Non-Bogomolny SU(N) BPS Monopoles

For N>2 we present static monopole solutions of the second order SU(N) BPS Yang-Mills-Higgs equations which are not solutions of the first order Bogomolny equations. These spherically symmetric solutions may be interpreted as monopole anti-monopole configurations and their construction involves harmonic maps into complex projective spaces.Comment: 14 pages, 1 figur

Low Energy States in the SU(N) Skyrme Models

We show that any solution of the SU(2) Skyrme model can be used to give a topologically trivial solution of the SU(4) one. In addition, we extend the method introduced by Houghton et al. and use harmonic maps from S2 to CP(N-1) to construct low energy configurations of the SU(N) Skyrme models. We show that one of such maps gives an exact, topologically trivial, solution of the SU(3) model. We study various properties of these maps and show that, in general, their energies are only marginally higher than the energies of the corresponding SU(2) embeddings. Moreover, we show that the baryon (and energy) densities of the SU(3) configurations with baryon number B=2-4 are more symmetrical than their SU(2) analogues. We also present the baryon densities for the B=5 and B=6 configurations and discuss their symmetries.Comment: latex : 25 pages, 9 Postscript figures, uses eps

Can two wrongs make a right? Reconsidering minimum resale price maintenance in the light of Allianz Hungária

Minimum resale price maintenance (RPM) agreements constitute hard-core vertical restraints and are treated as object restrictions in EU competition law. This article suggests that the time may have come where this approach is revised. After, first, discussing the economic theory behind RPM and the EU Court’s approach to object restrictions, it argues that the recent widening of the object analysis and the concomitant blurring of the object and effect categories may aid EU competition law to reconceptualise the approach to minimum RPM

Astroglial-axonal interactions during early stages of myelination in mixed cultures using in vitro and ex vivo imaging techniques

<b>Background</b><p></p> Myelination is a very complex process that requires the cross talk between various neural cell types. Previously, using cytosolic or membrane associated GFP tagged neurospheres, we followed the interaction of oligodendrocytes with axons using time-lapse imaging in vitro and ex vivo and demonstrated dynamic changes in cell morphology. In this study we focus on GFP tagged astrocytes differentiated from neurospheres and their interactions with axons.<p></p> <b>Results</b><p></p> We show the close interaction of astrocyte processes with axons and with oligodendrocytes in mixed mouse spinal cord cultures with formation of membrane blebs as previously seen for oligodendrocytes in the same cultures. When GFP-tagged neurospheres were transplanted into the spinal cord of the dysmyelinated shiverer mouse, confirmation of dynamic changes in cell morphology was provided and a prevalence for astrocyte differentiation compared with oligodendroglial differentiation around the injection site. Furthermore, we were able to image GFP tagged neural cells in vivo after transplantation and the cells exhibited similar membrane changes as cells visualised in vitro and ex vivo.<p></p> <b>Conclusion</b><p></p> These data show that astrocytes exhibit dynamic cell process movement and changes in their membrane topography as they interact with axons and oligodendrocytes during the process of myelination, with the first demonstration of bleb formation in astrocytes

Multiscale Poromechanics of Wet Cement Paste

Capillary effects such as imbibition-drying cycles impact the mechanics of granular systems over time. A multiscale poromechanics framework was applied to cement paste, that is the most common building material, experiencing broad humidity variations over the lifetime of infrastructure. First, the liquid density distribution at intermediate to high relative humidities is obtained using a lattice gas density functional method together with a realistic nano-granular model of cement hydrates. The calculated adsorption/desorption isotherms and pore size distributions are discussed and compare well to nitrogen and water experiments. The standard method for pore size distribution determination from desorption data is evaluated. Then, the integration of the Korteweg liquid stress field around each cement hydrate particle provided the capillary forces at the nanoscale. The cement mesoscale structure was relaxed under the action of the capillary forces. Local irreversible deformations of the cement nano-grains assembly were identified due to liquid-solid interactions. The spatial correlations of the nonaffine displacements extend to a few tens of nm. Finally, the Love-Weber method provided the homogenized liquid stress at the micronscale. The homogenization length coincided with the spatial correlation length nonaffine displacements. Our results on the solid response to capillary stress field suggest that the micronscale texture is not affected by mild drying, while local irreversible deformations still occur. These results pave the way towards understanding capillary phenomena induced stresses in heterogeneous porous media ranging from construction materials, hydrogels to living systems.Comment: 6 figures in main text, 4 figures in the SI appendi

Weyl Equation and (Non)-Commutative SU(n+1) BPS Monopoles

We apply the ADHMN construction to obtain the SU(n+1)(for generic values of n) spherically symmetric BPS monopoles with minimal symmetry breaking. In particular, the problem simplifies by solving the Weyl equation, leading to a set of coupled equations, whose solutions are expressed in terms of the Whittaker functions. Next, this construction is generalized for non-commutative SU(n+1) BPS monopoles, where the corresponding solutions are given in terms of the Heun B functions.Comment: 16 pages, Latex. Few typos corrected, version to appear in JHE

Monopoles from Rational Maps

The moduli space of charge k SU(2) BPS monopoles is diffeomorphic to the moduli space of degree k rational maps between Riemann spheres. In this note we describe a numerical algorithm to compute the monopole fields and energy density from the rational map. The results for some symmetric examples are presented.Comment: 8 pages, 2 figures. To appear in Phys. Lett.

Topological discrete kinks

A spatially discrete version of the general kink-bearing nonlinear Klein-Gordon model in (1+1) dimensions is constructed which preserves the topological lower bound on kink energy. It is proved that, provided the lattice spacing h is sufficiently small, there exist static kink solutions attaining this lower bound centred anywhere relative to the spatial lattice. Hence there is no Peierls-Nabarro barrier impeding the propagation of kinks in this discrete system. An upper bound on h is derived and given a physical interpretation in terms of the radiation of the system. The construction, which works most naturally when the nonlinear Klein-Gordon model has a squared polynomial interaction potential, is applied to a recently proposed continuum model of polymer twistons. Numerical simulations are presented which demonstrate that kink pinning is eliminated, and radiative kink deceleration greatly reduced in comparison with the conventional discrete system. So even on a very coarse lattice, kinks behave much as they do in the continuum. It is argued, therefore, that the construction provides a natural means of numerically simulating kink dynamics in nonlinear Klein-Gordon models of this type. The construction is compared with the inverse method of Flach, Zolotaryuk and Kladko. Using the latter method, alternative spatial discretizations of the twiston and sine-Gordon models are obtained which are also free of the Peierls-Nabarro barrier.Comment: 14 pages LaTeX, 7 postscript figure