The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. II. Droplet arrangement at the sharp interface level via the renormalized energy

This is the second in a series of papers in which we derive a $\Gamma$-expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small "droplets" of the minority phase in a "sea" of the majority phase. In our previous paper, we computed the $\Gamma$-limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order $\Gamma$-limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg-Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Without thus appealing to the Euler-Lagrange equation, we establish for all configurations which have "almost minimal energy" the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of $\Gamma$-equivalence, the obtained results also yield an expansion of the minimal energy for the original Ohta-Kawasaki energy. This leads to expecting to see triangular lattices of droplets as energy minimizers

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Selective excitation of homogeneous spectral lines

It is possible, for homogeneously broadened lines, to excite selectively the response signals, which are orders of magnitude narrower than the original lines. The new type of echo, which allows detecting such signals, and the formalism, useful for understanding the phenomenon, as well as the experimental examples from NMR spectroscopy are presented.Comment: 19 pages, 8 figure

Parallax measurements of cool brown dwarfs

Accurate parallax measurements allow us to determine physical properties of brown dwarfs, and help us to constrain evolutionary and atmospheric models, break the age-mass degeneracy and reveal unresolved binaries. We measured absolute trigonometric parallaxes and proper motions of 6 cool brown dwarfs using background galaxies to establish an absolute reference frame. We derive the absolute J-mag. The six T brown dwarfs in our sample have spectral types between T2.5 and T7.5 and magnitudes in J between 13.9 and 18.0, with photometric distances below 25 pc. The observations were taken in the J-band with the Omega-2000 camera on the 3.5 m telescope at Calar Alto, during a time period of 27 months, between March 2011 and June 2013. The number of epochs varied between 11 and 12 depending on the object. The reduction of the astrometric measurements was carried out with respect to the field stars. The relative parallax and proper motions were transformed into absolute measurements using the background galaxies in our fields. We obtained absolute parallaxes for our six brown dwarfs with a precision between 3 and 6 mas. We compared our results in a color-magnitude diagram with other brown dwarfs with determined parallax and with the BT-Settl 2012 atmospheric models. For four of the six targets we found a good agreement in luminosity with objects of similar spectral types. We obtained an improved accuracy in the parallaxes and proper motions in comparison to previous works. The object 2MASS J11061197+2754225 is more than 1 mag overluminous in all bands pointing to binarity or high order multiplicity.Comment: 9 pages, 15 figures. Astronomy & Astrophysics, 201

Open charm tomography of cold nuclear matter

We study the relative contribution of partonic sub-processes to D meson production and D meson-triggered inclusive di-hadrons to lowest order in perturbative QCD. While gluon fusion dominates the creation of large angle DD-bar pairs, charm on light parton scattering determines the yield of single inclusive D mesons. The distinctly different non-perturbative fragmentation of c quarks into D mesons versus the fragmentation of quarks and gluons into light hadrons results in a strong transverse momentum dependence of anticharm content of the away-side charm-triggered jet. In p+A reactions, we calculate and resum the coherent nuclear-enhanced power corrections from the final state partonic scattering in the medium. We find that single and double inclusive open charm production can be suppressed as much as the yield of neutral pions from dynamical high-twist shadowing. Effects of energy loss in p+A collisions are also investigated phenomenologically and may lead to significantly weaker transverse momentum dependence of the nuclear attenuation.Comment: 24 pages, 21 figure