The phrase "analytical equations and" is correct and usable in written English.
It can be used in contexts discussing mathematical or scientific concepts, particularly when referring to equations that involve analysis or problem-solving.
Example: "In our research, we will focus on analytical equations and their applications in modeling complex systems."
Alternatives: "analytical formulas and" or "analytical expressions and".
The comparisons show that both the new analytical equations and numerical solutions give a remarkably good description of the data.
In contrast to complex and time-consuming numerical simulations, analytical equations and heuristicapproximations are used to model the system performance.
At first, the finite element analysis of cantilever based biosensors is evaluated utilizing analytical equations and published experimental results.
Then, a quantitative way by analytical equations and graphs is proposed to evaluate the grasp stabilization with respect to spring stiffness.
In order to reduce computational time, some approximations and simplifications have been applied to make analytical equations and calculations simpler and manageable.
The self-contained and ready-to-implement set of analytical equations and logical operations is presented along with the main underlying physical-mechanical principles and assumptions.
However, although the issue is "only" to understand the single droplet, merely in a few basic cases analytical equations are available and applicable, and results based on CFD methods have to be judged with care.
So it is concluded that the same analytical equations of mass and charge transfer can be used in both the RDE and the IRDE reactor.
Analytical equations for porosity and formation resistivity factor, which govern the flow of electricity through the model were derived with no adjustable parameters.
The general formula is applied on the set of parameters typically available for structural stainless steels in Europe (0.2% and 1.0% proof strength and ultimate strength) and compared to the existing models by curve-fitting of analytical equations to measured stresses and strains of austenitic, duplex and ferritic stainless steels.
The authors established geometric and analytical equations to satisfactorily express the discomfort that vehicle occupants experience while traversing an RPC and the crossing risk to pedestrians.
