A method for direct calculation of quadratic turning points

For a given one-parameter nonlinear system, the simplest bifurcation is the quadratic turning bifurcation where the Jacobian matrix becomes singular due to rank deficiency 1. To overcome the difficulty in solving the quadratic turning point caused by the singularity of the Jacobian matrix, the conventional Newton method can be applied to the so-called Moore-Spence determination system to solve for the quadratic turning point. However, the Moore-Spence system has much higher dimensions and causes much more complexity in factorisation of the extended Jacobian matrix. In the paper, by introducing an auxiliary variable and an auxiliary linear equation into Newton iterations in solving the Moore-Spence determination system, a matrix reduction technique can be worked out to solve the Moore-Spence extended equations much more efficiently. The high dimensions of the matrix can thus be reduced and the complexity involved in matrix factorisation can be reduced noticeably. The technique is proposed for general nonlinear systems. Formulation is derived for applying this technique to solving quadratic turning points, or say nose points, on load-flow solution curves of power systems. Computer tests on the IEEE 30-busbar system and a 2416-busbar East China power system are reported to show the effectiveness of the suggested technique.published_or_final_versio

λϕ4\lambda\phi^4 model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Basing on new regularization-renormalization method, the $\lambda\phi^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with the SU(2)$\times$U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated as $m_H\approx$138GeV. The critical temperature ($T_c$) for restoration of symmetry of Higgs field, the critical energy scale ($\mu_c$, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale ($\mu_{max}$, at which the symmetry of the Higgs field is restored) in the standard model are $T_c\approx$476 GeV, $\mu_c\approx 0.547\times 10^{15}$GeV and $\mu_{\max}\approx 0.873 \times 10^{15}$ GeVv respectively.Comment: 12 pages, LaTex, no figur

Optimal Bidding Strategies for Generation Companies in Electricity Markets with Transmission Capacity Constraints Taken into Account

In the electricity market environment, how to build optimal bidding strategies has become a major concern for generation companies. The deficiency of transmission capacity could lead to congestion, and as a result, the whole electricity market can then be actually divided into two or more submarkets. A direct consequence of transmission congestion is the change of competitive positions of generation companies concerned in the electricity market, and the optimal bidding strategies of them should accordingly be changed. In this paper, the problem of developing optimal bidding strategies for generation companies is systematically investigated with transmission capacity constraints taken into account. A stochastic optimization model is first formulated under the presumption that the bidding behaviors of rival generation companies could be modeled as normal probability distributions. An approach is next presented for solving the optimization problem using the well-known Monte Carlo simulation method and the genetic algorithm. Finally, a simple sample example and the modified IEEE 14-bus system are employed to illustrate the essential features of the proposed model and method.published_or_final_versio

Observation of a pressure-induced transition from interlayer ferromagnetism to intralayer antiferromagnetism in Sr4Ru3O10

Sr4Ru3O10 is a Ruddlesden-Popper compound with triple Ru-O perovskite layers separated by Sr-O alkali layers. This compound presents a rare coexistence of interlayer (c-axis) ferromagnetism and intralayer (basal-plane) metamagnetism at ambient pressure. Here we report the observation of pressure-induced, intralayer itinerant antiferromagnetism arising from the interlayer ferromagnetism. The application of modest hydrostatic pressure generates an anisotropy that causes a flattening and a tilting of RuO6 octahedra. All magnetic and transport results from this study indicate these lattice distortions diminish the c-axis ferromagnetism and basal-plane metamagnetism, and induce a basal-plane antiferromagnetic state. The unusually large magnetoelastic coupling and pressure tunability of Sr4Ru3O10 makes it a unique model system for studies of itinerant magnetism.Comment: 6 figure

Suspension of the fiber mode-cleaner launcher and measurement of the high extinction-ratio (10^{-9}) ellipsometer for the Q & A experiment

The Q & A experiment, first proposed and started in 1994, provides a feasible way of exploring the quantum vacuum through the detection of vacuum birefringence effect generated by QED loop diagram and the detection of the polarization rotation effect generated by photon-interacting (pseudo-)scalar particles. Three main parts of the experiment are: (1) Optics System (including associated Electronic System) based on a suspended 3.5-m high finesse Fabry-Perot cavity, (2) Ellipsometer using ultra-high extinction-ratio polarizer and analyzer, and (3) Magnetic Field Modulation System for generating the birefringence and the polarization rotation effect. In 2002, the Q & A experiment achieved the Phase I sensitivity goal. During Phase II, we set (i) to improve the control system of the cavity mirrors for suppressing the relative motion noise, (ii) to enhance the birefringence signal by setting-up a 60-cm long 2.3 T transverse permanent magnet rotatable to 10 rev/s, (iii) to reduce geometrical noise by inserting a polarization-maintaining optical fiber (PM fiber) as a mode cleaner, and (iv) to use ultra-high extinction-ratio (10^{-9}) polarizer and analyzer for ellipsometry. Here we report on (iii) & (iv); specifically, we present the properties of the PM-fiber mode-cleaner, the transfer function of its suspension system, and the result of our measurement of high extinction-ratio polarizer and analyzer.Comment: 8 pages, 6 figures, presented in the 6th Edoardo Amaldi Conference on Gravitational Waves, Okinawa, Japan, June 2005, and accepted by "Journal of Physics: Conference Series". Modifications from version 2 were made based on the referees' comments on figures. Ref. [31] were update

A Theoretical Framework for Cost Allocations in a Monopoly System with Application to the Allocation of Transmission Losses

In this paper, fundamental characteristics of a general monopolistic service system with a simple structure are first investigated, and a theoretical framework for allocations of common costs is then developed. The concepts of "fairness" and "rationality" are characterized mathematically for the general cost allocation problem. Under the proposed framework, several available allocation methods of transmission losses could be well unified.published_or_final_versio

The concept and algorithm of 'conductor renting' and its application in transmission losses allocation

The cost of transmission losses represents an important part of transmission costs. In the context of competitive electricity marketplace, the costs caused by transmission losses should be reasonably allocated to various market participants, but the nonlinearity of the transmission losses function makes the allocation very difficult. In this paper, the concept of 'conductor renting' is proposed for the first time and is used to solve transmission losses allocation problem. The analysis indicates that the active power losses caused by different current components are in proportion to the conductor section acreage and the corresponding conductance used by the current components, and the reactive power losses caused by current components have similar characteristics. Based on the concept of conductor renting, it is easy to solve the losses allocation problem, and the interaction effect of the transactions is eliminated.published_or_final_versio

Development of bidding strategies in electricity markets using possibility theory

In the electricity market environment, bidding strategies employed by generation companies may have significant impacts on their own benefits, and on the operating behaviors of an electricity market as well. Hence, how to develop optimal bidding strategies for generation companies or how to analyze strategic behaviors of them and hence to figure out the potential market power abuse is now a very active research area. A possibility theory based approach is proposed in this work for building optimal bidding strategies for generation companies. Based on historical bidding data, the available (production cost) data before the power industry restructuring and experts' heuristic knowledge, the well-known fuzzy set theory is employed to represent the estimated bidding behaviors of rival generation companies, and a fuzzy programming model is developed and a solution method follows. The approach is especially suitable for those electricity markets recently launched, since sufficient historical bidding data is not available and hence probability methods cannot be employed. Finally, a sample example with six generation companies participating in an electricity market is served for demonstrating the essential features of the presented approach.published_or_final_versio