Theoretical Outline

The tunnel current given by (1) measures the overlap of the electronic wave functions of the tip and the sample at the gap distance. The tip wave functions probe the sample wave functions as schematically shown in Fig. Ic. According to Bardeen [12] jt, the tunnel current density, takes the following form, 

To evaluate it is necessary to know explicitly the wave functions of the tip and the sample. Unfortunately, the geometry and the structure of the tip at the atomic level are generally poorly defined so that accurate calculations of the tip wave functions are not feasible. This problem can be solved through a different approach proposed by Tersoff and Hamann [14]. This model considers an ideal tip with the smallest dimension compatible with the highest resolution and it intends to measure the properties of the sample surface instead of the properties of tip-sample system. Thus, the tip on the limit i —0, is replaced by a point located at the distance fq perpendicular to the surface sample. For small Vt and r, jt is given by 

the tunneling current is a measure of the local density of states (LDOS) (p) at the Fermi level at the tip position. For a real tip, Fq should be assigned to the tip radius of curvature. More realistic models [15] lead to the same results, i.e. STM images represent closely p(fo, Ef) at the sample surface. Thus, the tip maps profiles of constant LDOS at the Fermi level. 

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Theoretical Outline - Dynamics of Junctions and Trapped Linear Chains... 

Theoretical Outline—Influence of the Static Structure on the Dynamics... 

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Prior to this discussion of experimental n.m.r. data, a brief theoretical outline of annulene chemistry will be included, which begins with a consideration of the phenomenon of bond alternation in the next section. An understanding of bond alternation is necessary as it augments Hiickel s rule in delineating more precisely the relationship between the annulenes and the corresponding linear polyenes. A section will then be devoted to a consideration of some of the more important experimental parameters (other than magnetic properties) which have been studied in relation to aromaticity. 

Theoretical investigations by Brand [ 135] and Brand and Pleiner [136] predicted that a monodomain liquid-crystalline elastomer exhibiting a cholesteric or a chiral smectic C phase should display piezoelectric properties due to a modification of the pitch of the helix under strain. So, a piezoelectric voltage should be observed across the sample when a mechanical field is applied parallel to the helicoidal axis. In this description, the crosslinking density is supposed to be weak enough to allow the motion of the director, and deformations of the sample (compression, elongation, etc.) are assumed to be much smaller than those that should lead to a suppression of the helix. The possibility of a piezoelectric effect do not only concern cholesteric and chiral smectic C phases, but was also theoretically outlined for more exotic chiral layered systems such as chiral smectic A mesophases [137]. 

Monteil, J.M. (in press) Toward a social psychology of cognitive functioning Theoretical outline and empirical illustrations. In M. Von Cranach, W. Doise, G. Mugny (Eds.) Social representations and the social bases of knowledge. 

In what follows we give a theoretical outline of the methods and then take the reader through the steps using a practical example. For further information and examples the reader may consult references (7-9). 

The following theoretical outline is limited to a presentation of the definitions and equations necessary for the description of the diffraction of electrons from free molecules. More detailed theoretical surveys, including the deduction of the equations, have been given by various authors. > ... 

A. Source As is clear from the theoretical outline, an exponential assembly requires an external source of neutrons to maintain a steady state. Ideally, the energy distribution of these source neutrons should be equivalent to the neutron spectrum of the lattice. This is approximately realized in practice by the introduction of thermal neutrons into the assembly. 

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