Survival, probability decrease

As time proceeds, the survival probability decreases and asymptotically tends to a constant value p(t-> oo] r0, f0 = 0) =, the ultimate survival... 

FIGURE 16.27 SPT diagram for medical grade AI2O3. The survival probability decreases with increasing stress and longer times. 

This small figure may also be compatible with a logarithmic decay [34,57]. Also, the survival probability of a blob of A species embedded in a B sea (separated by a wall of empty sites) decreases in time with exponent 6 = 0.80 0.20 (see Eq. (6)), reminiscent of critical behavior of the ZGB model at the first-order IPT [34]. 

Hong and Noolandi [72], Berg [278], and Pedersen and Sibani [359] have also noted the connection between the survival probability and homogeneous density distribution. Finally, the escape probability of an ion pair formed with a separation, r0, with an arbitrary monotonically decreasing potential energy of interaction and with electric field-dependent mobility and diffusion coefficient ions was found by Baird et al. [350] to be (see also Tachiya [357])... 

This formula demonstrates that the tunneling splitting is determined—like the imaginary part of metastable state energy (A.20)—as a normalized probability flux through the dividing line. In the present case this flux corresponds to coherent probability oscillations between the wells rather than exponential decrease of the survival probability in the well, so A is a real value. 

Figure 10.4 A plot of survival probability, against strength

We observe from numerical simulations an exponential decrease of the survival probability Sf(t) in the potential well, at the bottom of which we initialize the process. Moreover, we find that the mean crossing time assumes the scaled form (114) with scaling exponent p being approximately constant in the range 1 < a // 1.6, followed by an increase before the apparent divergence at a = 2, that leads back to the exponential form of the Brownian case, Eq. (113). An analytic calculation in the Cauchy limit a = 1 reproduces, consistently with the constant flux approximation commonly applied in the Brownian case, the scaling Tc 1/D, and, within a few percent error, the numerical value of the mean crossing time Tc. 

Fig. 2 shows that if V < cs, the survival probability first decreases and then approaches the constant value of about 0.85, almost independent on V. This behavior reveals the physical reason for the short-time non exponential decay the initial conditions Eq. (2) imply that, initially, the impurity atom is surrounded by no virtual phonons, while in the steady state, the impurity atom must be surrounded by a cloud of virtual phonons (cf. the polaronic effect for electrons in a crystal, [Isihara 1971]). Thus the non-exponential stage of the decay is associated with the formation of such a phonon cloud. 

A plot of this equation is shown in Fig. 11.22, where the relationship between strength and volume is plotted. The salient point here is that as either the volume increases or the Weibull modulus decreases, the more severe the downgrading of the design stress required to maintain a given survival probability. 

As time advances from t = 0, the survival probability starts at the value 1, then (at least in many cases) gradually decreases. There are frequently a number of oscillations superimposed upon the declining function S(t) these are due to partial recurrences of the time evolving wave packet upon the starting wave packet. The relationship between the survival amplitude and the lineshape function will be described in Section II. Examples of survival probability plots will be shown later in Sections III and IV. 

The term e never really assumes a value of 0, except abstractly when time is infinite. Because there cannot be fractional numbers of cells present, when Equation 4.3.4 predicts less than one cell, there will be a small probability that a cell survives, but this probability decreases as time goes on. This fact is important in processes that sterilize food or medical products (see Section 6.23). 

The probability of survival for a credit may be viewed as a decreasing function against time. The survival probabilities for each traded reference credit can be derived from it s credit curve. The survival probability is a decreasing function because it reflects the fact that the probability of survival for a credit reduces over time. For example, the probability of survival to year 3 is higher than the probability of survival to year 5. 

Change a target s properties such that it is not recognised as a potential target (i.e. to increase survivability and decrease probability of detection (POD)). 

Let us return to our problem of a chemical reaction. In chemical kinetics, it is usually the population decrease of A molecules of concentration [A], rather than their survival probability, that is expressed. The rate of change of [A] is described by a relation of type... 

Inmitively, it is clear that the survival probability S(t) decreases in time with the rate equal to the probability current into the absorbing state Sj. diS(t,Sj. S.) = -J t,Sj. S ). This provides a prescription for obtaining the... 

Hot-fusion reactions were employed in the discoveries of the elements beyond mendelevium as far as element 106, producing the first three members of the domain of superheavy elements. Higher transactinides have also been synthesized in these reactions. As before, the general trends with increasing atomic number were shorter half-lives and smaller production cross sections, a consequence of decreased survival probability in the evaporation process [132, 133]. The probability of decay from the nuclear ground state by spontaneous fission became significant in these elements. The techniques used in the experiments still included radiochemistry and off-line radiation counting [134]. As half-lives dropped below minutes into seconds it became more common to use direct techniques like transportation in gas jets to mechanisms like wheels and tapes (see Sect. 3.3 and Experimental Techniques ). Detection of new nuclides resulted from the detailed... 

The concentration of surviving macroradicals decreases with time after irradiation [13]. Their living time is on the order of 24 hours in the amorphous phase, but macro alkyl radicals can be found in the polymer bulk even after years, probably trapped in the crystalline phase [14]. The mechanism of decay of macro alkyl radicals is still unknown. 

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