Double-diffusive instabilities at a horizontal boundary after the sudden onset of heating

When a deep body of fluid with a stable salinity gradient is heated from below at a horizontal boundary a destabilizing temperature gradient develops and can lead to instabilities. We will focus on two variants of this problem: the sudden increase in the boundary temperature at the initial time and the sudden turning on of a constant heat flux. These generate time-dependent temperature profiles. We look at the growing phase of the linear instabilities as an initial value problem where the initial time for the instabilities is a parameter to be determined. We determine numerically the optimal initial conditions and the optimal starting time for the instabilities to ensure that the maximum growth occurs at some given later time. The method that is used is an extension of the method developed by Kerr & Gumm (2017) in their investigation of the stability of developing temperature boundary layers at horizontal and vertical boundaries. This requires the use of an appropriate measure of the amplitude of the disturbances which is identified. The efectiveness of this approach is verified by looking at the classic problem of double-diffusive convection in a horizontal layer, where we look at both the salt-finger regime and the diffusive regime. We show that this approach is an effective way of investigating instabilities where the background gradients time dependent. For the problem of heating a salinity gradient from below, as the heat diffuses into the fluid the effective thermal Rayleigh number based on the instantaneous diffusion length-scale grows. For the case of a sudden increase in the temperature by a fixed amount the effective thermal Rayleigh number is proportional to t3=2, and for a constant heat flux it is proportional to t2, where t is the time since the onset of heating. However, the effective salt Rayleigh number also grows as t2. We will show that for the constant temperature case the thermal Rayleigh number initially dominates and the instabilities undergo a phase where the convection is essentially thermal, and the onset is essentially instantaneous. As the salt Rayleigh number becomes more significant the instability undergoes a transition to oscillatory double-diffusive convection. For the constant heat flux the ratio of the thermal and salt Rayleigh numbers is constant, and the instabilities are always double-diffusive in their nature. These instabilities initially decay. Hence, to achieve the largest growth at some given fixed time, there is an optimal time after the onset of heating for the instabilities to be initiated. These instabilities are essentially double-diffusive throughout their growth

Critical Rayleigh number of an error function temperature profile with a quasi-static assumption

When a semi-infinite body is heated from below by a sudden increase in temperature (or cooled from above) an error function temp erature profile grows as the heat diffuses into the fluid. The stability of such a profile is investigated using a large-wavelen gth asymptotic expansion under the quasi-static, or frozen-time, approximation. The critical Rayleigh number for this layer is f ound to be Ra=√(1/2) based on the length-scale √(κ t) where κ is the thermal diffusivity and t the time since the onset of heating

The sensitivity of saccharomyces mutants to palmitoleic acid may provide a means to study the controls of membrane fluidity in eukaryotes

The mechanisms which control the fluidity of eukaryotic membranes are unknown. We have identified S. cerevisiae deletion strains whose growth is impaired by palmitoleic (PO; C16:1) but not oleic (C18:1) acid. PO-sensitivity is suppressed by oleate thus perhaps identifying a signaling pathway that controls the ratio of these fatty acids in membrane phospholipid. Growth of these mutants is also inhibited by a known fluidizer, benzyl alcohol, thus indicating that PO has a fluidizing effect. Removal of Pkc1, known to play a key role in cell wall integrity control, leads to acute PO-sensitivity. Removal of Bck1, Mkk1, Mkk2, Slt2, or Swi6 downstream components of the cell wall integrity pathway, cause modest POsensitivity. Suppression by 1M sorbitol of the PO-sensitivity of these four mutants implies that PO/oleate ratio influences the cell wall. Acute PO-sensitivity of the pkc1Δ strain, even in the presence of 1M sorbitol, suggests the cell wall to be more severely compromised by PO addition to this strain. Alternatively, the failure to control the PO/oleate ratio could have an additional effect on the pkc1 strain, perhaps by disabling a 2nd pathway downstream of Pkc1 thus allowing PO addition to cause excess membrane fluidity. We are attempting to distinguish these two models by a variety of genetic, biochemical, and physical methods. Most notably, the effect of PO on the fluidity of the plasma membrane is being examined by measuring the depolarization of laurdan fluorescence

Thermal instability in a time-dependent base state due to sudden heating

When a large body of fluid is heated from below at a horizontal surface the heat diffuses into the fluid, giving rise to a gravitationally unstable layer adjacent to the boundary. A consideration of the instantaneous Rayleigh number using the thickness of this buoyant layer as a length scale would lead one to expect that the heated fluid is initially stable, and only becomes unstable after a finite time. This transition would also apply to other situations, such as heating a large body of fluid from the side, where a buoyant upward flow develops near the boundary. In such cases when the evolving thermal boundary layer first becomes unstable the time-scale for the growth of the instabilities may be comparable to the time-scale of the evolution of the background temperature profile, and so analytical approximations such as the quasi-static approximation, where the time-evolution of the background state is ignored, are not strictly appropriate. We develop a numerical scheme where we find the optimal growth of linear perturbations to the background flow over a given time interval. Part of this problem is to determine an appropriate measure of the amplitude to the disturbances, as inappropriate choices can lead to apparent growth of disturbances over finite time intervals even when the fluid is stable. By considering the Rayleigh–B´enard problem, we show these problems can be avoided by choosing a measure of the amplitude that uses both the velocity and temperature perturbations, and which minimizes the maximum growth. We apply our analysis to the problems of heating a semi-infinite body of fluid from horizontal and vertical boundaries. We will show that for heating from a vertical boundary there are large and small Prandtl number modes. For some Prandtl numbers both modes may play a role in the growth of instabilities. In some cases there is transition during the evolution of the most unstable instabilities in fluids such as water, where initially the instabilities are large Prandtl number modes and then morph into small Prandtl number modes part of the way through their evolution

Refreshment by the case: Use of multimedia in case study assessment

This paper outlines a novel approach to developing, presenting and using a multimedia case study for the assessment of a large (circa 230 students) Operations Management module at undergraduate level on a Business Studies programme. Engagement, realism and handling complexity are important issues in Operations Management teaching, learning and assessment. It is argued that traditional text based case studies do not address these concerns sufficiently and consequently can encourage surface learning approaches. Consultancy and simulation are more likely to be effective on these issues with the greater focus on experiential learning. However the constraints of these techniques restrict use as assessment options, particularly for large undergraduate programmes. This paper offers tutors of Operations Management an alternative approach to facilitating experiential learning using a multimedia case. The action research reported here develops this multimedia approach, identifies the practical considerations and the potential for improved student learning outcomes. The findings indicate that this multimedia approach was engaging, realistic and challenging hence facilitated greater student interest, understanding and skills

Letters between O. T. Geckeler and W. J. Kerr

Letters concerning a position in the mathematics department at Utah Agricultural College as well as a booklet describing O. T. Geckeler\u27s education

Letters between O. B. Sears and W. J. Kerr

Letters concerning a position at Utah Agricultural College

Is My Exercise Partner Similar Enough? Partner Characteristics as a Moderator of the Köhler Effect in Exergames

Objective: Recent research has shown the Köhler motivation gain effect (working at a task with a more capable partner where one's performance is indispensable to the group) leads to greater effort in partnered exercise videogame play. The purpose of this article was to examine potential moderators of the Köhler effect by exploring dissimilarities in one's partner's appearance, namely, having an older partner (compared with a same-age partner) and having a heavier-weight partner (compared with a same-weight partner). Subjects and Methods: One hundred fifty-three male and female college students completed a series of plank exercises using the “EyeToy: Kinetic™” for the PlayStation® 2 (Sony, Tokyo, Japan). Participants first completed the exercises individually and, after a rest, completed the same exercises with a virtually present partner. Exercise persistence, subjective effort, self-efficacy beliefs, enjoyment, and intentions to exercise were recorded and analyzed. Results: A significant Köhler motivation gain was observed in all partner conditions (compared with individual controls) such that participants with a partner held the plank exercises longer (P<0.001) and reported higher subjective effort (P<0.01). These results were unmoderated by partner's age and weight, with one exception: Males tended to persist longer when paired with an obese partner (P=0.08). Conclusions: These results suggest that differences in age and weight do not attenuate the Köhler effect in exergames and may even strengthen it

An experimental evaluation of a loop versus a reference design for two-channel microarrays

Motivation: Despite theoretical arguments that socalled "loop designs" of two-channel DNA microarray experiments are more efficient, biologists keep on using "reference designs". We describe two sets of microarray experiments with RNA from two different biological systems (TPA-stimulated mammalian cells and Streptomyces coelicor). In each case, both a loop and a reference design were performed using the same RNA preparations with the aim to study their relative efficiency. Results: The results of these experiments show that (1) the loop design attains a much higher precision than the reference design, (2) multiplicative spot effects are a large source of variability, and if they are not accounted for in the mathematical model, for example by taking log-ratios or including spot-effects, then the model will perform poorly. The first result is reinforced by a simulation study. Practical recommendations are given on how simple loop designs can be extended to more realistic experimental designs and how standard statistical methods allow the experimentalist to use and interpret the results from loop designs in practice