Growth Rate Equation Research Articles

ESTIMACIÓN DE LA REGIÓN DE CRECIMIENTO ESTÁNDAR DE GUAJOLOTES NATIVOS (Meleagris gallopavo L.) CALCULADA MEDIANTE LA ECUACIÓN DE RICHARDS

<p><strong>Background. </strong>A variety of mathematical models explain animal growth, showing a sigmoid curve. Richards' model includes four parameters, allowing a better fit to experimental data, as evidenced by a high coefficient of determination and a low standard error of estimation. However, it does not always converge and some of its parameters are difficult to interpret biologically. It is useful to model a standard growth zone to estimate, at a given age, the weight of native turkeys within confidence limits, to obtain useful management conclusions.<strong> Objective. </strong>To establish a standard average growth region for male native turkeys on the coast of Oaxaca, for productive purposes, using the Richards equation. <strong>Methodology. </strong>The weights of 23 male native turkeys were recorded weekly from hatching to 54 weeks of age. Non-linear regression to fit the data to Richards' equation was performed using the free software GeoGebra®. The standard growth zone consisted of a lower and upper limit, which were determined by adding and subtracting the standard error of the estimate from Richards' model. The growth rate equation and graph were developed, showing its asymmetry, maximum value and age at which said value is reached.<strong> Results. </strong>Determination coefficient of 0.993, standard error of the estimate of 190.5 g, and maximum growth rate of 322.11 g*week-1 at 18.22 weeks of age were obtained.<strong> Implications. </strong>The use of the standard growth zone, under intensive production conditions, is valuable in the study and evaluation of the growth of male native turkeys<strong>. Conclusions. </strong>The standard growth zone is a very useful concept, allowing for the establishment of weight limits that animals should have at the optimal age, facilitating decision-making to optimize management and feeding practices, as well as maximizing efficiency and performance.</p>

Reactive Crystallization Kinetics Study of Boehmite in Ammonia Solution by Adding Ammonium Aluminum Sulfate

As an important intermediate product in new techniques for extracting alumina from coal fly ash, boehmite is obtained by the reaction between ammonium aluminum sulfate and ammonia. The reactive crystallization kinetics of boehmite is investigated using a continuous steady-state method. The Mydlarz and Jones (MJ3) models are in considerable agreement with the experimental results by a non-linear regression method; furthermore, crystal nucleation and growth rate equations are proposed. The results revealed that the suspension density and agitation rates present considerable influence on nucleation. Additionally, high levels of supersaturation are not conducive for crystal growth, and the supersaturation index for crystal growth was small due to its poor water solubility. Moreover, the maximum d0.5 (average particle size) was 27.968 μm under the agitation condition and the feed rates of 250 r/s and 0.5 g/10 min. Fast crystal growth speed is associated with the crystal structure’s high AlO6-unit and bulk-oxygen content. Our study on crystal nucleation and growth kinetics will be beneficial to the industrial production of boehmite.

Anticipating of ash agglomeration behavior in a fluidized bed by population balance equation

Ash agglomeration as a potential problem in fluidized bed gasifiers, leading to defluidization, was investigated in this study in a lab-scale fluidized bed. The experiments were carried out in batch mode in the temperature range of 600–950 °C and atmospheric pressure. The defluidization temperature was determined from the total pressure drop across the bed. The effect of superficial gas velocity on the defluidization temperature was also investigated. With increasing the gas velocity, the defluidization temperature increases up to about 960 °C, beyond which it remained almost constant. The particle size distribution at the end of the tests (defluidization state) was estimated from the population balance equation. Assuming a first order growth rate of agglomerates, the parameters of the rate equation were determined by fitting the population balance equation to the size of the agglomerates at the moment of defluidization. The results showed that as the gas velocity increases, the frequency factor of the growth rate equation initially decreases up to the fluidization number 3, after which it remains constant.

Stocks and fishery of cod (<i>Gadus macrocephalus, Gadidae</i>) in the northwestern Bering Sea in 1965–2022

For pacific cod in the northwestern Bering Sea, biomass of the summer-fall feeding aggregations in the specified area of their highest density (polygon) is considered as a stock unit. The fish in these aggregations belong to the populations spawn in both local and adjacent areas. The stock values, biological parameters, and annual catches are determined for the period from 1965 to 2022 on the materials collected in research surveys and commercial expeditions, as well as on the data of fishery statistics and cited data. The average length of cod caught by different commercial fishing gears is determined as 42.01 cm for Danish seine, 53.01 cm for bottom trawls, 58.15 cm for midwater trawls, 61.94 cm for longlines. The midwater and bottom trawls used in research surveys are equipped with the rigging for better account of juvenile fish, therefore the average length of cod in their catches is 46.42 and 36.52 cm, respectively. The cod aged from 3 to 12 years are presented in the longline catches, with the modal group of 5 years old, but the age range is wider for bottom trawls, from yearlings to 12–13 years old fish, with a modal group varying from 2 to 5 years old in different years. The parameters of von Bertalanffy equation of linear growth for pacific cod are determined as: L∞ = 111.993 cm, K = 0.159, and t0 = –0.024 and for the equation of weight growth rate: W∞ = 14.006 kg, K = 0.245, and t0 = 1.221. The age of mass maturation is 4.4 years. The instantaneous coefficient of natural mortality, calculated by Tyurin, is age-dependent, with the minimum for 5 years old fish (0.345 year–1), 1.245 year–1 for yearlings, 1.231 year–1 for 11 years old fish, and 1.860 year–1 for 12 years old fish. History of the cod fishery in the northwestern Bering Sea is traced since its start in 1965. The cod fishery was realized with various types of fishing vessels (from small seiners to supertrawlers) and fishing gears, but the bulk of annual catch was landed with longlines (65.9 % in the 2010–2022, whereas only 21.4 % was landed with bottom trawls and 12.7 % with Danish seine). Overfishing happened in 1971, when the annual catch increased to 91,600 t on the background of poor replenishment, after that the catch decreased to 760–1420 t in 1976–1979. Then the stock had recovered and the catch increased from 3890 t in 1980 to 58,480 t in 1986. Next decline to 13,810 t in 2009 was followed by a new growth to the record value of 106.2 . 103 t in 2020, but recently the annual catch decreased again (61.5 . 103 t in 2022). This dynamics corresponded to the stock fluctuations: according to the trawl surveys data, the spawning stock within the polygon ranged between 66.5–282.6 . 103 tons in the 1965–1974, decreased to 24.5 . 103 t in 1977 because of overfishing, gradually recovered to 108.1 . 103 t in 1980, 173.0 . 103 t in 1982, and 561.6 . 103 t in 2000, then declined again to 151.4 . 103 t in 2001 and grew in the last two decades to the maximum values of 1,297.9 . 103 t in 2018. Recently a rapid decline of the stock is observed to 475.0 . 103 t in 2022. The changes of the assessed spawning stock generally precede for two years the CPUE changes due to relatively younger age composition in the catches of research bottom trawl used for the stock calculation, in comparison with the age composition in commercial catches. The stock dynamics within the polygon in the northwestern Bering Sea is driven by variations of the cod feeding migration to this area that correlates with the extension of the coldwater pool at the sea bottom around St. Lawrence Island. From the other hand, the migration depends on the cod abundance on the spawning grounds that could be negatively impacted by the bottom trawl fishery in the spawning season. Since 2002, the fishing pressure was moderate, and fishing mortality did not exceed the fishing exploitation target. However, overfishing is possible in the next 3–4 years, if the fishing mortality goes beyond the target benchmark.

Process optimization and crystallization kinetics of ammonium sulfate from wet ammonia‐based desulfurization

AbstractThere are some problems in the production of ammonium sulfate, a byproduct of the ammonia desulfurization process, such as small crystal size and uneven distribution. The evaporative crystallization kinetics of ammonium sulfate and the factors affecting the crystallization of ammonium sulfate for improving the quality of ammonium sulfate were studied. The results showed that the largest mean diameter of ammonium sulfate was obtained at a stirring speed of 400 r/min, evaporation temperature of 60 °C, and pH of 5.0. The particle size of the ammonium sulfate increased when the crystal seed was introduced. The metastable region of ammonium sulfate was determined by laser method. The crystallization process of ammonium sulfate was studied using population balance equations and intermittent dynamic method, and the empirical equation of nucleation rate and growth rate of ammonium sulfate crystallization was obtained. This experiment can provide a solution for the problems existing in the production of ammonium sulfate in the process of ammonia desulfurization.

Thermodynamic calculations using reverse Monte Carlo: Simultaneously tuning multiple short-range order parameters for 2D lattice adsorption problem.

Lattice simulations are an important class of problems in crystalline solids, surface science, alloys, adsorption, absorption, separation, catalysis, to name a few. We describe a fast computational method for performing lattice thermodynamic calculations that is based on the use of the reverse Monte Carlo (RMC) technique and multiple short-range order (SRO) parameters. The approach is comparable in accuracy to the Metropolis Monte Carlo (MC) method. The equilibrium configuration is determined in 5-10 Newton-Raphson iterations by solving a system of coupled nonlinear algebraic SRO growth rate equations. This makes the RMC-based method computationally more efficient than MC, given that MC typically requires sampling of millions of configurations. The technique is applied to the interacting 2D adsorption problem. Unlike grand canonical MC, RMC is found to be adept at tackling geometric frustration, as it is able to quickly and correctly provide the ordered c(2 × 2) adlayer configuration for Cl adsorbed on a Cu (100) surface.

Thermally Activated Crack Growth and Fracture Toughness Evaluation of Pipeline Steels Using Acoustic Emission

The article presents an approach to assessing the fracture toughness of structural alloys based on thermally activated crack growth and recording acoustic emission signals. The kinetic and structural features of the stable growth of the initiated crack are estimated using a multilevel acoustic emission model based on the time dependence of the logarithm of the cumulative acoustic emission count. The article provides an evaluation of the stable kinetic constants included in the equation of the thermal fluctuation steps of a crack according to literature sources and using the acoustic emission method. It is shown that parameters such as activation energy, activation area before the crack tip, and the rate of non-activation crack growth are stable and show a satisfactory correspondence between the reference literature and real experiments. The approach does not require a set of laboratory experiments to determine the empirical constants of traditional crack growth rate equations, and it also differs in that it takes into account the unique features of the destruction of a particular specimen or technological equipment and allows for a non-destructive assessment of fracture toughness. The values obtained are conservative. The concentration criterion of destruction requires further investigation.

Experimental and probabilistic study of fatigue crack growth behavior of steel Q345qC under different stress ratios

The stress ratio effects and the scatter of the fatigue test results are the key issues in the design of steel fatigue performance. This paper reports an experimental and probabilistic investigation of the fatigue crack growth (FCG) behavior of steel Q345qC. Firstly, the microstructural characteristics and mechanical properties of steel Q345qC were examined via an optical microscope and tensile tests. Next, the FCG behavior of steel Q345qC was investigated under different stress ratios. The fatigue crack growth rate (FCGR) equations incorporating survival probabilities were proposed based on Paris and Walker laws. Finally, the theoretical FCG life under different survival probabilities in the crack stable growth region is calculated based on the integral formulas of Paris and Walker law and compared with the tested FCG life. The experimental results demonstrate that the larger the stress ratio, the shorter the length of stress intensity factor (SIF) amplitude experienced in the stable growth region and the smaller the SIF at the end of this region. Both probabilistic Paris and Walker equations can be used for FCGR calculations when the survival probability is set as 50%. The FCG life is calculated using the integral formula based on the Walker law with a high safety tolerance and a wide application interval of stress ratio when the survival probability is set as 90%.

Theoretical assessment of fatigue life of metal materials at constant cycle stress range

A computational model is proposed for theoretical evaluation of fatigue life of samples made of metallic materials at a constant applied cycle stress range. The total fatigue life is divided into two stages: the stage of crack nucleation, i.e., the number of loading cycles before its initiation (stage 1) and the stage of crack growth (stage 2). Different approaches are used to estimate the duration of each stage. For stage 1, the power law fatigue life equation is obtained from the condition that the accumulated strain energy is equal to the specific cracking energy, and for stage 2, the number of cycles is obtained by integrating the crack growth rate equation, where the effective range of the stress intensity factor (SIF), defined as the difference between the applied "external" range of the SIF and the "internal" range of the SIF, which characterizes the material's resistance to crack growth, is taken as its driving force. The initial data for the calculation, in addition to the loading parameters, are the characteristics of the static strength and microstructure of the initial material. Calculations based on the proposed fatigue life model for steel 0.45%C specimens show good agreement with experimental results.

Analysis Method for Post-Impact Damage Development in Carbon Fiber Reinforced Laminate under Repeated Loading

In the current work, an analysis method for obtaining post-impact damage propagation under cyclic compressive load in flat carbon fiber reinforced plastic (CFRP) panels is presented. The solution for damage growth life is given based on the introduced hypothesis of reference damage mode (RDM). The critical size of damage for obtaining damage growth life was informed by the analysis of crack driving force versus damage size conducted using finite element analysis (FEA). The applicability of the damage tolerance principle for the case of compression–compression cyclic loading of the structural element containing impact damage is discussed and illustrated by the example. The results of using the introduced simplified approach to the calculation of characteristics of damage growth life suggest that the use of the slow-growth approach in composite structures is possible, though the necessity of obtaining the exact parameters of the damage growth rate equation with regard to the chosen crack driving force measure must be addressed.

On the strain energy release rate and fatigue crack growth rate in metallic alloys

The field of fracture mechanics started with Griffith’s energy concept for brittle fracture in 1920. In 1963, Paris et al. used a fracture mechanics’ parameter to introduce an equation for the fatigue crack growth rate in ductile materials and this equation is now commonly known as the ‘Paris law’. However, the Paris law and the semi-empirical models that followed ever since do not fully account for the main intrinsic and extrinsic properties involved with fatigue crack growth in metallic alloys. In contrast, here a dimensionally correct fatigue crack growth rate equation is introduced that is based on the original crack driving force as introduced by Griffith and the presence of plasticity in a metal to withstand crack propagation. In particular it is shown that the fatigue crack growth rate shows a power law relationship with the cyclic strain energy release rate over the maximum stress intensity factor. The new description corrects for the ratio between the minimum and maximum stress in a cycle during constant amplitude loading and for crack growth retardation under variable amplitude loading. The method has been successfully applied to variable amplitude crack growth with spectra that are representative of different fatigue dominated aircraft locations. As such, it allows for accurate predictions of variable amplitude fatigue crack growth life in aerospace structures.

Solution of Population Growth Rate Linear Differential Model via Two Parametric SEE Transformation

The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations

A robust probabilistic fatigue crack growth model based on walker’s crack growth rate equation for metallic materials

The fatigue crack growth data inherits statistical variation despite carefully controlled test procedures. The available probabilistic models rely extensively on fatigue crack growth test data of the coupon material under replicate loading conditions. In view of the often unavailability of such a database, this work proposes a new probabilistic model based on Walker’s crack growth rate equation and considers the variability in both the stress intensity factor range, ΔK and stress ratio, R. The optimum estimates of the model parameters are established using the maximum likelihood estimation (MLE) method. The model is examined using selected sets of measured fatigue crack growth curves of 7075-T6 and 2024-351 aluminum alloys. It demonstrates acceptable predictions for fatigue crack growth data on replicate and variable R-ratio loadings with failure probabilities in the range of 0.10 ≤pF≤ 0.90. The error on the observed fatigue crack growth rate data is normally distributed. The criterion of the minimum number of replicate tests for a valid probabilistic assessment of the fatigue crack growth data is established. Based on the mean squared error (MSE) parameter, the model provides a better representation of the mean fatigue crack growth rate behavior of the material for fatigue loading with variable R-ratios.

The Development of Tubular Photobioreactor for Microalgae Cultivation

In a tubular photobioreactor, microalgae cells obscure one another (Self-shading), leading to the microalgae at the bottom of the tube getting less light. The objective of this research was to design and develop Tubular Photobioreactor with 93.5 liters for microalgae cultivation. The experiments had two steps. The first step was designing the solar receiver by inserting the fin into each tube wall as follows: 12-34, 1-2-3-4, 1234, and 13-24. Then, FLUENT software was used to simulate flow behavior inside the tube by Computational Fluid Dynamics by observing the pressure drop, the amount of energy consumption, and the swirling velocity to select the best fin-type. The best fin-type with the growth rate equation is introduced in the next step to simulate the microalgae's growth and movement using the user-defined function technique. The comparison of a tubular photobioreactor is investigated between fin and without fin by observing biomass production. The results showed that algae's optimum inlet velocity is 0.15 meters per second with the tubes containing fin-type 13-24. When simulating the growth behavior of microalgae, results show that the tubes without fins had lower biomass content than the 13-24 fin-type, which were 0.675 and 0.806 grams per liter, respectively, because the 13-24 fin-type will make well microalgae distribution leading to increase the light distribution too. Tubular photobioreactor fins type 13-24 had more biomass production, up to 19.4 percent.

Microalgae growth rate multivariable mathematical model for biomass production

BackgroundThe use of microalgae has been emerging as a potential technology to reduce greenhouse gases and bioremediate polluted water and produce high-value products as pigments, phytohormones, biofuels, and bioactive compounds. The improvement in biomass production is a priority to make the technology implementation profitable in every application mentioned before. MethodsThe present study was conducted to explore the use of microalgae from genus Chlorella and Tetradesmus for the generation of substances of interest with UV absorption capacity. A mathematical model was developed for both microalgae to characterize the production of microalgae biomass considering the effects of light intensity, temperature, and nutrient consumption. The model was programmed in MATLAB software, where the three parameters were incorporated into a single specific growth rate equation. ResultsIt was found that the optimal environmental conditions for each genus (Chlorella T=36°C, and I<787 μmol/m2s; Tetradesmus T=23°C and I<150 μmol/m2s), as well as the optimal specific growth rate depending on the personalized values of the three parameters. ConclussionThis work could be used in the production of microalgae biomass for the design and development of topical applications to replace commercial options based on compounds that compromise health and have a harmful impact on the environment.

Stress ratio effect on crack growth behavior of dissimilar friction stir welded butt joint between AA6061 and AA7075 alloys

Many engineering components are subjected to random nature of loading during their life period. In this work, the fatigue crack growth in friction stir welded dissimilar AA6061 and AA7075 was investigated under different stress ratio. AA6061 was kept on the advancing side due to having a higher solidus temperature and softer than AA7075 for smooth material flow. The microstructure characterization, tensile and crack growth behavior was studied. It was observed that the joint material exhibited lower strength and ductility as compared to the base material. About 41%, 34%, and 66% reduction in tensile strength, yield strength, and percentage of elongation as compared to AA6061 (base material) were observed. About 27% higher hardness in the HAZ of retreating side than the advancing side was noticed. The crack deflection and tortuosity features were observed in the fatigue fractured specimens. In this paper, a comparative study using different crack growth models has been studied and a simple crack growth rate equation has been proposed considering the crack closure effect.

Measurement and Analysis of Contribution Rate for China Rice Input Factors via a Varying-Coefficient Production Function Model

To explore the internal driving force of the growth of rice yield per unit area in China, a model based on varying-coefficient production function is proposed in this study, which comes from the idea that the constant elasticity parameters in the Cobb-Douglas production function can be extended to functional forms. Applying such model to economic growth analysis, on the one hand, the dynamic contribution rate of each input factor can be measured, and, on the other hand, the contribution rate of the input factor can be decomposed into net factor contribution rate and interaction factor contribution rate, thus expanding the explanatory ability of growth rate equation. Using such model, the output elasticity of capital and labor in China’s rice yield growth are calculated from 1978 to 2020, and the dynamic characteristics of the contribution rate of capital, labor and generalized technological progress are analyzed. Next, the capital contribution rate is decomposed according to the composition of the total capital. The results show that: (1) The capital elasticity and labor elasticity are indeed not constant in different years. In China, from 1978 to 2020 the value of capital elasticity was between 0.3209 to 0.3589, with a mean of 0.3437, and the value of labor elasticity was between −0.1759 to −0.1640, with a mean of −0.1730. (2) Natural disasters do affect capital elasticity and labor elasticity in rice production. (3) When the annual proportion of crop disasters increases, the contribution rate of interaction between capital and natural disaster (KDR) value is negative, whereas the contribution rate of interaction between labor and natural disaster (LDR) value is positive. (4) Compared with 1978, the generalized technological progress contribution rate (GTPR) of the rice yield growth in China from 1979 to 2020 shows a declining trend in fluctuations, whereas the total capital contribution rate (TKR) shows a rising trend in fluctuations and the total labor contribution rate (TLR) is relatively stable in the same period. Since 2000, capital investment has become the main factor for the rice yield growth per unit area in China, of which machinery, chemical fertilizer, seed and pesticide are the four most important input factors.

Three-Dimensional Numerical Simulation of Creep Crack Growth Behavior for 316H Steel Using a Stress-Dependent Model

Based on detailed three-dimensional numerical simulation, creep crack growth behavior of C(T) specimen with different thicknesses of 316H steel was predicted using a stress-dependent creep ductility and strain rate model. Three regions were observed in the relation of creep crack growth rate versus fracture parameter C ∗ . The C(T) specimen with higher thickness exhibits higher CCG rate. The turning point 1 location from low C ∗ region to transition C ∗ region increases with increasing thickness, while that of turning point 2 seems to be independent of specimen thickness. Based on the finite element results, constraint-dependent turning point 1 location and creep crack growth rate equations were fitted. More accurate and realistic life assessment may be made when the stress-dependent model and the constraint effect were considered for creep life assessments of high-temperature components subjecting to a low applied load.

Scour around underwater unexploded ordnances (UXOs): An experimental and computational investigation

Underwater unexploded ordnances (UXOs) pose a significant threat to human health and safety as well as the environment. The understanding of the scour around UXOs is essential for remediation actions. Many previous studies simplified UXOs as cylinders. We report an experimental and computational study on the hydrodynamics and morphodynamics around a real UXO and the comparison with a cylinder. With detailed flume data and simulation results, we show the UXO shape has a great impact on the hydrodynamics and the consequent scour and burial process. The shape effects also convolute with the flow’s angle of attack, making it even more important to consider the shape of UXOs. Hence, two angles of attack, 45° and 90° were investigated. The bulk behavior of scour around UXOs is akin to scour around any slender object placed on a sediment bed. However, the detailed scour process is significantly different. Our results show that flow contraction near the two ends of UXOs, recirculation behind the object, vortex shedding downstream, and jet-like flow under the object all play dominant roles during different stages of scour. In addition, we generalized the scour process around UXOs and other objects by applying a scaling analysis based on first principles of physics. A fitted saturation growth-rate equation relating scour volume and time collapses data reasonably well.

'biogeom': An R package for simulating and fitting natural shapes.

Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.