Orientational behaviour of thermotropic and lyotropic liquid crystal polymer systems under shear flow

A comparison is made of the development of global orientation during shearing of lyotropic solutions of hydroxypropylcellulose with that observed for the thermotropic phase of hydroxypropylcellulose. At shear rates the behaviour of the two systems is similar, both during steady-state shear, and in terms of relaxation following cessation of shear flow. At low shear rates, the levels of orientation observed for the thermotropic system are substantially greater than observed for the lyotropic solutions. The relationship of these differences to variations in molecular parameters, viscous stress and to director tumbling is discussed.

The state estimation of flow demands in gas networks from sparse pressure telemetry

This paper presents novel observer-based techniques for the estimation of flow demands in gas networks, from sparse pressure telemetry. A completely observable model is explored, constructed by incorporating difference equations that assume the flow demands are steady. Since the flow demands usually vary slowly with time, this is a reasonable approximation. Two techniques for constructing robust observers are employed: robust eigenstructure assignment and singular value assignment. These techniques help to reduce the effects of the system approximation. Modelling error may be further reduced by making use of known profiles for the flow demands. The theory is extended to deal successfully with the problem of measurement bias. The pressure measurements available are subject to constant biases which degrade the flow demand estimates, and such biases need to be estimated. This is achieved by constructing a further model variation that incorporates the biases into an augmented state vector, but now includes information about the flow demand profiles in a new form.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

A model of the dynamic relationship between blood flow and volume changes during brain activation

The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level-dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBV proportional to CBFPhi has been used extensively in the literature. Two similar models, the Balloon (Buxton et al., 1998) and the Windkessel (Mandeville et al., 1999), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.

Granular flow in the marginal ice zone

The region of sea ice near the edge of the sea ice pack is known as the marginal ice zone (MIZ), and its dynamics are complicated by ocean wave interaction with the ice cover, strong gradients in the atmosphere and ocean and variations in sea ice rheology. This paper focuses on the role of sea ice rheology in determining the dynamics of the MIZ. Here, sea ice is treated as a granular material with a composite rheology describing collisional ice floe interaction and plastic interaction. The collisional component of sea ice rheology depends upon the granular temperature, a measure of the kinetic energy of flow fluctuations. A simplified model of the MIZ is introduced consisting of the along and across momentum balance of the sea ice and the balance equation of fluctuation kinetic energy. The steady solution of these equations is found to leading order using elementary methods. This reveals a concentrated region of rapid ice flow parallel to the ice edge, which is in accordance with field observations, and previously called the ice jet. Previous explanations of the ice jet relied upon the existence of ocean currents beneath the ice cover. We show that an ice jet results as a natural consequence of the granular nature of sea ice.

Causes of plasma flow bursts and dayside auroral transients: An evaluation of two models Invoking reconnection pulses and changes in the Y component of the magnetosheath field

Longitudinal flow bursts observed by the European Incoherent Scatter (EISCAT) radar, in association with dayside auroral transients observed from Svalbard, have been interpreted as resulting from pulses of enhanced reconnection at the dayside magnetopause. However, an alternative model has recently been proposed for a steady rate of magnetopause reconnection, in which the bursts of longitudinal flow are due to increases in the field line curvature force, associated with the By component of the magnetosheath field. We here evaluate these two models, using observations on January 20, 1990, by EISCAT and a 630-nm all-sky camera at Ny Ålesund. For both models, we predict the behavior of both the dayside flows and the 630-nm emissions on newly opened field lines. It is shown that the signatures of steady reconnection and magnetosheath By changes could possibly resemble the observed 630-nm auroral events, but only for certain locations of the observing site, relative to the ionospheric projection of the reconnection X line: however, in such cases, the flow bursts would be seen between the 630-nm transients and not within them. On the other hand, the model of reconnection rate pulses predicts that the flows will be enhanced within each 630-nm transient auroral event. The observations on January 20, 1990, are shown to be consistent with the model of enhanced reconnection rate pulses over a background level and inconsistent with the effects of periodic enhancements of the magnitude of the magnetosheath By component. We estimate that the reconnection rate within the pulses would have to be at least an order of magnitude larger than the background level between the pulses.

Comment on “B_y fluctuations in the magnetosheath and azimuthal flow velocity transients in the dayside ionosphere” by Newell and Sibeck

Newell and Sibeck [1993] (hereafter N&S) list some objections to our interpretation of dayside auroral transients and associated azimuthal flow bursts in terms of pulsed reconnection [e.g. Lockwood et al., 1989; 1993a]. They present what they term an “apparently overlooked” alternative explanation in terms of steady reconnection and fluctuations in the magnitude of the By component of the magnetosheath field. The objections of N&S can all be answered by reference to our previous publications and their alternative explanation was only “overlooked” in so far as it fails to explain the observations. Here we discuss just some of the reasons why the objections of N&S are invalid, and then give reasons why the events are not simply due to magnetosheath |By| changes.

On flow reversal boundaries and transpolar voltage in average models of high-latitude convection

The implications of polar cap expansions, contractions and movements for empirical models of high-latitude plasma convection are examined. Some of these models have been generated by directly averaging flow measurements from large numbers of satellite passes or radar scans; others have employed more complex means to combine data taken at different times into large-scale patterns of flow. In all cases, the models have implicitly adopted the assumption that the polar cap is in steady state: they have all characterized the ionospheric flow in terms of the prevailing conditions (e.g. the interplanetary magnetic field and/or some index of terrestrial magnetic activity) without allowance for their history. On long enough time scales, the polar cap is indeed in steady state but on time scales shorter than a few hours it is not and can oscillate in size and position. As a result, the method used to combine the data can influence the nature of the convection reversal boundary and the transpolar voltage in the derived model. This paper discusses a variety of effects due to time-dependence in relation to some ionospheric convection models which are widely applied. The effects are shown to be varied and to depend upon the procedure adopted to compile the model.

Kinetics analysis and automated online screening of aminocarbonylation of aryl halides in flow

Temperature, pressure, gas stoichiometry, and residence time were varied to control the yield and product distribution of the palladium-catalyzed aminocarbonylation of aromatic bromides in both a silicon microreactor and a packed-bed tubular reactor. Automation of the system set points and product sampling enabled facile and repeatable reaction analysis with minimal operator supervision. It was observed that the reaction was divided into two temperature regimes. An automated system was used to screen steady-state conditions for offline analysis by gas chromatography to fit a reaction rate model. Additionally, a transient temperature ramp method utilizing online infrared analysis was used, leading to more rapid determination of the reaction activation energy of the lower temperature regimes. The entire reaction spanning both regimes was modeled in good agreement with the experimental data.