Morphology of rain water channelization in systematically varied model sandy soils

We visualize the formation of fingered flow in dry model sandy soils under different raining conditions using a quasi-2d experimental set-up, and systematically determine the impact of soil grain diameter and surface wetting property on water channelization phenomenon. The model sandy soils we use are random closely-packed glass beads with varied diameters and surface treatments. For hydrophilic sandy soils, our experiments show that rain water infiltrates into a shallow top layer of soil and creates a horizontal water wetting front that grows downward homogeneously until instabilities occur to form fingered flows. For hydrophobic sandy soils, in contrast, we observe that rain water ponds on the top of soil surface until the hydraulic pressure is strong enough to overcome the capillary repellency of soil and create narrow water channels that penetrate the soil packing. Varying the raindrop impinging speed has little influence on water channel formation. However, varying the rain rate causes significant changes in water infiltration depth, water channel width, and water channel separation. At a fixed raining condition, we combine the effects of grain diameter and surface hydrophobicity into a single parameter and determine its influence on water infiltration depth, water channel width, and water channel separation. We also demonstrate the efficiency of several soil water improvement methods that relate to rain water channelization phenomenon, including pre-wetting sandy soils at different level before rainfall, modifying soil surface flatness, and applying superabsorbent hydrogel particles as soil modifiers

Effective gluon interactions in the Colour Superconductive Phase of two flavor QCD

The gluon self-energies and dispersion laws in the color superconducting phase of QCD with two massless flavors are calculated using the effective theory near the Fermi surface. These quantities are calculated at zero temperature for all the eight gluons, those of the remaining SU(2) color group and those corresponding to the broken generators. The construction of the effective interaction is completed with the one loop calculation of the three- and four-point gluon interactions.Comment: LaTeX, p 17, 4 figures. Final version to be published in Phys. Lett. B. Several corrections have been done and some point clarifie

Effective Field Theory for the Crystalline Colour Superconductive Phase of QCD

We present an effective field theory for high density, low temperature QCD in the crystalline colour superconductive phase (LOFF phase). This interesting phase of QCD is characterized by a gap parameter with a crystalline pattern, breaking traslational and rotational invariance, and could have astrophysical applications. In the effective theory the fermions have a Majorana mass, which, besides colour, breaks translation and rotation symmetries. Fermions couple to the three phonons arising from the breaking of rotation and translation invariance. Integrating out the fermions leads eventually to an effective lagrangian in terms of the phonon fields only, which satisfies an anisotropic dispersion relation.Comment: Latex, 17 pages, Modifications in the effective goldstone boson descriptio

Numerical solution of the color superconductivity gap in a weak coupling constant

We present the numerical solution of the full gap equation in a weak coupling constant $g$. It is found that the standard approximations to derive the gap equation to the leading order of coupling constant are essential for a secure numerical evaluation of the logarithmic singularity with a small coupling constant. The approximate integral gap equation with a very small $g$ should be inverted to a soft integral equation to smooth the logarithmic singularity near the Fermi surface. The full gap equation is solved for a rather large coupling constant $g\ge 2.0$. The approximate and soft integral gap equations are solved for small $g$ values. When their solutions are extrapolated to larger $g$ values, they coincide the full gap equation solution near the Fermi surface. Furthermore, the analytical solution matches the numerical one up to the order one O(1). Our results confirm the previous estimates that the gap energy is of the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV. They also support the validity of leading approximations applied to the full gap equation to derive the soft integral gap equation and its analytical solution near the Fermi surface.Comment: 7 pages+ 6 figs, Stanford, Frankfurt and Bethlehe

Superconductivity from perturbative one-gluon exchange in high density quark matter

We study color superconductivity in QCD at asymptotically large chemical potential. In this limit, pairing is dominated by perturbative one-gluon exchange. We derive the Eliashberg equation for the pairing gap and solve this equation numerically. Taking into account both magnetic and electric gluon exchanges, we find $\Delta\sim g^{-5}\exp(-c/g)$ with $c=3\pi^2/\sqrt{2}$, verifying a recent result by Son. For chemical potentials that are of physical interest, $\mu< 1$ GeV, the calculation ceases to be reliable quantitatively, but our results suggest that the gap can be as large as 100 MeV.Comment: 19 pages, 6 figures. I accidentally replaced the paper with an outdated version. This version has typos corrected and will appear in PR

Quark description of nuclear matter

We discuss the role of an adjoint chiral condensate for color superconducting quark matter. Its presence leads to color-flavor locking in two-flavor quark matter. Color is broken completely as well as chiral symmetry in the two-flavor theory with coexisting adjoint quark-antiquark and antitriplet quark-quark condensates. The qualitative properties of this phase match the properties of ordinary nuclear matter without strange baryons. This complements earlier proposals by Schafer and Wilczek for a quark description of hadronic phases. We show for a class of models with effective four-fermion interactions that adjoint chiral and diquark condensates do not compete, in the sense that simultaneous condensation occurs for sufficiently strong interactions in the adjoint chiral channel.Comment: 15 pages, 3 figure

Dispersion Laws for In-medium Fermions and Gluons in the CFL Phase of QCD

We evaluate several quantities appearing in the effective lagrangian for the color-flavor locked phase of high density QCD using a formalism which exploits the approximate decoupling of fermions with energy negative with respect to the Fermi energy. The effective theory is essentially two-dimensional and exhibits a Fermi velocity superselection rule, similar to the one found in the Heavy Quark Effective Theory. Within the formalism we reproduce, using gradient expansion, the results for the effective parameters of the Nambu-Goldstone bosons. We also determine the dispersion laws for the gluons. By coupling the theory to fermions and integrating over the two-dimensional degrees of freedom we obtain the effective description of in-medium fermions.Comment: 17 pages, LaTex, 2 figures. Version published in Phys. Lett. B with an arithmetic misprint corrected in eq. (62) (and as a consequence in eqs. (63), (66) and (73)

Gapless Color Superconductivity

We present the dispersion relations for quasiparticle excitations about the color-flavor locked ground state of QCD at high baryon density. In the presence of condensates which pair light and strange quarks there need not be an energy gap in the quasiparticle spectrum. This raises the possibility of gapless color superconductivity, with a Meissner effect but no minimum excitation energy. Analysis within a toy model suggests that gapless color superconductivity may occur only as a metastable phase.Comment: 4 pages, Revtex, eps figures include