Face pairing graphs and 3-manifold enumeration

The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal P^2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumeration algorithm. Results are offered for both orientable and non-orientable triangulations.Comment: 30 pages, 57 figures; v2: clarified some passages and generalised the final theorem to the non-orientable case; v3: fixed a flaw in the proof of the conical face lemm

Perfect tag identification protocol in RFID networks

Radio Frequency IDentification (RFID) systems are becoming more and more popular in the field of ubiquitous computing, in particular for objects identification. An RFID system is composed by one or more readers and a number of tags. One of the main issues in an RFID network is the fast and reliable identification of all tags in the reader range. The reader issues some queries, and tags properly answer. Then, the reader must identify the tags from such answers. This is crucial for most applications. Since the transmission medium is shared, the typical problem to be faced is a MAC-like one, i.e. to avoid or limit the number of tags transmission collisions. We propose a protocol which, under some assumptions about transmission techniques, always achieves a 100% perfomance. It is based on a proper recursive splitting of the concurrent tags sets, until all tags have been identified. The other approaches present in literature have performances of about 42% in the average at most. The counterpart is a more sophisticated hardware to be deployed in the manufacture of low cost tags.Comment: 12 pages, 1 figur

A dual view of the 3d Heisenberg model and the abelian projection

The Heisenberg model in 3d is studied from a dual point of view. It is shown that it can have vortex configurations, carrying a conserved charge(U(1) symmetry). Vortices condens in the disordered phase. A disorder parameter \leftangle\mu\rightangle is defined dual to the magnetization \leftangle\vec n\rightangle, which signals condensation of vortices, i.e. spontaneous breaking of the dual U(1) symmetry. This study sheds light on the procedure known as abelian projection in non abelian gauge theories.Comment: LateX, 15 pages, 3 figure

Gravity duals of supersymmetric gauge theories on three-manifolds

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1) x U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.Comment: 74 pages, 2 figures; v2: minor change

Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories

We give further support for our conjecture relating eigenvalue distributions of the Kapustin-Willett-Yaakov matrix model in the large N limit to numbers of operators in the chiral ring of the corresponding supersymmetric three-dimensional gauge theory. We show that the relation holds for non-critical R-charges and for examples with {\mathcal N}=2 instead of {\mathcal N}=3 supersymmetry where the bifundamental matter fields are nonchiral. We prove that, for non-critical R-charges, the conjecture is equivalent to a relation between the free energy of the gauge theory on a three sphere and the volume of a Sasaki manifold that is part of the moduli space of the gauge theory. We also investigate the consequences of our conjecture for chiral theories where the matrix model is not well understood.Comment: 27 pages + appendices, 5 figure

Multidomain switching in the ferroelectric nanodots

Controlling the polarization switching in the ferroelectric nanocrystals, nanowires and nanodots has an inherent specificity related to the emergence of depolarization field that is associated with the spontaneous polarization. This field splits the finite-size ferroelectric sample into polarization domains. Here, based on 3D numerical simulations, we study the formation of 180$^{\circ }$ polarization domains in a nanoplatelet, made of uniaxial ferroelectric material, and show that in addition to the polarized monodomain state, the multidomain structures, notably of stripe and cylindrical shapes, can arise and compete during the switching process. The multibit switching protocol between these configurations may be realized by temperature and field variations