A note on global dynamics and imbalance effects in the Lucas-Uzawa model

In the traditional literature on the Lucas-Uzawa model, it is proved that in the neighborhood of the long-run balanced growth path, human capital stock grows at a rate greater than its long-run counterpart when the ratio physical to human capi- tal is above its long run value if and only if the capital share in the production of physical good is lower than the inverse of the elasticity of intertemporal substitution in consumption. We first prove that the claim is true outside the neighborhood of balanced growth paths. More importantly, we identify a crucial asymmetry: what- ever the position of the capital share with respect to the inverse of the elasticity of intertemporal substitution, physical capital stock always grows at a rate lower than its long-run counterpart when the ratio physical to human capital is above its long run value.Lucas-Uzawa, hypergeometric functions, imbalance e®ects, global dynamics.

Growth vs. level effect of population change on economic development: An inspection into human-capital-related mechanisms

This paper studies the different mechanisms and the dynamics through which demography is channelled to the economy. We analyze the role of demographic changes in the economic development process by studying the transitional and the long-run impact of both the rate of population growth and the initial population size on the levels of per capita human capital and income. We do that in an enlarged Lucas-Uzawa model with intergenerational altruism. In contrast to the existing theoretical literature, the long-run level effects of demographic changes, i.e. their impact on the levels of the variables along the balanced growth path, are deeply characterized in addition to the more standard long-run growth effects. We prove that the level effect of the population rate of growth is non-negative (positive in the empirically most relevant case) for the average level of human capital, but a priori ambiguous for the level of per capita income due to the interaction of three transmission mechanisms of demographic shocks, a standard one (dilution) and two non-standard (altruism and human capital accumulation). Overall, the sign of the level effects of population growth depend on preference and technology parameters, but numerically we show that the joint negative effect of dilution and altruism is always stronger than the finduced positive human capital effect. The growth effect of population growth depends basically on the attitude to intergenerational altruism and intertemporal substitution. Moreover, we also prove that the long-run level effects of population size on per capita human capital and income may be negative, nil, or positive, depending on the relationship between preferences and technology, while its growth effect is zero. Finally, we show that the model is able to replicate complicated time relationships between economic and demographic changes. In particular, it entails a negative effect of population growth on per capita income, which dominates in the initial periods, and a positive effect which restores a positive correlation between population growth and economic performance in the long term.Human Capital, Population Growth, Population Size, Endogenous Growth, Level Effect, Growth Effect

Light transmission in nanocellular polymers: Are semi-transparent cellular polymers possible?

This work presents the light transmission through a collection of solid cellular polymers based on poly (methyl methacrylate) (PMMA) with cells sizes covering the micro and nano-scale. The obtained results showed that the behavior of light transmission when cell size is in the nano-scale is opposite to the one shown by microcellular foams or the one predicted by theoretical models of light scattering (LS). In fact, the expected trend is that a reduction of cell size increases the opacity of the samples. However, for nanocellular polymers based on amorphous polymers reducing the cell size increases the light transmission. Therefore, this result indicates that a further reduction of the cell size could result in cellular polymers optically semi-transparen

The U(1)A anomaly in noncommutative SU(N) theories

We work out the one-loop $U(1)_A$ anomaly for noncommutative SU(N) gauge theories up to second order in the noncommutative parameter $\theta^{\mu\nu}$. We set $\theta^{0i}=0$ and conclude that there is no breaking of the classical $U(1)_A$ symmetry of the theory coming from the contributions that are either linear or quadratic in $\theta^{\mu\nu}$. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in $\theta^{\mu\nu}$. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde

Long-range effects in granular avalanching

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to $r^{-\rho}$, $r$ being the distance traveled by a grain in a single topling event. The exponent $\rho$ controls the average rolling distance. We have shown that the crossover from power law to stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for $1<\rho<2$ where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short range regime for $\rho>2$, where the average rolling distance is independent of the system size.Comment: 5 pages, 3 figure

Directed Molecular Stacking for Engineered Fluorescent Three-Dimensional Reduced Graphene Oxide and Coronene Frameworks

[EN] Three‐dimensional fluorescent graphene frameworks with controlled porous morphologies are of significant importance for practical applications reliant on controlled structural and electronic properties, such as organic electronics and photochemistry. Here we report a synthetically accessible approach concerning directed aromatic stacking interactions to give rise to new fluorogenic 3D frameworks with tuneable porosities achieved through molecular variations. The binding interactions between the graphene‐like domains present in the in situ‐formed reduced graphene oxide (rGO) with functional porphyrin molecules lead to new hybrids via an unprecedented solvothermal reaction. Functional free‐base porphyrins featuring perfluorinated aryl groups or hexyl chains at their meso‐ and β‐positions were employed in turn to act as directing entities for the assembly of new graphene‐based and foam‐like frameworks and of their corresponding coronene‐based hybrids. Investigations in the dispersed phase and in thin‐film by XPS, SEM and FLIM shed light onto the nature of the aromatic stacking within functional rGO frameworks (denoted rGOFs) which was then modelled semi‐empirically and by DFT calculations. The pore sizes of the new emerging reduced graphene oxide hybrids are tuneable at the molecular level and mediated by the bonding forces with the functional porphyrins acting as the “molecular glue”. Single crystal X‐ray crystallography described the stacking of a perfluorinated porphyrin with coronene, which can be employed as a molecular model for understanding the local aromatic stacking order and charge transfer interactions within these rGOFs for the first time. This opens up a new route to controllable 3D framework morphologies and pore size from the Ångstrom to the micrometre scale. Theoretical modelling showed that the porosity of these materials is mainly due to the controlled inter‐planar distance between the rGO, coronene or graphene sheets. The host‐guest chemistry involves the porphyrins acting as guests held through π‐π stacking, as demonstrated by XPS. The objective of this study is also to shed light into the fundamental localised electronic and energy transfer properties in these new molecularly engineered porous and fluorogenic architectures, aiming in turn to understand how functional porphyrins may exert stacking control over the notoriously disordered local structure present in porous reduced graphene oxide fragments. By tuning the porosity and the distance between the graphene sheets using aromatic stacking with porphyrins, it is also possible to tune the electronic structure of the final nanohybrid material, as indicated by FLIM experiments on thin films. Such nanohybrids with highly controlled pores dimensions and morphologies open the way to new design and assembly of storage devices and applications incorporating π‐conjugated molecules and materials and their π‐stacks may be relevant towards selective separation membranes, water purification and biosensing applications.S.I.P. and S.W.B. thank The Royal Society and STFC for funding. B.Y.M. thanks the University of Bath for a studentship (ORS). D.G.C. thanks the Fundación General CSIC for funding (ComFuturo Program). Dr. Jose A. Ribeiro Martins, Professors Jeremy K. M. Sanders and Paul Raithby are acknowledged for training, helpful discussions and porphyrin supramolecular chemistry. The S.I.P. group thanks the EPSRC for funding to the Centre of Graphene Science (EP/K017160/1) and to the Centre for Doctoral Training in Sustainable Chemical Technologies (EP/L016354/1). The authors thank EPSRC National Service for Mass Spectrometry at Swansea and EPSRC National Service for Crystallography at Southampton for data collection. The authors also acknowledge the ERC for the Consolidator Grant O2SENSE (617107, 2014–2019)

Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models

We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical simulations show that there exists a power-law sensitivity to the initial conditions at the statistically stationary state (self-organized critical state). Corresponding growth exponent $\alpha$ for the Hamming distance and the dynamical exponent $z$ are calculated. These values allow us to observe a clear data collapse of the finite size scaling for both versions of the Bak-Sneppen model. Moreover, it is shown that the growth exponent of the distance in the isotropic and anisotropic Bak-Sneppen models is strongly affected by the choice of the transient time.Comment: revised version, 9 pages, 5 eps figures, use of svjour.st

Deducing high pressure behavior for chemically fragile systems: the polymorphism of spironolactone

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Pressure-temperature phase diagram of the dimorphism of the anti-inflammatory drug nimesulide

Understanding the phase behavior of active pharmaceutical ingredients is important for formulations of dosage forms and regulatory reasons. Nimesulide is an anti-inflammatory drug that is known to exhibit dimorphism; however up to now its stability behavior was not clear, as few thermodynamic data were available. Therefore, calorimetric melting data have been obtained, which were found to be TI-L = 422.4 ± 1.0 K, ¿I ¿ LH = 117.5 ± 5.2 J g-1, TII-L = 419.8 ± 1.0 K and ¿II ¿ LH = 108.6 ± 3.3 J g-1. In addition, vapor-pressure data, high-pressure melting data, and specific volumes have been obtained. It is demonstrated that form II is intrinsically monotropic in relation to form I and the latter would thus be the best polymorph to use for drug formulations. This result has been obtained by experimental means, involving high-pressure measurements. Furthermore, it has been shown that with very limited experimental and statistical data, the same conclusion can be obtained, demonstrating that in first instance topological pressure-temperature phase diagrams can be obtained without necessarily measuring any high-pressure data. It provides a quick method to verify the phase behavior of the known phases of an active pharmaceutical ingredient under different pressure and temperature conditions.Postprint (author's final draft

Crystal structure of polymorph II and the pressure-temperature phase diagram of the dimorphic anesthetic butamben

The crystal structure of the low-temperature form II of butamben has been solved in a P21/c space group very similar to that of form I. Form II possesses virtually the same packing as that of the high-temperature form I, and the dimorphism is mainly represented by a small discontinuous change in the size of the unit cell and by a difference in the enthalpy. Because of the small enthalpy difference between the two polymorphs of 375 J·mol–1, it will be difficult to predict the change in the stability hierarchy by computer-aided methods. The pressure–temperature phase diagram, constructed using volume and enthalpy differences between the two phases at ordinary pressure, corresponds to a case of overall enantiotropy, as the I–II and I–L equilibrium lines diverge with increasing pressure. This conclusion is confirmed by the experimental pressure–temperature phase diagram obtained with differential thermal analysis measurements under pressurePeer ReviewedPostprint (author's final draft