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As train speeds increase, the aerodynamic effects generated during the passage of high-speed trains in tunnels become more pronounced. This article investigates the influence of line spacing on the aerodynamic forces during the passage of high-speed trains in tunnels at different speeds. The research methodology is based on the three-dimensional transient compressible Reynolds-averaged Navier-Stokes (RANS) equations and the k-ω Shear Stress Transport (SST) turbulence model, using overset grid technology to simulate the train passing process in the tunnel. The results show that the aerodynamic drag, lateral force, and lift experienced by the train increase as the line spacing decreases and as the speed increases. line spacing has the greatest impact on aerodynamic lift, followed by lateral force, with drag having the smallest impact. Compared to line spacing, speed has a much larger effect on aerodynamic forces. The aerodynamic forces experienced by the train during tunnel passage are proportional to the square of the train's speed and have an exponential relationship with the line spacing during train passage. [ABSTRACT FROM AUTHOR]

Abstract As train speeds increase, the aerodynamic effects generated during the passage of high-speed trains in tunnels become more pronounced. This article investigates the influence of line spacing on the aerodynamic forces during the passage of high-speed trains in tunnels at different speeds. The research methodology is based on the three-dimensional transient compressible Reynolds-averaged Navier-Stokes (RANS) equations and the k-ω Shear Stress Transport (SST) turbulence model, using overset grid technology to simulate the train passing process in the tunnel. The results show that the aerodynamic drag, lateral force, and lift experienced by the train increase as the line spacing decreases and as the speed increases. line spacing has the greatest impact on aerodynamic lift, followed by lateral force, with drag having the smallest impact. Compared to line spacing, speed has a much larger effect on aerodynamic forces. The aerodynamic forces experienced by the train during tunnel passage are proportional to the square of the train’s speed and have an exponential relationship with the line spacing during train passage.

The article focuses on the presentation and comparison of selected heuristic algorithms for solving the inverse problem for the anomalous diffusion model. Considered mathematical model consists of time-space fractional diffusion equation with initial boundary conditions. Those kind of models are used in modelling the phenomena of heat flow in porous materials. In the model, Caputo's and Riemann-Liouville's fractional derivatives were used. The inverse problem was based on identifying orders of the derivatives and recreating fractional boundary condition. Taking into consideration the fact that inverse problems of this kind are ill-conditioned, the problem should be considered as hard to solve. Therefore,to solve it, metaheuristic optimization algorithms popular in scientific literature were used and their performance were compared: Group Teaching Optimization Algorithm (GTOA), Equilibrium Optimizer (EO), Grey Wolf Optimizer (GWO), War Strategy Optimizer (WSO), Tuna Swarm Optimization (TSO), Ant Colony Optimization (ACO), Jellyfish Search (JS) and Artificial Bee Colony (ABC). This paper presents computational examples showing effectiveness of considered metaheuristic optimization algorithms in solving inverse problem for anomalous diffusion model. [ABSTRACT FROM AUTHOR]

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This work provides a systematic recipe for computing accurate high order Fourier expansions of quasiperiodic invariant circles (and systems of such circles) in area preserving maps. The recipe requires only a finite data set sampled from the quasiperiodic circle. Our approach, being based on the parameterization method of [A. Haro and R. de la Llave, SIAM J. Appl. Dyn. Syst., 6 (2007), pp. 142--207; A. Haro and R. de la Llave, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261--1300; A. Haro and R. de la Llave, J. Differential Equations, 228 (2006), pp. 530--579], uses a Newton scheme to iteratively solve a conjugacy equation describing the invariant circle (or systems of circles). A critical step in properly formulating the conjugacy equation is to determine the rotation number of the quasiperiodic subsystem. For this we exploit the weighted Birkhoff averaging method of [S. Das et al., Nonlinearity, 30 (2017), pp. 4111--4140; S. Das et al., The Foundations of Chaos Revisited, Springer, Cham, 2016, pp. 103--118; S. Das and J. A. Yorke, Nonlinearity, 31 (2018), pp. 491--501]. This approach facilities accurate computation of the rotation number given nothing but the already mentioned orbit data. The weighted Birkhoff averages also facilitate the computation of other integral observables like Fourier coefficients of the parameterization of the invariant circle. Since, the parameterization method is based on a Newton scheme, we only need to approximate a small number of Fourier coefficients with low accuracy (say, a few correct digits) to find a good enough initial approximation so that Newton converges. Moreover, the Fourier coefficients may be computed independently, so we can sample the higher modes to guess the decay rate of the Fourier coefficients. This allows us to choose, a priori, an appropriate number of modes in the truncation. We illustrate the utility of the approach for explicit example systems including the area preserving H\'enon map and the standard map (polynomial and trigonometric nonlinearity respectively). We present example computations for invariant circles and for systems of invariant circles with as many as 120 components. We also employ a numerical continuation scheme (where the rotation number is the continuation parameter) to compute large numbers of quasiperiodic circles in these systems. During the continuation we monitor the Sobolev norm of the parameterization, as explained in [R. Calleja and R. de la Llave, Nonlinearity, 23 (2010), pp. 2029--2058], to automatically detect the breakdown of the family. [ABSTRACT FROM AUTHOR]

Abstract The pressure of the recovered sample is intricately connected to seawater temperature, the recovery velocity, and the pressure of the pre-charged gas. To better understand the sample pressure dynamics during the sampling recovery process, we focus on a gas-tight sediment sampler, delving into its pressure-compensation and pressure-retaining mechanisms. A comprehensive thermal and thermodynamic analysis is conducted throughout the entire pressure-retaining sampling process, examining the temporal variations in the temperatures of seawater and nitrogen within the sampler at various descending velocities. The heat transfer and thermodynamics are examined throughout the entire pressure-retaining sampling process to determine how changes in the temperatures of seawater and nitrogen, as well as the descent velocity, affect the pressure-retaining performance. The influence of pre-charging pressure and recovery velocities on the pressure-retaining performance of the sampler is examined. Then the proposed numerical model was well verified by the ultra-high-pressure vessel experiments of the sampler under 115 MPa. Finally, the sea trial results further verified the accuracy of the numerical model.

The aim of this work is to solve a numerical computation of the neutral fractional functional integro-differential equation based on a new approach to the Legendre wavelet method. The concept of fractional derivatives was examined in the sense of Caputo. The properties of the Legendre wavelet and function approximation were employed to determine the approximate solution of a given dynamical system. Moreover, the error estimations and convergence analysis of the truncated Legendre wavelet expansion for the proposed problem were discussed. The validity and applicability of this proposed technique to numerical computation were shown by illustrative examples. Eventually, the results of this technique demonstrate its great effectiveness and reliability.

The aim of this work is to solve a numerical computation of the neutral fractional functional integro-differential equation based on a new approach to the Legendre wavelet method. The concept of fractional derivatives was examined in the sense of Caputo. The properties of the Legendre wavelet and function approximation were employed to determine the approximate solution of a given dynamical system. Moreover, the error estimations and convergence analysis of the truncated Legendre wavelet expansion for the proposed problem were discussed. The validity and applicability of this proposed technique to numerical computation were shown by illustrative examples. Eventually, the results of this technique demonstrate its great effectiveness and reliability. [ABSTRACT FROM AUTHOR]

In multi-body system dynamics modelling, the body which rotate in space is complex and not easily to be expressed by Newton method, because the space rotation is realized by multi-joints rotation coupling with different direction. In this exploration, the Lie group variational integrator method is used to the dynamics modelling problem of multi-body system with three orthogonal direction joints coupling. Firstly, a mechanism accords with Cardan rotation regular is designed which can represent 3 different directions coupling, the kinematics model is derived out by matrix operation without triangle function. With inertia matrix and mass matrix of the multi-body system according to the topology structure, and the Lagrange function is built, and the dynamics equation is derived out with Lie group variational integrator method. With Legendre transformation, the Hamilton dynamics model is obtained. The differential computation of the momentum part is avoided, the scale of the dynamics model is greatly reduced. The Hamilton dynamics model with two different kinematics part are compared in simulation. The simulation results indicate that the different kinematic expression can lead to different structure conservation characters under same numerical computation method. This exploration offers a benefit attempt of using geometry method to dynamics modelling problem of tree structure multi-body system with different structure rotation matrixes coupling. [ABSTRACT FROM AUTHOR]

Orthotropic plates were analogized to gridwork systems, and the compatibility and incompatibility between these 2 structure types in static and dynamic analyses were discussed. The results show that, the gridwork results converge to the theoretical solution of plates through the grid refinement for compatible problems with simply supported and/or clamped boundaries. All the formulas for calculation of various internal forces were derived, and the algorithms required in solving the gridwork systems were proposed by means of the 3D structural mechanics solver. A wide range of numerical examples, including rectangular and circular plates, were given to verify the validity of the proposed theory and algorithms. [ABSTRACT FROM AUTHOR]

Digital rock physics is based on imaging, segmentation and numerical computations of rock samples. Due to challenges regarding the handling of a large 3-dimensional (3D) sample, 2D algorithms have always been attractive. However, in 2D algorithms, the efficiency of the pore structures in the third direction of the generated 3D sample is always questionable. We used four individually captured µCT-images of a given Berea sandstone with different resolutions (12.922, 9.499, 5.775, and 3.436 µm) to evaluate the super-resolution 3D images generated by multistep Super Resolution Double-U-Net (SRDUN), a 2D algorithm. Results show that unrealistic features form in the third direction due to section-wise reconstruction of 2D images. To overcome this issue, we suggest to generate three 3D samples using SRDUN in different directions and then to use one of two strategies: compute the average sample (reconstruction by averaging) or segment one-directional samples and combine them together (binary combination). We numerically compute rock physical properties (porosity, connected porosity, P- and S-wave velocity, permeability and formation factor) to evaluate these models. Results reveal that compared to one-directional samples, harmonic averaging leads to a sample with more similar properties to the original sample. On the other hand, rock physics trends can be calculated using a binary combination strategy by generating low, medium and high porosity samples. These trends are compatible with the properties obtained from one-directional and averaged samples as long as the scale difference between the input and output images of SRDUN is small enough (less than about 3 in our case). By increasing the scale difference, more dispersed results are obtained. [ABSTRACT FROM AUTHOR]

This research introduces a novel Probabilistic Graph Modeling-based Safety Classifier Algorithm designed for the purpose of classifying road safety in smart transportation systems. Leveraging a combination of numerical integration methods and Gaussian kernel density estimation models, the proposed algorithm offers an effective approach to assess and categorizing the safety levels of roads. The integration of these techniques enables a comprehensive analysis, allowing for a more nuanced understanding of the complex interactions within transportation networks. The algorithm's efficacy in road safety classification holds promising implications for enhancing traffic management and promoting safer urban environments. [ABSTRACT FROM AUTHOR]

It has been suggested in the literature that the sound velocity of the nuclear matter vs exceeds the so-called sound velocity bound vs≤c/3 at high density, where c is the speed of light. In this paper, we revisit the issue of neutron star properties, comparing current measurements of mass, radius, and tidal deformability with 105 different equations of state. These equations are parametrized at low density and saturate the sound velocity bound beyond twice the saturation density. This allows us to conservatively determine the maximum mass compatible with observed neutron star properties and the sound velocity bound. We find that majority of the models are eliminated by the incompatibility with the observations and, especially, the recently detected massive pulsar (2.35±0.17M⊙) is hardly realized by our simulations. Our study strongly supports that the sound velocity bound is not satisfied in nature.

The intriguing thermophysical properties of nanoparticles have considerable potential in thermal transportation for engineering applications. The inclusion of solid nanoparticles in the base fluid raises the fluid's thermal conductivity, which improves thermal transfer characteristics. Thus, an analysis is performed by assuming the Tiwari and Das model, for the flow and energy transportation aspects of hybrid nanoparticles in a shrinkable porous medium. The current study focuses on the thermal heat transfer performance on the dynamic of ethylene glycol-based titania and alumina nanoparticles. The flow-controlling system of PDEs is transformed into a system of non-linear ODEs by using similarity transformations, and the resulting equations are then solved numerically through the solver bvp4c in Matlab function with a limit of tolerance 10−6. The multiple branches of solutions are noted for distinct values of suction and shrinking parameters. The outcomes reveal that the inclusion of titania and alumina nanocomposites improves the thermophysical properties of the base fluid significantly. The findings indicate that hybrid nanofluids are more effective for increasing the thermal transport rate. Further, in the upper branch solution, the friction drags, and energy transportation rate raises for the higher influence of suction strength while it declines for the lower branch.

The doubly non-central F distribution is a widely applied probability distribution. The cumulative distribution function (CDF) of the doubly non-central F distribution can be expressed using the infinite doubly series. In this paper, a CDF calculation method that allows for controlled precision is derived through the study of the infinite doubly series. By setting parameters, this method can provide an upper limit of error for the computed results, thereby allowing for precision control in the calculations. Experimental results demonstrate that this method achieves a good balance between computational precision and speed.

High hydrostatic pressure can cause common problems such as cracking and leakage in the lining of railway tunnels during operation. A clear understanding of the magnitude and distribution characteristics of hydrostatic pressure in tunnel lining under high-pressure conditions is crucial for optimizing the structural design of tunnel lining. In this study, professional equipment was first selected to measure the lining water pressure of two typical sections of Tunnel A on site, and the pressure distribution characteristics were analyzed; Then, a calculation model of the tunnel under high hydrostatic pressure was established using FLAC3D numerical calculation software. Select several calculation parameters and within a reasonable range of values, select multiple values for each parameter instead of just taking one value to form 60 working conditions, and calculate the corresponding tunnel lining water pressure for each working condition. Analyze the correlation between static water pressure and calculation parameters under various working conditions, propose a preliminary calculation formula for tunnel lining static water pressure, and finally use SPSS statistical calculation software to fit the final calculation formula for lining water pressure. This formula is applicable to the calculation of lining hydrostatic pressure under various parameters and is a universal calculation formula for tunnel lining hydrostatic pressure. Our proposed formula is very consistent with on-site measured data under similar geology conditions, providing a new method for calculating the hydrostatic pressure of tunnel lining.

We give a fast algorithm to optimally compose privacy guarantees of differentially private (DP) algorithms to arbitrary accuracy. Our method is based on the notion of \emph{privacy loss random variables} to quantify the privacy loss of DP algorithms. The running time and memory needed for our algorithm to approximate the privacy curve of a DP algorithm composed with itself $k$ times is $\tilde{O}(\sqrt{k})$. This improves over the best prior method by Koskela et al. (2021) which requires $\tilde{\Omega}(k^{1.5})$ running time. We demonstrate the utility of our algorithm by accurately computing the privacy loss of DP-SGD algorithm of Abadi et al. (2016) and showing that our algorithm speeds up the privacy computations by a few orders of magnitude compared to prior work, while maintaining similar accuracy.

In order to study the amplification effect of vehicle excitation force on partially concrete-filled rectangular steel tubular composite truss bridge, a three-span continuous partially concrete-filled rectangular steel tubular composite truss bridge was taken as the research object. The deflection impact coefficients and axial force impact coefficients of the truss bridge were obtained by the definition of bridge impact coefficient. The influence of different vehicle speed, bridge deck roughness, vehicle weight and concrete filling coefficient on the impact coefficient of truss bridge was compared and analyzed. The MATLAB software was used to test the goodness of fit of 867 impact coefficients, and the statistical value of impact coefficient of truss bridge under 95% guarantee rate was obtained. The results show that the dynamic responses of the lower chords of the rectangular steel tubular composite truss bridge can be effectively reduced by partial concrete filling, but the dynamic amplification effect of the truss bridge under vehicle load can not be reduced. The influence of vehicle speed on impact coefficient of truss bridge is unpredictable. The bridge deck roughness is an important factor affecting the impact coefficient. The impact coefficients of key sections of the truss bridge increase significantly with the deterioration of the bridge deck, and the maximum increase is about 400% . With the decrease of vehicle weight, the impact coefficients of key sections of truss bridge increase, and the maximum increase is about 200% . With the increase of concrete filling coefficient, the impact coefficients of key sections of truss bridge increase slightly due to the increase of relative stiffness of lower chords of truss bridge. The axial force impact coefficients of key sections of truss bridge are greater than the deflection impact coefficients. Under 95% guarantee rate, the statistical value of the impact coefficient of the partially concrete-filled rectangular steel tubular composite truss bridge is 0. 223, the impact coefficient is less than that of American code, Australian code, British code and Canadian code, but more than that of Chinese code, which should be paid more attention by bridge designers. [ABSTRACT FROM AUTHOR]

In industrial process, improving the transfer of heat has become the primary focus. In comparison with convectional heat transfer fluids and nanofluids containing single nanoparticles, hybrid nanofluids have the potential to offer improved heat transfer performance and thermophysical features. In order to approximate the flow and thermal transport properties, a numerical investigation is conducted in this study. The present study investigates the radiative hybrid silica–alumina/ethylene glycol nanofluid flow properties of heat transfer and fluid flow toward thin needle. The fluid flow model is designed to be governed by a partial differential equation. The PDEs are turned into ODEs using similarity requirements, and then solved numerically using the finite difference approach via the built-in MATLAB function bvp4c. The outcome of flow controlling parameters on velocity, temperature, friction drag, and heat transport rate is presented. The study exhibits that duality of solutions occurs in a particular range when χ c < χ ≤ - 2.2 and unique solution at χ > - 2.2. The results revel that reduction in skin friction and heat transport rate occurs by the inclusion of magnetic strength in hybrid nanofluid. It is also found that when the size of solid nanoparticle increased, the rate of heat transfer across the needle's surface dramatically improved. [ABSTRACT FROM AUTHOR]

High hydrostatic pressure can cause common problems such as cracking and leakage in the lining of railway tunnels during operation. A clear understanding of the magnitude and distribution characteristics of hydrostatic pressure in tunnel lining under high-pressure conditions is crucial for optimizing the structural design of tunnel lining. In this study, professional equipment was first selected to measure the lining water pressure of two typical sections of Tunnel A on site, and the pressure distribution characteristics were analyzed; Then, a calculation model of the tunnel under high hydrostatic pressure was established using FLAC3D numerical calculation software. Select several calculation parameters and within a reasonable range of values, select multiple values for each parameter instead of just taking one value to form 60 working conditions, and calculate the corresponding tunnel lining water pressure for each working condition. Analyze the correlation between static water pressure and calculation parameters under various working conditions, propose a preliminary calculation formula for tunnel lining static water pressure, and finally use SPSS statistical calculation software to fit the final calculation formula for lining water pressure. This formula is applicable to the calculation of lining hydrostatic pressure under various parameters and is a universal calculation formula for tunnel lining hydrostatic pressure. Our proposed formula is very consistent with on-site measured data under similar geology conditions, providing a new method for calculating the hydrostatic pressure of tunnel lining. [ABSTRACT FROM AUTHOR]

Let p be an odd prime and Zp the residue class ring modulo p. In this paper, we study representations of any element of Zp as the sum of a Lehmer number and a primitive root in Zp, and give an explicit inequality better than asymptotic formula for the number of representations. From this inequality, we obtained that each element of Zp can be represented as the sum of a Lehmer number and a primitive root for p > 2.5×1014. Moreover, using the algorithm we provided, we examined all the cases when p < 106 by computer. We also analyzed the time complexity of the algorithm and illustrated that it is extremely difficult to verify all the cases up to the bound 2.5×1014, and conjectured that any given element n ∈ Zp can be represented as the sum of a Lehmer number and a primitive root in Zp for all primes p except 2, 3, 5, 7, 11, 19, 31. [ABSTRACT FROM AUTHOR]

An algorithm and a MATLAB implementation for computing the Kummer function U(a,b,x) and its derivative is given in this paper. The algorithm is efficient and accurate. Numerical tests show that the MATLAB algorithm allows the computation of the function with ∼ 1 0 − 14 relative accuracy in the parameter region (a,b,x) ∈ (0,500) × (0,500) × (0,1000) in double-precision floating point arithmetic. [ABSTRACT FROM AUTHOR]

Accurate temperature rise prediction of the gas‐insulated transmission lines (GIL) can help to lower the cost of equipment through optimization design. To investigate the temperature rise of GIL and the heat transfer efficiency of new eco‐friendly insulating gas, the electromagnetic‐thermal‐fluid field coupling method that considers the thermal properties of solid and gaseous media is proposed. The finite element method is applied to solve the eddy‐current field and obtain the Joule loss of the conductive rod and the enclosure accurately. The GIL temperature distribution of different insulating gases is computed based on their thermophysical parameters. The heat transfer efficiency is found to be positively correlated with gas density, constant pressure heat capacity and thermal conductivity. A parameter that characterizes the heat transfer efficiency of the insulating gas is defined, such that a larger value indicates a higher heat transfer efficiency. This parameter helps to quickly determine the heat transfer capacity of new eco‐friendly insulating gas, and facilitate the optimal design of GIL equipment. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

In terms of SST prediction tasks by machine learning approaches, high-resolution and accurate prediction can hardly be achieved with easily accessible SST data. This is because most of the SST data is spatiotemporally discrete and sparse, meaning a small sample size since it is hard to learn the spatiotemporal correlation given the data of limited density. This paper presents a numerical computation-based few-shot learning method for intelligent SST prediction. The proposed method generates synthetic SST sequences via ROMS and merges them with SST data captured by satellites to deal with small sample size. Convolutional LSTM (Conv-LSTM) network is trained end-to-end in order to learn spatiotemporal correlation of time-varying SST and eventually obtain high-resolution and accurate SST predictions. SST data from August to December in 2011 are employed for model training, and the prediction results are compared to reliable SST reanalysis datasets in the experiment, which shows fine performance of the proposed method. [ABSTRACT FROM AUTHOR]

This article concerns the dynamic transitions of a non‐Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is performed by deriving the principle of exchange of stability condition, which shows the system loses stability when the thermal Rayleigh number exceeds a threshold. Second, we consider the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transition types. Our results show that both continuous and jump transitions can occur for certain parameters when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, but only continuous transition induced by real eigenvalues is observed when the diffusivities from big to small is the opposite of the previous case. [ABSTRACT FROM AUTHOR]

We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterization of such operators is performed in the Laplace domain, it is necessary to resort to accurate numerical methods to derive the corresponding behaviours in the time domain. In this regard, we develop a computational procedure to solve variable-order fractional differential equations of this novel class. Furthermore, we provide some numerical experiments to show the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop a physical model and investigate the bactericidal effect of an automated hand-washing system through numerical computation, which is essential in areas affected by COVID-19 to ensure safety and limit the spread of the pandemic. The computational fluid dynamics approach is used to study the movement of the solution inside the hand-washing chamber. The finite element method with the k- ε model is applied to solve the incompressible Navier–Stokes equations. The numerical results provide insights into the solution's hydrodynamic values, streamlines, and density in the two cases of with a hand and without a hand. The pressure and mean velocity of the fluid in the hand-washing chamber increases when the inlet flow rates increase. When the hand-washing chamber operates, it creates whirlpools around the hands, which remove bacteria. In addition, the liquid inlet flow affects the pressure in the hand-washing chamber. The ability to predict the hydraulic and cleaning performance efficiencies of the hand-washing chamber is crucial for evaluating its operability and improving its design in the future. [ABSTRACT FROM AUTHOR]

Airfoil fin printed circuit heat exchangers (PCHEs) have broad application prospects in the naval, aerospace, electric power, and petrochemical industries. The channel structure is a critical factor affecting their thermal-hydraulic characteristics. In this study, a novel PCHE channel structure with staggered NACA 0025 airfoil-shaped fins was proposed; accordingly, the thermal-hydraulic characteristics of the novel channel structure using carbon dioxide as the working fluid at different fin heights under different operating conditions (trans-, near-, and far-critical) were investigated. The results indicated that the thermal-hydraulic performance of the PCHE under the trans-critical operating condition was better than that under the near-critical and far-critical operating conditions. Compared with conventional airfoil fin channels, the novel airfoil fin channel attained comparable comprehensive performance while reducing the fin volume by 50%, thus achieving a more lightweight PCHE design. The comprehensive performance of the PCHE was the poorest when the fin height was slightly below the channel height, which should be avoided during the design of airfoil fin PCHEs. The results provide theoretical support for the design and optimization of airfoil fin PCHEs. [ABSTRACT FROM AUTHOR]

Under the background of teaching in the new era, image recognition, operation, and processing of experimental data are still the focus of calculus teaching. Mathematica has powerful functions as mathematical software and was developed by Wolfram Research. Aiming at the complex symbols and data operation problems in many fields, the software flexibly combines mathematics branches such as geometry and algebra, dramatically simplifying the operation process. This paper takes Mathematica’s existing mathematical software as a reference to discuss whether the addition of such software helps improve the effectiveness of daily teaching. The study found that using this software can stimulate students’ interest and enhance the quality of education.

This paper describes atomistic device models of a multiple-chain polyaniline (PANI) gas sensing component, utilizing the non-equilibrium Green’s functions formalism. The numerical results are compared with experimental data of ammonia and nitrogen dioxide detection. Multiple molecules of PANI in the form of emeraldine salt were studied with more than one absorbed molecule of ammonia or nitrogen dioxide. From the I–V characteristics of the system with and without adsorbed gas molecules for gas concentrations of 3, 6, 9, and 12 ppm, the effective resistance changes, (R − R0)/R0, were obtained and compared with experimental results. A good agreement with the measured values was obtained. In summary, PANI as emeraldine salt was numerically modeled for several adsorbed gas concentrations, several gas configurations, and different PANI molecule positions, including carrier hopping between them. The results are comparable to the experiment and show good properties for the application as gas sensor device for NH3 detection and rather good properties for NO2 detection.

Recent studies have proven that a coolant crossflow influences the cooling performance of film-cooling gas turbine holes. The present paper evaluates the cooling performance for several innovative cratered film-cooling holes fed by a perpendicular crossflow channel. The flow fields, discharge coefficients, and the cooling effectiveness are analyzed and compared based on the results predicted by the methods of computational fluid dynamics (CFD) for cylindrical, concentric cratered, and contoured cratered holes. The investigated blowing ratio varies from 0.5 to 2.0. The ratio of the velocity at the crossflow channel inlet to the mainstream flow velocity is equal to 0.6. The study indicates that the character of the vortex pair and the velocity distribution depend on the specific hole shape and blowing ratio. A contoured cratered hole is shown to provide a higher cooling effectiveness than cylindrical and concentric cratered holes. In addition, it exhibits the highest discharge coefficients everywhere over the range of the blowing ratios studied. [ABSTRACT FROM AUTHOR]

The Clausen functions arise in numerous applications. An efficient summation/integration method for the numerical calculation of these functions of arbitrary order is proposed in this paper. The method is based on a modification of an earlier method and it does not require the construction of the coefficients in the three-term recurrence relation for the corresponding orthogonal polynomials, but only a transformation of orthogonal polynomials from the real line to the positive semiaxis. Numerical experiments are also included. [ABSTRACT FROM AUTHOR]

The current study delivers a numerical investigation on the performance of heat transfer and flow of micropolar fluid in porous Darcy structures with isothermal and isoflux walls (boundary conditions) of a stretching sheet. The dynamics and mechanism of such fluid flows are modelled by nonlinear partial differential equations that are reduced to a system of nonlinear ordinary differential equations by utilizing the porosity of medium and similarity functions. Generally, the explicit or analytical solutions for such nonlinear problems are hard to calculate. Therefore, we have designed a computer or artificial intelligence-based numerical technique. The reliability of neural networks using the machine learning (ML) approach is used with a local optimization technique to investigate the behaviours of different material parameters such as the Prandtl number, micropolar parameters, Reynolds number, heat index parameter, injection/suction parameter on the temperature profile, fluid speed, and spin/rotational behaviour of the microstructures. The approximate solutions determined by the efficient machine learning approach are compared with the classical Runge–Kutta fourth-order method and generalized finite difference approximation on a quasi-uniform mesh. The accuracy of the errors lies around 10−8 to 10−10 between the traditional analytical solutions and machine learning strategy. ML-based techniques solve different problems without discretization or computational work, and are not subject to the continuity or differentiability of the governing model. Moreover, the results are illustrated briefly to help implement microfluids in drug administering, elegans immobilization, and pH controlling processes. [ABSTRACT FROM AUTHOR]

In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various Floquet solutions give rise to an entire function whose zeros are exactly the eigenvalues of the Coulomb spheroidal wave equation. This entire function can be calculated by means of a recurrence formula with arbitrary accuracy and low computational cost. In the end, one obtains an easy-to-use method for computing spheroidal eigenvalues and spheroidal wave functions. [ABSTRACT FROM AUTHOR]

Objective: There is increasing interest in simultaneous endovascular delivery of more than one drug from a drug-loaded stent into a diseased artery. There may be an opportunity to obtain a therapeutically desirable uptake profile of the two drugs over time by appropriate design of the initial drug distribution in the stent. Due to the non-linear, coupled nature of diffusion and reversible specific/non-specific binding of both drugs as well as competition between the drugs for a fixed binding site density, a comprehensive numerical investigation of this problem is critically needed. Methods: This paper presents numerical computation of dual drug delivery in a stent-artery system, accounting for diffusion as well as specific and non-specific reversible binding. The governing differential equations are discretized in space, followed by integration over time using a stiff numerical solver. Three different cases of initial dual drug distribution are considered. Results: For the particular case of sirolimus and paclitaxel, results show that competition for a limited non-specific binding site density and the significant difference in the forward/backward reaction coefficients play a key role in determining the nature of drug uptake. The nature of initial distribution of the two drugs in the stent is also found to influence the binding process, which can potentially be used to engineer a desirable dual drug uptake profile. Conclusions: These results help improve the fundamental understanding of endovascular dual drug delivery. In addition, the numerical technique and results presented here may be helpful for designing and optimizing other drug delivery problems as well. [ABSTRACT FROM AUTHOR]

In order to study the influence of different boundary constraints on the bearing characteristics of the bolt anchorage section, the stress conditions of the bolt in the state of tension bearing and bolt-surrounding rock coordinated deformation bearing state were analyzed, and the numerical calculation with different boundary constraints was carried out. The research results show that the axial force of the bolt decreases along the anchorage length under different boundary constraints, and the attenuation speed is faster under lateral constraints. Under the condition of top fixed and lateral restraint, the axial force of the bolt decreases at 1/2 of the anchorage length, obviously slows down and approaches to zero. The axial force of the bottom fixed lateral restraint bolt decreases slowly within 5 cm of the anchorage beginning, and then decreases in a power function. Under the condition of top fixed and lateral restraint, the shear stress peak of the bolt-anchorage agent interface appears at 2 cm of the outer end of the anchorage, while under the condition of bottom fixed and lateral restraint, the shear stress peak is at 9-10 cm of the anchorage depth. Under the condition of top fixed and lateral restraint, the peak shear stress of anchorage agent-surrounding rock interface is located at the outer end of anchorage, and the peak shear stress under the condition of bottom fixed lateral restraint is located at 8 cm outside the anchorage. The magnitude and location of the shear stress peak value of the two interfaces are different, which is the important influencing factor of various anchorage failure modes.

Empirical Kinetic Models have been used to describe and establish the Anaerobic Digestion kinetics of pig slurry’s (8% TS) Biochemical Chemical Potential. A wide selection of Empirical Kinetic Models were fitted to the experimental data collected in batch assays of different Substrate to Inoculum ratios, 0.65 (BMP1) and 1 (BMP2). For the selection of the most suitable model for each BMP assay, the statistical tools R2 and the RMSE, along with the Information Criterion AIC and BIC, were taken into consideration. From all the studied models, the Weibull model proved to be the most suitable for kinetic parameter prediction for both BMP1 and BMP2 assays. This model presented the lowest values of AIC and BIC, along with the highest value of R2 and the lowest RMSE. In this regard, a R2=0.998, and a RMSE=0.004, was obtained for BMP1, and a R2=0.999 and a RMSE=0.008 for BMP2.