Controlling statistical properties of a Cooper pair box interacting with a nanomechanical resonator

We investigate the quantum entropy, its power spectrum, and the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator, the first initially prepared in its excited state, the second prepared in a “Schrödinger-cat” state. The method employs the Jaynes–Cummings model with damping, with different decay rates of the Cooper pair box and different ranges of detuning, going from resonant to off-resonant cases, including time dependent detunings. Concerning the entropy, it is found that the time dependent detuning turns the entanglement more stable in comparison with previous results in the literature. With respect to the Cooper pair box excitation inversion, while the presence of detuning destroys the collapses and revivals, it is shown that convenient time dependent detunings recover such effects in a nice way.     

Classicalization times of parametrically amplified “Schrödinger cat” states coupled to phase-sensitive reservoirs

The exact Wigner function of a parametrically excited quantum oscillator in a phase-sensitive amplifying/attenuating reservoir is found for initial even/odd coherent states. Studying the evolution of negativity of the Wigner function we show the difference between the “initial positivization time” (IPT), which is inversely proportional to the square of the initial size of the superposition, and the “final positivization time” (FPT), which does not depend on this size. Both these times can be made arbitrarily long in maximally squeezed high-temperature reservoirs. Besides, we find the conditions when some (small) squeezing can exist even after the Wigner function becomes totally positive.     

A general method for convergent synthesis of functionalized exo-glycals based on halogenation and Suzuki cross-coupling of 1-exo-methylene sugars

Functionalized exo-glycals can be readily obtained by palladium catalyzed Suzuki cross-coupling of halo-exo-glycals with boronic acids.     

Physics of compaction of fine cohesive particles

Fluidized fractal clusters of fine particles display critical-like dynamics at the jamming transition, characterized by a power law relating consolidation stress with volume fraction increment [sigma--(c) proportional, variant(Deltaphi)(beta)]. At a critical stress clusters are disrupted and there is a crossover to a logarithmic law (Deltaphi = nu logsigma--(c)) resembling the phenomenology of soils. We measure lambda identical with- partial differentialDelta(1/phi)/ partial log(sigma--(c) proportional, variant Bo(0.2)(g), where Bo(g) is the ratio of interparticle attractive force (in the fluidlike regime) to particle weight. This law suggests that compaction is ruled by the internal packing structure of the jammed clusters at nearly zero consolidation.     

Stability analysis of a substructured model of the rotating beam

One of the most well-known situations in which nonlinear effects must be taken into account to obtain realistic results is the rotating beam problem. This problem has been extensively studied in the literature and has even become a benchmark problem for the validation of nonlinear formulations. Among other approaches, the substructuring technique was proven to be a valid strategy to account for this problem. Later, the similarities between the absolute nodal coordinate formulation and the substructuring technique were demonstrated. At the same time, it was found the existence of a critical angular velocity, beyond which the system becomes unstable that was dependent on the number of substructures. Since the dependence of the critical velocity was not so far clear, this paper tries to shed some light on it. Moreover, previous studies were focused on a constant angular velocity analysis where the effects of Coriolis forces were neglected. In this paper, the influence of the Coriolis force term is not neglected. The influence of the reference conditions of the element frame are also investigated in this paper.     

“Living” radical polymerization of styrene catalyzed by cyclometalated ruthenium(II) complexes bearing nonlabile ligands

Cationic substitutionally inert cyclometalated ruthenium (II) and osmium (II) complexes, ([Mt(o‐C₆H₄‐2‐py)(LL)₂]PF₆), where LL‐1,10‐phenanthroline (phen) or 2,2′‐bipyridine (bipy), were used for radical polymerization of styrene. Gradual modification of the complexes within the series allowed comparison of the catalytic activity and the redox properties. There was no correlation between the reducing powers of the complexes and their catalytic activities. The osmium compound of the lowest reduction potential was not active. All the ruthenium complexes catalyzed the polymerization of styrene in a controlled manner; but the level of control and the catalytic activity were different under the same polymerization conditions. [Ru(o‐C₆H₄‐2‐py)(phen)₂]PF₆ demonstrated the best catalytic performance though its redox potential was the highest. It catalyzed the “living” polymerization with a reasonable rate at a catalyst‐to‐initiator ratio of 0.1. 1 equiv. of Al(OiPr)₃ accelerated the polymerization and improved the control, but higher amount of Al(OiPr)₃ did not speed up the polymerization and moved the process into the uncontrollable regime. Under the most optimal conditions, the controlled polymerization occurs fast without any additive and the catalyst degradation. Added free ligands inhibited the polymerization suggesting that the catalytically active ruthenium intermediates are generated via the reversible dechelation of bidentate phen or bipy ligands. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3814–3828, 2009     

Viscoelasticity: Fractal parameters studied on mammalian erythrocytes under shear stress

In this work, experimental determinations are carried out using a home-made device called an erythrodeformeter, which has been developed and constructed for rheological measurements on red blood cells subjected to definite fluid shear stress. A numerical method formulated on the basis of the fractal approximation for ordinary and fractionary Brownian motion¹ is proposed to evaluate the viscoelastic behavior of mammalian erythrocyte membranes. The diffraction pattern, which is circular when the mammalian erythrocyte membranes are at rest, becomes elliptical when the cells undergo shear stress. Photometric readings of light intensity variation along the major axis of the elliptical diffraction pattern are recorded during the creep and recovery process. These data series are used to calculate, fractal rheological parameters of self-affine Brownian motion on the erythrocytes, averaged over several millions of cells. Three different parameters over the time dependent process could be obtained, which are: correlation coefficient <C(t)>, correlation integral, andK ₂-entropy, and very different results were obtained.     

Probing the nature of the contact between fine particles by using ultrasound propagation

The propagation velocity (vs) of an ultrasonic signal through a granular material depends on the type of interparticle contact. For noncohesive glass beads, a power law behavior for consolidation stresses applied (σc) above 1 MPa has been measured in previous work. This equation is compatible with Hertz's interaction law between elastic solids. In the present work, we have tested the propagation velocity of ultrasound signals through a sample of fine powder. The tensile strength and compactivity of the powder were previously measured by means of the Seville powder tester (SPT), indicating plastic deformation of the surface asperities in contact for small to moderate consolidation stresses. However, the measurements of ultrasound propagation at high consolidations presented here are compatible with Hertz's law. This finding suggests that for high consolidation stresses, surface asperities are flattened, and it is therefore the elastic deformation of the bulk of the particles that determines the transmission of ultrasonic pulses.     

Feedback control variables to restrain the Babesiosis disease

In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations.     

Local Isoperimetric Inequalities for Sectors on Surfaces and Cones

On surfaces we give conditions under which the solution of a restricted local isoperimetric problem for sectors with small solid angle is the circular sector and we characterize these surfaces. Also we study this problem for general spherical cones on hypersurfaces in higher dimensional Riemannian manifolds.