Nonparallel stability of the flow in an axially rotating pipe

The linear stability of the developing flow in an axially rotating pipe is analyzed using parabolized stability equations (PSE). The results are compared with those obtained from a near-parallel stability approximation that only takes into account the axial variation of the basic flow. Though the PSE results obviously coincide with the near-parallel ones far downstream, when the flow has reached a Hagen-Poiseuille axial velocity profile with superimposed solid-body rotation, they differ significantly in the developing region. Therefore, the onset of instability strongly depends on the axial evolution of the perturbations. The PSE results are also compared with experimental data from Imao et al. [Exp. Fluids 12 (1992) 277], showing a good agreement in the frequencies and wavelengths of the unstable disturbances, that take the form of spiral waves. Finally, a simple method for detecting one of the conditions to characterize the onset of absolute instability using PSE is given.     

Diffusion mechanism during the swelling hidroxy-methyl cellulose membrane formation

The conduction properties of HMC polymer gel prepared by the phase inversion method were investigated through the diffusion coefficient in order to confirm the conduction mechanism. The solution introduced in the polymer is stored in the pores and then penetrates into the polymer chains. For swelling the polymer network. A model describing the swelling hidroxy-methyl cellulose is presented. The model is used to predict the type liquid–liquid phase separation (instantaneous or delayed) that occurs when HMC-PVPD-Solvent-Water casting solutions are immersed in a gelation bath. The model includes the thermodynamic interactions parameters and the transport parameters. The predictions of the model agree with the experimental observations.     

Finiteness and Bifurcations of some Symmetrical Classes of Central Configurations

We consider here the classical question of finiteness (see Smale [13] and Wintner [15]) – given n point masses, is the corresponding number of central configurations finite? We prove finiteness for a particular family of d-dimensional symmetrical configurations of d+2 point masses. Also, we study the bifurcations of these configurations and provide the exact number of central configurations when d=2, 3. All our results stem from the application of a new method for studying symmetrical classes of central configurations, which is presented in this work. (Accepted September 23, 2002) Published online February 14, 2003 Communicated by P. Rabinowitz     

Global Bifurcation Analysis of a Controlled Underactuated Mechanical System

In this paper, bifurcation theory is employed to classify different dynamical behaviors arising in an underactuated mechanical system subject to bounded controls. The methodology is applied to an inertia wheel pendulum consisting of a simple pendulum with a rotating disk at the end. Restricting the magnitude of the control action places an important obstacle to the design of a continuous controller capable of swinging-up and stabilize the pendulum at the inverted position: the arm only can reach that position by means of oscillations of increasing amplitude. The controller is derived from a simple nonlinear state-feedback law, followed by a saturating device that limits the maximum amplitude of the control action applied to the system. This bound gives birth to a rich dynamical behavior, including pitchfork and Hopf bifurcations of equilibria, saddle-node bifurcations of periodic orbits, homoclinic and heteroclinic bifurcations. The global dynamics is analyzed in terms of certain control gains and a two-parameter bifurcation diagram is derived. It is shown that the dynamics on this bifurcation diagram is organized in a pair of codimension-two rotationally symmetric bifurcation points. Finally, it is found out that when the control gains lie on a certain region in the parameter space simultaneous stabilization of the upright position together with a large basin of attraction is obtained. Simulation results show that almost global stabilization of the system can be achieved.     

Density functional theory: Foundations reviewed

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N$N$-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N$N$-representability conditions on the 2-RDM have recently been attained.     

Surface‐enhanced Raman scattering of N‐acetylneuraminic acid on silver nanoparticle surface

N‐Acetylneuraminic acid (sialic acid, Neu5Ac) has recently gained interest as a potential marker for a variety of pathophysiological processes, although no Raman study has been reported for this important biomolecule. In this paper, the vibrational properties of Neu5Ac were studied by means of Raman, surface‐enhanced Raman scattering (SERS), and density functional theory calculations. By adsorption of Neu5Ac on silver nanoparticle surface, strongly enhanced Raman intensities are obtained, allowing easy measurement of small amounts of aqueous Neu5Ac (10 µl of a 10⁻⁷ m solution) utilizing low laser power and short exposure time. The mechanism of adsorption of Neu5Ac on the silver surface is discussed on the basis of the experimental and theoretical results. This study demonstrates that SERS can provide an effective tool for development of a label‐free, rapid, and sensitive optical platform for identification of Neu5Ac. Copyright © 2014 John Wiley & Sons, Ltd.     

Producing acoustic ‘Frozen Waves’: Simulated experiments with diffraction/attenuation resistant beams in lossy media

The so-called Localized Waves (LW), and the “Frozen Waves” (FW), have raised significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction —self-healing— property (after obstacles with size smaller than the antenna’s  ); while the FWs, a sub-class of LWs, offer the possibility of arbitrarily modeling the longitudinal field intensity pattern inside a prefixed interval, for instance 0?z?L$0?z?L$, of the wave propagation axis. More specifically, the FWs are localized fields “at rest”, that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization.     

Fret Studies of Conformational Changes in Heparin-Binding Peptides

FRET (Förster Resonance Energy Transfer) was applied to study structural properties of heparin-binding peptides containing the sequence XBBBXXBX where ‘X’ represents hydropathic or uncharged and ‘B’ represents basic amino acids. Internally quenched fluorogenic peptides were synthesized containing the fluorescent donor oaminobenzoic acid (o-Abz) and the acceptor dinitrophenyl ethylenediamine (Eddnp) group. Using the CONTIN computational package, distance distributions were recovered from time resolved fluorescence data, associated to end-to-end distances of the peptides. The peptides containing three or four repeat units have random structure in aqueous medium, and the interaction with low molecular weight heparin stabilized short end-to end distances. Experiments in water/trifluoroethanol (TFE) mixtures showed changes in distance distributions compatible with compact conformations stabilized above 40 % volume content of TFE in the mixture. Similar changes in distance distributions were also observed for the peptides in interaction with SDS micelles in aqueous suspensions and circular dichroism data revealed alpha-helix formation in the peptides in interaction with heparin, SDS micelles or the co-solvent TFE. The process is dependent on electrostatic and hydrogen bond interactions and the end-to-end distances obtained are smaller than expected for the peptides in linear α-helix conformation, indicating the occurrence of structural arrangements leading to additional decrease in the distances.