Curves Local characteristics

The global characteristics of the curve such as its control, degree, and class are defined for the entire curve. Calculations during creation, modification, and application of a curve use the following local characteristics (Figure 3-30) ... 

For a distillation process not only the stationary point type, but also the behavior of the residue curve in the vicinity of the stationary point is of special importance. If the residue curves in the vicinity of the specific point are tangent to any straight line (singular line) (Fig. 1.4a, b, d, e, g, h), the location of this straight line is of great importance. A special point type and behavior of residue curves in its vicinity are called stationary point local characteristics. 

In this study, in order to compare the empirical and analytical DPMs, previously available fragility curves for masonry and reinforced concrete buildings are used (Erberik 2008a, b). These curves are derived using the analytical method described previously, and they present the local characteristics of existing reinforced concrete and masonry buildings in Turkey. They are also validated against real data from... 

Apparatus stress X local stream curve Characteristics in ... 

Curves showing the cnrrent densities as functions of x are presented for two val-nes of electrode thickness in Fig. 18.5. The parameter L has the dimensions of length it is called the characteristic length of the ohmic process. It corresponds approximately to the depth x at which the local current density has fallen by a factor of e (approximately 2.72). Therefore, this parameter can be nsed as a convenient characteristic of attenuation of the process inside the electrode. 

The formation of pores during anodization of an initially flat silicon electrode in HF affects the I-V characteristics. While this effect is small for p-type and highly doped n-type samples, it becomes dramatic for moderate and low doped n-type substrates anodized in the dark. In the latter case a reproducible I-V curve in the common sense does not exist. If, for example, a constant potential is applied to the electrode the current density usually increases monotonically with anodization time (Thl, Th2]. Therefore the I-V characteristic, as shown in Fig. 8.9, is sensitive to scan speed. The reverse is true for application of a certain current density. In this case the potential jumps to values close to the breakdown bias for the flat electrode and decreases to much lower values for prolonged anodization. These transient effects are caused by formation of pores in the initially flat surface. The lowering of the breakdown bias at the pore tips leads to local breakdown either by tunneling or by avalanche multiplication. The prior case will be discussed in this section while the next section focuses on the latter. 

The resultant pair potentials for sodium, magnesium, and aluminium are illustrated in Fig. 6.9 using Ashcroft empty-core pseudopotentials. We see that all three metals are characterized by a repulsive hard-core contribution, Q>i(R) (short-dashed curve), an attractive nearest-neighbour contribution, 2( ) (long-dashed curve), and an oscillatory long-range contribution, 3(R) (dotted curve). The appropriate values of the inter-atomic potential parameters A , oc , k , and k are listed in Table 6.4. We observe that the total pair potentials reflect the characteristic behaviour of the more accurate ab initio pair potentials in Fig. 6.7 that were evaluated using non-local pseudopotentials. We should note, however, that the values taken for the Ashcroft empty-core radii for Na, Mg, and Al, namely Rc = 1.66, 1.39, and... 

---