Catastrophe, interpreting

Consider the following example in which the worker risk from a catastrophic accident has been calculated to be 2 X 10 fatalities per year. It is possible to interpret this number in many ways, but one of the most common ways is the following there is one chance in 5000 per year that a worker will be fatally injured at the plant. However, you should be cautious when interpreting single risk estimates that are the sums of products of frequency and consequence of many accidents. The way you believe (and act) may be affected by the frequency/consequence profile that the number represents (see Sections 3.2.4 and 4.2.5.) That is, your reaction to an accident that occurs once every 100 years and kills 1 person (Risk = 10 fatalities per year) and your reaction to an accident that occurs once every 10,000 years and kills 100 people (Risk = 10 fatalities per year) are likely to be very different. 

The failure of plant by corrosion can be gradual or catastrophic. Gradual failure has few implications for safety providing it is monitored. Direct corrosion-monitoring techniques are described in Section 53.8. Indirectly, the correct interpretation of records relating to metal contamination of products or the loss of efficiency of heat exchangers, etc. can provide useful information. 

It is not only the vast difference of about 1.8 billion years which is so surprising the timescale for the separation point of the main branches of the tree of life is clearly shifted. The catastrophe hypothesis put forward to explain this difference appears unlikely, since there are no signs of such a phenomenal obliteration of all life on Earth. Another explanation could be that the data from the amino acid sequences provide only information on the way in which life forms diverged, but not on the timescale (Schopf, 1998). This interpretation of the Doolittle event by Schopf was provided at a time when doubts had not yet been cast on the dating of the first fossils at 3.45 billion years, published by him in 1993. 

This passage was repeated with little alteration in the 1912 and 1920 editions of The Interpretation of Radium, the change being to change the nature of the catastrophe from a single mistake to some unknown reason. Sclove notes that Soddy s belief in an earlier atomic age wavered in later years (175). 

In general, the use of FE signals accompanying the deformation and fracture of composites offer elucidation of failure mechanisms and details of the sequence of events leading upto catastrophic failure. The extent of interfacial failure and fiber pull-out are also potential parameters that can be determined. FE can assist in the interpretation of AE and also provide an independent probe of the micro-events occurring prior to failure. FE has been shown to be sensitive to the locus of fracture and efforts are underway to relate emission intensity to fracture mechanics parameters such as fracture toughness (Gjp). Considerable work still remains to fully utilize FE to study the early stages or fracture and failure modes in composites. 

As was noted in Section 2.1.1, the concentration oscillations observed in the Lotka-Volterra model based on kinetic equations (2.1.28), (2.1.29) (or (2.2.59), (2.2.60)) are formally undamped. Perturbation of the model parameters, in particular constant k, leads to transitions between different orbits. However, the stability of solutions requires special analysis. Assume that in a given model relation between averages and fluctuations is very simple, e.g., (5NASNB) = f((NA), (A b)), where / is an arbitrary function. Therefore k in (2.2.67) is also a function of the mean values NA(t) and NB(t). Models of this kind are well developed in population dynamics in biophysics [70], Since non-linearity of kinetic equations is no longer quadratic, limitations of the Hanusse theorem [23] are lifted. Depending on the actual expression for / both stable and unstable stationary points could be obtained. Unstable stationary points are associated with such solutions as the limiting cycle in particular, solutions which are interpreted in biophysics as catastrophes (population death). Unlike phenomenological models treated in biophysics [70], in the Lotka-Volterra stochastic model the relation between fluctuations and mean values could be indeed calculated rather than postulated. 

Despite the fact that formalism of the standard chemical kinetics (Chapter 2) was widely and successfully used in interpreting actual experimental data [70], it is not well justified theoretically in fact, in its derivation the solution of a pair problem with non-screened potential U (r) = — e2/(er) is used. However, in the statistical physics of a system of charged particles the so-called Coulomb catastrophes [75] have been known for a long time and they have arisen just because of the neglect of the essentially many-particle charge screening effects. An attempt [76] to use the screened Coulomb interaction characterized by the phenomenological parameter - the Debye radius Rd [75] does not solve the problem since K(oo) has been still traditionally calculated in the same pair approximation. 

What is certain is that the initiation and propagation of a tear is a real and very important factor in the failure of rubber products, being involved in fatigue and abrasion processes as well as the catastrophic growth of a cut on the application of a stress. There is, therefore, considerable interest in the tearing resistance of rubbers. What is uncertain is how tear resistance should be measured and the results interpreted. 

We here summarize the results of Bader et a/.118 which are concerned with the definition of molecular structure and with the extension of this concept, together with the associated concept of a bond, to the dynamic case. A precise description and physical interpretation of the making and breaking of chemical bonds is presented by these workers in a quantitative analysis of the evolution of molecular structure. The topological analysis of the dynamic system, as pointed out by Collard and Hall,119 falls naturally into the realm of an existing and elegant mathematical theory, the catastrophe theory of Thom.120... 

The empty-site requirement in Eq. (28) can be physically interpreted in one of two different ways either the adsorbed A and B have to rearrange prior to reaction, or they are bound to more than one adsorption site. For the latter case, the intermediate concentration is low, thus allowing a pseudo-steady-state assumption. Through the application of bifurcation analysis and catastrophe theory this model was found to predict a very rich bifurcation and dynamic behavior. For certain parameter values, sub- and supercritical Hopf bifurcations as well as homoclinic bifurcations were discovered with this simple model. The oscillation cycle predicted by such a model is sketched in Fig. 6c. This model was also used to analyze how white noise would affect the behavior of an oscillatory reaction system... 

Precise U-Pb zircon analyses have further highlighted that major contemporaneous episodes spread across different continents, such as between 2.74 Ga and 2.66 Ga, and prompted speculation that these are the products of catastrophic turnover events in the Earth s mantle (Stein and Hofmann, 1994 Condie, 1998). Such interpretations are consistent with models of mantle processes in a hotter Earth (Hill, 1993 Davies, 1995). However, Archean rocks are preserved in just 7.5% of the Earth s surface (Goodwin, 1991), and so there is some uncertainty over the extent these age distributions and inferred episodicity are representative of major events in the Archean. 

Most experimental observations on polymer crystallization can be interpreted reasonably well by a number of crystallization theories, some of which differ fundamentally in their starting premises. Apart from the 61 catastrophe, the experimental AT dependencies of crystal thickness and growth rate can... 

Schenker, F., and Dietrich, V. J. (1986) The Lake Nyos gas catastrophe (Cameroon) a magmatological interpretation, Schweiz. Mineral. 

Unfortunately, the interpretation of health statistics is not reserved to the competent and the responsible, so we find growing out of the same body of vital data a catastrophe folklore on the one hand and a superman... 

The above observation has a physical interpretation. The unavailable region BD of the isotherm, at a continuous evolution on the catastrophe surface, corresponds to the region bounded by the curve BKC in Fig. 38. The sections AB and CD correspond to the superheated liquid and the supercooled vapour, respectively. It should be emphasized that the unavailability of the states BD derives from a model of the A3 catastrophe provided... 

The slow surface (3.78) corresponds to the catastrophe surface M3 of a cusp catastrophe (A3), see Fig. 54 in which the values of the control parameter which cannot be exceeded in a living organism are marked on the b-axis (recall that b is related to a biochemical state of the heart muscle). The four fundamental states of dynamics of the heartbeat may now be described in terms of the value of parameter a (tension of the cardiac muscle). Since the parameter a is constant for a given state, the states of the system lie on the sections a = const of the cusp catastrophe surface. The four states are conveniently represented in the (x, b) plane, Fig. 55, the parameter xn having to have such a value that the linearized system (3.76) does not have a stable stationary point. The four states shown in Fig. 55 have the following interpretation ... 

The Catastrophe. Population increases are not effected without hazard. If the initial rate is too steep or if N is too high, the sigmoid gives way to a peaked curve whose residual level is some fraction of the maximum population. This behavior, observed in latexes, has been interpreted (51) in terms of the percentage of substrate that is occupied by polymer. Most films break away from the substrate in the form of discrete Islands, reflecting the domain character of the residual stresses (in contrast with the stretched membrane analogy). Both cohesive and adhesive failures are observed. 

Submerged wave-cut notches (Blanchon et al. 2002), evidence for the catastrophic drainage of large volumes of meltwater from ice-dammed lakes into the ocean (Clarke et al. 2001) and buried barrier complexes (Stapor Stone 2004) all suggest that millennial/centennial oscillations in sea-level must have occurred in the Holocene. Some interpretations of regional Holocene sea-level... 

The interplay of those influences which inhibit adhesion and those which promote it must be recognized in interpreting two commonly encountered aspects of rubbing contact smooth, regular, controlled wear on the one hand, and destructive, self-accelerating catastrophe on the other. Figure 12-25 shows the appearance of two locations on a disk of hardened steel used in a pin-and-disk wear experiment at a contact pressure of 1069 MPa (10,900 kg/cm ) and a rubbing speed of 0.508 m/s with... 

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