Decay continuum

Melillo, J. M., Aber, J. D., Linkins, A. E., Ricca, A.,Fry, B., and Nadelhoffer, K. J. (1989). Carbon and nitrogen dynamics along the decay continuum plant litter to soil organic matter. Plant Soil 115,189-198. 

Rustad L. E. (1994) Element dynamics along a decay continuum in a red spruce ecosystem in Maine, USA. Ecology (Tempe) 85(4), 867-879. 

If the decay continuum has got some structure, it may be approximated by a set of poles on the second sheet of the lower plane. In that case, the decay can be described in terms of pseudo-modes similar to our faked continuum [Garraway 1997 (a) Garraway 1997 (b)]. 

At the ecosystem scale, the flux of carbon among various reservoirs is a continuous process and follows a steady decay continuum. In a stepwise manner, carbon dioxide fixed during photosynthesis is returned to the atmosphere by the decomposition process, and the undecomposed organic matter is retained in the soil (Figure 5.7). The steps are as follows ... 

FIGURE 5.7 Decay continuum of organic matter decomposition and accretion in wetlands. 

The preceding discussion was limited mostly to VP processes occurring by direct coupling of the quasibound state of the complex to the dissociative continuum, which is the simplest and most commonly observed decay route for the complexes. However, these systems also serve as ideal venues for studying an array of more complicated dynamical processes, including IVR, and electronic predissociation. This brief section will focus on the former, underscoring some of the inherent dynamical differences between Rg XY complexes by discussing the IVR behavior of a few systems. 

The first element on the right-hand side of Eq. (40) describes excitation into a resonance manifold, which, given Eq. (35), is comprised of direct excitation of the i) and excitation via the continuum with which the /) are coupled. The second element describes the dynamics in the resonance manifold and allows for coupling between the resonances. The third element accounts for decay of the resonance into the continuum. 

In the limit of an isolated vibronic resonance are real, decay of the resonances arises only from interaction with the continuum, Eq. (52) reduces to... 

Information and knowledge develop on a continuum. Facts and information gained during the years of our formal education represent a thin slice on this continuum. Some of what we learn from the academic curriculum does remain viable unfortunately, much decays and becomes incomplete and inaccurate. Health care professionals and scientists must constantly renew and add to their skills, resources, and knowledge. This is fundamental to the profession. The Millis Commission in 1975 eloquently stated [26] ... 

Next, we discuss the J = 0 calculations of bound and pseudobound vibrational states reported elsewhere [12] for Li3 in its first-excited electronic doublet state. A total of 1944 (1675), 1787 (1732), and 2349 (2387) vibrational states of A, Ai, and E symmetries have been computed without (with) consideration of the GP effect up to the Li2(63 X)u) +Li dissociation threshold of 0.0422 eV. Figure 9 shows the energy levels that have been calculated without consideration of the GP effect up to the dissociation threshold of the lower surface, 1.0560eV, in a total of 41, 16, and 51 levels of A], A2, and E symmetries. Note that they are genuine bound states. On the other hand, the cone states above the dissociation energy of the lower surface are embedded in a continuum, and hence appear as resonances in scattering experiments or long-lived complexes in unimolecular decay experiments. They are therefore pseudobound states or resonance states if the full two-state nonadiabatic problem is considered. The lowest levels of A, A2, and E symmetries lie at —1.4282,... 

In gas clouds containing one or more hot stars (7 cn > 30 000 K), hydrogen atoms are ionized by the stellar UV radiation in the Lyman continuum and recombine to excited levels their decay gives rise to observable emission lines such as the Balmer series (see, for example, Fig. 3.22). Examples are planetary nebulae (PN), which are envelopes of evolved intermediate-mass stars in process of ejection and... 

The thermal healing has been studied most extensively for one-dimensional gratings. Above roughening, the gratings acquire, for small amplitude to wavelength ratios, a sinusoidal form, as predicted by the classical continuum theory of Mullins and confirmed by experimenf-s and Monte Carlo simulations. - The decay of the amplitude is, asymptotically, exponential in time. This is true for both evaporation dynamics and (experimentally more relevant) surface diffusion. 

In the case of evaporation kinetics, continuum theory predicts, e.g., that the amplitude of the wire decays with f, with w= 1/5. Simulations, for rather small systems, show strong deviations. The simulated profile shapes also differ appreciably from the predicted ones, even when conservation of mass at the surface is taken into account, especially near the top. The differences may be traced back to the fact that the mo-... 

In marked contrast, the classical continuum theory by mullins describes the sim-ulational data (profile shapes and amplitude decay) above roughening for wires even with small geometries surprisingly well, both for surface diffusion and evaporation-condensation The agreement may be a little bit fortuituous, because of a compensation of the competing effects of the anisotropic surface tension and anisotropic mobility, whereas continuum theory assumes isotropic quantities. In any event, the predicted decay laws with w= 1/4 for surface diffusion and w= 1/2 for evaporation kinetics are readily reproduced in the simulations. 

Below roughening, pronounced lattice effects show up in the simulations, as in the case of wires. The meandering of the top(bottom) steps and the islanding on the top(bottom) terrace leads to slow and fast time scales in the decay of the amplitude. The profile shapes near the top(bottom) broaden at integer values of the amplitude and acquire a nearly sinusoidal form in between. Again, these features are not captured by the continuum theory. For evaporation kinetics, continuum theory suggests that the decay of the profile amplitude z scales like z t,L) = where g =... 

Above roughening (see Figure 6), the decay of the gratings is well described by the classical continuum theory for sufficiently small ratios amplitude/wavelenght, with g = 2 for evaporation, and 4 for surface diffusion. Deviations, observed otherwise, can be explained mostly by the anisotropy of the surface tension. ... 

Below roughening, the relaxation is driven by the lowering of the line tension of the curved steps. For evaporation kinetics, continuum theory and simulations show a shrinking of the bumps in the late stages of the decay. At small amplitudes, the radially symmetric profile scales with z r,t) Z(V ct + r )), where r is the distance from the center, and c is a constant. The continuum theory fails to describe the layerwise relaxation monitored in the simulations. ... 

The continuum limit of the Hamiltonian representation is obtained as follows. One notes that if the friction function y(t) appearing in the GLE is a periodic function with period T then Eq. 4 is just the cosine Fourier expansion of the friction function. The frequencies coj are integer multiples of the fundamental frequency and the coefficients Cj are the Fourier expansion coefficients. In practice, the friction function y(t) appearing in the GLE is a decaying function. It may be used to construct the periodic function y(t T) = Y(t TiT)0(t-... 

Quantum-state decay to a continuum or changes in its population via coupling to a thermal bath is known as amplitude noise (AN). It characterizes decoherence processes in many quantum systems, for example, spontaneous emission of photons by excited atoms [35], vibrational and collisional relaxation of trapped ions [36] and the relaxation of current-biased Josephson junctions [37], Another source of decoherence in the same systems is proper dephasing or phase noise (PN) [38], which does not affect the populations of quantum states but randomizes their energies or phases. 

---