The two dimensional one component plasma 2dOCP is a classical system consisting of N identical particles with the same charge q confined in a two dimensional surface with a neutralizing background. The Boltzmann factor at temperature T may be expressed as a Vandermonde determinant to the power Γ = q 2 /(kBT ). Several statistical properties of the 2dOCP have been studied by expanding the Boltzmann factor in the monomial basis for even values of Γ. In this work, we use this formalism to compute the energy of the 2dOCP on a sphere. Using the same approach the entropy is computed. The entropy as well as the free energy in the thermodynamic limit have a universal finite-size correction term χ 12 log N , where χ = 2 is the Euler characteristic of the sphere. A non-recursive formula for coefficients of monomial functions expansion is used for exploring the energy as well as structural properties for sufficiently large values of Γ to appreciate the crystallization features for N = 2, 3, . . . , 9 particles. Finally, we make a brief comparison between the exact and numerical energies obtained with the Metropolis method for even values of Γ.

We present an analytic strategy to find the electric field generated by surface electrode SE with angular dependent potential. This system is a planar region A kept at a fixed but non-uniform electric potential V (φ) with an arbitrary angular dependence. We show that the generated electric field is due to the contribution of two fields: one that depends on the circulation on the contour of the planar region -in a Biot-Savart-Like (BSL) term-, and another one that accounts for the angular variations of the potential in A. This approach can be used to find exact solutions of the BSL electric field for circular or polygonal contours of the planar region with periodic distributions of the electric potential. Analytic results are validated with numerical computations and the Finite Element Method.

Electric vector potential Θ(r) is a legitimate but rarely used tool to calculate the steady electric field in free-charge regions. Commonly, it is preferred to employ the scalar electric potential Φ(r) rather than Θ(r) in most of the electrostatic problems. However, the electric vector potential formulation can be a viable representation to study certain systems. One of them is the surface electrode SE, a planar finite region A− kept at a fixed electric potential with the rest grounded including a gap of thickness ν between electrodes. In this document we use the Helmholtz Decomposition Theorem and the electric vector potential formulation to provide integral expressions for the surface charge density and the electric field of the SE of arbitrary contour ∂A. We also present an alternative derivation of the result found in [M. Oliveira and J. A. Miranda 2001 Eur. J. Phys. 22 31] for the gapless (ν = 0) surface electrode GSE without invoking any analogy between the GSE and magnetostatics. It is shown that electric vector potential and the electric field of the gapped circular SE at any point can be obtained from an average of the gapless solution on the gap.

The potential of sawmill wastes as a raw material in pyrolysis process is presented in this study. Non-isothermal thermogravimetric analysis (TGA and DTG) and isoconversional methods were employed to determine triplet kinetic (activation energy, reaction model and pre-exponential factor). Through TGA and DTG, the conversion degree is described as a function of temperature for five heating rates (10, 20, 30, 40 and 50o C/min) and four model-free methods (Flynn-Wall-Ozawa (FWO), Kissinger-Akahira-Sunose (KAS), Friedman, and Vyazovkin) with temperatures ranging from 25 to 1000°C were employed. Isoconversional lines were built for every method at different isoconversional degrees α∈true[0,1true]. The activation energy E was found as a function of α in the interval χII=true[0.2,0.7true] where each isoconversional methods were in agreement and the estimated error was sufficiently small. Findings show the same activation energy profile independently of the isoconversional method. In particular the total variation of E in χII was as follows: 209.909–228.238 kJ/mol (FWO); 211.235–229.277 kJ/mol (KAS); 223.050–188.512 kJ/mol (Friedman), and 211.449 kJ/mol-229.512 kJ/mol (Vyazovkin). The reaction model of the process in χII matched with a two-dimensional diffusion (D2) by using a master-plot analysis. The calculated and reported parameters are fundamental information for the pyrolysis reactor design using Sawmill wastes as feedstock.