Dynamic bias

Recently, a novel hybrid radioactive particle tracking (RPT) facility has been developed where the calibration step for the radioactive particle was eliminated (Khane and Al-Dahhan, 2013). The new technique is claimed to minimize the dynamic bias associated with the original CARPT... 

Because the prior distribution is not imiform, the characterization of a dynamical bias is a distribution of final states that is deviant Ifom the prior distribution. This, by itself, is already an insightful point. Because the total eneigy is conserved, when we specify, say, the vibrational state of the product we at the same time implicitly specify limitations on what other states are accessible. This is particularly the case for the vibration because it can take up large chunks of the total energy, but it is equally true if we were to specify, say, a rotation. There are 2j + 1 quantum states of a given j, but in the absence of a dynamical bias the rotational state distribution will not quite go as Ij + 1 because of the implications of the conservation of energy. 

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

For an artificial lipid bilayer of any size scale, it is a general feature that the bilayer acts as a two-dimensional fluid due to the presence of the water cushionlayer between the bilayer and the substrate. Due to this fluidic nature, molecules incorporated in the lipid bilayer show two-dimensional free diffusion. By applying any bias for controlling the diffusion dynamics, we can manipulate only the desired molecule within the artificial lipid bilayer, which leads to the development of a molecular separation system. 

The most intriguing aspect of the self-spreading lipid bilayer is that any molecule in the bilayer can be transported without any external bias. The unique characteristic of the spreading layer offers the chance to manipulate molecules without applying any external biases. This concept leads to a completely non-biased molecular manipulation system in a microfluidic device. For this purpose, the use of nano-space, which occasionally offers the possibility of controlling molecular diffusion dynamics, would be a promising approach. 

Figure 8.9 Dynamics of STM-driven desorption and dissociation of chlorobenzene at Si(lll) (7 x 7) (a) before and (b) after a desorption scan the circles indicate the positions of chlorobenzene molecules before and after desorption (c) appearance of a chlorine adatom formed by dissociation of chlorobenzene with corresponding 3D image (d) measured rates of desorption and dissociation as a function of tunnelling current for a sample bias of + 3 V. (Reproduced from Ref. 26).

We will now turn our attention to the reconstruction of free energy profiles using the Jarzynski identity. This identity can be cast in terms of an equilibrium average, (8.49), as explained in Chap. 5. We can then bias the dynamics to follow the motion of the pulling potential, enhancing sampling of the low-work tail of the work distribution and thereby increasing the accuracy of the calculation. 

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