We set up and study the hydrodynamic theory for active fluid and tethered membranes. We focus on those membranes which are inversion-symmetric. We show that such membranes are either described by appropriate linear hydrodynamic equations, which are exact in the asymptotic long wavelength limit, giving stable flat phases with positional quasi long range orders, or be linearly unstable, implying crumpling of the membranes. We argue that in a such an active membrane thermal noises dominate over any active noises, and use it to calculate the correlation functions of the undulation and in-plane displacements of the membrane in the stable case, and the associated correlation functions of the embedding bulk flow velocities.
This chapter studies spatio temporal trends of air quality, its relation with urban forms, and Land Surface Temperature (LST) in Kolkata Metropolitan Area, the world's 55th most polluted city according to the World Health Organization. Air quality data were procured from 34 monitoring stations operated by West Bengal Pollution Control Board for 2005-18. Trend analysis showed declining NO2, SO2 values but a rise in PM10 concentration. Interpolation analysis showed high concentration of pollutants along the Hugli industrial belt, Dhulagarh, and Kolkata Municipal Corporation Area. Urban forms such as built-up density, distances from water bodies, parks, and bus stops demonstrated their reasonable influence on air pollution condition. LST generated from Landsat Thermal Infrared bands showed increase in temperature conditions from 2005-2018. Positive Correlation was identified between Land surface temperature and air pollution. Their relationship was assessed to have become stronger over the decades.
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