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...
Theoretical or Mathematical/ Boltzmann equationelectric potentialelectron beam effectselectron radiationgamma-ray effectspotential energy functions/ high-energy electron multiplicationirradiated materialsBoltzmann kinetic equationelectron collision cascade formationnonrelativistic high-energy electrons...
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 =...
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 ...
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 ...
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
The <η| representation seems to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.关键词: Theoretical or Mathematical/ eigenvalues and eigenfunctions energy states Morse potential quantum theory/ energy level formula Morse oscillator kinetic coupling ...
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 ...
Mathematical Physics Partial Differential Equations Statistical Mechanics Stochastic Partial Differential Equations Notes To be more precise, the cubic stochastic heat equation corresponds to the overdamped Langevin equation induced by (1.5). The energy (1.5) also induces an underdamped Langevin equation...
Catoire, F., Wang, W.-M.: Bounds on Sobolev norms for the defocusing nonlinear Schrödinger equation on general flat tori. Commun. Pure Appl. Anal.9(2), 483–491 (2010) MathSciNetMATHGoogle Scholar Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Dilute Gases...