Aggregate Growth Model Research Articles

Self-assembly of supermicro- and meso-porous silica and silica/gold nanoparticles using double-chained surfactants

Porous silica nanosized particles were prepared using tetramethylorthosilicate and two double carbon chained templates, n-didecyldimethylammonium bromide and n-didodecyldimethylammonium bromide. Samples were prepared using a simple modification of the Stöber method for synthesis of colloidal silica for template to silica ratios of 0.2 and 0.1 under homogeneous cosolvent conditions. Silica/gold nanocomposites were prepared similarly except for the addition of a gold colloid suspension prior to self-assembly. All samples were analyzed using X-ray diffraction, transmission electron microscopy and liquid nitrogen adsorption. The diameters of the pores were measured using three methods: volumetric-XRD; Gurvitsch; and BJH. The diameters of the pores ranged from 1.9 to 2.5 nm using the Volumetric-XRD method with pore wall diameters from 0.64 to 1.1 nm. The presence of supermicro- and meso-pores were confirmed using comparison t-plots. Both the volumetric-XRD and Gurvitsch methods were consistent with the t-plot analysis, whereas the BJH method underestimated pore diameters significantly. Samples had pore volumes in excess of 0.37 cm g −1 at STP and surface areas greater than 700 m 2 g −1. The symmetry of the silica pore structure was found to vary depending on both the template to silica ratio and the addition of a gold tag. The diameter of nanoparticles ranged from 58 to 590 nm and the position of the gold seed in each particle was consistent with a three-stage aggregative growth model.

The Effect of Health on Economic Growth: A Production Function Approach

We estimate a production function model of aggregate economic growth including two variables that microeconomists have identified as fundamental components of human capital: work experience and health. Our main result is that good health has a positive, sizable, and statistically significant effect on aggregate output even when we control for experience of the workforce. We argue that the life expectancy effect in growth regressions appears to be a real labor productivity effect, and is not the result of life expectancy acting as a proxy for worker experience.

Effects of temperature on the early stages of rat spinal motoneurone development in vitro

Effects of temperature on rat spinal motoneurone morphogenesis during the early stages of development were investigated in vitro through a statistical morphometric analysis, and examined in the frame of a basic theoretical aggregation growth model. Morphological measurements in the 31.0–39.4°C range revealed that: (1) primary neurite initiation was promoted by increased temperatures; (2) collateral branches formation was particularly enhanced over 37°C; and (3) the elongation properties of all processes were not significantly altered. In parallel, an Arrhenius analysis proved that: (4) an activation energy of about 23 kcal/mol was required for primary neurites to emerge from a soma. These results suggest that the very first molecular events underlying neuritogenesis are rather sensitive to temperature and could imply both the transport and assembly properties of microtubules.

The stochastic turnpike property without uniformity in convex aggregate growth models

The proof of the “late” turnpike property in optimal growth theory requires constructing a bounded value-loss process that records a strictly positive value-loss when paths of capital accumulation from different initial stocks diverge. Uniformity assumptions strengthen this sensitivity by ensuring that value-loss is independent of time and state of environment in which the divergence occurs, and are acknowledged as strong restrictions on the model. This paper argues that uncertainty can obviate the need for uniformity. The multiplicity of states afforded by a stochastic framework permits constructing a value-loss process over an “extended” time-line that is a martingale; if capital stocks diverge, then the martingale registers an upcrossing across a band of uniform width on its extended time-line, thereby giving uniform value-loss. The Martingale Upcrossing theorem and the first Borel–Cantelli lemma then clinch the turnpike property.

Optimal multiregional global economic growth: Formulation of an optimal growth program, growth prospects, and convergence

The analysis of the issues related to long- and medium-term growth of the world economy with the help of numerical computerized global economic models has been an important area of study in economics. This paper addresses some of the main issues in optimal global economic growth with the help of a multiregional aggregative optimal economic growth model of the world economy: MURO-GOG-1. MURO-GOG-1 is a multiregional equilibrium growth model of the global economy, showing its structures of optimal economic growth. The model can determine the rates at which the world should save and consume out of the global income. It can also characterise the rates at which other economic variables and parameters of the global economy should grow so that the global economy expands at the maximum growth rate in the future. The global model contains the elements of an optimal growth program and is solved as a dynamic optimisation problem. The modelling study focuses on the issues of optimal structures of growth paths and the long-term dynamics of the world economy and its characteristics. The paper analyses the issues of global economic growth in terms of the results produced by the model. The nature and patterns of optimal global economic dynamics and growth suggested by the model's results are especially stressed.

Silver Nanoparticle Formation: Predictions and Verification of the Aggregative Growth Model

The mechanisms of growth of 5−30 nm silver particles produced from the reduction of silver perchlorate by sodium borohydride are explored. Evidence is provided that, within 5 s of mixing of silver perchlorate with borohydride, the concentration of ionic silver has dropped 2 orders of magnitude, initially resulting in the formation of ∼2.5 nm silver particles. We hypothesize that growth takes place over the next 20−50 min by an aggregative growth mechanism. This hypothesis is tested by comparing model predictions with experimental results of particle growth rates over a range of ionic strengths and reaction temperatures. The model assumes particles interact via electrostatic and van der Waals forces, and comparison of numerical solutions to population balance models for aggregation and coalescence demonstrates that particle growth rates and final sizes can be predicted with surface potentials within 20% of those previously reported under reaction conditions.

Synthesis of Microporous Silica Spheres

Spherical microporous silica powders with a narrow size distribution have been prepared by a precipitation technique involving the hydrolysis reaction of a silicon alkoxide in ethanol. The formation of the important microporosity has been investigated following two templating methods: the co-hydrolysis and condensation of two alkoxides, one of which presents porogen function, and the adsorption of an organic compound (glycerol) as the porogen. In both processes, the organic porogen is removed by a simple calcination. In the first method, the addition of more than 20 mol% of the porogen alkoxide, necessary for generating enough microporosity, disturbs completely the condensation process resulting in microporous, nonuniform silica particles of large size distribution. The best result has been obtained with the glycerol method where submicrometer-sized silica spheres with a very narrow size distribution and about 40 vol% porosity have been synthesized. The presence of glycerol during the synthesis considerably affects the precipitation mechanism, resulting in a larger mean particle size. The use of an aggregative growth model has successfully been employed to explain the effect of the porogen during particle formation. The precipitation mechanism of silica involves the aggregation between particles of similar size until a critical size is reached, resulting in a uniform particle size distribution. In the presence of glycerol, it has been shown that a second aggregative growth between still-nucleating primary particles and large particles occurred with increasing reaction time. This second aggregative growth appears at an intermediate stage of the precipitation process and is due to both the precipitation of smaller primary particles and the destabilization of the colloidal stability of the system. This explains why the final particle size reached in this system is larger compared to silica particles synthesized without glycerol and shows how glycerol is incorporated in the silica particles. The synthesis of silica microporous spheres of narrow size distribution, by varying particle size and porosity, should yield a wide range of aqueous silica slurries for particular chemical mechanical polishing applications.

Fractal characteristic of the microstructure in Alnico8

Alnico alloys are of technological importance owing to their excellent magnetic stability and good comprehensive properties. Considerable interest has arisen concerning the chemical compositions of the Fe-Co and Ni-Al rich phases which evolve from the spinodal decomposition of a bcc single phase solution at high temperatures [1–5]. However, emphasis has been seldom placed on kinetics of microstructural evolution at high temperatures. Recently, we have observed the splitting of Fe-Co rich particles in Alnico8 thermomagnetically treated [6]. On the other hand, some investigations [7– 9] have shown that microstructures in some materials have been found to be of fractal characteristics. However, different structures often exhibit different fractal natures, which implies that they are formed usually by different kinetic mechanisms. To this end, in this paper, our attention is focused on development of fractal characteristics in the microstructure formed during thermomagnetic treatment, which is expected to enhance understanding of the mechanisms of the microstructural evolution in Alnico8. The chemical composition of the Alnico8 studied is as follows (at mass percentage): 33.2Co, 16.3Ni, 5.3Al, 3.6Ti, 3.0Cu, 1.5Si, 1.0Nb, bal. Fe. The bulk Alnico8 was solution treated for 50 min at 1250 ◦C and then vacuum quenched. Thin laminar samples were cut from the quenched Alnico8 and subsequently subjected to a magnetic heat treatment with a field of 270 kA m−1 perpendicular to the section plane at 800 ◦C for various times such as 1.5, 5 and 10 min, and finally vacuum quenched. Transmission electron microscope (TEM) observations were made using a JEOL 200CX microscope with an accelerating voltage of 200 kV. Small angle X-ray scattering (SAXS) performed in transmission geometry with Cu Kα radiation on a Rigaku diffractometer was employed to evaluate the spatial fractal characteristics in size and morphology of Fe-Co rich particles. Fig. 1 shows TEM micrographs of the samples thermomagnetically treated at 800 ◦C for various times. TEM images were taken with electron beams along the [001] direction. The dark and isolated areas in all TEM images corresponded to rod-like Fe-Co rich particles, the long axis of which was parallel to the [001] direction [6]. The splitting of large Fe-Co rich particles was observed in the specimens with thermomagnetic treatment for 1.5 and 5 min, respectively, as the arrows in Fig. 1a and b indicate. In Fig. 1a small particles originated from the splitting of larger ones [6]. To compare Fig. 1a with b, it is easily found that the split particles coarsened. As a result of splitting, the resultant microstructure was fine and homogenous as shown in Fig. 1c. For a fractal object, N (R) is proportional to Rdf , where N (R) represents the number of particles within a radius R around a given particle, and df is the fractal dimension [10]. Based on this, direct measurements from TEM images have been taken on Fe-Co rich particles for all samples in two-dimensional Euclidian space, which covered wide ranges of R. Logarithmic plots of N (R) versus R for all samples measured are shown in Fig. 2. Each set of data are well described by a power-law behavior, as expected for a fractal. The linear least-squares fits to the data sets give estimates of fractal dimensions for 1.5, 5 and 10 min, which are 1.941, 1.945 and 1.784, respectively. In addition, SAXS experiments were also performed on all samples with different treatments to obtain directly three-dimensional information about the fractal behavior of Fe-Co rich particles. It has been however pointed out that since a fractal object has the spatial self-similarity, the scattering intensity obeys a power-law decay: I ∼ q−p [11]. If p 3, then p= df− 2d, where d is the Euclidian space dimension 3, which is the case of a compact object with smooth or rough surface depending on the value of p. Fig. 3 shows the curves of lgI versus lgq for the samples thermomagnetically treated for various times. On the curves, there exist obvious linear regions between lgI and lgq for all samples, which also indicates clearly that Fe-Co rich particles with different sizes are self-similar and of fractal characteristic in statistical sense. The exponents p for 1.5, 5 and 10 min are 2.566, 2.687 and 1.917, respectively, which are all less than 3 and thus equivalent exactly to the fractal dimensions. The fractal dimensions 2.566 and 2.687 obtained from the SAXS data for 1.5 and 5 min are in good agreement with the theoretical dimension 2.5, which has been figured out by Meakin on the basis of the diffusion-limited aggregation (DLA) model in threedimensional space [12]. In addition, for 10 min, a fractal dimension 1.917 derived from the SAXS data is also basically in accord with the fractal dimension 1.8 calculated from the cluster-cluster aggregation (CCA) growth model reported in Reference [13]. This gives a hint that the evolution of Fe-Co rich particles for

On the Existence of Chaotic Policy Functions in Dynamic Optimization

Applying the characterization results from Mitra and Sorger (1999), we show that topological chaos is a robust phenomenon in standard aggregative growth models even under arbitrary mild discounting. Furthermore, we state exact discount factor restrictions, under which two of the most popular examples of chaotic dynamics, the logistic map and the tent map, can be optimal policy functions of aggregative growth models. JEL Classification Numbers: C61, O41.

Rationalizing Policy Functions by Dynamic Optimization

We derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be the solution of such a problem. If the maintained assumptions include free disposal and monotonicity, then we obtain a complete characterization of all optimal policy and optimal value functions. This is the case, e.g., in the standard aggregative optimal growth model.

Financial Development and Economic Growth of Developed versus Asian Developing Countries: A Pooling Time-Series and Cross-Country Analysis

This paper examines the relationship between financial market development and economic growth. By pooling the data of both developed and developing countries, we test the relation between the real GDP growth rate and financial development variables suggested by the aggregate capital endogenous growth model. We find that the capital absorption and saving rates have a significant positive relation with economic growth whereas the interest rate has a negative relation. Since the behavior of these explanatory variables reflects financial development, our results suggest that financial intermediation plays a significant role in economic growth. Furthermore, we find that there was a shift in the economic performance of Asian developing economies in the 1980s. Financial reforms in this region have resulted in a transitory adverse impact on the capital absorption rate. It also appears that economic growth has slowed down recently for most of these newly industrialized economies. Our result suggests that the lack of efficient financial markets may have hindered the economic performance of these economies.

The preparation of silica from the olivine process and its possible use as a catalyst support

The production of silica from the dissolution of olivine in sulphuric acid has been studied. Variations in grainsize of the olivine result in different specific surface areas of the silica. The microporosity of the silica supports an aggregative growth model responsible for the increasing particle size. The silica is used in the preparation of a nickel catalyst. The performance of the produced catalyst is equal to a nickel catalyst based on commercially available silica

Asymptotic methods for aggregate growth models

Abstract We use perturbation methods to compute optimal policy functions in simple continuous- and discrete-time aggregate growth models. We demonstrate that computing the kth degree Taylor expansion of the policy function around the steady state involves solving one quadratic equation and k − 1 linear equations. We also compute Pade expansions, and show that both Taylor and Pade expansions can provide excellent solutions far from the steady state.

Endogenous Time Preference and Endogenous Growth

This paper develops a one-sector aggregate endogenous growth model with intertemporal preference dependence. The resultant model possesses the fundamental property of growth convergence, in the sense that countries with identical parameters regarding technology, preference, and government policy will converge to a steady state with the same (positive) growth rate. A notable tax policy implication of the model is that, even in the absence of externalities, the growth effects of an income tax are shown to be a priori ambiguous and dependent on the relative magnitudes of the tax rate and the tax elasticity of the savings rate.

Endogenous Time Preference and Endogenous Growth

This paper develops a one-sector aggregate endogenous growth model with intertemporal preference dependence. The resultant model possesses the fundamental property of growth convergence, in the sense that countries with identical parameters regarding technology, preference, and government policy will converge to a steady state with the same (positive) growth rate. A notable tax policy implication of the model is that, even in the absence of externalities, the growth effects of an income tax are shown to be a priori ambiguous and dependent on the relative magnitudes of the tax rate and the tax elasticity of the savings rate.

Influence of Process Parameters on the Precipitation of Organic Nanoparticles by Drowning-Out

Ethylcellulose (the organic substance), ethanol (the solvent) and water (the nonsolvent) are chosen as a model system for the production of uniform nanoparticles by drowning-out. Experiments carried out under various operating conditions show that many process parameters, such as the type of stirrer and the stirring speed, the temperature and the solvent–nonsolvent ratio, have practically no influence on the formation of ethylcellulose particles. On the other hand, the ethylcellulose concentration in the initial alcoholic solution seems to be the most important parameter controlling the particle size distribution. A comparison is made between experimental results and predictions of classical nucleation theories or aggregative growth models.

Martingale analysis of dynamic tax incidence in a nonstationary growth model

Abstract This paper develops a new martingale technique to study dynamic incidence of a capital income tax in nonstationary aggregate growth models. The stochastic Euler conditions are utilized to generate a submartingale process which is sensitive to a divergence between the no-tax and after-tax return to capital per unit. This submartingale process is instrumental in generalizing the classical result on the long-run incidence of a capital income tax in a stationary deterministic paradigm to nonstationary stochastic growth models. Since the Euler characterization is immediately available in aggregate growth models, the method developed here can also be utilized to study the dynamic incidence of other forms of taxation in general nonstationary aggregate growth models.

Recursive utility, martingales, and the asymptotic behaviour of optimal processes

Abstract This paper develops a new approach to the asymptotic behaviour of optimal programs in aggregate growth models permitting nonstationarities in the description of the technology and the stochastic environment. Added generality is provided by specifying a recursive utility description of preferences. The analysis makes critical use of martingale methods afforded by a stochastic specification and is applicable to growth models with both convex and nonconvex technologies.

Engendering macroeconomics: A reconsideration of growth theory

Macroeconomics is gender-biased because of its neglect of the reproductive sector. This neglect is formalized in the assumptions, supporting most macroeconomic models, that population and the mapping from population to the labor force are determined exogenously. The use of these assumptions is demonstrated for the case of the aggregate growth models which have evolved from Harrod's original contribution. In addition, the development growth literature is shown to harbor a similar neglect. Some suggestions are made as to how these assumptions might be relaxed and some elements of a consequent theory and data project outlined.

Human capital and economic growth in an overlapping generations model

The paper describes an aggregative optimal growth model, the essential features of which are that individuals are mortal and obtain their labor skill through educational training. The process of human capital formation is described by an education function which relates the pass rate to the educational expenditure per student. Two alternative scenarios, private and public education regimes, are separately investigated. Under the decentralized education regime, risk-neutral individuals borrow to finance their education when young. Under the centralized education regime, the cost of education is financed by taxes imposed on the workers in the economy, and the central government maximizes a long-term social target function. The equilibria of both regimes are analyzed and various comparative static results derived. It is shown that educational investment in a decentralized equilibrium is higher than that in the centralized steady state. We also establish that there exists a time discount rate at which or above which the decentralized per capita consumption exceeds that of the centralized steady state whereas for time rates of discount sufficiently near the population growth rate, the above result will be reversed.