Explicit Formulation Research Articles

Step-drawdown tests: linear and nonlinear head loss components

Coefficients B and C of the Jacob (1947) equation, usually derived from step-drawdown tests, are commonly attributed to “aquifer losses” and “well losses”, respectively. This paper analyzes and separates the linear laminar, nonlinear laminar and turbulent losses occurring during flow from an aquifer to a screened well. From this, one can derive a detailed physical meaning for both coefficients. The coefficient B does not contain only aquifer losses but also linear losses from the gravel pack and wellbore skin, if present. Coefficient C contains nonlinear laminar losses from the gravel pack and turbulent losses caused by screen inflow and vertical flow through the screen and casing. In some cases, the turbulent losses are small enough to be omitted. For transient flow at larger times, the changes in linear laminar losses within the aquifer become important. A new, explicit formulation of the Jacob equation was compared to long-duration field step-drawdown tests, three in confined unconsolidated formations and one in a fractured rock aquifer. Jacob C.E. (1947) Drawdown test to determine effective radius of artesian wells. Trans. Am. Soc. Civil Eng. 112:1047–1070.

Heat Transfer Analysis of an Electric Motor Cooled by a Large Number of Oil Sprays Using Computational Fluid Dynamics

<div class="section abstract"><div class="htmlview paragraph">This paper reports on an analytical study of the heat transfer and fluid flow in an electric vehicle e-Motor cooled by twenty five sprays/jets of oil. A three-dimensional, quasi-steady state, multi-phase, computational fluid dynamics (CFD) and conjugate heat transfer (CHT) model was created using a commercial CFD software. The transport equations of mass, momentum, energy and volume fraction were solved together with models for turbulence and wall treatment. An explicit formulation of the volume of fluid (VOF) technique was used to simulate the sprays, a time-implicit formulation was used for the flow-field and three dimensional conduction heat transfer with non-isotropic thermal conductivities was used to simulate the heat transfer in the windings. An important challenge was to formulate an efficient solution algorithm that can rigorously comprehend twenty five sprays in order to accurately predict the temperature distributions in the windings, without thrifting physics, and within reasonable total analysis turn-around times. The latter includes both model set-up times as well as run times. User functions were coded in order to implement the efficient solution methodology. The outcome of this effort was a novel solution technique which due to its economical analysis times of the order of a week or so, can play a key role in virtually optimizing the e-Motor design, reduce dependence on costly and time consuming tests and shorten product development times. The predicted temperatures of the windings show good agreement with thermocouple measurements.</div></div>

Multi-objective optimization of lateral stability strength of transversely loaded laminated composite beams with varying I-section

In this research, the lateral buckling analysis and layup optimization of the laminated composite of web and flanges tapered thin-walled I-beams based on maximizing lateral-torsional stability strength and minimizing mass/cost of the structure are investigated. The classical lamination theory and Vlasov’s model for thin-walled cross-section are adopted to establish the total potential energy for thin-walled symmetric balanced laminated beams with varying I-section. By implementing the Ritz method, an explicit formulation for the lateral-torsional buckling load of a double-tapered beam subjected to transverse loading is then derived in terms of the load height parameter and stiffness quantities. Subsequently, the optimal arrangements of layer sequences are obtained using the non-dominated sorting genetic algorithm (NSGA-II) and properly defined objective function. The critical factors of fitness function as lateral buckling strength and the mass of the structure with critical limitations as ply angle, number of layers for the web and flanges, and the thickness of all section walls are considered in this study. Finally, the optimal layer arrangement for the web and flanges are separately determined and discussed. The results show that the presented optimization procedure and layups patterns lead to increasing the lateral-torsional buckling capacity about 52% compared to the conventional angle-ply and unidirectional layups for the web and flanges, respectively.

Success Is Not the Entire Story for a Scientific Theory: The Case of the Phonological Deficit Theory of Dyslexia

In a recent paper, Share discussed four different “Common Misconceptions about the Phonological Deficit Theory of Dyslexia” and described this theory as “a model of true scientific progress” and a clear “success story”. In this note, I argue that at least part of the success of this theory is due to the lack of explicit predictions which make it very difficult (if possible) to test its predictions, and, possibly, falsify the theory. Some areas of pertinent research, including categorical phoneme perception, picture naming, and phonological awareness are summarized. Furthermore, two lines of research in which groups of researchers have attempted to formulate more explicit predictions are briefly outlined. It is concluded that, although much research has variously referred to the phonological deficit theory of dyslexia, the resulting large body of evidence presents a complex pattern of results which, in the absence of an explicit formulation of the theory, is extremely difficult to frame within a unitary interpretation. Overall, what seems needed is a theoretical formulation that, on the one hand, can account for the complex pattern of available evidence and, on the other hand, provide testable predictions for future research.

Simplified Analytical Solutions for Deep Tunnels Subjected to vertically incident shear wave with arbitrary vibration direction

A circular tunnel in a homogeneous infinite ground subjected to a vertically incident shear wave with an arbitrary vibration direction in the horizontal plane is considered in this study. A simplified analytical solution with explicit formulations for the deformation and stress of the tunnel lining is presented here. The superposition of two solutions under SH and SV waves are derived first. In the analytical solutions, the tunnel lining is taken as a thick-walled cylinder, which enables more precise forecasts and is much closer to practical engineering than the thin shell model adopted in other previous solutions. Moreover, the analytical solutions consider the slippage effect at the ground-lining interface by introducing a spring-type flexibility coefficient into the interaction force-displacement relationship. The results of the analytical solutions are verified by a comparison with the results of the dynamic numerical solutions via a 3-D ground-lining interaction model under earthquakes; the results show good agreement. By using the analytical solutions, the effects of the vibration direction, ground condition, lining thickness and flexibility coefficient on the seismic response of the tunnel are investigated. Additionally, the appropriate range of seismic wavelengths for the analytical solutions is discussed. The proposed solutions can be applied to the seismic analysis and design of tunnel structures.

The Association between the Occurrence of Asthma and Antecedents of Exposure to Environmental Tobacco Smoke in the Previous Year in Children: An Incidence-Density Study.

In previous studies, the strength of the association between childhood asthma and environmental tobacco smoke (ETS) differed depending on the way ETS was assessed and the type of study conducted. We investigated the relationship between asthma occurrence in children and recent exposure to ETS based on an incidence-density study driven by the explicit formulation of a theoretical design. Additionally, we assessed whether the relationship is modified by perinatal ETS exposure and parental inhalation atopy. The event was conceptualized as ‘first doctor’s diagnosis of asthma’. Population time was probed by sampling population moments. Exposure to ETS was conceptualized as recent exposure (1 year prior to diagnosis or at sampling) and perinatal exposure (in utero and/or during the first year of life). Thirty-nine events and 117 population moments were included. There was no indication for effect modification by perinatal exposure to ETS or parental inhalation atopy. After adjustment for confounding, an association was observed between occurrence of a first asthma diagnosis and recent ETS exposure: incidence-density ratio 4.94 (95% confidence interval 1.21, 20.13). Asthma occurrence in children is associated with recent exposure to ETS, and this association seems not to be modified by perinatal ETS exposure or parental inhalation atopy.

Absorption and scattering by perforated facings with periodic narrow slits.

This paper develops a theory for the sound absorption and scattering of perforated slit absorbers. A rigid plane, perforated periodically in one dimension with absorbing slits, scatters incoming sound waves as discrete wave components in different directions. The absorbing slits are assumed to be line-like in the sense that their width is much shorter than the wavelengths. The equation for the sound field is solved in the wavenumber domain. The slits are described with an impedance description, assuming local reaction of the slits (typically a Helmholtz resonator). The solution is found by means of an inverse transform, back to the spatial domain. This results in an explicit formulation of the sound field, including a sum consisting of components that either radiate energy in discrete directions or are surface waves. A similar sum is also included in a term that can be interpreted as radiation impedance. The explicit expressions for the absorption and scattering coefficients are found with the aid of the radiating part of the scattered and reflected field. Numerical results of the absorption and scattering coefficients are presented. The result is verified with finite element method and compared with the result from an alternative general formulation of the problem.

Определение осевой силы при расчете продольных колебаний коленчатого вала поршневых двигателей

When calculating the axial vibrations of the piston engine crankshaft, the finite element method is preferable choice for determining the longitudinal (axial) disturbing force of the cranks. The article considers a practical way of finding it as a reaction of body parts to the loading of the crank by radial force. In contrast to calculations using empirical formulas, the proposed method allows taking into account tangential forces when determining the longitudinal compliance. The article shows the appropriateness of calculating the longitudinal vibrations of a full-size crankshaft of a piston engine by the finite element method in the Explicit formulation due to its informativeness.

Hydroelastic lumps in shallow water

Hydroelastic solitary waves propagating on the surface of a three-dimensional ideal fluid through the deformation of an elastic sheet are studied. The problem is investigated based on a Benney–Luke-type equation derived via an explicit non-local formulation of the classic water wave problem. The normal form analysis is carried out for the newly developed equation, which results in the Benney–Roskes–Davey–Stewartson (BRDS) system governing the coupled evolution of the envelope of a carrier wave and the wave-induced mean flow. Numerical results show three types of free solitary waves in the Benney–Luke-type equation all of which are predicted by the BRDS system: plane solitary wave, lump (i.e., fully localized traveling waves in three dimensions), and transversally periodic solitary wave. They are linked together by a dimension-breaking bifurcation where plane solitary waves and lumps can be viewed as two limiting cases, and transversally periodic solitary waves serve as intermediate states. The stability and interaction of solitary waves are investigated via a numerical time integration of the Benney–Luke-type equation. For a localized load moving on the elastic sheet with a constant speed, it is found that there exists a transcritical regime of forcing speed for which there are no steady solutions. Instead, periodic shedding of lumps can be observed if the forcing moves at speed in this range.

Auxiliary harmonic excitation generalized method for random vibration analysis of linear structures under non-stationary Gaussian excitation

Frequency-domain methods are the most fundamental and effective methods for non-stationary random vibration analysis. However, the existing frequency-domain methods often involve truncation for degree of mode or decomposition of the power spectrum in multi-correlation conditions, which may have impact on the computational accuracy and efficiency of the methods. To avoid the truncation for degree of mode and the decomposition of the power spectrum, an accurate and efficient auxiliary harmonic excitation generalized method is proposed for random vibration analysis of linear structures under non-stationary Gaussian excitation. First, several existing frequency-domain analysis methods are investigated and discussed. Second, the generalized impulse response function, the generalized frequency response function, and the evolutionary generalized frequency response function are proposed. Meanwhile, the physical meaning of the evolutionary frequency response function is re-investigation, in which the response for the evolutionary harmonic excitation and the evolutionary frequency response function proves equivalent. Subsequently, according to the physical meaning, a novel and easy-to-implement algorithm of the response PSD is proposed. The response for the evolutionary auxiliary harmonic excitation can be quickly evaluated based on the time-domain explicit formulation method. Finally, two examples are investigated to verify the accuracy and efficiency of the proposed method.

Full dynamic model of 3-UPU translational parallel manipulator for model-based control schemes

AbstractOptimal mechanical design, model-based control, and robot dynamic calibration mainly rely on the analytical formulation of robot dynamics. In this paper, the kinematics equations of a general 3-UPU translational parallel manipulator (TPM) are derived, and then, by using the principle of the virtual work theorem, the full implicit dynamic model is derived. Furthermore, by making some modifications, the explicit dynamic formulation of the robot is attained, which is the basis of a wide range of advanced model-based controllers. To validate the proposed formulation, a prototype of the 3-UPU TPM is modeled in MSC-ADAMS® software, and the results of the dynamic formulation are validated using this model. The results show the high accuracy of the proposed dynamic formulation presented in this article.

The Graph Structure of the Generalized Discrete Arnold's Cat Map

Chaotic dynamics is an important source for generating pseudorandom binary sequences (PRBS). Much efforts have been devoted to obtaining period distribution of the generalized discrete Arnold&#x0027;s Cat map in various domains using all kinds of theoretical methods, including Hensel&#x0027;s lifting approach. Diagonalizing the transform matrix of the map, this article gives the explicit formulation of any iteration of the generalized Cat map. Then, its real graph (cycle) structure in any binary arithmetic domain is disclosed. The subtle rules on how the cycles (itself and its distribution) change with the arithmetic precision <inline-formula><tex-math notation="LaTeX">$e$</tex-math><alternatives><mml:math><mml:mi>e</mml:mi></mml:math><inline-graphic xlink:href="li-ieq1-3051387.gif"/></alternatives></inline-formula> are elaborately investigated and proved. The regular and beautiful patterns of Cat map demonstrated in a computer adopting fixed-point arithmetics are rigorously proved and experimentally verified. The results can serve as a benchmark for studying the dynamics of the variants of the Cat map in any domain. In addition, the used methodology can be used to evaluate randomness of PRBS generated by iterating any other maps.

Transverse wave dynamics in short tubes with axisymmetric headwall injection

This work describes both traveling and standing vorticoacoustic waves in circular tubes that are driven by axisymmetric headwall injection. In this process, perturbation tools, field decomposition, and boundary-layer theory are jointly used. First, perturbation expansions are initiated to linearize the Navier–Stokes equations. Second, a Helmholtz decomposition of the first-order disturbances is pursued to identify a suitable set of acoustic wave equations. The last step consists of solving for the vortical mode using boundary-layer theory and a viscous expansion of the unsteady rotational set. At the outset, an explicit formulation for arbitrary headwall injection is obtained and confirmed both numerically and through limiting process verifications; the latter take into account special cases involving uniform and bell-shaped injection profiles. The resulting formulation is then described using both laminar and turbulent injection patterns. Using four canonical cases, the characteristics of the evolving vorticoacoustic wave, including its penetration depth, spatial wavelength, and overshoot factor, are systematically explored and discussed. Several fundamental flow features are also unraveled including the radial, tangential, and axial velocities of the time-dependent vortical field. Most rotational flow features are found to depend on the penetration number, the Strouhal number, and the distance from the centerline. The corresponding standing modes are expressed in closed form and shown to be appreciable in view of their amplitudes that twice exceed those associated with strictly traveling waves. Finally, by extending the boundary-layer analysis from the headwall to the sidewall, a uniformly valid wave approximation is achieved, which remains observant of the no-slip requirement everywhere.

The cooling phase, a key factor in the post-fire performance of RC columns

The focus of recent literature is primarily on the heating phase of concrete columns in relation to possible delayed failure, in combination with a linear descending cooling phase. The research is only recently started, and this is mainly based on a parametric temperature-time curve, including a linear cooling regime as the first kind of approximation suitable for design purposes. Gernay (2019) [1] proposed a straightforward linear relationship between the burn-out resistance of a column subjected to a parametric fire and the ISO fire rating time, valid for heavily loaded columns. However, it is known that the linear cooling curve in the case of the parametric fire does not follow Newton's fundamental law of cooling in a transient situation and, and therefore, is non-natural. Exploring the importance of the cooling regime delivers the need to investigate more profoundly other slopes of, or shapes than, linear cooling, which might be closer to reality. Also, the importance of the load level should carefully be investigated. Indeed, in real buildings, not every column is heavily loaded to obtain some uniformity in dimensions. A simple column is chosen and heated on four, three, or two sides to investigate the effects of the cooling regime and the load level. A combination of thermal loads coming from the parametric fire, the more natural cooling BFD curve, a heavily forced, very slow cooling regime was created. For the material model, a proposed strength loss of 10% (EN 1994-1-2, 2005) is verified and compared against a 20% loss observed in several other experiments out of literature. Explicit formulation of creep will be used to account for the time-dependent loss in strength. Research relevance can be found in the assessment of the residual capacity of concrete structures in post-fire circumstances. This capacity can be expressed in terms of load-bearing capacity or post-fire fire rating; both are important to assess the reliability of a structure for further use after it has been subjected to a fire. It is shown that a difference in the cooling regime, load level, number of exposed sides can cause failure and do influence the post-fire bearing capacity.

Towards robust and accurate Reynolds-averaged closures for natural convection via multi-objective CFD-driven machine learning

Robust and accurate Reynolds-averaged stresses and scalar fluxes closure models for natural convection developed by machine learning are presented in this work. In comparison to passive scalar flows, the complexity of turbulence modelling for natural convection problems is increased as the velocity and scalar fields are strongly coupled by the buoyancy force. Therefore, the appropriate Reynolds-averaged closure models for natural convection ought to capture this interaction within the second-moment terms. Previous data-driven turbulence modelling approaches have treated the unclosed terms of the velocity and thermal fields separately, which has lead to inaccurate predictions when handling natural convection problems. In this study, we therefore develop fully coupled buoyancy-extended models by using a novel multi-objective and multi-expression machine-learning framework that is based on CFD-driven training (Zhao et al., J. Comput. Phys., 411, 109413, (2020)). The model candidates obtained from a Gene-Expression Programming approach, and thus available in symbolic form, are evaluated by running RANS solvers for different Rayleigh number cases during the model training process. This novel framework is applied to vertical natural convection, with the emphasis of this paper on the importance of coupling the explicit closure model formulations, the choice of cost functions, and the appropriate input flow features (i.e. a generalised flux Richardson number) for developing accurate models. It is shown that the resulting machine-learnt models improve the predictions of quantities of interests, e.g. mean velocity and temperature profiles, across a wide range of Rayleigh numbers.

A Noniterative Problem-Dependent Formula for Stiff Dynamic Problems

Abstract A novel one-step formula is proposed for solving initial value problems based on a concept of eigenmode. It is characterized by problem dependency since it has problem-dependent coefficients, which are functions of the product of the step size and the initial physical properties to define the problem under analysis. It can simultaneously combine A-stability, explicit formulation, and second-order accuracy. A-stability implies no limitation on step size based on stability consideration. An explicit formulation implies no nonlinear iterations for each step. The second-order accuracy with an appropriate step size can have good accuracy in numerical solutions. Thus, it seems promising for solving stiff dynamic problems. Numerical tests affirm that it can have the same performance as that of the trapezoidal rule for solving linear and nonlinear dynamic problems. It is evident that the most important advantage is of high computational efficiency in contrast to the trapezoidal rule due to no nonlinear iterations of each step.

Gadamer and Aristotle. Problems of a Hermeneutic Appropriation

ABSTRACT When Gadamer elaborates his conception of philosophical hermeneutics as a transcendental inquiry, he appeals to Aristotle’s practical philosophy as a “model”, which can elucidate his own conceptualization of understanding as intrinsically bound to the specific circumstances of every interpretation. The explicit formulation of the analogy between Aristotelian ethics and philosophical hermeneutics provides a framework that clarifies Gadamer’s principal intention; it also reveals some of the crucial tensions inherent in the Aristotelian conception of practical philosophy and its relation to praxis and phronêsis. In the 1970s, however, Gadamer suggests a practical transformation of hermeneutics, claiming for it the role of an “heir of the older tradition of practical philosophy”. Against Gadamer’s late “turn”, construed as a deviation from the initial analogy, I defend Aristotle’s practical philosophy as an exemplary model for philosophical hermeneutics, but I also maintain that the two projects pursue distinct epistemic goals.

Process Optimization under Parameter Uncertainty Conditions in CCU Process

In order to produce methanol using CO2 and H2, several processes about the related catalytic reaction has been suggested and simulated. There may be systematic uncertainties like parameters of reaction kinetics, so a modelling method considering the parametric uncertainty is proposed and can give more informative data compared to the conventional modelling methods. However, the resulting distributional model requires large computational burdens due to the iterative calculations for convergence. To solve the problem, generalized extreme value distribution (GEVD) and neural network (NN) modellings are utilized. The formation parameters of GEVD are fitted by NN and as a result distributional reactor model in an explicit formulation is proposed. Compared to the shallow structured neural network for learning the formulation parameters, the deep neural network shows improved performance especially adjacent to the boundary layers of process inputs. As its explicit and distributional formulation, the proposed model is expected to be utilized for real-time stochastic model based approaches in optimization and control with reduced computational load.

Simultaneous extension of continuous and uniformly continuous functions

The first known continuous extension result was obtained by Lebesgue in 1907. In 1915, Tietze published his famous extension theorem generalising Lebesgue’s result from the plane to general metric spaces. He constructed the extension by an explicit formul

Formula neiterativnog modela zida za neravnotežne tokove graničnog sloja

A novel non-iterative (explicit) formulation of generalized wall functions that applies to equilibrium and non-equilibrium boundary layer flows was proposed. The proposed formulation uses a set of variables that are more useful for computational fluid dynamics codes as they allow for calculating wall shear stress without an iterative procedure. In addition, an explicit form of the formulation was provided that applies to wall models with and without pressure gradients. The new variable transformation casts the generalizedwall function into a new form that simplifies the implementation and evaluation of wall-shear stress in computational codes.