Simultaneous Solution Research Articles

Practical Realization of Simultaneous Equations Solutions with Elimination Method and Its Effects on Students Performance in Some Selected Schools in Ekiti and Ondo States of Nigeria

Practical Realization of Simultaneous Equations Solutions with Elimination Method and Its Effects on Students Performance in Some Selected Schools in Ekiti and Ondo States of Nigeria

Motion Retargeting for Humanoid Robots Based on Simultaneous Morphing Parameter Identification and Motion Optimization

This paper presents a novel method for retargeting human motions onto a humanoid robot. The method solves the following three simultaneous problems: the geometric parameter identification that morphs the human model to the robot model, motion planning for a robot, and the inverse kinematics of the human motion-capture data. Simultaneous solutions can imitate the original motion more accurately than conventional approaches, which solve the problems sequentially. The proposed method can reconstruct the human motion within the physical constraints imposed by robot dynamics. A reconstruction step enables quantitative analysis of the retargeting results through direct comparison with the original human motion. The method can also provide the precise morphing function as well as subject-specific models, which can handle the different body dimensions of human subjects. This new framework is suitable for applications that require an accurate generation of human-like motions with quantitative evaluation criteria, such as humanoid robots that evaluate assistive devices. Experimental tests of the proposed method were performed with humanoid robot HRP-4.

Simulated annealing for calibrating the Manning’s roughness coefficients for general channel networks on a basin scale

The practical application of simultaneous solutions to the problem of steady state gradually varied flow in a general channel network depends significantly on the reliability of the estimated Manning roughness coefficients based on the calibration of the flow models against observed data. Manning roughness coefficients are needed for all the cross sections of the channel network. Systematic approaches for the calibration of Manning roughness coefficients for such a flow model are very sparse in the literature. This study proposes simulated annealing as an optimizer to the problem of calibrating Manning’s roughness coefficients for a steady state varied flow in a general channel network and presents its application to a case study in Quangnam basin of Vietnam.

The Real Picture of Professional Multidimensionality

<p>Professional multidimensionality is ability of a specialist to correlate the directions, approaches (integrity) and/or to combine performance of several functions (multifunctionality), to conjoin the simultaneous solution of several tasks (multitasking). The empirical research on identification of a real picture of professional multidimensionality of specialists in three fields of activity was performed by research associates group of the Nizhnekamsk office of UNESCO department at A.I. Herzen Russian State Pedagogical University under the leadership of the authors of this article. In their professional activity specialists most often apply such basic multidimensional competences as multifunctionality, multitasking and integrity. Empirical experiment covered 180 representatives of different spheres of professional activity. On the basis of experimental studies we received the following results. Rather high level of professional multidimensionality is shown by research associates – 27,9% of them possess multifunctionality, 23,3% – multitasking, 18,6% – integrity, 13,8% – the combined multidimensional competences. Among elementary school teachers professional multidimensionality is demonstrated thus: 21,1 % of them show multifunctionality, 24,7% – multitasking, 15,3% – integrity, 7.2% – the combined multidimensional competences. Professional multidimensionality among drivers of buses is demonstrated thus: 15,4 % of them possess multifunctionality, 13,5% – multitasking. Drivers of buses show absence of integrity and the combined multidimensional competences.</p>

Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Ideal adsorbed solution theory

Recently an efficient method for the simulation of packed bed adsorbers with implicit adsorption isotherms was presented. It uses a method of lines approach and exploits standard software for the simultaneous solution of the resulting differential algebraic equations (DAEs). Application was demonstrated for stoichiometric ion exchange. In the present paper, the approach is extended to systems described by the adsorbed solution theory. For that purpose, the relation between the differential index of the DAE system and the spectral properties of the underlying adsorption equilibrium is established. In particular, it is shown that real and positive eigenvalues of the Jacobian of the underlying conservation equations will lead to a differential index of one. It is further shown that real and positive eigenvalues of the Jacobian related to the IAST can be guaranteed for binary mixtures with any type of pure component adsorption isotherm or for multicomponent mixtures with certain restricted types of pure component isotherms. The new method is illustrated for different explicit and implicit pure component adsorption isotherms belonging to this class. It is compared with alternative solution approaches using the modified FastIAS method by Do and Myers and semi-analytical solutions from equilibrium theory.

An experimental and theoretical analysis of a foil-air bearing rotor system

Although there is considerable research on the experimental testing of foil-air bearing (FAB) rotor systems, only a small fraction has been correlated with simulations from a full nonlinear model that links the rotor, air film and foil domains, due to modelling complexity and computational burden. An approach for the simultaneous solution of the three domains as a coupled dynamical system, introduced by the first author and adopted by independent researchers, has recently demonstrated its capability to address this problem. This paper uses this approach, with further developments, in an experimental and theoretical study of a FAB-rotor test rig. The test rig is described in detail, including issues with its commissioning. The theoretical analysis uses a recently introduced modal-based bump foil model that accounts for interaction between the bumps and their inertia. The imposition of pressure constraints on the air film is found to delay the predicted onset of instability speed. The results lend experimental validation to a recent theoretically-based claim that the Gümbel condition may not be appropriate for a practical single-pad FAB. The satisfactory prediction of the salient features of the measured nonlinear behavior shows that the air film is indeed highly influential on the response, in contrast to an earlier finding.

Hydroassets portfolio management for intraday electricity trading from a discrete time stochastic optimization perspective

Hydro storage system optimization is becoming one of the most challenging tasks in energy finance. While currently the state-of-the-art of the commercial software in the industry implements mainly linear models, we would like to introduce risk aversion and a generic utility function. At the same time, we aim to develop and implement a computational efficient algorithm, which is not affected by the curse of dimensionality and does not utilize subjective heuristics to prevent it. For the short term power market we propose a simultaneous solution for both dispatch and bidding problems. Following the Blomvall and Lindberg (Eur J Oper Res 143(2):452–461, 2002) interior point model, we set up a stochastic multiperiod optimization procedure by means of a “bushy”recombining tree that provides fast computational results. Inequality constraints are packed into the objective function by the logarithmic barrier approach and the utility function is approximated by its second order Taylor polynomial. The optimal solution for the original problem is obtained as a diagonal sequence where the first diagonal dimension is the parameter controlling the logarithmic penalty and the second one is the parameter for the Newton step in the construction of the approximated solution. Optimal intraday electricity trading and water values for hydroassets as shadow prices are computed. The algorithm is implemented in Mathematica.

Numerical Studies on Thrust Augmentation in High Area Ratio Rocket Nozzles by Secondary Injection

Single stage to orbit propulsion devices are being developed as part of low cost access to space endeavors. Sea level operation of high area ratio rocket nozzle used in rocket engines leads to an overexpanded flow condition resulting in high side loads. Secondary injection of propellants in high area ratio nozzle is an attractive option to overcome the inefficiency of operation of such nozzles in sea level conditions in addition to the augmentation of thrust. A numerical study on thrust augmentation in high area ratio nozzle by secondary injection of propellants is presented here. The turbulent compressible reacting flow in rocket nozzle with auxiliary injection is simulated using conservation equations for chemical species based on finite rate chemistry model and compressible Navier-Stokes equations with AUSM+-up upwind scheme based unstuctured finite volume solver. An optimized eight step, six species reduced H2-O2finite chemistry reaction model is used to model the supersonic combustion. The indigenously developed solver has an efficient rescaling algorithm to alleviate the effect of stiffness in conventional explicit algorithm for simultaneous solution of reacting flow. The code is validated using the wall pressure and hydrogen concentration values reported for the similar high area ratio rocket nozzle. Accurate prediction of nozzle performance is possible with present turbulent reacting flow simulation as it take care of all losses in nozzle flow. Extensive computations have been performed for the performance estimation of high area ratio rocket nozzle for various prospective auxiliary injection options.

A global particular solution meshless approach for the four-sided lid-driven cavity flow problem in the presence of magnetic fields

The global meshless method of approximate Stokes particular solutions (MASPS) is used to solve a two-dimensional incompressible fluid flow in the presence of a uniform magnetic field, i.e. the Navier–Stokes equations with the Lorentz force as a source term in the momentum equations. Magnetohydrodynamic (MHD) problems at low magnetic Reynolds number (Rem) but finite flow Reynolds number (Re) are considered, so the fluid flow is affected by the magnetic field which remains unaltered by the fluid flow. The base functions to approximate the variables of the problem are the particular solutions of an auxiliary Stokes flow field in which a multiquadric (MQ) radial basis function (RBF) is applied as source term. The nonlinear equations resulting from the discretization in a fully implicit finite-difference form are solved by a variable step Newton–Raphson method. The capability of the numerical scheme to simulate MHD problems for different geometries is shown by solving the one-sided lid-driven cavity and the backward facing step flows in the presence of horizontal and vertical magnetic fields, respectively. The existence of simultaneous steady-state solutions in the four-sided lid-driven cavity (4S-LDC) problem is studied with the MASPS for Re between 0 and 1000 and Hartmann numbers (Ha) up to 10. Critical Reynolds numbers (Rec), corresponding to stationary and Hopf bifurcations, are evidenced. Bifurcation diagrams are constructed based on simultaneous solutions and their stability analyses. The increase of Ha modifies the bifurcation diagram and causes the displacement of bifurcation points towards higher Re. Three types of bifurcation, detected by the MASPS in the 4S-LDC flow, are classified based on the stability state analyses. Vertical and oblique magnetic fields are imposed on the flow to study their influence on the bifurcation maps. The effects of the vertical magnetic field on the map are stronger than those of the oblique field.

The formation of medical students` competence in the process of studing the discipline «Physical culture and sports»

The article considers the successful formation of medical students cultural competence for school-classes on physical culture. Formation of competences is a complex pedagogical process in connection with the fact that physical education classes are conducted with a large number of simultaneously engaged in sports halls, which makes it difficult to study the theoretical sections of curricula. Most of today's students has a low level of physical fitness. Students wishing to become doctors, do not understand the value of physical activity role in life of the doctor. It is noted that students' interest in independent studies increases when they study self-assessment of their physical development and compare it with normative indicators, then together with the teacher develop recommendations for correcting lagging indicators of physical development and after a certain training period evaluate the results achieved during training. This allows you to more intelligently approach the choice of physical activity and understanding its positive effects. Formation of competences is possible subject to simultaneous solution of two tasks – increasing the level of physical preparedness of students and their acquisition of specific knowledge about the influence of regular physical loads on the functional state of the organism.

Corrigendum: Geothermobarometry of spinel peridotites from southern British Columbia: implications for the thermal conditions in the upper mantle

Spinel lherzolite xenoliths within alkali basalts exposed at Rayfield River and Big Timothy Mountain, south-central British Columbia, represent samples of the underlying lithospheric mantle. Electron microprobe analysis shows that most xenoliths comprise compositionally homogeneous grains of olivine, orthopyroxene, clinopyroxene, and spinel. We applied the following mineral-pair geothermometers to these rocks: orthopyroxene–clinopyroxene, spinel–orthopyroxene, and spinel–olivine. Temperatures calculated using the Brey and KOhler calibration of two-pyroxene thermometry were constrained in pressure by being required to lie on a model geotherm we develop for this region of B.C. The model geotherm is constrained to produce a temperature at the Moho (33 km) of 825 ± 25 °C to match the lowest temperature peridotite xenoliths recovered in this study. Although the overall effect of pressure on the temperature calculations is negligible (∼2 °C for 0.1 GPa), the simultaneous solution of the model geotherm and the pressure-dependent Brey–KOhler two-pyroxene thermometry removes the need for adopting an arbitrary pressure. We take these temperatures to represent peak mantle lithosphere temperatures. Fourteen Rayfield River xenoliths return two-pyroxene temperatures between 841 and 962 °C corresponding to depths of 34–42 km. Orthopyroxene–spinel and olivine–spinel results are 889 ± 60 and 825 ± 88 °C, respectively. Five Big Timothy xenoliths have two-pyroxene temperatures spanning 840–1058 °C and corresponding to depths of 34–48 km. Mean orthopyroxene–spinel and olivine–spinel temperatures are 844 ± 63 and 896 ± 232 °C, respectively. We argue that the differences in ranges of temperature do not represent closure temperatures imposed during cooling either in the mantle or during transport by the magma. Rather, these differences reflect differences in the original calibrations of the geothermometers or different degrees of equilibration in exchange reactions in dry rocks. Isochemical phase diagrams (pseudosections) constrain the pressure–temperature ( P–T ) field in which spinel is stable. These diagrams suggest that the spinel-bearing peridotites equilibrated at pressures ranging from ∼9.6 to 14 kbar (10 kbar = 1 GPa).

Improved dynamic power flow model with DFIGs participating in frequency regulation

Summary The primary frequency regulation of the DFIGs is newly introduced to dynamic power flow to analyze the post-disturbance power flow and system frequency. Based on the overspeed/pitch angle control, the equivalent inertia of the DFIGs is quantified by their inherent inertia and the adjustable range of the rotor speed, which together with the inertia of the SGs determines the system frequency. With simultaneous solution to the constraints of the DFIGs and power system, the captured power by the wind turbine, the rotor speed, and the slip of the DFIGs are adjusted in dynamic power flow, thus to quantify power loss and active output of the DFIGs, and avoid optimistic judgment to the frequency regulation capability of the DFIGs. With increasing wind power, the wind turbine generators are expected to participate in the frequency regulation to save the burden of synchronous generators (SGs). The primary frequency regulation of doubly fed induction generator (DFIG) using the dynamic power flow is proposed. The equivalent inertia of the DFIG is decided by the inherent inertia and the rotor speed. Its captured power and rotor speed respond to the change of the system frequency. The constraints of the DFIG and power system are solved simultaneously to quantify the active loss of the DFIG. Then, the power flow is solved alternatively with the dynamic equation describing system frequency. The numerical results validate the feasibility of the proposed model and quantify the frequency-support capability of the DFIG. The proposed model helps to balance the utilization of wind power with the stability of system frequency, while reducing the reserve requirement to the SGs.

Dynamic Modeling of the Two-Phase Leakage Process of Natural Gas Liquid Storage Tanks

The leakage process simulation of a Natural Gas Liquid (NGL) storage tank requires the simultaneous solution of the NGL’s pressure, temperature and phase state in the tank and across the leak hole. The methods available in the literature rarely consider the liquid/vapor phase transition of the NGL during such a process. This paper provides a comprehensive pressure-temperature-phase state method to solve this problem. With this method, the phase state of the NGL is predicted by a thermodynamic model based on the volume translated Peng-Robinson equation of state (VTPR EOS). The tank’s pressure and temperature are simulated according to the pressure-volume-temperature and isenthalpic expansion principles of the NGL. The pressure, temperature, leakage mass flow rate across the leak hole are calculated from an improved Homogeneous Non-Equilibrium Diener-Schmidt (HNE-DS) model and the isentropic expansion principle. In particular, the improved HNE-DS model removes the ideal gas assumption used in the original HNE-DS model by using a new compressibility factor developed from the VTPR EOS to replace the original one derived from the Clausius-Clayperon equation. Finally, a robust procedure of simultaneously solving the tank model and the leak hole model is proposed and the method is validated by experimental data. A variety of leakage cases demonstrates that this method is effective in simulating the dynamic leakage process of NGL tanks under critical and subcritical releasing conditions associated with vapor/liquid phase change.

1-D diffusion based solidification model with volumetric expansion and shrinkage effect: A semi-analytical approach

Volumetric expansion and shrinkage due to different densities of solid and liquid phases are common phenomena during solidification process. Simple analytical models addressing effect of volumetric expansion/shrinkage during solidification are rarely found. The few existing 1-D solidification models are valid only for semi-infinite domain with limitations of their application for finite domain size. The focus of the present work is to develop a 1-D semi-analytical solidification model addressing effects of volumetric expansion/shrinkage in a finite domain. The proposed semi-analytical scheme involves finding simultaneous solution of transient 1-D heat diffusion equations at solid and liquid domain coupled at the interface by Stefan condition. The change of the total domain length during solidification due to volumetric expansion/shrinkage is addressed by using mass conservation. For validation of the proposed model, solidification of water in a finite domain is studied without considering volumetric expansion/shrinkage effect and results are compared with those obtained from existing enthalpy updating based numerical model. After validation, case studies pertaining to volumetric expansion and shrinkage are performed considering solidification of water and paraffin respectively and physically consistent results are obtained. The study is relevant for understanding unidirectional crystal growth under the effect of controlled boundary condition.

Circumventing velocity uncertainty in imaging complex structures

In areas with irregular topography, complex near surface, and complex subsurface, there is much uncertainty in rms velocity estimation for prestack time migration, whereas interval velocity estimation for prestack depth migration is despairingly challenging. We often attribute the velocity uncertainty to various factors, including strong to severe lateral velocity variations, heterogeneity, anisotropy, mode conversion, and three-dimensional behavior of complex structures. Nevertheless, it is not easy to identify the cause of and account for the uncertainty as it often is a combination of the various factors. And the analyst struggles with much difficulty when estimating a velocity field, whether it is for prestack time or depth migration. Velocity uncertainty invariably gives rise to erroneously high or low migration velocities, which then causes two problems with prestack migration: (1) we fail to preserve reflector amplitudes, and (2) we also fail to position the reflectors correctly and focus diffractions to their apexes. We may choose to solve both problems simultaneously as we currently attempt to do with prestack migration workflows, or we may choose to solve them one after the other as we used to do in the 1980s and '90s by workflows that included dip-moveout correction. The quality of image gathers associated with prestack migration may not be adequate for velocity updating and verification and thus may or may not warrant the simultaneous solution. In areas with irregular topography, complex near surface, and complex subsurface, it may not. What then? I propose a workflow, applicable to both 2-D and 3-D seismic data, to solve the two problems with prestack time migration one after the other. The workflow is based on synthesis of a zero-offset wavefield to capture and preserve all reflections and diffractions, followed by zero-offset time migration.

The utilization of closed‐loop prediction for dynamic real‐time optimization

Real‐time optimization (RTO) is a layer within the hierarchical process automation architecture in which economically optimal set‐points are computed for the underlying plant control system. RTO calculations are traditionally based on steady‐state models, but an increasingly global and dynamic marketplace has led to the development of dynamic RTO (DRTO) strategies. Typical DRTO approaches optimize process input trajectories based on the open‐loop response dynamics of the process, with controller set‐point trajectories constructed from the resulting output response. This paper describes recent developments that utilize closed‐loop prediction in the DRTO calculations for MPC regulated processes. A rigorous closed‐loop DRTO problem is formulated as a multilevel dynamic optimization problem due to the inclusion of a sequence of MPC quadratic programming subproblems to generate the closed‐loop response dynamics. A simultaneous solution strategy is applied in which the MPC subproblems are replaced by their equivalent Karush‐Kuhn‐Tucker (KKT) optimality conditions, permitting reformulation of the original problem as a single‐level mathematical program with complementarity constraints (MPCC). Closed‐loop approximation techniques are proposed to reduce the dimension of the DRTO problem while maintaining good closed‐loop prediction accuracy. The performance of the proposed approaches is illustrated using case studies. Conclusions are drawn, and further research directions identified.

Multi-time wave functions

In non-relativistic quantum mechanics of N particles in three spatial dimensions, the wave function ψ(q1, …, qN, t) is a function of 3N position coordinates and one time coordinate. It is an obvious idea that in a relativistic setting, such functions should be replaced by ϕ((t1, q1), …, (tN, qN)), a function of N space-time points called a multi-time wave function because it involves N time variables. Its evolution is determined by N Schrödinger equations, one for each time variable; to ensure that simultaneous solutions to these N equations exist, the N Hamiltonians need to satisfy a consistency condition. This condition is automatically satisfied for non-interacting particles, but it is not obvious how to set up consistent multi-time equations with interaction. For example, interaction potentials (such as the Coulomb potential) make the equations inconsistent, except in very special cases. However, there have been recent successes in setting up consistent multi-time equations involving interaction, in two ways: either involving zero-range (δ potential) interaction or involving particle creation and annihilation. The latter equations provide a multi-time formulation of a quantum field theory. The wave function in these equations is a multi-time Fock function, i.e., a family of functions consisting of, for every n = 0, 1, 2, …, an n-particle wave function with n time variables. These wave functions are related to the Tomonaga–Schwinger approach and to quantum field operators, but, as we point out, they have several advantages.

Complex double-mass dynamic model of rotor on thrust foil gas dynamic bearings

The present paper considers simulation of a rotor’s dynamics behaviour on thrust foil gas dynamic bearings based on simultaneous solution of gas dynamics differential equations, equations of theory of elasticity, motion equations and some additional equations. A double-mass dynamic system was considered during the rotor’s motion simulation which allows not only evaluation of rotor’s dynamic behaviour, but also to evaluate the influence of operational and load parameters on the dynamics of the rotor-bearing system.

Simultaneous Mass Determination for Gravitationally Coupled Asteroids

Abstract The conventional least-squares asteroid mass determination algorithm allows us to solve for the mass of a large subject asteroid that is perturbing the trajectory of a smaller test asteroid. However, this algorithm is necessarily a first approximation, ignoring the possibility that the subject asteroid may itself be perturbed by the test asteroid, or that the encounter’s precise geometry may be entangled with encounters involving other asteroids. After reviewing the conventional algorithm, we use it to calculate the masses of 30 main-belt asteroids. Compared to our previous results, we find new mass estimates for eight asteroids (11 Parthenope, 27 Euterpe, 51 Neimausa, 76 Freia, 121 Hermione, 324 Bamberga, 476 Hedwig, and 532 Herculina) and significantly more precise estimates for six others (2 Pallas, 3 Juno, 4 Vesta, 9 Metis, 16 Psyche, and 88 Thisbe). However, we also find that the conventional algorithm yields questionable results in several gravitationally coupled cases. To address such cases, we describe a new algorithm that allows the epoch state vectors of the subject asteroids to be included as solve-for parameters, allowing for the simultaneous solution of the masses and epoch state vectors of multiple subject and test asteroids. We then apply this algorithm to the same 30 main-belt asteroids and conclude that mass determinations resulting from current and future high-precision astrometric sources (such as Gaia) should conduct a thorough search for possible gravitational couplings and account for their effects.

Accelerated Electrochemical Machining Tool Design via Multiphysics Modeling

A significant challenge preventing wider industrial adoption of electrochemical machining (ECM) is the lack of efficient, a priori means for selection of a tool design to achieve a target part shape with high accuracy. Tight coupling among the numerous physical phenomena active in industrial electrochemical processes confounds the simplification approaches available in other contexts. Recent developments in computational hardware and software allow simultaneous solution of the relevant governing equations, potentially enabling practical tool design methods by solution of the “inverse electric field problem.” This paper discusses recent work comparing primary current distribution simulations to indentations fabricated by ECM of steel panels. Good agreement was obtained for a subset of the tests performed. The results highlight the importance of including additional physical phenomena such as flow effects and electrochemical polarization in order to obtain more accurate simulations. In particular, the current efficiency of the metal dissolution reaction likely must be considered.