Route to Lambda in conformally coupled phantom cosmology

In this Letter we investigate acceleration in the flat cosmological model with a conformally coupled phantom field and we show that acceleration is its generic feature. We reduce the dynamics of the model to a 3-dimensional dynamical system and analyze it on a invariant 2-dimensional submanifold. Then the concordance FRW model with the cosmological constant Λ   is a global attractor situated on a 2-dimensional invariant space. We also study the behaviour near this attractor, which can be approximated by the dynamics of the linearized part of the system. We demonstrate that trajectories of the conformally coupled phantom scalar field with a simple quadratic potential crosses the cosmological constant barrier infinitely many times in the phase space. The universal behaviour of the scalar field and its potential is also calculated. We conclude that the phantom scalar field conformally coupled to gravity gives a natural dynamical mechanism of concentration of the equation of state coefficient around the magical value weff=−1$w_{\mathrm{eff}}=-1$. We demonstrate route to Lambda through the infinite times crossing the weff=−1$w_{\mathrm{eff}}=-1$ phantom divide.     

Asymmetric deformation of bubble shape: cause or effect of vortex-shedding?

Two perpendicular projections of rising bubbles were observed in counter-current downstream diverging flow. Evidently, the bubbles did not enter the boundary layer at the channel wall and a plug liquid flow assumption was acceptable in our experimental equipment. This confirmed that the experiment was appropriate for simulation of bubble rises in a quiescent liquid column. Recent data obtained by a high-speed camera permitted recording over a period of 60 s. Image analysis by a tailor-made program provided a time-series of quantities related to the position, size, and shape of bubbles. In addition to determination of the aspect ratio of the equivalent oblate ellipsoid, deviation from this shape was investigated in respect of the difference between the bubble’s centre of mass and the geometrical centre of bubble projection. Autocorrelation of the data indicated that the bubble inclination oscillated harmonically with a frequency of 5–10 Hz; cross correlation showed that the horizontal shift of the centre of mass, as well as the horizontal velocity, increased with increasing bubble inclination, and the vertical shift of the centre of mass increased with an increases in the absolute value of the bubble inclination. There is no significant phase shift in the oscillation of these quantities. The bulky bottom side of the bubbles is in accordance with the model of bubble oscillation induced by instability of the equilibrium of gravity and surface tension forces. The oscillation frequency dependence on surface forces (Eötvös number) is evident, while viscosity does not play a significant role in low-viscosity liquids. Therefore, vortex-shedding is more likely to be an effect of the oscillation and not its cause.     

X-Ray and 31P CP MAS NMR studies of bis(dialkoxythiophosphoryl) disulfides

The crystal and molecular structures of the title compounds were determined by X-ray diffraction technique from diffractometer intensity measurements. It has been found that two homologous disulfides, bis(dimethoxythiophosphoryl) disulfide 1 and bis(dineopentoxythiophosphoryl) disulfide 2 , form different molecular and crystal structures with space groups C2/c and P&1macr;, respectively. These results were confirmed by ³¹P CP MAS NMR studies, which showed that under favorable conditions the solid state NMR may lead to determination of the number of crystallographically unique phosphorus atoms. Moreover, the variation of the disulfide S–S bond length versus torsional P–S–S–P angles was observed.     

Nucleophilic Substitution at Heteroatoms—Identity Substitution Reactions at Phosphorus and Sulfur Centers: Do They Proceed in a Concerted (SN2) or Stepwise (A–E) Way?

The mechanisms of three selected identity substitution reactions at phosphorus and sulfur occurring with stereospecific inversion have been investigated using density functional theory (DFT). The first identity reaction between methoxyl anion and methyl ethylphenylphosphinate 1 reported in 1963 has been shown to proceed in a stepwise fashion according to the addition–elimination (A–E) mechanism involving formation of a pentacoordinate phosphorus intermediate (TBI-1). In contrast, the results of DFT studies of the identity chloride exchange reaction in (ethoxy)ethylphosphonochloridothionate 3 in acetone solution provided evidence that it proceeds synchronously according to the classical Ingold’s S_N2-P mechanism. DFT calculations of the methoxyl–methoxy exchange reaction at sulfur in methyl p-toluenesulfinate 4 catalyzed by trifluoroacetic acid in methanol revealed that it proceeds stepwise (A–E mechanism), involving the formation of the high-coordinate sulfurane intermediate. In both identity transesterification reactions, 1 and 4, the transiently formed trigonal bipyramidal intermediates with the two methoxyl groups occupying apical positions (TBI-1 and TBI-4) have higher free energy barriers for the Berry-type pseudorotation than those for direct decomposition to starting phosphinate and sulfinate ensuring stereospecific inversion of configuration at the phosphinyl and sulfinyl centers. Thus, the DFT method proved its usefulness in the distinction between both mechanisms that are often indistinguishable by kinetic measurements.     

Electric Double Layer in Water-Organic Mixed Solvents: Titania in 50% Ethylene Glycol

Ethylene glycol (EG) and its mixtures with water are popular components of nanofluids used as heat transfer fluids. The stability of nanofluids against coagulation is correlated with their zeta potential. The electrophoretic mobility of titania nanoparticles in 50-50 w/w EG was studied as a function of the concentration of various solutes. HCl, NaOH, SDS and CTMABr at concentrations up to 0.01 M are strong electrolytes in 50% EG, that is, the conductance of their solutions is proportional to the concentration. HCl, NaOH and CTMABr were very efficient in inducing a high zeta potential for titania in 50% EG. NaOH induced a negative zeta potential in excess of 70 mV, and HCl and CTMABr induced a positive zeta potential in excess of 70 mV at concentrations below 10⁻⁴ M. Apparently, HCl, NaOH and CTMABr are also more efficient than SDS in terms of nanofluid stabilization against coagulation. An overdose of base (>1 mM) results in depression of the negative zeta potential. This result may be due to the specific adsorption of sodium on titania from 50% EG.     

Tight multipartite Bell's inequalities involving many measurement settings

We derive tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are violated by some classes of states, for which all standard Bell's inequalities with two measurement settings per observer are satisfied.     

Remote Fluorination and Fluoroalkyl(thiol)ation Reactions

Remote functionalization reactions have the power to transform a C−H (or C−C) bond at a distant position from a functional group. This Review summarizes recent advances and key breakthroughs in remote fluorination, trifluoromethylation, difluoromethylation, trifluoromethylthiolation, and fluoroalkenylation reactions. Several powerful strategies have emerged to control the reactivity and distal selectivity such as the undirected radical approach, the 1,5-hydrogen atom transfer, the metal migration, the use of distant directing groups, and the ring-opening reactions. These unconventional and predictable C−H (and C−C) functionalization transformations should allow for the preparation of a wide range of otherwise-difficult-to-access alkyl, aromatic, heteroaromatic, and structurally complex fluorides.     

Mobility and non-separability

A mobility phenomenon is typical for a large class of non-linear evolutions. It is shown that the mobility can be responsible for a malignant form of quantum mechanical non separability of two correlated systems. An explicit example based on Weinberg's non linear quantum mechanics is considered. We show that in such a theory a transfer of information without a transfer of energy is possible and discuss physical roots of this phenomenon. In Polchinski's approach this effect is not present.1 Permanent address: Laboratory of Dielectrics and Organic Semiconductors, Technical University of Gdask, Gdask, Poland.     

Heteroclinic solutions for a class of the second order Hamiltonian systems

We shall be concerned with the existence of heteroclinic orbits for the second order Hamiltonian system , where q∈Rn and V∈C¹(R×Rn,R), V?0. We will assume that V and a certain subset M⊂Rn satisfy the following conditions. M is a set of isolated points and #M?2. For every sufficiently small ε>0 there exists δ>0 such that for all (t,z)∈R×Rn, if d(z,M)?ε then −V(t,z)?δ. The integrals , z∈M, are equi-bounded and −V(t,z)→∞, as |t|→∞, uniformly on compact subsets of Rn?M. Our result states that each point in M is joined to another point in M by a solution of our system.