Disordered systems scaling behavior

Fractals can be considered as disordered systems with a non-integral dimension, called the fractal dimension. An important property of fractal objects is that they are self-similar, independent of scale. This means that if part of them is cutout, and then this part is magnified, the resulting object will look exactly the same as the original one. The other distinct property of a fractal is the power law or scaling behavior, where the property and variable of a system are related in the following manner ... 

The charge transport properties in the direction of free-carrier motion in a restricted-dimensional system have important consequences for the magnetotransport effects. This is treated in Sect. 5.3.4. For disordered systems, when the Mott variable-range hopping mechanism [3.58] dominates the conductivity, the temperature scaling law depends on the dimensionality the 3-D conductivity (T3.d varies with temperature following the law log (T3-D oc T, whereas the 2-D conductivity varies as log (T2.D oc T. The transition from 3-D to 2-D behavior has been demonstrated for films of amorphous Ge at a thickness d of 50 nm, as illustrated in Fig. 5.3-9 [3.54]. 

In the second study, Ruscio, Ruscio, and Keane (2002) examined the taxonicity of PTSD in a large sample of male combat veterans (N = 1,230), who were seen at the Behavioral Sciences Division of the Veterans Affairs Boston Healthcare System s National Center for posttraumatic stress disorder between 1985 and 2000. All the participants completed the Mississippi scale (Keane, Caddell,. Taylor, 1988), a 35-item measure of combat-related posttraumatic stress disorder symptoms rated on a five-point scale a subset of this sample (n = 841) was assessed with the Clinician Administered Posttraumatic Stress Disorder Scale (CAPS), an interview measure of posttraumatic stress disorder symptoms that a clinician rates on a five-point scale. According to the CAPS, 68% of the sample qualified for a posttraumatic stress disorder diagnosis. 

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