Theoretical or Mathematical/ Boltzmann equationelectric potentialelectron beam effectselectron radiationgamma-ray effectspotential energy functions/ high-energy electron multiplicationirradiated materialsBoltzm
length 1 (atomic units), and the Schrödinger equation for one electron was solved extremely precisely. Up to 200 cases were used to train an ML model\(T_{\rm{s}}^{{\rm{ML}}}[n]\)for the non-interacting kinetic energy functionalTs[n] via KRR (for details, see Supplementary ...
for the differential equation, which tells us how the density goes down as we go up in energy. 寻找n 和h 之间的关系,就是要找一个微分方程。找微分方程,常常需要这样一个出发点:即在一个微元上找一个力的平衡方程。在这里就是 dPdS= −mgndhdS We thus have an equation for the particle densi...
Thus, a semidiscretisation mimicking this equation might be desirable near the incompress- ible limit. Definition 1 A numerical flux f num = (fρnum, fρnvum, fρneum) for the Euler equations is called kinetic energy preserving (KEP), if the momentum flux can be written as fρnvum =...
Hill-limit; these effects may also be assessed in combination. Equation (3) then gains two additional terms that account for the loss of work to gravitational potential energy, and for the truncation of the strain rate accessible to muscle [see Supplementary Note1and also refs.26,47,48,49]...
The gas laws that we have seen to this point, as well as the ideal gas equation, are empirical, that is, they have been derived from experimental observations. The mathematical forms of these laws closely describe the macroscopic behavior of most gases at pressures less than about 1 or 2 ...
The flux of element A from species j to species k through reaction step i can be calculated5 using the following equation: (1)Aijk=nA,jnA,kriNA,i where nA,j and nA,k are the number of atoms A in species j and k, respectively, and NA,i is the sum of the number of atoms A ...
The Bragg–Hawthorne equation became the mathematical foundation for the throughflow theory of turbomachines. However, Oates et al. [26] introduced a variational formulation of the throughflow problem, leading to robust finite element algorithms. Their variational functional corresponds to the integral of...
Examining enzyme kinetics is critical for understanding cellular systems and for using enzymes in industry. The Michaelis-Menten equation has been widely used for over a century to estimate the enzyme kinetic parameters from reaction progress curves of s
We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear Schrödinger (NLS) equation at the kinetic timescale, under a