Decay of a superfluid current of ultra-cold atoms in a toroidal trap

Using a numerical implementation of the truncated Wigner approximation, we simulate the experiment reported by Ramanathan et al. in Phys. Rev. Lett. 106, 130401 (2011), in which a Bose-Einstein condensate is created in a toroidal trap and set into rotation via a phase imprinting technique. A potential barrier is then placed in the trap to study the decay of the superflow. We find that the current decays via thermally activated phase slips, which can also be visualized as vortices crossing the barrier region in the radial direction. Adopting the notion of critical velocity used in the experiment, we determine it to be lower than the local speed of sound at the barrier, in contradiction to the predictions of the zero-temperature Gross-Pitaevskii equation. We map out the superfluid decay rate and critical velocity as a function of temperature and observe a strong dependence. Thermal fluctuations offer a partial explanation of the experimentally observed reduction of the critical velocity from the phonon velocity.Comment: 15 pages. 11 figure

Creating a supersolid in one-dimensional Bose mixtures

We identify a one-dimensional supersolid phase in a binary mixture of near-hardcore bosons with weak, local inter-species repulsion. We find realistic conditions under which such a phase, defined here as the coexistence of quasi-superfluidity and quasi-charge density wave order, can be produced and observed in finite ultra-cold atom systems in a harmonic trap. Our analysis is based on Luttinger liquid theory supported with numerical calculations using the time-evolving block decimation method. Clear experimental signatures of these two orders can be found, respectively, in time-of-flight interference patterns, and the structure factor S(k) derived from density correlations.Comment: 4 pages, 5 figures, changed Fig. 4, and minor edit

Mixing-Demixing transition in 1D boson-fermion mixture at low fermion densities

We numerically investigated the mixing-demixing transition of the boson-fermion mixture on a 1D lattice at an incommensurate filling with the fermion density being kept below the boson density. The phase diagram we obtained suggested that the decrease of the number of the fermions drove the system into the demixing phase

Critical velocity for a toroidal Bose-Einstein condensate flowing through a barrier

We consider the setup employed in a recent experiment (Ramanathan et al 2011 Phys. Rev. Lett. 106 130401) devoted to the study of the instability of the superfluid flow of a toroidal Bose-Einstein condensate in presence of a repulsive optical barrier. Using the Gross-Pitaevskii mean-field equation, we observe, consistently with what we found in Piazza et al (2009 Phys. Rev. A 80 021601), that the superflow with one unit of angular momentum becomes unstable at a critical strength of the barrier, and decays through the mechanism of phase slippage performed by pairs of vortex-antivortex lines annihilating. While this picture qualitatively agrees with the experimental findings, the measured critical barrier height is not very well reproduced by the Gross-Pitaevskii equation, indicating that thermal fluctuations can play an important role (Mathey et al 2012 arXiv:1207.0501). As an alternative explanation of the discrepancy, we consider the effect of the finite resolution of the imaging system. At the critical point, the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, $v_{\rm barr}=c_{\rm l}$. In particular, in the hydrodynamic regime (not reached in the above experiment), the critical point is determined by applying the Landau criterion inside the barrier region. On the other hand, the Feynman critical velocity $v_{\rm f}$ is much lower than the observed critical velocity. We argue that this is a general feature of the Gross-Pitaevskii equation, where we have $v_{\rm f}=\epsilon\ c_{\rm l}$ with $\epsilon$ being a small parameter of the model. Given these observations, the question still remains open about the nature of the superfluid instability.Comment: Extended versio

Generating phosphinidene - N-methylimidazole adducts under mild conditions

The nucleophilic attack of N-methylimidazole at the bridge phosphorus of a 7-phosphanorbornadiene pentacarbonylmolybdenum complex induces the collapse of the bridge. According to DFT calculations, the resulting zwitterion displays a very long and weak P - Mo bond. The excess of, N-methylimidazole thus appears to be able to displace the phosphinidene from its molybdenum complex. The final result is a phosphinidene- N-methylimidazole adduct whose structure has also been computed. When applied to the phenyl derivative at 40°C in toluene, this reaction effectively generates the [PhP] adduct, which decomposes to give essentially Ph 4P 4 and Ph 5P 5. At 80°C, PhPH 2 is also produced. In the presence of CCl 4 the phosphinidene adduct inserts into the C-Cl bond to give PhP(Cl)CCl 3. © 2006 American Chemical Society

Mathematical formulation of a dynamical system with dry friction subjected to external forces

We consider the response of a one-dimensional system with friction. S.W. Shaw (Journal of Sound and Vibration, 1986) introduced the set up of different coefficients for the static and dynamic phases (also called stick and slip phases). He constructs a step by step solution, corresponding to an harmonic forcing. In this paper, we show that the theory of variational inequalities provides an elegant and synthetic approach to obtain the existence and uniqueness of the solution, avoiding the step by step construction. We then apply the theory to a real structure with real data and show that the model is quite accurate. In our case, the forcing motion comes from dilatation, due to temperature

Optimization of 3D Cooling Channels in Injection Molding using DRBEM and Model Reduction

Issu de : ESAFORM 2009 - 12th ESAFORM Conference on material forming, Enschede, THE NETHERLANDS, 27-29 April 2009International audienceToday, around 30% of manufactured plastic goods rely on injection moulding. The cooling time can represent more than 70% of the injection cycle. In this process, heat transfer during the cooling step has a great influence both on the quality of the final parts that are produced, and on the moulding cycle time. In the numerical solution of three-dimensional boundary value problems, the matrix size can be so large that it is beyond a computer capacity to solve it. To overcome this difficulty, we develop an iterative dual reciprocity boundary element method (DRBEM) to solve Poisson’s equation without the need of assembling a matrix. This yields a reduction of the computational space dimension from 3D to 2D, avoiding full 3D remeshing. Only the surface of the cooling channels needs to be remeshed at each evaluation required by the optimisation algorithm. For more efficiency, DRBEM computing results are extracted stored and exploited in order to construct a model with very few degrees of freedom. This approach is based on a model reduction technique known as proper orthogonal (POD) or Karhunen-Loève decompositions. We introduce in this paper a practical methodology to optimise both the position and the shape of the cooling channels in 3D injection moulding processes. First, we propose an implementation of the model reduction in the 3D transient BEM solver. This reduction permits to reduce considerably the computing time required by each direct computation. Secondly, we present an optimisation methodology applied to different injection cooling problems. For example, we can minimize the maximal temperature on the cavity surface subject to a temperature uniformityconstraint. Thirdly, we compare our results obtained by our approach with experimental results to show that our optimisation methodology is viable

Bose-Fermi mixtures in 1D optical superlattices

The zero temperature phase diagram of binary boson-fermion mixtures in two-colour superlattices is investigated. The eigenvalue problem associated with the Bose-Fermi-Hubbard Hamiltonian is solved using an exact numerical diagonalization technique, supplemented by an adaptive basis truncation scheme. The physically motivated basis truncation allows to access larger systems in a fully controlled and very flexible framework. Several experimentally relevant observables, such as the matter-wave interference pattern and the condensatefraction, are investigated in order to explore the rich phase diagram. At symmetric half filling a phase similar to the Mott-insulating phase in a commensurate purely bosonic system is identified and an analogy to recent experiments is pointed out. Furthermore a phase of complete localization of the bosonic species generated by the repulsive boson-fermion interaction is identified. These localized condensates are of a different nature than the genuine Bose-Einstein condensates in optical lattices.Comment: 18 pages, 9 figure

Reaction of terminal phosphinidene complexes with acetylenic alcohols: Intramolecular hydrophosphination of a phosphirene ring

The transient phosphinidene complex [PhP-Mo(CO) 5], as generated from the appropriate 7-phosphanorbornadiene complex at 110°C in toluene, selectively reacts with the C=≡C triple bond of 4-phenyl-3-butyn-1-ol to give the corresponding phosphirene complex 4. Upon further heating, this phosphirene evolves via two pathways. The minor pathway involves the formal addition of the OH bond of the alcohol function onto the phosphirene P-C ring bond to give the 3-benzylidene-1,2-oxaphospholane complex 5. The major pathway involves the reaction of a second molecule of [PhP-Mo(CO) 5] with the OH group of 4, giving an intermediate phosphirene with an additional secondary alkoxyphosphine functionality (7). An intramolecular hydrophosphination of one P-C bond of the phosphirene ring then immediately takes place to give the cis-1,2-bis(phosphino)ethene [MoCCO) 4] complex 8 as a mixture of two diastereomers. After methylation of the PH group of 8, decomplexation can be efficiently achieved by reaction with sulfur. Structures have been ascertained by X-ray analysis for 5, 8, and the disulfide 10