Bifurcation study for a vertical channel with constant flux and large aspect ratio

Using suitable coupled Navier-Stokes Equations for an incompressible Newtonian fluid we investigate the linear and non-linear steady state solutions for both a homogeneously and a laterally heated fluid with finite Prandtl Number (Pr=7) in the vertical orientation of the channel. Both models are studied within the Large Aspect Ratio narrow-gap and under constant flux conditions with the channel closed. We use direct numerics to identify the linear stability criterion in parametric terms as a function of Grashof Number (Gr) and streamwise infinitesimal perturbation wavenumber (making use of the generalised Squire’s Theorem). We find higher harmonic solutions at lower wavenumbers with a resonance of 1:3exist, for both of the heating models considered. We proceed to identify 2D secondary steady state solutions, which bifurcate from the laminar state. Our studies show that 2D solutions are found not to exist in certain regions of the pure manifold, where we find that 1:3 resonant mode 2D solutions exist, for low wavenumber perturbations. For the homogeneously heated fluid, we notice a jump phenomenon existing between the pure and resonant mode secondary solutions for very specific wavenumbers .We attempt to verify whether mixed mode solutions are present for this model by considering the laterally heated model with the same geometry. We find mixed mode solutions for the laterally heated model showing that a bridge exists between the pure and 1:3 resonant mode 2D solutions, of which some are stationary and some travelling. Further, we show that for the homogeneously heated fluid that the 2D solutions bifurcate in hopf bifurcations and there exists a manifold where the 2D solutions are stable to Eckhaus criterion, within this manifold we proceed to identify 3D tertiary solutions and find that the stability for said 3D bifurcations is not phase locked to the 2D state. For the homogeneously heated model we identify a closed loop within the neutral stability curve for higher perturbation wavenumubers and analyse the nature of the multiple 2D bifurcations around this loop for identical wavenumber and find that a temperature inversion occurs within this loop. We conclude that for a homogeneously heated fluid it is possible to have abrup ttransitions between the pure and resonant 2D solutions, and that for the laterally heated model there exist a transient bifurcation via mixed mode solutions.

The fall and rise of tear albumin levels:a multifactorial phenomenon

Albumin in tears is used as a diagnostic marker of ocular insult and inflammation, but whether its presence in tears is responsive or part of an adaptive reaction remains unresolved. A review of the literature on tear albumin concentration emphasizes that variables such as collection method, stimulus, assay technique, and disease state influence the quoted values to different extents. Influence of assay technique is negligible in comparison to variation in sampling conditions. Ocular disease increases albumin concentrations but not in a specific manner. The literature review also highlighted that little systematic research has been carried out on the daily cycle of tear albumin levels. In order to remedy this shortcoming, we investigated variations in tear albumin concentration during the waking day. The concentration of albumin in 400 tear samples collected from 13 subjects was assessed at 2-hourly intervals throughout the waking day. Highest daytime albumin concentrations were obtained within 10 minutes of waking, with a mean concentration of >50 ± 22 µg/ml. Albumin levels were at their lowest, but most consistent, 2-6 hours post-waking. This pattern was followed by a progressive increase in albumin concentration during the latter part of the day. Although individual subject-to-subject concentration differences were observed, this distinctive pattern of diurnal variation was found in all subjects. The results presented suggest a regulated, not random, pattern of variation within the period of study. © 2013 Elsevier Inc. All rights reserved.

Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.

Intercultural intertextuality as a translation phenomenon

Texts as communicative occurrences are characterised by their interdependence on other texts, either of the same genre or of a different genre. This characteristic feature is known as intertextuality (or discursivity). The relationship can either be to texts originating in the same language and culture, or to texts originating in another language and culture. This paper comments on the discourse phenomenon of 'intercultural intertextuality' from the point of view of translation (studies). It illustrates strategies employed in the original texts for referring to the source language/culture. Subsequently, the paper explores the translation strategies used in authentic target texts in dealing with the phenomenon of intercultural intertextuality. A variety of political speeches (mainly of the language pair English and German) are used as illustrative examples.

Technology sourcing and reverse productivity spillovers in the MNE:global or regional phenomenon?

The focus of this paper is the importance of regions in technology transfer by the multinational firm. Specifically, we focus on an issue that has become known as knowledge or technology sourcing via 'reverse spillovers', i.e. productivity effects running from domestic firms to foreign establishments. Traditionally this issue has presented a challenge for international business scholars, both in terms of identifying the phenomenon and in terms of determining the success of the strategy. In this paper we examine these questions within the context of the debate on globalization/regionalization. For a set of some 4500 subsidiaries of multinationals across a wide range of countries we show that reverse productivity spillovers via technology sourcing are significant but that they tend to be concentrated within 'triad regions' rather than across them. We also find that reverse spillovers from host country multinational enterprises are greater than those from other host country firms or from other foreign affiliates. © 2013 British Academy of Management.

Cortical mechanisms of attention in time:neural correlates of the Lag-1-sparing phenomenon

If humans monitor streams of rapidly presented (approximately 100-ms intervals) visual stimuli, which are typically specific single letters of the alphabet, for two targets (T1 and T2), they often miss T2 if it follows T1 within an interval of 200-500 ms. If T2 follows T1 directly (within 100 ms; described as occurring at 'Lag 1'), however, performance is often excellent: the so-called 'Lag-1 sparing' phenomenon. Lag-1 sparing might result from the integration of the two targets into the same 'event representation', which fits with the observation that sparing is often accompanied by a loss of T1-T2 order information. Alternatively, this might point to competition between the two targets (implying a trade-off between performance on T1 and T2) and Lag-1 sparing might solely emerge from conditional data analysis (i.e. T2 performance given T1 correct). We investigated the neural correlates of Lag-1 sparing by carrying out magnetoencephalography (MEG) recordings during an attentional blink (AB) task, by presenting two targets with a temporal lag of either 1 or 2 and, in the case of Lag 2, with a nontarget or a blank intervening between T1 and T2. In contrast to Lag 2, where two distinct neural responses were observed, at Lag 1 the two targets produced one common neural response in the left temporo-parieto-frontal (TPF) area but not in the right TPF or prefrontal areas. We discuss the implications of this result with respect to competition and integration hypotheses, and with respect to the different functional roles of the cortical areas considered. We suggest that more than one target can be identified in parallel in left TPF, at least in the absence of intervening nontarget information (i.e. masks), yet identified targets are processed and consolidated as two separate events by other cortical areas (right TPF and PFC, respectively).

Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Analysis of rogue wave phenomenon in optical fiber based on soliton's eigenvalue

The impact of third-order dispersion (TOD) on optical rogue wave phenomenon is investigated numerically. We validate the TOD coefficient by utilizing the eigenvalue of the associated equation of the nonlinear Schrödinger equation (NLSE). © 2014 OSA.

Bifurcation and stability in a low-dimensional model for multiple-frequency mode-locked lasers

Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels. © 2010 The American Physical Society.

On the dual-cone nature of the conical refraction phenomenon

In conical refraction (CR), a focused Gaussian input beam passing through a biaxial crystal and parallel to one of the optic axes is transformed into a pair of concentric bright rings split by a dark (Poggendorff) ring at the focal plane. Here, we show the generation of a CR transverse pattern that does not present the Poggendorff fine splitting at the focal plane, i.e., it forms a single light ring. This light ring is generated from a nonhomogeneously polarized input light beam obtained by using a spatially inhomogeneous polarizer that mimics the characteristic CR polarization distribution. This polarizer allows modulating the relative intensity between the two CR light cones in accordance with the recently proposed dual-cone model of the CR phenomenon. We show that the absence of interfering rings at the focal plane is caused by the selection of one of the two CR cones. (C) 2015 Optical Society of America

Characterizing the transition dynamics for multi-pulsing in mode-locked lasers

We consider experimentally and theoretically a refined parameter space near the transition to multi-pulse modelocking. Near the transition, the onset of instability is initiated by a Hopf (periodic) bifurcation. As cavity energy is increased, the band of unstable, oscillatory modes generates a chaotic behavior between single- and multi-pulse operation. Both theory and experiment are in good qualitative agreement and they suggest that the phenomenon is of a universal nature in mode-locked lasers at the onset of multi-pulsing from N to N + 1 pulses per round trip. This is the first theoretical and experimental characterization of the transition behavior, made possible by a highly refined tuning of the gain pump level. © 2010 Copyright SPIE - The International Society for Optical Engineering.