On the embedding of spacetime in five-dimensional Weyl spaces

We revisit Weyl geometry in the context of recent higher-dimensional theories of spacetime. After introducing the Weyl theory in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Weyl geometries and show how a Riemannian spacetime may be locally and isometrically embedded in a Weyl bulk. We discuss the problem of classical confinement and the stability of motion of particles and photons in the neighbourhood of branes for the case when the Weyl bulk has the geometry of a warped product space. We show how the confinement and stability properties of geodesics near the brane may be affected by the Weyl field. We construct a classical analogue of quantum confinement inspired in theoretical-field models by considering a Weyl scalar field which depends only on the extra coordinate.Comment: 16 pages, new title and references adde

Programmed buckling by controlled lateral swelling in a thin elastic sheet

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure

Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference

Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we investigate the possibility of describing the macroscopic behavior of complex systems in terms of the underlying statistical structure of their microscopic degrees of freedom by use of statistical inductive inference and information geometry. We review the Maximum Relative Entropy (MrE) formalism and the theoretical structure of the information geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special focus is devoted to the description of the roles played by the sectional curvature, the Jacobi field intensity and the information geometrodynamical entropy (IGE). These quantities serve as powerful information geometric complexity measures of information-constrained dynamics associated with arbitrary chaotic and regular systems defined on the statistical manifold. Finally, the application of such information geometric techniques to several theoretical models are presented.Comment: 29 page

Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape

An estimate is derived for the volume fraction of a subset $C_{\epsilon}^{P} = \{U : ||grad J(U)|\leq {\epsilon}\}\subset\mathrm{U}(N)$ in the neighborhood of the critical set $C^{P}\simeq\mathrm{U}(\mathbf{n})P\mathrm{U}(\mathbf{m})$ of the kinematic quantum ensemble control landscape J(U) = Tr(U\rho U' O), where $U$ represents the unitary time evolution operator, {\rho} is the initial density matrix of the ensemble, and O is an observable operator. This estimate is based on the Hilbert-Schmidt geometry for the unitary group and a first-order approximation of $||grad J(U)||^2$. An upper bound on these near-critical volumes is conjectured and supported by numerical simulation, leading to an asymptotic analysis as the dimension $N$ of the quantum system rises in which the volume fractions of these "near-critical" sets decrease to zero as $N$ increases. This result helps explain the apparent lack of influence exerted by the many saddles of $J$ over the gradient flow.Comment: 27 pages, 1 figur

Up conversion from visible to ultraviolet in bulk ZnO implanted with Tm ions

We report on the up-converted ultraviolet near-band edge emission of bulk ZnO generated by visible and ultraviolet photons with energies below the band gap. This up-converted photoluminescence was observed in samples intentionally doped with Tm ions, suggesting that the energy levels introduced by the rare earth ion in the ZnO band gap are responsible for this process.FCT/FEDER - POCTI/CTM/45236/02FCT/FEDER - POCTI/FAT/4882

Surface modification of Co-doped ZnO nanocrystals and its effects on the magnetic properties

A series of chemically prepared Co2+-doped ZnO colloids has been surface modified either by growing shells of ZnSe or by the in situ encapsulation in poly styrene . The surface modification effects using these two distinct chemical strategies on the magnetic properties of the nanocrystals were probed by electron paramagnetic resonance EPR . Structural characterization by means of x-ray diffraction and transmission electron microscopy gave no evidence of second phase formation within the detection limits of the used equipment. The EPR analysis was carried out by simulations of the powderlike EPR spectra. The results confirm that in the core of these nanocrystals Co was incorporated as Co2+, occupying the Zn2+ sites in the wurtzite structure of ZnO. Additionally we identify two Co signals stemming from the nanocrystals’ shell. The performed surface modifications clearly change the relative intensity of the EPR spectrum components, revealing the core and shell signals

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

Surfaces immersed in Lie algebras associated with elliptic integrals

The main aim of this paper is to study soliton surfaces immersed in Lie algebras associated with ordinary differential equations (ODE's) for elliptic functions. That is, given a linear spectral problem for such an ODE in matrix Lax representation, we search for the most general solution of the wave function which satisfies the linear spectral problem. These solutions allow for the explicit construction of soliton surfaces by the Fokas-Gel'fand formula for immersion, as formulated in (Grundland and Post 2011) which is based on the formalism of generalized vector fields and their prolongation structures. The problem has been reduced to examining three types of symmetries, namely, a conformal symmetry in the spectral parameter (known as the Sym-Tafel formula), gauge transformations of the wave function and generalized symmetries of the associated integrable ODE. The paper contains a detailed explanation of the immersion theory of surfaces in Lie algebras in connection with ODE's as well as an exposition of the main tools used to study their geometric characteristics. Several examples of the Jacobian and P-Weierstrass elliptic functions are included as illustrations of the theoretical results.Comment: 22 pages, 3 sets of figures. Keywords: Generalized symmetries, integrable models, surfaces immersed in Lie algebra