Modes number

Figure 3 Anharmonicity factor versus quasi-harmomc mode number from a 200 ps vacuum simulation of BPTI. It can be seen that beyond about the 200th mode the anharmonicity factors are about 1.0, indicating harmomcity. Those below mode number 200 show progressively greater anharmonicity factors, indicating that they span a space within which energy barriers are crossed. A similar picture was found for a I ns simulation of human lysozyme m water [61]. (Adapted from Ref. II.)...

If the core only corresponds to one speckle spot the fibre is monomode. Otherwise the waveguide is multimode. This back to the envelop calculation intuitively shows the origin of the mode number. Note that N is wavelength dependent the larger the wavelength, the lower the number of mode. 

The mode index p counts the number of modes along the chain. A small mode number, e.g. p N, (15), is approximated by... 

Fig. 10a, b. Contributions of the different modes to the relaxation of the dynamic structure factor S(Q,t)/S(Q,0) (see text) for PE of molecular masses, a Mw = 2.0 x 103 g/mol and b Mw = 4.8 x 103 g/mol. The experimental Q-values are indicated by vertical lines curves correspond to mode numbers increasing from bottom to top. (Reprinted with permission from [52]. Copyright 1993 The American Physical Society, Maryland)... 

Fig. 17. Time-dependent correlators for different Rouse modes in the Hess model. The calculations where performed for PE of Mw = 6500 g/mol. The mode numbers increase from the top commencing with p = 1. (Reprinted with permission from [36]. Copyright 1994 American Chemical Society, Washington)...

The morphological stability of initially smooth electrodeposits has been analyzed by several authors [48-56]. In a linear stability analysis, the current distribution on a low-amplitude sinusoidal surface is found as an expansion around the distribution on the flat surface. The first order current distribution is used to calculate the rate of amplification of the surface corrugation. A plot of amplification rate versus mode number or wavelength separates the regimes of stable and unstable fluctuation and... 

Fig. 8.33 Calculated sensitivity in bulk index sensing for different radial mode numbers with the same azimuthal number m 700...

Each of the resonances appearing in the spectra are identified and characterized by the type (TE or TM), mode number n, and mode order 5 (i.e., TE J. Allowances were made in the fit for a small amount of scattered light polarized perpendicular to the scattering plane (due to imperfect alignment of the polarizer) and a small change in the particle radius due to evaporation during the experiment. Once the resonances are identified there are no adjustable parameters in the simulation of an excitation spectrum of a... 

The higher the mode number, the smaller becomes the square of the Fourier components. Using periodic boundary conditions and considering that a segment vector is given by the difference of adjacent position vectors the statistical average (R(qf) in Fourier space becomes ... 

The eigenvalues Eq. 5.15a lead to two branches of the relaxation time rand the propagation frequency co. For experimental parameters appropriate for PIB, Fig. 5.1 displays the dependence of the relaxation times on the mode number... 

Fig. 5.1 Mode number dependence of the relaxation times Tj and T2 (solid lines). The dashed-dotted line shows the relaxation time ip in the Rouse model (Eq. 3.12). The horizontal dashed line displays the value of r. The dashed and the dotted lines represent the relaxation time when the influence of the chain stiffness is considered mode description of the chain statistics iq (dashed, Eq. 5.11) and bending force model tp (dotted, Eq. 5.7). The behaviour of the relaxation time used in the phenomenological description is also shown for the lowest modes (see text). (Reprinted with permission from [217]. Copyright 1999 American Institute of Physics)...

Fig. 5.2 Mode number dependence of the relaxation times and T2 solid lines) found for PIB in dilute solution at 327 K. The dashed-dotted line shows the relaxation time of the Rouse-Zimm model. The horizontal dashed line displays the value of (Reprinted with permission from [186]. Copyright 2001 American Chemical Society)...

The single-mode laser naturally gives less output power than a multimode laser with the same active volume since its induced emission is concentrated into a smaller frequency range. This loss in intensity, however, is much less than one would expect from the ratio of linewidths or from the reduction in oscillating mode number 3i. 32,41) jbis is due to the fact, that not only atoms with the exact transition frequency can contribute to the induced emission, but also those inside the homogeneous linewidth which is determined by collision processes in the case of gas lasers or by crystal line broadening in solid lasers... 

Key for descriptions of approximate group vibrations, see Table 12.1 AA and GA mode numbers given in parentheses. 

The symmetry properties of M alone are sufficient to prove that only the odd eigenvalues of A are affeded by subtraction of M. Thus, according to this view, only the relaxation times of odd order are affected by entanglement coupling. Furthermore, the shifts diminish rapidly as mode number increases, so only the longest odd relaxation times are affected. 

Fig. 2. Relaxation times as a function of mode number in a one-dimensional chain of 10,000 links, for different values of the bond correlation parameter fJ. Reduced relaxation time t,/- is plotted semilogarithmically against reduced mode number PIN.

Fig. 9 Typical ranges of Aitken and accumulation mode number concentrations (separated by 100 nm dry diameter) in different European environments. The areas show the densest parts of the different environment concentration scatter (see Asmi et al. [18] for details, adapted from the same article)...

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