Results for the schematic models

The thus specified Hamiltonians are then used in a dynamic Monte Carlo simulation (see Chapter 1) that is a numerical realization of the discrete time master equation 

A large computational effort has gone into ensuring a high statistical accuracy of the data. The results for Hamiltonian A are averages over 12 800 chains or 128 000 monomers, those for Hamiltonian B were obtained for 28 800 chains and 288 000 monomers, and those for Hamiltonian C used 6600 chains and 132000 monomers. The simulations were done on 64 (A), 500 (B, Id), 16 or 160 (B, 3J) and 33 (Q replicas of a basic simulation box of size 10Q2 (A), 60 (B, Id), 30 (B, 3rf) and 40 (C). 

In order to quantify the qualitative observations from the configurations one should calculate quantities which are sensible to the structural changes 

6 Magnification of the encircled polymer of Fig. 6.4(b) together with parts of its environment. Most of the bonds of the shaded polymer belong to the equivalence class [2,2] since the energy of the chain then becomes small. The open circles mark sites which are blocked by the bond vectors belonging to the classes [3, 0] and [3, 1], respectively. 

---

Fig. 23 column Reduced flow curves (filled squares) for different volume fractions. The solid lines are the results of the schematic model, the dashed line represent the pseudo power law behaviour from [33]. Right column Reduced frequency dependent moduli for different volume fractions. Full symbols/solid lines represent G, hollow symbols/dashed lines represent G". Thick lines ate the results of the schematic model, the thin lines the results of the microscopic MCT. Graphs in one row represent the continuous and dynamic measurements at one volume fraction, (a) and (b) at <]>eff = 0.530, (c) and (d) at (/>eff = 0.595, (e) and (f) at = 0.616, (g) and (h) at < eff = 0.625. and (i) and (j) at = 0.627... 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

In PSpice both a 7414 and a CD4093 were used. The 7414 is the digital model for the Schmitt trigger inverter. To use the digital device for an analog measurement, E sources (voltage-controlled voltage sources) were used as buffers. The schematic used for the PSpice model is shown in Fig. 8.59. The results are displayed in Fig. 8.60. 

From the schematic model of the plasma membrane we have just depicted, it is clear that the two sides, the inner and the outer surfaces, should have different functions as a result of different structures. Moreover, the lipid bilayer may be considered as a hydrophobic barrier preventing diffusion of water-soluble molecules from both sides, thus maintaining a permanent distinction between the inside and outside of a cell. It also allows the membrane to form closed vessels, which appear to be an absolute requirement for maintaining the fixed asymmetric orientations of the cell membrane constituents. 

Figure 17 Main results obtained by combined LEED and XPD measurements on the Sn/Pt(l 11) system. The left row is a schematic representation of the surface structure. The center row shows the XPD results for the SnSds/i peak. The absence of oscillations in the pattern indicates either a disordered surface ( as deposited ) or a single atomic layer (after high temperature annealing) where forward scattering effects cannot play a role. The right row shows the LEED results corresponding to the. structural models described in the text. From [37].

Figure 5. Explanation of an S- T0-type CIDNP net effect with vector models (left), resulting schematic population diagram (center), and NMR spectrum (right). The example describes a radical pair with one proton in radical 1, triplet precursor, product of the singlet exit channel, gq > g2, and positive hyperfine coupling constant. For the vector models, a clockwise sense of precession has been chosen, the labels 1 and 2 designate the radical and a> and /i) the nuclear spin state, and the dotted vertical lines in the projections give the amount of singlet character. For further details, see the text.

Unigraph can he used to visualise the correlation between different variables in the model (Kurowicka et al., 2006). Typically one could start an analysis by selecting a subset of all variables. In the next step one could choose a limited range of one of the variables and look at the resulting visuahzation. As an example in Fig. 1 the top 10 percentile of variable A is selected. The result for the other variables is schematically depicted. 

These two models are represented schematically in Figure 10. The micromodel can approximately represent the behavior of the larger macro-model if they are connected by the displacement coupling technique. The contact results of the macro-model are not used in the further evaluations, and only the displacement results of the proper surfaces are transferred to the micro-model as boundary conditions. The contact problem is solved again in order to find the contact parameters (location of the contact area and the contact pressure distribution) for the micro-model. In order to solve the contact problem, contact elements were located between the contacting bodies. The contact solution follows a linear elastic material law for each component of the models. 

From the analytical results, it is possible to generate a model of the mixture consisting of an number of constituents that are either pure components or petroleum fractions, according to the schematic in Figure 4.1. The real or simulated results of the atmospheric TBP are an obligatory path between the experimental results and the generation of bases for calculation of thermodynamic and thermophysical properties for different cuts. 

---