Flat landscape

In transport-limited conditions, however, susceptibility is not so important due to the isolating effect of thick soils. In the extreme situation of a flat landscape lowering at a uniform rate, the erosional contribution by a particular rock type should be related only to the area exposed. Solids would be cation-deficient. 

Figure 6.2 Relief map of the electron density in the molecular plane of SCI2. The vertical direction (z axis) is used to show the value of p, which depends on the two coordinates (x,y) describing the molecular plane. The value of p at the nuclear positions is of the order of 3 X 103 au but the peaks have been truncated at 15 au. Note the dramatic behavior of the electron density in the vicinity of the nuclei there are huge peaks appearing on a nearly flat landscape.

At the Endeavor (formerly Elura) Mine (43 km NNW of Cobar), the main lens of the Elura Zn-Pb-Ag orebodies is subcropping with a small patch of gossanous float present in an essentially flat landscape. There Pb in saprolite (>50 ppm in an area 1.4 x 1.0 km) and lag (>50 ppm in an area 2.5 x 1.6 km) define the underlying mineralisation. However Zn in soil is anomalous for >1 km to the southwest of the main lens (Lorrigan... 

Simulations of RNA secondary structure landscapes provide insight into the necessary mutation rate to drive adaptation. Huynen etal. (1996) found that the ability of a population to adapt is determined by the error threshold of the fitness and not the sequence. Indeed, they found that any mutation rate greater than zero will cause the population to drift on the neutral network [The error threshold on landscapes with high neutrality approaches zero (Derrida and Peliti, 1991).] A second, higher mutation threshold causes the fitness information to be lost. To accelerate the diffusion of the population on the neutral network, it is necessary to be above the sequence error threshold and as close to the fitness error threshold as possible. Under these criteria, the population will diffuse rapidly without losing fitness information. On a flat landscape, the diffusion constant D0 for a population of M sequences of length N can be approximated by Eq. (37). 

Fig. 21. The diffusion constant on a neutral network D0 is plotted versus the mutation rate pm. The simulations ( ) are for RNA sequence length N = 76 and population size M = 1000 and are allowed to equilibirate before the statistics are taken. The solid line is the theoretical D0 and ( ) are flow-reactor simulations for a flat landscape. The dotted line is calculated for D0X, where A = 0.3 is the estimated fraction of neutral mutants. Reprinted from Huynen etal. (1996) with permission. Copyright (1996) National Academy of Sciences, USA.

Northwest Utah is the site of the Bonneville Salt Flats—an area covered with a hard, flat, salt crust that formed in ancient times. Located near F80, the salt flats cover 46 square miles (119 square kilometers) and are mainly comprised of sodium chloride (common table salt). The flat landscape, which is home to the Bonneville Speedway, has helped many auto racers set speed records for nearly 100 years. IMAGE COPYRIGHT 2009, MDD. USED UNDER LICENSE FROM SHUTTERSTOCK.COM. 

Figure 4 A sketch of the process of metadynamics. First the system evolves according to a normal dynamics, then a Gaussian potential is deposited (solid gray line). This lifts the system and modifies the free-energy landscape (dashed gray line) in which the dynamics evolves. After a while the sum of Gaussian potentials fills up the first metastable state and the system moves into the second metastable basin. After this the second metastable basin is filled, at this point, the system evolves in a flat landscape. The summation of the deposited bias (solid gray profile) provides a first rough negative estimate of the free-energy profile.

At the equilibriuni potential, some steps are uphill in free energy, meaning that the reaction on the surface is slow. A perfect catalyst in this analysis would be characterized by a flat potential energy landscape at the equilibrium potential, i.e., by all steps having the same height at zero potential. Whereas no such catalyst has yet been found, we can define the highest potential at which all steps are just downhill in free energy, C/qrr-Below we would say that the reaction starts to be transport-limited. At potentials... 

Comparing Figure 4-5 with the corresponding plot from the straight line fit in Figure 4-3, an important difference is that the landscape is no longer parabolic. There is a flat region and a very steep increase at the back comer. Nevertheless, the contour lines clearly indicate that there is a minimum near the correct position. 

Fig. 4. (a) Snapshots of the energy distribution after initial excitation of Chls B12 (left) and B27 (right). All Chls are illustrated by dots at 0 fs for clarity, after 0 fs, only Chls with substantial excitation are illustrated, (b) Same as (a) except in an artificially flat energy landscape. 

Fig. 5 ID example of a cost function hypersurface (broken line) and the landscape of the flat plateaux that is formed from the minimised cost function (solid line). Here, it may be easier to find the global minimum of the solid line rather than that of the broken line as the former contains no barriers...

---