The Unified Segment Tree and its Application to the Rectangle Intersection Problem

In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that arise naturally in this variation, and we show some properties concerning the relationships between the nodes, and the regions those nodes represent. We think these properties will enable the data to be utilized in new situations, beyond those previously studied. As an example, we show that the data structure can be used to solve the Rectangle Intersection Problem in a more straightforward and natural way than had be done in the past.Comment: 14 pages, 6 figure

Extended Uncertainty Principle for Rindler and cosmological horizons

We find exact formulas for the Extended Uncertainty Principle (EUP) for the Rindler and Friedmann horizons and show that they can be expanded to obtain asymptotic forms known from the previous literature. We calculate the corrections to Hawking temperature and Bekenstein entropy of a black hole in the universe due to Rindler and Friedmann horizons. The effect of the EUP is similar to the canonical corrections of thermal fluctuations and so it rises the entropy signalling further loss of information.Comment: 7 pages, 6 figures, REVTEX 4.1, minor changes, refs update

Fermions in the pseudoparticle approach

The pseudoparticle approach is a numerical technique to compute path integrals without discretizing spacetime. The basic idea is to integrate over those field configurations, which can be represented by a sum of a fixed number of localized building blocks (pseudoparticles). In a couple of previous papers we have successfully applied the pseudoparticle approach to pure SU(2) Yang-Mills theory. In this work we discuss how to incorporate fermionic fields in the pseudoparticle approach. To test our method, we compute the phase diagram of the 1+1-dimensional Gross-Neveu model in the large-N limit.Comment: 11 pages, 10 figure

Magnets position X-ray film for weld inspection

Film-positioning device uses magnets to hold X ray film for weld inspection in nonferrous structures, such as tanks, where access to interior points is difficult

A modification of the convective constraint release mechanism in the molecular stress function model giving enhanced vortex growth

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements