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.     

Influence of copper solute on the creep rate sensitivities of aluminium

The presence of copper atoms as continuous networks at the grain boundaries of an aluminium-copper alloy has been considered not preventing the moving of dislocations during creep (or at least partially). The dislocations can bs absorbed by these boundaries and penetrate through them. That leads to changés of shape and structure of grains and also to the sliding of grains against each other. This was deduced from the accelerating increase in the sensitivity of the steady state creep rate to the applied stress of an aluminium 2·8 wt% copper alloy examined at wide range of temperatures (50–350 °C) and applied stresses (7–170 MPa). This rapid increase in the sensitivity parameter of the steady state creep rate occurs in Al-Cu alloys at quite higher ranges of applied stresses and may be attributed mainly to the contribution of the grain boundary movements to the creep strain.     

On the approximation of convex functions by Bernstein-type operators

As a consequence of Jensen's inequality, centered operators of probabilistic type (also called Bernstein-type operators) approximate convex functions from above. Starting from this fact, we consider several pairs of classical operators and determine, in each case, which one is better to approximate convex functions. In almost all the discussed examples, the conclusion follows from a simple argument concerning composition of operators. However, when comparing Szász-Mirakyan operators with Bernstein operators over the positive semi-axis, the result is derived from the convex ordering of the involved probability distributions. Analogous results for non-centered operators are also considered.     

Biomagnetic measurements utilising a superparamagnetic marker: a feasibility study

Summary A preliminary study is here reported on a new potential marker for biomagnetic measurements. The marker consists of superparamagnetic polymer microspheres which were detected in the presence of external steady magnetic fields by means of an r.f.-SQUID magnetometer. The particles were prepared in samples differing in the concentration value and immersed in a homogeneous magnetic field of variable intensity. A simple model was taken into account for the distribution of the microspheres in the samples, so that the theoretical values were compared to the marker field values measured by the biomagnetic sensor. The overall sensitivity of the experimental apparatus and the minimum concentration value of the marker were then estimated.     

Effect of support on the synergy in HDS of thiophene and HDN of pyridine over Mo sulfide catalysts promoted by Rh

The effect of support (SiO₂-Al₂O₃, Al₂O₃,MgO) of the Rh-Mo(S) sulfide catalysts on the synergy in hydrodesulfurization (HDS) of thiophene and hydrodenitrogenation (HDN) of pyridine was studied. The synergy in HDS was between 7–10 regardless of the kind of support used. The synergy in HDN varied from none over the MgO supported sample to about 3 over SiO₂-Al₂O₃ supported catalyst, in accord with the positive effect of increasing support acidities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Thermal properties of some complexes of quinolinic acid with divalent metal ions

Studies of the complexes of pyridinecarboxylic acids with divalent metal ions as a function of the position of the carboxyl groups were extended. The thermal properties of the complexes of quinoline acid (pyridine-2,3-dicarboxylic acid) with several divalent metal ions were determined by thermogravimetry (TG) and differential thermal analysis (DTA). A correlation between these compounds and others obtained by reaction between the studied metal ions with similar acids (lutidinic acid (pyridine-2,4-dicarboxylic acid) and isocinchomeronic acid (pyridine-2,5-di-carboxylic acid) is discussed in terms of the position of the carboxyl group far from the aza group. The thermal stability of the metal complexes is in the order Mn(II) > Fe(II) > Zn(II) ? Co(II) > Ni(II) > Cu(II).     

Unexpected differences in the alpha-halogenation and related reactivity of sulfones with perhaloalkanes in KOH-t-BuOH

Most alkyl phenyl sulfones are readily alpha-chlorinated with CCl(4) and alpha-brominated with CBrCl3 in KOH-t-BuOH via radical-anion radical pair (RARP) reactions. While isopropyl mesityl sulfone (4) is easily alpha-chlorinated with CCl(4), it was completely recovered when treated with the more reactive CBrCl3. Subsequent investigations showed the latter result to be due to the poor acidity of 4 together with the rapid depletion of CBrCl3 and KOH by their reaction with each other, and led to a variety of other important results. 4-Hydroxyphenyl isopropyl sulfone (6) is unreactive with either CCl4 or CBrCl3 in KOH-t-BuOH, its phenoxide anion strongly reducing the electronegativity of the sulfonyl group, thereby inhibiting alpha-anion formation. This effect is reversed by the electron-withdrawing influence of two alpha-phenyls, so that benzhydryl 4-hydroxyphenyl sulfone (8) is readily alpha-halogenated in KOH-t-BuOH with CCl4 or CBrCl3. On further contact with KOH-t-BuOH the alpha-halogenated sulfones from 8 are decomposed into benzophenone and phenol. While the alpha-halogenated derivatives of 4-methoxyphenyl benzhydryl sulfone (9) are stable to base, they are decomposed even under mildly acidic conditions into 4-methoxyphenyl 4-methoxybenzenethiolsulfonate (9c), phenol, and benzophenone. Mono-alpha-halogenation of benzyl phenyl sulfone (10) enhances the rate of the subsequent halogenation, so that alpha,alpha-dihalogenation is attained while much substrate is still present and the mono-alpha-halogenated product is not detected. The ease of reductive debromination of alpha-bromo sulfones with Cl3C- was correlated with the stability of the formed alpha-anions, explaining the success with alpha-bromobenzylic sulfones but failure with alpha-bromoalkyl sulfones. In the presence of air and the absence of competing halogenation, formation of the alpha-anions of alkyl aryl sulfones is quickly accompanied by oxidative cleavage by atmospheric O2, leading to the formation of arenesulfonyl alcohols, arenesulfonyl halides, and haloarenes.     

Copper bronze catalyzed Heck reaction in ionic liquids

Heck reaction of aryl iodides and activated aryl bromides catalyzed by copper bronze in tetrabutylammonium bromide as solvent and tetrabutylammonium acetate as base was developed. The effective catalysts are Cu nanoparticles deriving from the reaction of iodobenzene with copper bronze. These nanoparticles are very stable in tetraalkylammonium salts, are easily recycled, and can be stored for months without a loss of catalytic efficiency. [reaction: see text]     

Determination of decabromodiphenyl ether in sediments using selective pressurized liquid extraction followed by GC–NCI-MS

A method based on selective pressurized liquid extraction (SPLE) followed by gas chromatography–negative ion chemical ionization-mass spectrometry (GC–NCI-MS) has been evaluated for analysis of decabromodiphenyl ether (PBDE-209) in sediment samples. Instrumental operating conditions such as source temperature and system pressure were optimized in the NCI-MS system, giving an instrumental detection limit of 2 pg. The limit of determination of the entire SPLE–GC–NCI-MS procedure was around 50 pg g^–1 dry weight (dw), with repeatability of replicates between 4 and 21% relative standard deviation. Application of the method to 13 different river and marine sediment samples collected in Spain revealed that levels of decabromodiphenyl ether ranged between 2 and 132 ng g^–1 dry weight.