Wide-area control of aggregated power systems

This paper proposes a new method for stabilizing disturbed power systems using wide area measurement and FACTS devices. The approach focuses on both first swing and damping stability of power systems following large disturbances. A two step control algorithm based on Lyapunov Theorem is proposed to be applied on the controllers to improve the power systems stability. The proposed approach is simulated on two test systems and the results show significant improvement in the first swing and damping stability of the test systems.

Converse Bergmann cline in a eucalyptus herbivore, paropsis atomaria olivier (coleoptera: chrysomelidae) : phenotypic plasticity or local adaptation?

Aim To measure latitude-related body size variation in field-collected Paropsis atomaria Olivier (Coleoptera: Chrysomelidae) individuals and to conduct common-garden experiments to determine whether such variation is due to phenotypic plasticity or local adaptation. Location Four collection sites from the east coast of Australia were selected for our present field collections: Canberra (latitude 35°19' S), Bangalow (latitude 28°43' S), Beerburrum (latitude 26°58' S) and Lowmead (latitude 24°29' S). Museum specimens collected over the past 100 years and covering the same geographical area as the present field collections came from one state, one national and one private collection. Methods Body size (pronotum width) was measured for 118 field-collected beetles and 302 specimens from collections. We then reared larvae from the latitudinal extremes (Canberra and Lowmead) to determine whether the size cline was the result of phenotypic plasticity or evolved differences (= local adaptation) between sites. Results Beetles decreased in size with increasing latitude, representing a converse Bergmann cline. A decrease in developmental temperature produced larger adults for both Lowmead (low latitude) and Canberra (high latitude) individuals, and those from Lowmead were larger than those from Canberra when reared under identical conditions. Main conclusions The converse Bergmann cline in P. atomaria is likely to be the result of local adaptation to season length.

Application of a new discreet form of Gauss’ theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss’ theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference ± one standard deviation were 1.2 ± 2.3, 5.5 ± 4.7, 3.0 ± 3.2 and −1.2 ± 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

Balls up : the converse blank canvas project

Research background: For decades the Chuck Taylor All Star basketball shoe (first designed in 1921 by Converse, an American shoe company), has been an iconic item of fashion apparel, particularly for the youth oriented market - as a form of self expression and identify, adolescents have for generations been customising their Converse sneakers to create innovative and unique footwear. Although originally developed purely for sport, sneakers gradually crossed over into fashion and the majority of athletic shoes are now purchased for street fashion or leisure wear. Artisan Gallery (Brisbane), in conjunction with the exhibition Reboot: Function, Fashion and the Sneaker, a history of the sneaker, selected 20 designers to customise and re-design the classic Converse Chuck Taylor All Stars shoe and in doing so highlighted the diversity of forms possible for creative outcomes. As Artisan Gallery Curator Kirsten Fitzpatrick states “the ‘sports show’, designed to coincide with the Olympics, is also about exploring the sneaker as a platform for creativity... and (one) of the more bazaar creations was Dean Brough's deconstructed shoes to make men’s underwear.” The exhibition ran from 21 June – 16 August 2012: http://artisan-ideaskillproduct.blogspot.com.au/2012/06/converse-blank-canvas-project.html Research question: Even though the sneaker is a fashion item, it still is fundamentally used for foot protection and historically was aligned to ball sports, principally Basketball - as a fashion designers/practitioner how can I connect (in a whimsical manner) this history of usage for ball sports to the sneaker and re-design and re-use all the physical elements of the shoe to produce a unique wearable item of clothing - the selected medium for this challenge and experimentation was the classic archetypal men’s white boxer shorts. Artisan Statement BALLS UP - The Converse Sneaker, it’s almost impossible to imagine a better rounded item to maintain peak performance for all types of ball sports. Gentlemen, your other most precious balls also deserve this level of comfort and support to sustain the hard times – the Converse Boxer, balls up, bats out, get ready to play hard. Research contribution: The project highlighted some of the unique and diverse creative manifestations that are possible from the classic sneaker. From a fashion practitioners’ perspective, the design outcomes (men’s boxer short made from converse sneakers) demonstrated the strong association to iconic fashion apparel, and recognised the connection to wearability and comfort that is requisite in both footwear and men’s underwear. Research significance: The exhibition was viewed by in excess of 1000 people and generated exceptional media coverage and public exposure/impact. As Artisan Gallery Curator Kirsten Fitzpatrick states “20 of Brisbane's best designers were given the opportunity to customise their own Converse Sneakers, with The Converse Blank Canvas Project.” And to be selected in this category demonstrates the calibre of importance for design prominence.

Converse consumption : the converse blank canvas project

Research background For almost 80 years the Chuck Taylor (or Chuck T's) All Star basketball shoe has been an iconic item of fashion apparel. The Chuck T's were first designed in 1921 by Converse, an American shoe company and over the decades they became a popular item not purely for sports and athletic purposes but rather evolved into the shoe of choice for many subcultural groups as a fashion item. In some circles the Chuck Taylor is still seen as the "coolest" sneaker of all time - one which will never go out of fashion regardless of changing trends. With over 600 millions pairs sold all over the world since its release, the Converse shoe is representative of not only a fashion culture - but also of a consumption culture - that evolved as the driving force behind the massive growth of the Western economic system during the 20th Century. Artisan Gallery (Brisbane), in conjunction with the exhibition Reboot: Function, Fashion and the Sneaker, a history of the sneaker, selected 20 designers to customise and re-design the classic Converse Chuck Taylor All Stars shoe and in doing so highlighted the diversity of forms possible for creative outcomes. As Artisan Gallery Curator Kirsten Fitzpatrick states “We were expecting people to draw and paint on them. Instead, we had shoes... mounted as trophies.." referring to the presentation of "Converse Consumption". The exhibition ran from 21 June – 16 August 2012: Research question The Chuck T’s is one of many overwhelmingly commercially successful designs of the last century. Nowadays we are faced with the significant problems of overconsumption and the stress this causes on the natural ecosystem; and on people as a result. As an active member of the industrial design fraternity – a discipline that sits at the core of this problem - how can I use this opportunity to comment on the significant issue of consumption? An effective way to do this was to associate consumption of goods with consumption of sugar. There are significant similarities between our ceaseless desires to consume products and our fervent need to consume indulgent sweet foods. Artisan Statement Delicious, scrumptious, delectable... your pupils dilate, your blood pressure spikes, your liver goes into overdrive. Immediately, your brain cuts off the adenosine receptors, preventing drowsiness. Your body increases dopamine production, in-turn stimulating the pleasure receptors in your brain. Your body absorbs all the sweetness and turns it into fat – while all the nutrients that you actually require are starting to be destroyed, about to be expelled. And this is only after one bite! After some time though, your body comes crashing back to earth. You become irritable and begin to feel sluggish. Your eyelids seem heavy while your breathing pattern changes. Your body has consumed all the energy and destroyed all available nutrients. You literally begin to shut down. These are the physiological effects of sugar consumption. A perfect analogy for our modern day consumer driven world. Enjoy your dessert! Research contribution “Converse Consumption” contributes to the conversation regarding over-consumption by compelling people to reflect on their consumption behaviour through the reconceptualising of the deconstructed Chuck T’s in an attractive edible form. By doing so the viewer has to deal with the desire to consume the indulgent looking dessert with the contradictory fact that it is comprised of a pair of shoes. The fact that the shoes are Chuck T’s make the effect even more powerful due to their iconic status. These clashing motivations are what make “Converse Consumption” a bizarre yet memorable experience. Significance The exhibition was viewed by an excess of 1000 people and generated exceptional media coverage and public exposure/impact. As Artisan Gallery Curator Kirsten Fitzpatrick states “20 of Brisbane's best designers were given the opportunity to customise their own Converse Sneakers, with The Converse Blank Canvas Project.” And to be selected in this category demonstrates the calibre of importance for design prominence.

Stabilization of parametric roll resonance with active u-tanks via Lyapunov control design

Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via simulation on a high-fidelity model of a vessel under parametric roll resonance.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

Converse results to the Wiener attack on RSA

A well-known attack on RSA with low secret-exponent d was given by Wiener about 15 years ago. Wiener showed that using continued fractions, one can efficiently recover the secret-exponent d from the public key (N,e) as long as d < N 1/4. Interestingly, Wiener stated that his attack may sometimes also work when d is slightly larger than N 1/4. This raises the question of how much larger d can be: could the attack work with non-negligible probability for d=N 1/4 + ρ for some constant ρ > 0? We answer this question in the negative by proving a converse to Wiener’s result. Our result shows that, for any fixed ε > 0 and all sufficiently large modulus lengths, Wiener’s attack succeeds with negligible probability over a random choice of d < N δ (in an interval of size Ω(N δ )) as soon as δ > 1/4 + ε. Thus Wiener’s success bound dconverse result for a natural class of extensions of the Wiener attack, which are guaranteed to succeed even when δ > 1/4. The known attacks in this class (by Verheul and Van Tilborg and Dujella) run in exponential time, so it is natural to ask whether there exists an attack in this class with subexponential run-time. Our second converse result answers this question also in the negative.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Robust Controller Design of Networked Control Systems with Nonlinear Uncertainties

We address robust stabilization problem for networked control systems with nonlinear uncertainties and packet losses by modelling such systems as a class of uncertain switched systems. Based on theories on switched Lyapunov functions, we derive the robustly stabilizing conditions for state feedback stabilization and design packet-loss dependent controllers by solving some matrix inequalities. A numerical example and some simulations are worked out to demonstrate the effectiveness of the proposed design method.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.