Superposition theory

The response to a collection of excitations is given by the sum of responses to the individual excitations (i.e., superposition theory holds). 

O. Tapia, Quantum linear superposition theory for chemical processes A generalized electronic diabatic approach, Adv. Quantum Chem. 56 (2009) 31-93. 

Hamaker s linear superposition theory provides a single parameter (the Hamaker constant) to describe the interaction between macroscopic bodies. The force per unit area, /132, between infinite flat plates of media 1 and 2, separated by medium 3, is given... 

Fig. 1. Equation of state in the low density region. SUP—superposition theory, VIR—five-term virial expansion, fv—free-volume theory, 4—four particle results the dots refer to the machine calculations for systems with 32 or more particles.

The numerical results obtained for the equation of state of the three-dimensional hard sphere system in the low density region are shown in Fig. 1. A comparison is made with the equation of state obtained by numerical integration of Eq. (13) subject to Eq. (15), the superposition theory [cf. Eq. (11)], the free-volume equation of state (23), and the five-term virial expansion (32). The last... 

At intermediate densities, 1.5 < v/wq < 1.8, there exists a much more complex two-state behavior of the system. This is of considerable interest in view of the indication from the numerical solution of the superposition theory of a phase transition at or near / 1.5. In the intermediate density region the systems... 

Helfand and Stillinger have recently employed this theory to obtain a suitable "local density correction of the superposition theory for the hard sphere system. While the numerical solution of the modified integral equation is not available at this time, the equation is unique among other approximate theories in )delding the exact value of the fourth virial coefficient. 

Predicting viscoelastic behaviour over long timescales has been attempted using various models, such as developments from the Maxwell and Kelvin/ Voigt models and from time-temperature superposition theory [4]. One durability study on unreinforced thermoplastics [18] involved a loading... 

Another BEM modeling of a jet in the atomization regime was done by Park and Heister [24]. They simulated a swirling jet by using the superposition theory, which implements a complex potential containing a vortex. This potential vortex provides a vortical flow that acts as the circumferential pressure caused by the swirling. Annular ligaments pinched from the parent surface are presumed to break into the... 

The Phenomenology of the Linear Theory of Viscoelasticity. One of the powers of the linear viscoelasticity theory is that it is predictive. The constitutive law that comes from Boltzmann superposition theory requires simply that the material functions discussed above be known for a given material. Then, for an arbitrary stress or deformation history, the material response can be obtained. In addition, the elastic-viscoelastic correspondence principle can be used so that boundary value problems such as beam bending, for which an elastic solution exists, can be solved for linear viscoelastic materials as well. Both of these subjects are treated in this section. 

Fig.la, lb, and Ic show G and G master curves of the pulp 1 at various cellulose concentrations in NMMO H2O solutions according to the time-temperature superposition theory [13]. In terms of the Tuminello diluted assumption theory [6-8,14], these curves are converted to relative differential MIVD curves of the pulp 1 at different cellulose concentrations in NMMO H2O solutions shown in Fig.2a. Using the same ptrocedure, relative differential MIVD curves of the pulp 2 and 3 are obtained at various cellulose concentrations in NMMO H2O solutions and presented in Fig.2b and 2c, respectively. Meanwhile, the calculated log (1/cDp), cr and PDI values of the three pulps are given in Table 1.

---