Symmetry of uniaxial global Landau-de Gennes minimizers in the\ud theory of nematic liquid crystals

We extend the recent radial symmetry results by Pisante [23] and Millot & Pisante [19] (who show that all entire solutions of the vector-valued Ginzburg-Landau equations in superconductivity theory, in the three-dimensional space, are comprised of the well-known class of equivariant solutions) to the Landau-de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau-de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau-de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures

Nanoscale Phase Coexistence and Percolative Quantum Transport

We study the nanoscale phase coexistence of ferromagnetic metallic (FMM) and antiferromagnetic insulating (AFI) regions by including the effect of AF superexchange and weak disorder in the double exchange model. We use a new Monte Carlo technique, mapping on the disordered spin-fermion problem to an effective short range spin model, with self-consistently computed exchange constants. We recover `cluster coexistence' as seen earlier in exact simulation of small systems. The much larger sizes, $\sim 32 \times 32$, accessible with our technique, allows us to study the cluster distribution for varying electron density, disorder, and temperature. We track the magnetic structure, obtain the density of states, with its `pseudogap' features, and, for the first time, provide a fully microscopic estimate of the resistivity in a phase coexistence regime, comparing it with the `percolation' scenario.Comment: 4 Pages, 2 column revtex, 5 figures. Final version, to appear in Phys. Rev. Let

Impact of Economic Growth on Income Inequality: A Regional Perspective

Impact of Economic Growth on Income Inequality: A Regional Perspective Shibalee Majumdar and Mark Partridge Egalitarianism refers to the doctrine of the equality of mankind and the desirability of political, economic and social equality. In this paper, we are going to refer to the concept of economic equality. Theory shows that income inequality is a condition that prevails along with economic growth. According to the utilitarian view, income inequality must exist along with economic growth in order to maximize social welfare. This is in sharp contrast to the egalitarian view according to which, all members of the society should have equal access to all economic resources in terms of economic power, wealth and contribution. Kuznets (1955) introduced the inverted U-shaped Kuznets curve that showed that in an economic system, at the initial level of low economic growth, income inequality is low and as growth occurs, income inequality increases till a threshold, after which, income inequality decreases with increased economic growth. In the United States, income inequality remained stable till the 1970s but then began to increase as earnings increased. This has been called the great U-turn by Harris, et. al (1986). Partridge et. al (1996) notes that while Kuznets held the manufacturing sector as the main driver of the economic growth, the current economic growth is being spearheaded by the services sector. While one school of research shows how income inequality might harm economic growth, empirical studies show that in the United States, a positive linkage between economic growth and income inequality has existed since the 1970s. The causality between economic growth and income inequality is an important one. The relationship may differ depending on regions or size of an economy. Fallah and Partridge (2007) show that the impact of inequality on economic growth is opposite in rural and urban settings. Most of the research dealing with the inequality-growth relationship has either looked at the impact of inequality on economic growth (Fallah and Partridge, 2007) or the impact of various socio-economic variables on inequality. Though there has been some research on finding out the causality between economic growth and wage inequality, research assessing whether economic growth affects income inequality, and that too whether the degree of the impact varies between rural and urban regions, are few. The aim of this paper is to see how economic growth affects income inequality. Does improved economic growth lead to a more redistributive system of social welfare or does the polarization become more acute? Does the impact of economic growth on income inequality differ between metropolitan and non-metropolitan areas? Does inequality vary depending on the nature of the agglomeration or the demographic composition of a region? The empirical equation is: ginicsy = gcsy-1 + educsy + popcsy + lcsy + ethcsy + immigcsy + strcsy + σcs + σy + ε where, gini denotes the gini coefficient, g denotes per capita income, edu denotes educational attainment, pop denotes population density, l denotes labour market size, eth denotes ethnic diversity, immig denotes international immigration, str denotes the structural change index, σcs denotes state fixed effects and σy denotes time fixed effects. The subscripts c, s and y denotes county, state and year, respectively. A lagged value of the per capita income is used in order to avoid any endogeneity issues. The analysis for this paper will be done at the county-level. For the dependant variable and all explanatory variables except the per capita income, a panel will be constructed using county-level data for two decades, 1990 and 2000. The gini coefficient will be calculated using the income data from the U.S. Census Bureau. Data on per capita income, educational attainment, population density and international migration can be obtained from the U.S. Census Bureau. The ethnic diversity measure will be calculated using the population data from the U.S. Census Bureau. The structural change index will be calculated by using data from the Bureau of Economic Analysis, Regional Economic Information System. The aim of the paper is to find out whether per capita income (representing economic growth) has an impact on the gini coefficient (representing income inequality), and to show whether this impact varies between rural and urban areas. The expected results are as follows. Economic growth may have a negative impact on income inequality since economic growth is often positively associated with higher investments, higher employment-generating processes and higher employment, hence giving greater access to jobs and income to a larger number of people. The degree of the impact may vary between rural and urban areas because of the following reasons. A higher population density in the urban area may lead to greater job competition and hence lead to lower access to jobs than in rural areas. International immigration is usually higher in urban areas than in rural areas. The greater influx of immigrants, as well as often seen, the willingness of the immigrants to work at lower wages may lead to lower access to jobs for the locals. This should hold true for the low-skilled jobs. For the high-skilled jobs on the other hand, educational attainment of the people will play a more important role on their ability to get jobs in the urban areas than in the rural areas. However, growth may reduce income inequality in the urban areas because higher population density results in more personal contacts, better networking and access to information, and hence more opportunities to access more and better jobs. If the results show that economic growth has a negative impact on income inequality, it will be possible to comment on the causality of the inequality-growth relationship. More so, if it is seen that economic growth has a stronger impact in decreasing income inequality in the urban areas than in the rural areas, it will show that the higher wages and more diverse job opportunities in the urban areas have a greater spillover effect than in the rural areas. The policy implication such a result may have is that higher investments will have to be made in educational and vocational training in order to generate a stream of skilled labourers, which in turn will add to economic growth and thus will lead to lower income inequality and better social cohesion.Regional development, income inequality, spatial relation, Community/Rural/Urban Development,

Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers

We consider three independent Brownian walkers moving on a line. The process terminates when the left-most walker (the `Leader') meets either of the other two walkers. For arbitrary values of the diffusion constants D_1 (the Leader), D_2 and D_3 of the three walkers, we compute the probability distribution P(m|y_2,y_3) of the maximum distance m between the Leader and the current right-most particle (the `Laggard') during the process, where y_2 and y_3 are the initial distances between the leader and the other two walkers. The result has, for large m, the form P(m|y_2,y_3) \sim A(y_2,y_3) m^{-\delta}, where \delta = (2\pi-\theta)/(\pi-\theta) and \theta = cos^{-1}(D_1/\sqrt{(D_1+D_2)(D_1+D_3)}. The amplitude A(y_2,y_3) is also determined exactly

Persistence of a Brownian particle in a Time Dependent Potential

We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times -- leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the confinement, an exponential and an algebraic decay. Analytical calculations and numerical simulations show, that for the case of the exponential relaxation, the dynamics of Brownian particle at short and long times are independent of the parameters of the relaxation. On the contrary, for the algebraic decay of the confinement, the dynamics at long times is determined by the exponent of the decay. Finally, using the two-time correlation function for the position of the Brownian particle, we construct the persistence probability for the Brownian walker in such a scenario.Comment: 7 pages, 5 figures, Accepted for publication in Phys. Rev.