Analytical Counterpart Research Articles

RISK ANALYSIS IN CONSTRUCTION NETWORKS USING A MODIFIED STOCHASTIC ASSIGNMENT MODEL

A review of construction network analysis indicates that new methods are needed for quantifying risks in project evaluation. The paper proposes a new analytical method, the Modified Stochastic Assignment Model (MSAM), for the prediction of project duration. The proposed method is inspired by a previous method used solely in traffic networks, the Stochastic Assignment Model (SAM). The MSAM method applies Clark's approximation to find the longest project duration. Two cases are used to demonstrate the validity and application of the MSAM in construction project evaluations. The accuracy of the MSAM is assessed by comparing it with the Monte Carlo Simulation (MCS). A comparison of the MSAM with other methods, such as PERT and PNET, has also been presented. It is found that the new method is an analytical counterpart of the MCS and is very efficient in saving computational time whilst taking full account of the correlations between paths.

Smooth Measures and Regular Strongly Supermedian Kernels Generating Sub-Markovian Resolvents

In the context of a transient Borel right Markov process with a fixed excessive measure ξ, we characterize the regular strongly supermedian kernels, producing smooth measures by the Revuz correspondence. In the case of the measures charging no ξ-semipolar sets, this is the analytical counterpart of a probabilistic result of Revuz, Fukushima, and Getoor and Fitzsimmons, concerning the positive continuous additive functionals. We also consider the case of the measures charging no set that is both ξ-polar and ρ-negligible (ρ○U being the potential part of ξ), answering to a problem of Revuz.

Time-correlation functions from band-shape fits without Fourier transform

A fitting method is described which enables one to model real line profiles intermediate between Lorentzian and Gaussian by an analytical function which has an analytical counterpart in the time domain. The applications of this method comprise: (1) finding time correlation functions and correlation times by fits in the frequency domain without Fourier transforms; and (2) the decomposition of overlap lines obtaining dynamic parameters at the same time.

SENSITIVITY ANALYSIS FOR BOUNDARY ELEMENT ERROR ESTIMATION AND MESH REFINEMENT

The subject of this paper is the sensitivity analysis of approximate boundary element solutions with respect to the positions of the collocation points. The direct differentiation approach is considered here and the analysis is performed analytically. Since only the collocation points are perturbed, the shape of the body and the corresponding discretization remain unaltered. This aspect makes the present work quite different in spirit with respect to earlier analyses on shape sensitivities. Sensitivities of approximate BEM solutions with respect to the positions of collocation points are shown to be related to the residual of hypersingular integral equations. Numerical results confirm that the present approach can be seen as the analytical counterpart of an adaptive scheme for mesh refinement presented by the same author in some recent papers. Some other advantages of the present approach over the former one are also outlined.

SENSITIVITY ANALYSIS FOR BOUNDARY ELEMENT ERROR ESTIMATION AND MESH REFINEMENT

The subject of this paper is the sensitivity analysis of approximate boundary element solutions with respect to the positions of the collocation points. The direct differentiation approach is considered here and the analysis is performed analytically. Since only the collocation points are perturbed, the shape of the body and the corresponding discretization remain unaltered. This aspect makes the present work quite different in spirit with respect to earlier analyses on shape sensitivities. Sensitivities of approximate BEM solutions with respect to the positions of collocation points are shown to be related to the residual of hypersingular integral equations. Numerical results confirm that the present approach can be seen as the analytical counterpart of an adaptive scheme for mesh refinement presented by the same author in some recent papers. Some other advantages of the present approach over the former one are also outlined.

Photorefractive phase conjugation of pulses: A numerical and analytical comparison

We study numerically the temporal behavior of the phase conjugation of a pulse, by a single four-wave mixing grating, in photorefractive media. We solve numerically the time-dependent coupled-wave equations obtained from a currently used generalization of the Khuktarev model, under the standard restriction of undepleted pump and slowly varying envelope approximations. The fully numerical solutions presented here are terminal solutions that do not require solving any intermediate steps such as the reflectivity. However, we compare the numerical reflectivity with its analytical counterpart, when available, and discuss the differences on their predictions of the phase conjugate pulse.

Dissociation–recombination relaxation behind a normal shock

Mathematical methods developed originally for thermal explosion theory are used to study the evolution of a dissociation–recombination process occurring in a compressible gas behind a normal shock. The dissociation–recombination reaction, AB+M■A+B+M, is assumed to have a relatively large dissociation temperature, so that high activation energy perturbation techniques can be used to derive general parameter dependent analytical solutions. Spatial variation of the dependent variables is described in three zones, each of distinct length scale and physical character. Initially, small changes in temperature, concentrations, density, and pressure occur in the relatively high temperature dissociation initiation zone. In the subsequent broader major dissociation region, most of the specie AB is converted to A and B and there are significant variations in all physical variables. In the last and thickest zone, recombination becomes important as the reactive flow evolves to a final equilibrium state. The results provide an analytical counterpart to numerical solutions obtained earlier by Freeman [J. Fluid Mech. 4, 407 (1958)] and Matthews [Phys. Fluids 2, 170 (1959)] for the now classical problem of idealized diatomic gas dissociation.

Some remarks on the structure of intermediate magnetohydrodynamic shocks

Though being unstable in the framework of ideal dynamics, intermediate MHD shocks can often be realized in the presence of dissipative effects. Numerical experiments by Wu which predict this phenomenon have an analytical counterpart: Mathematical proofs are reported here for the fact that for arbitrary positive values of the four dissipation coefficients (two coefficients of fluid viscosity, one for electrical resistivity, and one for heat conductivity) many shocks of the types 0 → 3, 0 → 2, and 1 → 2 possess structure. Consequently, this is the case for physically interesting values of these coefficients.

The dynamics of a non‐linear discrete oscillator

AbstractThe dynamic behaviour of a simple second‐order discrete system with a single non‐linear factor, specified by (x, y)‐ (Ax + B(y + sin(2π(x +y))), x), (A, B) ϵ D = {(A, B): A, B ≥ 0, A + B < 1} ‐ is studied. the parameter subspace of D is analysed in detail. the bifurcation sets of the system are found. the existence of chaos in the system is proved by applying Marotto's theorem. the result of computer simulation agrees well with its analytical counterpart, and confirms that the single non‐linear factor ϕ = sin(2π(x + y)) is indeed the crucial point of a very complicated dynamic behaviour, including the alternative emergence of periodic, quasi‐periodic and chaotic phenomena, of this simple second‐order oscillator.

Dielectrophoretic capture on single rods in creeping flow: Theory, trajectories and experimental data

The theoretical aspects of dielectrophoresis with a rod matrix are presented briefly with emphasis on the creeping flow regime. Particle trajectories are computed numerically in the general case and the critical trajectory ordinates in the numerical solution are compared to their analytical counterpart. Experimental results obtained with a high-frequency field provide qualitative verification of the theory.

Internal consistency of a water analysis and uncertainty of the calculated distribution of aqueous species at 25°C

Many water analyses contain more than the minimum number of analytical determinations needed to calculate the distribution of species at ~ 25°C. The speciation of a water that contains n cations and ligands other than H + and OH − can be calculated if just n analytical determinations are available. In the frequent case where n + 1 (or more) determinations are available, one can calculate from the speciation a value for the ( n + 1)th variable. The comparison between this computed value and its analytical counterpart (not used in calculating the speciation) constitutes a test for internal consistency among the n + 1 determinations that make up the whole analysis. Application of this test requires knowing the uncertainties of the calculated speciation and of the value computed for the ( n + 1)th variable from the speciation. Such uncertainties have been ignored in previous algorithms, but have been determined herein by a Monte Carlo method of error propagation which is very well suited to systems of nonlinear algebraic equations. By comparing the titration alkalinity against the alkalinity calculated from the speciation, several published analyses for which the cation/anion balance is < 3% can be shown to be internally inconsistent. Such analyses may be unsuitable for geochemical calculations (water/rock interaction, estimation of reservoir temperatures, etc.). Several existing speciation algorithms disregard the possibility that the analytical data used as input are internally inconsistent.

Queueing Theory in Fast Time Simulation of Air Traffic Control

the use of queueing theory in understanding certain Air Traffic Control problems is discussed. Two primary areas of application are given as: (a) Providing a theoretical comparison for experimental (simulation) results; (b) Obtaining solutions to certain small scale problems not justifying a simulation study. A brief introduction on the general theory is given, followed by a presentation of certain developments found in the literature applicable to Air Traffic Control, and especially as an analytical counterpart to Fast-Time Simulation. Two examples illustrate applications.