Stokes parameters, rotation

It is fairly obvious from either (2.81) or (2.83) that there are three quantities associated with the Stokes parameters that are invariant under rotation of the reference directions I, Q2 + U2, and V. In addition, the Stokes parameters are not all independent ... 

Circular dichroism and optical rotation for particulate media may be operationally defined in terms of the Stokes parameters (2.80), which in the circular polarization representation are written... 

The controlling variables for polarization and rotation modulation are given in Table III (see page 724). We can note that the Stokes parameters (.v0,.vi AAAf) defined over the SU(2) dimensional variables, v /, %, of 2,(v(/, x) are sufficient to describe polarization/rotation modulation, and relate those variables to the SO(3) dimensional variables, oo(r,z),8, of Q (0), 5), which are sufficient to describe the static polarization/rotation conditions of linear, circular, left/right-handed polarization/ rotation. 

Figure 11.4 Measurement of the Stokes parameters with a retarder and an ideal perfect linear polarizer rotated with respect to the laboratory reference frame.

When a quarter-wave rotating phase plate is used in a polarization modulator, it is possible to measure parameters of linear and eireular polarization simultaneously, but the aeeuraey of determining Q and U parameters is half that of parameter V. When a PSP with a phase shift of A = 126.52° is used, the accuracy of measurements of all three Stokes parameters is idenrieal. When 92= 0, the formula for right modulation beeomes... 

The same idea was used in the development of a spectropolarimeter for simultaneous measurement of all four Stokes parameters [3-5]. A 127-degree SPSP is rotated with frequency 61 Hz and modulated intensity (4) was divided into 8 equal intervals with the use of special electronic keys ... 

Santamato et ai assumed that with homeotropic boundary conditions the normal component of the optical torque cannot be balanced by an elastic torque, hence the molecules are set into rotation. is balanced by a viscous torque arising from the precession of the director. They established a simple relation between the angular velocity of the director rotation and the total change of the Stokes parameter, S3. This relation was experimentally verified. 

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

Here x is a phenomenological parameter measuring the chirality and / is a size scale factor. Since here the Reynolds number is small ( 10 s), the Stokes equation can be used to get r = DS2. where D is the hydrodynamic drag coefficient and 2 is the rotational speed. The drag coefficient for a cylindrical object rotating about its axis with cross-sectional radius r and length L is D = 4ztT)r2L, where tj is the viscosity of the medium [19]. Therefore, D /3 and the rotational speed 2 of the rotor will scale as... 

A spectroscopic technique that probes membrane fluidity can either directly measure mobility and order parameters for membrane constituents (NMR) or use probes (ESR, fluorescence). Some fluorescent and ESR probes are shown in Fig. 4. The connection between the rotational correlation time of a membrane embedded probe and the membrane fluidity can be illustrated using the example of a simple isotropic liquid, in which fluidity is merely a reciprocal viscosity ri and the rotational correlation time Xc for a molecule with a hydrodynamic volume V is given by the well-known Debye-Stokes-Einstein relation Xc = r VlkT, where k is the Boltzmann constant and T is the... 

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