Asymptotic Model Research Articles

Strain model and experimental study of elastic viscoplastic for crack-tip zone of X80 steel pipe

The mechanical state of the process zone at the crack-tip is one of the main factors that affect crack initiation and growth in the long-term safe operation of oil and gas pipelines. Many tests showed that the stress and strain fields in the fracture-tip process zone can be used to define the crack propagation behavior. The goal of this paper is to improve the Hutchinson, Rice, and Rosengren (HRR) model by using cubic asymptotic polynomials to describe the stress-strain field at the crack-tip, as well as to validate the model by a thorough comparison with full-scale burst test results that account for the fracture zone's mechanical properties. The asymptotic polynomial elastic viscoplastic distribution model of stress-strain displacement field at the crack-tip is developed, and the HRR method is modified reasonably. The crack propagation test of the X80 steel pipeline in the burst test site is carried out. Experimentally, the distribution of stress and strain field in the crack-tip process zone of the X80 testing pipeline is obtained, then compared with the theoretical solution. The final results showed consistency, and the elastic viscoplastic model matched well with the running fracture test data for the X80 gas pipeline. Besides, the stress and strain fields distribution in the crack-tip process zone is verified through the full-scale test of the X80 steel pipeline, which provides a theoretical basis for the integrity evaluation of the steel pipeline.

Efficiency gains of a multi-scale integration method applied to a scale-separated model for rapidly rotating dynamos

Numerical geodynamo simulations with parameters close to an Earth-like regime would be of great interest for understanding the dynamics of the Earth's liquid outer core and the associated geomagnetic field. Such simulations are far too computationally demanding owing to the large range in spatiotemporal scales. This paper explores the application of a multi-scale timestepping method to an asymptotic model for the generation of magnetic field in the fluid outer core of the Earth. The method is based on the heterogeneous multiscale modelling (HMM) strategy, which incorporates scale separation and utilises several integrating models for the fast and slow fields. Quantitative comparisons between the multi-scale simulations and direct solution of the asymptotic model in the limit of rapid rotation and low Ekman number are performed. The multi-scale method accurately captures the varying temporal and spatial dynamics of the mean magnetic field at lower computational costs compared to the direct solution of the asymptotic model.

Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties

A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This asymptotic model inherits the dielectric properties of the insulating layer. It involves the electrostatic potential in the device and the deformation of the elastic plate defining the geometry of the device. The electrostatic potential is given by an elliptic equation with mixed boundary conditions in the possibly non-Lipschitz region between the two plates. The deformation of the elastic plate is supposed to be a critical point of an energy functional which, in turn, depends on the electrostatic potential due to the force exerted by the latter on the elastic plate. The energy functional is shown to have a minimizer giving the geometry of the device. Moreover, the corresponding Euler–Lagrange equation is computed and the maximal regularity of the electrostatic potential is established.

Physical and Chemical Properties of Wolf–Rayet Planetary Nebulae

Abstract Wolf–Rayet ([WR]) and weak-emission-line (wels) central stars of planetary nebulae (PNs) have hydrogen-deficient atmospheres, whose origins are not well understood. In the present study, we have conducted plasma diagnostics and abundance analyses of 18 Galactic PNs surrounding [WR] and wels nuclei, using collisionally excited lines (CELs) and optical recombination lines (ORLs) measured with the Wide Field Spectrograph on the Australian National University 2.3 m telescope at the Siding Spring Observatory complemented with optical archival data. Our plasma diagnostics imply that the electron densities and temperatures derived from CELs are correlated with the intrinsic nebular Hβ surface brightness and excitation class, respectively. Self-consistent plasma diagnostics of heavy-element ORLs of N2+ and O2+ suggest that a small fraction of cool (≲7000 K), dense (∼104–105 cm−3) materials may be present in some objects, though with large uncertainties. Our abundance analyses indicate that the abundance discrepancy factors (ADFs ≡ ORLs/CELs) of O2+ are correlated with the dichotomies between forbidden-line and He i temperatures. Our results likely point to the presence of a tiny fraction of cool, oxygen-rich dense clumps within diffuse warm ionized nebulae. Moreover, our elemental abundances derived from CELs are mostly consistent with asymptotic giant branch models in the range of initial masses from 1.5 to 5 M ⊙. Further studies are necessary to understand better the origins of abundance discrepancies in PNs around [WR] and wels stars.

Birds and the Fire Cycle in a Resilient Mediterranean Forest: Is There Any Baseline?

This study investigates the effects of recurrent wildfires on the resilience of a typical Mediterranean ecosystem. It is based on uninterrupted monitoring over 42 years of the avifauna in a cork oak forest that burned three times during this time interval. The monitoring involved two line-transect counts in spring accompanied by the simultaneous and independent estimation of the vegetation cover profile. One of the two transects was initially designed to serve as an unburned control before it also burned during the second fire. Many forest bird species were already present from the first spring postfire due to the rapid regeneration of the canopy. Some open-habitat bird species colonized the burned area during the first 2–4 years after the fire, resulting in an initial phase of high diversity. The postfire bird succession was mainly driven by sedentary species that recolonized the burned area after the first winter, whereas most migratory species present before the fire resettled as early as the first postfire spring, probably because of site tenacity. It was found that the impact of the second fire on avifauna was lower than that of the first or third fire. The return to an avifauna and forest structure successionally equivalent to the prefire control was achieved in about 15 years, which can be considered as the recovery time. Afterwards, both vegetation and avifauna in the burned areas tended to take on more forest characteristics than in the prefire control. These findings suggest that: (i) the recurrence of fire does not necessarily result in the cumulative degradation of the ecosystem at each repetition; (ii) the asymptotic resilience model is not adapted to the case of disturbances in non-mature environments; (iii) the notion of returning to an original undisturbed baseline is illusive in an area that has been under continuous human influence since ancient times.

Vegetation structure and fuel dynamics in fire-prone, Mediterranean-type Banksia woodlands

Increasing extreme wildfire occurrence globally is boosting demand to understand the fuel dynamics and fire risk of fire-prone areas. This is particularly pressing in fire-prone, Mediterranean climate-type vegetation, such as the Banksia woodlands surrounding metropolitan Perth, southwestern Australia. Despite an extensive wildland-urban interface and frequent fire occurrence, fuel accumulation and the spatial variation in fuel risk is not well quantified across the broad extent of this ecosystem. Using a space for time sampling approach to generate a chronosequence of time since fire, we selected sites that spanned across two distinct sandy soil types (Spearwood and Bassendean sands) and a rainfall gradient (550 to 750 mm north–south). We examined 82 sites in Banksia woodlands, southwestern Australia. Of the 82 sites, 44 burnt during the measurement period (2016 to 2021), which provided the opportunity for fuel measurements following fire (resulting in total N = 126). We wanted to answer two key questions: 1) How do measures of fuel load (mass) and arrangement (structure and continuity) vary across space and time, particularly with respect to time since the last fire? 2) How do biophysical drivers, such as soil type and rainfall, influence fuel accumulation and arrangement, and do these covariates improve litter fuel modelling beyond traditional asymptotic models? We found that fine surface fuel loads (litter and small twigs) differed between sand types, accumulating faster and reaching a higher peak on Spearwood sands (7–9 Mg ha−1) compared to Bassendean sands (6–7 Mg ha−1). Shrub layer fuel loads also accumulated faster on Spearwood sands than on Bassendean sands. While shrub layer fuels on Spearwood sands peaked at 14 years and declined thereafter, those on Bassendean sand did not decline over time but have lower overall connectivity. Total fine fuels (fine surface plus fine shrub layer fuels) had no significant decline over the same time period, on either sand type. Total fine fuel loads reached a peak of 9–10 Mg ha−1 between 13- and 20-years following fire, depending on the underlying sand type. Our quantitative fuel accumulation models confirmed the strength of time since fire as a predictor of hazard, but nonetheless included up to 40% unexplained variance. Importantly, while components fluctuated over time, the combined total of fine fuels did not decline with the long absence of fire, suggesting fire risk does not necessarily decrease in long unburned vegetation.

Asymptotic Model of Refractory and Buildup State of the Blast Furnace Hearth

Asymptotic Model of Refractory and Buildup State of the Blast Furnace Hearth

Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations

Abstract The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.

Evaluation of Heat Transfer Coefficient of Two-Phase Flow Boiling with R290 in Horizontal Mini Channel

Various experiments have been conducted on the heat transfer coefficient of two-phase flow boiling in mini channel tubes. In addition to obtaining data on the heat transfer coefficients through experiments, many researchers have also compared their experimental data using existing correlations. This research aims to determine the characteristics of the heat transfer coefficient of refrigerant R290 from the data used by processing and knowing the best heat transfer coefficient correlation in predicting the experimental data so that the results are expected to be a reference for designing a heat exchanger or for further research. The experimental data predicted is the two-phase flow boiling in a horizontal tube 3 mm diameter, with the mass flux of 50-180 kg/m2s, heat flux of 5-20 kW/m2, saturation temperature of 0-11 °C, and vapor quality of 0-1. The correlation used in this research is based on the asymptotic flow model, where the model is a combination of the nucleate and convective flow boiling mechanisms. The results show an effect of mass flux and heat flux on the experimental heat transfer coefficient and the predicted R290 heat transfer coefficient with asymptotic correlations had a good and similar result to the experimental data.

Gravity-driven film flow down a uniformly heated smoothly corrugated rigid substrate

Gravity induced film flow over a rigid smoothly corrugated substrate heated uniformly from below, is explored. This is achieved by reducing the governing equations of motion and energy conservation to a manageable form within the mathematical framework of the well-known long-wave approximation; leading to an asymptotic model of reduced dimensionality. A key feature of the approach and to solving the problem of interest, is proof that the leading approximation of the temperature field inside the film must be nonlinear to accurately resolve the thermodynamics beyond the trivial case of ‘a flat film flowing down a planar uniformly heated incline.’ Superior predictions are obtained compared with earlier work and reinforced via a series of corresponding solutions to the full governing equations using a purpose written finite element analogue, enabling comparisons to be made between free-surface disturbance and temperature predictions, as well as the streamline pattern and temperature contours inside the film. In particular, the free-surface temperature is captured extremely well at moderate Prandtl numbers. The stability characteristics of the problem are examined using Floquet theory, with the interaction between the substrate topography and thermo-capillary instability modes investigated as a set of neutral stability curves. Although there are no relevant experimental data currently available for the heated film problem, recent existing predictions and experimental data concerning the behaviour of corresponding isothermal flow cases are taken as a reference point from which to explore the effect of both heating and cooling.

TOWARDS A CHARACTERIZATION OF THE PROPERTY OF LEBESGUE

There are three main contributions in this work. First, the proof that every stabilized asymptotic-ℓ1 Banach space has the Property of Lebesgue is generalized to the coordinate-free case. Second, the proof that every Banach space with the Property of Lebesgue has a unique ℓ1 spreading model is generalized to cover a particular class of asymptotic models. Third, a characterization of the Property of Lebesgue is derived that applies to those Banach spaces with bases that admit in a strong sense favorable block bases. These results are significant because they demonstrate not only the efficacy of characterizing the Property of Lebesgue in terms of a connection between the local and the global asymptotic structures of certain Banach spaces, but also the possibility of finding a more general characterization in similar terms.

Cereal straw incorporation and ryegrass cover crops: The path to equilibrium in soil carbon storage is short

AbstractReduced use of fossil energy by removing cereal straw for bioenergy potentially threatens soil organic carbon (SOC) storage. Straw incorporation plays a key role for SOC storage in cereal‐based cropping systems, but the use of cover crops (CCs) may compensate for straw removal. However, assessing the SOC sequestration potential of management changes requires field experiments with long continued treatments and frequent soil sampling. Based on a field experiment initiated in 1981 on a sandy loam soil at Askov Experimental Station (Denmark), we examined the effect of annual additions of spring barley straw (0, 4, 8 and 12 Mg ha−1) and undersown ryegrass CC on SOC storage in the 0‐ to 20‐cm layer. The effect of straw incorporation and CC on SOC was additive. At steady‐state conditions, the SOC stock based on equivalent soil mass (SOC stockFM) increased 3.9, 6.7 and 9.3 Mg C ha−1 after annual incorporation of 4, 8 and 12 Mg straw ha−1, respectively. The ryegrass CC increased SOC stockFM by 3.3 Mg C ha−1 and thus almost compensated for removal of 4 Mg straw ha−1. An asymptotic regression model best described the temporal changes in SOC and showed that the effect of straw incorporation and ryegrass CC on SOC sequestration peaks after 10–15 years when a new equilibrium between input and output of C is reached. Clearly, reliable assessments of SOC sequestration potentials following changes in management require field experiments with frequent soil sampling until reaching steady‐state conditions.Highlights SOC sequestration potentials of straw incorporation and CCs were assessed. The crucial issue of sequestration duration of experimental treatments is often neglected. The effect of straw and CC peaked after 10–15 years when a new equilibrium in SOC was reached. Reliable assessments require frequent soil sampling until reaching steady‐state conditions.

Mathematical modelling of thermoelasticity problems for thin biperiodic cylindrical shells

The objects of consideration are thin linearly thermoelastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss two new averaged mathematical models for the analysis of selected dynamic thermoelasticity problems for the shells under consideration: the non-asymptotictolerance and the consistent asymptotic models. The starting equations are the well-known governing equations of linear Kirchhoff-Love theory of thin elastic cylindrical shells combined with Duhamel–Neumann thermoelastic constitutive relations and coupled with the known linearized Fourier heat conduction equation in which the heat sources are neglected. For the microperiodic shells under consideration, the starting equations mentioned above have highly oscillating, non-continuous and periodic coefficients. The tolerance model is derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. It has constant coefficients depending also on a cell size. Hence, this model makes it possible to study the effect of a microstructure size on the global shell thermoelasticity (the length-scale effect). The consistent asymptotic model is obtained using the consistent asymptotic approach. It has constant coefficients being independent of the period lengths. Moreover, the comparison between the tolerance model for biperiodic shells proposed here and the known tolerance model for cylindrical shells with a periodic structure in the circumferential direction only (uniperiodic shells) is presented.

The surface tension effect revealed via the indentation scaling index

The axisymmetric frictionless indentation problem for an isotropic elastic half-space with the uniform surface tension is considered. The first-order regular and singular asymptotic models are constructed for the limit situations of relatively small (in the membrane limit) or large (in the Hertzian limit) values of the contact radius. By using the method of collocation, a two-parameter analytical approximate solution is developed with coefficients evaluated in triple quadratures. The accuracy of the obtained analytical models is investigated in the case of a paraboloidal indenter by comparison with numerical solutions available in the literature. Based on the asymptotic behavior of the solution in the limit situations, the so-called indentation scaling index is introduced for the analysis of the depth-sensing indentation data. By making use of the novel contact parameter it is possible to extract the surface tension effect independently of determining the reduced elastic modulus of a tested semi-infinite sample. It is shown that by employing an appropriate normalization, the contact problem can be reduced to that parameterized by only one parameter (relative contact radius), which implies that irrespectively of the combination of the material parameters, the force–displacement curve drawn in the normalized variables will be universal.

New insight into the radial forging process by an asymptotic-based axisymmetric analysis

In this paper, an analytical approach based on the asymptotic analysis is proposed to develop an axisymmetric model for the radial forging process of rods. This model is able to predict the deformation inhomogeneity in the radial direction and approves that the profile of the neutral plane is not a planar cross section of the workpiece. For the first time, a relationship has been developed between the die angle, friction coefficient and back-push stress that can be used as a criterion for examining the feasibility of the radial forging process. A breakthrough method has also been proposed that can effectively find the location of the neutral plane far easier and faster than the traditional approach. Finite element simulation of the process has been performed to validate the deformation pattern obtained by the asymptotic model. Models are also verified against available experimental data. The findings of this study are especially useful for online design, analysis and control of the radial forging process.

Impact of viscosity ratio on falling two-layer viscous film flow inside a tube

A two-layer falling film consisting of two viscous fluids with identical density but different viscosity lining the interior of a vertical tube is studied using a long-wave asymptotic model. The impact of the viscosity ratio on the film linear stability and nonlinear dynamics are explored. It is shown that a less viscous outer layer can decrease the total film thickness required for plugs to form; the significance of this study for applications, including human airways, is briefly discussed.

288 Inclusion Effects of Quebracho (Schinopsis Balansaie) Extract and Active Dry Yeast (Saccharomyces Cerevisiae) in Beef Cattle Limit-fed a Grower Ration

Abstract Plant secondary metabolites (PSM) and yeast supplemented in growing cattle have been reported as improving dry matter digestibility (DMD) and reducing enteric methane emissions. This study aimed to evaluate the effect of combined supplementation with condensed tannin (CT; Schinopsis balansae) extract and active dry yeast (ADY; Saccharomyces cerevisiae) on fermentation dynamics, utilizing in vitro gas production (IVGP) technique. A 2 × 2 Latin square design was used to study fermentation patterns of four dietary treatments (CON- no CT and no ADY, ADY alone, CT alone or combined CT + ADY). Animals received daily CT at 1% DM and 10 g of ADY, respectively. On d 0, 7, 14, 21, 28, and 35 rumen inoculum was collected from 23 fistulated steers (284.3 ± 4.1 kg) four hours post-feeding. Samples were incubated under anaerobic conditions at 39oC for 48 h with 200 mg of a grower diet (14.8% CP, 40.6% NDF, 88.5% DM). Gas parameters were analyzed using a mixed linear statistical model. There was a day effect for total gas production (TGP; P < 0.001), non-fiber carbohydrate degradation (P = 0.031) and fractional degradation assuming an asymptote model (P = 0.015). Both asymptote and non-fiber fractional degradation rate estimates had an interaction between Day × TRT (P = 0.001 and 0.0104, respectively). Data were analyzed using polynomial contrasts showed a difference in non-fiber fractional rate of fermentation for CON × CT and CT × ADY (P = 0.052 and 0.054, respectively). This was also true if an asymptote model was assumed (P = 0.0 34 and 0.034, respectively). We concluded that combined supplementation of CT and ADY exhibited similar IVGP trends over time, this may be because animals only received a grower diet at 1.5% shrunk BW. Future studies should investigate the impact of combined supplementation on varying levels of concentrate diets.

Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.

Dynamic asymptotic model of rolling bearings with a single fault in the inner raceway

In the previous models of rolling bearings with a single fault, the displacement deviation caused by the collision of the fault to the rolling element changes instantly. However, the displacement deviation should change gradually. Here, the asymptotic idea is introduced to describe the change of the displacement deviation. The calculation method of the deviation is given. An asymptotic model of rolling bearings with an inner raceway fault is constructed. Then, the simulation of the SKF6205 bearing with a single fault is carried out. The differences between the previous model and the asymptotic model for the responses and the displacement deviation are compared. The effects of the speed and fault size on the dynamic characteristics are analyzed. Finally, the experiments are carried out to corroborate the rationality of the constructed model. The research results can provide theoretical support for the dynamic analysis, fault diagnosis, and reliability analysis of rolling bearings.

Elastic Surface Waves Induced by Internal Sources

The paper is focused on the surface wave field induced by an internal time-harmonic point source embedded in the elastic half space. By using the superposition principle, we first analyze the disturbances caused by the embedded source in an unbounded half space. The problem is then reformulated in terms of the discrepant stresses on the surface of a homogeneous half space. Our analysis is based on the hyperbolic- elliptic asymptotic model of surface elastic waves neglecting the contribution of the bulk waves. Explicit results for the contribution of surface waves are obtained, including the arising frequency- dependent factor.