Efficient Filter Design

Chirped Managed Laser for Multilevel Modulation Formats: A Semi-Analytical Approach for Efficient Filter Design