Ordinary Form Research Articles

Entropy optimization of MHD second-grade nanofluid thermal transmission along stretched sheet with variable density and thermal-concentration slip effects

The goal of present investigation is to explore the influence of exponential variable density and entropy optimization on second-grade nanofluid heating efficiency and mass-concentration transmission along extended surface using external magnetic-field and temperature-concentration slip effects. To enhance the motion of nanoparticles and thermal efficiency, the influence of exponential form of temperature-based density on magnetically charged second-grade nanomaterial is main novelty of this research. For higher temperature difference, the entropy optimization is used. The defined formulation of stream functions and similarities are used to convert leading second-grade nanofluid model into ordinary differential form. The efficient Keller box method and Newton Raphson technique are applied to compute numerical results. The final algebraic equations are solved through global matrix for unknown physical quantities. The consequence of all physical constraints on velocity/U profile, temperature/θ field, concentration/ϕ shapes, skin friction coefficient, Nusselt and Sherwood number are analyzed pictorially and numerically. The following range of parameters 0.1 ≤ ξ ≤ 2.0, 0.0 ≤ n ≤ 1.2, 0.1 ≤ Ec ≤ 2.0, 0.07 ≤ Pr ≤ 7.0, 0.01 ≤ Nt ≤ 0.8, 0.01 ≤ Nb ≤ 0.9 is used. It is found that velocity field increases with maximum amplitude as variable density, magnetic force and temperature-slip constraint. It is noted that the slip behavior in temperature field and concentration field are increased with convective boundary conditions. It is depicted that local Nusselt quantity and local Sherwood quantity increases as buoyancy force and Prandtl coefficient increases.

On the hydrothermal features of MHD nanofluid flow over a differently shaped thin needle influenced by Hall current with nonlinear thermal radiation

PurposeThe investigation has appraised the problem of an incompressible laminar steady magnetohydrodynamic (MHD) nanofluid stream over three distinct slendering thin isothermal needles of paraboloid, cylindrical and cone shapes. Water as a base liquid is assumed in this flow model. The influences of the Hall current and variable sorts of magnetic forces have enriched our investigation. Energy and concentration expressions consist of thermophoresis and Brownian migration phenomena. The analysis of thermal and mass slips of the presumed model has also been performed.Design/methodology/approachA relevant transformation is implemented for the alteration of the leading partial differential equations (PDEs) to the equations with nonlinear ordinary form. Due to the strong nonlinearity of the foremost equations, the problem is solved numerically by embedding the well-known RK-4 shooting practice. The software MAPLE 2017 has been exploited in reckoning the entire computation. To enunciate the investigated upshots, some graphical diagrams have been regarded here. According to technological interest, we measured the engineering quantities like the Sherwood number, the coefficient of drag friction and the Nusselt number in tabular customs.FindingsThe obtained consequences support that Hall current intensifies fluid movement when the needle is in a cone shape, while the superior velocity is noticed for cylindrical-shaped needles. The transference of heat responds inversely along with the growths of thermal and mass slip factors.Originality/valueNo work has been performed on the flow model of radiated nanofluid over a variable-shaped thin needle under Hall current, the variable magnetic field and different slip factors.

Thermal slip and variable viscosity analysis on heat rate and magnetic flux through accelerating non-conducting wedge in the presence of induced magnetic field

The focus of present study is to incorporate the variable viscosity and temperature slip impact on heating rate and induced magnetic gradient along the moving non-conducting wedge under magnetic field. In industrial and engineering procedures, the impact of induced magnetization improves the efficiency of thermal systems to main the heating rates. The similarity transformations and stream functions are applied to reduce the governing equations into ordinary form. During this transformation, the pertinent parameters such as wedge parameter, moving parameter, Prandtl factor, viscosity parameter and temperature-slip parameter is obtained. These parameters play a prominent role on the physical values of fluid velocity, induced magnetic field and temperature distributions. The skin friction, Nusselt coefficient and induced magnetic gradient are incorporated through these parameters. The numerical values are executed by using the Keller box analysis with Newton–Raphson technique. It is depicted that the maximum slip in fluid velocity and temperature distribution is obtained for each values of thermal-slip parameter. It is noticed that maximum magnitude in induced magnetic field is reported for each wedge factor. The maximum velocity slip and temperature slip is observed for each choice of moving parameter. It is reported that the maximum variation in heating rate and induced magnetic gradient is obtained for magnetic force and viscosity parameter. The enhancing behavior of skin friction is observed for maximum values of Prandtl number.

Investigation of Analytical Soliton Solutions to the Non-Linear Klein–Gordon Model Using Efficient Techniques

Nonlinear distinct models have wide applications in various fields of science and engineering. The present research uses the mapping and generalized Riccati equation mapping methods to address the exact solutions for the nonlinear Klein–Gordon equation. First, the travelling wave transform is used to create an ordinary differential equation form for the nonlinear partial differential equation. This work presents the construction of novel trigonometric, hyperbolic and Jacobi elliptic functions to the nonlinear Klein–Gordon equation using the mapping and generalized Riccati equation mapping methods. In the fields of fluid motion, plasma science, and classical physics the nonlinear Klein–Gordon equation is frequently used to identify of a wide range of interesting physical occurrences. It is considered that the obtained results have not been established in prior study via these methods. To fully evaluate the wave character of the solutions, a number of typical wave profiles are presented, including bell-shaped wave, anti-bell shaped wave, W-shaped wave, continuous periodic wave, while kink wave, smooth kink wave, anti-peakon wave, V-shaped wave and flat wave solitons. Several 2D, 3D and contour plots are produced by taking precise values of parameters in order to improve the physical description of solutions. It is noteworthy that the suggested techniques for solving nonlinear partial differential equations are capable, reliable, and captivating analytical instruments.

The effects of bioconvection, non‐Fourier heat flux, and thermal radiations on Williamson nanofluids and Maxwell nanofluids transportation with prescribed thermal conditions

AbstractThe utilization of nanoentities in common fluids has opened new opportunities in the area of heat transportation. The rising requirements to enhance the efficiency of compact heat exchangers can be achieved by using various nanofluids. In this article, the thermal output of Maxwell and Williamson nanofluids transport over a prolonging sheet with bioconvection of self‐motivated organisms is scrutinized. A magnetic flux and the porous effects of a medium influence the flow of fluids. The fundamental principles for conservation of mass, concentration, momentum, and energy yield a nonlinear set of partial differential equations that can then be altered into ordinary differential form. A heat transfer flux is presented along with temperature boundary conditions, PST, and PHF (prescribed surface temperature and prescribed heat flux). The numerical results are acquired by executing the Runge–Kutta method with a shooting procedure in MATLAB coding. By fluctuating the inputs of influential variables of the dependent functions, a precise overview of the scheme is acquired. It can be seen that velocity decreases with the rising values of buoyancy ratio, magnetic force, Raleigh number, and porosity. Also, the temperature of the fluids begins to rise directly with the rising values of thermophoresis and Brownian motion parameters. The present study addresses bioconvection, non‐Fourier heat flow, and thermal radiations while combining the special properties of Williamson and Maxwell nanofluids. The field of biomedical engineering may benefit from this study, particularly with regard to therapies for hyperthermia and drug delivery systems. This study can be useful in cutting‐edge cooling systems, bioengineering, solar energy conversion and biotechnology.

𝑝-adic limit of the Eisenstein series on the exceptional group of type 𝐸_{7,3}

In this paper, we show that the p p -adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type E 7 , 3 E_{7,3} acts is an ordinary modular form for a congruence subgroup.

Optical soliton solutions of nonlinear differential Boussinesq water wave equation via two analytical techniques

In this article, we examine the optical soliton solutions of the 4th-order nonlinear Boussinesq water wave equation using the modified (G′/G2)− expansion and F-expansion methods. We utilize the similarity transformation to transform the partial differential form of the equation into an ordinary differential form. These techniques present a variety of solutions, including bright, dark, singular, dark-periodic, and singular-periodic soliton solutions. We plot the derived solutions in several profiles, such as 2D, 3D, and contour, to illustrate their physical appearance. The determined findings might be useful and have an enormous effect on the research of nonlinear phenomena in a variety of physical areas of science, like shallow water waves, acoustics, fluid dynamics, laser optics, communication systems, and heat transfer. The achieved results demonstrate the validity, applicability, and effectiveness of the presented method. We plot and validate the found solutions using the computational program MATHEMATICA.

Abundant Soliton Solutions to the Generalized Reaction Duffing Model and Their Applications

The main aim of this study is to obtain soliton solutions of the generalized reaction Duffing model, which is a generalization for a collection of prominent models describing various key phenomena in science and engineering. The equation models the motion of a damped oscillator with a more complex potential than in basic harmonic motion. Two effective techniques, the mapping method and Bernoulli sub-ODE technique, are used for the first time to obtain the soliton solutions of the proposed model. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals, is applied, and a nonlinear ordinary differential equation form is derived. These approaches effectively retrieve a hyperbolic, Jacobi function as well as trigonometric solutions while the appropriate conditions are applied to the parameters. Numerous innovative solutions, including the kink wave, anti-kink wave, bell shape, anti-bell shape, W-shape, bright, dark and singular shape soliton solutions, were produced via the mapping and Bernoulli sub-ODE approaches. The research includes comprehensive 2D and 3D graphical representations of the solutions, facilitating a better understanding of their physical attributes and proving the effectiveness of the proposed methods in solving complex nonlinear equations. It is important to note that the proposed methods are competent, credible and interesting analytical tools for solving nonlinear partial differential equations.

Pochówek ciał i przechowywanie prochów wiernych zmarłych. Aspekt kanoniczno-liturgiczny

The purpose of this paper is to present the problem of the burial of bodies and the storage of ashes of the faithful departed in the canonical-liturgical aspect. The Church demands respect for human bodies and ashes. The first part of the article presents the burial of corpses in the ground as an ordinary and basic form of Christian burial. The second part presents the problem of cremation as an acceptable way of burying the bodies of the faithful departed, while the second part discusses the question of the place of burial of the bodies and storing the ashes of the faithful departed.

Modeling of micropolar hybrid nanofluids flow across porous medium between permeable parallel plates with nonlinear thermal radiative in MHD

The study pertains on the dynamics and thermal distribution of magnetohydrodynamics (MHD) micropolar hybrid nanofluids flowing between two parallel plates channel. It explores the enhancement of heat transport processes by blending the base fluid with nanoparticles at varying concentrations. A system of nonlinear partial differential equations is developed as governing equations for momenta and heat energy. To facilitate numerical solutions for fluid temperature and velocities, this formulation is translated into ordinary differential form using the necessary similarity transformation. By utilizing Matlab code for the Runge–Kutta method and shooting approach, we evaluate the results. It has been observed that an increase in the concentration of hybrid nanoparticles enhance the heat transmission. The salient findings of this study reveal alteration in the velocity profiles for both nanofluid (SWCNT/water) and hybrid nanofluids (SWCNT + MWCNT/water) flow. Notably, with a substantial input of magnetic field strength (M) and porosity parameters (P0), the velocity is increased near the walls but it decelerates toward the center of channel. Additionally, the temperature rises for hybrid nanofluids. Furthermore, an increase in the θ w temperature ratio parameter leads to an enhanced thermal distribution.

Hopf bifurcation control of a modified continuum traffic flow model

The stability of the transportation system refers to the structural stability of the system. When the system structure is unstable, local or global bifurcation phenomena will occur, which is one of the main reasons for nonlinear traffic phenomena such as congestion. To truly understand the internal mechanism of the formation of these phenomena, it is necessary to analyze the bifurcation of traffic flow. In this paper, the Hopf bifurcation control of a modified viscous macroscopic traffic flow model is studied by using the linear state feedback method, which changes the characteristics of the bifurcation phenomenon of the dynamic system and obtains the required dynamic behavior of the system. First, we can convert the original traffic model into the nonlinear ordinary differential form suitable for bifurcation analysis, solve the equilibrium point of the system, and carry out phase plane analysis. Then, the linear state feedback term is added and the corresponding controlled system is generated, the existence and type of Hopf bifurcation and the existence of saddle node bifurcation are proved. Numerical simulation results show that the analysis and control of Hopf bifurcation in the traffic model are well realized in this paper.

On the Iwasawa main conjecture for generalized Heegner classes in a quaternionic setting

Abstract We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form f and an imaginary quadratic field satisfying a “relaxed” Heegner hypothesis. Let Λ be the anticyclotomic Iwasawa algebra. Following the approach of Howard and Longo–Vigni, we construct the Λ-adic Kolyvagin system of generalized Heegner classes coming from Heegner points on a suitable Shimura curve. As its application, we also prove one divisibility relation in the Iwasawa–Greenberg main conjecture for the p-adic L-function defined by Magrone.

Convective heat mechanism in Williamson nanoliquid over an escalating surface through an interface with viscous heating

This analysis explains the magneto-hydrodynamic flow on Williamson nanofluids previous stretching surface surrounded by the permeable media. The apt magnetic field was suggested for the angle of the axial direction of the flow. Anyhow, this flow phenomenon was characterized into the added heat source/sink and conjunction of radiating heat. The impacts of convective heating and viscous heating by expanding surface were again the significant feature of the analysis. This originality arises by the combination of the cross-diffusion effects of reverse behavior on the thermophoresis and Brownian motion. This form sketched into the aforesaid phenomenon was modified into the nonlinear ordinary form by the appropriate assumptions on comparison transformations. Therefore, the sets of equations were controlled for the numerical access using Lobatto-IIIa collocation method applicable to this Matlab bvp4c shooting process. This parametric performance of many components about their statistical values was given numerical imitations graphically by the rate coefficients in tabular forms. The validation and the compliance of the current result were acquired by the past study on the specific case. Further, the significant results of this analysis were: This non-Newtonian Williamson parameter combination of that magnetizing property diminishes the fluid velocities. In addition, the important influence of both viscosity parameter and radiation parameter of heating process was noted.

Bootstrapping bulk locality. Part I: Sum rules for AdS form factors

The problem of constructing local bulk observables from boundary CFT data is of paramount importance in holography. In this work, we begin addressing this question from a modern bootstrap perspective. Our main tool is the boundary operator expansion (BOE), which holds for any QFT in AdS. Following Kabat and Lifschytz, we argue that the BOE is strongly constrained by demanding locality of correlators involving bulk fields. Focusing on ‘AdS form factors’ of one bulk and two boundary insertions, we reformulate these locality constraints as a complete set of sum rules on the BOE data. We show that these sum rules lead to a manifestly local representation of form factors in terms of ‘local blocks’. The sum rules are valid non-perturbatively, but are especially well-adapted for perturbative computations in AdS where they allow us to bootstrap the BOE data in a systematic fashion. Finally, in the flat space limit, we show that the AdS form factor reduces to an ordinary QFT form factor. We provide a phase shift formula for it in terms of the BOE and CFT data. In two dimensions, this formula makes manifest Watson’s equations for integrable form factors under certain extremality assumptions on the CFT. We discuss the eventual modifications of our formalism to account for dressed operators in AdS.

Optical solitons for the dispersive concatenation model with spatio-temporal dispersion having multiplicative white noise

This investigation of the current work presents the dispersive concatenation model that integrates the spatio-temporal dispersion and the effect of multiplicative white noise in the Itô sense. The study aims to secure stochastic optical soliton solutions within this framework. To achieve this purpose, we implemented the enhanced Kudryashov technique and the new projective Riccati equations strategy. Initially, the traveling wave transform hypothesis was applied to convert the stochastic model into its nonlinear ordinary differential equation form, encompassing real and imaginary components with emerging the related parametric restrictions. Subsequently, we introduced the enhanced Kudryashov and the new projective Riccati equations techniques successfully employed in analyzing the generated nonlinear ordinary differential equation. By utilizing the appropriate solution sets, which encompass variables with unknown values and necessary transformations, we have derived many stochastic optical soliton-type solutions for the model. Detailed discussions for the dynamics of some selected soliton solutions are presented with the supporting of the 3D and 2D graphs that illustrate the white noise effect on these solitons.

Pembacaan kembali Traditionis Custodes Paus Fransiskus terhadap penggunaan Missale Romanum 1962. Sebuah tinjauan Liturgis-Eklesiologis dalam terang reformasi Konsili Vatikan II

<p>Traditionis Custodes is an Apostolic letter issued by Pope Francis in the form of a Motu Proprio, i.e. on his own initiative. The content of this letter is about the use of the Roman Liturgy prior to the Reform of 1970. The main object of focus is the celebration of Mass with the Missale Romanum 1962. The Motu Proprio of the two previous Popes, John Paul II and Benedict XVI, permitted the use of the Missale Romanun 1962. The aim was to make room for those who were still attached to earlier forms of liturgical celebration. The implication is that the Missale Romanum 1962 is permitted as an extraordinary form of liturgical celebration, while the Missale Romanum 1970 is the ordinary or normal form. Pope Francis, through Traditionis Custodes, abrogated all the norms, instructions, consensus and customs of the previous Motu Proprio. He established the Missale Romanum 1970 as the only lex orandi (prayer order of the Church) of the Roman rite. This decision caused turmoil in the Church,<br />especially strong criticism from users of the Missale Romanum 1962. This Motu Proprio was seen as a regression of the Church and a personal desire to abolish Church Tradition. Is this really the case? Why did Pope Francis<br />abrogate the norms of the previous Motu Proprio? What is different about the 1962 and 1970 Missale Romanum? This article attempts to answer these questions with a liturgical-ecclesiological overview of the reforms of the Second Vatican Council.</p><p><br />Key words: Ecclesial communion; liturgical reform; Traditionis Custodes; Summorum Pontificum; Missale<br />Romanum 1962.</p>

Synthesis and efficacy of cinnamon oil formulations and their sustainable release against common house mosquito larvae

BackgroundControl of mosquitoes is considered an essential public health priority. This study was designed to estimate the larvicidal activity of two formulations of Cinnamomum zeylanicum EO for controlling Culex pipiens larvae.ResultsThe prepared formulations were a nanoemulsion of cinnamon (CNE), cinnamon (CN) alone and ordinary cinnamon essential oil mixed with sesame oil (CSO). The cinnamon + sesame oil (CSO) was added as one part cinnamon to 3 parts SO. Different concentrations were prepared and applied following the WHO larvicidal bioassay protocol. Our findings revealed that the LC50 of the CNE form ranged from 85.3 µg/mL to 28.30 µg/mL. The LC50 of SO alone was 1265 µg/mL but when mixed with CNE to form the CSO mixture, this decreased to 159.00 µg/mL. In terms of residual effect, the ordinary form of cinnamon had a residual effect in water for 72 h at a dose of 1000 µg/ml, but this extended to 120 h at the same dose when the CNE form was used. However CSO did not have a residual effect, however.ConclusionThe nanoemulsion form significantly improved the efficacy and residual effect of cinnamon against Culex pipiens larvae. Additionally, mixing cinnamon with sesame oil had a synergistic effect. This may assist control strategies against the house mosquito, Culex pipiens.

Optical solitons of stochastic perturbed Radhakrishnan–Kundu–Lakshmanan model with Kerr law of self-phase-modulation

This study aims to obtain the optical soliton solutions of the stochastic perturbed Radhakrishnan–Kundu–Lakshmanan equation which models the optical solitons in optical waveguides such as silica fibers with Kerr law in the presence of chromatic and third-order dispersions by multiplicative white noise in Itô calculus. The study constitutes one of the works aimed at adapting the model in accordance with the importance of the noise effect in nonlinear optics. In the first step, the nonlinear ordinary differential form of the investigated problem has been obtained by using an appropriate complex wave transformation. The enhanced Kudryashov technique, which is the combination of Kudryashov and the new Kudryashov methods, is applied to the nonlinear ordinary differential form. As the result, bright, dark and singular stochastic soliton solutions of the analyzed problem have been carried out by assigning appropriate parameter values and the impact of noise effect on the soliton behavior has been investigated. Lastly, the graphical representations and required comments have been presented in the related sections.

‘Constructing the test to the teaching’ – and the complexities of assessing learning in ethics education

ABSTRACT This study draws on a research project where a model of fiction-based ethics education was developed and put into practice during a school year in five classes in compulsory school, two in grade 5 and three in grade 8. A test was constructed with the purpose of evaluating a multi-dimensional ethical competence. The test was given at the beginning and the end of the school year to the students in the five classes, but also to students in five other classes who received the ordinary form of ethics education. The test was constructed by using tasks from earlier Swedish national tests on ethics education, but in this study new assessment instructions were developed. According to this test, almost no significant differences were found between the classes with fiction-based ethics education and the other classes. However, this contrasts with the fruitfulness of the fiction-based model, as identified through other forms of evaluation. The findings raise questions about whether and how ethics education can be meaningfully tested, which in this article is self-critically reflected on. A concluding discussion on target competence, teaching intervention and ways of evaluation – in relation to each other – ends the article.

On the revealing of optical soliton solutions of the stochastic perturbed nonlinear Schrödinger equation in the presence of the Kerr law of self-phase modulation

In this study, an attempt to obtain optical soliton solutions of stochastic perturbed (1+1)-dimensional nonlinear Schrödinger equation having the Kerr law nonlinearity is presented. With the help of complex wave transform, the investigated nonlinear partial differential equation was converted into the nonlinear ordinary differential form. Analytical stochastic optical soliton solutions of the ordinary differential form were derived by applying the Kudryashov auxiliary equation method. By replacing the wave transformation and the appropriate solution set parameters, the main equation is provided. Graphic presentations were made for better interpretation of the results.