Upwind solution of singular differential equations arising from steady channel flows

We study ordinary nonlinear singular differential equations which arise from steady conservation laws with source terms. An example of steady conservation laws which leads to those scalar equations is the Saint–Venant equations. The numerical solution of these scalar equations is sought by using the ideas of upwinding and discretisation of source terms. Both the Engquist–Osher scheme and the Roe scheme are used with different strategies for discretising the source terms.

Transpolar voltage and polar cap flux during the substorm cycle and steady convection events

Transpolar voltages observed during traversals of the polar cap by the Defense Meteorological Satellite Program (DMSP) F-13 spacecraft during 2001 are analyzed using the expanding-contracting polar cap model of ionospheric convection. Each of the 10,216 passes is classified by its substorm phase or as a steady convection event (SCE) by inspection of the AE indices. For all phases, we detect a contribution to the transpolar voltage by reconnection in both the dayside magnetopause and in the crosstail current sheet. Detection of the IMF influence is 97% certain during quiet intervals and >99% certain during substorm/SCE growth phases but falls to 75% in substorm expansion phases: It is only 27% during SCEs. Detection of the influence of the nightside voltage is only 19% certain during growth phases, rising during expansion phases to a peak of 96% in recovery phases: During SCEs, it is >99%. The voltage during SCEs is dominated by the nightside, not the dayside, reconnection. On average, substorm expansion phases halt the growth phase rise in polar cap flux rather than reversing it. The main destruction of the excess open flux takes place during the 6- to 10-hour interval after the recovery phase (as seen in AE) and at a rate which is relatively independent of polar cap flux because the NENL has by then retreated to the far tail. The best estimate of the voltage associated with viscous-like transfer of closed field lines into the tail is around 10 kV.

Gonadotrophins modulate hormone secretion and steady-state mRNA levels for activin receptors (type I, IIA, IIB) and inhibin co-receptor (betaglycan) in granulosa and theca cells from chicken prehierarchical and preovulatory follicles

Ovarian follicle development is regulated through endocrine and local mechanisms. Increasing evidence indicates roles for transforming growth factor beta superfamily members, including inhibins and activins. We recently identified divergent expression of mRNAs encoding activin receptors (ActR) and inhibin co-receptor betaglycan in chicken follicles at different stages of maturation. Here, we compare the actions of LH and FSH (0, 1, 10, 100 ng/ml) on levels of mRNA for ActRI, ActRIIA, ActRIIB and betaglycan in chicken granulosa and theca cells (GC and TC) from preovulatory (F1) and prehierarchical (6-8 mm) follicles. The expression of mRNAs for LH-R and FSH-R and production of inhibin A, oestradiol and progesterone were also quantified. FSH decreased ActRIIB and ActRI mRNA levels in 6-8 mm GC, whereas LH increased the mRNA levels. Both LH and FSH enhanced ActRIIA (5- and 8.5-fold) and betaglycan mRNA expression (2- and 3.5-fold) in 6-8 mm GC. In 6-8 mm TC, LH and FSH both increased the betaglycan mRNA level (7- and 3.5-fold respectively) but did not affect ActRI, ActRIIA and ActRIIB transcript levels. In F1 GC, both LH and FSH stimulated ActRI (2- and 2.4-fold), ActRIIB (3.2- and 2.7-fold) and betaglycan (7- and 4-fold) mRNA levels, while ActRIIA mRNA was unaffected. In F1 TC, LH and FSH reduced ActRIIA (35-50%) and increased (4.5- and 7.6-fold) betaglycan mRNA, but had no effect on ActRI and ActRIIB transcript levels. Results support the hypothesis that expression of ActR and betaglycan are differentially regulated by gonadotrophins during follicle maturation in the hen. This may represent an important mechanism for fine-tuning follicle responsiveness to local and systemic activins and inhibins.

Steady-spectrum contexts and perceptual compensation for reverberation in speech identification

Perceptual compensation for reverberation was measured by embedding test words in contexts that were either spoken phrases or processed versions of this speech. The processing gave steady-spectrum contexts with no changes in the shape of the short-term spectral envelope over time, but with fluctuations in the temporal envelope. Test words were from a continuum between "sir" and "stir." When the amount of reverberation in test words was increased, to a level above the amount in the context, they sounded more like "sir." However, when the amount of reverberation in the context was also increased, to the level present in the test word, there was perceptual compensation in some conditions so that test words sounded more like "stir" again. Experiments here found compensation with speech contexts and with some steady-spectrum contexts, indicating that fluctuations in the context's temporal envelope can be sufficient for compensation. Other results suggest that the effectiveness of speech contexts is partly due to the narrow-band "frequency-channels" of the auditory periphery, where temporal-envelope fluctuations can be more pronounced than they are in the sound's broadband temporal envelope. Further results indicate that for compensation to influence speech, the context needs to be in a broad range of frequency channels. (c) 2007 Acoustical Society of America.

An analysis of arithmetic averaging in approximate Riemann solvers with an application to steady, supercritical flows

An analysis of various arithmetic averaging procedures for approximate Riemann solvers is made with a specific emphasis on efficiency and a jump capturing property. The various alternatives discussed are intended for future work, as well as the more immediate problem of steady, supercritical free-surface flows. Numerical results are shown for two test problems.

An efficient shock capturing scheme for the pseudo-unsteady equations representing steady inviscid flow

An efficient algorithm is presented for the solution of the steady Euler equations of gas dynamics. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme is applied to a standard test problem of flow down a channel containing a circular arc bump for three different mesh sizes.

A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

Shock capturing scheme for steady, supersonic, isentropic flow

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, isentropic flow. The scheme incorporates numerical characteristic decomposition, is shock-capturing by design and incorporates space marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

A finite difference scheme for steady, supersonic, two-dimensional, compressible flow of real gases

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, compressible flow of real gases. The scheme incorparates numerical characteristic decomposition, is shock-capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.