Unified Equation Research Articles

Web crippling design of lean duplex stainless steel tubular members under interior loading conditions

Numerical analysis and design of cold-formed lean duplex stainless steel (CFLDSS) tubular members undergoing web crippling are presented in this paper. The tubular members were subjected to the loading conditions of Interior-One-Flange (IOF), Interior-Two-Flange (ITF) and Interior Loading (IL). Finite element (FE) models were developed to simulate the members under these three interior loading conditions. The results obtained from the FE analysis were used to compare with test results in terms of failure modes, strengths and load-deformation curves. After successful verification, the FE models were employed for an extensive parametric study. The key parameters in the parametric study included the ratios of flat web height to thickness, load bearing length to web thickness, load bearing length to flat web height and section inner radius. The parametric study results together with the test results were used to compare with the nominal strengths predicted by using the current specifications (ASCE, AS/NZS, NAS and EC3), and the design equations in the literature. New sets of coefficients are proposed for the unified design equation in NAS and the direct strength method (DSM) for the web crippling design of CFLDSS tubular members. Overall, the modified design rules were able to provide more accurate predictions compared with the design rules in current specifications and literature. The results showed that the proposed design methods are suitable for the design of web crippling of CFLDSS tubular members under the IOF, ITF and IL conditions.

A Complement to Decline Curve Analysis

Summary Decline curve analysis (DCA) has been the mainstay in unconventional reservoir evaluation. Because of the extremely low matrix permeability, each well is evaluated economically for ultimate recovery as if it were its own reservoir. Classification and normalization of well potential is difficult because of ever-changing stimulation total contact area and a hyperbolic curve fit parameter that is disconnected from any traditional reservoir characterization descriptor. A new discrete fracture model approach allows direct modeling of inflow performance in terms of fracture geometry, drainage volume shape, and matrix permeability. Running such a model with variable geometrical input to match the data in lieu of standard regression techniques allows extraction of a meaningful parameter set for reservoir characterization, an expected outcome from all conventional well testing. Because the entirety of unconventional well operation is in transient mode, the discrete fractured well solution to the diffusivity equation is used to model temporal well performance. The analytical solution to the diffusivity equation for a line source or a 2D fracture operating under constrained bottomhole pressure consists of a sum of terms, each with exponential damping with time. Each of these terms has a relationship with the constant rate, semisteady-state solution for inflow, although the well is not operated with constant rate, nor will this flow regime ever be realized. The new model is compared with known literature models, and sensitivity analyses are presented for variable geometry to illustrate the depiction of different time regimes naturally falling out of the unified diffusivity equation solution for discrete fractures. We demonstrate that apparent hyperbolic character transitioning to exponential decline can be modeled directly with this new methodology without the need to define any crossover point. The mathematical solution to the physical problem captures the rate transient functionality and any and all transitions. Each exponential term in the model is related to the various possible interferences that may develop, each occurring at a different time, thus yielding geometrical information about the drainage pattern or development of fracture interference within the context of ultralow matrix permeability. Previous results analyzed by traditional DCA can be reinterpreted with this model to yield an alternate set of descriptors. The approach can be used to characterize the efficacy of evolving stimulation practices in terms of geometry within the same field and thus contribute to the current type curve analyses subject to binning. It enables the possibility of intermixing of vertical and horizontal well performance information as simply gathering systems of different geometry operating in the same reservoir. The new method will assist in reservoir characterization and evaluation of evolving stimulation technologies in the same field and allow classification of new type curves.

Influence of freeze–thaw cycling on the soil mechanical properties of open-pit mine dump under different moisture contents

Freeze–thaw circulation under different moisture contents is the main influencing factor of the soil strength characteristics at a dumping site. The fine-grained sand materials of an internal dumping site in the Yuanbaoshan open-pit mine of China were selected as the research object; the changes of soil strength and deformation characteristics of 5 types of freeze–thaw (F–T) cycles were studied under 8 types of moisture contents. The stress–strain curve of soil sample shows strain hardening after different F–T cycles. The shear strength of the soil material decreases unevenly with increasing number of F–T cycles, and the greatest decrease in the shear strength occurs after the first F–T cycle. Under the condition of the same F–T cycles, the cohesion and internal friction angle (shear strength parameters) of the soil material decrease nonlinearly with increasing moisture content and decay in the form of a power function. For the same moisture content, the effect of F–T cycling on the internal friction angle of the soil is small, but the cohesion of the soil decreases as the number of F–T cycles increases, eventually stabilising. A quadratic polynomial equation can accurately describe the quantitative relationship between the cohesion and number of F–T cycles, at the same time, the unified regression equations of cohesion, moisture content and F–T cycle are established. The research results provide an important idea for the design of dumps and slope stability analysis, especially for the first year after dumping.

Static response of functionally graded piezoelectric-piezomagnetic hollow cylinder/spherical shells with axial/spherical symmetry

The magneto-electro-elastic coupling static problem for a functionally graded piezoelectric-piezomagnetic (FGPEPM) cylinder/spherical shell is studied for various axial/spherical symmetric loads. On the basis of unified basic equations with geometric parameters and the material assumption of exponential inhomogeneous properties, the analytical solutions for the physical quantities of displacement, stress, electric potential, and magnetic potential of the FGPEPM hollow cylinder/spherical shell are obtained. In the numerical discussions, the static response of the FGPEPM cylinder/spherical shell is numerically solved under mechanical load on the inner surface or given an electric/magnetic potential difference between the inner and outer surfaces when the material on the inner surface is assumed to be BaTiO3-CoFeO4. The distribution of radial and circumferential stress and the electric and magnetic potentials under different functionally graded (FG) parameters are presented. The influence of FG parameters on the positive (converse) piezoelectric, positive (converse) piezomagnetic, and positive (converse) magnetoelectric potentials is discussed in detail.

Microstructure evolution and a unified constitutive model for a Ti-55511 alloy deformed in β region

The microstructure evolution of a Ti-55511 alloy deformed at high temperatures (from 1163 K to 1253 K) and wide strain rate range (from 10 s−1 to 0.001 s−1) is studied by isothermal compression tests. Based on the sensitivity of dislocation density to deformation conditions, a unified constitutive equation is established to describe the evolution of flow stress, grain size and dynamic recrystallization (DRX) fraction. The results show that the initial grain boundaries are serrated, and the sub-grains and DRX grains are formed with the further deformation. Furthermore, the discontinuous and geometric DRX mechanisms are dominant recrystallization mechanism. Increasing the deformation temperature can increase the DRX fraction and sub-grain size. However, the abnormal growth of β grains occurs at 1253 K. The DRX fraction decreases with the increased strain rate. Meanwhile, the chain-like small DRX grains and the flow localization occur at high strain rates. Also, the established constitutive model is verified by the experimental results, and the correlation coefficient is 0.9929, indicating the excellent prediction ability of the established constitutive model.

Fractional stress-dilatancy equation based on critical state lines with arbitrary form

The original state-dependent fractional stress-dilatancy (FSD) equation for soils is developed based on the critical state lines (CSLs) with linear form. However, experimental evidences showed that the CSLs of soil in the p ′ –q and e–p ′ planes could be both nonlinear as well due to significant material degradation. This note aims to propose a unified FSD equation for soils with arbitrary types of CSLs. Detailed derivations are provided. To validate the proposed FSD equation, a series of triaxial test results of ballast and rockfill are simulated.

Aeroacoustic noise calculations of non-compact bodies with permeable boundaries

A hybrid computational aeroacoustic method with permeable boundary is developed to evaluate non-compact noise induced by low Mach number flow over arbitrarily shaped bodies. Based on Lighthill’s equation and the boundary element method, the unified integral equations are established in which the integral boundary surrounding the objects can be selected arbitrarily. Validation studies are developed for noise induced by two-dimensional NACA0012 airfoil and three-dimensional circular cylinder. For NACA0012 airfoil, the directivity patterns of calculated noise with different permeable boundaries agree well with Howe’s analytical solution for trailing edge model. The acoustic noise generated by circular cylinder has a good agreement with Revell’s experimental data and FW-H equation. It demonstrates that the noise predicted by different permeable boundary is as accurate as that calculated by the body surface.

Closed-Form Solutions for the Probability Distribution of Time-Variant Maximal Value Processes for Some Classes of Markov Processes

The time-variant maximal value process (MVP) of a Markov process has significant applications in various science and engineering fields. In the present paper, the closed-form solutions for the probability distribution of the time-variant MVP for some classes of Markov process are studied. For general continuous Markov processes, a unified Volterra integral equation governing the evolution of the cumulative distribution functions (CDFs) of the time-variant MVP of a Markov process is established for the first time. Closed-form or numerical solutions for MVP of some special continuous Markov processes are derived according to this equation. For the compound Poisson process, which is a discontinuous Markov process, the closed-form solution of concentrated probability of the time-variant MVP at zero point is given analytically. Finally, several examples are illustrated as case studies of these theoretical results, demonstrating the effectiveness of the results. Though the analytical results are now only applicable to one-dimensional Markov process, it provides at least some benchmark results for the checking of future possible analytical or numerical methods for the probability density function (PDF) of MVP of more general and high-dimensional Markov process. Further, it provides insights that might stimulate more sophisticated results in the future.

Solitons in magneto-optics waveguides for the nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index using the unified auxiliary equation method

In this paper, we introduce the coupled system of magneto-optics waveguides for the nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index. The unified auxiliary equation method is used to construct optical solitons and other solutions to this system. The Jacobi elliptic function solutions have been located. In particular, bright, dark, singular solitons are obtained. In addition, we have combo singular solitons and combination of dark and singular solitons. Other solutions are also given.

Unified comprehension of the kinetics of isothermal ceramic processes under field-free and resonant wave-field conditions

Abstract This paper proposes a unified comprehension of the isothermal ceramic process kinetics stemming from mesoscopic irreversible thermodynamics. Accordingly, a unified process kinetic equation (UPKE) is derived, which predicts that the global isothermal process rate of any ceramic process is, in general, nonlinearly related both to its activation energy and its affinity. Nevertheless, for a low-affinity ceramic process conducted either in a field-free or resonant wave-field condition, its global isothermal rate, according to the proposed UPKE, is approximately linearly related to its affinity in the spirit of Fick’s diffusion law. Therefore, the rate enhancement of a low-affinity process occurring in any resonant wave-field may be caused either by a reduction in activation energy, as in microwave-enhanced sintering, or by activation energy reduction along with an affinity augmentation, as in microwave-assisted glass-crystallization. Conversely, for a high-affinity ceramic process, e.g., a chemical reaction, the ‘degenerate’ UPKE predicts that its kinetics is exclusively dictated by the activation energy in the spirit of Arrhenius’s rate law. Hence, isothermal rate enhancements of chemical reactions in ceramic processing under resonant wave-field conditions are believed to predominantly result from a field-induced reduction in activation energy.

R-mode Stability of GW190814's Secondary Component as a Supermassive and Superfast Pulsar

Abstract The nature of GW190814's secondary component m 2 of mass 2.50–2.67 M ⊙ in the mass gap between the currently known maximum mass of neutron stars and the minimum mass of black holes is currently under hot debate. Among the many possibilities proposed in the literature, m 2 was suggested to be a superfast pulsar, while its r-mode stability against runaway gravitational radiation through the Chandrasekhar–Friedman–Schutz mechanism is still unknown. Previously, Fortin et al. constructed a sample of 33 unified equations of state using the same nuclear interactions from the crust to the core consistently; from that sample we use those equations that fulfill all currently known astrophysical and nuclear physics constraints to compare the minimum frequency required for m 2 to rotationally sustain a mass greater than 2.50 M ⊙ with the critical frequency above which the r-mode instability occurs. We use two extreme damping models assuming that the crust is either perfectly rigid or elastic. Using the stability of 19 observed low-mass X-ray binaries as an indication that the rigid crust damping of the r-mode dominates within the models studied, we find that m 2 is r-mode-stable while rotating with a frequency higher than 870.2 Hz (0.744 times its Kepler frequency of 1169.6 Hz) as long as its temperature is lower than about 3.9 × 107 K, further supporting the proposal that GW190814's secondary component is a supermassive and superfast pulsar.

Experimental study on rectangular cut-throated flume: Effects of flume walls slopes and channel longitudinal slope

This research conducted to study the flow through a rectangular cut-throated flume (RCTF). The flume is simply formed by placing two vertical triangular prisms (two vertical folded plates) on either side of a rectangular open channel. Both channel and flume cross-sections are rectangular. The investigated flume is inexpensive, easy to install and does not require high maintenance. A wide experimental investigation, carried out under free outflow conditions and under upstream subcritical flow regime to investigate the effects of the channel longitudinal slope, the flume throat width, and slopes of upstream and downstream flume walls on the stage-discharge relationship. The stage-discharge relationships were deduced by applying the dimensional analysis and were calibrated using the data of this study. The proposed stage-discharge equation for horizontal channel has an average absolute relative error of 2.97% with the relative errors restricted in the range of ±10%, and 80% of the data points are in the error range of ±5%. The proposed stage-discharge equation for sloping channel has an average absolute relative error of 3.97% with the relative errors restricted in the range of ±10%, and 66% of the data points are in the error range of ±5%. The measurements indicate that slopes of upstream and downstream walls affect the stage-discharge relationship of the CTFs only in sloping channels and flow discharge is not influenced by the flume walls slopes in a horizontal channel. The proposed unified stage-discharge equation for both horizontal and sloping channels has an average absolute relative error of 3.38% with the relative errors restricted in the range of ±10%, and 74% of the data points are in the error range of ±5%. The proposed stage-discharge model demonstrates favorable accurate and convenient estimation of discharge for flows through the CTFs.

Entrainment effects in neutron-proton mixtures within the nuclear energy-density functional theory. II. Finite temperatures and arbitrary currents

Mutual entrainment effects in hot neutron-proton superfluid mixtures are studied in the framework of the self-consistent nuclear energy-density functional theory. The local mass currents in homogeneous or inhomogeneous nuclear systems, which we derive from the time-dependent Hartree-Fock-Bogoliubov equations at finite temperatures, are shown to have the same formal expression as the ones we found earlier in the absence of pairing at zero temperature. Analytical expressions for the entrainment matrix are obtained for application to superfluid neutron-star cores. Results are compared to those obtained earlier using Landau's theory. Our formulas, valid for arbitrary temperatures and currents, are applicable to various types of functionals including the Brussels-Montreal series for which unified equations of state have been already calculated, thus laying the ground for a fully consistent microscopic description of superfluid neutron stars.

Role of dense matter in tidal deformations of inspiralling neutron stars and in gravitational waveforms with unified equations of state

The role of dense-matter properties in the tidal deformability of a cold nonaccreted neutron star is further investigated. Using the set of Brussels-Montreal unified equations of state, we have computed the gravitoelectric Love numbers ${k}_{\ensuremath{\ell}}$ and the gravitomagnetic Love numbers ${j}_{\ensuremath{\ell}}$ up to $\ensuremath{\ell}=5$. Their relative importance and their sensitivity to the symmetry energy and the neutron-matter stiffness are numerically assessed. Their impact on the phase of the gravitational-wave signal emitted by binary neutron star inspirals is also discussed.

Loading rates dependency of strength anisotropy in coal: Based on the three‐dimensional reconstruction modeling technology

AbstractWe explored the dependency of strength anisotropy on loading rate in coal both experimentally and numerically. An improved numerical modeling method was developed for this investigation to reduce the random error caused by the mechanical differences of coal specimens. After that, specimens with different anisotropy angles (the angle between the coring direction and bedding plane orientation) were processed (0°, 15°, 30°, 45°, 60°, and 90°). These specimens were then scanned by the X‐ray Computed Tomography (CT) and tested by unconfined loading frame. Uniaxial compressive simulations were performed on 15 numerical models with different anisotropy angles at various loading rates (1.0 × 10−6, 5.0 × 10−6, 10.0 × 10−6, and 20.0 × 10−6 mm/step). The results indicate that the uniaxial compressive strength (UCS) of coal generally first decreases and then increases as the anisotropy angle increases from 0° to 90° for all loading rates. It is also found that the UCS increases significantly with the increasing loading rate at anisotropic angles of 30° and 45°, while it is less obvious at anisotropic angles of 0° and 90°. This results in a reduced USC anisotropy at high loading rates. Meanwhile, a negative exponential equation is obtained to describe the variation of UCS with the loading rate at different anisotropic angles. And a unified equation is then developed and verified to define the UCS as a function of the loading rate and anisotropic angle.

A novel one-domain approach for modeling flow in a fluid-porous system including inertia and slip effects

A new one-domain approach is developed in this work yielding an operational average description of one-phase flow in the classical Beavers and Joseph configuration including a porous medium topped by a fluid channel. The model is derived by considering three distinct regions: the homogeneous part of the porous domain, the inter-region, and the free fluid region. The development is carried out including inertial flow and slip effects at the solid–fluid interfaces. Applying an averaging procedure to the pore-scale equations, a unified macroscopic momentum equation, applicable everywhere in the system and having a Darcy form, is derived. The position-dependent apparent permeability tensor in this model is predicted from the solution of two coupled closure problems in the inter-region and in the homogeneous part of the porous medium. The performance of the model is assessed through in silico validations in different flow situations showing excellent agreement between the average flow fields obtained from direct numerical simulations of the pore-scale equations in the entire system and the prediction of the one-domain approach. Furthermore, validation with experimental data is also presented for creeping flow under no-slip conditions. In addition to the fact that the model is general from the point of view of the flow situations it encompasses, it is also simple and novel, hence providing a practical and interesting alternative to models proposed so far using one- or two-domain approaches.

Charge Balance Control for DC/DC Converter Systems: From Single-Input Systems to Multiple-Input Systems

DC–DC converters with high dynamic performance are attracting more and more attentions in industry and academia. The charge balance control (CBC) method enables the single-input dc–dc (SIDD) converter system to achieve optimal dynamic performance. In this article, the CBC method for the multiport converter is proposed, and the analogy and the innovative transplantation approach of the CBC from single-input systems to multi-input systems are developed. First, general steps and unified equations of the CBC for SIDD converter are summarized. Second, through analogy analysis, the CBC method is transplanted to a full-bridge three-port converter (FB-TPC) system to improve the dynamic performance under load step change. Third, through innovative transplantation, a CBC strategy based on magnetizing current three-stage regulation is proposed, achieving optimal dynamic performance for the FB-TPC system under power distribution step change. Experimental results on an FB-TPC verify the feasibility and effectiveness of the CBC methods for multiport converter and the transplantation method.

Impact of dynamical dark energy on the neutron star equilibrium

We study the density distribution of the minimally-coupled scalar field dark energy inside a neutron star. The dark energy is considered in the hydrodynamical representation as a perfect fluid with three parameters (background density, equation of state, and effective sound speed). The neutron star matter is modeled with three unified equations of state, developed by the Brussels-Montreal group. With the calculated density distribution of the dark energy inside a neutron star (and its dependence on the dark energy parameters) we investigate how its presence impacts the macroscopic characteristics and the value of the mass limit for neutron stars. From this impact we derive the possible constraints on the effective speed of sound of dark energy with the help of maximal known masses of observed neutron stars. In this approach, we have found, that the squared effective speed of sound can not be smaller than ∼ 10−2 in units of squared speed of light.

Web crippling of cold-formed carbon steel, stainless steel, and aluminium channels: Investigation and design

Cold-Formed (CF) structural members have recently drawn significant attention in light gauge steel construction. The employment of the different materials, for example CF carbon steel, stainless steel and aluminium, are becoming more common. These structural members are often subjected to concentrated loading conditions, which ultimately leads to failure through web crippling. A plethora of experimental and numerical studies have investigated the web crippling strength and behaviour of CF carbon steel lipped channel sections. However, only limited studies are available for CF stainless steel and aluminium members.This paper presents the investigation of the web crippling strength of CF lipped channel beams under End Two Flange (ETF) loadings and aims to propose a unified equation considering strength factor. Finite Element (FE) models of CF carbon steel, aluminium, and stainless steel lipped channel beams were developed and validated against the available web crippling ETF load case experimental data. Subsequently, a detailed parametric study was performed based on the validated FE models, to establish a wide-ranging data set. New ETF load case web crippling unified design guidelines were proposed for the CF lipped sections made of carbon steel, stainless steel, and aluminium.

Patterns and networks of language control in bilingual language production

Many studies have examined the cognitive and neural mechanisms of bilingual language control, but few of them have captured the pattern information of brain activation. However, language control is a functional combination of both cognitive control and language production which demonstrates distinct patterns of neural representations under different language contexts. The first aim of the present study was to explore the brain activation patterns of language control using multivoxel pattern analysis (MVPA). During the experiment, Chinese-English bilinguals were instructed to name pictures in either Chinese or English according to a visually presented cue while being scanned with functional magnetic resonance imaging (fMRI). We found that patterns of neural activity in frontal brain regions including the left dorsolateral prefrontal cortex, left inferior frontal gyrus, left supplementary motor area, anterior cingulate cortex, bilateral precentral gyri, and the left cerebellum reliably discriminated between switch and non-switch conditions. We then modeled causal interactions between these regions by applying effective connectivity analyses based on an extended unified structure equation model (euSEM). The results showed that frontal and fronto-cerebellar connectivity were key components of the language control network. These findings further reveal the engagement of the cognitive control network in bilingual language production.