Search Results (15)

In this paper, the entire downhole fluid-sucker rod-pump system is replaced with a viscoelastic vibration model, namely a third-order differential equation with an inhomogeneous forcing term. Both Kelvin’s and Maxwell’s viscoelastic models can be implemented along with the dynamic behaviors of a mass point attached to the viscoelastic model. By employing the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic dynamic model, we have obtained the displacement responses, which match closely with the experimental measurements in actual operations, through an iterative process. The key discovery of this work is the feasibility of the so-called inverse optimization procedure, which can be utilized to identify the equivalent scaling factor and viscoelastic system parameters. The proposed Newton–Raphson iterative method, with some terms in the Jacobian matrix expressed with averaged rates of changes based on perturbations of up to two independent parameters, provides a feasible tool for optimization issues related to complex engineering problems with mere information of input and output data from either experiments or comprehensive simulations. The same inverse optimization procedure is also implemented to model the entire fluid delivery system of a very viscous non-Newtonian polymer modeled as a first-order ordinary differential equation (ODE) system similar to the transient entrance developing flow. The convergent parameter reproduces transient solutions that match very well with those from fully fledged computational fluid dynamics models with the required inlet volume flow rate and outlet pressure conditions. Full article

We show that Einstein’s conformal gravity can explain, simply, and on the geometric ground, galactic rotation curves, without the need to introduce any modification in both the gravitational as well as in the matter sector of the theory. The geometry of each galaxy is described by a metric obtained, making a singular rescaling of Schwarzschild’s spacetime. The new exact solution, asymptotically anti-de Sitter, manifests an unattainable singularity at infinity that cannot be reached in finite proper time; namely, the spacetime is geodetically complete. It deserves to be noticed that, in this paper, we have a different opinion from the usual one. Indeed, instead of making the metric singularity-free, we make it apparently but harmlessly even more singular than Schwarzschild’s. Finally, it is crucial to point out that Weyl’s conformal symmetry is spontaneously broken into the new singular vacuum rather than the asymptotically flat Schwarzschild’s one. The metric is unique according to the null energy condition, the zero acceleration for photons in the Newtonian regime, and the homogeneity of the Universe at large scales. Once the matter is conformally coupled to gravity, the orbital velocity for a probe star in the galaxy turns out to be asymptotically constant consistent with the observations and the Tully–Fisher relation. Therefore, we compare our model with a sample of 175 galaxies and show that our velocity profile very well interpolates the galactic rotation curves after a proper choice of the only free parameter in the metric. The mass-to-luminosity ratios of galaxies turn out to be close to 1, consistent with the absence of dark matter. Full article

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples in the literature do not provide third-order accuracy in two stages. The scheme was explicit and correct to the third order. The stability region and consistency analysis of the scheme for linear ODE are provided in this paper. Moreover, a mathematical model of heat and mass transfer for the non-Newtonian Casson nanofluid flow is given under the effects of the induced magnetic field, which was explored quantitatively using the method of Levenberg–Marquardt back propagation artificial neural networks. The governing equations were reduced to ODEs using suitable similarity transformations and later solved by the proposed scheme with a third-order accuracy. Additionally, a neural network approach for input and output/predicted values is given. In addition, inputs for velocity, temperature, and concentration profiles were mapped to the outputs using a neural network. The results are displayed in different types of graphs. Absolute error, regression studies, mean square error, and error histogram analyses are presented to validate the suggested neural networks’ performance. The neural network technique is currently used on three of these four targets. Two hundred points were utilized, with 140 samples used for training, 30 samples used for validation, and 30 samples used for testing. These findings demonstrate the efficacy of artificial neural networks in forecasting and optimizing complex systems. Full article

A non-Newtonian stagnation point fluid flow towards two different inclined heated surfaces is mathematically formulated with pertinent effects, namely mixed convection, viscous dissipation, thermal radiations, heat generation, and temperature-dependent thermal conductivity. Mass transfer is additionally considered by the use of a concentration equation. The flow narrating equations are solved numerically by using the shooting method along with the Runge–Kutta scheme. A total of 80 samples are considered for five different inputs, namely the velocities ratio parameter, temperature Grashof number, Casson fluid parameter, solutal Grashof number, and magnetic field parameter. A total of 70% of the data are used for training the network; 15% of the data are used for validation; and 15% of the data are used for testing. The skin friction coefficient (SFC) is the targeted output. Ten neurons are considered in the hidden layer. The artificial networking models are trained by using the Levenberg–Marquardt algorithm. The SFC values are predicted for cylindrical and flat surfaces by using developed artificial neural networking (ANN) models. SFC shows decline values for the velocity ratio parameter, concentration Grashof number, Casson fluid parameter, and solutal Grashof number. In an absolute sense, owning to a prediction by ANN models, we have seen that the SFC values are high in magnitude for the case of an inclined cylindrical surface in comparison with a flat surface. The present results will serve as a helpful source for future studies on the prediction of surface quantities by using artificial intelligence. Full article

In this work, the objective is to get the exact analytical solution of a generalized Casson fluid model with heat generation and chemical reaction described by the Caputo fractional operator, using the approach that the Laplace transform method includes the Laplace transform of the Caputo derivative. After the exact solution, it will be studied the impact of the order of the fractional derivative and the most essential parameters included in the modeling like the Prandtl number, the thermal Grashof number, the mass Grashof number, the Schmidt number, the heat generation parameter, and the chemical reaction parameter. The physical points of view of the influence will be discussed and analyzed. The findings of the paper will be illustrated by several graphics. The development in industry and engineering science, it makes important to study the flow behavior of non-Newtonian fluids. The domains of applications of the flow behavior of non-Newtonian fluids are diverse such as geophysics, biorheology, and chemical and petroleum industries. Full article

Stochastic simulations enable researchers to incorporate uncertainties beyond numerical discretization errors in computational fluid dynamics (CFD). Here, the authors provide examples of stochastic simulations of incompressible flows and numerical solutions for validating these newly emerging stochastic modeling methods. A numerical scheme is constructed for finding solutions to stochastic parabolic equations. The scheme is second-order accurate in time for the constant coefficient of the Wiener process term. The stability analysis of the scheme is also provided. The scheme is applied to the dimensionless heat and mass transfer model of mixed convective non-Newtonian nanofluid flow over oscillatory sheets. Both the deterministic and stochastic energy equations use temperature-dependent thermal conductivity. The stochastic model is more general than the deterministic model. The results are calculated for both flat and oscillatory plates. Casson parameter, mixed convective parameter, thermophoresis, Brownian motion parameter, Prandtl number, Schmidt number, and reaction rate parameter all impact the velocities, temperatures, and concentrations shown in the graphs. Under the influence of the oscillating plate, the results reveal that the concentration profile decreases with increasing Brownian motion parameters and increases with increasing thermophoresis parameters. The behavior of the velocity profile for the deterministic and stochastic models is provided, and contour plots for the stochastic model are also displayed. This article aims to provide a state-of-the-art overview of recent achievements in the field of stochastic computational fluid dynamics (SCFD) while also pointing out potential future avenues and unresolved challenges for the computational mathematics community to investigate. Full article

In this paper, we extend a paper by Milgrom (2009, MNRAS 398, 1023) dealing with the existence of a quasi-universal surface density for object of all mass and structure, if they are in the Newtonian regime, i.e., that their mean acceleration is larger than MOND typical acceleration $a_0$. This result is in agreement with Donato et al. (2009)’s results, claiming the existence of a quasi-universal surface density in all masses in galaxies. The Milgrom paper also predicts that objects with mean inner acceleration smaller than the values discussed do not show the quasi-universal behavior of the surface density discussed. In the present paper, we extend the result of Milgrom’s paper, based on a point mass model, considering spiral galaxies, modelled with a double exponential disk. Similar to Milgrom’s results, we find the existence of a universal surface density for galaxies with large surface density, and a different behavior for galaxies having small surface density. Full article

The mechanical and rheological characterizations of flexible investment casting patterns capable of 3D printing are reported. The wax pattern was composed of microcrystalline hydrocarbon wax (DMW7478), Piccotex 75 (a copolymer of α–methyl–styrene and vinyl toluene with a 75/25 molar ratio, respectively) and Escorene (a copolymer of ethylene and vinyl acetate with a 72/28 mass ratio, respectively). It was found that in order to obtain a wax pattern with appreciable mechanical properties, the content of the microcrystalline hydrocarbon wax in these blends should not exceed 30% (m/m). Thus, a series of patterns with 28% (m/m) wax and varying Piccotex and Escorene contents spanning from 0 to 72% (m/m) was prepared. The dependence of the dynamic viscosities of the wax patterns on the composition was described using a stretched exponential model, whereas their variations with the temperature were interpreted in terms of the Arrhenius–Guzman equation. Furthermore, the slopes of the lines fitted to the viscosity versus temperature curves at the pour point decreased linearly with the Piccotex content. Non-Newtonian changes in the shear stress with the shear rate and shear stress crystallization were observed at temperatures near the pour points. The mechanical properties were evaluated using the uniaxial tensile mode and by three-point bending experiments. It was found that the stress (σ) versus the relative elongation (ε) curves can effectively be rendered by means of the standard linear solid (SLS) viscoelastic model. In addition, it was also established that the Young’s modulus varied according to a sigmoid-type curve with the piccotex content, while the yield stress decreased linearly with the concentration of Piccotex. In addition, based on the spooling suitability and printability, the patterns were rated and it was found that the most appropriate wax pattern compositions for 3D printing were those which contained 30% (m/m) and 35% (m/m) Piccotex. Full article

This paper shows that a simple and relativistic extension of Newtonian gravity that takes into account Lorentz relativistic mass leads to predictions that fit supernova observations of magnitude versus redshift without the need to introduce dark energy. To test the concept, we look at 580 supernova data points from the Union2 database. Some relativistic extensions of Newtonian gravity have been investigated in the past, but we have reason to believe the efforts were rejected prematurely before their full potential was investigated. Our model suggests that mass, as related to gravity, is also affected by Lorentz relativistic effects, something that is not the case in standard gravity theory, and this adjustment gives supernova predictions that fit the observations. Our model seems very robust with respect to supernova data, as no arbitrary parameters are introduced. Since recent investigations of Lorentz’s relativistic mass also seem to solve other challenges in physics, we think it is worthwhile for the physics community to look into this more carefully, at least before rejecting it based on prejudice. After all, no one has been able to detect dark energy despite massive efforts to do so. Until dark energy is really confirmed, other alternative models should be worth investigating further. Full article

This research investigates the influence of the combined effect of the chemically reactive and thermal radiation on electrically conductive stagnation point flow of nanofluid flow in the presence of a stationary magnetic field. Furthermore, the effect of Newtonian heating, thermal dissipation, and activation energy are considered. The boundary layer theory developed the constitutive partial differential momentum, energy, and diffusion balance equations. The fundamental flow model is changed to a system of coupled ordinary differential equations (ODEs) via proper transformations. These nonlinear-coupled equations are addressed analytically by implementing an efficient analytical method, in which a Mathematica 11.0 programming code is developed for numerical simulation. For optimizing system accuracy, stability and convergence analyses are carried out. The consequences of dimensionless parameters on flow fields are investigated to gain insight into the physical parameters. The result of these physical constraints on momentum and thermal boundary layers, along with concentration profiles, are discussed and demonstrated via plotted graphs. The computational outcomes of skin friction coefficient, mass, and heat transfer rate under the influence of appropriate parameters are demonstrated graphically. Full article

Interplanetary interactions are the largest forces in our Solar System that disturb the planets from their elliptical orbits around the Sun, yet are weak (<10⁻³ Solar). Currently, these perturbations are computed in pairs using Hill’s model for steady-state, central forces between one circular and one elliptical ring of mass. However, forces between rings are not central. To represent interplanetary interactions, which are transient, time-dependent, and cyclical, we build upon Newton’s model of interacting point-mass pairs, focusing on circular orbits of the eight largest bodies. To probe general and evolutionary behavior, we present analytical and numerical models of the interplanetary forces and torques generated during the planetary interaction cycles. From symmetry, over a planetary interaction cycle, radial forces dominate while tangential forces average to zero. Our calculations show that orbital perturbations require millennia to quantify, but observations are only over ~165 years. Furthermore, these observations are compromised because they are predominantly made from Earth, whose geocenter occupies a complex, non-Keplerian orbit. Eccentricity and inclination data are reliable and suggest that interplanetary interactions have drawn orbital planes together while elongating the orbits of the two smallest planets. This finding is consistent with conservation principles governing the eight planets, which formed as a system and evolve as a system. Full article

To explain rotation curves of spiral galaxies through Newtonian orbital models, massive halos of non-baryonic dark matter (NBDM) are commonly invoked. The postulated properties are that NBDM interacts gravitationally with baryonic matter, yet negligibly interacts with photons. Since halos are large, low-density gaseous bodies, their postulated attributes can be tested against classical thermodynamics and the kinetic theory of gas. Macroscopic models are appropriate because these make few assumptions. NBDM–NBDM collisions must be elastic to avoid the generation of light, but this does not permit halo gas temperature to evolve. If no such collisions exist, then the impossible limit of absolute zero would be attainable since the other available energy source, radiation, does not provide energy to NBDM. The alternative possibility, an undefined temperature, is also inconsistent with basic thermodynamic principles. However, a definable temperature could be attained via collisions with baryons in the intergalactic medium since these deliver kinetic energy to NBDM. In this case, light would be produced since some proportion of baryon collisions are inelastic, thereby rendering the halo detectable. Collisions with baryons are unavoidable, even if NBDM particles are essentially point masses. Note that <0.0001 × the size of a proton is needed to avoid scattering with γ-rays, the shortest wavelength used to study halos. If only elastic collisions exist, NBDM gas would collapse to a tiny, dense volume (zero volume for point masses) during a disturbance—e.g., cosmic rays. NBDM gas should occupy central galactic regions, not halos, since self-gravitating objects are density stratified. In summary, properties of NBDM halos as postulated would result in violations of thermodynamic laws and in a universe unlike that observed. Full article

With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation model (DEM) in the Newtonian integration. For efficient and accurate gravity forward modelling in the spatial domain, we developed a new MATLAB-based program called, terrain gravity field (TGF). Our new software is capable of calculating the gravity field generated by an arbitrary topographic mass-density distribution. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries (i.e., polyhedron, prism, tesseroid and point-mass) and DEMs with different spatial resolutions. Compared to some publicly available algorithms depending on one type of geometric approximation, this enables accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent gravity field functionals, supports two types of density inputs (constant density value and digital density map), and considers the curvature of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. In this contribution, the TGF software is introduced to the geoscience community and its capabilities are explained. Results from internal and external numerical validation experiments of TGF confirmed its accuracy at the sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms the capability of TGF for dealing with large datasets. Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations. Full article

The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed. Full article

The work shows that the evolution of the field of the free Klein–Gordon equation (KGE), in the hydrodynamic representation, can be represented by the motion of a mass density $\propto |\psi {|}^2$ subject to the Bohm-type quantum potential, whose equation can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been covariantly extended to the curved space-time, the gravity equation (GE), determining the geometry of the space-time, is obtained by minimizing the overall action comprehending the gravitational field. The derived Einstein-like gravity for the KGE field shows an energy-impulse tensor density (EITD) that is a function of the field with the spontaneous emergence of the “cosmological” pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant (CC). The energy-impulse tensor of the theory shows analogies with the modified Brans–Dick gravity with an effective gravity constant G divided by the field squared. Even if the classical cosmological constant is set to zero, the model shows the emergence of a theory-derived quantum CPTD that, in principle, allows to have a stable quantum vacuum (out of the collapsed branched polymer phase) without postulating a non-zero classical CC. In the classical macroscopic limit, the gravity equation of the KGE field leads to the Einstein equation. Moreover, if the boson field of the photon is considered, the EITD correctly leads to its electromagnetic energy-impulse tensor density. The work shows that the cosmological constant can be considered as a second order correction to the Newtonian gravity. The outputs of the theory show that the expectation value of the CPTD is independent by the zero-point vacuum energy density and that it takes contribution only from the space where the mass is localized (and the space-time is curvilinear) while tending to zero as the space-time approaches to the flat vacuum, leading to an overall cosmological effect on the motion of the galaxies that may possibly be compatible with the astronomical observations. Full article