Computation of bifurcation boundaries for power systems: A new Delta-plane method

This paper is devoted to the problems of finding the load flow feasibility, saddle node, and Hopf bifurcation boundaries in the space of power system parameters. The first part contains a review of the existing relevant approaches including not-so-well-known contributions from Russia. The second part presents a new robust method for finding the power system load flow feasibility boundary on the plane defined by any three vectors of dependent variables (nodal voltages), called the Delta plane. The method exploits some quadratic and linear properties of the load now equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). In addition to benefits for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally efficient for any quadratic algebraic problem.

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

Spring-neap tide-induced beach water table fluctuations in a sloping coastal aquifer

Predictions of water table fluctuations in coastal aquifers are needed for numerous coastal and water resources engineering problems. Most previous investigations have been based on the Boussinesq equation for the case of a vertical beach. In this note an analytical solution based on shallow water expansion for the spring- neap tide- induced water table fluctuations in a coastal aquifer is presented. Unlike most previous investigations, multitidal signals are considered with a sloping coastal aquifer. The new solution is verified by comparing with field observations from Ardeer, Scotland. On the basis of the analytical approximation the influences of higher- order components on water table elevation are examined first. Then, a parametric study has been performed to investigate the effects of the amplitude ratio (lambda), frequency ratio (omega), and phases (delta(1) and delta(2)) on the tide- induced water table fluctuations in a sloping sandy beach.

Numerical modelling of tide-induced beach water table fluctuations

Field studies have shown that the elevation of the beach groundwater table varies with the tide and such variations affect significantly beach erosion or accretion. In this paper, we present a BEM (Boundary Element Method) model for simulating the tidal fluctuation of the beach groundwater table. The model solves the two-dimensional flow equation subject to free and moving boundary conditions, including the seepage dynamics at the beach face. The simulated seepage faces were found to agree with the predictions of a simple model (Turner, 1993). The advantage of the present model is, however, that it can be used with little modification to simulate more complicated cases, e.g., surface recharge from rainfall and drainage in the aquifer may be included (the latter is related to beach dewatering technique). The model also simulated well the field data of Nielsen (1990). In particular, the model replicated three distinct features of local water table fluctuations: steep rising phase versus flat falling phase, amplitude attenuation and phase lagging.

Beach water table fluctuations due to wave run-up: Capillarity effects

High-frequency beach water table fluctuations due to wave run-up and rundown have been observed in the field [Waddell, 1976]. Such fluctuations affect the infiltration/exfiltration process across the beach face and the interstitial oxygenation process in the beach ecosystem. Accurate representation of high-frequency water table fluctuations is of importance in the modeling of (1) the interaction between seawater and groundwater, more important, the effects on swash sediment transport and (2) the biological activities in the beach ecosystem. Capillarity effects provide a mechanism for high-frequency water table fluctuations. Previous modeling approaches adopted the assumption of saturated flow only and failed to predict the propagation of high-frequency fluctuations in the aquifer. In this paper we develop a modified kinematic boundary condition (kbc) for the water table which incorporates capillarity effects. The application of this kbc in a boundary element model enables the simulation of high-frequency water table fluctuations due to wave run-up. Numerical tests were carried out for a rectangular domain with small-amplitude oscillations; the behavior of water table responses was found to be similar to that predicted by an analytical solution based on the one-dimensional Boussinesq equation. The model was also applied to simulate the water table response to wave run-up on a doping beach. The results showed similar features of water table fluctuations observed in the field. In particular, these fluctuations are standing wave-like with the amplitude becoming increasingly damped inland. We conclude that the modified kbc presented here is a reasonable approximation of capillarity effects on beach water table fluctuations. However, further model validation is necessary before the model can confidently be used to simulate high-frequency water table fluctuations due to wave run-up.

The preparation of reach to grasp movements in adults with Down syndrome

The aim of this study was to determine the extent to which adults with Down syndrome (DS) are able to utilise advance information to prepare reach to grasp movements. The study comprised ten adults with DS; ten children matched to an individual in the group with DS on the basis of their intellectual ability, and twelve adult controls. The participants used their right hand to reach out and grasp illuminated perspex blocks. Four target blocks were positioned on a table surface, two to each side of the midsagittal plane. In the complete precue condition, participants were provided with information specifying the location of the target. In the partial precue condition, participants were given advance information indicating the location of the object relative to the midsagittal plane (left or right). In the null condition, advance information concerning the position of the target object was entirely ambiguous. It was found that both reaction times and movement times were greater for the participants with DS than for the adults without DS. The reaction times exhibited by individuals with DS in the complete precue condition were lower than those observed in the null condition, indicating that they had utilised advance information to prepare their movements. In the group with DS, when advance information specified only the location of the target object relative to the midline, reaction times were equivalent to those obtained when ambiguous information was given. In contrast, the adults without DS exhibited reaction times that were lower in both the complete and partial precue conditions when compared to the null condition. The pattern of results exhibited by the children was similar to that of the adults without DS. The movement times exhibited by all groups were not influenced by the precue condition. In summary, our findings indicate that individuals with DS are able to use advance information if it specifies precisely the location of the target object in order to prepare a reach to grasp movement. The group with DS were unable, however, to obtain the normal advantage of advance information specifying only one dimension of the movement goal (i.e., the position of an object relative to the body midline). (C) 2001 Elsevier Science B.V. All rights reserved.

Ab initio modelling of basal plane oxidation of graphenes and implications for modelling char combustion

Ab initio calculations have been performed to determine the energetics of oxygen atoms adsorbed onto graphene planes and the possible reaction path extracting carbon atorns in the form of carbon monoxide. Front the energetics it is confirmed that this reaction path will not significantly contribute to the gasification of well ordered carbonaceous chars. Modelling results which explore this limit Lire presented. (C) 2002 Elsevier Science Ltd, All rights reserved.

A framework for table driven testing of Java classes

With the advent of object-oriented languages and the portability of Java, the development and use of class libraries has become widespread. Effective class reuse depends on class reliability which in turn depends on thorough testing. This paper describes a class testing approach based on modeling each test case with a tuple and then generating large numbers of tuples to thoroughly cover an input space with many interesting combinations of values. The testing approach is supported by the Roast framework for the testing of Java classes. Roast provides automated tuple generation based on boundary values, unit operations that support driver standardization, and test case templates used for code generation. Roast produces thorough, compact test drivers with low development and maintenance cost. The framework and tool support are illustrated on a number of non-trivial classes, including a graphical user interface policy manager. Quantitative results are presented to substantiate the practicality and effectiveness of the approach. Copyright (C) 2002 John Wiley Sons, Ltd.

Tide-induced water table fluctuations in coastal aquifers bounded by rhythmic shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer's properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Modified logit life table system: Principles, empirical validation, and application

Despite its widespread use, the Coale-Demeny model life table system does not capture the extensive variation in age-specific mortality patterns observed in contemporary populations, particularly those of the countries of Eastern Europe and populations affected by HIV/AIDS. Although relational mortality models, such as the Brass logit system, can identify these variations, these models show systematic bias in their predictive ability as mortality levels depart from the standard. We propose a modification of the two-parameter Brass relational model. The modified model incorporates two additional age-specific correction factors (gamma(x), and theta(x)) based on mortality levels among children and adults, relative to the standard. Tests of predictive validity show deviations in age-specific mortality rates predicted by the proposed system to be 30-50 per cent lower than those predicted by the Coale-Demeny system and 15-40 per cent lower than those predicted using the original Brass system. The modified logit system is a two-parameter system, parameterized using values of l(5) and l(60).

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.