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.

Analysis of small signal stability margins using genetic optimization

Power system small signal stability analysis aims to explore different small signal stability conditions and controls, namely: (1) exploring the power system security domains and boundaries in the space of power system parameters of interest, including load flow feasibility, saddle node and Hopf bifurcation ones; (2) finding the maximum and minimum damping conditions; and (3) determining control actions to provide and increase small signal stability. These problems are presented in this paper as different modifications of a general optimization to a minimum/maximum, depending on the initial guesses of variables and numerical methods used. In the considered problems, all the extreme points are of interest. Additionally, there are difficulties with finding the derivatives of the objective functions with respect to parameters. Numerical computations of derivatives in traditional optimization procedures are time consuming. In this paper, we propose a new black-box genetic optimization technique for comprehensive small signal stability analysis, which can effectively cope with highly nonlinear objective functions with multiple minima and maxima, and derivatives that can not be expressed analytically. The optimization result can then be used to provide such important information such as system optimal control decision making, assessment of the maximum network's transmission capacity, etc. (C) 1998 Elsevier Science S.A. All rights reserved.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

Probability of axillary node involvement in patients with tubular carcinoma of the breast

The aim of this study was to investigate the frequency of axillary metastasis in women with tubular carcinoma (TC) of the breast. Women who underwent axillary dissection for TC in the Western Sydney area (1984-1995) were identified retrospectively through a search of computerized records. A centralized pathology review was performed and tumours were classified as pure tubular (22) or mixed tubular (nine), on the basis of the invasive component containing 90 per cent or more, or 75-90 per cent tubule formation respectively. A Medline search of the literature was undertaken to compile a collective series (20 studies with a total of 680 patients) to address the frequency of nodal involvement in TC. A quantitative meta-analysis was used to combine the results of these studies. The overall frequency of nodal metastasis was five of 31 (16 per cent); one of 22 pure tubular and four of nine mixed tumours (P = 0.019). None of the tumours with a diameter of 10 mm or less (n = 16) had nodal metastasis compared with five of 15 larger tumours (P = 0.018). The meta-analysis of 680 women showed an overall frequency of nodal metastasis in TC of 13.8 (95 per cent confidence interval 9.3-18.3) per cent. The frequency of nodal involvement was 6.6 (1.7-11.4) per cent in pure TC (n = 244) and 25.0 (12.5-37.6) per cent in mixed TC (n = 149). A case may be made for observing the clinically negative axilla in women with a small TC (10 mm or less in diameter).

Treatment implications of a positive sentinel lymph node biopsy for patients with early-stage breast carcinoma

BACKGROUND. Sentinel lymph node (SLN) mapping and biopsy is emerging as an alternative to axillary lymph node dissection (ALND) in determining the lymph node status of patients with early-stage breast carcinoma. The hypothesis of the technique is that the SLN is the first lymph node in the regional lymphatic basin that drains the primary tumor. Non-SLN (NSLN) metastasis in the axilla is unlikely if the axillary SLN shows no tumor involvement, and, thus, further axillary interference may be avoided. However, the optimal treatment of the axilla in which an SLN metastasis is found requires ongoing evaluation. The objectives of this study were to evaluate the predictors for NSLN metastasis in the presence of a tumor-involved axillary SLN and to examine the treatment implications for patients with early-stage breast carcinoma. METHODS. Between June 1998 and May 2000, 167 patients participated in the pilot study of SLN mapping and biopsy at Westmead Hospital. SLNs were identified successfully and biopsied in 140 axillae. All study patients also underwent ALND. The incidence of NSLN metastasis in the 51 patients with a SLN metastasis was correlated with clinical and pathologic characteristics. RESULTS. Of 51 patients with a positive SLN, 24 patients (47%) had NSLN metastases. The primary tumor size was the only significant predictor for NSLN involvement. NSLN metastasis occurred in 25% of patients (95% confidence interval [95%CI], 10-47%) with a primary tumor size less than or equal to 20 mm and in 67% of patients (95%CI, 46-83%) with a primary tumor size > 20 mm (P = 0.005). The size of the SLN metastasis was not associated significantly with NSLN involvement. Three of 7 patients (43%) with an SLN micrometastasis (< 1 mm) had NSLN involvement compared with 38 of 44 patients (48%) with an SLN macrometastasis (greater than or equal to 1 mm). CONCLUSIONS. The current study did not identify a subgroup of SLN positive patients in whom the incidence of NSLN involvement was low enough to warrant no further axillary interference. At present, a full axillary dissection should be performed in patients with a positive SLN. (C) 2001 American Cancer Society.

A Century of Change in Coral Reef Status in Southeast and Central Pacific: Polynesia Mana Node, Cook Islands, French Polynesia, Kiribati, Niue, Tokelau, Tonga, Wallis and Futuna

The Polynesia Mana Node of the southeast and central Pacific contains 7 independent or autonomous countries or territories with only 6,000 km2 of land on 347 islands, but surrounded by 12 million km2 of EEZ. These seas contain 13,000 km2 of coral reefs as the main natural ecosystem providing food resources and opportunities for development, especially for tourism and pearl culture for 500,000 inhabitants. During the 19th and first half of the 20th centuries, there was major exploitation by the colonial powers of mother-of-pearl oysters for the button industry, as well as guano, sandalwood and trepang. The Polynesian people were largely involved in a subsistence economy and all coral reefs and lagoons were healthy. During the last two decades of the 20th, all countries experienced rapid development and urbanization, rising populations, and some increased agriculture. These developments were limited to a few islands of each country (i.e. 15 islands amongst the 347) with resulting degradation of the coral reefs around these sites. The other islands remained mostly uninhabited and pristine, and continued with a subsistence economy. Generally, there was more damage to the coral reefs through natural events such as cyclones and coral bleaching, than by human activities. There is however, an urgent need to combat the threats on some islands from increased sedimentation, over-fishing, dredging and nutrient pollution.

On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Postoperative vaginal vault brachytherapy for node-negative Stage II (occult) endometrial carcinoma

Objective. The aim of this study is to look at the efficacy of extended surgical staging and postoperative vaginal vault brachytherapy in patients with Stage II (occult) endometrial carcinoma. Methods. Between January 1989 and December 1997, there were 30 patients with Stage II (occult) endometrial carcinoma who received postoperative vaginal vault brachytherapy as the only adjuvant treatment. The study group consisted of 15 of these patients who had extended surgical staging (including lymphadenectomy). Results. At a median follow-up of 36 months (range 17 to 113 months), there has been no recurrence. There were no major complications from surgery. Only 1 patient had mild rectal bleeding following vaginal vault brachytherapy and there were no grade 3 or 4 bowel toxicities. Conclusions. Extended surgical staging and postoperative vaginal vault brachytherapy for Stage II (occult) endometrial carcinoma is associated with minimal morbidity and excellent survival. (C) 2001 Academic Press.

Occult Axillary Lymph Node Metastases in Breast Cancer Do Matter: Results of 10-Year Survival Analysis

Axillary lymph node status is one of the most powerful prognostic factors for patients with breast cancer and is often critical in stratifying patients into adjuvant treatment regimens. In 203 apparently node-negative cases of breast cancer, a combination of immunohistochemical staining and step-sectioning identified occult metastases in 25% of cases. Ten-year follow-up information is available for these patients. Histologic features of the primary tumor and immunohistochemical staining for estrogen receptor, progesterone receptor, Her-2, and p53 were also evaluated. With multivariate analysis, both occult metastases and higher histologic grade of the primary tumor were independent predictors of disease-free survival. Histologic grade was the only significant independent predictor of overall survival. Estrogen receptor, progesterone receptor, Her-2, and p53 status did not predict the presence of metastases or survival when all tumor types were considered together. Metastases >0.5 mm significantly predicted a poorer disease-free survival when invasive ductal carcinomas were considered alone. Histologic grade was significantly associated with disease-free survival in the premenopausal and perimenopausal patients but not in the postmenopausal patients. The presence of occult metastases approached significance for overall survival in the premenopausal and perimenopausal patients but not in the postmenopausal patients.

Sentinel node biopsy for breast cancer: Using local results for estimation of risk to the patient

Background: Sentinel node biopsy (SNB) is being increasingly used but its place outside randomized trials has not yet been established. Methods: The first 114 sentinel node (SN) biopsies performed for breast cancer at the Princess Alexandra Hospital from March 1999 to June 2001 are presented. In 111 cases axillary dissection was also performed, allowing the accuracy of the technique to be assessed. A standard combination of preoperative lymphoscintigraphy, intraoperative gamma probe and injection of blue dye was used in most cases. Results are discussed in relation to the risk and potential consequences of understaging. Results: Where both probe and dye were used, the SN was identified in 90% of patients. A significant number of patients were treated in two stages and the technique was no less effective in patients who had SNB performed at a second operation after the primary tumour had already been removed. The interval from radioisotope injection to operation was very wide (between 2 and 22 h) and did not affect the outcome. Nodal metastases were present in 42 patients in whom an SN was found, and in 40 of these the SN was positive, giving a false negative rate of 4.8% (2/42), with the overall percentage of patients understaged being 2%. For this particular group as a whole, the increased risk of death due to systemic therapy being withheld as a consequence of understaging (if SNB alone had been employed) is estimated at less than 1/500. The risk for individuals will vary depending on other features of the particular primary tumour. Conclusion: For patients who elect to have the axilla staged using SNB alone, the risk and consequences of understaging need to be discussed. These risks can be estimated by allowing for the specific surgeon's false negative rate for the technique, and considering the likelihood of nodal metastases for a given tumour. There appears to be no disadvantage with performing SNB at a second operation after the primary tumour has already been removed. Clearly, for a large number of patients, SNB alone will be safe, but ideally participation in randomized trials should continue to be encouraged.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.