Heat conduction from irregular surfaces

The effect of irregularities on the rate of heat conduction from a two-dimensional isothermal surface into a semi infinite medium is considered. The effect of protrusions, depressions, and surface roughness is quantified in terms of the displacement of the linear temperature profile prevailing far from the surface. This shift, coined the displacement length, is designated as an appropriate global measure of the effect of the surface indentations incorporating the particular details of the possibly intricate geometry. To compute the displacement length, Laplace's equation describing the temperature distribution in the semi-infinite space above the surface is solved numerically by a modified Schwarz-Christoffel transformation whose computation requires solving a system of highly non-linear algebraic equations by iterative methods, and an integral equation method originating from the single-layer integral representation of a harmonic function involving the periodic Green's function. The conformal mapping method is superior in that it is capable of handling with high accuracy a large number of vertices and intricate wall geometries. On the other hand, the boundary integral method yields the displacement length as part of the solution. Families of polygonal wall shapes composed of segments in regular, irregular, and random arrangement are considered, and pre-fractal geometries consisting of large numbers of vertices are analyzed. The results illustrate the effect of wall geometry on the flux distribution and on the overall enhancement in the rate of transport for regular and complex wall shapes

Modeling the effect of copper availability on bacterial denitrification

When denitrifying bacteria such as Paracoccus denitrificans respire anaerobically they convert nitrate to dinitrogen gas via a pathway which includes the potent greenhouse gas, nitrous oxide (NO). The copper-dependent enzyme Nitrous Oxide reductase (Nos) catalyzes the reduction of NO to dinitrogen. In low-copper conditions, recent experiments in chemostats have demonstrated that Nos efficiency decreases resulting in significant NO emissions. For the first time, a chemostat-based mathematical model is developed that describes the anaerobic denitrification pathway based on Michaelis-Menten kinetics and published kinetic parameters. The model predicts steady-state enzyme levels from experimental data. For low copper concentrations, the predicted Nos level is significantly reduced, whereas the levels for the non copper-dependent reductases in the pathway remain relatively unaffected. The model provides time courses for the pathway metabolites that accurately reflect previously published experimental data. In the absence of experimental data purely predictive analyses can also be readily performed by calculating the relative Nos level directly from the copper concentration. Here, the model quantitatively estimates the increasing level of emitted NO as the copper level decreases. We have developed a mathematical model for the denitrification pathway based on existing experimental results, Michaelis-Menten kinetics and experimentally obtained kinetic constants. This is the first such model to incorporate the copper concentration in order to predict emissions of the potent greenhouse gas, nitrous oxide (NO), as well as the other nitrogenous compounds in the pathway. The model predicts increasing NO emissions as the copper level is lowered, in agreement with experimental observations in chemostats. © 2013 The Authors. MicrobiologyOpen published by John Wiley & Sons Ltd.

Flow in a slowly-tapering channel with oscillating walls

The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a time-periodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou \cite{HP}. A careful study of the governing partial differential system for the first order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry-breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window stability is again lost to exponentially growing solutions as the Reynolds number is increased

Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis

Experimental investigation of hysteresis in the break-up of liquid curtains

Findings from an experimental investigation of the break-up of liquid curtains are reported, with the overall aim of examining stability windows for multi-layer liquid curtains composed of Newtonian fluids, where the properties of each layer can be kept constant or varied. For a single-layer curtain it is known that the minimum flow rate required for initial stability can be violated by carefully reducing the flow rate below this point, which defines a hysteresis region. However, when two or three layers are used to form a composite curtain, the hysteresis window can be considerably reduced depending on the experimental procedure used. Extensive quantitative measurements of this hysteresis region are provided alongside an examination of the influence of physical properties such as viscosity and surface tension. The origins of curtain break-up for two different geometries are analysed; first where the curtain width remains constant, pinned by straight edge guides; and second where the curtain is tapered by angled edge guides. For both cases, the rupture speed is measured, which appears to be consistent with the Taylor-Culick velocity. Observations of the typical linearly spaced jets which form after the break-up has transpired and the periodicity of these jets are compared to the Rayleigh-Taylor wavelength and previous experimental measurements. Furthermore, the curtain stability criterion originally developed by Brown (1961), summarised in terms of a Weber number, has recently been extended to multi-layer curtains by Dyson et al. (2009); thus this report provides the first experimental measurements which puts this to the test. Ultimately, it is found that only the most viscous and polymer-based liquids violate this criterion

Plasma Wakefield Acceleration with a Modulated Proton Bunch

The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found in this case.Comment: 9 pages, 7 figure

The energy dependence of ptp_t angular correlations inferred from mean-ptp_{t} fluctuation scale dependence in heavy ion collisions at the SPS and RHIC

We present the first study of the energy dependence of $p_t$ angular correlations inferred from event-wise mean transverse momentum fluctuations in heavy ion collisions. We compare our large-acceptance measurements at CM energies $\sqrt{s_{NN}} =$ 19.6, 62.4, 130 and 200 GeV to SPS measurements at 12.3 and 17.3 GeV. $p_t$ angular correlation structure suggests that the principal source of $p_t$ correlations and fluctuations is minijets (minimum-bias parton fragments). We observe a dramatic increase in correlations and fluctuations from SPS to RHIC energies, increasing linearly with $\ln \sqrt{s_{NN}}$ from the onset of observable jet-related fluctuations near 10 GeV.Comment: 10 pages, 4 figure

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation