Theory of water and charged liquid bridges

The phenomena of liquid bridge formation due to an applied electric field is investigated. A new solution for the charged catenary is presented which allows to determine the static and dynamical stability conditions where charged liquid bridges are possible. The creeping height, the bridge radius and length as well as the shape of the bridge is calculated showing an asymmetric profile in agreement with observations. The flow profile is calculated from the Navier Stokes equation leading to a mean velocity which combines charge transport with neutral mass flow and which describes recent experiments on water bridges.Comment: 10 pages 12 figures, misprints corrected, assumptions more transparen

Parkes-CDSCC telemetry array: Equipment design

A unique combination of Deep Space Network (DSN) and non-DSN facilities in Australia provided enhanced data return from the Voyager spacecraft as it encountered the planet Uranus. Many of the key elements are duplicated from Voyager's encounters with Jupiter and Saturn. Some are unique extensions of that technology

Analytic Harmonic Approach to the N-body problem

We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, center position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N-body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions like density matrices can then be computed analytically. As a first application of our formalism, we consider the N-boson problem in two- and three dimensions where we fit the two-body interactions to agree with the well-known zero-range model for two particles in a harmonic trap. Subsequently, condensate fractions, spectra, radii, and eigenmodes are discussed as function of dimension, boson number N, and scattering length obtained in the zero-range model. We find that energies, radii, and condensate fraction increase with scattering length as well as boson number, while radii decrease with increasing boson number. Our formalism is completely general and can also be applied to fermions, Bose-Fermi mixtures, and to more exotic geometries.Comment: 30 pages, 12 figures, updated reference

On the Abundance of Circumbinary Planets

We present here the first observationally based determination of the rate of occurrence of circumbinary planets. This is derived from the publicly available Kepler data, using an automated search algorithm and debiasing process to produce occurrence rates implied by the seven systems already known. These rates depend critically on the planetary inclination distribution: if circumbinary planets are preferentially coplanar with their host binaries, as has been suggested, then the rate of occurrence of planets with $R_p>6R_\oplus$ orbiting with $P_p<300$\ d is $10.0 ^{+18}_{-6.5}$\% (95\% confidence limits), higher than but consistent with single star rates. If on the other hand the underlying planetary inclination distribution is isotropic, then this occurrence rate rises dramatically, to give a lower limit of 47\%. This implies that formation and subsequent dynamical evolution in circumbinary disks must either lead to largely coplanar planets, or proceed with significantly greater ease than in circumstellar disks. As a result of this investigation we also show that giant planets (${>}10R_\oplus$) are significantly less common in circumbinary orbits than their smaller siblings, and confirm that the proposed shortfall of circumbinary planets orbiting the shorter period binaries in the Kepler sample is a real effect.Comment: Accepted for publication in MNRAS (1st August 2014). 12 pages. Update to match final version, including clarifications and new figures. Results are unchange

Two-Dimensional Sigma-Hole Systems in Boron Layers: A First-Principles Study on Mg_{1-x}Na_xB_2 and Mg_{1-x}Al_xB_2

We study two-dimensional sigma-hole systems in boron layers by calculating the electronic structures of Mg_{1-x}Na_xB_2 and Mg_{1-x}Al_xB_2. In Mg_{1-x}Na_xB_2, it is found that the concentration of sigma holes is approximately described by (0.8 + 0.8 x) * 10^{22} cm^{-3} and the largest attainable concentration is about 1.6 * 10^{22} cm^{-3} in NaB_2. In Mg_{1-x}Al_xB_2, on the other hand, it is found that the concentration of sigma holes is approximately described by (0.8 - 1.4 x) * 10^{22} cm^{-3} and sigma holes are disappeared at x of about 0.6. These relations can be used for experimental studies on the sigma-hole systems in these materials.Comment: 5 pages, 5 figure

Bound States and Universality in Layers of Cold Polar Molecules

The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound state properties as a function of the interaction strength. The results clearly show that a least one bound state will always be present in the system. In addition, bound states at zero energy show universal behavior and extend to very large radii. These results suggest that non-trivial bound complexes of more than two particles are likely in the bilayer and in more complicated chain structures in multi-layer systems.Comment: 6 pages, 5 figures. Revised version to be publishe

Weakly bound states of polar molecules in bilayers

We investigate a system of two polarized molecules in a layered trap. The molecules reside in adjacent layers and interact purely via the dipole-dipole interaction. We determine the properties of the ground state of the system as a function of the dipole moment and polarization angle. A bound state is always present in the system and in the weak binding limit the bound state extends to a very large distance and shows universal behavior.Comment: Presented at the 21st European Conference on Few-Body Problems in Physics, Salamanca, Spain, 30 August - 3 September 201

Role of Boron p-Electrons and Holes in Superconducting MgB2, and other Diborides: A Fully-Relaxed, Full-Potential Electronic Structure Study

We present the results of fully-relaxed, full-potential electronic structure calculations for the new superconductor MgB2, and BeB2, NaB2, and AlB2, using density-functional-based methods. Our results described in terms of (i) density of states (DOS), (ii) band-structure, and (iii) the DOS and the charge density around the Fermi energy EF, clearly show the importance of B p-band for superconductivity. In particular, we show that around EF, the charge density in MgB2, BeB2 and NaB2 is planar and is associated with the B plane. For BeB2 and NaB2, our results indicate qualitative similarities but significant quantitative differences in their electronic structure due to different lattice constants a and c.Comment: 4 pages, 4 figures, Submitted to Phys Rev. Lett. on March 6, 2001; resubmission on April 2

Bound states of Dipolar Bosons in One-dimensional Systems

We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole-dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three, four, and five-body problems in two or more tubes. Our results indicate that in the weakly-coupled limit the inter-tube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom. This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known.Comment: 22 pages, 7 figures, revised versio

Algebraic Aspects of Abelian Sandpile Models

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G, and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of toppling matrix. We construct scalar functions, linear in height variables of the pile, that are invariant toppling at any site. These invariants provide convenient coordinates to label the recurrent configurations of the sandpile. For an L X L square lattice, we show that g = L. In this case, we observe that the system has nontrivial symmetries coming from the action of the cyclotomic Galois group of the (2L+2)th roots of unity which operates on the set of eigenvalues of the toppling matrix. These eigenvalues are algebraic integers, whose product is the order |G|. With the help of this Galois group, we obtain an explicit factorizaration of |G|. We also use it to define other simpler, though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3