Marangoni propulsion is a form of locomotion wherein an asymmetric release of surfactant by a body located at the surface of a liquid leads to its directed motion. We present in this paper a mathematical model for Marangoni propulsion in the viscous
regime. We consider the case of a thin rigid circular disk placed at the surface of a viscous fluid and whose perimeter has a prescribed concentration of an insoluble surfactant, to which the rest of its surface is impenetrable. Assuming a linearized equation of state between surface tension and surfactant concentration, we derive analytically the surfactant, velocity and pressure fields in the asymptotic limit of low Capillary, Peclet and Reynolds numbers. We then exploit these results to calculate the Marangoni propulsion speed of the disk. Neglecting the stress contribution from Marangoni flows is seen to over-predict the propulsion speed by 50%.
We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stoch
astic projected Gross-Pitaevskii theory to provide the first quantitative description of the full momentum distribution measurements of Van Amerongen et al., Phys. Rev. Lett. 100, 090402 (2008). We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry.
The classical-field formalism has been widely applied in the calculation of normal correlation functions, and the characterization of condensation, in finite-temperature Bose gases. Here we discuss the extension of this method to the calculation of m
ore general correlations, including the so-called anomalous correlations of the field, without recourse to symmetry-breaking assumptions. Our method is based on the introduction of U(1)-symmetric classical-field variables analogous to the modified quantum ladder operators of number-conserving approaches to the degenerate Bose gas, and allows us to rigorously quantify the anomalous and non-Gaussian character of the field fluctuations. We compare our results for anomalous correlation functions with the predictions of mean-field theories, and demonstrate that the nonlinear classical-field dynamics incorporate a full description of many-body processes which modify the effective mean-field potentials experienced by condensate and noncondensate atoms. We discuss the role of these processes in shaping the condensate mode, and thereby demonstrate the consistency of the Penrose-Onsager definition of the condensate orbital in the classical-field equilibrium. We consider the contribution of various noncondensate-field correlations to the overall suppression of density fluctuations and interactions in the field, and demonstrate the distinct roles of phase and density fluctuations in the transition of the field to the normal phase.
A fluid droplet located on a super-hydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction,
and super-hydrophobic surfaces display strong drag-reduction in the laminar regime. Here we consider theoretically a super-hydrophobic surface composed of circular posts (so called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially-dependent strength, we derive the effective surface slip length for a planar shear flow on such a fakir surface as the solution to an infinite series of linear equations. In the asymptotic limit of small surface coverage by the posts, the series can be interpreted as Riemann sums, and the slip length can be obtained analytically. For posts on a square lattice, our analytical results are in excellent quantitative agreement with previous numerical computations.
Laminar flow over a bubble mattress is expected to experience a significant reduction in friction since the individual surfaces of the bubbles are shear-free. However, if the bubbles are sufficiently curved, their protrusion into the fluid and along
the flow direction can lead to an increase in friction as was recently demonstrated experimentally and computationally. We provide in this paper a simple model for this result. We consider a shear flow at low Reynolds number past a two-dimensional array of bubbles, and calculate analytically the effective slip length of the surface as function of the bubble geometry in the dilute limit. Our model is able to reproduce quantitatively the relationship between effective friction and bubble geometry obtained in numerical computations, and in particular: (a) The asymmetry in friction between convex and concave bubbles, and (b) the existence of a geometric transition from reduced to enhanced friction at a critical bubble protrusion angle.
We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form t
o the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develo
We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms,
including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.
We develop a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a {em rotating} dilute Bose gas. The theory is used to model the dynamical and equilibrium properties of a rapidly rotating Bose gas quenched thro
ugh the critical point for condensation, as in the experiment of Haljan et al. [Phys. Rev. Lett., 87, 21043 (2001)]. In contrast to stirring a vortex-free condensate, where topological constraints require that vortices enter from the edge of the condensate, we find that phase defects in the initial non-condensed cloud are trapped en masse in the emerging condensate. Bose-stimulated condensate growth proceeds into a disordered vortex configuration. At sufficiently low temperature the vortices then order into a regular Abrikosov lattice in thermal equilibrium with the rotating cloud. We calculate the effect of thermal fluctuations on vortex ordering in the final gas at different temperatures, and find that the BEC transition is accompanied by lattice melting associated with diminishing long range correlations between vortices across the system.
We investigate the harmonically trapped interacting Bose gas in a quasi-2D geometry using the classical field method. The system exhibits quasi-long-range order and non-classical rotational inertia at temperatures below the Berezinskii-Kosterlitz-Tho
uless cross-over to the superfluid state. In particular, we compute the scissors-mode oscillation frequencies and find that the irrotational mode changes its frequency as the temperature is sweeped across the cross-over thus providing microscopic evidence for the emergence of superfluidity.
We develop a pairing mean-field theory to describe the quantum dynamics of the dissociation of molecular Bose-Einstein condensates into their constituent bosonic or fermionic atoms. We apply the theory to one, two, and three-dimensional geometries an
d analyze the role of dimensionality on the atom production rate as a function of the dissociation energy. As well as determining the populations and coherences of the atoms, we calculate the correlations that exist between atoms of opposite momenta, including the column density correlations in 3D systems. We compare the results with those of the undepleted molecular field approximation and argue that the latter is most reliable in fermionic systems and in lower dimensions. In the bosonic case we compare the pairing mean-field results with exact calculations using the positive-$P$ stochastic method and estimate the range of validity of the pairing mean-field theory. Comparisons with similar first-principle simulations in the fermionic case are currently not available, however, we argue that the range of validity of the present approach should be broader for fermions than for bosons in the regime where Pauli blocking prevents complete depletion of the molecular condensate.
