Rotational kick

If a shallow kick off in soft formation is required (e.g. to steer the borehole away underneath platforms) a technique using jet bit deflection or badgering is employed (Fig. 3.16). A rock bit is fitted with two small and one large jet. With the bit on bottom and oriented in the desired direction the string is kept stationary and mud is pumped through the nozzles. This causes asymmetric erosion of the borehole beneath the larger jet. Once sufficient hole has been jetted, the drill bit will be rotated again and the new course followed. This process will be repeated until the planned deviation is reached. 

The kick-off procedure required numerous single-shot runs to start the deviation in the correct direction. Since, during this phase, the drillpipe was not rotating a steering tool was developed to be lowered on an electric wireline instead of the single shot. The measurements were then made while drilling. 

You have replied that your molecule has a 5-fold axis of rotation. Verify that it also has 15 binary axes and ten ternary axes. Note that it belongs to one of the icosahedral groups. If you play soccer, consider the ball. Before you kick it, look at it. What is its symmetry ... 

Actually, this is not that difficult to understand. We all know that the more stable form of diesters between fumarate and maleate is the fumarate due to the trans configuration, which minimizes the crowdedness of the esters. In the case of phthalic esters, the aromatic esters cannot possibly rotate to any trans forms and are therefore in a state with a high strain energy. In order to release this energy, these esters would rather prefer to kick-off the esters. This is why they are so prone to attack by hydrolysis, and is why GP resins will fail in any water-immersion type of test, especially under elevated temperature. 

To include the effects of collisions on the rotational motion part of any of the above C(t) functions, one must introduce a model for how such collisions change the dipole-related vectors that enter into C(t). The most elementary model used to address collisions applies to gaseous samples which are assumed to undergo unhindered rotational motion until struck by another molecule at which time a randomizing "kick" is applied to the dipole vector and after which the molecule returns to its unhindered rotational movement. 

The effects of such collisionally induced kicks are treated within the so-called pressure broadening (sometimes called collisional broadening) model by modifying the free-rotation correlation function through the introduction of an exponential damping factor exp( -Itl/x) ... 

This type of energy exchange in an autoionization process may correspond with the behavior of a kicked rotator in classical mechanics, which is known to exhibit chaos. It would be worthwhile to consider an autoionization process of a simple diatomic molecule in its Rydberg states to understand experimentally the essential dynamics of a quantum system, whose classical counterpart exhibits chaos. 

The preceding considerations are essentially based on the model of random-matrix ensembles proposed by Dyson and others in the 1960s. Recent works, in particular by Casati and co-workers [89], have focused on band random matrices. Such matrices naturally arise in quantum systems with subspaces coupled only to next-neighboring subspaces such as for electronic states in a chain of atoms or in the kicked rotator. In such systems, localized states are observed that present a level statistics interme-... 

Figure 52. Quantum and classical anomalous diffusion in a modified kicked rotor system. Shown here is the time dependence of the average scaled rotational energy, denoted as Eq (solid line) and Ec (dashed line) for the quantum and classical ensembles, respectively. Note that the quantum result is well above the classical result. [From J. B. Gong, H. J. Womer, and P. Brumer, Phys. Rev. E 68, 026209 (2003).]...

The plan of Chapter 5 is the following. In order to get a feeUng for the dynamics of the kicked molecule, we approximate it by a one-dimensional schematic model by restricting its motion to rotation in the x, z) plane and ignoring motion of the centre of mass. In this approximation the kicked molecule becomes the kicked rotor, probably the most widely studied model in quantum chaology. This model was introduced by Casati et al. in 1979. The classical mechanics of the kicked rotor is discussed in Section 5.1. Section 5.2 presents Chirikov s overlap criterion, which can be applied generally to estimate analytically the critical control parameter necessary for the onset of chaos. We use it here to estimate the onset of chaos in the kicked rotor model. The quantum mechanics of the kicked rotor is discussed in Section 5.3. In Section 5.4 we show that the results obtained for the quantum kicked rotor model are of immediate... 

Fig. 5.10. Average energy of the quantum kicked rotor as a function of K = fcr for T = 1/10. The rotor was prepared at t = 0 in the rotational state lo = 10).

In the following numerical experiment we show that it is possible to demonstrate the difference between locahzed and resonant rotor dynamics with Csl molecules. At time t = 0 the molecules are prepared in their rotational ground state ( 4 (t = 0)) = J = 0, M = 0)). For t > 0 they are exposed to a string of microwave pulses. The control parameters r and k determine the repetition frequency and the strength of the pulses. In order to be able to compare with the results for the planar kicked rotor discussed in Section 5.3, we choose k = 5 and r = 1 (for the nonresonant case) and r = 7t/3 (for the resonant case). This choice of control parameters translates into a driving frequency oi u = 1/T w 9 GHz and a field strength of q w IkV/cm. For the pulse shape we choose... 

The shape of the pulse (5.4.28) is shown in Fig. 5.11. The shape (5.4.28) was chosen because it may be possible to actually synthesize pulses resembling (5.4.28) with an array of phase-locked microwave generators (see discussion below). Kicking the Csl molecules with the pulses (5.4.28) results in the excitation of rotational states. 

As thus far described, in the parameter region we are interested in, coupling resonances have to be seriously taken into account. Then, before we go forward to detailed investigation, we check how global structures are affected by a form of coupling term. To clarify this, we employ a kicked and asymmetric coupled rotators described by... 

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