Oscillation Model linear density

By measuring 6, in warp direction, yam linear density, and fabric deformation angle in pullout test, /tg, and of oscillation model can be computed using Equa-... 

The strategy, usually adopted to achieve a theoretical description of this complex dynamics, is to describe the influence of the solvent environment on the electron-transfer reaction within linear response theory [5, 26, 196, 197] as linear coupling to a bath of harmonic oscillators. Within this model, all properties of the bath enter through a single function called the spectral density [5, 168]... 

The effect of dislocation line oscillations on the probability of its separation from the defect was accounted for by Natsik [211, 212], who has considered the following model A dislocation line moves in the slipping plane under the action of the one-axis stress. The dislocation is characterized by the linear mass density p and tension coefficient C. Pinning in A and B sites is considered to be rigid, and the dislocation detachment from the defect located in the zero point is considered (Figure 21). At a li, I2 < d [d is... 

The natural line width of the spectral line is a significant result of the dissipative quantum process which accompanies the spontaneous emission of an atom. We will treat this emission process in a dissipative two-state model. We consider the two states of the atom as the zeroth and the first occupation number state of a linearly damped oscillator. In this case, the spontaneous emission of a photon is the consequence of the transition from the first occupations number state to the equilibrium state of the damped oscillator. In this model, the spectrum density of the emitted photon follows from Equation (92)... 

Here we apply the LAND-map approach to compute of the time dependent average population difference, A t) = az t)), between the spin states of a spin-boson model. Here az = [ 1)(1 — 2)(2 ]. Within the limits of linear response theory, this model describes the dissipative dynamics of a two level system coupled to an environment [59,63-65]. The environment is represented by an infinite set of harmonic oscillators, linearly coupled to the quantum subsystem. The characteristics of the system-bath coupling are completely described by the spectral density J(w). In the following, we shall restrict ourselves to the case of an Ohmic spectral density... 

The spectral density (see also Sections (7-5.2) and (8-2.5)) plays a prominent role in models of thermal relaxation that use harmonic oscillators description of the thermal environment and where the system-bath coupling is taken linear in the bath coordinates and/or momenta. We will see (an explicit example is given in Section 8.2.5) that /(co) characterizes the dynamics of the thermal environment as seen by the relaxing system, and consequently determines the relaxation behavior of the system itself. Two simple models for this function are often used ... 

The Golden Rule formula (9.5) for the mean rate constant assumes the Unear response regime of solvent polarization and is completely equivalent in this sense to the result predicted by the spin-boson model, where a two-state electronic system is coupled to a thermal bath of harmonic oscillators with the spectral density of relaxation J(o)) [38,71]. One should keep in mind that the actual coordinates of the solvent are not necessarily harmonic, but if the collective solvent polarization foUows the Unear response, the system can be effectively represented by a set of harmonic oscillators with the spectral density derived from the linear response function [39,182]. Another important point we would like to mention is that the Golden Rule expression is in fact equivalent [183] to the so-called noninteracting blip approximation [71] often used in the context of the spin-boson model. The perturbation theory can be readily applied to... 

Faster computers and development of better numerical algorithms have created the possibility to apply RPA in combination with semiempirical Hamiltonian models to large molecular sterns. Sekino and Bartlett - derived the TDHF expressions for frequency-dependent off-resonant optical polarizabilities using a perturbative expansion of the HF equation (eq 2.8) in powers of external field. This approacii was further applied to conjugated polymer (iialns. The equations of motion for the time-dependent density matrix of a polyenic chain were first derived and solved in refs 149 and 150. The TDHF approach based on the PPP Hamiltonian - was subsequently applied to linear and nonlinear optical response of neutral polyenes (up to 40 repeat units) - and PPV (up to 10 repeat units). " The electronic oscillators (We shall refer to eigenmodes of the linearized TDHF eq with eigenfrequencies Qv as electronic oscillators since they represent collective motions of electrons and holes (see Section II))... 

In the above equations coq is the frequency of a noninteraction oscillator, X(o)) is the eoupling function between the oscillator and the external field, and RHg (ro) is the field density of states. With Eqs (67)-(74) it will now be possible to predict the spectral behavior for localized harmonic oscillators linearly coupled with different model boson continua. 

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