Bifurcation phenomena in viscoelastic flows through a symmetric 1:4 expansion

In this work we present an investigation of viscoelastic flow in a planar sudden expansion with expansion ratio D/d = 4. We apply the modified FENE–CR constitutive model based on the non-linear finite extensibility dumbbells (FENE) model. The governing equations were solved using a finite volume method with the high-resolution CUBISTA scheme utilised for the discretisation of the convective terms in the stress and momentum equations. Our interest here is to investigate two-dimensional steady-state solutions where, above a critical Reynolds number, stable asymmetric flow states are known to occur. We report a systematic parametric investigation, clarifying the roles of Reynolds number (0.01 < Re < 100), Weissenberg number (0 < We < 100) and the solvent viscosity ratio (0.3 < β < 1). For most simulations the extensibility parameter of the FENE model was kept constant, at a value L² = 100, but some exploration of its effect in the range 100–500 shows a rather minor influence. The results given comprise flow patterns, streamlines and vortex sizes and intensities, and pressure and velocity distributions along the centreline (i.e. y = 0). For the Newtonian case, in agreement with previous studies, a bifurcation to asymmetric flow was observed for Reynolds numbers greater than about 36. In contrast viscoelasticity was found to stabilise the flow; setting β = 0.5 and We = 2 as typical values, resulted in symmetric flow up to a Reynolds number of about 46. We analyse these two cases in particular detail.     

On the confinement of a viscous fluid by means of a feedback external field

In this work we consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the standard Stokes system. We show how this fluid can be stopped at a finite distance from the entrance of the semi-infinite strip by means of a feedback source depending in a sublinear way on the velocity field. This localization effect is proved by reducing the problem to a non-linear biharmonic type one for which the localization of solutions is obtained through the application of an energy method, in the spirit of the monograph by S.N. Antontsev, J.I. Díaz and S.I. Shmarev (Energy Methods for Free Boundary Problems: Applications to Non-Linear PDEs and Fluid Mechanics, Birkäuser, Boston, 2002). Since the presence of the non-linear terms defined by the source is not standard in fluid mechanics literature, we give also some results about the existence and uniqueness of weak solutions for this problem. To cite this article: S.N. Antontsev et al., C. R. Mecanique 330 (2002) 797–802.     

Sound propagation in acoustically lined elliptical ducts

Sound propagation in ducts with elliptical cross-sections can be described in terms of modes characterized by Mathieu functions of orders specified by the boundary conditions. For ducts with locally reacting liners there is coupling between modes because the admissible solutions are linear combinations of Mathieu functions of different orders and the eigenvalues are roots of an infinite determinant. The amount of mode coupling depends on the eccentricity of the duct. For the case of small eccentricity of the duct, approximate general solutions are derived and an example is discussed, where solutions are found.     

Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ ₀〉 = cos α | 10〉 + sin α | 01〉 and | ? ₀〉 = cos α | 11〉 + sin α | 00〉 cover three-dimensional surfaces in the diagram C _ij × C _ik × C _il , where C _mn stands for the concurrence between qubits m and n, varying 0 ≤ α ≤ π / 2. In the first case, projections of the surfaces on a diagram C _ij × C _kl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.     

Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario

We show that relativistic contributions to the ground-state energy of the hydrogen atom from a minimal length introduced by a Lorentz-covariant algebra are more important than non-relativistic contributions; the non-relativistic approach is therefore unsuitable. We compare our result with experimental data to estimate an upper bound of the order 10^?20m for the minimal length.     

Validation of Photodynamic Action via Photobleaching of a New Curcumin-Based Composite with Enhanced Water Solubility

Motivated by the photochemical and photophysical properties of curcumin-based composites, the characteristics of a new curcumin-based water-soluble salt were investigated via absorption and fluorescence spectroscopy. Photobleaching was investigated using a set of LEDs in three different wavelengths (405 nm, 450 nm and 470 nm) to illuminate an aqueous solution of curcumin, evaluating its degradation for five different exposure times (0, 5, 15, 45 and 105 minutes). The results were compared with equivalent measurements of dark degradation and illumination in the presence of a singlet-oxygen quencher. Three solution concentrations (50, 100 and 150 μg/ml) were studied. To measure the fluorescence, it was used low power 405 nm excitation laser source. Time dependent photodegradation of curcumin was observed, as compared to the natural degradation of samples maintained on a dark environment. Two main absorption peaks were detected and their relation responded to both concentration and wavelength of the illumination source. A spectral correlation between absorption of curcumin and the emission bands of the sources showed an optimal spectral overlap for the 450 nm LED. For this source, photobleaching showed a less intense degradation on the presence of singlet oxygen quencher. This last result confirmed singlet oxygen production in vitro, indicating a strong potential of this composite to be used as a blue-light-activated photosensitizer.     

2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems

Cutting and packing problems have been extensively studied in the literature in recent decades, mainly due to their numerous real-world applications while at the same time exhibiting intrinsic computational complexity. However, a major limitation has been the lack of problem generators that can be widely and commonly used by all researchers in their computational experiments. In this paper, a problem generator for every type of two-dimensional rectangular cutting and packing problems is proposed. The problems are defined according to the recent typology for cutting and packing problems proposed by Wäscher, Haußner, and Schumann (2007) and the relevant problem parameters are identified. The proposed problem generator can significantly contribute to the quality of the computational experiments run with cutting and packing problems and therefore will help improve the quality of the papers published in this field.     

Determination of dissolved zinc in seawater using micro-Sequential Injection lab-on-valve with fluorescence detection

This paper introduces the preliminary design and optimization of a micro-Sequential Injection lab-on-valve system (μSI-LOV) with fluorescence detection for the direct determination of trace Zn(2+) in an unacidified seawater matrix. The method capitalizes on the sensitivity and selectivity of FluoZin-3, which was originally designed to measure zinc in living cells. The optimum reaction conditions, sources of blank signal and physical parameters of the μSIA-LOV are evaluated with the requirements of trace metal analysis in mind, namely high sensitivity and low background signals. A detailed investigation of the effect of sample and reagent sequencing on sensitivity is presented for the first time using μSIA-LOV. We find that the order of sequencing greatly influences peak shape and analytical sensitivity with the highest and smoothest peaks obtained when a large volume of sample (75 μL) is aspirated last in the sequence prior to flow reversal and detection. The optimized reaction conditions and reagent/sample sequencing protocol yield a detection limit of 0.3 nM Zn(2+), high precision (RSD < 2.5%), a linear quantification range up to 40 nM and an analytical cycle of ～1 min per sample. This work demonstrates that μSI-LOV is capable of attaining detection limits that are close to those needed for open ocean determinations of Zn(2+) without preconcentration or separation of the analyte from the seawater matrix. The low reagent consumption (50 μL per sample), full automation and minimal maintenance requirements of μSI-LOV make it well suited for shipboard analysis and, eventually, for development to meet the pressing need for trace element measurements in unattended locations.     

Core-softened fluids, water-like anomalies, and the liquid-liquid critical points

Molecular dynamics simulations are used to examine the relationship between water-like anomalies and the liquid-liquid critical point in a family of model fluids with multi-Gaussian, core-softened pair interactions. The core-softened pair interactions have two length scales, such that the longer length scale associated with a shallow, attractive well is kept constant while the shorter length scale associated with the repulsive shoulder is varied from an inflection point to a minimum of progressively increasing depth. The maximum depth of the shoulder well is chosen so that the resulting potential reproduces the oxygen-oxygen radial distribution function of the ST4 model of water. As the shoulder well depth increases, the pressure required to form the high density liquid decreases and the temperature up to which the high-density liquid is stable increases, resulting in the shift of the liquid-liquid critical point to much lower pressures and higher temperatures. To understand the entropic effects associated with the changes in the interaction potential, the pair correlation entropy is computed to show that the excess entropy anomaly diminishes when the shoulder well depth increases. Excess entropy scaling of diffusivity in this class of fluids is demonstrated, showing that decreasing strength of the excess entropy anomaly with increasing shoulder depth results in the progressive loss of water-like thermodynamic, structural and transport anomalies. Instantaneous normal mode analysis was used to index the overall curvature distribution of the fluid and the fraction of imaginary frequency modes was shown to correlate well with the anomalous behavior of the diffusivity and the pair correlation entropy. The results suggest in the case of core-softened potentials, in addition to the presence of two length scales, energetic, and entropic effects associated with local minima and curvatures of the pair interaction play an important role in determining the presence of water-like anomalies and the liquid-liquid phase transition.