We consider Coulomb gas models for which the empirical measure typically concentrates, when number of particles becomes large, on an equilibrium minimizing electrostatic energy. study behavior is conditioned a rare event. first show that special case quadratic confinement and linear constraint exactly solvable due to remarkable factorization, conditioning has then simple effect shifting cloud w...

Super Earth exoplanets are being discovered with increasing frequency and some will be able to retain stable H2-dominated atmospheres. We study biosignature gases on exoplanets with thin H2 atmospheres and habitable surface temperatures, by using a model atmosphere with photochemistry, and biomass estimate framework for evaluating the plausibilty of a range of biosignature gas candidates. We fi...

There are only a handful reports about the sensor systems having the ability of detecting the existence of the noble gases. Chemical reluctance of these gaseous species causes them to have no chemical interactions like hydrogen bonding with the chemically designed nano-sized sensors. Noble gasses usually have no atomic charges nor do change the total polarity of the molecular sensor systems. Th...

Super Earth exoplanets are being discovered with increasing frequency and some will be able to retain stable H2-dominated atmospheres. We study biosignature gases on exoplanets with thin H2 atmospheres and habitable surface temperatures, by using a model atmosphere with photochemistry, and biomass estimate framework for evaluating the plausibilty of a range of biosignature gas candidates. We fi...

Simultaneous reactions between solids and gases are very important in the chemical and metallurgical processes. In the modeling, the chemical reaction and diffusion of gases must be considered. Therefore, a set of coupled partial differential equations is found. When the kinetic is a function of solid concentration, there is not any analytical solution for these equations. Therefore, numerical ...