Conventional Equation Research Articles

A fast two-phase non-isothermal reduced-order model for accelerating PEM fuel cell design development

A reduced-order model (ROM) is developed for proton exchange membrane fuel cells (PEMFCs) considering the non-isothermal two-phase effects, with the goal of enhancing computational efficiency and thus accelerating fuel cell design development. Using analytical order reduction and approximation methods, the fluxes and source terms in conventional 1D conservation equations are reduced to six computing nodes at the interfaces between each cell component. The errors associated with order reduction are minimized by introducing new approximation methods for the potential distribution, the transport properties, and the membrane hydration status. The trade-off between model accuracy and computational efficiency is studied by comparing the simulation results and computational times of the new model with a full 1D model. The new model is nearly two orders of magnitude faster without sacrificing too much accuracy (<4% difference) compared to the 1D model. The new model is then used to analyze the influence of the membrane electrode assembly (MEA) design on cell performance and internal state distributions, offering insights into MEA structural optimization. The model can be readily extended to account for more detailed physico-chemical processes, such as Knudsen diffusion or the influence of micro-porous layers, and it can be an effective tool for understanding and designing PEMFCs.

Analytical and Numerical Treatment of Continuous Ageing in the Voter Model

The conventional voter model is modified so that an agent’s switching rate depends on the ‘age’ of the agent—that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We show how the resulting individual-based system with non-Markovian dynamics and concentration-dependent rates can be handled both computationally and analytically. The thinning algorithm of Lewis and Shedler can be modified in order to provide an efficient simulation method. Analytically, we demonstrate how the asymptotic approach to an absorbing state (consensus) can be deduced. We discuss three special cases of the age-dependent switching rate: one in which the concentration of voters can be approximated by a fractional differential equation, another for which the approach to consensus is exponential in time, and a third case in which the system reaches a frozen state instead of consensus. Finally, we include the effects of a spontaneous change of opinion, i.e., we study a noisy voter model with continuous ageing. We demonstrate that this can give rise to a continuous transition between coexistence and consensus phases. We also show how the stationary probability distribution can be approximated, despite the fact that the system cannot be described by a conventional master equation.

Prediction of Blast-Induced Ground Vibration at a Limestone Quarry: An Artificial Intelligence Approach

Ground vibration is one of the most unfavourable environmental effects of blasting activities, which can cause serious damage to neighboring homes and structures. As a result, effective forecasting of their severity is critical to controlling and reducing their recurrence. There are several conventional vibration predictor equations available proposed by different researchers but most of them are based on only two parameters, i.e., explosive charge used per delay and distance between blast face to the monitoring point. It is a well-known fact that blasting results are influenced by a number of blast design parameters, such as burden, spacing, powder factor, etc. but these are not being considered in any of the available conventional predictors and due to that they show a high error in predicting blast vibrations. Nowadays, artificial intelligence has been widely used in blast engineering. Thus, three artificial intelligence approaches, namely Gaussian process regression (GPR), extreme learning machine (ELM) and backpropagation neural network (BPNN) were used in this study to estimate ground vibration caused by blasting in Shree Cement Ras Limestone Mine in India. To achieve that aim, 101 blasting datasets with powder factor, average depth, distance, spacing, burden, charge weight, and stemming length as input parameters were collected from the mine site. For comparison purposes, a simple multivariate regression analysis (MVRA) model as well as, a nonparametric regression-based technique known as multivariate adaptive regression splines (MARS) was also constructed using the same datasets. This study serves as a foundational study for the comparison of GPR, BPNN, ELM, MARS and MVRA to ascertain their respective predictive performances. Eighty-one (81) datasets representing 80% of the total blasting datasets were used to construct and train the various predictive models while 20 data samples (20%) were utilized for evaluating the predictive capabilities of the developed predictive models. Using the testing datasets, major indicators of performance, namely mean squared error (MSE), variance accounted for (VAF), correlation coefficient (R) and coefficient of determination (R2) were compared as statistical evaluators of model performance. This study revealed that the GPR model exhibited superior predictive capability in comparison to the MARS, BPNN, ELM and MVRA. The GPR model showed the highest VAF, R and R2 values of 99.1728%, 0.9985 and 0.9971 respectively and the lowest MSE of 0.0903. As a result, the blast engineer can employ GPR as an effective and appropriate method for forecasting blast-induced ground vibration.

Modified geodesic equations of motion for compact bodies in alternative theories gravity

We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in a class of alternative theories of gravity to general relativity. We use a prescription proposed by Eardley for incorporating the effects of self-gravity within gravitationally bound bodies, in which their masses may depend on invariant quantities constructed from the auxiliary scalar, vector or tensor fields introduced by such theories, evaluated in the vicinity of each body. The forms of the equations are independent of the field equations of the chosen theory. In the case where the masses are strictly constant, the equations reduce to the conventional geodesic equations of general relativity. These equations may be useful tools for deriving equations of motion for compact bodies to high post-Newtonian orders in alternative theories of gravity.

Equations of fluid dynamics with the ℓ–conformal Galilei symmetry

Equations of fluid dynamics are formulated, which hold invariant under the action of the ℓ–conformal Galilei group. They include the conventional continuity equation, a higher order material derivative analogue of the Euler equation, and a suitable modification of the conventional equation of state. Conserved charges associated with the ℓ–conformal Galilei symmetry transformations are presented.

Joint elasticity produces energy efficiency in underwater locomotion: Verification with deep reinforcement learning.

Underwater snake robots have received attention because of their unique mechanics and locomotion patterns. Given their highly redundant degrees of freedom, designing an energy-efficient gait has been a main challenge for the long-term autonomy of underwater snake robots. We propose a gait design method for an underwater snake robot based on deep reinforcement learning and curriculum learning. For comparison, we consider the gait generated by a conventional parametric gait equation controller as the baseline. Furthermore, inspired by the joints of living organisms, we consider elasticity (stiffness) in the joints of the snake robot to verify whether it contributes to the generation of energy efficiency in the underwater gait. We first demonstrate that the deep reinforcement learning controller can produce a more energy-efficient gait than the gait equation controller in underwater locomotion, by finding the control patterns which maximize the effect of energy efficiency through the exploitation of joint elasticity. In addition, appropriate joint elasticity can increase the maximum velocity achievable by a snake robot. Finally, simulation results in different liquid environments confirm that the deep reinforcement learning controller is superior to the gait equation controller, and it can find adaptive energy-efficient motion even when the liquid environment is changed. The video can be viewed at https://youtu.be/wpwQihhntEY.

The improved modified extended tanh-function method to develop the exact travelling wave solutions of a family of 3D fractional WBBM equations

The improved modified extended tanh-function (imETF) method is used to develop exact traveling wave solutions of a family of 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations. Bright solitons, dark solitons, bright-dark solitons, single solitons, and multiple solitons are obtained by using the imETF method. Also, periodic solutions, singular periodic solutions, hyperbolic function solutions, rational function solutions, trigonometric function solutions, and exponential function solutions are reported. Through companionable wave transformation, the governing equations are simplified to conventional ordinary differential equations. The alternative solution relates to the earlier phase. The anticipated solution's power coefficients are compared to create a system of algebraic equations (SAE). The links between parameters and coefficients that are required to create solutions are provided by a resilient coefficients scheme. For various parameter combinations, certain solutions are modeled.

Integrated denoising and extraction of both temperature and strain based on a single CNN framework for a BOTDA sensing system.

We have proposed and demonstrated a denoising and extraction convolutional neural network (DECNN) composed of 1D denoising convolutional autoencoder (DCAE) and 1D residual attention network (RANet) modules to extract temperature and strain simultaneously in a Brillouin optical time-domain analysis (BOTDA) system. With DCAE for high-fidelity denoising and RANet for accurate and robust information extraction, integrated denoising and extraction of both temperature and strain have been realized for the first time under a single CNN framework. Both simulation and experiment have been conducted to statistically analyze the performance of the proposed scheme and compare it with the conventional equation solving method (CESM), which show that DECNN has large noise tolerance and robustness over a wide range of temperature/strain and signal-to-noise ratio (SNR) conditions. The mean standard deviation (SD) and root mean square error (RMSE) of the temperature/strain extracted by DECNN over a wide range of SNRs are only 0.2°C/9.7µɛ and 2°C/32.3µɛ at the end of 19.38 km long sensing fiber, respectively. At a relatively low SNR of 8.8 dB, DECNN shows 196 times better temperature/strain uncertainty and 146 times faster processing speed when compared with CESM.

Artificial intelligence-based gene expression programming (GEP) model for assessing sprayed seal performance

This research predicts residual solvent (α), which is a key component of the performance assessment for a sprayed/chip seal. In this study, conventional equations for α were assessed that showed prediction inefficiency (R 2 value as low as 0.82) under different experimental conditions. Accordingly, gene expression programming (GEP), an emerging branch in artificial intelligence, was utilised to resolve these difficulties by developing empirical models for α. The data required for model development was obtained from extensive laboratory tests conducted on bitumen-solvent binder films in this research. Model evaluation results showed an excellent degree of correspondence between predictions and experimental results (R 2 = 0.94). This is the first study to model a key component of sprayed seal performance using GEP. The model is recommended for pre-design purposes or as a tool to determine residual solvent in a sprayed seal when laboratory testing is not feasible, thereby saving time and expenditure.

Prediction of Solar Radiation Using Data Driven Models

The local climatic conditions play a significant role in the amount of Solar Radiation that reaches the Earth’s surface. In India, most of the locations, receive ample Solar Radiation. The exact evaluation of SR is most essential for engineering studies on energy and climate. For the present investigations, the meteorological data for Hyderabad city in Telangana state for the period 2009 - 2020 is adopted. Five climatological variables viz., Max. Temp. (Tmax), Min. Temp. (Tmin) and Mean Air Temp. (Tmean), Sunshine hours (n), and Relative Humidity (RH) were collected from the weather forecast. In the present investigations, two conventional empirical equations viz., Abdalla, and Angstrom are adopted for analytical estimation of Solar Radiation (SR). Furthermore, two data-driven models via., Artificial Neural Networks (ANN) and Multi Gene-genetic Programming (MGGP) are used to develop an equation for estimating Solar Radiation (Rs). The model equations were developed based on the parameters adopted for each conventional equation. These results are compared with conventional equation results. The present investigation exhibited that, the expected results of the Solar radiation of the arrangement formed by the data are favourable and also simplify the testing data. The corresponding R2 values for random data are 0.976 for the training dataset, while the value for the testing dataset is 0.964. Based on the performance analysis for each equation, the efficiency and reliability of the proposed MGGP and ANN model are validated and predicted for the year 2021. The predicted results were found to be in good agreement with the analytical results evaluated from three properly used equations.

Multivariate analysis of sources of polyunsaturated fatty acids, selenium, and chromium on the productive performance of second-cycle laying hens

An experiment was conducted to evaluate the effect of the intake of a mixture of fish and sacha inchi oils (iOM), organic selenium (iSe), and organic chromium (iCr) on egg production (EP) and feed conversion ratio (FCR) of Isa Brown second-cycle laying hens (SCLH) for 16 weeks (91-106 weeks old). Egg production and FCR were evaluated using multivariate models that included conventional equations and artificial neural networks (ANN) to study multiple nutritional interactions as alternatives to univariate dose-response models. [...]

Entropy Flow Analysis of Thermal Transmission Process in Integrated Energy System Part I: Theoretical Approach Study

It is very important to accurately describe the dynamic processes of thermal energy transmission for coupling with Integrated Energy System (IES). In order to study the thermodynamic characteristics of heat supply, this paper theoretically suggested a generalized model of entropy flow by deducing the expression of entropy conduction and convection based on thermodynamic law and heat transfer analysis. Taking temperature and entropy as the intensity and extension properties, the equivalent distributed and lumped parameter models are established to describe the features of heat loss and transmission delay. The effectiveness of current models is verified by comparing with solutions of conventional Partial Differential Equations (PDE) of heat transfer. The numerical simulation and verification procedure were conducted by Matlab/simulink. The proposed models were applied to simulate the response of temperature and entropy flow of a pipe with length of 100 m under different discrete conditions. The results show that for a distributed parameter model the maximum relative error is 1.275% when the pipe is divided into 100 sections, and for a lumped parameter model, the overall relative error is in the order of 10−3, which can be ignored in practical applications. All these prove the correctness of proposed models in this paper.

A unified equation for predicting gross traction for wheels on clay over a range of braked, towed, and powered operations

A characteristic curve is presented for predicting gross traction of a wheel over a range of powered, towed, and braked modes on clay soils for slip ranging from positive 100% powered slip to negative 100% skid slip. The characteristic curve is a unified approach that relates the ratio of the contact pressure of the wheel to soil strength and predicts the gross traction coefficient over a continuous range of slip. The unified equation is defined by five inflection points: maximum/minimum traction, traction at zero slip, max change in traction with slip, and a shape factor coefficient. The inflection points aim to simplify the calibration of gross traction, slip, soil strength, and contact pressure by using functions adaptable to machine learning. The unified equation is comparable to historic traction equations but is unique in its ability to predict asymmetric braking and powered gross traction. The unified equation is supported and substantiated via error analysis by utilizing the Database Records for Off-road Vehicle Environments (DROVE) – a database constructed around the archived laboratory and field tests for wheels and tracks operating on different soils. The accuracy of the proposed model is assessed and compared to other conventional equations such as the Brixius equation and Maclaurin’s extension of the Pacejka equation for off-road traction.

Neutron diffraction, finite element and analytical investigation of residual strains of autofrettaged thick-walled pressure vessels

Residual strain distributions, positions of elastic-plastic juncture and 1st yielding etc. of autofrettaged thick-walled pressure vessels were revealed quantitatively using Neutron Diffraction (ND), Finite Element (FE) and Analytical solution. FE models were validated with ND results. Relationships between autofrettage pressures (Pmii, Pmao, Paopt) and load bearing capacity versus radius ratio K were respectively established via FE parametric study, by which optimal radius ratio K = 3 rather than K = 4 was identified for some existing vessels. Based on ND and FE results, new formula for calculating optimal juncture radius rjopt was deduced which narrowed the gap between analytical and FE results by 0.5 mm. Four coefficients Cj were proposed to modify conventional equations for calculating juncture radius rj, that facilitated a tool to address residual strains of autofrettaged pressure vessels. These results may be referred to for the design, manufacture, and proper application of the autofrettage technique onto pressure vessels and relevant engineering components.

Converted state equation Kalman filter for nonlinear maneuvering target tracking

Handling the nonlinearity between the measurement and kinematic states is the core issue in target tracking based on radar or sonar. The main novelty of this paper is the proposal of a new filter with a linear structure to achieve nonlinear tracking by integrating information in the polar coordinate system. The state vectors composed of the range, bearing and their differentials are constructed to make the measurement equations linear. After discretizing the ordinary differential dynamic equations in the polar coordinate system, linear time-varying state transition matrixes are established for two common Cartesian motions: constant velocity (CV) and constant acceleration (CA). For the process noises converted from the Cartesian coordinate system to the polar coordinate system, the first and second moments are derived with a closed form. Consequently, the coordinate system of the conventional state equations is converted so that the tracking can be conducted by a standard Kalman filter. Several simulation scenarios show that such a new filter effectively improves the tracking accuracy. The reasons for the superior performance of the proposed method are analyzed and exemplified. In addition, different posterior Cramer–Rao lower bounds (PCRLBs) for fusion estimation in Cartesian coordinates and polar coordinates are given and compared.

Comparison of haemodynamics in carotid endarterectomy: primary closure versus patch angioplasty

We investigated differences in haemodynamic forces between carotid arteries that underwent primary closure (PC) or patch angioplasty (PA) using computational fluid dynamics (CFD). A total of 30 subjects were enrolled in this study, consisting of 10 subjects who underwent PC, 10 who underwent PA and 10 healthy subjects. Three-dimensional models of carotid arteries were reconstructed using patient-specific computed tomography angiography images. The conventional Navier-Stokes, continuity equation and constitutive stress-strain law with a stabilized Petrov-Galerkin scheme were solved with Newtonian and incompressible assumptions. The boundary conditions employed patient-specific velocity profiles as the inflow and lumped parameters of the three-element Windkessel model as the outflow with a rigid wall assumption. Thus, the CFD results exhibited good agreement with measurements from the subjects (r = .78). The carotid arteries of the PC group were exposed to abnormal haemodynamic forces related to building atherosclerosis in a smaller (p .05) to healthy arteries. The morphological characteristics of the carotid artery were significantly associated with the area exposed to abnormal haemodynamic forces. We identified that abnormal haemodynamic forces could be avoided by selecting appropriate surgical techniques that produce less bifurcation expansion.

Delay Model Study of Single Ended Ring Oscillator (SERO)

In this study, a new general expression for the frequency of a SERO is constructed, which includes two additional variables, Kd and Rw, and improves upon the traditional equations by accounting for all analysis models and various width ratios. When compared with the the conventional equations, the proposed equation is a better alternate to study the frequency response when the width ratio is concerned parameter for researchers which is addressed by the variable Rw. A three stage SERO is simulated in 90 nm technology using Cadence Virtuoso platform to establish this equation. The value of Kd obtained remains almost equal which justifies the reason for using this approach traditionally to calculate the delay.

Numerical simulation of viscoelastic &amp; thixo-viscoelastoplastic complex flows at highly non-linear regimes

<h2>Abstract</h2> The High Weissenberg Number Problem (HWNP), which is the ceiling posed by the degree of non-linearity a numerical scheme can resolve in the approximation of the solution to a complex flow, is one of the main challenges to the Computational Rheology community (Walters & Webster, 2003). Research on this facet of non-Newtonian Fluids Mechanics has been traditionally focused on increasing resolution and capability to computationally capture non-linear phenomena in complex flow (Walters & Webster, 2003). In this talk, a proposal is presented to increase the critical Weissenberg number <i>Wi</i>_crit a numerical scheme can attain, via the generally applicable ABS-f and the VGR corrections reported previously (López-Aguilar et al., 2015), and their use to predict some experimental and numerical signatures in complex flow. The ABS-f correction acts upon stress-invariants used to promote non-linear features in conventional differential-type constitutive equations for viscoelastic fluids, helping in problem-regularisation and physically consistent material-property calculation in complex deformations (López-Aguilar et al., 2015). The VGR correction deals with proper velocity-gradient estimation, used to impose conservation-of-mass discretely over the flow-domain and to consistently specify velocity-gradient components at boundary symmetry lines (López-Aguilar et al., 2015). Here, predictions with an advanced hybrid finite-element/volume algorithm on the benchmark circular 4:1:4 contraction-expansion flow of concentrated wormlike micellar solutions prove notably extended in their <i>Wi</i>-span, where <i>Wi</i>_crit-adjustment is reported over three orders-of-magnitude from uncorrected variants, and with some cases presenting no limitation (López-Aguilar et al., 2015); (López-Aguilar et al., 2016a). Finally, use of these computational tools is exemplified in various contraction-expansion flow settings through the prediction of key experimental features for Boger fluids (López-Aguilar & Tamaddon-Jahromi, 2020; Webster et al., 2019), thixo-viscoelastoplasticity in sharp-cornered geometries (López-Aguilar et al., 2018) and shear-banding in contraction-expansion flow of highly concentrated wormlike micellar solutions (López-Aguilar et al., 2017a).

Heat and mass transfer analysis above an unsteady infinite porous surface with chemical reaction

The flow of viscous nanofluid with heat and mass transmission above a porous flat surface in the existence of a constant magnetic field is addressed in this article. Brownian motion, Thermophoresis, and viscous dissipation are all taken into account. The motion is described by a system of equations that are transformed into conventional non-linear differential equations by appropriate transformations and then tackled numerically using the boundary value problem approach at MATLAB. The convergence criterion for the solution is 10 − 6 . The found solutions are functions of the problem's physical properties. The effects of different study parameters for velocity, temperature, and concentration profiles are explored through graphs and tables. An increase in the Prandtl number increases the Sherwood and Nusselt number while Brownian motion reduces the Sherwood number. Viscoelastic parameter increases the skin friction and decreases the nusselt number.

A low-cost model for slug tests in a confined aquifer with skin-zone effect

While the effect of small-scale skin has been extensively investigated, numerical models incorporating the effect require expensive computational cost due to fine spatial discretization of the skin and have not been widely available. This study develops a new model for slug tests at a partially-penetrating well in a two-zone confined aquifer of skin and formation zones. A new basic formulation defines transient flow in the skin with an additional skin factor reflecting the skin storage effect. The formulation assumes horizontal flow in the skin with excluding the vertical skin hydraulic conductivity. The analytical solution and finite element solution of the model are developed. The analytical expression relating the skin factor to the skin specific storage is derived. Results suggest the formulation is a useful alternative to conventional flow equation for the skin in achieving coarse spatial discretization and low computational cost. The present solution agrees well with the field head data obtained from Butler (2019). To conclude, this study presents theoretical advance and efficient simulation in modeling of well hydraulics.