Renewal processes

Danckwerts assumed a random surface renewal process in which the probability of surface renewal is independent of its age. If s is the fraction of the total surface renewed per unit time, obtain the age distribution function for the surface and show that the mean mass transfer rate Na over the whole surface is ... 

The first type of model considers the heat transfer surface to be contacted alternately by gas bubbles and packets of closely packed particles. This leads to a surface renewal process whereby heat transfer occurs primarily by transient conduction between the heat transfer surface and the particle packets during their time of residence at the surface. Mickley and Fairbanks (1955) provided the first analysis of this renewal mechanism. Treating the particle packet as a pseudo-homogeneous medium with solid volume fraction, e, and thermal conductivity (kpa), they solved the transient conduction equation to obtain the following expression for the average heat transfer coefficient due to particle packets,... 

The mechanical strength of the bones is regulated by their alignment of HAp crystals. The alignment is continually remodeled by a coupling of osteoblast and osteoclast. The bone tissue is always maintained by a renewal process (Figure 6.3). An osteoblast contributes bone formation, for example the growth in the stature of... 

Among potential commercial processes, the Renew process is proposed to filter color from a glycolysis product, while the Recopet process creates TPA... 

In addition to specific applications, the dynamic bond percolation model has been extended to focus on the importance of lattice considerations. The role of correlations among different renewal processes and the... 

Further evidence for a dynamic cardiac renewal process in the adult heart comes from the recent identification of a novel population of early tissue-committed stem cells that may be part of a group of circulating progenitor cells involved in cardiac repair [40]. 

The retinal receptors have a very active metabolism. Human rod cells (Fig. 23-40) may live and function for a hundred years.190 A self-renewal process leads to a casting off of the older membranous discs from the end of the rod194 and replacement by new discs at the end nearest to the nucleus. The rod outer segment is surrounded by a plasma membrane. Within the membrane but apparently not attached to it are -500 stacked discs of -2 pm diameter and with a repeat distance between centers of -32 nm. Each disc is enclosed by a pair of membranes each - 7 nm thick with a very narrow space between them. From electron micrographs it appears that this space within the discs is sealed off at the edges. Somewhat larger spaces separate adjacent discs. 

Harano, K.-I. and Sasaki, M. (2006). Renewal process of nestmate recognition template in European honeybee Apis melliffera L. (Hymenoptera Apidae). Appl. Entomol. Zool., 41, 325-330. 

XV. Non-Poisson and Renewal Processes A Problem for Decoherence Theory... 

XVI. Non-Poisson Renewal Processes A Property Conflicting with Modulation Theories... 

Note that the crisis of the GME method, based on the density approach, is generated by non-Poisson renewal processes. Therefore, we find it important to illustrate, by means of Section V, the model for intermittence, on which our theoretical arguments are based. 

At this stage, we are confident that a clear connection between Levy statistics and critical random events is established. We have also seen that non-Poisson renewal yields a class of GME with infinite memory, from within a perspective resting on trajectories with jumps that act as memory erasers. The non-Poisson and renewal character of these processes has two major effects. The former will be discussed in detail in Section XV, and the latter will be discussed in Section XVI. The first problem has to do with decoherence theory. As we shall see, decoherence theory denotes an approach avoiding the use of wave function collapses, with the supposedly equivalent adoption of quantum densities becoming diagonal in the pointer basis set. In Section XV we shall see that the decoherence theory is inadequate to derive non-Poisson renewal processes from quantum mechanics. In Section XVI we shall show that the non-Poisson renewal properties, revealed by the BQD experiments, rule out modulation as a possible approach to complexity. 

In this review we show that there are two main sources of memory. One of them correspond to the memory responsible for Anderson localization, and it might become incompatible with a representation in terms of trajectories. The fluctuation-dissipation process used here to illustrate Anderson localization in the case of extremely large Anderson randomness is an idealized condition that might not work in the case of correlated Anderson noise. On the other hand, the non-Poisson renewal processes generate memory properties that may not be reproduced by the stationary correlation functions involved by the projection approach to the GME. Before ending this subsection, let us limit ourselves to anticipating the fundamental conclusion of this review The CTRW is a correct theoretical tool to address the study of the non-Markov processes, if these correspond to trajectories undergoing unpredictable jumps. 

In the case where the correlation function <3> (f) has the form of Eq. (148), with p fitting the condition 2 < p < 3, the generalized diffusion equation is irreducibly non-Markovian, thereby precluding any procedure to establish a Markov condition, which would be foreign to its nature. The source of this fundamental difficulty is that the density method converts the infinite memory of a non-Poisson renewal process into a different type of memory. The former type of memory is compatible with the occurrence of critical events resetting to zero the systems memory. The second type of memory, on the contrary, implies that the single trajectories, if they exist, are determined by their initial conditions. 

As simple and heuristic these arguments are, they serve the purpose of clarifying an issue that is causing some confusion in literature. This has to do with the fact that a renewal process, where the occurrence of a failure is totally unpredictable, has the effect of resetting to zero the memory of the system however, a form of infinite memory may exist. Let us see why it is so. We have seen that in the Poisson case there is no way to establish, through experimental observation, when the Gibbs system was prepared. In the non-Poisson case, it is not so. In that case, the decay of v fta(t) is slower than the decay of v /(t) = ita=0(t), and the experimental observation of the former, once the latter... 

In the earlier sections we have seen the GME of Eq. (59) in action with the memory kernel defined by Eq. (66). In Section X we have seen that non-Poisson renewal processes are characterized by aging. Thus, this is the right moment to establish the age of the GME of Eq. (59). In this section we show that this is the GME corresponding to a brand new condition. Thus, we have also to establish the form of the aged GME, if this ever exists. 

XV. NON-POISSON AND RENEWAL PROCESSES A PROBLEM FOR DECOHERENCE THEORY... 

XVI. NON-POISSON RENEWAL PROCESSES A PROPERTY CONFLICTING WITH MODULATION THEORIES... 

This section is devoted to illustrating a proposal to the BQD complexity that accounts for two fundamental requests (a) This proposal must yield aging (b) This proposal must account for the non-Poisson nature of this renewal process and must relate it to a form of cooperation. 

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