Spin jj Dirac Operators on the Fuzzy 2-Sphere

The spin 1/2 Dirac operator and its chirality operator on the fuzzy 2-sphere $S^2_F$ can be constructed using the Ginsparg-Wilson(GW) algebra [arxiv:hep-th/0511114]. This construction actually exists for any spin $j$ on $S^2_F$, and have continuum analogues as well on the commutative sphere $S^2$ or on $\mathbb{R}^{2}$. This is a remarkable fact and has no known analogue in higher dimensional Minkowski spaces. We study such operators on $S^2_F$ and the commutative $S^2$ and formulate criteria for the existence of the limit from the former to the latter. This singles out certain fuzzy versions of these operators as the preferred Dirac operators. We then study the spin 1 Dirac operator of this preferred type and its chirality on the fuzzy 2-sphere and formulate its instanton sectors and their index theory. The method to generalize this analysis to any spin $j$ is also studied in detail.Comment: 16 pages, 1 tabl

Coupling currents in Rutherford cables under time varying conditions

A network model is presented to simulate fully transposed Rutherford cables under time varying conditions. The intrinsic properties of the cable and the external applied conditions can be changed spatially. Several statistical distributions of the contact resistances are built in to investigate local differences in the coupling loss and in the eddy currents. The average loss is quite independent of the resistance distribution but locally both the loss and the eddy currents can increase significantly. The self field distribution of the cable is included, resulting in a saturation of the strands which depends on the relative direction between the magnetic field, the field sweep rate, and the transport current. Mutual inductances between strands are introduced, allowing the use of the model for nonstationary problems. Time constants can be calculated for both the coupling currents in the strands and for the local and global dissipatio

A technique for improved stability of adaptive feedforward controllers without detailed uncertainty measurements

Model errors in adaptive controllers for reduction of broadband noise and vibrations may lead to unstable systems or increased error signals. Previous work has shown that the addition of a low-authority controller that increases damping in the system may lead to improved performance of an adaptive, high-authority controller. Other researchers have suggested to use frequency dependent regularization based on measured uncertainties. In this paper an alternative method is presented that avoids the disadvantages of these methods namely the additional complex hardware, and the need to obtain detailed information of the uncertainties. An analysis is made of an active noise control system in which a difference exists between the secondary path and the model as used in the controller. The real parts of the eigenvalues that determine the stability of the system are expressed in terms of the amount of uncertainty and the singular values of the secondary path. Based on these expressions, modifications of the feedforward control scheme are suggested that aim to improved performance without requiring detailed uncertainty measurements. For an active noise control system in a room it is shown that the technique leads to improved performance in terms of robustness and the amount of reduction of the error signals

Super Coupling Currents in Rutherford Type of Cables due to Longitudinal Non-homogeneities of dB/dt

In this paper it is shown that nonhomogeneities in the field sweep rate dB/dt along the length of a Rutherford cable provoke a nonhomogeneous current distribution during a field sweep. This process can be described by means of super coupling currents (SCCs) flowing through the strands over lengths far larger than the cable pitch. These SCCs can be characterised by a characteristic length, a characteristic time, and a propagation velocity. The dependence of these three parameters on the strand resistance and the contact resistance between strands is illustrated. Two longitudinal nonhomogeneities in dB/dt are considered which are present in accelerator magnets. Firstly, an increase in dB/dt from 0 to a certain value simulating that part of the cable where the cable enters the magnet field. Secondly, a longitudinal decrease in dB/dt which occurs mainly in the heads of the magnet. It is shown that in accelerator magnets a nonhomogeneous current distribution induced by the field sweep can not be avoided. However, it seems to be very difficult to estimate the amplitude of the effec

Adaptive multichannel control of time-varying broadband noise and vibrations

This paper presents results obtained from a number of applications in which a recent adaptive algorithm for broadband multichannel active noise control is used. The core of the algorithm uses the inverse of the minimum-phase part of the secondary path for improvement of the speed of convergence. A further improvement of the speed of convergence is obtained by using double control filters for elimination of adaptation loop delay. Regularization was found to be necessary for robust operation. The regularization technique which is used preserves the structure to eliminate the adaptation loop delay. Depending on the application at hand, a number of extensions are used for this algorithm. For an application with rapidly changing disturbance spectra, the core algorithm was extended with an iterative affine projection scheme, leading to improved convergence rates as compared to the standard nomalized lms update rules. In another application, in which the influence of the parametric uncertainties was critical, the core algorithm was extended with low authority control loops operating at high sample rates. In addition, results of other applications are given, such as control of acoustic energy density and control of time-varying periodic and non-periodic vibrations

Quantum Geons and Noncommutative Spacetimes

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group $S_N$. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the commutative spacetime algebras of geons as well to noncommutative algebras. The latter support twisted actions of diffeos of geon spacetimes and associated twisted statistics. The notion of covariant fields for geons is formulated and their twisted versions are constructed from their untwisted versions. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli principle, seem to be the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out.Comment: 41 page

The competition for souls: Sava of Serbia and consumer choice in religion in the thirteenth century Balkans

SUMMARY The word αίρεσις , heresy means choice and in a world where religious belief was taken for granted the history of Catharism in Europe can be explained through believers exercising many of the criteria they were later to adapt to choosing secular consumer goods. Believers in the west in the C12 and early C13 had a choice of religions. Catharism became popular in France and Italy on the basis of the virtuous lifestyle of its protagonists, its relative cheapness compared with Catholicism and the simplicity of its theology of individual salvation. Its decline was as much to do with Catholicism being ‘re-packaged’ by groups such as the Franciscans, lay guilds and the Beguines as by any persecution. A similar analysis of heresy in eastern Europe would be valuable, despite the relative scarcity of sources. There is some evidence that opposition to the Bogomils focused on the capacity of the Orthodox Church to bring material well being to believers and to provide contact with a world of affluence the lay individual could mostly only dream of. Hugh Eteriano’s Contra Patarenos gives numerous examples of earthly prosperity springing from making the right spiritual choices and both he and later writers against the Bogomils such as Patriarch Germanus II emphasised the physical value and beauty of objects used in Orthodox worship, as opposed to the austerity of Bogomil sermons delivered in private houses. Outside Constantinople the Orthodox Church of the thirteenth century faced the threat of heresy from both Catholic and Bogomil missionaries without the resources available within the capital, and unable to deploy coercion as in the West. Archbishop Sava of Serbia therefore used a variety of methods to maintain the allegiance of the population to Orthodoxy. At the assembly at Žiča in 1221 he outlined gentle courses of repentance for both groups and used his links with his brother, king Stephen Prvovenčani to promise gifts to returning noble heretics. Sava also emphasised the Orthodox Church’s capacity to enrich the life of the laity, sending out ‘exarchs’ or trained priests to preach in Slavonic and encourage the sacrament of marriage, thus targeting families and future mothers. On an inevitably limited scale Sava was also able to stress the sensuous experience of Orthodox worship. His programme of church building included vivid programmes of wall painting to impress the laity. These occasionally conveyed a materialist message, such as the picture of Christ distributing bread from a basket labelled ‘Provider’. In short, Sava combined the responses to heresy of east and west. He deployed the appeal to sensuous experience and material well being of Orthodoxy he had seen in Constantinople and Nicaea, but also emphasised lifestyle, vernacular preaching and facilitating lay access to the sacraments which had been articulated in 1215 at the Fourth Lateran Council. Insofar as neither Bogomilism or Catholicism regained their potency as threats in the region the strategy seems to have been successful