RMS displacement length

It is quite simple to alculate the RMS displacement length (r ) from Equation (3.7) since (r > can be given in an integral form as... 

Calculate the RMS displacement length of a polyethylene molecule of relative molecular mass 119 980 taking into account fixed bond angles, but not the effects of restricted rotation. Compare this value with its contour length. 

We are often interested in the rms thermal displacements in A. They correspond to the contravariant components UJk along covariant axes of unit length, rather than along the non-unit length a, b, c axes. The rms displacements are obtained from... 

The root-mean-square (RMS) bond length fiuctuation J , which is calculated at the end of trajectories has been often used for bulk materials. A sharp increase of the 5 value is known as the Lindemann criterion for bulk melting, while in the context of finite-size clusters it has been taken as an indication of transition from solid-like to liquid-like state. However, large atomic displacements can occur which are not representative of isomerization processes... 

However, calculation of a practical micro-cantilever is more complicated than that of an ideal cantilever. A tested sample was fabricated as a cantilever, 15 /rm in width and 90 /rm in length. The bottom electrode was a Pt/Ti layer on the substrate (LTO) and an upper electrode was Pt, coated on a PLZT surface. When a DC voltage was applied across the PLZT layer of the cantilever sample, the PLZT layer was shrunk due to the counter-piezoelectric effect and the cantilever was bent up, as shown in Figure 22-14. The displacement of the cantilever tip can be measured by using a laser interferometer (e.g.. Pan Cross, 1989). The displacement, S, of a cantilever is approximately proportional to the applied voltage V, when V is not very high (V< 10 V). The relationship between S and V can be expressed by the following equation ... 

Here, B is the magnetic field strength, mc is the critical mass (40), q is the charge of the ion in question, rm is the maximum radius required for ejection, a is the inside length of the cubic cell, r is a radial displacement, V-p is the voltage applied to the trap plates, and a = 1.3871 (49) a geometry constant. 

The length scale associated with diffusive transport can be characterized in terms of the root-mean-square (rms) Brownian displacement, which is given by (Hinds 1999) ... 

A craze at the crack tip in glassy polymer has a crack opening displacement of 4 /rm. Given that the fracture toughness is 1 MNm / and the plane strain modulus is 1.5 GPa, calculate the length of the craze and the craze stress. 

Once position versus time data are obtained and stored on a PC hard disk, time differentiation of displacements yields local instantaneous velocities. Ensemble averaged velocity, rms velocity and other turbulence quantities are computed after acquiring the data for a sufficient length of time (e.g. several hours) at fixed operating conditions. 

Simulations were then carried out for 116 ps for both the wild-type and the mutant. The RMS (simulation structure vs starting equilibrated structure) for the mutant [G12A] structure did not equilibrate, whereas the wild-type strucmre did equilibrate over the length of the simulation. Whereas the N-terminus attachment to the main body of the mutant protein remained, the mutation at position 12 led to a relative displacement of the residue 31-47 domain from the residue 1-30 domain. 

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