Finally, a dynamic equations of sintering driving force and neck growth rate are obtained under the assumption of constant temperature, and the dynamic equation of neck growth was proved to be valid in different phase field parameters and sintering temperatures....
Jiahua Li1,2, Xiaoxue Yang1 & Ying Wu1 We propose a potentially valuable scheme to measure the properties of an external time-harmonic- driving force with frequency ω via investigating its interaction with the combination of a pump field and a probe field in a generic optomechanical sy...
4.2.1. Equation for the equilibrium constant K In this section we recall the relation of K with the midpoint potential of the reactants and their concentration (pH, [O2]). The redox equilibrium between the O2/H2O and S4/S0 couples implies:(3)EO2+RT4FlnO2H+4H2O2=E40+RT4FlnS4H+nS0 ...
11. This is consistent with the previously reported empirical lower limit of a 0.3 eV driving force required for efficient CT in typical polymer:fullerene blends12,13. Understanding the impact of driving force on the CT dynamics is particularly important in organic solar cells, since the...
The total force has been broken down into its three parts (see equation 3): the pressure gradient force (Figures 2a and 2b and 3a and 3b), the magnetic pressure force (Figures 2c and 2d and 3c and 3d) and the magnetic tension force (Figures 2e and 2f and 3e and 3f). Figures 2a...
included the target into the variable range and gave the update equation of the target; they decouple the position, speed and direction. The position and speed are calculated by the uniform speed model, and the direction is determined by the strategy; this model also considers the influence of...
Assuming now a time-dependent λ(t) in the KPZ equation (1), there are a number of interesting properties, three of which we now describe. Our main working hypothesis will be that the scaling relation (2) still remains valid. 1. The equation has an invariance under a generalized “Galile...
We derive a linear viscoelastic generalization of Frenkel's model that predicts the deformation of two spheres compressed by a force, F, and surface tension, γ. The resulting equation is then embedded in field equations governing the collapse of macroscopic films. Assuming a uniaxial compression ...
Pontryagin's minimum principle (PMP), formulated in 1956 by the Russian mathematician Lev Pontryagin and his students, is a special case of Euler-Lagrange equation of the calculus of variations. The principle stipulates that the optimal solution to the global optimisation problem must satisfy the co...
Bio-economic models contain a single mathematical equation to represent a biological process. The logistic equation is the most commonly used function to capture the essential features of population densities in fishery and forestry management. However, there exists an increasing trend towards simulation ...