An analogue of the Narasimhan-Seshadri theorem and some applications

We prove an analogue in higher dimensions of the classical Narasimhan-Seshadri theorem for strongly stable vector bundles of degree 0 on a smooth projective variety $X$ with a fixed ample line bundle $\Theta$. As applications, over fields of characteristic zero, we give a new proof of the main theorem in a recent paper of Balaji and Koll\'ar and derive an effective version of this theorem; over uncountable fields of positive characteristics, if $G$ is a simple and simply connected algebraic group and the characteristic of the field is bigger than the Coxeter index of $G$, we prove the existence of strongly stable principal $G$ bundles on smooth projective surfaces whose holonomy group is the whole of $G$.Comment: 42 pages. Theorem 3 of this version is new. Typos have been corrected. To appear in Journal of Topolog

Tensor product theorem for Hitchin pairs -An algebraic approach

We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields $k$ of characteristic $0$ and characteristic $p$, with $p$ satisfying some natural bounds. We also prove the corresponding theorem for polystable bundles.Comment: To appear in Annales de l'Institut Fourier, Volume 61 (2011

A Bionic Coulomb Phase on the Pyrochlore Lattice

A class of three dimensional classical lattice systems with macroscopic ground state degeneracies, most famously the spin ice system, are known to exhibit "Coulomb" phases wherein long wavelength correlations within the ground state manifold are described by an emergent Maxwell electrodynamics. We discuss a new example of this phenomenon-the four state Potts model on the pyrochlore lattice-where the long wavelength description now involves three independent gauge fields as we confirm via simulation. The excitations above the ground state manifold are bions, defects that are simultaneously charged under two of the three gauge fields, and exhibit an entropic interaction dictated by these charges. We also show that the distribution of flux loops shows a scaling with loop length and system size previously identified as characteristic of Coulomb phases

Semistable principal bundles-II (positive characteristics)

Let H be a semisimple algebraic group and let X be a smooth projective curve defined over an algebraically closed field k. The principal aim of this paper is to prove the existence and projectivity of the moduli spaces of principal H-bundles on X for fields of characteristic p, p > Ψ, where Ψ is a certain representation-theoretic index associated to H. The projectivity is a consequence of the semistable reduction theorem for principal H-bundles

A variant of noether normalisation

Let X be an affine variety over an infinite field k, together with a collection of finite morphisms ƒi : X → Ani. We prove that for the general 'product' linear projection πi Pi : πi Ani the composite → πi A si, the composite po (πiƒi) : X → A∑isi is finite, provided ∑i si ≥ dimX. This generalizes the Noether Normalisation theorem, in a manner analogous to Nori'a generalisation of the 'Whitney embedding theorem' for smooth affine varieties. It also extends Nori's theorem (and its generalisation to non-smooth varieties) to more than 2 factors

The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at \nu=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.Comment: 4 pages, 1 figur

Soliton States in the Quantum-Chromodynamic Effective Lagrangian

The work of Skyrme has shown that the SU(2)×SU(2) chiral model has nontrivial topological sectors which admit solitons for generic chiral Lagrangians. In this paper, we study such models in the presence of baryon fields. The baryon number and strangeness of the solitons, and the bound states of the nucleon to the soliton are investigated. It is found that long-lived levels with large baryon number B and strangeness (≳6 in magnitude) and masses somewhere in the range 1.8 to 5.6 GeV must exist. Some of these levels have half-integral electric charge and exotic relation between B and spin s (e.g., even B and half-integer s). It is speculated that these levels may be related to the anomalous nuclei whose existence has been confirmed in cosmic-ray and LBL Bevalac experiments

Quot schemes and Fourier-Mukai transformation

We consider several related examples of Fourier-Mukai transformations involving the quot scheme. A method of showing conservativity of these Fourier-Mukai transformations is described.Comment: Final versio

Active Vibration Control of a Smart Cantilever Beam on General Purpose Operating System

All mechanical systems suffer from undesirable vibrations during their operations. Their occurrence is uncontrollable as it depends on various factors. However, for efficient operation of the system, these vibrations have to be controlled within the specified limits. Light weight, rapid and multi-mode control of the vibrating structure is possible by the use of piezoelectric sensors and actuators and feedback control algorithms. In this paper, direct output feedback based active vibration control has been implemented on a cantilever beam using Lead Zirconate-Titanate (PZT) sensors and actuators. Three PZT patches were used, one as the sensor, one as the exciter providing the forced vibrations and the third acting as the actuator that provides an equal but opposite phase vibration/force signal to that of sensed so as to damp out the vibrations. The designed algorithm is implemented on Lab VIEW 2010 on Windows 7 Platform.Defence Science Journal, 2013, 63(4), pp.413-417, DOI:http://dx.doi.org/10.14429/dsj.63.486

Low-mass Solitons from Fractional Charges in Quantum Chromodynamics

Slansky, Goldman, and Shaw have proposed a model to account for the observation of fractionally charged states. We show that in this model, there are expected to be several low-mass solitons (four being in the mass range ∼20-60 MeV) associated with the third homotopy group π3(SU(3)/SO(3))=Z4, besides a low-mass (∼30 MeV) Z2 monopole. Confirmation of these levels and hence of the model has important implications for Cabrera\u27s results on the magnetic monopole. An efficient algorithm for the calculation of π3(G/H) for a general Lie group G and a subgroup H is developed. It is pointed out that solitons associated with the third homotopy group are predicted by some grand-unified-theory scenarios