The calculation of accurate triode characteristics using a modern high-speed computer

This paper presents a novel way to determine new reaction rate parameters (A’s and Ea’s in the Arrhenius expression) in a semi-detailed reaction mechanism for the thermal degradation of aviation fuel and surface fouling. The technique employed is a specialised optimisation procedure, namely a genetic algorithm (GA), which utilises an abstraction of the Darwinian principle of survival of the fittest in order to “breed” good solutions over a predefined number of “generations”. Deposition rates for a given fuel which have been measured experimentally over a range of conditions are reproduced by solving the conservation equations of mass, momentum, energy and species using a CFD code and the optimised set of rate constants obtained using a genetic algorithm inversion process. The new set of rate constants lie within predefined boundaries based upon previous values found in the literature for the mechanism being used. In addition, this powerful technique promises the ability to develop reaction mechanisms whose newly optimised rate constants reproduce closely all the experimental data available, enabling a greater confidence in their predictive capabilities. The process is also shown to be an effective tool to facilitate the elucidation of shortcomings in current global chemistry models of fuel degradation. Therefore, the results of this study demonstrate that the genetic algorithm inversion process may be used to develop and calibrate more detailed models for the thermal stability behaviour of aviation fuels than have been seen previously and, subsequently, accurately predict the locations and rates of deposit build-up in fuel handling systems. Furthermore, it has been demonstrated that, modern high speed computers allow for evaluation of increasingly complex and expensive GA objective functions.

A theory of the current distribution in triodes with positive grid is developed on the assumption that space charge and the initial velocities of both primary and secondary electrons may be neglected. This theory, which is originally due to De Lussanct de la Sabloniere, has been put in a more lucid form; and a graphical method has been developed to check the applicability of this theory to any set of observations. From the graphs used for this purpose the different distribution functions which enter the equations can be read off in a very simple manner. In some cases theory and experiment are in excellent agreement; discrepancies occurring in other cases are discussed. In connection with these observations the basic assumptions underlying the theory are subjected to a closer scrutiny.

Recently, there has been much interest in the use of Bayesian statistical methods for performing genetic analyses. Many of the computational difficulties previously associated with Bayesian analysis, such as multidimensional integration, can now be easily overcome using modern high-speed computers and Markov chain Monte Carlo (MCMC) methods. Much of this new technology has been used to perform gene mapping, especially through the use of multi-locus linkage disequilibrium techniques. This review attempts to summarise some of the currently available methods and the software available to implement these methods.

The technique of real-time simulation for studying air traffic control problems has been employed for many years. This technique has enabled investigators to simulate live air traffic situations for the purpose of evaluating new concepts and their relationship to the air traffic controller. The modern high-speed digital computer has increased the scope of these real-time simulation studies to include large scale air traffic control systems employing such computers in the control process.

Computer simulation and analysis techniques for reliable circuit design

Many problems of optimization, search, or decision-making are combinatorial in nature and basically non-numerical. The advent of the modern high-speed digital computer has opened the way for us to solve many of these problems. Although virtually all of these problems are finite, it is well-known that their size grows extremely rapidly and we can usually expect the computer to do by exhaustive search just a few cases larger than what can be done by hand. Intelligent search procedures such as banach and bound (Little, Murty, Sweeney and Karel (1963), Lawles and Wood (1964)), back-track programming (Golomb and Baument (1965), Walker (1960)), linear or dynamic programming (Gomery (1963), Bellman (1962), Held and Karp (1962)), together with isomorphic rejection (Swift, 1960) help to reduce the total number of cases to be considered but more often than not, we are interested in the solution to problems which are still too large for these techniques. Here some sort of heuristics have to be employed, whereby we hope that the solution (in the instance where a solution when found may be readily verified), or a probably solution, or a useful partial or approximate solution may be obtained in reasonable computation time.

A confidence interval is an interval estimate of a parameter of a population calculated from a sample drawn from the population. Bootstrapping method, which involves producing several new data sets that are resampled from the original data in order to estimate parameter for each newly created data set, allowing an empirical distribution for the parameter to be estimated. Since certain statistics are harder to estimate, confidence intervals are rarely employed. Several statistics might necessitate multi-step formulas assuming that are impractical for calculating confidence intervals. This paper reviews research on the concept of bootstrapping and bootstrap confidence interval. The current narrative analysis was developed to answer the main research question: (1) What is the concept of the bootstrap method and bootstrap confidence interval? (2) What are the methods of bootstrapping to obtain confidence interval? This study has found general bootstrap method idea, various techniques of bootstrap methods, its advantages and disadvantages, and its limitations. There are normal interval method, percentile bootstrap method, basic method, first-order normal approximation method, bias-corrected bootstrap, accelerated bias-corrected bootstrap and bootstrap-t method. This study concludes that the advantages of using bootstrap CI is that it does not require any assumptions about the shape of distribution and universality of the approach. Bootstrapping is a computer-intensive statistical technique that relies significantly on modern high-speed digital computers to do massive computations.

Using a semiclassical model, we investigate the effect of the initial longitudinal velocity of the tunnel-ionized electron on low-energy structure (LES) in above-threshold ionization (ATI) spectra. Our analysis shows that the effect (reduction or enhancement) of the initial longitudinal velocity pz0 on the LES is dependent on the direction of the initial longitudinal velocity. For the initial longitudinal velocity along the direction of the laser electric field at the moment of tunneling (i.e., pz0 > 0), the Coulomb interaction between the photoelectron and ion core is enhanced, while for the initial longitudinal velocity in the opposite direction (i.e., pz0 < 0), the Coulomb effect is reduced. Our work provides solid evidence that the initial electron longitudinal velocity has considerable effect on the photoelectron dynamics in the ATI process.

The theoretical treatment is given for the case when the emission or absorption of a weak-fied photon of arbitrary frequency ω1 during a scattering process takes places in the presence of a strong laser field. The general formulation of the theory which is given in detail corresponds more properly to the case when an electron is scattered by a static potential in the presence of two arbitrary radiation fields. Part of theory is expected to cover also the process of the stimulated bremsstrahlung. A selected set of calculations is performed in the first order in the scattering potential for the case when one of the two fields is weak. The effects of the two fields are always treated exactly. The chosen geometry is the parallel one, in which the two linearly polarized fields are parallel to the initial electron velocity. The presence of a strong assisting field is found to yield several significant modification of the characteristics of emission/absorption of a weak-field photon. In paritcular, i) the final electron energy distribution is drastically altered; ii) angular distributions and total cross-sections of emission and absorption are modified up to become largely similar; iii) when the oscillatory velocity v0 is approximately equal to the incoming velocity vi, the cross-sections experience rapid variations, generally in the sense of the growth; iv) for higher intensities, when v0>vi the strong field is found instead to dump considerably all the cross-sections, besides making emission and absorption similar. Accordingly, in the high-intensity domain, the question whether or not emissions prevail over absorptions looses part of its importance. In general, calculation shows that the quantities, accounting for the balance between emission and absorption, exhibit strong oscillations above and below zero either as a function of the strong-field intensity or as a function of the weak-field frequency.

The net absorption coefficient allowing for stimulated emission in a nonrelativistic plasma is calculated using the cross sections found by Bunkin and Fedorov. The computations range over many values of their two parameters, which are determined by the initial electron velocity and the frequency and intensity of the electromagnetic field. The energy absorbed is found at strong enough flux to decrease with increasing flux and to be primarily determined by single photon processes for all parameter values considered.

A technique to take into account the initial transverse electron thermal velocities in converged sheet electron beams has been developed. This determines the main integral characteristics of a thermal beam in a gun and transportation region of the paraxial approximation via chosen characteristic electron trajectories. We have equations of characteristic electrons motion, initial conditions to solve equations, and formulas for the current density distribution in the thermal beam cross-section and current fraction in conventional boundary. The derived equations and formulas may be used in modeling electron-optical systems and choosing parameters in which the effect of heat electron motion on beam characteristics will lie within tolerable limits.

Universal 1/f noise is shown to originate from the variations in the initial velocities of conduction electrons after collisions with defects. Defect atoms, after being struck by conduction electrons, recoil and form an impacted mass of lattice atoms. Conduction electrons emitted after a collision have an average initial velocity which steadily decreases as the impacted mass builds up. It is shown that this process yields a noise spectrum of the form f−n where n is in the vicinity of one and has an amplitude given by the Hooge empirical formula. Variations from the Hooge result are discussed. The model described applies to all semiconductors and metals.

Much of the published data on steam cycles cannot be applied to modern power stations owing to the advanced steam conditions and complex cycles now used. Plant optimization therefore requires the detailed analysis of a large number of cycles over a wide range of steam conditions Modern high-speed digital computers offer the engineer relief from the tedium of lengthy calculations and the uncertainty of broad simplifying assumptions. The Ferranti ‘Mercury’ computer is used in the present work and, for economy in computing time, separate boiler and turbine programmes are written and the results combined through a short desk calculation The turbine programme, which is applicable to both conventional and nuclear stations, is sufficiently general to deal with all anticipated steam conditions and cycle arrangements and it also takes account of minor cycle corrections. Possible variations in boiler design, however, make a similarly general treatment more difficult and several separate programmes are described here, each dealing with a steam cycle and boiler design suitable for use with the low-temperature gas-cooled reactors being built in Britain at present Application of the programmes to the design optimization of a complete nuclear power station is discussed

Modern high-speed digital computers have made possible the solution, by theoretical-numerical techniques, of many problems in electromagnetics that have traditionally been solvable only by experimental methods. Formulated in terms of integral equations, the techniques described yield answers, with an accuracy and completeness unobtainable by experimental methods, in a small fraction of the time and at much less cost than by the experimental approach. Computer programs utilizing these techniques have been developed in the areas of radiation and scattering from arbitrary wire-antenna structures, bodies of revolution, and cylindrical bodies of arbitrary cross section.

The results of numerical simulations of a triode source of an intense radial converging electron beam are presented. The role of the initial transverse velocity of electrons, defocusing effect of the controlling grid, the beam self-magnetic field, backscattering of electrons, and ion flow from the target is analyzed. It was found that the ion flow from the target essentially increases the value of the electron current. The influence of the beam self-magnetic field on electron trajectories leads to the fact that there is a critical value of the cathode-grid voltage dividing the mode of the source operation into stable and unstable. The influence of initial transverse electron energies on the beam focusing is essentially higher than the influence of the controlling grid. Backscattering of the beam electrons from the target surface increases the target ion current so that the source operation may become unstable and the distribution of the beam power density on the target becomes nonuniform with a maximum in the center. Electrons passing by the target drift along the source axis. This leads to diminishing the power density at the center of the target and to the exit of peripheral electrons from the source. Conditions for achieving required electron beam parameters (the electron kinetic energy—120 keV, the beam energy density on the target ∼40 J/cm2 on a maximum possible length of the target surface) were determined.