Exact time dependent Hopf solitons in 3+1 dimensions

We construct an infinite number of exact time dependent soliton solutions, carrying non-trivial Hopf topological charges, in a 3+1 dimensional Lorentz invariant theory with target space S2. The construction is based on an ansatz which explores the invariance of the model under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S2. The model is a rare example of an integrable theory in four dimensions, and the solitons may play a role in the low energy limit of gauge theories. © SISSA 2006.

Some implications of the cosmological constant to fundamental physics

In the presence of a cosmological constant, ordinary Poincaré special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime. In consequence, the ordinary notions of energy and momentum change, and will satisfy a different kinematic relation. Such a theory is a different kind of a doubly special relativity. Since the only difference between the Poincaré and the de Sitter groups is the replacement of translations by certain linear combinations of translations and proper conformal transformations, the net result of this change is ultimately the breakdown of ordinary translational invariance. From the experimental point of view, therefore, a de Sitter special relativity might be probed by looking for possible violations of translational invariance. If we assume the existence of a connection between the energy scale of an experiment and the local value of the cosmological constant, there would be changes in the kinematics of massive particles which could hopefully be detected in high-energy experiments. Furthermore, due to the presence of a horizon, the usual causal structure of spacetime would be significantly modified at the Planck scale. © 2007 American Institute of Physics.

Search for violation of Lorentz invariance in top quark pair production and decay

Using data collected with the D0 detector at the Fermilab Tevatron Collider, corresponding to 5.3fb -1 of integrated luminosity, we search for violation of Lorentz invariance by examining the tt̄ production cross section in lepton+jets final states. We quantify this violation using the standard-model extension framework, which predicts a dependence of the tt̄ production cross section on sidereal time as the orientation of the detector changes with the rotation of the Earth. Within this framework, we measure components of the matrices (c Q) μν33 and (c U) μν33 containing coefficients used to parametrize violation of Lorentz invariance in the top quark sector. Within uncertainties, these coefficients are found to be consistent with zero. © 2012 American Physical Society.

Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings

We consider a family of two-dimensional nonlinear area-preserving mappings that generalize the Chirikov standard map and model a variety of periodically forced systems. The action variable diffuses in increments whose phase is controlled by a negative power of the action and hence effectively uncorrelated for small actions, leading to a chaotic sea in phase space. For larger values of the action the phase space is mixed and contains a family of elliptic islands centered on periodic orbits and invariant Kolmogorov-Arnold-Moser (KAM) curves. The transport of particles along the phase space is considered by starting an ensemble of particles with a very low action and letting them evolve in the phase until they reach a certain height h. For chaotic orbits below the periodic islands, the survival probability for the particles to reach h is characterized by an exponential function, well modeled by the solution of the diffusion equation. On the other hand, when h reaches the position of periodic islands, the diffusion slows markedly. We show that the diffusion coefficient is scaling invariant with respect to the control parameter of the mapping when h reaches the position of the lowest KAM island. © 2013 American Physical Society.

Invariance of quantum optimal control fields to experimental parameters

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

DE SITTER TRANSITIVITY, CONFORMAL TRANSFORMATIONS AND CONSERVATION LAWS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The electromagnetic gauge invariance in SU(3)L ⊗ U(1)N models of electroweak unification reexamined

Two models with SU(3)C ⊗ SU(3)L U(1)N gauge symmetry are considered. We show that the masslessness of the photon does not prevent the neutrinos from acquiring Majorana masses. That is, there is no relation between the VEVs of Higgs fields and the electromagnetic gauge invariance contrary to what has been claimed recently. © 1998 Elsevier Science B.V. All rights reserved.

Discrete quantum phase spaces and the mod N invariance

An extended Weyl-Wigner transformation which maps operators onto periodic discrete quantum phase space representatives is discussed in which a mod N invariance is explicitly implemented. The relevance of this invariance for the mapped expression of products of operators is discussed. © 1992.

Hirota's solitons in the affine and the conformal affine Toda models

We use Hirota's method formulated as a recursive scheme to construct a complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different types of degeneracies encountered in Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the affine Toda model valid for all underlying Lie groups. Embedding of the affine Toda model in the conformal affine Toda model plays a crucial role in this analysis.

Evaluating Measurement Invariance with Censored Ordinal Data: A Monte Carlo Comparison of Alternative Model Estimators and Scales of Measurement

Evaluations of measurement invariance provide essential construct validity evidence. However, the quality of such evidence is partly dependent upon the validity of the resulting statistical conclusions. The presence of Type I or Type II errors can render measurement invariance conclusions meaningless. The purpose of this study was to determine the effects of categorization and censoring on the behavior of the chi-square/likelihood ratio test statistic and two alternative fit indices (CFI and RMSEA) under the context of evaluating measurement invariance. Monte Carlo simulation was used to examine Type I error and power rates for the (a) overall test statistic/fit indices, and (b) change in test statistic/fit indices. Data were generated according to a multiple-group single-factor CFA model across 40 conditions that varied by sample size, strength of item factor loadings, and categorization thresholds. Seven different combinations of model estimators (ML, Yuan-Bentler scaled ML, and WLSMV) and specified measurement scales (continuous, censored, and categorical) were used to analyze each of the simulation conditions. As hypothesized, non-normality increased Type I error rates for the continuous scale of measurement and did not affect error rates for the categorical scale of measurement. Maximum likelihood estimation combined with a categorical scale of measurement resulted in more correct statistical conclusions than the other analysis combinations. For the continuous and censored scales of measurement, the Yuan-Bentler scaled ML resulted in more correct conclusions than normal-theory ML. The censored measurement scale did not offer any advantages over the continuous measurement scale. Comparing across fit statistics and indices, the chi-square-based test statistics were preferred over the alternative fit indices, and ΔRMSEA was preferred over ΔCFI. Results from this study should be used to inform the modeling decisions of applied researchers. However, no single analysis combination can be recommended for all situations. Therefore, it is essential that researchers consider the context and purpose of their analyses.

An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Scaling invariance for the escape of particles from a periodically corrugated waveguide

The escape dynamics of a classical light ray inside a corrugated waveguide is characterised by the use of scaling arguments. The model is described via a two-dimensional nonlinear and area preserving mapping. The phase space of the mapping contains a set of periodic islands surrounded by a large chaotic sea that is confined by a set of invariant tori. When a hole is introduced in the chaotic sea, letting the ray escape, the histogram of frequency of the number of escaping particles exhibits rapid growth, reaching a maximum value at n(p) and later decaying asymptotically to zero. The behaviour of the histogram of escape frequency is characterised using scaling arguments. The scaling formalism is widely applicable to critical phenomena and useful in characterisation of phase transitions, including transitions from limited to unlimited energy growth in two-dimensional time varying billiard problems. (C) 2011 Elsevier B.V. All rights reserved.

Search for Lorentz invariance and CPT violation with muon antineutrinos in the MINOS Near Detector

We have searched for sidereal variations in the rate of antineutrino interactions in the MINOS Near Detector. Using antineutrinos produced by the NuMI beam, we find no statistically significant sidereal modulation in the rate. When this result is placed in the context of the Standard Model Extension theory we are able to place upper limits on the coefficients defining the theory. These limits are used in combination with the results from an earlier analysis of MINOS neutrino data to further constrain the coefficients.

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)

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.