Regularization of 2d supersymmetric Yang-Mills theory via non commutative geometry

The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The supersymmetric version is also studied and more precisely in the case of the Schwinger model on supersphere [14]. This paper is a generalization of this latter work to more general gauge groups

Factors affecting the monitoring of the early setting of concrete by ultrasonic P-waves

Ultrasonic P-wave measurements are widely used to monitor concrete setting. Although the largest wave velocity increase occurs during setting, the earliest increase is rather caused by other factors. Air bubble migration, internal settling, formation of ettringite and early C-S-H, workability loss and thixotropy might affect the velocity change in time. Tests on mortar in which cement was replaced by bentonite, confirmed the possible influence of thixotropy on the measurements. The effect of air bubble migration, internal settling and workability loss was proven to be restricted by testing a mixture in which the cement was replaced by inert material. In a cement mixture, the precipitation of hydration products might however accelerate settling and workability loss. During cement hydration simulations, the change in porosity due to the formation of early C-S-H and ettringite was considered for the calculation of the elastic properties of the granular framework. Nevertheless, the calculated velocity hardly increased before percolation and thus could not confirm that the first velocity increase is attributed to formation of early hydration products. Thus, apart from thixotropy, none of the other factors could unarguably be indicated as the cause of early velocity increase

Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator

It is shown that the local axial anomaly in $2-$dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to contain an edge effect which corresponds precisely to the ``fuzzy'' $U(1)_A$ axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant expansion of the quark propagator in the form $\frac{1}{{\cal D}_{AF}}=\frac{a\hat{\Gamma}^L}{2}+\frac{1}{{\cal D}_{Aa}}$ where $a=\frac{2}{2l+1}$ is the lattice spacing on ${\bf S}^2_F$, $\hat{\Gamma}^L$ is the covariant noncommutative chirality and ${\cal D}_{Aa}$ is an effective Dirac operator which has essentially the same IR spectrum as ${\cal D}_{AF}$ but differes from it on the UV modes. Most remarkably is the fact that both operators share the same limit and thus the above covariant expansion is not available in the continuum theory . The first bit in this expansion $\frac{a\hat{\Gamma}^L}{2}$ although it vanishes as it stands in the continuum limit, its contribution to the anomaly is exactly the canonical theta term. The contribution of the propagator $\frac{1}{{\cal D}_{Aa}}$ is on the other hand equal to the toplogical Chern-Simons action which in two dimensions vanishes identically .Comment: 26 pages, latex fil

Use of acoustic emission analysis to evaluate the self-healing capability of concrete

It has been estimated that, in Europe, 50% of the annual construction budget is spent on refurbishment and remediation of the existing structures [1]. Therefore, self-healing of concrete structures, which are very sensitive to cracking, would be highly desirable. In this research, encapsulated healing agents were embedded in the concrete matrix in order to obtain self-healing properties. Upon crack appearance, the capsules break and the healing agent is released, resulting in crack repair. The efficiency of this crack healing technique was evaluated by using acoustic emission (AE) analysis. Breakage of the capsules was proven as events with an energy higher than the energy related to concrete cracking were noticed. Upon reloading of beams with untreated cracks, fewer emissions were detected compared to beams with healed cracks. From this study it was shown that AE is a suitable technique to evaluate self-healing of cracks in concrete

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mathematical Physic

CR-EST: a resource for crop ESTs

The crop expressed sequence tag database, CR-EST (http://pgrc.ipk-gatersleben.de/cr-est/), is a publicly available online resource providing access to sequence, classification, clustering and annotation data of crop EST projects. CR-EST currently holds more than 200 000 sequences derived from 41 cDNA libraries of four species: barley, wheat, pea and potato. The barley section comprises approximately one-third of all publicly available ESTs. CR-EST deploys an automatic EST preparation pipeline that includes the identification of chimeric clones in order to transparently display the data quality. Sequences are clustered in species-specific projects to currently generate a non-redundant set of ∼22 600 consensus sequences and ∼17 200 singletons, which form the basis of the provided set of unigenes. A web application allows the user to compute BLAST alignments of query sequences against the CR-EST database, query data from Gene Ontology and metabolic pathway annotations and query sequence similarities from stored BLAST results. CR-EST also features interactive JAVA-based tools, allowing the visualization of open reading frames and the explorative analysis of Gene Ontology mappings applied to ESTs

Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4

We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutative limit N -> infinity. The model can be used as a regularization of gauge theory on noncommutative R^4_\theta in a particular scaling limit, which is studied in detail. We also find topologically non-trivial U(1) solutions, which reduce to the known "fluxon" solutions in the limit of R^4_\theta, reproducing their full moduli space. Other solutions which can be interpreted as 2-dimensional branes are also found. The quantization of the model is defined non-perturbatively in terms of a path integral which is finite. A gauge-fixed BRST-invariant action is given as well. Fermions in the fundamental representation of the gauge group are included using a formulation based on SO(6), by defining a fuzzy Dirac operator which reduces to the standard Dirac operator on S^2 x S^2 in the commutative limit. The chirality operator and Weyl spinors are also introduced.Comment: 39 pages. V2-4: References added, typos fixe

Minimal Unitary Models and The Closed SU(2)-q Invariant Spin Chain

We consider the Hamiltonian of the closed $SU(2)_{q}$ invariant chain. We project a particular class of statistical models belonging to the unitary minimal series. A particular model corresponds to a particular value of the coupling constant. The operator content is derived. This class of models has charge-dependent boundary conditions. In simple cases (Ising, 3-state Potts) corresponding Hamiltonians are constructed. These are non-local as the original spin chain.Comment: 19 pages, latex, no figure

The size of two-body weakly bound objects : short versus long range potentials

The variation of the size of two-body objects is investigated, as the separation energy approaches zero, with both long range potentials and short range potentials having a repulsive core. It is shown that long range potentials can also give rise to very extended systems. The asymptotic laws derived for states with angular momentum l=1,2 differ from the ones obtained with short range potentials. The sensitivity of the asymptotic laws on the shape and length of short range potentials defined by two and three parameters is studied. These ideas as well as the transition from the short to the long range regime for the l=0 case are illustrated using the Kratzer potential.Comment: 5 pages, 3 figures, submitted to Physical Review Letter

The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection

On the fuzzy sphere, no state saturates simultaneously all the Heisenberg uncertainties. We propose a weaker uncertainty for which this holds. The family of states so obtained is physically motivated because it encodes information about positions in this fuzzy context. In particular, these states realize in a natural way a deformation of the stereographic projection. Surprisingly, in the large $j$ limit, they reproduce some properties of the ordinary coherent states on the non commutative plane.Comment: 18 pages, Latex. Minor changes in notations. Version to appear in JHE