Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group

We study the pure gauge model on a lattice manifold with trivial fundamental homotopy group, homotopically equivalent to an $S_4$. Monopole loops may fluctuate freely on that lattice without restrictions due to the boundary conditions. For the original Wilson action on the hypertorus there is an established two-state signal in energy distribution functions which disappears for the new geometry. Our finite size scaling analysis suggests stringent upper bounds on possible discontinuities in the plaquette action. However, no consistent asymptotic finite size scaling behaviour is observed.Comment: 18 pages (3 figures), LaTeX + POSTSCRIPT (287 KB), preprint BI-TP 94/3

U(1) Gauge Theory with Villain Action on Spherical Lattices

We have studied the U(1) gauge field theory with Villain (periodic Gaussian) action on spherelike lattices. The effective size of the systems studied ranges from 6 to 16. We do not observe any 2-state signal in the distribution function of the plaquette expectation value at the deconfining phase transition. The observed finite-size scaling behavior is consistent with a second order phase transition. The obtained value of the critical exponent is nu =0.366(12) and thus neither Gaussian (nu = 0.5) nor discontinuous (nu=0.25) type, indicating a nontrivial continuum limit.Comment: 10 pages, LaTeX, 2 figure

Stresses in a half space due to Newtonian gravitation

An efficient general solution is obtained for the problem of the elastic half space z > 0 with a traction-free surface experiencing gravitational attraction to an arbitrarily shaped body located in z < 0. Many components of the stress field can be written down immediately if the potential of the attracting body is known. Results are given for the case of attraction to a uniform sphere.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42687/1/10659_2005_Article_4105.pd

Lee-Yang zeroes and logarithmic corrections in the Φ44 theory

The leading mean-field critical behaviour of φ 4 4-theory is modified by multiplicative logarithmic corrections. We analyse these corrections both analytically and numerically. In particular we present a finite-size scaling theory for the Lee-Yang zeroes and temperature zeroes, both of which exhibit logarithmic corrections. On lattices from size 8 4 to 24 4, Monte-Carlo cluster methods and multi-histogram techniques are used to determine the partition function zeroes closest to the critical point. Finite-size scaling behaviour is verified and the logarithmic corrections are found to be in good agreement with our analytical predictions. 1

Electron-hadron shower discrimination in a liquid argon time projection chamber

By exploiting structural differences between electromagnetic and hadronic showers in a multivariate analysis we present an efficient Electron-Hadron discrimination algorithm for liquid argon time projection chambers, validated using Geant4 simulated data

Geometric measure of entanglement and applications to bipartite and multipartite quantum states

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (see Shimony 1995 and Barnum and Linden 2001), is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states. In particular, a detailed analysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W states. Along the way, we point out connections of the geometric measure of entanglement with entanglement witnesses and with the Hartree approximation method.Comment: 13 pages, 11 figures, this is a combination of three previous manuscripts (quant-ph/0212030, quant-ph/0303079, and quant-ph/0303158) made more extensive and coherent. To appear in PR

Globally Optimal Spatio-temporal Reconstruction from Cluttered Videos

International audienceWe propose a method for multi-view reconstruction from videos adapted to dynamic cluttered scenes under uncontrolled imaging conditions. Taking visibility into account, and being based on a global optimization of a true spatio-temporal energy, it oilers several desirable properties: no need for silhouettes, robustness to noise, independent from any initialization, no heuristic force, reduced flickering results, etc. Results on real-world data proves the potential of what is, to our knowledge, the only globally optimal spatio-temporal multi-view reconstruction method

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces

Fine structure in the azimuthal transverse momentum correlations at sNN=200\sqrt{s_{NN}}=200 GeV using the event shape analysis

The experimental results on transverse momentum azimuthal hadron correlations at RHIC have opened a rich field for parton energy loss analysis in heavy-ion collisions. Recently, a considerable amount of work has beendevoted to study the shapes of the ``away-side'' jet which exhibit an interesting and unexpected ``double hump'' structure not observed in the analogous treatment of $pp$ data. Driven by the possibility that the latter result might just mean that such structure exists already in the case of $pp$ collisions, but that its relative intensity could be small, here we use the Event Shape Analysis to show that it is possible to identify and select well defined event topologies in $pp$ collisions, among which, a double hump structure for the away-side jet emerges. Using two shape parameters, the sphericity in the transverse plane and the recoil to analyze a sample of PYTHIA generated $pp$ collisions at $\sqrt{s_{NN}}=200$ GeV, we show that this structure corresponds to two jets emitted in the backward hemisphere. Finally, we show that Q-PYTHIA qualitatively reproduces the decrease in the yield of dijet events and the increase of the double hump structure in the away side observed in heavy ion collisions. The implications for the treatment of parton energy loss in heavy-ion collisions are discussedComment: 6 pages, 7 fugures: One figure was changed, references were added. This version will appear in Eur. Phys. J.

Renormalization group analysis of finite-size scaling in the ø44 model

A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the leading scaling behaviour is identical to that of mean field theory, there exist multiplicative logarithmic corrections too. A non-perturbative test of these formulae in the form of a high precision Monte Carlo analysis reveals good quantitative agreement with the analytical predictions.Comment: 25 p + 3 PS-figures, UNIGRAZ-UTP-07-10-92 (Revision 08-10-92: only PS-figures, which originally had too long lines exceeding 80 characters