Magnetic operations: a little fuzzy physics?

We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.Comment: 28 pages, 8 figure

Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

In the previous study, we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative nature of the geometry. We aim at formulating renormalization group equations including such nonlocal interactions and finding existence of nontrivial field theory with antipodal interactions on the fuzzy sphere. We find several nontrivial fixed points and calculate the scaling dimensions associated with them. We also consider the noncommutative plane limit and then no consistent fixed point is found. This contrast between the fuzzy sphere limit and the noncommutative plane limit would be manifestation in our formalism of the claim given by Chu, Madore and Steinacker that the former does not have UV/IR mixing, while the latter does.Comment: 1+47 pages, no figure; Ver. 2, references and some comments are added; Ver. 3, typos corrected. Version to appear in JHE

Improving small signal stability of power systems in the presence of harmonics

This thesis investigates the impact of harmonics as a power quality issue on the dynamic behaviour of the power systems. The effectiveness of the power system stabilizers in distorted conditions is also investigated. This thesis consists of three parts as follows:The first part focuses on the operation of the power system under distorted conditions. The conventional model of a synchronous generator in the dq-frame of reference is modified to include the impact of time and space harmonics. To do this, the synchronous generator is first modelled in the harmonic domain. This model helps in calculating the additional parts of the generator fundamental components due to the harmonics. Then the Park transformation is used for calculating the modified fundamental components of the synchronous generator in dq axes. The modified generator rotor angle due to the presence of harmonics is calculated and the impact of damper windings under the influence of harmonics is investigated. This model is used to study the small-signal stability of a distorted Single Machine Infinite Bus (SMIB) system. The eigenvalue analysis method is employed and the system state space equations are calculated by linearizing the differential equations around the operating point using an analytical method. The simulation results are presented for a distorted SMIB system under the influence of different harmonic levels. The impact of damper windings and also harmonics phase angles are also investigated.In the second part of the thesis, the effectiveness of the power system damping controllers under distorted conditions is studied. This investigation is done based on a distorted SMIB system installed with a Static Synchronous Series Compensator (SSSC). In the first step, the system state space equations are derived. A Power Oscillation Damping (POD) controller with a conventional structure is installed on the SSSC to improve the system dynamic behaviour. A genetic-fuzzy algorithm is proposed for tuning the POD parameters. This method along with the observability matrix is employed to design a POD controller under sinusoidal and distorted conditions. The impact of harmonics on the effectiveness of the POD controller under distorted conditions is investigated.In the last part, the steady state and dynamic operation of an actual distributed generation system under sinusoidal and distorted conditions are studied. A decoupled harmonic power flow program is employed for steady state analysis. The nonlinear loads are modelled as decoupled harmonic current sources and the nonlinear model of synchronous generator in harmonic domain is used to calculate the injected current harmonics. For the system dynamic stability study, the power system toolbox with the modified model of the synchronous generator is used. The system eigenvalues are calculated and the effectiveness of the installed Power System Stabilisers (PSS) is investigated under sinusoidal and distorted conditions. Simulation results show that in order to guarantee the effectiveness of a PSS in distorted conditions, it is necessary to consider the harmonics in tuning its parameters

On the asymptotic period of powers of a fuzzy matrix

AbstractIn our prior study, we have examined in depth the notion of an asymptotic period of the power sequence of an n×n fuzzy matrix with max-Archimedean-t-norms, and established a characterization for the power sequence of an n×n fuzzy matrix with an asymptotic period using analytical-decomposition methods. In this paper, by using graph-theoretical tools, we further give an alternative proof for this characterization. With the notion of an asymptotic period using graph-theoretical tools, we additionally show a new characterization for the limit behaviour, and then derive some results for the power sequence of an n×n fuzzy matrix with an asymptotic period

A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability

Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter $\theta$, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on $\theta$ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.Comment: 29 pages, 23 figures, references adde