Disordered System

A. Bunde, S. Havlin. Fractals and Disordered Systems. Berlin Springer-Verlag, 1991, pp. 1-350. 

Natterniann. Roughening transition of interfaces in disordered systems. Phys Rev Lett S7 1469 (1998). 

Cambridge) and J. H. van Vleck (Harvard) fundamental theoretical investigations of the electronic structure of magnetic and disordered systems. 

For the electronic structure calculations in a disordered system, f is chosen to be the Green function (zI-H( n )) where H is the Hamiltonian of the system and n are the random site occupation variables. According to ASF configuration averaged density of states (DOS) is given by ... 

Figure 6 Theoretical and experimental results for an ordered and a disordered system on the left theoretical data for a CusPt single crystal and on the right experimental findings for a CusPt alloy overlayer on a platinum substrate. The spectra for the ordered species are traced with continuous lines, whereas those for the disordered species are given in dotted lines. The spectra were normalized to equal peak height.

In summary, the OP-term introduced by Brooks and coworkers has been transferred to a corresponding potential term in the Dirac equation. As it is demonstrated this approach allows to account for the enhancement of the spin-orbit induced orbital magnetic moments and related phenomena for ordered alloys as well as disordered. systems by a corresponding extension of the SPR-KKR-CPA method. 

Gonis, A., 1992, Green Functions for Ordered and Disordered Systems, North Holland Elsevier Science Publishers B.V., Amsterdam. 

Since each site of an N, k = A )-net receives inputs from all other sites of the net, this case represents a maximally disordered system at each time step, each site is replaced by a random choice among the 2 possible states. 

In the above consideration it has been tacitly assumed that the charge carrier mobility docs not depend on the electric field. This is a good approximation for molecular crystals yet not for disordered systems in which transport occurs via hopping. Abkowitz et al. [37] have solved that problem for a field dependence of ft of the form p-po (FIFU) and trap-free SCL conduction. Their treatment predicts... 

Commenting on above we should mention that initial expressions (1.59) - (1.63) are valid for disordered systems with exponentially broad spectrum of local values of electric conductivity. Due to existing dependence of 0 on over long times in our case the broad preadsorption spread in can grow narrow. At specific ratios between parameters of the absorbate-adsorbent system it can either vanish at all or there is a notable concentration of leveled-off barriers being formed with the fraction higher than the threshold one Xe- The straightforward analysis of each specific case characterized by a certain relationships between parameters of the system enables one easily obtain conditions... 

The effect can be applied, for example, to estimate a bond length or atomic spacing, to observe valence electron spin distribution around a specific atom and to derive information of the nearest neighbor atom distribution in a disordered system such as amorphous, under an expansion of the theory. 

Lekner J (1991) Summation of coulomb fields in computer-simulated disordered-systems. Physica A 176(3) 485-498... 

The ROA spectra of partially unfolded denatured hen lysozyme and bovine ribonuclease A, prepared by reducing all the disulfide bonds and keeping the sample at low pH, together with the ROA spectra of the corresponding native proteins, are displayed in Figure 5. As pointed out in Section II,B, the short time scale of the Raman scattering event means that the ROA spectrum of a disordered system is a superposition of snapshot ROA spectra from all the distinct conformations present at equilibrium. Because of the reduced ROA intensities and large... 

Fig. 3. Amide F FTIR (left) and VCD (right) of effectively fully disordered systems, unblocked (L-Lys)2 (bottom) and (L-Lys)3 (top) in D2O, having one and two amide groups, respectively. The large deflection to low wavenumber is due to the terminal COO- group. The breadth of the K3 spectrum is due to different environments for the two C=0 groups. Spectra are offset for clarity, and the actual signals measured are roughly at our detection limits for reasonable S/N (A A 5 x 10-6).

This branch of polymer physics is closely connected to another of I.M. Lif-shitz favorite directions in physics, namely, the theory of disordered systems [73]. The situation when different samples have only statistical similarity is typical for the physics of chaos, and many concepts I.M. Lifshitz developed are also quite naturally applied in the physics of disordered polymers. The idea of self-averaging in general and self-averaging of free energy [74], in particular, are examples of such concepts. 

One of the specific features of biology is the possibility of using a living cell in order to produce a macroscopic number of perfectly identical disordered systems (and not just statistically similar systems). This feature of biology opens new perspectives for physics (and for physicists), but, as usual, also presents new challenges. 

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