Rare event

Berne B J 1985 Molecular dynamics and Monte Carlo simulations of rare events Multiple Timescales ed J V Brackbill and B I Cohen (New York Academic Press)... 

This chapter concentrates on describing molecular simulation methods which have a counectiou with the statistical mechanical description of condensed matter, and hence relate to theoretical approaches to understanding phenomena such as phase equilibria, rare events, and quantum mechanical effects. 

Some people prefer to use the multiple time step approach to handle fast degrees of freedom, while others prefer to use constraints, and there are situations in which both techniques are applicable. Constraints also find an application in the study of rare events, where a system may be studied at the top of a free energy barrier (see later), or for convenience when it is desired to fix a thennodynamic order parameter or ordering direction... 

With the rapid development of computer power, and the continual hmovation of simulation methods, it is impossible to predict what may be achieved over the next few years, except to say that the outlook is very promising. The areas of rare events, phase equilibria, and quantum simulation continue to be active. 

Carter E A, Ciccotti G, Hynes J T and Kapral R 1989 Constrained reaction coordinate dynamics for the simulation of rare events Chem. Phys. Lett. 156 472-7... 

A substantial sunnner school proceedings, concentrating on modem teclmiques for studying rare events and quantum mechanical phenomena. 

In the rare event in which the solid is known to be composed of cubes or spheres all of the same size, the problem is simple. Equation (l.Sl) can be applied and we have... 

Finding a totally new pigment class or chromophore is a rare event. The latest commerciali2ation of a new family of pigments is represented by the pyrrolopyrroles discovered ia 1983. The discovery years of important pigments are compiled ia the foUowiag. 

There are a variety of ways to express absolute QRA results. Absolute frequency results are estimates of the statistical likelihood of an accident occurring. Table 3 contains examples of typical statements of absolute frequency estimates. These estimates for complex system failures are usually synthesized using basic equipment failure and operator error data. Depending upon the availability, specificity, and quality of failure data, the estimates may have considerable statistical uncertainty (e.g., factors of 10 or more because of uncertainties in the input data alone). When reporting single-point estimates or best estimates of the expected frequency of rare events (i.e., events not expected to occur within the operating life of a plant), analysts sometimes provide a measure of the sensitivity of the results arising from data uncertainties. 

Synthesizing the frequencies of rare events involves (1) determining the important combinations of failures and circumstances that can cause the accidents of interest, (2) developing basic failure data from available... 

Absolute risk estimates can be difficult to use when there is no apparent human experience against which to calibrate them. By definition, there never exists enough experience about catastrophic rare events (fortunately) with which to calibrate the thinking about their significance. If there were enough data, you would not have elected to do the QRA in the first place. So, now thatyou have a bottom line estimate... 

The basic chemical description of rare events can be written in terms of a set of phenomenological equations of motion for the time dependence of the populations of the reactant and product species [6-9]. Suppose that we are interested in the dynamics of a conformational rearrangement in a small peptide. The concentration of reactant states at time t is N-n(t), and the concentration of product states is N-pU). We assume that we can define the reactants and products as distinct macrostates that are separated by a transition state dividing surface. The transition state surface is typically the location of a significant energy barrier (see Fig. 1). 

If the form of the distributional model is only approximately eorreet, then the tails may differ substantially from the tails of the aetual distribution. This is beeause the model parameters, related to low order moments, are determined from typieal rather than rare events. In this ease, design deeisions will be satisfaetory for bulk... 

The original steam generators were simple pressure vessels that were prone to caiasirophic failures and loss of life. Due to better boiler design, tube-fired boilers, and boiler inspections, the incidence of catastrophic failure is now to a rare event (about once every 100,000 vessel-years). In Great Britain in 1866, there were 74 steam boiler explosions causing 77 deaths. This was reduced to 17 explo.sions and 8 deaths in 1900 as a result of inspections performed by the Manchester Steam User Association. In the United States, the American Society of Mechanical Engineers established the ASME Pressure Ves.sel Codes with comparable reductions. 

Mosleh, A. and G. Apostolakis. Some Properties of Distributions Useful in the Study of Rare Events. IEEE Transactions on Reliability, Vol. R-31, April 1982, pp. 87-94. 

The plate heat exchanger consists of a frame in which closely spaced metal plates are clamped between a head and follower. The plates have corner ports and are sealed by gaskets around the ports and along the plate edges. A double seal forms pockets open to atmosphere to prevent mixing of product and service liquids in the rare event of leakage past a gasket. 

Very few 1-unsubstituted 17/-azcpines have been isolated and, as a consequence, substitution at nitrogen is a rare event however, 1-mesyl-l//-azepine (8) and l-(trimethylsilyl)-l //-azepine (9) can be obtained by treating 1//-azepine (7) with mesyl chloride and with trimethylsilyl trifluoromethanesulfonate, respectively.9... 

Repeated splitting of lineages of organisms into separate species has resulted in the great richness and diversity of life that lived in the past and is found on Earth today. Earth would be very different if speciation had been a rare event during the life s history. Biogeochemical cycles are influenced by millions of species, each adapted to live under a particular range of conditions and to use environmental resources in a particular way. 

An example is a view given to us by a discovery manager that if a drug candidate could not reach a successful market launch, the next best thing for a discovery team would be to have their compound progress to late stages of development before failure, because this implies that any problem was hard to predict, for example, a rare event. Yet this is exactly the most expensive kind of failure. 

The rate is thus the number of collisions between A and B - a very large number - multiplied by the reaction probability, which may be a very small number. For example, if the energy barrier corresponds to 100 kj mol , the reaction probability is only 3.5 x lO l at 500 K. Hence, only a very small fraction of all collisions leads to product formation. In a way, a reaction is a rare event For examples of the application of collision theory see K.J. Laidler, Chemical Kinetics 3 Ed. (1987), Harper Row, New York. 

As is well known in calculations of rare events [6, 16, 96], it is notoriously inefficient to start the simulation of trajectories with initial conditions sampled in one of the metastable states. Instead, initial conditions should be sampled at the transition state, which ensures that all trajectories cross the transition state at least once and thereby drastically improves the sampling of reactive events. In the model system (48), such an ensemble is given by... 

Burgundy s horse was killed in the first charge. It is not a rare event, a common but unlucky chance, and almost all men spoke of it thus. There were rumors, but none believed them. Next day we fought with axes, but Edward stopped the fight after half a dozen strokes that we might end alive and equal in honor. 

The symbols refer to a single component. Since molecular collisions are rare events in Knudsen flow, flow and diffusion are synonymous and each component of a mixture behaves as if it alone were present. Numerical values of the Knudsen diffusivity for molecules of ordinary weight at ordinary temperatures range from 0.01 cm2/sec for pores with a radius of 10 A up to about 10 cm2/sec for pores with 10,000 A radii. 

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