Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement

We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with $\delta$-functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths are all calculated in terms of two parameters, namely the mass ratio: $m_{\text{L}}/m_{\text{H}}$, and ratio $g_{\text{HH}}/g_{\text{HL}}$ of the $\delta$-function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic process become energetically allowed. In the Tonks-Girardeau limit ($g_{\text{HH}}\rightarrow \infty$), our results are relevant to experiments involving trapped fermions with an impurity atom

A study of the factors affecting boundary layer two-dimensionality in wind tunnels

The effect of screens, honeycombs, and centrifugal blowers on the two-dimensionality of a boundary layer on the test section floors of low-speed blower tunnels is studied. Surveys of the spanwise variation in surface shear stress in three blower tunnels revealed that the main component responsible for altering the spanwise properties of the test section boundary layer was the last screen, thus confirming previous findings. It was further confirmed that a screen with varying open-area ratio, produced an unstable flow. However, contrary to popular belief, it was also found that for given incoming conditions and a screen free of imperfections, its open-area ratio alone was not enough to describe its performance. The effect of other geometric parameters such as the type of screen, honeycomb, and blower were investigated. In addition, the effect of the order of components in the settling chamber, and of wire Reynolds number were also studied

Three-Body Recombination in One Dimension

We study the three-body problem in one dimension for both zero and finite range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all combinations of the parity and exchange symmetries. For bosons, we provide a numerical demonstration of several universal features that appear in the three-body system, and discuss how certain universal features in three dimensions are different in one dimension. We show that the probability for inelastic processes vanishes as the range of the pair-wise interaction is taken to zero and demonstrate numerically that the recombination threshold law manifests itself for large scattering length.Comment: 15 pages 7 figures Submitted to Physical Review

Glassy dynamics in granular compaction

Two models are presented to study the influence of slow dynamics on granular compaction. It is found in both cases that high values of packing fraction are achieved only by the slow relaxation of cooperative structures. Ongoing work to study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter, proceedings of the Trieste workshop on 'Unifying concepts in glass physics

Minimizing Higgs Potentials via Numerical Polynomial Homotopy Continuation

The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like nonlinearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gr\"obner basis approach.Comment: 9 pages, 4 figure

The Energetic Costs of Cellular Computation

Cells often perform computations in response to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds (Landuer's Principle), it is expected that such computations require cells to consume energy. Here, we explicitly calculate the energetic costs of computing ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg-Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments such as the spore germination networks of bacteria.Comment: 9 Pages (including Appendix); 4 Figures; v3 corrects even more typo

Smoothing of sandpile surfaces after intermittent and continuous avalanches: three models in search of an experiment

We present and analyse in this paper three models of coupled continuum equations all united by a common theme: the intuitive notion that sandpile surfaces are left smoother by the propagation of avalanches across them. Two of these concern smoothing at the `bare' interface, appropriate to intermittent avalanche flow, while one of them models smoothing at the effective surface defined by a cloud of flowing grains across the `bare' interface, which is appropriate to the regime where avalanches flow continuously across the sandpile.Comment: 17 pages and 26 figures. Submitted to Physical Review