Collective Tunnelling of Strongly Interacting Cold Atoms in a Double-Well Potential

It is known that under resonance conditions, a group of strongly interacting bosonic atoms, trapped in a double-well potential, mimics a single particle, performing Rabi oscillations between the wells. By implication, all atoms need to tunnel at roughly the same time, even though the Bose–Hubbard Hamiltonian accounts only for one-atom-at-a-time transfers. The mechanism of this collective behavior is analyzed, the Rabi frequencies in the process are evaluated, and the limitation of this simple picture is discussed. In particular, it is shown that the small rapid oscillations superimposed on the slow Rabi cycle result from splitting the transferred cluster at the sudden onset of tunnelling, and disappear if tunnelling is turned on gradually.     

A characterization of projective-planar signed graphs

A signed graph has a plus or minus sign on each edge. A simple cycle is positive or negative depending on whether it contains an even or odd number of negative edges, respectively. We consider embeddings of a signed graph in the projective plane for which a simple cycle is essential if and only if it is negative. We characterize those signed graphs that have such a projective-planar embedding. Our characterization is in terms of a related signed graph formed by considering the theta subgraphs in the given graph.     

Stable nonequilibrium probability densities and phase transitions for meanfield models in the thermodynamic limit

A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered.     

Approximation in weighted Hardy spaces

This paper is concerned with several approximation problems in the weighted Hardy spacesH ^p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH ^p(Ω) coincides, moduloH ^p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan sets forH ^p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH ^p(D), 1 ⪯p < ∞. Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday.     

The first ruthenium-alkyne-dihydride reported is now recognized as an intermediate in the homogeneous hydrogenation of diphenylacetylene: Crystal structure of (μ-H)2Ru3(CO)9(μ3-η2-∥-C2Ph2)

The title complex (complex1) was the first alkyne-substituted triruthenium dihydrido cluster to be reported and was characterized by spectroscopy as a triangular cluster with the alkyne parallel to a Ru-Ru edge. Recently, we have found that1 is a key intermediate in the homogeneous hydrogenation of diphenylacetylene catalyzed by tetrahedral Ru₄ and FeRu₃ clusters. Since the discovery of1, a great number of complexes with alkynes parallel to a cluster edge have been reported; at present this is the more common bonding mode for alkynes on trinuclear clusters. The structural features of1 allow a comparison with those of other ruthenium-containing derivatives and help to draw suggestions of the role of1 in hydrogenation catalysis.     

Maximal Cluster Sets of L-Analytic Functions Along Arbitrary Curves

Let Ώ be a domain in the N-dimensional real space, let L be an elliptic differential operator, and let (T_n) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ώ. This paper establishes the existence of a dense linear manifold of L-analytic functions all of whose nonzero members have maximal cluster sets under the action of every T_n along any curve ending at the boundary of Ώ such that its closure does not contain any component of the boundary. The above class contains all partial differentiation operators ∂^α, hence the statement extends earlier results due to Boivin, Gauthier, and Paramonov, and due to the first, third, and fourth authors.     

Mercury removal from aqueous solution and flue gas by adsorption on activated carbon fibres

The use of two activated carbon fibres, one laboratorial sample prepared from a commercial acrylic textile fibre and one commercial sample of Kynol^®, as prepared/received and modified by reaction with powdered sulfur and H₂S gas in order to increase the sulfur content were studied for the removal of mercury from aqueous solution and from flue gases from a fluidized bed combustor. The sulfur introduced ranged from 1 to 6 wt.% depending on the method used. The most important parameter for the mercury uptake is the type of sulfur introduced rather than the total amount and it was found that the H₂S treatment of ACF leads to samples with the highest mercury uptake, despite the lower sulfur amount introduced. The modified samples by both methods can remove HgCl₂ from aqueous solutions at pH 6 within the range 290-710 mg/g (ACF) which can be favourably compared with other studies already published. The use of a filter made with an activated carbon fibre modified by powdered sulfur totally removed the mercury species present in the flue gases produced by combustion of fossil fuel.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

Thermal behavior of the maleic anhydride modified poly(3-hydroxybutyrate)

Poly(3-hydroxybutyrate), PHB has been structurally modified through reaction with maleic anhydride, MA. Transesterification reaction was carried out fixing the PHB and MA and besides time and temperature the concentration of the triethylamine (used as catalyst) was changed. Glass transition, melting and crystallization temperature obtained from DSC curves and thermal degradation temperatures obtained from TG traces were used to evaluate the influence of the reaction conditions on the modification of PHB according to factorial design. On the base of the results the optimum conditions are to perform the PHB modification reaction with MA reaction at 110°C for 1 h with 5% v/v triethylamine.