767 research outputs found
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
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