Order Scheme Research Articles

Finite-Time Regulation of Robot Manipulators in the Task-Space

This paper proposes a control scheme in order to attain finite-time regulation of robots manipulators in the task-space. The stability analysis is carried out by means of strict Lyapunov functions since the well-known results of homogeneous systems cannot be applied directly. Simulations results verify the performance of the proposed control scheme.

Fractional Order Tracking Control for Diferential Mobile Robots with Skidding and Slipping Effects

The development of a fractional order tracking control for a differential wheeled mobile robot under the effect of skidding and slipping effects is presented in this paper. The kinematic model of a differential mobile robot with disturbances are used to solve the tracking problem. The control scheme proposed is based on backstepping, feedback passivity and fractional sliding modes techniques. Numeric simulations are shown to prove the effectiveness of the proposed method and a comparison with entire order scheme is also provided.

Enhanced electrocaloric effect in KNN-based ceramic via polymorphic phase transition

A large adiabatic temperature change (ΔT) in lead-free ceramics is highly desired to develop eco-friendly and high efficiency solid-state refrigeration device based on electrocaloric effect (ECE). However, a large ΔT is often obtained near high Curie temperature (Tc > 100 °C), which impedes the practical applications for electrocaloric refrigeration technology. Herein, the lead-free (1-x)(K0.48Na0.535)0.03Li0.07(Nb0.99Sb0.01)O3-xBaZrO3 (x = 0, 0.02, 0.04 and 0.06) ceramics were synthesized through a conventional solid-state sintering method. A polymorphic phase transition (PPT) region is constructed by composition engineering to achieve large ECE near the ambient temperature. A ΔT of 0.48 K under 50 kV/cm is obtained at 60 °C by using the direct measurement in KNLNS-0.02BZ ceramic with coexistence of R-O-T phase. This work suggests that building multi-phase coexistence is a feasible design scheme in order to achieve ECE near the room temperature.

Australian Selectors in the Nineteenth Century and Discrepancies in Imaginings and Realities: Critical Family History

Queensland became an independent state in 1859, separating from New South Wales. Almost immediately, an ambitious plan on migration was embarked upon in order to attract emigrants to Queensland, above all other possible colony destinations in the British Empire. Henry Jordan was instrumental as the Emigration Commissioner (1861–1866) in devising the land order scheme and Richard Daintree, as Agent-General, wooed, through modern techniques on never-before-seen photography in colour, small capitalists to the isolated outreaches of Queensland, where settlement was encouraged. Life there for those that migrated was, however, vastly different from what either they knew in Britain, or what they expected. But, ultimately, they settled, took possession of considerable stretches of lands, as selectors, or pastoral land owners, with disregard for the indigenous populations there. In this article, I examine one migration story on an ancestor in the nineteenth century, Andrew Milne, from London to Queensland, through the lens of critical settler family history theory. I take up the challenge for historians to question who their ancestors were, since the past is telling of the present, and the perceptions that are longed for in the future selves. Namely, in the construction of the future self, an individual must also confront their past, and the lives of those that preceded them. In particular, in the case of Australia, settlement, colonisation, and the possession of land are not benign, and are not isolated events, but have an impact on the present and future lives of both descendants of those that possessed the land, and those from whom it was taken away. The legacy of racial segregation (through the Stolen Generations), and despite the attempt to ‘close the gap’ since 2008, Aboriginal peoples in Australia still suffer the consequences of objectification and dehumanisation to which they were subjected. The consequences are not only financial and economic, but are visible in health, education, social status, and in their mistrust of public services.

Higher-order adaptive methods for exit times of Itô diffusions

Abstract We construct a higher-order adaptive method for strong approximations of exit times of Itô stochastic differential equations (SDEs). The method employs a strong Itô–Taylor scheme for simulating SDE paths, and adaptively decreases the step size in the numerical integration as the solution approaches the boundary of the domain. These techniques complement each other nicely: adaptive timestepping improves the accuracy of the exit time by reducing the magnitude of the overshoot of the numerical solution when it exits the domain, and higher-order schemes improve the approximation of the state of the diffusion process. We present two versions of the higher-order adaptive method. The first one uses the Milstein scheme as the numerical integrator and two step sizes for adaptive timestepping: $h$ when far away from the boundary and $h^2$ when close to the boundary. The second method is an extension of the first one using the strong Itô–Taylor scheme of order 1.5 as the numerical integrator and three step sizes for adaptive timestepping. Under some regularity assumptions, we show that for any $\xi>0$, the strong error is ${\mathcal{O}}(h^{1-\xi })$ and ${\mathcal{O}}(h^{3/2-\xi })$ for the first and second method, respectively. Provided quite restrictive commutativity conditions hold for the diffusion coefficient, we further show that the expected computational cost for both methods is ${\mathcal{O}}(h^{-1} \log (h^{-1}))$. This results in a near doubling/trebling of the strong error rate compared to the standard Euler–Maruyama-based approach, while the computational cost rate is kept close to order one. Numerical examples that support the theoretical results are provided, and we discuss the potential for extensions that would further improve the strong convergence rate of the method.

PROFESSIONAL TRAINING OF THE COACH-SPECIALIST DEPENDING ON THE CURRENT REQUIREMENTS OF THE MODERN SPORT

The high professional training of the specialist-coach at the present time is conditioned by the alert dynamics of modern sports at all Olympic events and has become a direct dependent of this phenomenon. Nowadays, the professional competence and the coach's ability to support the requirements of the athletes' training for the competition program are highlighted by the maximum possible and correct utilization of all the information and forms of training in all the directions that the respective sports event takes. Thus, the coordinates of the professional training of the coach propagate a clear definition of the training/education of the performance athlete, all of which are oriented towards the highest possible result. The professional training process itself, determined by its complex character, implies the functionality of a much more creative and well-defined instructional system. The structure of the specialist trainer's skills training program, at the present time, requires the clear expression of all knowledge actions, which should be able to subordinate the training schemes in order to develop and improve the full bio-psycho-motor potential of the athlete. In the context of the above, it should be mentioned that in front of higher education, in which the high professional training of the future specialist-coach takes place, the problem of developing and establishing modernist didactic strategies, which propel the realization of the set of educational standards and specialized objectives to obtain a high quality product. In this case, the educational unit, which educates a well-trained professional coach, must exercise all its instructional activities at an excellent level, aiming at the high degree of acquisition of pedagogical skills and the education of the highest possible sports mastery. The present study provides the determination of the set of skills characteristic of a high degree of professional training of the specialist-coach, which, being coupled and systematized on modules, would be able to complete the vast arsenal of knowledge of the subject for the most effective centralized training of the athlete. Certainly, such a classification can complete the specialist-coach's professional profile with those characteristics, which must necessarily be consistent with the needs of training athletes depending on the current requirements of modern sports.

Stability, convergence and error analysis of B-spline collocation with Crank–Nicolson method and finite element methods for numerical solution of Schrodinger equation arises in quantum mechanics

In the present study, the complex-valued Schrodinger equation (CVSE) is solved numerically by a nonic B-spline finite element method (FEM) in quantum mechanics. The approach employed is based on the collocation of nonic B-splines over spatial finite elements, so that we have continuity of the dependent variable and its first eight derivatives throughout the solution range. For time discretization, the Crank-Nicolson scheme of second order based on FEM is employed. The method is shown to be unconditionally stable and accurate to order. Three problems are considered to validate the algorithm. Comparisons are made with existing methods and analytical solutions. The proposed method exhibits good conservation properties and performs well with regards to analytical solutions for different error norms and conservative constants related to parameters in quantum classes in Physics. The computational complexity of (2N+18) arithmetic operations with the help of a nonic-diagonal matrix is also tackled by the present scheme.

A kinetic energy and entropy preserving (KEEP) finite volume scheme on unstructured meshes for compressible flows

A kinetic energy and entropy preserving (KEEP) finite-volume scheme on unstructured meshes is proposed for non-dissipative and stable compressible flow computations. The KEEP finite volume scheme proposed in the present study is based on the existing KEEP schemes developed for finite difference methods. The KEEP schemes have shown superior numerical robustness without numerical dissipation in previous studies. The KEEP schemes are discretized such that the numerical fluxes discretely replicate the key analytical relations that the governing equations hold, leading to preservation of kinetic energy and a superior entropy preservation property in the incompressible and inviscid limits. This study proposes using cell-vertex discretization for the proposed KEEP finite volume scheme in order to maintain this characteristic property of the KEEP scheme and achieve second-order accuracy in space on simplex meshes and arbitrary meshes that are not highly irregular. In the numerical tests performed in this study, the proposed KEEP finite volume scheme successfully performs long-time stable computations on various unstructured meshes. Also, the proposed KEEP scheme shows much better numerical stability and spatial accuracy than the KEEP scheme with cell-centered discretization.

Implication of radiation on the thermal behavior of a partially wetted dovetail fin using an artificial neural network

The simultaneous convection-radiation heat transfer of a partially wetted dovetail extended surface is investigated in this study. Also, the temperature variance behavior of the dovetail extended surface (DES) is estimated through thermal models for partially wet and dry conditions using the neural network with the Levenberg-Marquardt scheme (NNLMS). The corresponding governing energy equations of a dovetail fin are presented as a set of ordinary differential equations (ODE), which are reduced to a non-dimensional form using dimensionless terms. Further, the resulting coupled conductive, convective, and radiative dimensionless ODEs are numerically solved utilizing the Runge-Kutta-Fehlberg fourth-fifth order (RKF-45) scheme. Using graphical illustrations, the resultant solutions are physically determined by considering the effects of various nondimensional variables on thermal behavior. From the outcomes, it is established that the thermal conductivity parameter enhances the thermal distribution in a partially wetted dovetail fin, and an upsurge in convection-conduction variable, temperature ratio parameter, radiation-conduction, and wet parameter diminishes the temperature profile of the considered extended surface. The modelled problem's NNLMS efficacy is demonstrated by achieving the best convergence and unique numerically assessed quantified results. The outcomes indicate that the strategy successfully resolves the partially wetted fin problem.

Splitting schemes for the semi-linear wave equation with dynamic boundary conditions

This paper introduces novel bulk–surface splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For kinetic boundary conditions, we propose a reinterpretation of the system equations as a coupled system. This means that the bulk and surface dynamics are modeled separately and connected through a coupling constraint. This allows the implementation of splitting schemes, which show first-order convergence in numerical experiments. On the other hand, acoustic boundary conditions naturally separate bulk and surface dynamics. Here, Lie and Strang splitting schemes reach first- and second-order convergence, respectively, as we reveal numerically.

High order schemes for gradient flow with respect to a metric

New criteria for energy stability of multi-step, multi-stage, and mixed schemes are introduced in the context of evolution equations that arise as gradient flow with respect to a metric. These criteria are used to exhibit second and third order consistent, energy stable schemes, which are then demonstrated on several partial differential equations that arise as gradient flow with respect to the 2-Wasserstein metric.

Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem

AbstractTwo‐dimensional, nonlinear diffusion‐limited colliding plumes simulations were used to demonstrate the improved solution accuracy with very high order O9–18 flux schemes, including upwind‐biased and even‐centred constant grid flux and Crowley constant grid flux schemes, and odd order weighted essentially non‐oscillatory (WENO) flux schemes, along with variations and hybrids of these. All schemes were coupled with comparably high order even‐centred Lagrangian interpolations and pressure gradient/divergence approximations, and O18 spatial filtering. Subgrid‐scale (SGS) turbulent flux calculations, with a constant eddy‐mixing coefficient, were made with O2 spatial approximations (O4–20 accurate SGS turbulent fluxes had little impact). Using a range of resolutions from Δx = Δz = 25–166.66… m for all schemes comparisons against an O17 flux, 25 m resolution reference solution showed solutions made with ≥O9 fluxes produced (often substantially) improved solutions, both visually and usually objectively, compared to solutions produced with lower order (<O9/10) fluxes, especially at intermediate resolutions (33.33–100 m). Expectedly, odd order solutions were increasingly damped as accuracy was decreased, especially from O9 to O3, especially for WENO solutions, while even order solutions were increasingly contaminated with dispersion and aliasing errors as accuracy was decreased, especially from O10 to O4. Odd order schemes also produced better solutions than even order schemes for <O9/10 fluxes, while the highest order (≥O13/14) schemes produced the best solutions, for any given resolution. Even order flux and Crowley flux (WENO) solutions were the least (most) computationally expensive, based on either floating‐point operations (FPO) or CPU times. Efficient WENO‐Sine and proposed hybrid Crowley‐WENO(‐Sine) schemes required fewer FPOs to produce more accurate solutions than traditional WENO schemes. We are encouraged by the often much improved visual and objective accuracy of very high order (≥O9) fluxes in simulations of a complex problem, and encourage further testing in numerical weather prediction models.

Bio-Convective Hartmann Flow of Couple Stress Hybrid Nanofluid Between Two Dilating Parallel Walls with Heat and Mass Transfer

The study of bio-convective flow of hybrid nanofluid attracted many researchers because of tremendous applications in the fields of biofuel biotechnology, enzyme-based biosensors and biomedical science. The present work addresses a comparative study of CuO/Al2O3-water and CuO-water nanoparticles on heat and mass transfer characteristics of the squeezing flow of MHD couple stress fluid between two parallel plates by suspending motile micro-organisms. An approximated numerical technique (Shooting method along with Runge-Kutta 4th order scheme) have been employed to analyse the system of coupled nonlinear ordinary differential equations. The above numerical investigations were carried out for various governing parameters such as couple stress parameter, Hartmann number, bioconvection Peclet number, squeezing parameter etc. The effects of these physical parameters are illustrated graphically over velocity components, temperature distribution, diffusion of concentration and density of motile microorganisms. In addition to this the numerical values of skin friction, the local Nusselt number and local Sherwood number are tabulated at the upper plate for CuO-water and CuO–Al2O3-water at the expanding and squeezing cases. The numerical results for temperature profiles are in good consistency with earlier research.

Computational study for the Caputo sub-diffusive and Riesz super-diffusive processes with a fractional order reaction–diffusion equation

A Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion model is considered in this paper. Based on finite difference schemes, we formulate both second-order and fourth-order numerical methods for the approximation of the Riesz space fractional reaction–diffusion-like equation of Fisher type. In the experiment, it was observed that the fourth-order scheme has better accuracy than the second-order method when applied to solve the fractional diffusion equation. It should be mentioned that the lower order scheme computes rapidly and save more computational time as displayed in the table of results. Finally, some simulation results are presented to justify the effectiveness and applicability of the numerical methods. The one- two- and three-dimensional results obtained for some instances of fractional order (α,β) depict some amazing complex and spatiotemporal patterns which are applicable in applied sciences and engineering.

The stability analysis of a nonlinear mathematical model for typhoid fever disease

Typhoid fever is a contagious disease that is generally caused by bacteria known as Salmonella typhi. This disease spreads through manure contamination of food or water and infects unprotected people. In this work, our focus is to numerically examine the dynamical behavior of a typhoid fever nonlinear mathematical model. To achieve our objective, we utilize a conditionally stable Runge–Kutta scheme of order 4 (RK-4) and an unconditionally stable non-standard finite difference (NSFD) scheme to better understand the dynamical behavior of the continuous model. The primary advantage of using the NSFD scheme to solve differential equations is its capacity to discretize the continuous model while upholding crucial dynamical properties like the solutions convergence to equilibria and its positivity for all finite step sizes. Additionally, the NSFD scheme does not only address the deficiencies of the RK-4 scheme, but also provides results that are consistent with the continuous system's solutions. Our numerical results demonstrate that RK-4 scheme is dynamically reliable only for lower step size and, consequently cannot exactly retain the important features of the original continuous model. The NSFD scheme, on the other hand, is a strong and efficient method that presents an accurate portrayal of the original model. The purpose of developing the NSFD scheme for differential equations is to make sure that it is dynamically consistent, which means to discretize the continuous model while keeping significant dynamical properties including the convergence of equilibria and positivity of solutions for all step sizes. The numerical simulation also indicates that all the dynamical characteristics of the continuous model are conserved by discrete NSFD scheme. The theoretical and numerical results in the current work can be engaged as a useful tool for tracking the occurrence of typhoid fever disease.

Nonlinear Approximation for Mixed Convection Flow From a Vertical Plate With Exponentially Decaying Internal Heat Generation and Nonlinear Thermal Radiation

Abstract This study considered dynamic features of mixed convection flow over a vertical plate influenced by nonlinear thermal radiation and exponentially decaying internal heat generation. The importance of the nonlinear density variation with temperature (NDT) and convective heating is also analyzed. The governing equations are transformed into ordinary differential equations using the similarity variables and solved in MAPLE 2022 by a Runge–Kutta Ferhlberg fourth-fifth order scheme. The results obtained show that, with an increase in the convection process, the internal heat generation convects more fluid away and consequently reduced the rate of heat flowing back into the plate. For a weak internal heat generation λx=0.5, the plate temperature is less than one (1) and the heat is observed to flow from the plate into the fluid on the surface of the right plate. Furthermore, for weak convection and nonlinear thermal radiation effects, the rate at which the heat flows into the plate increases with the convective heat transfer parameter increase. However, for a strong nonlinear thermal radiation effect, the rate at which the heat flows out of the plate increases. The flow feature is not only governed by the rate of internal heat generation but the generation as well reverses the heat flow from the plate since the temperature of the near the plate surface T is much higher than the environmental temperature Tf.

Impact of variable thermal conductivity on flow of trihybrid nanofluid over a stretching surface.

The present article describes the impact of variable thermal conductivity on the flow of ternary hybrid nanofluid with cylindrical shape nanoparticles over a stretching surface. Three nanoparticles combine in base fluid polymer. The assumption made will be used to model an equations. Modeled equations are in the form of a system of partial differential equations are difficult to solve can be converted to system of an ordinary differential equations, through resemblance substitutions, and will be solved numerically. Numerical scheme of Runge-Kutta order four is coupled with the shooting method to solve the resulting equations. The graphs in the study illustrate how physical quantities, such as magnetic field, injection/suction, nanoparticles volume fraction, and variable thermal conductivity, affected the velocity, skin friction, temperature, and local Nusselt number. The velocity profiles deflate as the volume fraction rises. While the temperature rises with an increase in the volume fraction of nanoparticles for both injection and suction, the velocity profiles also decline as the injection and suction parameter increases. Furthermore, as the magnetic field increases, the temperature profile rises while the velocity profile falls. The temperature curves increase as thermal conductivity increases. Finally, as the magnetic field is strengthened, the Nusselt number and skin friction decrease. The combination of mathematical modeling, numerical solution techniques, and the analysis of physical quantities contributes to the advancement of knowledge in this ternary hybrid nanofluid.

Framing the features of nanolayer and diameter of carbon nanotubes in the flow of blood over a stretching cylinder in presence of magnetic induction

This study explores the slip boundary layer electrically conducting flow of nanofluid over a stretching cylinder. Flow type in present study is considered to be steady and incompressible flow with mixture of SWCNTs/MWCNTs and human blood. Thermal conductivity of present flow model is measured by merging the consequence of diameter of SWCNTs/MWCNTs nanoparticles and solid–liquid interfacial-layer. Velocity slip, non-linear radiation, and induced magnetic-flux are considered in flow. The mode of heat transmission in flow is presented in appearance of dual heat flux, that is, Cattaneo-Christov heat flux and prescribed heat flux. By executing similarity exploration, we modernize the leading PDEs of the acknowledged flow model into ODEs. The consequential equations are solved numerically by recalling Runge–Kutta–Fehlberg fourth-fifth order scheme through shooting system. Deliberations on consequence of flow features on flow specific are organized accurately via graphs and charts. The professed numerical consequences are novel and distinctive. These consequences can contribute to other scholars on electing the suitable factors to enlarge the heat conduction technique in medical science, society, and the industry.

Impact of bioconvection on Darcy‐Forchheimer flow of MHD Carreau fluid with Arrhenius activation energy

AbstractThis research examines the bioconvection impact on mixed convective Carreau fluid flowing toward permeable stretched surface with joule heating and Darcy‐Forchheimer effect. The evaluation has been attained in the presence of convective conditions, Joule heating, thermal radiative, mixed convective and motile microorganisms, which have not been dreamed before. Flow in permeable medium is characterized by utilizing Darcy‐Forchheimer model. Appropriate similarity factors are utilized to obtain the ordinary differential equations (ODEs). The derived mathematical formulation is now numerically solved with the help of R‐K 4th order scheme based on shooting approach. The results of the motile microorganism number, velocity, Sherwood number, temperature, motile density number, drag coefficient, concentration, and local Nusselt number are revealed graphically. The effect of bioconvection Lewis number on the motile microorganisms and motile density profile are quite inverse. Further, higher values of Schmidt number decrease the concentration field.

A deep reinforcement learning framework for dynamic optimization of numerical schemes for compressible flow simulations

Marginal or under-resolved simulations of compressible flow configurations that often occur in practical applications classically are enabled by administering sufficient numerical dissipation to keep the simulation stable. Such measures, however, often are physically inconsistent due to non-selectively altering of dynamics across scales. Sustaining physically consistent large scale dynamics requires the numerical solution to effectively model non-resolved small scale dynamics. In this work, we propose a general deep-reinforcement-learning framework for devising an agent to interact with high-resolution scheme in order to balance dissipation and dispersion such that physically consistent modeling of non-resolved scales is achieved. A densely distributed reward function without involving labeled data is defined. The agent is trained on low-resolution uniform grids that capture the dominant flow structures. We demonstrate that it can be applied directly to high-resolution simulations without the need for retraining or fine-tuning, thereby, demonstrating significantly improved modeling performance compared to empirically designed high-resolution schemes. The proposed methodology opens a new path for self-adaptive numerical solutions whose truncation errors act as physically consistent model for unresolved scales of widely differing flow configurations.