We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight μ exp[−Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity μ and the bending rigidity J . In the limit μ → 0, the mean perimeter has the asymptotic behaviour 〈t〉/4 √ A ≃ 1−K...

We review the overlap pathology of the Glasgow reweighting method for finite density QCD, and discuss the sampling bias that effects the determination of the ensemble-averaged fugacity polynomial expansion coefficients that form the Grand Canonical Partition function. The expectation of the difference in free energies between canonical partition functions generated with different measures is pr...

Abstract Magma oceans (MOs) are episodes of large-scale melting the mantle terrestrial planets. The energy delivered by Moon-forming impact induced a deep MO on young Earth, corresponding to last episode core-mantle equilibration. crystallization this led outgassing volatiles initially present in Earth’s mantle, resulting formation secondary atmosphere. During outgassing, acts as chemical buffe...

Sulfur is a key element in terrestrial magmatic processes yet its geochemical behavior remains one of the most difficult to model due heterovalent chemistry. The maximum amount sulfur silicate melt can dissolve before saturating with sulfide (e.g., pyrrhotite) or sulfate anhydrite) changes redox state system and has important implications for budget system. Several empirical models have been de...

Perfume is a non-ideal complex mixture of chemicals originating from the extraction essential oils and these are volatile components extracted plants, some animals, or even synthesized. For this reason, to compose fragrance, there countless possibilities combine one element another, which makes process slow expensive. Therefore, in study, we will three most known accepted cosmetic industry that...