Multi-particle Correlations in Quaternionic Quantum Systems

We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1

The muon content of EAS as a function of primary energy

The muon content of extensive air showers (EAS) was measured over the wide primary energy range 10 to the 16th power to 10 to the 20th power eV. It is reported that the relative muon content of EAS decreases smoothly over the energy range 10 to the 17th power to 10 to the 19th power eV and concluded that the primary cosmic ray flux has a constant mass composition over this range. It is also reported that an apparent significant change in the power index occurs below 10 to the 17th power eV rho sub c (250 m) sup 0.78. Such a change indicates a significant change in primary mass composition in this range. The earlier conclusions concerning EAS of energy 10 to the 17th power eV are confirmed. Analysis of data in the 10 to the 16th power - 10 to the 17th power eV range revealed a previously overlooked selection bias in the data set. The full analysis of the complete data set in the energy range 10 to the 16th power - 10 to the 17th power ev with the selection bias eliminated is presented

The gap exponent of XXZ model in a transverse field

We have calculated numerically the gap exponent of the anisotropic Heisenberg model in the presence of the transverse magnetic field. We have implemented the modified Lanczos method to obtain the excited states of our model with the same accuracy of the ground state. The coefficient of the leading term in the perturbation expansion diverges in the thermodynamic limit (N --> infinity). We have obtained the relation between this divergence and the scaling behaviour of the energy gap. We have found that the opening of gap in the presence of transverse field scales with a critical exponent which depends on the anisotropy parameter (Delta). Our numerical results are in well agreement with the field theoretical approach in the whole range of the anisotropy parameter, -1 < Delta < 1.Comment: 6 pages and 4 figure

Finite element analysis applied to redesign of submerged entry nozzles for steelmaking

The production of steel by continuous casting is facilitated by the use of refractory hollow-ware components. A critical component in this process is the submerged entry nozzle (SEN). The normal operating conditions of the SEN are arduous, involving large temperature gradients and exposure to mechanical forces arising from the flow of molten steel; experimental development of the components is challenging in so hazardous an environment. The effects of the thermal stress conditions in relation to a well-tried design were therefore simulated using a finite element analysis approach. It was concluded from analyses that failures of the type being experienced are caused by the large temperature gradient within the nozzle. The analyses pointed towards a supported shoulder area of the nozzle being most vulnerable to failure and practical in-service experience confirmed this. As a direct consequence of the investigation, design modifications, incorporating changes to both the internal geometry and to the nature of the intermediate support material, were implemented, thereby substantially reducing the stresses within the Al2O3/graphite ceramic liner. Industrial trials of this modified design established that the component reliability would be significantly improved and the design has now been implemented in series production

Syk-dependent Phosphorylation of CLEC-2: A Novel Mechanism of Hem-Immunoreceptor Tyrosine-Based Activation Motif Signaling

The C-type lectin-like receptor CLEC-2 signals via phosphorylation of a single cytoplasmic YXXL sequence known as a hem-immunoreceptor tyrosine-based activation motif (hemITAM). In this study, we show that phosphorylation of CLEC-2 by the snake toxin rhodocytin is abolished in the absence of the tyrosine kinase Syk but is not altered in the absence of the major platelet Src family kinases, Fyn, Lyn, and Src, or the tyrosine phosphatase CD148, which regulates the basal activity of Src family kinases. Further, phosphorylation of CLEC-2 by rhodocytin is not altered in the presence of the Src family kinase inhibitor PP2, even though PLCγ2 phosphorylation and platelet activation are abolished. A similar dependence of phosphorylation of CLEC-2 on Syk is also seen in response to stimulation by an IgG mAb to CLEC-2, although interestingly CLEC-2 phosphorylation is also reduced in the absence of Lyn. These results provide the first definitive evidence that Syk mediates phosphorylation of the CLEC-2 hemITAM receptor with Src family kinases playing a critical role further downstream through the regulation of Syk and other effector proteins, providing a new paradigm in signaling by YXXL-containing receptors

Topological Phase Transitions and Holonomies in the Dimer Model

We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite size corrections to the bulk partition function correspond to a massless Dirac Fermion in the presence of a flat connection with nontrivial holonomy. For general bond activities we find that the phase transition in this model is a topological one, where the torus degenerates and its modular parameter becomes real at the critical temperature. We argue that these features are generic to bipartite dimer models and we present a more general lattice whose continuum partition function is that of a massive Dirac Fermion.Comment: 7 pages, 4 figures. Minor corrections with additional figure

Manifestations of quantum holonomy in interferometry

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam's geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.Comment: Some changes, journal reference adde

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Labeling Schemes for Bounded Degree Graphs

We investigate adjacency labeling schemes for graphs of bounded degree $\Delta = O(1)$. In particular, we present an optimal (up to an additive constant) $\log n + O(1)$ adjacency labeling scheme for bounded degree trees. The latter scheme is derived from a labeling scheme for bounded degree outerplanar graphs. Our results complement a similar bound recently obtained for bounded depth trees [Fraigniaud and Korman, SODA 10], and may provide new insights for closing the long standing gap for adjacency in trees [Alstrup and Rauhe, FOCS 02]. We also provide improved labeling schemes for bounded degree planar graphs. Finally, we use combinatorial number systems and present an improved adjacency labeling schemes for graphs of bounded degree $\Delta$ with $(e+1)\sqrt{n} < \Delta \leq n/5$