Fiber Bundles, Connections, General Relativity, and the Einstein-Cartan Theory – Part II

The formalism of tetrads and spin connections is presented, and with it, the Einstein-Cartan (E-C) equations are derived from the usual actions. It is shown how torsion vanishes in the case of pure gravity. Then, the equations in the presence of the Dirac and the Maxwell fields are derived. A possibility of choosing a locally inertial coordinate system in the presence of a totally antisymmetric torsion is proved. We discuss a conflict between torsion and the local gauge invariance of the electromagnetic field. Finally, we study Lorentz and Poincaré gauge invariance of general relativity and the E-C theory.     

Pattern definition of the p-efficiency concept

This study revisits the celebrated p-efficiency concept introduced by Prékopa (Z.?Oper. Res. 34:441?C461, 1990) and defines a p-efficient point (pLEP) as a combinatorial pattern. The new definition uses elements from the combinatorial pattern recognition field and is based on the combinatorial pattern framework for stochastic programming problems proposed in Lejeune (Stochastic programming e-print series (SPEPS) 2010-5, 2010). The approach is based on the binarization of the probability distribution, and the generation of a consistent partially defined Boolean function representing the combination (F,p) of the binarized probability distribution F and the enforced probability level p. A combinatorial pattern provides a compact representation of the defining characteristics of a pLEP and opens the door to new methods for the generation of pLEPs. We show that a combinatorial pattern representing a pLEP constitutes a strong and prime pattern and we derive it through the solution of an integer programming problem. Next, we demonstrate that the (finite) collection of pLEPs can be represented as a disjunctive normal form (DNF). We propose a mixed-integer programming formulation allowing for the construction of the DNF that is shown to be prime and irreducible. We illustrate the proposed method on a problem studied by Prékopa (Stochastic programming: handbook in operations research and management science, vol.?10, Elsevier, Amsterdam, 2003).     

Predicting initial erosion during the hole erosion test by using turbulent flow CFD simulation

CFD simulation with enhanced modeling of turbulence and near-wall treatment is used to model water–clay mixtures flowing through a cylindrical pipe domain. Effects on the wall-shear stress resulting from varying water clay content and applied hydraulic gradient are analyzed. Various parametric studies were performed and had shown that the two-dimensional modelling introduced in the present study does not yield a uniform wall-shear stress along the pipe wall and that clay concentration affects significantly the wall-shear stress value. This is in contrast with the common hypothesis used in one-dimensional modeling approaches where this stress is assumed constant and which gives rise to uniform erosion along the pipe wall. The obtained results had enabled predicting more realistically erosion amount and had allowed for understanding the irregular eroded hole wall shape as observed experimentally after performing the standard hole erosion test.     

Stability of periodic Kuramoto–Sivashinsky waves

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized Kuramoto–Sivashinsky equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of decay. The approach extends readily to other second- and higher-order parabolic equations, for example, the Cahn Hilliard equation or more general thin film models.     

A branch-and-price approach for harvest scheduling subject to maximum area restrictions

Recently, research on exact methods has been undertaken to solve forest management problems subject to constraints on the maximum clearcut area by using the area restriction model approach. Three main basic integer programming models for these problems have been discussed in the literature: the so-called cluster, path and bucket formulations. Solving these models via branch-and-bound, where all variables and constraints are used a priori, is adequately suited for real problems of a small to medium size, but is not appropriate for larger problems. In this paper, we describe a branch-and-price approach for the cluster model, and we show that this formulation dominates the bucket model, by completing the results of the dominance relationships between the bounds of the three models. Branch-and-price was tested on real and hypothetical forests ranging from 45 to 2945 stands and temporal horizons ranging from three to twelve periods were employed. Results show that the solutions obtained by the proposed approach stood within 1% of the optimal solution and were achieved in a short computation time. It was found that branch-and-bound was unable to produce solutions for most forests from 850 stands with either eleven or an average number of stands per clearcut greater or equal than eight.     

H?lder continuity for Trudinger’s equation in measure spaces

We complete the study of the regularity for Trudinger’s equation by proving that weak solutions are H?lder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling.     

Integration of gold nanoparticles in optical resonators

The optical absorption of one-dimensional photonic crystal based resonators containing different types of gold nanoparticles is controllably modified by means of the interplay between planar optical cavity modes and localized surface plasmons. Spin-casting of metal oxide nanoparticle suspensions was used to build multilayered photonic structures that host (silica-coated) gold nanorods and spheres. Strong reinforcement and depletion of the absorptance was observed at designed wavelength ranges, thus proving that our method provides a reliable means to modify the optical absorption originated at plasmonic resonances of particles of arbitrary shape and within a wide range of sizes. These observations are discussed on the basis of calculations of the spatial and spectral dependence of the optical field intensity within the multilayers.     

In situ hydrolysis of imine derivatives on Au(111) for the formation of aromatic mixed self-assembled monolayers: multitechnique analysis of this tunable surface modification

This paper presents a novel method for preparing aromatic, mixed self-assembled monolayers (SAMs) with a dilute surface fraction coverage of protonated amine via in situ hydrolysis of C═N double bond on gold surface. Two imine compounds, (4'-(4-(trifluoromethyl)benzylideneamino)biphenyl-4-yl)methanethiol (CF(3)-C(6)H(4)-CH═N-C(6)H(4)-C(6)H(4)-CH(2)-SH, TFBABPMT) and (4'-(4-cyanobenzylideneamino)biphenyl-4-yl)methanethiol (CN-C(6)H(4)-CH═N-C(6)H(4)-C(6)H(4)-CH(2)-SH, CBABPMT), self-assembled on Au(111) to form highly ordered monolayers, which was demonstrated by infrared reflection absorption spectroscopy (IRRAS) and X-ray photoelectron spectroscopy (XPS). A nearly upright molecular orientation for CF(3)- and CN-terminated SAM was detected by near edge X-ray absorption fine structure (NEXAFS) measurements. Afterward, the acidic catalyzed hydrolysis was carried out in chloroform or an aqueous solution of acetic acid (pH = 3). Systematic studies of this hydrolysis process for CN-terminated SAM in acetic acid at 25 °C were performed by NEXAFS measurements. It was found that about 30% of the imine double bonds gradually cleaved in the first 40 min. Subsequently, a larger hydrolysis rate was observed due to the freer penetration of acetic acid in the SAM and resultant more open molecular packing. Furthermore, the molecular orientation in mixed SAMs did not change during the whole hydrolysis process. This partially hydrolyzed surface contains a controlled amount of free amines/ammonium ions which can be used for further chemical modifications.     

Multiphoton reactive surfaces using ruthenium(II) photocleavable cages

Photoreactive surfaces derived from a new photocleavable surface modification agent and with photosensitivity in the Vis and IR region are described. A ruthenium(II) caged aminosilane, [Ru(bpy)(2)(PMe(3))(APTS)](PF(6))(2), was synthesized and attached to silica surfaces. Light irradiation removed the cage and generated surface patterns with reactive amine groups. The photosensitivity of this compound under single (460 nm) and two-photon (900) excitation is demonstrated. Functional patterns with site-selective attachment of other molecular species are described.     

Fragmentation trees for the structural characterisation of metabolites

Metabolite identification plays a crucial role in the interpretation of metabolomics research results. Due to its sensitivity and widespread implementation, a favourite analytical method used in metabolomics is electrospray mass spectrometry. In this paper, we demonstrate our results in attempting to incorporate the potentials of multistage mass spectrometry into the metabolite identification routine. New software tools were developed and implemented which facilitate the analysis of multistage mass spectra and allow for efficient removal of spectral artefacts. The pre-processed fragmentation patterns are saved as fragmentation trees. Fragmentation trees are characteristic of molecular structure. We demonstrate the reproducibility and robustness of the acquisition of such trees on a model compound. The specificity of fragmentation trees allows for distinguishing structural isomers, as shown on a pair of isomeric prostaglandins. This approach to the analysis of the multistage mass spectral characterisation of compounds is an important step towards formulating a generic metabolite identification method. Copyright ? 2012 John Wiley & Sons, Ltd.