Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

Nonlocal growth processes and conformal invariance

Up to now the raise-and-peel model was the single known example of a one-dimensional stochastic process where one can observe conformal invariance. The model has one parameter. Depending on its value one has a gapped phase, a critical point where one has conformal invariance, and a gapless phase with changing values of the dynamical critical exponent z. In this model, adsorption is local but desorption is not. The raise-and-strip model presented here, in which desorption is also nonlocal, has the same phase diagram. The critical exponents are different as are some physical properties of the model. Our study suggests the possible existence of a whole class of stochastic models in which one can observe conformal invariance.

Effects of 3-Dimensional Conformal or Intensity-modulated Radiotherapy on Dental Pulp Sensitivity during and after the Treatment of Oral or Oropharyngeal Malignancies

Introduction: Radiation therapy (RT) of malignant tumors in the head and neck area may have damaging effects on surrounding tissues. The aim of this investigation was to evaluate the effects of RI delivered by 3-dimensional conformal radiotherapy (3D-RT) or intensity-modulated radiotherapy (IMRT) on dental pulp sensitivity. Methods: Twenty patients with oral or oropharyngeal cancer receiving RT with 3D-RT or IMRT underwent cold thermal pulp sensitivity testing (PST) of 2 teeth each at 4 time points: before RT (TP1), the beginning of RT with doses between 30 and 35 Gy (TP2), the end of RT with doses between 60 and 70 Gy (TP3), and 4 to 5 months after the start of RT (TP4). Results: All 40 teeth showed positive responses to PST at TP1 (100%) and 9 at TP2 (22.5%; 3/16 [18.8%] for 3D-RT and 6/24 [25.0%] for IMRT). No tooth responded to PST at TP3 and TP4 (0%). A statistically significant difference existed in the number of positive pulp responses between different time points (TP1 through TP4) for all patients receiving RT (P <= .05), IMRT (P <= .05), and 3D-RT (P <= .05). No statistically significant differences in positive sensitivity responses were found between 3D-RT and IMRT at any time point (TP1, TP3, TP4, P = 1.0; TP2, P = .74). A statistically significant correlation existed between the location of the tumor and PST at TP2 for IMRT (P <= .05) but not for 3D-RT (P = .14). Conclusions: RT decreased the number of teeth responding to PST after doses greater than 30 to 35 Gy. The type of RT (3D-RT or IMRT) had no influence on the pulp responses to PST after the conclusion of RT. (J Endod 2012;38:148-152)

Nonlocal asymmetric exclusion process on a ring and conformal invariance

We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter u controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram, and consequently the values of the current, depend on u and the density of particles. In the special case of half-lling and u = 1 the system is conformal invariant and an exact value of the current for any size L of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For u > 1 the current has a non-analytic dependence on the density when the latter approaches the half-lling value.

Topology Verification for Isosurface Extraction

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

Tomotherapy dose distribution verification using MAGIC-f polymer gel dosimetry

Purpose: This paper presents the application of MAGIC-f gel in a three-dimensional dose distribution measurement and its ability to accurately measure the dose distribution from a tomotherapy unit. Methods: A prostate intensity-modulated radiation therapy (IMRT) irradiation was simulated in the gel phantom and the treatment was delivered by a TomoTherapy equipment. Dose distribution was evaluated by the R2 distribution measured in magnetic resonance imaging. Results: A high similarity was found by overlapping of isodoses of the dose distribution measured with the gel and expected by the treatment planning system (TPS). Another analysis was done by comparing the relative absorbed dose profiles in the measured and in the expected dose distributions extracted along indicated lines of the volume and the results were also in agreement. The gamma index analysis was also applied to the data and a high pass rate was achieved (88.4% for analysis using 3%/3 mm and of 96.5% using 4%/4 mm). The real three-dimensional analysis compared the dose-volume histograms measured for the planning volumes and expected by the treatment planning, being the results also in good agreement by the overlapping of the curves. Conclusions: These results show that MAGIC-f gel is a promise for tridimensional dose distribution measurements. (C) 2012 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4704496]

New cosmic accelerating scenario without dark energy

We propose an alternative, nonsingular, cosmic scenario based on gravitationally induced particle production. The model is an attempt to evade the coincidence and cosmological constant problems of the standard model (Lambda CDM) and also to connect the early and late time accelerating stages of the Universe. Our space-time emerges from a pure initial de Sitter stage thereby providing a natural solution to the horizon problem. Subsequently, due to an instability provoked by the production of massless particles, the Universe evolves smoothly to the standard radiation dominated era thereby ending the production of radiation as required by the conformal invariance. Next, the radiation becomes subdominant with the Universe entering in the cold dark matter dominated era. Finally, the negative pressure associated with the creation of cold dark matter (CCDM model) particles accelerates the expansion and drives the Universe to a final de Sitter stage. The late time cosmic expansion history of the CCDM model is exactly like in the standard Lambda CDM model; however, there is no dark energy. The model evolves between two limiting (early and late time) de Sitter regimes. All the stages are also discussed in terms of a scalar field description. This complete scenario is fully determined by two extreme energy densities, or equivalently, the associated de Sitter Hubble scales connected by rho(I)/rho(f) = (H-I/H-f)(2) similar to 10(122), a result that has no correlation with the cosmological constant problem. We also study the linear growth of matter perturbations at the final accelerating stage. It is found that the CCDM growth index can be written as a function of the Lambda growth index, gamma(Lambda) similar or equal to 6/11. In this framework, we also compare the observed growth rate of clustering with that predicted by the current CCDM model. Performing a chi(2) statistical test we show that the CCDM model provides growth rates that match sufficiently well with the observed growth rate of structure.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

Lyotropic mixture made of potassium laurate/1-undecanol/K2SO4/water presenting high birefringences and large biaxial nematic phase domain: a laser conoscopy study

The lyotropic liquid crystalline quaternary mixture made of potassium laurate (KL), potassium sulphate, 1-undecanol and water was investigated by experimental optical methods (optical microscopy and laser conoscopy). In a particular temperature and relative concentrations range, the three nematic phases (two uniaxial and one biaxial) were identified. The biaxial domain in the temperature/KL concentration surface is larger when compared to other lyotropic mixtures. Moreover, this new mixture gives nematic phases with higher birefringence than similar systems. The behavior of the symmetric tensor order parameter invariants sigma(3) and sigma(2) calculated from the measured optical birefringences supports that the uniaxial-to-biaxial transitions are of second order, described by a mean-field theory.

Entanglement of excited states in critical spin chains

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the conformal field theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done by Alcaraz et al in 2011 (see reference [1], of which this work is a completion). An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c = 1, 1/2 universality classes. Oscillations of the Renyi entropy in excited states are also discussed.

Entanglement entropy in long-range harmonic oscillators

We study the Von Neumann and Renyi entanglement entropy of long-range harmonic oscillators (LRHO) by both theoretical and numerical means. We show that the entanglement entropy in massless harmonic oscillators increases logarithmically with the sub-system size as S - c(eff)/3 log l. Although the entanglement entropy of LRHO's shares some similarities with the entanglement entropy at conformal critical points we show that the Renyi entanglement entropy presents some deviations from the expected conformal behaviour. In the massive case we demonstrate that the behaviour of the entanglement entropy with respect to the correlation length is also logarithmic as the short-range case. Copyright (c) EPLA, 2012

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q = 2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.