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We study the application of a square perturbing lattice to the naturally forming hexagonal arrays of dipolar droplets in a dipolar Bose-Einstein condensate. We find that the application of the lattice causes spontaneous pattern formation and leads to frustration in some regimes. For certain parameters, the ground state has neither the symmetry of the intrinsic hexagonal supersolid nor the symmetry of the square lattice. These results may give another axis on which to explore dipolar Bose-Einstein condensates and to probe the nature of supersolidity.

A finite element analysis is used to study the elastic-plastic contact of a coated sphere compressed by a rigid flat under the stick contact condition. This was done for a wide range of hard coating material properties and coating thicknesses. A comparison with the slip contact condition is presented in terms of the critical contact parameters (at yield inception) and plasticity evolution. Empirical expressions are provided for critical interferences of the first and second yield inceptions, in the coating and on the substrate side of the interface, respectively. An expression is also provided for the dimensionless coating thickness for optimal resistance to plasticity under the stick contact condition. Additionally, the relations between different contact parameters in the elastic-plastic regime are presented. In general, it was found that the contact condition has a negligible effect on the contact parameters, except for phenomena occurring close to the contact area.

We describe the 2dF Galaxy Redshift Survey (2dFGRS), and the current status of the observations. In this exploratory paper, we apply a Principal Component Analysis to a preliminary sample of 5869 galaxy spectra and use the two most significant components to split the sample into five spectral classes. These classes are defined by considering visual classifications of a subset of the 2dF spectra, and also by comparing to high quality spectra of local galaxies. We calculate a luminosity function for each of the different classes and find that later-type galaxies have a fainter characteristic magnitude, and a steeper faint-end slope. For the whole sample we find M*=-19.7 (for Omega=1, H_0=100 km/sec/Mpc), alpha=-1.3, phi*=0.017. For class 1 (`early-type') we find M*=-19.6, alpha=-0.7, while for class 5 (`late-type') we find M*=-19.0, alpha=-1.7. The derived 2dF luminosity functions agree well with other recent luminosity function estimates., Comment: 15 pages, 14 ps and eps figures, Latex, MNRAS, accepted

We emphasize that the macroscopic collapse of a dipolar Bose-Einstein condensate in a pancake-shaped trap occurs through local density fluctuations, rather than through a global collapse to the trap center. This hypothesis is supported by a recent experiment in a chromium condensate., Proceedings of 17th International Laser Physics Workshop

We study the BCS superfluid transition in a single-component fermionic gas of dipolar particles loaded in a tight bilayer trap, with the electric dipole moments polarized perpendicular to the layers. Based on the detailed analysis of the interlayer scattering, we calculate the critical temperature of the interlayer superfluid pairing transition when the layer separation is both smaller (dilute regime) and of the order or larger (dense regime) than the mean interparticle separation in each layer. Our calculations go beyond the standard BCS approach and include the many-body contributions resulting in the mass renormalization, as well as additional contributions to the pairing interaction. We find that the many-body effects have a pronounced effect on the critical temperature, and can either decrease (in the very dilute limit) or increase (in the dense and moderately dilute limits) the transition temperature as compared to the BCS approach., 23 pages, 10 figures, final approval from S. Ronen was not received due to his no-response

We study the propagation of sound in a homogeneous dipolar gas at zero temperature, known as zero sound. We find that undamped sound propagation is possible only in a range of solid angles around the direction of polarization of the dipoles. Above a critical dipole moment, we find an unstable mode, by which the gas collapses locally perpendicular to the dipoles' direction., Comment: Significant changes due to newly found instability

We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we calculate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum, is tunable as a function of particle number, we thereby propose an experiment that can simultaneously measure the Landau critical velocity of a dipolar BEC and demonstrate the presence of the roton in this system., 5 pages, 4 figures, version accepted to PRL

We explore the structure and dynamics of dipolar Bose-Einstein condensates (DBECs) near their threshold for instability. Near this threshold a DBEC may exhibit nontrivial, biconcave density distributions, which are associated with instability against collapse into "angular roton" modes. Here we discuss experimental signatures of these novel features. In the first, we infer local collapse of the DBEC from the experimental stability diagram. In the second, we explore the dynamics of collapse and find that a nontrivial angular distribution is a signature of the DBEC possessing a biconcave structure., 9, 6 figure, version accepted to PRA

We study the stability of singly- and doubly-quantized vortex states of harmonically trapped dipolar Bose-Einstein Condensates (BECs) by calculating the low-lying excitations of these condensates. We map the dynamical stability of these vortices as functions of the dipole-dipole interaction strength and trap geometry by finding where their excitations have purely real energy eigenvalues. In contrast to BECs with purely contact interactions, we find that dipolar BECs in singly-quantized vortex states go unstable to modes with an increasing number of angular and radial nodes for more oblate trap aspect ratios, corresponding to \emph{local} collapse that occurs on a characteristic length scale. Additionally, we find that dipolar BECs in doubly-quantized vortex states are unstable to decay into a different topological state (with two singly-quantized vortices) for all interaction strengths when the trap geometry is sufficiently prolate to make the dipoles attractive, and in windows of interaction strength when the trap geometry is sufficiently oblate to make the dipoles repulsive., Comment: 8 pages, 4 figures, version accepted to PRA

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously-identified "roton-like" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously., 4 pages, 3 figures, version accepted to PRL

We simulate the growth of a dual species Bose-Einstein condensate using a Gross-Pitaevskii equation with an additional gain term giving rise to the growth. Such growth occurs during simultaneous evaporative cooling of a mixture of two gases. The ground state of a dual condensate is normally either a miscible mixture, or an immiscible phase with two spatially separated components. In a cigar trap the ground state typically consists of one component in the center, and the other component flanking it. Our simulations show that when the condensates are formed in a cigar trap and the mixture is phase separated, then the final state upon the end of the growth is generally far from the true ground state of the system. Instead it consists of multiple, interleaved bubbles of the two species. Such a pattern was observed recently in an experiment by Wieman's group at JILA [Papp, Pino, and Wieman, Phys. Rev. Lett. 101, 040402 (2008)], and our simulations are in good qualitative agreement with the experiment. We explain the pattern formation as due to the onset of modulation instability during growth, and study the dependence of the final state pattern on various parameters of the system.

We study a Bose-Einstein condensate (BEC) of a dilute gas with dipolar interactions, at finite temperature, using the Hartree-Fock-Bogoliubov (HFB) theory within the Popov approximation. An additional approximation involving the dipolar exchange interaction is made to facilitate the computation. We calculate the temperature dependence of the condensate fraction of a condensate confined in a cylindrically symmetric harmonic trap. We show that the bi-concave shaped condensates found in Ref. \cite{Ronen07} in certain pancake traps at zero temperature, are also stable at finite temperature. Surprisingly, the dip in the central density of these structured condensates is actually enhanced at low finite temperatures. We explain this effect., 9 figures

We study Bose-Einstein condensates with purely dipolar interactions in oblate (pancake) traps. We find that the condensate always becomes unstable to collapse when the number of particles is sufficiently large. We analyze the instability, and find that it is the trapped-gas analogue of the ``roton-maxon'' instability previously reported for a gas that is unconfined in two dimensions. In addition, we find that under certain circumstances, the condensate wave function attains a biconcave shape, with its maximum density away from the center of the gas. These biconcave condensates become unstable due to azimuthl excitation - an angular roton., 4 pages, 3 figures

We predict a new kind of instability in a Bose-Einstein condensate composed of dipolar particles. Namely, a comparatively weak dipole moment can produce a large, negative two-body scattering length that can collapse the Bose-Einstein condensate. To verify this effect, we validate mean-field solutions to this problem using exact, diffusion Monte Carlo methods. We show that the diffusion Monte Carlo energies are reproduced accurately within a mean-field framework if the variation of the s-wave scattering length with the dipole strength is accounted for properly.

We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment is essential to reproducing the correct energies and for predicting the stability of the condensate. We do this by comparing Gross-Pitaevskii calculations with diffusion Monte Carlo calculations. We find very good agreement between the results obtained by these two approaches once the dipole dependence of the scattering length is taken into account. We also examine the behavior of the condensate in non-isotropic traps.

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time-dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.

We analyse synthetic galaxy spectra from the evolutionary models of Bruzual&Charlot and Fioc&Rocca-Volmerange using the method of Principal Component Analysis (PCA). We explore synthetic spectra with different ages, star formation histories and metalicities, and identify the Principal Components (PCs) of variance in the spectra due to these different model parameters. The PCA provides a more objective and informative alternative to diagnostics by individual spectral lines. We discuss how the PCs can be used to estimate the input model parameters and explore the impact of noise in this inverse problem. We also discuss how changing the sampling of the ages and other model parameters affects the resulting PCs. Our first two synthetic PCs agree with a similar analysis on observed spectra obtained by Kennicutt and the 2dF redshift survey. We conclude that with a good enough signal-to-noise (S/N>> 10) it is possible to derive age, star formation history and metallicity from observed galaxy spectra using PCA., 11 pages, 17 figures, submitted to MNRAS