Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.Comment: 8 pages in Revtex 4.1 preprint format, to appear in Journal of Inequalities and Application

Phase Diagram Of The Biham-Middleton-Levine Traffic Model In Three Dimensions

We study numerically the behavior of the Biham-Middleton-Levine traffic model in three dimensions. Our extensive numerical simulations show that the phase diagram for this model in three dimensions is markedly different from that in one and two dimensions. In addition to the full speed moving as well as the completely jamming phases, whose respective average asymptotic car speeds $$ equal one and zero, we observe an extensive region of car densities $\rho$ with a low but non-zero average asymptotic car speed. The transition from this extensive low average asymptotic car speed region to the completely jamming region is at least second order. We argue that this low speed region is a result of the formation of a spatially-limited-extended percolating cluster. Thus, this low speed phase is present in $n > 3$ dimensional Biham-Middleton-Levine model as well.Comment: Minor clarifications, 1 figure adde

Arbitrage opportunities and feedback trading in emissions and energy markets

This paper extends Sentana and Wadhwani (SW 1992) model to study the presence of feedback trading in emissions and energy markets and the extent to which such behaviour is linked to the level of arbitrage opportunities. Applying our augmented models to the carbon emission and major energy markets in Europe, we find evidence of feedback trading in coal and electricity markets, but not in carbon market where the institutional investors dominate. This finding is consistent with the notion that institutional investors are less susceptible to pursuing feedback-style investment strategies. In further analysis, our results show that the intensity of feedback trading is significantly related to the level of arbitrage opportunities, and that the significance of such relationship depends on the market regimes

Design of permanent magnets to avoid chaos in PM synchronous machines

PURPOSE: The permanent-magnet synchronous machine (PMSM) is becoming more and more attractive for both industrial and electric vehicle applications [I] because of its inherent advantages of high power density and high efficiency. However, the investigation onto its chaos has been surprisingly little. Even so [2], the discussion was based on ac-hoc computer simulation, whereas the actual effect of PMs on the chaos in PMSMs was unexplored. In this paper, the relationship between the sizing of PMs and the chaos in PMSMs will be revealed. Both computer simulation and experimental results will be given to support the design criteria ...published_or_final_versio

Design of Permanent Magnets to Avoid Chaos in PM Synchronous Machines

This paper analyzes the effect of permanent magnets (PMs) on the occurrence of chaos in PM synchronous machines (PMSMs). Based on the newly derived nonlinear system equation, the bifurcation analysis shows that the sizing of PMs significantly determines the stability of PMSMs. Hopf bifurcation and chaos may even occur in the PMSMs if the PMs are not properly sized. Experimental results of two practical PMSMs are provided to support the theoretical analysis.published_or_final_versio

Development of a new brushless doubly-fed doubly-salient machine for wind power generation

published_or_final_versio

AI-based teaching package for open channel flow on Internet

Author name used in this publication: Kwokwing Chau2003-2004 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Design of permanent magnets to avoid chaos in doubly salient PM machines

This paper analyzes the effect of permanent magnets (PMs) on the formation of chaos in doubly salient PM (DSPM) machines. Based on the newly derived nonlinear system dynamical equation, the corresponding Poincaré map and bifurcation diagram show that the sizing of PMs significantly affects the stability of DSPM machines. Chaos may be resulted if the PMs are not properly designed. Both computer simulations and experimental results are provided to support the theoretical derivation.published_or_final_versio

Design, modeling, and analysis of a brushless doubly fed doubly salient machine for electric vehicles

This paper presents a new three-phase 12/8-pole brushless doubly fed doubly salient (BDFDS) machine for application to electric vehicles. It consists of two types of stator windings-polyphase armature winding and dc field winding. The key is to design, model, and analyze the proposed BDFDS machine. The output power equation is derived analytically, and the initial calculation of machine dimensions and parameters are also discussed. When we use finite-element analysis, the field distributions of the BDFDS machine at different loads and field currents are obtained, in which magnetic saturation and armature reaction are considered. Static characteristics of the proposed machine are also obtained. Based on these characteristics, the system mathematical model can be established. Hence, the evaluation of system performance is conducted by computer simulation. A 12/8-pole BDFDS machine is designed and built for experimentation. Experimental results are given to verify the theoretical analysis and simulation. © 2008 IEEE.published_or_final_versio

Design, modeling and analysis of a brushless doubly-fed doubly-salient machine for electric vehicles

This paper presents a new three-phase 12/8-pole brushless doubly-fed doubly-salient (BDFDS) machine for application to electric vehicles. The key is to design, modeling, analyze and control the proposed BDFDS machine. The output power equation is analytically derived, and the initial calculation of machine dimensions and parameters are also discussed. By using finite element analysis, the field distributions of the BDFDS machine at different load and field current are obtained, in which the magnetic saturation and the coupling between armature current flux and field current flux are considered; moreover, the static characteristics of the proposed machine are given. Based on the static characteristics, the system mathematical model has been established. Hence, the evaluation of system performances is conducted by computer simulations in which the simulation model combines the machine with a 3-phase half-bridge converter. A 12/8-pole BDFDS machine is designed and built for exemplification, and a drive system employing this new machine has been developed and investigated experimentally. Experimental results are also given to verify the validity of the theoretical analyses. © 2005 IEEE.published_or_final_versio