State the first condition of equilibrium. Explain static equilibrium. Explain dynamic equilibrium. The first condition necessary to achieve equilibrium is the one already mentioned: the net external force on the system must be zero. Expressed as an equation, this is simply netF= 0 Note that if ...
Redox conditionSignificant bromine (Br) isotope composition variations are found in natural salts and brines, which are often even larger than those of co-existing chlorine isotope compositions. The cause of such large Br isotope variations remains elusive. In this study, equilibrium Br isotope ...
On an equilibrium FOT line separating two phases,αandβ, the thermodynamic potentials of the two phases are equal to each other by definition. This condition leads to the Clausius–Clapeyron equation, which is given in the following form for the case of an equilibrium FOT line in anH−Tpha...
Based on the nonequilibrium Green's function (NEGF) and time-dependent density-functional theory (TDDFT), we propose a formalism to study the time-dependent transport behavior of molecular devices from first principles. While this approach is equivalent to the time-dependent wave-function approach ...
. Proof of the First Welfare Theorem (by contradiction) Suppose not: there exists a feasible allocation (x; y) such such that x i % i x i for all i , and x i i x i for some i . Since x i is an equilibrium, x i i x i implies p x i > p ! i + P j ij (p y j...
Half of the electron-electron interaction energy is subtracted from the one-electron value so that these terms are counted once. The full OPW wave function is used to calculate the electron-electron interaction. The results for the equilibrium lattice constant, bulk modulus, and cohesive energy ...
The proof is made on the basis of the observation that the orthogonality condition to the zero modes coincides with the ansatzs posed on the dissipative parts of the energy-momentum tensor and the particle current in the phenomenological equations. We also present an analytic proof that all our...
where mj represents the atomic mass of the jth atom in the primitive unit cell, t, the time, the α (α=x, y, z) component of the atomic displacement from its equilibrium position of the jth atom in the Pth reference primitive unit cell within a supercell. The first term in the righ...
Equilibrium volume, energy and bulk modulus of rutile SnO2 are also calculated. Our results are compared with other available experimental data and theoretical results.Research limitations/implications: Computer calculation speeds and its information storage area are limitations, it will be possible to ...
The calculated equilibrium structural parameters ofOsB2are in agreement with the available experimental results. The calculations indicate that OsB in tungsten carbide is more energetically stable under the ambient condition than the metastable cesium chloride phase of OsB. Results of bulk modulus show ...