5-Dimensional Kaluza-Klein Theory with a Source

A free test particle in 5-dimensional Kaluza-Klein spacetime will show its electricity in the reduced 4-dimensional spacetime when it moves along the fifth dimension. In the light of this observation, we study the coupling of a 5-dimensional dust field with the Kaluza-Klein gravity. It turns out that the dust field can curve the 5-dimensional spacetime in such a way that it provides exactly the source of the electromagnetic field in the 4-dimensional spacetime after the dimensional reduction.Comment: 8 pages, three references adde

Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment

This is the peer reviewed version of the following article: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.Peer ReviewedPostprint (author's final draft

Coordination chemistry of amide-functionalised tetraazamacrocycles: structural, relaxometric and cytotoxicity studies

Three different tetraazamacrocyclic ligands containing four amide substituents that feature groups (namely allyl, styryl and propargyl groups) suitable for polymerisation have been synthesised. Gadolinium(III) complexes of these three ligands have been prepared as potential monomers for the synthesis of polymeric MRI contrast agents. To assess the potential of these monomers as MRI contrast agents, their relaxation enhancement properties and cytotoxicity have been determined. A europium(III) complex of one of these ligands (with propargyl substituents) is also presented together with its PARACEST properties. In addition, to gain further insight into the coordination chemistry of the tetra-propargyl substituted ligand, the corresponding zinc(II) and cadmium(II) complexes have been prepared. The X-ray crystal structures of the tetra-propargyl ligand and its corresponding gadolinium(III), zinc(II) and cadmium(II) complexes are also presented

Enhanced Motor Function by Training in Spinal Cord Contused Rats Following Radiation Therapy

Weight-bearing stepping, without supraspinal re-connectivity, can be attained by treadmill training in an animal whose spinal cord has been completely transected at the lower thoracic level. Repair of damaged tissue and of supraspinal connectivity/circuitry following spinal cord injury in rat can be achieved by specific cell elimination with radiation therapy of the lesion site delivered within a critical time window, 2-3 weeks postinjury. Here we examined the effects of training in the repaired spinal cord following clinical radiation therapy. Studies were performed in a severe rat spinal cord contusion injury model, one similar to fracture/crush injuries in humans; the injury was at the lower thoracic level and the training was a combined hindlimb standing and stepping protocol. Radiotherapy, in a similar manner to that reported previously, resulted in a significant level of tissue repair/preservation at the lesion site. Training in the irradiated group, as determined by limb kinematics tests, resulted in functional improvements that were significant for standing and stepping capacity, and yielded a significant direct correlation between standing and stepping performance. In contrast, the training in the unirradiated group resulted in no apparent beneficial effects, and yielded an inverse correlation between standing and stepping performance, e.g., subject with good standing showed poor stepping capacity. Further, without any training, a differential functional change was observed in the irradiated group; standing capacity was significantly inhibited while stepping showed a slight trend of improvement compared with the unirradiated group. These data suggest that following repair by radiation therapy the spinal circuitries which control posture and locomotor were modified, and that the beneficial functional modulation of these circuitries is use dependent. Further, for restoring beneficial motor function following radiotherapy, training seems to be crucial

Quintessential Phenomena in Higher Dimensional Space Time

The higher dimensional cosmology provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Here we discuss two situations where starting with an ordinary matter field without any equation of state we end up with a Chaplygin type of gas apparently as a consequence of extra dimensions. In the second case we study the quintessential phenomena in higher dimensional spacetime with the help of a Chaplygin type of matter field. The first case suffers from the disqualification that no dimensional reduction occurs, which is, however, rectified in the second case. Both the models show the sought after feature of occurrence of \emph{flip} in the rate of expansion. It is observed that with the increase of dimensions the occurrence of \emph{flip} is delayed for both the models, more in line with current observational demands. Interestingly we see that depending on some initial conditions our model admits QCDM, $\Lambda$CDM and also Phantom like evolution within a unified framework. Our solutions are general in nature in the sense that when the extra dimensions are switched off the known 4D model is recovered.Comment: 17 Pages, 7 figure

Spatial distribution of photoelectrons participating in formation of x-ray absorption spectra

Interpretation of x-ray absorption near-edge structure (XANES) experiments is often done via analyzing the role of particular atoms in the formation of specific peaks in the calculated spectrum. Typically, this is achieved by calculating the spectrum for a series of trial structures where various atoms are moved and/or removed. A more quantitative approach is presented here, based on comparing the probabilities that a XANES photoelectron of a given energy can be found near particular atoms. Such a photoelectron probability density can be consistently defined as a sum over squares of wave functions which describe participating photoelectron diffraction processes, weighted by their normalized cross sections. A fine structure in the energy dependence of these probabilities can be extracted and compared to XANES spectrum. As an illustration of this novel technique, we analyze the photoelectron probability density at the Ti K pre-edge of TiS2 and at the Ti K-edge of rutile TiO2.Comment: Journal abstract available on-line at http://link.aps.org/abstract/PRB/v65/e20511

The velocity dispersion and mass-to-light ratio of the remote halo globular cluster NGC 2419

Precise radial velocity measurements from HIRES on the Keck I telescope are presented for 40 stars in the outer halo globular cluster NGC 2419. These data are used to probe the cluster's stellar mass function and search for the presence of dark matter in this cluster. NGC 2419 is one of the best Galactic globular clusters for such a study due to its long relaxation time (T_{r0} ~ 10^{10} yr) and large Galactocentric distance (R_{GC} ~ 90 kpc) -- properties that make significant evolutionary changes in the low-mass end of the cluster mass function unlikely. We find a mean cluster velocity of =-20.3 +- 0.7 km/sec and an internal velocity dispersion of \sigma = 4.14 +- 0.48 km/sec, leading to a total mass of (9.0 +- 2.2) * 10^5 Msun and a global mass-to-light ratio of M/L_V = 2.05 +- 0.50 in solar units. This mass-to-light ratio is in good agreement with what one would expect for a pure stellar system following a standard mass function at the metallicity of NGC 2419. In addition, the mass-to-light ratio does not appear to rise towards the outer parts of the cluster. Our measurements therefore rule out the presence of a dark matter halo with mass larger than ~10^7 Msun inside the central 500 pc, which is lower than what is found for the central dark matter densities of dSph galaxies. We also discuss the relevance of our measurements for alternative gravitational theories such as MOND, and for possible formation scenarios of ultra-compact dwarf galaxies.Comment: 11 pages, 7 figures, MNRAS in pres