Historical simulation method

The approach is similar to the historical simulation method, except that it creates the hypothetical changes in prices by random draws from a stochastic process. It consists of simulating various outcomes of a state variable (or more than one in case of multifactor models), whose distribution has to be assumed, and pricing the portfolio with each of the results. A state variable is the factor underlying the price of the asset that we want to estimate. It could be specified as a macroeconomic variable, the short-term interest rate or the stock price, depending on the economic problem. 

A rather crude, but nevertheless efficient and successful, approach is the bond fluctuation model with potentials constructed from atomistic input (Sect. 5). Despite the lattice structure, it has been demonstrated that a rather reasonable description of many static and dynamic properties of dense polymer melts (polyethylene, polycarbonate) can be obtained. If the effective potentials are known, the implementation of the simulation method is rather straightforward, and also the simulation data analysis presents no particular problems. Indeed, a wealth of results has already been obtained, as briefly reviewed in this section. However, even this conceptually rather simple approach of coarse-graining (which historically was also the first to be tried out among the methods described in this article) suffers from severe bottlenecks - the construction of the effective potential is neither unique nor easy, and still suffers from the important defect that it lacks an intermolecular part, thus allowing only simulations at a given constant density. 

The organization of this chapter is as follows. In the following section, Sec. 4.2, the elastic and inelastic interaction cross sections necessary for simulating track structure (geometry) will be discussed. In the next section, ionization and excitation phenomena and some related processes will be taken up. The concept of track structure, from historical idea to modern track simulation methods, will be considered in Sec. 4.4, and Sec. 4.5 deals with nonhomogeneous kinetics and its application to radiation chemistry. The next section (Sec. 4.7) describes some application to high temperature nuclear reactors, followed by special applications in low permittivity systems in Sec. 4.8. This chapter ends with a personal perspective. For reasons of convenience and interconnection, it is recommended that appropriate sections of this chapter be read along with Chapters 1 (Mozumder and Hatano), 2 (Mozumder), 3 (Toburen), 9 (Bass and Sanche), 12 (Buxton), 14 (LaVerne), 17 (Nikjoo), and 23 (Katsumura). 

For linear systems, the differential equation for the jth cumulant function is linear and it involves terms up to the jth cumulant. The same procedure will be followed subsequently with other models to obtain analogous differential equations, which will be solved numerically if analytical solutions are not tractable. Historically, numerical methods were used to construct solutions to the master equations, but these solutions have pitfalls that include the need to approximate higher-order moments as a product of lower moments, and convergence issues [383]. What was needed was a general method that would solve this sort of problem, and that came with the stochastic simulation algorithm. 

Reaction to Historic Washing Methods. A.A.T.C.C. Test Method 61-1962 IA was adapted to simulate historic cleaning methods. A 0.5% soap solution was substituted for the 0.5% detergent solution. Two kinds of soap were used, since, as reported in another study, both were available earlier in this century (1). 

A genuine history is not offered here, but some historical perspective is required to appreciate what has been achieved. We suggest a natural division of that history into three periods (a) a pioneering era prior to 1957 (the year that molecular simulation methods changed the field [Wood, 1986 Ciccotti etal., 1987 Wood, 1996]), (b) the decade or so after 1957 when the theory of serious prototype liquid models achieved an impressive maturity, and (c) the present era including the past three decades, approximately. 

To conclude, historical simulation with all its variants is another method that relies on past data to predict the future. It has problems coping with complex instruments, instruments with no history, and where the number of observations is limited. We look at a method that uses numerous computer simulations to overcome this, the Monte Carlo simulation, in the next section. 

However, both methods suffer from the same assumption whether you utilize a historical return distribution (historical simulation) or choose to model an arbitrary distribution (Monte Carlo), the dependence on such a distribution prevailing in the future can be dangerous, if not disastrous. (WorldCom, Enron, need we go on ) The resolution lies in analytics that make no such assumptions, and are flexible in modelling various scenarios or outcomes. 

Computer simulations also constitute an important basis for the development of the molecular theory of fluids. They could be regarded as quasiexpeiimental procedures to obtain datasets that connect the fluid s microscopic parameters (related mainly to the structure of the system and the molecular interactions) to its macroscopic properties (such as equation of state, dynamic coefficients, etc.). In particular, some of the first historical simulations were performed using two-dimensional fluids to test adaptations of commonly used computer simulation methods [14,22] Monte Carlo (MC) and molecular dynamics (MD). In fact, the first reliable simulation results were obtained by Metropolis et al. [315], who applied the MC method to the study of hard-sphere and hard-disk fluids. 

Timescales are important features of dynamical models. Whilst historically we may be used to identifying individual timescales with individual species within a mechanism, we demonstrated in Chap. 6 that within a nonlinear kinetic model, there is usually not a one-to-one relationship between them. Nevertheless, we showed that the relationship between species and timescales, and the dynamic changes in timescales during a model simulation, can be explored using perturbation methods. Timescales are related to the stiffness of dynamical models, which is an important feature for the selection of appropriate numerical simulation methods. However, the wide range of timescales and the timescale separation can be exploited within the context of model reduction, and therefore, there are important links between Chaps. 6 and 7 in this regard. 

All these observations tend to favour the Verlet algoritlnn in one fonn or another, and we look closely at this in the following sections. For historical reasons only, we mention the more general class of predictor-corrector methods which have been optimized for classical mechanics simulations, [40, 4T] further details are available elsewhere [7, 42, 43]. 

The model contains a surface energy method for parameterizing winds and turbulence near the ground. Its chemical database library has physical properties (seven types, three temperature dependent) for 190 chemical compounds obtained from the DIPPR" database. Physical property data for any of the over 900 chemicals in DIPPR can be incorporated into the model, as needed. The model computes hazard zones and related health consequences. An option is provided to account for the accident frequency and chemical release probability from transportation of hazardous material containers. When coupled with preprocessed historical meteorology and population den.sitie.s, it provides quantitative risk estimates. The model is not capable of simulating dense-gas behavior. 

Because efficient methods for computing free volumes from molecular simulations were introduced only recently, their connections to the dynamical properties of liquids have yet to be explored systematically. Nonetheless, initial investigations have already allowed scrutiny of some historical notions about these properties. Here, we briefly discuss two of these initial studies. Their results illustrate that some early free-volume based ideas about the origins of dynamics are consistent with simulation data, but those ideas will need significant revision if they are to be applied in a general way. 

An exact determination of the relative values of P for the BPTI and villin simulations is not possible, because some algorithmic developments reduce computational costs (particularly methods that allow one to increase the size of the time step and to efficiently treat long-range interactions), while others increase the costs (e.g., more detailed force fields and appropriate boundary conditions). But we can place reasonable bounds on the historical growth rate of P by using r=l and r=2 as lower and upper limits on the costs of calculating interatomic interactions. 

The Schrodinger equation can also be solved semi-empirically, with much less computational effort than ab initio methods. Prominent semi-empirical methods include MNDO, AMI, and PM3 (Dewar 1977 Dewar etal. 1985 Stewart 1989a Stewart 1989b). The relative computational simplicity of these methods is accompanied, however, by a substantial loss of accuracy (Scott and Radom 1996), which has limited their use in geochemical simulations. Historically, semi-empirical calculations have also been limited by the elements that could be modeled, excluding many transition elements, for example. Semi-empirical calculations have been used to predict Si, S, and Cl isotopic fractionations in molecules (Hanschmaim 1984), and these results are in qualitative agreement with other theoretical approaches and experimental results. 

The historical context of uncertainty estimation in exposure assessment can be traced to the convergence of developments in multiple disciplines. For example, Stanislaw Ulam and John von Neumann are typically credited with creation of the Monte Carlo method for simulation of random events in 1946 (see Metropolis Ulam, 1949 Eckhardt, 1987). However, a paper by Lord Kelvin in 1901 appears to apply concepts similar to Monte Carlo to a discussion of the Boltzmann equation, and there are other precedents (Kelvin, 1901). The modem incarnation of Monte Carlo was first used for prediction of neutron release during nuclear fission and has since been applied in a wide variety of disciplines. 

In this chapter we focus on a few selective new VCD applications reported in the last 5 years, along with a brief review of the basic experimental techniques and theoretical methods. The remainder of this chapter is organized as follows. In the next section, we will present the VCD experimental technique with a short review of VCD instrumentation and some recent developments, and describe the usual procedure to obtain VA and VCD measurements in solution and in thin film states. In Sect. 3 the associated VCD computational simulations will be illustrated. This includes a brief historical overview of the theory development, and some basics related to VCD calculations, as well as the typical procedure of carrying out VCD simulations. The main part of this chapter deals with the diverse applications of VCD spectroscopy, focusing on the new developments in the last 5 years. Since there are a large number of publications which are dedicated to AC determinations of many interesting and important chiral molecules, a comprehensive review of all... 

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