Steady Growth Rate Research Articles

Growing Yeast into Cylindrical Colonies

Micro-organisms often form complex multicellular assemblies such as bio-films and colonies. Understanding the interplay between assembly expansion, metabolic yield, and nutrient diffusion within a freely-growing colony remains challenging. Most data available about micro-organisms are from planktonic cultures, due to the lack of experimental tools to observe multicellular assemblies. Here, we propose a method to tackle this problem by constraining the growth of yeast colonies into simple geometric shapes such as cylinders. To this end, we designed a simple, inexpensive, versatile culture system to control the location of nutrient delivery below a growing colony. Under such culture conditions, yeast colonies grow vertically and only at the locations where nutrients are delivered. Colonies increase in height at a steady growth rate which is inversely proportional to the cylinder radius. We show that the vertical growth rate of cylindrical colonies is not defined by the single cell division rate, but rather by the colony metabolic yield. This contrasts with cells in liquid culture, in which the single cell division rate is the only parameter that defines the population growth rate. This method also provides a direct, simple method to estimate the metabolic yield of a colony. Our study further demonstrates the importance of the shape of colonies on setting their expansion. We anticipate our approach to be a starting point for elaborate studies of the population dynamics, evolution, and ecology of microbial colonies in complex landscapes.

Improved Methodology for Determining the Value of Energy from Distributed Renewables Using Statistical Analysis Combined with Normative Scenarios

The financial benefits of a distributed electric generation facility cannot be calculated without an expectation of the electricity's market value. Prediction of long-term future prices is a difficult but mandatory task, which is often reduced to constant annual prices with steady annual growth rates. This study provides a methodology for predicting electricity prices at an hourly resolution for long-term analysis, using the Swedish case as an example. It includes a statistical examination of historical data inspired by the meteorology sector to create a “typical year” of hourly price values. Future prices are calculated by applying annual rate changes to the typical year curve, using a monthly resolution to allow for seasonal variations. Rate changes are predicted using historical trends and current market conditions for near-term prices, and a normative scenario for mid- to long-term prices. The resulting methodology can be used in part or whole for any market in which historical data is available and a normative scenario created.

Effect of Different Catalyst Deposition Technique on Aligned Multiwalled Carbon Nanotubes Grown by Thermal Chemical Vapor Deposition

The paper reported the investigation of the substrate preparation technique involving deposition of iron catalyst by electron beam evaporation and ferrocene vaporization in order to produce vertically aligned multiwalled carbon nanotubes array needed for fabrication of tailored devices. Prior to the growth at 700°C in ethylene, silicon dioxide coated silicon substrate was prepared by depositing alumina followed by iron using two different methods as described earlier. Characterization analysis revealed that aligned multiwalled carbon nanotubes array of 107.9 µm thickness grown by thermal chemical vapor deposition technique can only be achieved for the sample with iron deposited using ferrocene vaporization. The thick layer of partially oxidized iron film can prevent the deactivation of catalyst and thus is able to sustain the growth. It also increases the rate of permeation of the hydrocarbon gas into the catalyst particles and prevents agglomeration at the growth temperature. Combination of alumina‐iron layer provides an efficient growth of high density multiwalled carbon nanotubes array with the steady growth rate of 3.6 µm per minute for the first 12 minutes and dropped by half after 40 minutes. Thicker and uniform iron catalyst film obtained from ferrocene vaporization is attributed to the multidirectional deposition of particles in the gaseous form.

Some gastrointestinal tract characteristics of Karayaka ram lambs slaughtered at different weights.

Thirty-one Karayaka ram lambs were slaughtered at different body weights (30 (n = 7) , 35 (n = 6) , 40 (n = 7) , 45 (n = 6) , and 50 (n = 5) kg of body weight at fast) to evaluate the growth of their gastrointestinal tract (GIT) characteristics, to determine the relationship among slaughter body weight (SBW) and empty body weight (EBW), whole GIT and segments, and the influence of slaughter weight on the pH of rumen, jejunum, and cecal contents. The effects of the SBW on GIT weight (P < 0.05) , stomach ( P < 0.001) , and intestine (P < 0.05) , the body length (P < 0.001) and caecum (P < 0.05) , and the relative weights of GIT (P < 0.05) , stomach (P < 0.001) , and intestine (P < 0.001) were linear whereas that for the length of intestine were quadratic. The effect of SBW were quadratic (P < 0.05) on ratios of stomach to GIT weight and intestine length to intestine weight and rumen pH while, for the intestine to GIT weight ratio (P < 0.001) and caecum pH (P < 0.05) , this effect was linear. The results indicated that for all parameters studied, with the exception of intestinal length and cecal pH, linear relationships were observed with SBW indicating steady growth rates for these tissues.

Are Real GDP Levels Stationary in African Countries?

AbstractIn this study, we apply flexible Fourier stationary unit root test proposed by Enders and Lee (2012) to assess the non‐stationary properties of the per capita real gross domestic product (GDP) for 32 African countries. We find that Fourier stationary unit root test has higher power than linear method if the true data‐generating process of per capita real GDP is in fact a stationary nonlinear process of an unknown form with structural change using the low frequency components. We investigate the stationarity of per capita real GDP from the nonlinear point of view and provide robust evidence that clearly indicates that real output is well characterised by a nonlinear, mean‐reverting process, namely Benin, Botswana, Burundi, Cameroon, Senegal, Sierra Leone and South Africa. Our evidence points that these seven countries are nonlinear stationary, implying that per capita real GDP follows a steady rate of growth, and policy innovations then have temporary effects. These results have important policy implications for African countries.

Efficient generation of biliary epithelial cells from rabbit intrahepatic bile duct by Y-27632 and Matrigel

Efficient culture of primary biliary epithelial cells (BECs) from adult liver is useful for both experimental studies and clinical applications of tissue engineering. However, an effective culture system for long-term proliferation of adult BECs is still unachieved. Laboratory rabbit has been used in a large number of studies; however, there are no reports of BECs from normal adult rabbit. As little as 5 g of normal rabbit liver tissue were minced, digested, and then clonally cultured in medium containing FBS and ITS. Cells were characterized by cell morphology, immunoassaying, and growth rate assay. Different combination of growth factors and substrates, including Y-27632 and Matrigel, were employed to assess their effect on cell proliferation. In the primary culture, the BECs cellular sheets consisting of cuboidal cells, as well as fibroblast-like cells and other hepatic cells, emerged with time of culture. The BECs cellular sheets were then manually split into cells clumps for further characterization. The subcultured cells had typical cell morphology of cholangiocytes, expressed the specific markers of BECs, including GGT, cytokeratin (CK18), and CK19, and possessed the capacity to form duct-like structure in three-dimensional Matrigel. Y-27632 and Matrigel-treated BECs had a steady growth rate as well as colony-formation capacity. The BECs were maintained in Y-27632 and Matrigel culture system for more than 3 mo. This is the first example, to our knowledge, of the successful culture of BECs from normal adult rabbit liver. Furthermore, our results indicate that treatment of BECs with Y-27632 and Matrigel is a simple method for efficient output of BECs.

Size, temperature and composition of a spherical droplet as a function of time at the transient stage of nonisothermal binary condensation or evaporation

The transient stage of evolution in size, temperature and composition of a droplet, which nonisothermaly condenses or evaporates in the diffusion or free-molecular regime in the atmosphere of two condensable vapors and neutral carrier gas, is considered. On this stage, both solution concentration and temperature in the droplet approach their stationary values, and the steady rate of the droplet growth or evaporation establishes. The fact that the temperature adjusts fast to the current value of solution concentration in the droplet allows us to express the current solution concentration as an analytical function of temperature and to find general integral relations expressing the droplet radius and time as nonlinear functions of current droplet temperature. Some numerical illustrations of the theory have been done in the situation when the droplet size changes in the diffusion regime and the solution in the droplet can be considered ideal. In order to cover arbitrary initial droplet size and component concentrations, two opposite initial concentrations of solution related to pure first and pure second components in the droplet have been considered. In particular, the appearance of nonmonotonic change of the droplet radius with time has been analyzed.

Determinants of customers' online purchase intention: an empirical study in India

Purpose – According to Associated Chambers of Commerce and Industry of India (ASSOCHAM), the size of the Indian online retail industry is INR 2000 crore and the industry is projected a steady annual growth rate of 35 per cent to reach INR 7000 crore by 2015. Given the growing importance of the online retail industry in India, it remains imperative for web retailers and internet marketers to understand the determinants of online customers' purchase intention to decipher what is important to the Indian online customer. This paper attempts to identify the determinants of online purchase intention among youth in the Indian context.Design/methodology/approach – Based on a detailed literature review, customer online purchase intention shopping orientation factors such as impulse purchase orientation, brand orientation and quality orientation were considered along with online trust and prior online purchase experience. The results are based on 95 valid responses received from the online survey.Findings – The res...

Surface-enhanced Raman scattering of graphene with photo-assisted-synthesized gold nanoparticles

This paper presents a convenient and reliable method to prepare gold nanoparticles (AuNPs) on graphene. Photo-assisted synthesis (PAS) was employed to grow AuNPs in AuCl(4)(-) electrolyte on graphene. The size of AuNPs could be as large as 130 nm. This optical method had a steady growth rate of AuNPs. The distribution of AuNPs was well controlled by focusing the laser for PAS. The minimum diameter of the distribution was approximately 1 μm. Surface-enhanced Raman scattering of graphene due to AuNPs was observed. Electrical fields near AuNPs calculated by the finite-difference time-domain algorithm ensured that the Raman enhancement was attributed to the localized surface plasmons of AuNPs.

Darryl Francis and the Making of Monetary Policy, 1966-1975

oday, it is widely acknowledged that thefundamental mission of monetary policy isto maintain the long-run stability of theprice level. Economists and policymakers generallyagree that persistent changes in the price level(inflation and deflation) are, in the long run, causedby growth of the money stock in excess of thegrowth of total output. It is thought, moreover, thatmonetary policy can best promote high employ-ment and maximum sustainable economic growthby maintaining reasonable stability of the pricelevel. The charter of the European Central Bank, aswell as legislation governing the behavior of centralbanks in several countries, specifies price stabilityas the sole objective for monetary policy. TheFederal Reserve, by contrast, is assigned multiplepolicy objectives—“maximum employment, stableprices, and moderate long-term interest rates”(Federal Reserve Reform Act of 1977). Nevertheless,in recent years U.S. monetary policy has been con-sistent with a gradual reduction in the rate of infla-tion to the point where many economists believethat price level stability, for practical purposes, hasbeen achieved.The consensus about the importance of pricelevel stability and the role of monetary policy is afairly recent development. The macroeconomicparadigm that emerged from the Great Depressionand dominated from the 1940s to about 1980 heldthat full employment should be the primary objec-tive of monetary and fiscal policy. Stabilizationpolicy was viewed as choosing from among a menuof unemployment and inflation rates along a stablePhillips curve. Many economists and policymakersviewed moderate inflation as an acceptable cost ofmaintaining full employment. During the 1950sthe Federal Reserve frequently was criticized forpaying “excessive” attention to inflation, to thedetriment of employment and output growth.Perhaps in part a response to such criticism, inthe early 1960s the Fed’s monetary policy generallybecame more expansionary. Inflation began to risein 1965 and continued to increase through the1970s. Unemployment fell at first, but during the1970s the average rate of unemployment was higherthan it had been during the preceding two decades.Moreover, inflation, unemployment, and real outputgrowth all became more variable as the average rateof inflation increased.Not surprisingly, the poor performance of themacroeconomy during the 1970s brought theFederal Reserve much criticism. Among profes sionaleconomists, once-dominant views about the roles ofmonetary and fiscal policy began to shift. Experiencedemonstrated the folly of those policies designedto exploit a tradeoff between unemployment andinflation and showed that expansionary monetarypolicy could not permanently lower the unemploy-ment rate or increase the growth rate of real output.By October 1979, when Federal Reserve officialsfinally resolved to bring inflation under control, thecosts of disinflating were substantially higher thanthey would have been earlier in the decade wheninflation was lower and less entrenched. This paper examines alternative views aboutmonetary policy within the Federal Reserve Systemfrom the mid-1960s to the mid-1970s. We highlightthe views of Darryl Francis, president of the FederalReserve Bank of St. Louis from 1966 to 1975. Incontrast to most of his Fed colleagues, Francis arguedthat monetary policy should concentrate on haltinginflation. He believed that the influence of monetarypolicy on the unemployment rate was unpre dictableand at best temporary. He was an early proponentof the view that the unemployment rate (and realoutput growth) tends toward a “natural” rate deter-mined by factors outside the control of monetarypolicymakers. Francis argued that the Fed shouldmaintain a steady growth rate of the money stockand blamed the Fed’s targeting of interest rates andmoney market conditions for producing destabilizingswings in money stock growth.

Experimental Study on Fatigue Crack Propagation of Glare3-3/2 with Mechanics Properties

This study is to investigate the fatigue crack growth behavior of Glare3-3/2 under various stress levels. The Glare3-3/2 specimen consists of three 2024-T3 aluminum alloy sheets and two layers of glass/epoxy composite lamina. Tensile-tensile cyclic fatigue tests were conducted on centrally notched specimen at four stress levels with various maximum values. A digital camera system was used to take photos of the propagating cracks on both sides of the specimen. Image processing software was adopted to accurately measure the length of the cracks on each photo. The test results show that 1) Compared to 2024-T3 aluminum alloy, the fatigue properties of Glare3-3/2 are much better: under the same loading condition with maximum stress level of 120MPa, the crack growth rate of Glare3-3/2 is roughly 5% of the corresponding value of 2024-T3 aluminum alloy, while the fatigue life is 4 times higher than that of 2024-T3 aluminum alloy. 2) The maximum stress level shows strong influence on fatigue crack propagation behavior of Glare3-3/2. The value of steady state crack growth rate increases linearly, while the number of load cycles decreases exponentially, with respect to the maximum stress values used in the fatigue tests.

Longevity and Growth Rates of the Gumboot Chiton,Cryptochiton stelleri, and the Black Leather Chiton,Katharina tunicata

Few studies have documented chiton growth rates, and lifespans for most chiton species remain unknown. This study presents the first size-at-age and longevity estimates for Cryptochiton stelleri and Katharina tunicata, two of the largest known species of chitons. Age estimates were based on growth ring counts obtained by cross-sectioning and polishing valves. This process alone showed clear growth rings in shell plates of K. tunicata. Valves of C. stelleri did not show conspicuous growth rings in cross section, so the acetate peel technique was used to highlight growth bands. Linear growth in terms of body length and shell width approached an asymptote in both species and was described with the von Bertalanffy growth function. Both C. stelleri and K. tunicata displayed indeterminate growth with regard to tissue weight and shell weight, continuing to maintain a steady growth rate throughout their lifespans. The oldest K. tunicata specimen was estimated to be 17 years old. The oldest C. stelleri was estimated to be 40 years old, making it the longest-lived chiton species known.

Evaluation of constraint effects on creep crack growth by experimental investigation and numerical simulation

Effects of constraint induced by crack depth on creep crack behavior of P92 steel was investigated by experimental investigation and numerical simulation. Creep crack growth tests were carried out on compact tension specimens with different crack depths. It revealed that the high constraint affected creep crack initiation time and steady creep crack growth rate. Then, the crack-opening stress distribution at crack tip during creep crack growth process was obtained by finite element method (FEM) analysis. The corresponding variation of constraint parameter Q was also obtained. Finally, a C*–Q approach was employed to characterize the creep crack growth rate.

AN EMPIRICAL GROWTH MODEL FOR MAJOR OIL EXPORTERS

This paper develops a long-run output relation for a major oil-exporting economy where the oil income-to-output ratio remains sufficiently high over a prolonged period. It extends the stochastic growth model developed in Binder and Pesaran (1999) by including oil exports as an additional factor in the capital accumulation process. The paper distinguishes between the two cases where the growth of oil income, go, is less than the natural growth rate (the sum of the population growth, n, and the growth of technical progress, g), and when go ≥ g + n. Under the former, the effects of oil income on the economy's steady growth rate will vanish eventually, while under the latter oil income enters the long-run output equation with a coefficient which is equal to the share of capital if it is further assumed that the underlying production technology can be represented by a Cobb–Douglas production function. The long-run theory is tested using quarterly data on nine major oil economies. Overall, the test results support the long-run theory, with the existence of long-run relations between real output, foreign output and real oil income established for six of the nine economies considered. Copyright © 2012 John Wiley & Sons, Ltd.

The two sector endogenous growth model: An atlas

In this paper we investigate the underlying structure of the Lucas (1988) endogenous growth model. We derive analytically, the restrictions on the parameter space that are necessary and sufficient for the existence of balanced growth paths and saddle-path stable local dynamics. We demonstrate that in contrast to the original model, with the addition of an external effect and depreciation in the human capital sector, the Lucas model can be made consistent with the high degrees of intertemporal elasticities of substitution increasingly estimated in the empirical literature—even if there is a significant degree of increasing returns to scale in the physical production sector of the economy. Finally we demonstrate that for a given baseline rate of steady state growth, with the inclusion of modest degrees of depreciation and external effects to the human capital production process, the model can accommodate the widest possible range of economies—including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the final goods sector, and also both the high rates of population growth and steady state per-capita output growth we observe in many parts of the world today.

Velocity of Micro Finance among Users Groups in Delta State, Nigeria: Implications for Economic Growth

The velocity of micro finance among User Groups in Delta State was investigated. Snow ball sampling technique was adopted in selecting 15 micro finance Users Groups for the study A five – year panel data (2000 – 2004) was collected with the aid of questionnaire Data collected was analysed with the aid of descriptive statistics, efficiency model, regression and correlation models. The result of the study shows that a mean of N18,655.33 was purchased by each member as loan, while a mean of N14,965.50 was repaid by each member of the group. Since the mean amount repaid is not significantly different from mean amount borrowed, 1.86 (P>0.05), the null hypothesis which states that there is no significant difference between the amount borrowed and amount repaid was upheld. This implies that the micro finance user groups were efficient in loan repayment/recovery ability. The micro finance users groups recorded loan marketing efficiency of 80.20%. A historical coefficient of variation of 14.77% and 13.8% indicate a relatively high velocity (steady growth rate) in amount of loan distributed and recovered respectively. It was therefore recommended that micro finance user groups should form linkage with financial institutions for the purpose of credit mobilization scheme. Also government policy of financial injection to transform the economy should adopt user group approach as a strategy.

Microstructural study of fatigue and dwell fatigue crack growth behaviour of ATI 718Plus alloy

A new superalloy, ATI 718Plus alloy (718Plus), has been developed to have a 55°C higher temperature capability over the traditionally used alloy 718, while maintaining favourable processing characteristics and intrinsic raw material costs. The fatigue and dwell fatigue behaviour of four microstructural variations of 718Plus are evaluated and compared with Waspaloy: standard heat treated condition (HT1), standard heat treated condition with thermal exposure at 732°C (1350°F) for 1000 h (HT2), fine grain condition with a modified δ phase (HT3) and fine grain overaged through modified heat treatment (HT4). Fatigue crack growth rate tests were performed at 649°C (1200°F) and 704°C (1300°F) under constant amplitude loading at 10 Hz or with a 100 s tension dwell. The results show that the steady state fatigue crack growth rates of each microstructural variation and both alloys are identical, with all of the 718Plus variations showing a clear advantage over Waspaloy in the fatigue crack threshold regime. The 718Plus variants HT1 and HT3 exhibited the highest fatigue crack growth threshold, followed closely by HT4 and finally HT2. At 649°C (1200°F), the 718Plus alloys had average threshold values ranging from 8·8 to 10·4 MPa m1/2 whereas the Waspaloy material was 6·1–7·5 MPa m1/2. At 704°C (1300°F), the advantage increased with the 718Plus alloys having average threshold values ranging from 10·1 to 11·6 MPa m1/2 compared with Waspaloy, which exhibited average threshold values of 6·6–7·7 MPa m1/2. Dwell fatigue results show that Waspaloy has better resistance to crack propagation under dwell conditions; however, optimisation of the precipitate phase (HT2) shows vast improvement in the dwell fatigue resistance of 718Plus.On a développé un nouveau superalliage, l’alliage ATI 718PlusÒ (718Plus), afin qu’il soit capable de supporter une température de 55°C plus élevée par rapport à l’alliage 718 utilisé traditionnellement, tout en maintenant des caractéristiques favorables de traitement et les coûts intrinsèques de métal brut. On évalue, et compare au Waspaloy, le comportement de fatigue et de pause-fatigue de quatre variations de microstructure du 718Plus. 1) Condition de traitement thermique standard (HT1); 2) condition de traitement thermique standard avec exposition thermique à 732°C (1350°F) de 1000 heures (HT2); 3) condition à grain fin avec une phase d modifiée (HT3); 4) grain fin avec vieillissement artificiel au moyen d’un traitement thermique modifié (HT4). On a effectué des essais de vitesse de croissance de fissure de fatigue à 649°C (1200°F) et à 704°C (1300°F) sous une charge à amplitude constante à 10 Hz ou avec une pause en traction de 100 secondes.Les résultats montrent que les vitesses de croissance de fissure de fatigue en régime permanent de chaque variation microstructurale et des deux alliages étaient identiques, alors que toutes les variations du 718Plus montraient un avantage clair sur le Waspaloy lors du régime seuil de fissure de fatigue. Les variantes HT1 et HT3 du 718Plus exhibaient le seuil de croissance de fissure de fatigue le plus élevé, suivies de près par HT4 et finalement par HT2. À 649°C (1200°F), les alliages 718Plus avaient des valeurs moyennes de seuil allant de 8·8 à 10·4 MPa-m1/2 alors que pour le matériau de Waspaloy, elles variaient de 6·1 à 7·5 MPa-m1/2. À 704°C (1300°F), l’avantage augmentait, les alliages 718Plus ayant des valeurs moyennes de seuil allant de 10·1 à 11·6 MPa-m1/2 comparés au Waspaloy, lequel exhibait des valeurs moyennes de seuil de 6·6 à 7·7 MPa-m1/2. Les résultats de pause-fatigue montrent que le Waspaloy a une meilleure résistance à la propagation de fissure sous des conditions de pause; cependant, l’optimisation de la phase de précipité (HT2) montre une vaste amélioration de la résistance à la pause-fatigue du 718Plus.

On the emergence of competitive equilibrium growth cycles

A basic discrete-time heterogeneous capital goods competitive environment is considered, its potential for displaying steady growth solutions analyzed and the properties of the latter characterized. A first composite good may be used for consumption or investment on a one-to-one basis, while a second good is only used for accumulation, solely capital inputs being part of the production process. This framework is first considered from the allocative standpoint through the derivation of the frontier of the production possibility set. Having defined the perfect foresight competitive equilibrium that also describes a Pareto optimum over time, attention is then given to the potential for unbounded steady growth solutions. Under interiority, summability, and expansivity restrictions, there is a unique optimal steady growth rate. For unitary depreciation rates of both capital goods, locally there exists a unique convergent sequence to this steady growth solution that exhibits a saddlepoint structure. However, as soon as one of the depreciation rates of the capital goods is non-unitary and the profit share accruing to the first capital stock is greater in the second pure accumulation industry than in the first composite good industry, the steady growth solution shows a loss of stability, and competitive equilibrium growth cycles emerge through the occurrence of a flip bifurcation in its neighborhood. This is the first optimal cycles result based upon a production set that does not explicitly incorporate any exogenously determined primary labor input in its definition.

Simultaneous establishing of stationary growth rate and composition of supercritical droplets at isothermal binary condensation in the diffusion-controlled regime

General integral relations expressing the droplet radius and time of the droplet nonstationary growth as nonlinear functions of solution concentration in the droplet have been derived. These relations are valid for a supercritical droplet (i.e., sufficiently large droplet, for which the Laplace pressure effect on the concentration at saturation of vapors is negligible) isothermally growing via stationary diffusion in the mixture of two condensing vapors and an incondensable carrier gas. The initial composition in the droplet may be arbitrary and partial molecular volumes of components are not fixed. Explicit analytical relations have been found for droplet composition and the droplet size as functions of time at small deviations from the stationary concentration in the growing droplet. These relations show that the assumption of the steady droplet growth rate is not valid for non-small deviations from the stationary concentration. Some illustrations of the general nonlinear theory have been done in situation when solution in the droplet can be considered ideal.

Investigating the effects of grain boundary energy anisotropy and second-phase particles on grain growth using a phase-field model

A phase-field model was used to investigate the simultaneous effects of grain boundary energy anisotropy and the presence of second-phase particles on grain growth in polycrystalline materials. The system of grains with anisotropic grain boundary energies was constructed by considering models of low and high misorientation angles between adjacent grains. Systems without particles reached a steady state grain growth rate, and this rate decreased by including the grain boundary energy anisotropy. In addition, the presence of particles significantly altered the microstructures during grain growth. This study showed that for systems including particles, the critical average grain size to stop grain growth depends not only on the volume fraction and size of particles, but also on the grain boundary energy anisotropy.