The free energy corresponds to a sum of harmonic oscillations with the frequencies ω1 and ω2, and is consistent with the two-dimensional version of Eq. (5.7) in9. When both a magnetic field and an external force are present, the propagator has not been obtained before. We calculate the...
Two-dimensional coherent interface with nearest-neighbor broken bonds. In a general crystal structure, let zS be the number of bonds across the interface counted per atom and let nS be the number of surface atoms per unit area within the surface plane. Accordingly, we have (6.23)EAAbroken=...
In an atom, an electron circulates around the hidden dimensional axis, and the circulation can further rotate. We propose the quantization conditions for the electron orbiting, and derive the wave functions in concrete for S and P orbitals, which are different from current perceptions. We also ...
It can be seen from Figure10that in the falling process, the hoisting motor of the purely electric drive shovel system is in the power generation state, with the maximum generated power of 262 kW, and the generated energy in this process is 1074 kJ. As for the hydraulic-electric hybrid dr...
Thepotential energyof a configuration of nuclei with their electrons may be represented as a point on anf-dimensional surface in anf+1-dimensional space, wherefis the number of independent variables required to specify the relative positions of all nuclei. For a diatomic molecule (like H2or HF)...
•The manuscript has not been published previously (partly or in full), unless the new work concerns an expansion of previous work (please provide transparency on the re-use of material to avoid the hint of text-recycling (“self-plagiarism”)). •A single study is not split up into ...
This algorithm has proven to be very effective in finding optimal solutions to a wide variety of optimization issues [24,25]. It has shown success, particularly for dynamic optimization issues involving multi-dimensional search spaces [26,27,28]. When compared to other evolutionary algorithms, it...
The total kinetic energy of a body or a system is equal to the sum of the kinetic energies resulting from each type of motion. See mechanics: Rotation about a moving axis.The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Adam Augustyn....
formula ABO3, where the A cations are generally of larger radii and have a 12-fold coordination, while the relatively smaller B metal ions occupy sixfold coordinated positions in the oxygen octahedra. The A-site ions typically have +2 or +3 nominal charge states, while the charge state of...
Consider a three-dimensional quantum harmonic oscillator, with wave functions described by the time-independent Schrödinger equation (in dimensionless units), with V=(x2+y2+z2)/2: (15.56)-12∇2ψ(x,y,z)+12(x2+y2+z2)ψ=Eψ.This equation must be solved subject to the condition th...