Frequency angular, defined

Here E(t) denotes the applied optical field, and-e andm represent, respectively, the electronic charge and mass. The (angular) frequency oIq defines the resonance of the hamionic component of the response, and y represents a phenomenological damping rate for the oscillator. The nonlinear restoring force has been written in a Taylor expansion the temis + ) correspond to tlie corrections to the hamionic... 

The constant h and the hypothesis that energy is quantized in integral multiples of hv had previously been introduced by M. Planck (1900) in his study of blackbody radiation.1 In terms of the angular frequency a> defined in equation (1.2), the energy E of a photon is... 

In angular units of frequency, the NQCC is given by x = eqe( lThe quadrupolar frequency is defined in angular units as (see Ref. 2)... 

The conditional frequency is defined according to (7.114), and the superscript (i) means that the scattering collision occurred with a nucleus of type i. In the present application we consider the case of one-dimensional symmetry so that spatial variation occurs only in the X direction, and the only angular variable of interest is the cosine of the angle between the x axis and the direction of motion of the neutron. The appropriate one-dimensional form of (12.11) is [cf. Eq. (7.336)]... 

The vector L is so strongly coupled to the electrostatic field and the consequent frequency of precession about the intemuclear axis is so high that the magnitude of L is not defined in other words L is not a good quantum number. Only the component H of the orbital angular momentum along the intemuclear axis is defined, where the quantum number A can take the values... 

The significance of G G tan 5, Tj, and Tj is that they can be determined experimentally and used to characterize real materials. These parameters depend on frequency and temperature, and this dependence can be used to define behavior. For example, viscoelastic fluids are often characterized by log—log plots of one or more of these quantities vs the angular frequency CO, as shown in Figure 21, which illustrates the behavior of a polymer melt (149). 

This is an important equation that defines the behaviour of a vibrating body under different conditions of applied force or motion F y From this it can be inferred that the response or movement of object x will depend upon t) and 7 is termed the fraction of critical damping and w , the angular natural frequency of the system. With the help of these equations, the response characteristics of an object to a force can be determined. 

System (A8.2)-(A8.4) defines completely the time variation of orientation and angular velocity for every path X(t). One can easily see that (A8.2)-(A8.4) describe the system with parametrical modulation, as the X(t) variation is an input noise and does not depend on behaviour of the solution of (Q(t), co(r). In other words, the back reaction of the rotator to the collective motion of the closest neighbourhood is neglected. Since the spectrum of fluctuations X(t) does not possess a carrying frequency, in principle, for the rotator the conditions of parametrical resonance and excitation (unrestricted heating of rotational degrees of freedom) are always fulfilled. In reality the thermal equilibrium is provided by dissipation of rotational energy from the rotator to the environment and... 

A and B are constants and they are independent of time. Bearing in mind that = X + iy, it is simple to find functions x t) and y t), which describe a motion of the pendulum on the earth s surface. In accordance with Equation (3.88) a solution is represented as a product of two functions. The first one characterizes a swinging of the pendulum with the angular velocity p, which depends only on the gravitational field and the length /, while the second is also a sinusoidal function and its period is defined by the frequency of the earth s rotation and the latitude of the point, (Foucault s pendulum). In order to understand the behavior of the pendulum at the beginning consider the simplest case when a rotation is absent, co — 0. Then, we have... 

We restrict the study of the adiabatic approximation to the case where the modulation parameters (30,/0, and gD, defined in Eqs. (6) and (7), are neglected. The effective angular frequency of the fast mode reduces to ... 

The limiting angular vibrational frequency, D, that exists defines the Debye temperature, 0D, as... 

H is the total Hamiltonian (in the angular frequency units) and L is the total Liouvillian, divided into three parts describing the nuclear spin system (Lj), the lattice (Ll) and the coupling between the two subsystems (L/l). The symbol x is the density operator for the whole system, expressible as the direct product of the density operators for spin (p) and lattice (a), x = p <8> ci. The Liouvillian (Lj) for the spin system is the commutator with the nuclear Zeeman Hamiltonian (we thus treat the nuclear spin system as an ensemble of non-interacting spins in a magnetic field). Ll will be defined later and Ljl... 

The theory presented above is valid as long as the Redfield condition is satisfied. In the case of susceptibility-induced relaxation, this condition may be written as Acotd < 3.4, where Aco is the equatorial magnetic field at the surface of the particle (expressed in angular frequency units). The Redfield condition defines thus the distinction between small and large particles. 

Figure 10.6 Two-dimensional REMPI spectrogram of the centrifuged Oj molecules. Ion signal is color coded as a function of the frequency of the ionizing laser field, which undergoes two-photon absorption on the C Yl v = 2) X L v" = 0) transition, and molecular angular momentum, which is defined by...

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