Theoretical Growth Model Research Articles

A Theoretical Growth Model for Ireland

Ireland is distinguished by the high degree of openness of its labour market and the importance of FDI in the economy. We develop a neo-classical growth model to explore the consequence of these characteristics for the response of an economy to the kinds of shocks that are widely recognised to have been of importance in driving the Irish boom.

General form of the dependences of nanowire growth rate on the nanowire radius

A theoretical model of nanowire growth by the vapor–liquid–solid mechanism is considered, that accounts for the Gibbs–Thomson effect, the nucleation-mediated growth and the diffusion of adatoms to the wire top. It is shown that, within the range of growth conditions, the dependence of nanowire growth rate on its radius R is a quadratic function of 1/ R. The coefficients of this dependence are obtained as functions of technologically controlled growth conditions. It is demonstrated that at sufficiently high surface temperatures, the growth is controlled by the direct impingement of material to the drop and wire growth rate that increases with increasing R due to the Gibbs–Thomson effect. When the temperature is decreased, the competition between the Gibbs–Thomson effect and the diffusion-induced contributions results in the length–radius curves with minima. Theoretical results are compared to available experimental data on the Au-assisted growth of GaAs wires by molecular beam epitaxy and good correlation is demonstrated between them.

Review on the fracture processes in nanocrystalline materials

An overview of experimental study, computer simulations and theoretical models of fracture of nanocrystalline materials is presented. The key experimentally detected facts on ductile and brittle fracture processes are discussed. Special attention is paid to computer simulations and theoretical models of nucleation and growth of nanocracks and nanopores in deformed nanocrystalline materials. Also, we discuss mechanisms for fracture suppression in such materials showing good ductility or superplasticity.

Toughening mechanisms of nanoparticle-modified epoxy polymers

An epoxy resin, cured with an anhydride, has been modified by the addition of silica nanoparticles. The particles were introduced via a sol–gel technique which gave a very well-dispersed phase of nanosilica particles which were about 20 nm in diameter. Atomic force and electron microscopies showed that the nanoparticles were well-dispersed throughout the epoxy matrix. The glass transition temperature was unchanged by the addition of the nanoparticles, but both the modulus and toughness were increased. The measured modulus was compared to theoretical models, and good agreement was found. The fracture energy increased from 100 J/m 2 for the unmodified epoxy polymer to 460 J/m 2 for the epoxy polymer with 13 vol% of nanosilica. The fracture surfaces were inspected using scanning electron and atomic force microscopies, and the results were compared to various toughening mechanisms proposed in the literature. The toughening mechanisms of crack pinning, crack deflection and immobilised polymer were discounted. The microscopy showed evidence of debonding of the nanoparticles and subsequent plastic void growth. A theoretical model of plastic void growth was used to confirm that this mechanism was indeed most likely to be responsible for the increased toughness that was observed due to the presence of the nanoparticles.

Growth kinetics of metastable (3 3 1) nanofacet on Au and Pt(1 1 0) surfaces

A theoretical epitaxial growth model with realistic barriers for surface diffusion is investigated by means of kinetic Monte Carlo simulations to study the growth modes of metastable (3 3 1) nanofacets on Au and Pt(1 1 0) surfaces. The results show that under experimental atomic fluxes, the (3 3 1) nanofacets grow by 2D nucleation at low temperature in the submonolayer regime. A metastable growth phase diagram that can be useful to experimentalists is presented and looks similar to the one found for the stationary growth of the bcc(0 0 1) surface in the kinetic 6-vertex model.

Design of mechanical properties of a Zn27Al alloy based on microstructure dendritic array spacing

The present work focuses on the influence of the as-cast dendritic microstructure of a ZA27 alloy (Zn–27 wt%Al) on tensile mechanical properties. A low carbon steel chill was used in a unidirectional solidification experimental set-up in order to permit a wide range of dendritic spacings to be obtained along the casting. Experimental results include transient metal/mold heat transfer coefficients ( h i ), tip growth rate ( V L), secondary dendrite arm spacing ( λ 2), ultimate tensile strength ( σ U) and yield strength ( σ y) as a function of solidification conditions imposed by the metal/mold system. Experimental laws relating σ U and σ y with secondary dendrite arm spacing are proposed. It was found that both tensile properties increase with decreasing λ 2. A predictive theoretical dendritic growth model has been compared with the present experimental observations. Expressions correlating tensile properties, dendritic spacing and solidification thermal variables have been established. Such expressions permit the control of as-cast microstructures by manipulating casting variables, such as the cooling rate and the tip growth rate and can be used as an alternative way to design mechanical properties.

Public infrastructure, employment and sustainable growth in a small open economy with and without foreign direct investment

The paper builds a theoretical model of endogenous growth motivated by the recent Indian paradox of an improving GDP growth rate in the face of unsatisfactory employment growth rate. The source of the problem is believed to be inadequate growth of manufacture for the absorption of unskilled or semi-skilled labour in rural sectors. The paper studies the impact of free trade on employment and GDP growth in a small, developing economy in the absence as well as presence of foreign direct investment. The model also recognizes the importance of public infrastructure accumulation to support the growth process. The results indicate that free trade with or without a corresponding free inflow of foreign capital into the manufacturing sector has a positive impact on employment and GDP growth. However, the beneficial effect is stronger in the presence of foreign capital. Foreign and domestic capital grow at equal rates in equilibrium.

Planar laser imaging and modeling of matrix-assisted pulsed-laser evaporation direct write in the bubble regime

A combination of planar laser imaging and theoretical modeling has been used to examine matrix-assisted pulsed-laser evaporation direct write (MAPLE-DW) in the bubble regime. MAPLE-DW is a method for patterning substrates via laser-initiated forward transfer of an organic fluid containing metallic particles and coated on a transparent support. For our conditions, best deposition of a silver-based, thick-film ink was found to occur when laser-initiated vaporization forces the ink outward as a bubble. Planar laser imaging was used to monitor bubble growth as a function of time for three different ink films with nominal thicknesses of 12, 25, and 50μm and two laser beam diameters of 30 and 60μm. From these measurements, correlations were developed for predicting the maximum height and velocity of bubbles via three known process variables: laser energy, ink thickness, and beam diameter. Further insight on the physics of the MAPLE-DW process was obtained by developing a theoretical model for bubble growth based on a simple force balance associating vapor-pocket pressure and viscous forces. Primary parameters specifying the subsequent differential equation were related to the above process variables. Numerical solutions to the differential equation were used to predict successfully bubble growth versus time for the conditions analyzed in the imaging experiments.

Growth of cortical neuronal networkin vitro: Modeling and analysis

We present a detailed analysis and theoretical growth models to account for recent experimental data on the growth of cortical neuronal networks in vitro [Phys. Rev. Lett. 93, 088101 (2004)]. The experimentally observed synchronized firing frequency of a well-connected neuronal network is shown to be proportional to the mean network connectivity. The growth of the network is consistent with the model of an early enhanced growth of connection, but followed by a retarded growth once the synchronized cluster is formed. Microscopic models with dominant excluded volume interactions are consistent with the observed exponential decay of the mean connection probability as a function of the mean network connectivity. The biological implications of the growth model are also discussed.

Extended interpretation of the structural attributes of pellet flocs in pelleting flocculation

Pelleting flocculation can be viewed as a technique that improves the sludge characteristics, which may be beneficial during the subsequent phase of solid–liquid separation. Generated flocs structures possess an appearance of nearly spherical beads with an enhanced stability. The literature provides two theoretical growth models of such pellet-like flocs: (i) series and (ii) parallel system. The parallel system concerns the formation of aggregates with a high degree of structural order that is called onion-like structure. Consequently, in reported cases of pelleting flocculation this kind of internal buildup of flocs was strongly suggested. Contrary to these statements, the reasoning presented here demonstrates that the predominantly non-uniform interior structure of pellet flocs, here termed raspberry-like structure, is the result of sludge conditioning by pelleting flocculation. The goal of this paper is to present and discuss the structural attributes of pellet floc aggregates in terms of internal buildup and to reorder the available literature on pelleting flocculation according to the proposed reinterpretation of the concepts of this technique.

Modelling aspects of cancer dynamics: a review

Cancer is a complex disease in which a variety of factors interact over a wide range of spatial and temporal scales with huge datasets relating to the different scales available. However, these data do not always reveal the mechanisms underpinning the observed phenomena. In this paper, we explain why mathematics is a powerful tool for interpreting such data by presenting case studies that illustrate the types of insight that realistic theoretical models of solid tumour growth may yield. These range from discriminating between competing hypotheses for the formation of collagenous capsules associated with benign tumours to predicting the most likely stimulus for protease production in early breast cancer. We will also illustrate the benefits that may result when experimentalists and theoreticians collaborate by considering a novel anti-cancer therapy.

Leaf Traits Determine the Growth‐Survival Trade‐Off across Rain Forest Tree Species

A dominant hypothesis explaining tree species coexistence in tropical forest is that trade-offs in characters allow species to adapt to different light environments, but tests for this hypothesis are scarce. This study is the first that uses a theoretical plant growth model to link leaf trade-offs to whole-plant performances and to differential performances across species in different light environments. Using data of 50 sympatric tree species from a Bolivian rain forest, we observed that specific leaf area and photosynthetic capacity codetermined interspecific height growth variation in a forest gap; that leaf survival rate determined the variation in plant survival rate under a closed canopy; that predicted height growth and plant survival rate matched field observations; and that fast-growing species had low survival rates for both field and predicted values. These results show how leaf trade-offs influence differential tree performance and tree species' coexistence in a heterogeneous light environment.

Dynamics of boiling succeeding spontaneous nucleation on a rapidly heated small surface

The dynamics of boiling succeeding spontaneous nucleation on a small film heater immersed in ethyl alcohol are investigated at heating rates ranging from 10 7 K/s to approximately 10 9 K/s, under which spontaneous nucleation is dominant for the inception of boiling. Immediately after the concurrent generation of a large number of fine bubbles, a vapor film that covers the entire surface is formed by coalescence and rapidly expands to a single bubble. As the heating rate is increased, the coalesced bubble flattens and only a thin vapor film grows before cavitation collapse. Similar behaviors are also observed for water. Based on the observed results, a theoretical model of the dynamic bubble growth due to the self-evaporation of the superheated liquid layer, which develops before boiling incipience, is presented. The calculated results are compared with the observed results.

Growth following adversity: Theoretical perspectives and implications for clinical practice

A number of literatures and philosophies throughout human history have conveyed the idea that there is personal gain to be found in suffering, and it is an idea central to the existential-humanistic tradition of psychology. However, it is only relatively recently that the topic of growth following adversity has become the focus for empirical and theoretical work. In this paper, we review theoretical models of growth, and discuss the implications of growth for clinical practice. Three main theoretical perspectives are reviewed, the functional-descriptive model, the meta-theoretical person-centered perspective, and the biopsychosocial-evolutionary view. It is proposed that these three approaches to theory offer different but complementary levels of analysis, and that theoretical integration between them is possible. We then go on to explore the implications of this theoretical integration for clinical practice, and conclude with a consideration of the role of therapy in facilitating growth following adversity.

Effect of light and nitrogen supply on internal C:N balance and control of root-to-shoot biomass allocation in grapevine

Theoretical plant growth models postulate that the relative rates of shoot and root growth are largely modulated by signals related to carbon and nitrogen status of the plant. To test this experimentally, 6-week-old vegetative cuttings of grapevine ( Vitis vinifera L. cv Merlot) were grown aeroponically in different controlled conditions of irradiance (13.8, 8.4 and 5.3 mol PAR m −2 day −1) and/or nitrogen nutrition (0.15, 1.20 and 7.11 mM N). Total non-structural carbohydrates (TNC) and amino acids (FAA) in leaves and roots were analysed 0, 6 and 28 days after treatment initiation. Both whole-plant biomass accumulation as well as C and N contents were highly responsive to light and N availability. At day 28, plant dry weight was significantly reduced in shaded vines (−35% of that of the control plants) and stimulated under the high irradiance environment (+30%). Deprivation of N enhanced root growth (+51%) at the expense of above-ground growth, whereas leaf dry weight was significantly greater in the high-N treatment than in the control. Vines grown under low-N and high irradiance conditions had the highest root-to-shoot ratios and those grown under low light and high N the lowest. Finally, redistribution of biomass among vegetative vine parts was significantly related to different indicators of the vine C:N status measured either at the whole-plant (N concentration) or at the organ level (TNC:FAA ratio), suggesting that root-to-shoot biomass partitioning was controlled by some aspect of plant C:N balance. Such relationships will be useful to improve allocation rules in a process-based growth model of grapevine.

Natural Volatility, Welfare and Taxation

Cyclical components are analytically computed in a theoretical model of stochastic endogenous fluctuations and growth. Volatility is shown to depend on the speed of convergence of the cyclical component, the expected length of a cycle and on the altitude of the slump. Taxes affect these channels and can therefore explain cross-country differences and breaks over time in volatility. With exogenous sources of fluctuations, a special case of our model, decentralized factor allocation is efficient. With endogenous fluctuations and growth, decentralized factor allocation is inefficient and (time-invariant) taxes can (de-) stabilize the economy. No unambiguous link exists between volatility and welfare.

Multinationals, Endogenous Growth, and Technological Spillovers: Theory and Evidence*

FDI has received surprisingly little attention in theoretical and empirical work on openness and growth. This paper presents a theoretical growth model where MNCs directly affect the endogenous growth rate via technological spillovers. This is novel since other endogenous growth models with MNCs, e.g. the Grossman‐Helpman model, assume away the knowledge-spillovers aspect of FDI. We also present econometric evidence (using industry-level data from seven OECD nations) that broadly supports the model. Specifically, we find industry-level scale effects and international knowledge spillovers that are unrelated to FDI, but we also find that bilateral spillovers are boosted by bilateral FDI.

A self-consistent theoretical model for macropore growth in n-type silicon

In this work, a theoretical study on the growth of macropores fabricated from n-type silicon by photoelectrochemical etching in HF-based electrolytes is reported. By solving the diffusion equation into the pores, we deduce a self-consistent model which can be used for quantitative prediction of the growth speed and pore depth. The limiting factor of the growth, i.e., the HF concentration at the pore tip, is shown to be a nonlinear function of the pore depth, a fact not accounted for by the current literature. A reduced model with a closed analytical solution is presented as well. Finally, the predictions of the full and reduced models are compared with the experimental data.

Theoretical model and experimental study of pore growth during thermal expansion of graphite intercalation compounds

A new technique, which allows one to simultaneously follow the mass and volume of graphite intercalation compounds (GICs) during thermal transformation into expanded graphite, was developed. This enabled us to elucidate the mechanism for the thermal expansion of GICs and formulate a quantitative model for the process. Effective activation parameters of the thermal decomposition of new GICs were obtained by using non-isothermal kinetics procedure. Thermal decomposition was described as a break of intermolecular bonds followed by diffusion.

Gravitational Lensing Signatures of Supermassive Black Holes in Future Radio Surveys

Observational measurements of the relationship between supermassive black holes (SMBHs) and the properties of their host galaxies are an important method for probing theoretical hierarchical growth models. Gravitational lensing is a unique mechanism for acquiring this information in systems at cosmologically significant redshifts. We review the calculations required to include SMBHs in two standard galactic lens models, a cored isothermal sphere and a broken power law. The presence of the SMBH produces two primary effects depending on the lens configuration, either blocking the ‘‘core’’ image that is usually predicted to form from a softened lens model or adding an extra, highly demagnified image to the predictions of the unaltered lens model. The magnitudes of these effects are very sensitive to galaxy core sizes and SMBH masses. Therefore, observations of these lenses would probe the properties of the inner regions of galaxies, including their SMBHs. Lensing cross sections and optical depth calculations indicate that to fully observe these characteristic signatures, flux ratios of order 10 6 or more between the brightest and faintest images of the lens must be detectable, and thus, the next generation of radio telescope technology offers the first opportunity for a serious observational campaign. Core images, however, are already detectable, and with additional observations their statistics may be used to guide future SMBH searches. Subject headings: black hole physics — galaxies: evolution — gravitational lensing — surveys — telescopes