Period doubling toward chaos in a driven magnetic macrospin

The Landau-Lifshitz-Gilbert equation is analyzed in the case of a configuration involving easy plane isotropy under the influence of a sinusoidally oscillating magnetic field and a demagnetizing field. Through the use of numerical techniques, chaotic behavior is found and analyzed. By reducing the system to a discrete map (numerically), bifurcation diagrams for the system are computed. The system is found to exhibit a period doubling cascade route to chaos, and it obeys certain convergence rules for chaotic transitions outlined by Feigenbaum. A connection is drawn between the route to chaos and the geometry of the system, and comparisons are made with similar systems. Within the chaotic regime, windows of arbitrarily large period are suspected to exist, and explicitly illustrated and discussed for a period three window.     

Experimental observation of four-photon entanglement from parametric down-conversion

We observe polarization entanglement between four photons produced from a single down-conversion source. The nonclassical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well suited for implementing advanced quantum communication schemes such as multiparty quantum key distribution, secret sharing, and telecloning.     

Twister quintessence scenario

We study generic solutions in a non-minimally coupled to gravity scalar field cosmology. It is shown that dynamics for both canonical and phantoms scalar fields with the potential can be reduced to the dynamical system from which the exact forms for an equation of the state parameter can be derived. We have found the stationary solutions of the system and discussed their stability. Within the large class of admissible solutions we have found a non-degenerate critical points and we pointed out multiple attractor type of trajectory travelling in neighborhood of three critical points at which we have the radiation dominating universe, the barotropic matter dominating state and finally the de Sitter attractor. We have demonstrated the stability of this trajectory which we call the twister solution. Discovered evolutional path is only realized if there exist the non-minimal coupling constant. We have found simple duality relations between twister solutions in phantom and canonical scalar fields in the radiation domination phase. For the twister trajectory we have found an oscillating regime of approaching the de Sitter attractor.     

New approach to solution of photorefractive transport equations

In our work we propose a novel method of analysis of photorefractive transport equations. The method based on a perturbative approach can be used in the case of two wave mixing and four wave mixing geometry, i.e. for the samples illuminated by interference patterns. Presented approach can be employed for a broad range of material and experimental parameters, particularly for arbitrary depth of light modulation pattern. The approximate analytical solution is compared with results of numerical calculations and a good agreement practically in every case was found. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Šwinoujście, Poland     

Effect of flow-rate on ethanol separation in membrane distillation process

The separation of diluted ethanol solutions and fermentation broths by membrane distillation was investigated. The influence of stream flow-rate on the ethanol flux was studied. An evaluation of the process conditions on the separation degree of ethanol was performed with the application of hydrophobic capillary membranes composed of polypropylene. By removing the alcohol via membrane distillation, it is possible to achieve a higher content of ethanol in the permeate than that in the broth. The enrichment coefficient amounted to 4–6.5, and decreased with an increase of the ethanol concentration in the broth. It was found that the flow-rate affects the value of the enrichment coefficient. A positive influence of carbon dioxide on the ethanol transport through the capillary membrane was observed. The evolution of CO₂ bubbles from the broth increases the stream turbulence, probably enhancing the alcohol concentration in the layer adjacent to the membrane surface.     

An Entry to the Optically Pure β-Lactam Skeleton Based on 1,3-Dipolar Cycloaddition of Nitrones to 4,6-Di-O-Acetyl-2,3-Dideoxy-D-Threo-Hex-2-Enono-1,5-Lactone

Abstract

Saturated lactone 8, easily available by 1,3-dipolar cycloaddition of nitrone 4 to unsaturated lactone 7 was transformed into the β-lactam 22having a polyol side chain at the C-3 position of the azetidinone ring. The same sequence of reactions, when applied to 9 and 10 failed to give the respective β-lactams owing to the removal of the nitrogen atoms from those molecules.     

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.