Evidence for the Gompertz curve in the income distribution of Brazil 1978–2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form G(x) = exp [exp (A-Bx)], where x is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution P(x) = βx^-α. This result means that similarly to other countries, Brazil’s income distribution is characterized by a well defined two class system. The parameters A, B, α, β were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil’s economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.     

Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz–Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (∼99%), with the Pareto power law, representing the tiny richest part (∼1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.     

Income distribution patterns from a complete social security database

We analyze the income distribution of employees for 9 consecutive years (2001–2009) using a complete social security database for an economically important district of Romania. The database contains detailed information on more than half million taxpayers, including their monthly salaries from all employers where they worked. Besides studying the characteristic distribution functions in the high and low/medium income limits, the database allows us a detailed dynamical study by following the time-evolution of the taxpayers income. To our knowledge, this is the first extensive study of this kind (a previous Japanese taxpayers survey was limited to two years). In the high income limit we prove once again the validity of Pareto’s law, obtaining a perfect scaling on four orders of magnitude in the rank for all the studied years. The obtained Pareto exponents are quite stable with values around α≈2.5$\alpha \approx 2.5$, in spite of the fact that during this period the economy developed rapidly and also a financial-economic crisis hit Romania in 2007–2008. For the low and medium income category we confirmed the exponential-type income distribution. Following the income of employees in time, we have found that the top limit of the income distribution is a highly dynamical region with strong fluctuations in the rank. In this region, the observed dynamics is consistent with a multiplicative random growth hypothesis. Contrarily with previous results obtained for the Japanese employees, we find that the logarithmic growth-rate is not independent of the income.     

Bipolar diffusion charging of high-aspect ratio aerosols

Recent studies have raised concerns over applicability of the conventional charging theories to non-spherical particles such as soot aggregates and single-walled carbon nanotube aerosols of complex shape and morphology. It is expected that the role of particle structure and shape on particle diffusion charging characteristics may be significant in the submicron size range for carbon nanotubes (CNTs) and nanofibers (CNFs). In this study, we report experimental data on equilibrium charging characteristics of high-aspect ratio aerosol particles such as CNFs and multi-walled CNTs (MWCNTs) when exposed to a bipolar ion atmosphere. A neutral fraction was measured, i.e., the fraction of particles carrying no electrical charge. A differential mobility analyzer (DMA) was used to classify aerosols, leaving a bipolar radioactive charger to infer the bipolar charging characteristics at different mobility diameters in the submicron size range. The measured neutral fractions for CNF aerosol particles were lower than the corresponding Boltzmann values by 24.4%, 42.0%, and 45.8% for mobility diameters of 400 nm, 600 nm, and 700 nm, respectively, while the neutral fractions for measured aerodynamic diameters of 221 nm, 242 nm, and 254 nm were much lower than those expected by Boltzmann charge distribution, by 43.8%, 63.1%, and 67.3%, respectively. Neutral fractions of spherical particles of polystyrene latex (PSL) and diethylhexyl sebacate (DEHS) particles, measured under identical experimental conditions and procedure, agreed well with the Boltzmann charge distribution. The measured neutral fractions for MWCNT aerosol particles were lower than the corresponding Boltzmann values by 22.3%–25.0% for mobility diameters in the size range from 279 nm to 594 nm. Charging-equivalent diameters of CNF particles correlated well with either mobility diameter or equal-area diameter, which were found to be larger than their mobility or equal-area diameters by up to a factor of 5 in the size range of 400 nm–700 nm, while those of MWCNT particles were larger than the corresponding diameters by a factor of 2 in the size range of 279 nm–594 nm.     

Nanostructural analysis of ZnO:Al thin films for carrier-transport mechanisms

The carrier mobility of sputter-deposited Al-doped ZnO transparent-conducting (ZnO:Al) thin films was controlled between 22 and 48 cm²/Vs by varying the ZnO:Al seed layer. The statistical distribution of the [001] grain misorientation was characterized from the X-ray diffraction rocking curve in the range from 0.043 (2.5°) to 0.179 rad (10.2°). The grain-boundary energy barriers (E_b) from Seto's model [1] clearly exhibit linear dependence on the grain-boundary misorientation angle (ω) according to the equation E_b = 78 ± 4 + 173 ± 32 ω meV.     

Evolutionary model of the personal income distribution

The aim of this work is to develop a qualitative picture of the personal income distribution. Treating an economy as a self-organized system the key idea of the model is that the income distribution contains competitive and non-competitive contributions. The presented model distinguishes between three main income classes. 1. Capital income from private firms is shown to be the result of an evolutionary competition between products. A direct consequence of this competition is Gibrat’s law suggesting a lognormal income distribution for small private firms. Taking into account an additional preferential attachment mechanism for large private firms the income distribution is supplemented by a power law (Pareto) tail. 2. Due to the division of labor a diversified labor market is seen as a non-competitive market. In this case wage income exhibits an exponential distribution. 3. Also included is income from a social insurance system. It can be approximated by a Gaussian peak. A consequence of this theory is that for short time intervals a fixed ratio of total labor (total capital) to net income exists (Cobb–Douglas relation). A comparison with empirical high resolution income data confirms this pattern of the total income distribution. The theory suggests that competition is the ultimate origin of the uneven income distribution.     

Formation of liquid cone jet dependent on rise time of driving voltage

This paper reports on transient dynamics of electrospray driven by high step voltage and its dependence on voltage rise time. Three rise times (50 ns, 1.8 μs, and 400 μs) were used to compare influence on liquid dynamics. It was found that, when the applied voltage exceeds a certain level, minute differences in voltage rise time significantly affect jet formation time. A rise time of 50 ns accelerates the jet ejection by about 20% compared with other rise times. These results indicate that optimization of rise time may enable drastic improvement of controllability of drop-on-demand electrospray.     

Fluctuations in Wikipedia access-rate and edit-event data

Internet-based social networks often reflect extreme events in nature and society by drastic increases in user activity. We study and compare the dynamics of the two major complex processes necessary for information spread via the online encyclopedia ‘Wikipedia’, i.e., article editing (information upload) and article access (information viewing) based on article edit-event time series and (hourly) user access-rate time series for all articles. Daily and weekly activity patterns occur in addition to fluctuations and bursting activity. The bursts (i.e., significant increases in activity for an extended period of time) are characterized by a power-law distribution of durations of increases and decreases. For describing the recurrence and clustering of bursts we investigate the statistics of the return intervals between them. We find stretched exponential distributions of return intervals in access-rate time series, while edit-event time series yield simple exponential distributions. To characterize the fluctuation behavior we apply detrended fluctuation analysis (DFA), finding that most article access-rate time series are characterized by strong long-term correlations with fluctuation exponents α≈0.9$\alpha \approx 0.9$. The results indicate significant differences in the dynamics of information upload and access and help in understanding the complex process of collecting, processing, validating, and distributing information in self-organized social networks.     

Scale-free human migration and the geography of social networks

The “gravitational law of social interaction”, by which the probability of a social link decreases inversely with the square of the geographic distance, has been recently documented. The source of this spatial property of social networks, however, is yet unknown. The formation of social links is related to human dynamics both on the day-to-day, typically small scale, level of mobility, and on larger scale migration (or reallocation) movements. In this study we analyze human migration patterns by investigating the migration of 46.8 million individuals across the US during 1995-2000. We find that the probability of migration decreases as a power law of the distance, with exponent −1. We show that this finding offers an explanation for the gravitational law of social interaction. Possible explanations and implications of the scale-free migration pattern are discussed.     

Income distribution dependence of poverty measure: A theoretical analysis

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the ‘global’ mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy.     

Charged surface states scattering in AlGaN/GaN heterostructures

The electron mobility limited by charged surface states scattering was calculated accurately based on a self-consistent Schrödinger and Poisson equations solver. For a AlGaN thickness less than 5 nm, this new scattering mechanism is the dominated scattering for electron mobility. Moreover, there is a “high electron mobility window” for a certain AlGaN thickness range from 4 to 7 nm, where the electron mobility can be as high as 3000 cm²/Vs at a low temperature, which is consistent with reported experimental data [1] (Cao and Jena, 2007).     

Effect of ultrasonic treatment on the activity of sugar metabolism relative enzymes and quality of coconut water

In this study, tender coconuts were treated with high-intensity ultrasound (US) for 20 min at a frequency of 20 kHz and a power of 2400 W. Compared with control group, US treated coconut water had a higher content of total soluble solid and sugar/acid ratio along with a lower pH value and conductivity, and the contents of sucrose, fructose and glucose were also higher. Results from HS-SPME/GC–MS showed that there was no significant difference in the content of volatile compounds in coconut water before and after US treatment. The activities of sugar metabolism enzymes such as sucrose phosphate synthase, sucrose synthase, acid invertase (AI) and neutral invertase were inhibited by US, of which AI had the strongest inactivation. Circular dichroism and fluorescence spectra showed that the secondary and tertiary structure of AI molecule were destroyed with the increase of US intensity and time, which was confirmed by the change of particle size distribution pattern and scanning electron microscopy. Molecular docking and molecular dynamics showed that US treatment prevented the recognition and binding of sucrose and AI molecules, thereby inhibiting the decomposition of sucrose. In conclusion, our results indicate that US can inhibit the activity of AI and maintain the sugar content to increase the quality as well as extend the shelflife of coconut water, which will bring more commercial value.     

The impact of quick-freezing methods on the quality,moisture distribution and microstructure of prepared ground pork during storage duration

The aim of present study was to investigate the influences of ultrasound-assisted immersion freezing (UIF), immersion freezing (IF) and air freezing (AF) on the quality, moisture distribution and microstructure properties of the prepared ground pork (PGP) during storage duration (0, 15, 30, 45, 60, 75 and 90 days). UIF treatment significantly reduced the freezing time by 60.32% and 39.02%, respectively, compared to IF and AF (P < 0.05). The experimental results of quality evaluation revealed that the L* and b* values, juice loss, cooking loss, TBARS values and carbonyl contents were decreased in the UIF treated samples, while the a* value, peak temperatures (T_m), enthalpy (ΔH) and sulfhydryl contents were significantly higher than those of IF and AF treated samples (P < 0.05). In addition, low-field nuclear magnetic resonance (LF-NMR) and differential scanning calorimetry (DSC) analysis demonstrated that UIF inhibited the mobility of immobilized water and reduced the loss of immobilized and free water, and then a high water holding capacity (WHC) was achieved. Compared to the IF and AF treatments, the UIF treated PGP samples possessed better microstructure. Therefore, UIF could induce the formation of ice crystals with smaller size and more even distribution during freezing process, which contributed to less damage to the muscle tissue and more satisfied product quality.     

2,5-di(thiophen-2-yl)thiazolo[5,4-d]thiazole-based donor-acceptor type copolymers for photovoltaic cells

Alternating donor-acceptor type copolymers, poly[{5,11-di(9′-heptadecanyl)indolo[3,2-b]carbazole}-alt-{2,5-di(thiophen-2-yl)thiazolo[5,4-d]thiazole-5,5′-diyl}] (PIC-TZ) and poly[{6,6′,12,12′-tetraoctylindeno[1,2-b]fluorene}-alt-{2,5-di(thiophen-2-yl)thiazolo[5,4-d]thiazole-5,5′-diyl}] (PIF-TZ), were synthesized and examined for applications in polymeric photovoltaic cells. The polymers have a fused coplanar main backbone with good planarity for intermolecular packing and high charge mobility. The indolocarbazole and indenofluorene units contain two or four binding sites for alkyl substituents that have pronounced solution processiblity compared to the carbazole and fluorene moieties. The number-average molecular weights (M_n) of the synthesized polymers were determined to be 11,000 g/mol (PDI = 2.27) for PIC-TZ, and 17,000 g/mol (PDI = 1.77) for PIF-TZ. The optical band gap of PIC-TZ and PIF-TZ in film was determined to be 2.14 eV and 2.21 eV, respectively, and an electrochemical study confirmed the desirable HOMO/LUMO levels of the copolymers, which enabled efficient electron transfer and a high open circuit voltage (V_OC) when blending them with fullerene derivatives. The space charge limited current mobility measurements showed a hole mobility of 10⁻³ cm² V⁻¹ s⁻¹ for the copolymers. When the polymers were blended with [6,6]phenyl-C₆₁-butyric acid methyl ester (PCBM), PIC-TZ showed the best performance with V_OC, short-circuit current and power conversion efficiency of 0.86 V, 4.16 mA/cm² and 1.64%, respectively, under AM 1.5G illumination conditions (100 mW cm⁻²).     

Preheated solvent exposure on P3HT:PCBM thin film: A facile strategy to enhance performance in bulk heterojunction photovoltaic cells

In this study, we explored the ability of a preheated solvent (methanol) to induce characteristic changes at the organic active layer/metal interface, thereby improving the performance of fabricated organic photovoltaic (OPV) cells composed of poly(3-hexylthiopene) (P3HT) and a [6,6]-phenyl-C₇₁-butyric acid methyl ester (PCBM) photoactive blend. Our results demonstrate that exposure to methanol (at room temperature, or preheated at 45 °C or 65 °C) improves the performance of the fabricated OPV cells. After preheated methanol exposure, the P3HT:PCBM thin films were tested for crystallinity, morphology, mobility, and photovoltaic characteristics. Our results revealed that use of the preheated solvent on the organic active layer significantly influences the micro/nano scale morphology and phase segregation of the P3HT:PCBM thin films, as well as the charge carrier mobility. It is hypothesized that the side chain ordering of P3HT and redistribution of PCBM could be results of the modified active layer. Consequently, OPV cells modified with the methanol preheated at 65 °C exhibited a power conversion efficiency (PCE) of 3.36%, with open-circuit voltage of 0.59 V, short-circuit current density of 13.83 mA/cm², and fill-factor of 0.41. In contrast, the unmodified P3HT:PCBM thin film (without methanol exposure) showed a PCE of only 2.13%.     

Room evacuation in the presence of an obstacle

The investigation of human behaviour while trying to escape from a room under panic is an important issue in complex systems research. Several authors have called attention to the fact that placing an obstacle near the exit improves the evacuation time of the room (Helbing et al. (2000, 2005) [2] and [8], Hughes (2003) [6], Johansson and Helbing (2005) [16], Piccoli and Tosin (2009) [5]). We studied this effect in the context of the “social force model” (Helbing et al. (2000) [2]). We show that placing an obstacle does not guarantee, by itself, better chances of survival for all pedestrians. The way they choose to avoid the obstacle is critical for their own performance. We found not only that the faster they try to escape, the slower they get out (“faster is slower” effect), but also, the short cut they might take in order to get to the exit will probably do no better (“clever is not always better” effect).     

Spectral variations in the optical transition matrix element and their impact on the optical properties associated with hydrogenated amorphous silicon

Using an empirical model for the density of states functions associated with hydrogenated amorphous silicon, in conjunction with an elementary model for the optical transition matrix elements, we aim to explore how variations in the matrix elements impact upon the spectral dependence of the optical properties associated with this material. We also wish to ascertain as to whether or not the hydrogenated amorphous silicon mobility gap result suggested by Jackson et al. [W.B. Jackson, S.M. Kelso, C.C. Tsai, J.W. Allen, S.-J. Oh, Phys. Rev. B 31 (1985) 5187] is consistent with the results of the experiment. We find that the mobility gap value suggested by Jackson et al. is too large. An upper bound on the mobility gap associated with hydrogenated amorphous silicon of 1.68 eV is suggested instead. Electrical measurements performed on undoped hydrogenated amorphous silicon yield a mobility gap value that is consistent with this bound.     

Microscopic study reveals the singular origins of growth

Anderson [Science 177, 293 (1972)] proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with reality. In the social sciences however, the possibilities to stage experiments to validate it are limited. During the 90's a series of dramatic political and economic events have provided the opportunity to do so. We exploit the resulting empirical evidence to validate a simple agent based alternative to the classical logistic dynamics. The post-liberalization empirical data from Poland confirm the theoretical prediction that the dynamics is dominated by singular rare events which insure the resilience and adaptability of the system. We have shown that growth is led by few singular “growth centers" (Fig. 1), that initially developed at a tremendous rate (Fig. 3), followed by a diffusion process to the rest of the country and leading to a positive growth rate uniform across the counties. In addition to the interdisciplinary unifying potential of our generic formal approach, the present work reveals the strong causal ties between the “softer" social conditions and their “hard" economic consequences.     

Relation of a New Interpretation of Stochastic Differential Equations to Ito Process

Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed. Different interpretations specify different dynamics. Recently, a new interpretation of SDE is put forward by one of us. This interpretation has a built-in Boltzmann-Gibbs distribution and shows the existence of potential function for general processes, which reveals both local and global dynamics. Despite its powerful property, its relation with classical ones in arbitrary dimension remains obscure. In this paper, we will clarify such connection and derive the concise relation between the new interpretation and Ito process. We point out that the derived relation is experimentally testable.