Positional fluctuations

Molecular dynamics simulations have also been used to interpret phase behavior of DNA as a function of temperature. From a series of simulations on a fully solvated DNA hex-amer duplex at temperatures ranging from 20 to 340 K, a glass transition was observed at 220-230 K in the dynamics of the DNA, as reflected in the RMS positional fluctuations of all the DNA atoms [88]. The effect was correlated with the number of hydrogen bonds between DNA and solvent, which had its maximum at the glass transition. Similar transitions have also been found in proteins. 

To measure the strength of the forces exerted on particles, various analytical techniques have been developed [6, 7]. Unfortunately, since most of these techniques are based on hydrodynamics, assumption of the potential profiles is required and the viscosities of the fiuid and the particle sizes must be precisely determined in separate experiments, for example, using the viscous flow technique [8,9] and power spectrum analysis of position fluctuation [10]. Furthermore, these methods provide information on ensemble averages for a mass of many particles. The sizes, shapes, and physical and chemical properties of individual particles may be different from each other, which will result in a variety of force strengths. Thus, single-particle... 

For the analysis, we developed a new method that makes it possible to observe correlated potentials between two trapped particles. The principle is shown in Figure 7.5. From the recorded position fluctuations of individual particles (indicated by the subscripts 1 and 2), histograms are obtained as a function of the three-dimensional position. Since the particle motion is caused by thermal energy, the three-dimensional potential proflle can be determined from the position histogram by a simple logarithmic transformation of the Boltzmarm distribution. Similarly, the... 

We also calculated the cross-correlations of the position fluctuations in the Xj- and %2-directions at each distance, which method has been utilized for analyzing the... 

Figure 7.7 Cross-correlations of position fluctuations in the Xi- and X2-directions. The distances between the surfaces of the two trapped particles were (a) 1, (b) 3, (c) 5, and (d) 20pm.

On the other hand, in order to observe the influence of the interaction, we also measured the kinetic potentials, which are plotted against the velocities of the particles 1 and 2, when changing the distance from 1 to 20 pm. Since the velocities of the X- and y-directions were obtained by the derivation of the position fluctuations of each particle, the low-frequency components were suppressed and the interaction of two particles would be clearly obtained rather than the position fluctuation. Surely, from the cross-correlation of the velocities and V2x (Figure 7.8), we can observe... 

Starting from the second law of thermodynamics, it is possible to derive a principle according to which the change of entropy production in the neighbourhood of a stationary state is always negative if the flows in the system are kept constant and only the forces varied. As already mentioned, the entropy production reaches a minimum value in the stationary state of the system. If it is at a minimum, and a positive fluctuation occurs, the system reverts to the minimum, and a stable state is again reached. 

Thus, 8 > 1 yields subdiffusion and 8 < 1 superdiffusion. Both cases imply memory. The condition 8 < 1 implies that a strong fluctuation in the positive direction is most probably followed by a fluctuation in the same direction. The condition 8 > 1, on the contrary, implies that after a positive fluctuation, a fluctuation in the opposite direction ensues. Both conditions are a form of memory. In conclusion, the dynamic approach to FBM is a nice way to create memory, with the memory of the variable being the signature of a coordinated and cooperative process, provided that 8 / 1. 

Properties of the membrane studied included the pressure on all six faces of the simulated volume, displacements of lipid molecules and atomic displacements, deuterium order parameter (S p) as a function of chain position, fluctuations of chain and head group dihedral angles, penetration of water, surface area per lipid molecule, and the lipid self-diffusion coefficient. Interesting re-... 

Renaud G, Belakhovsky M, Lefebvre S, Bessiere M (1995) Correlated chemical and positional fluctuations in the gold-nickel system-a synchrotron X-ray diffuse-scattering study. J Phys III 5 1391-1405... 

According to Eq. 13.22b, which was derived previously by Crommen et al. [21], the analyte system peak associated with a sample component corresponds to a positive fluctuation of the additive concentration if this component is eluted before the additive system peak (f.e., if fc >K. and to a negative fluctuation of the... 

Case 1. If m(0 > 0, then qz > 0 and Rf < 0. For this case, positive values of n tend to be associated with positive values of 0 and vice versa. This case corresponds to an unstable atmosphere (decreasing potential temperature with height). If an air parcel moves upward because of a positive fluctuation in its velocity u v it rises to a region of lower potential temperature. However, the air parcel temperature changes adiabatically during this small rapid fluctuation, and its potential temperature remains constant. As a result, the air parcel potential temperature will exceed the potential temperature of its surroundings and will cause a positive potential temperature fluctuation 0 in its new position. 

Such a discrete frequency spectrum can be obtained from the diagonalization of the dynamic matrix. We shall not go into the details here except to mention that the dynamic matrix is a 3V x 3N matrix formed by the mass weighted position fluctuations along the three spatial coordinates of each individual atom. However, if the spectrum is continuous, then the addition can be replaced by integration and a function describing the probability distribution of the frequencies of the spectmm appears. This new function is called the density of state (DOS) and the integration of this function over the whole frequency range is the total number of modes of vibration, 3N 6. 

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