Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Epistatic effects of potassium channel variation on cardiac repolarization and atrial fibrillation risk

Objectives The aim of this study was to evaluate the role of cardiac K+ channel gene variants in families with atrial fibrillation (AF). Background The K+ channels play a major role in atrial repolarization but single mutations in cardiac K+ channel genes are infrequently present in AF families. The collective effect of background K+ channel variants of varying prevalence and effect size on the atrial substrate for AF is largely unexplored. Methods Genes encoding the major cardiac K+ channels were resequenced in 80 AF probands. Nonsynonymous coding sequence variants identified in AF probands were evaluated in 240 control subjects. Novel variants were characterized using patch-clamp techniques and in silico modeling was performed using the Courtemanche atrial cell model. Results Nineteen nonsynonymous variants in 9 genes were found, including 11 rare variants. Rare variants were more frequent in AF probands (18.8% vs. 4.2%, p < 0.001), and the mean number of variants was greater (0.21 vs. 0.04, p < 0.001). The majority of K+ channel variants individually had modest functional effects. Modeling simulations to evaluate combinations of K+ channel variants of varying population frequency indicated that simultaneous small perturbations of multiple current densities had nonlinear interactions and could result in substantial (>30 ms) shortening or lengthening of action potential duration as well as increased dispersion of repolarization. Conclusions Families with AF show an excess of rare functional K+ channel gene variants of varying phenotypic effect size that may contribute to an atrial arrhythmogenic substrate. Atrial cell modeling is a useful tool to assess epistatic interactions between multiple variants.

The influence of Monte Carlo source parameters on detector design and dose perturbation in small field dosimetry

To obtain accurate Monte Carlo simulations of small radiation fields, it is important model the initial source parameters (electron energy and spot size) accurately. However recent studies have shown that small field dosimetry correction factors are insensitive to these parameters. The aim of this work is to extend this concept to test if these parameters affect dose perturbations in general, which is important for detector design and calculating perturbation correction factors. The EGSnrc C++ user code cavity was used for all simulations. Varying amounts of air between 0 and 2 mm were deliberately introduced upstream to a diode and the dose perturbation caused by the air was quantified. These simulations were then repeated using a range of initial electron energies (5.5 to 7.0 MeV) and electron spot sizes (0.7 to 2.2 FWHM). The resultant dose perturbations were large. For example 2 mm of air caused a dose reduction of up to 31% when simulated with a 6 mm field size. However these values did not vary by more than 2 % when simulated across the full range of source parameters tested. If a detector is modified by the introduction of air, one can be confident that the response of the detector will be the same across all similar linear accelerators and the Monte Carlo modelling of each machine is not required.

An experimental approach to air gap optimisation for a correction-less small field diode

Aim A recent Monte Carlo based study has shown that it is possible to design a diode that measures small field output factors equivalent to that in water. This is accomplished by placing an appropriate sized air gap above the silicon chip (1) with experimental results subsequently confirming that a particular Monte Carlo design was accurate (2). The aim of this work was to test if a new correction-less diode could be designed using an entirely experimental methodology. Method: All measurements were performed on a Varian iX at a depth of 5 cm, SSD of 95 cm and field sizes of 5, 6, 8, 10, 20 and 30 mm. Firstly, the experimental transfer of kq,clin,kq,msr from a commonly used diode detector (IBA, stereotactic field diode (SFD)) to another diode detector (Sun Nuclear, unshielded diode, (EDGEe)) was tested. These results were compared to Monte Carlo calculated values of the EDGEe. Secondly, the air gap above the EDGEe silicon chip was optimised empirically. Nine different air gap “tops” were placed above the EDGEe (air depth = 0.3, 0.6, 0.9 mm; air width = 3.06, 4.59, 6.13 mm). The sensitivity of the EDGEe was plotted as a function of air gap thickness for the field sizes measured. Results: The transfer of kq,clin,kq,msr from the SFD to the EDGEe was correct to within the simulation and measurement uncertainties. The EDGEe detector can be made “correction-less” for field sizes of 5 and 6 mm, but was ∼2% from being “correction-less” at field sizes of 8 and 10 mm. Conclusion Different materials will perturb small fields in different ways. A detector is only “correction-less” if all these perturbations happen to cancel out. Designing a “correction-less” diode is a complicated process, thus it is reasonable to expect that Monte Carlo simulations should play an important role.

Design and experimental testing of air slab caps which convert commercial electron diodes into dual purpose, correction-free diodes for small field dosimetry

Purpose Two diodes which do not require correction factors for small field relative output measurements are designed and validated using experimental methodology. This was achieved by adding an air layer above the active volume of the diode detectors, which canceled out the increase in response of the diodes in small fields relative to standard field sizes. Methods Due to the increased density of silicon and other components within a diode, additional electrons are created. In very small fields, a very small air gap acts as an effective filter of electrons with a high angle of incidence. The aim was to design a diode that balanced these perturbations to give a response similar to a water-only geometry. Three thicknesses of air were placed at the proximal end of a PTW 60017 electron diode (PTWe) using an adjustable “air cap”. A set of output ratios (ORfclin Det ) for square field sizes of side length down to 5 mm was measured using each air thickness and compared to ORfclin Det measured using an IBA stereotactic field diode (SFD). k fclin, f msr Qclin,Qmsr was transferred from the SFD to the PTWe diode and plotted as a function of air gap thickness for each field size. This enabled the optimal air gap thickness to be obtained by observing which thickness of air was required such that k fclin, f msr Qclin,Qmsr was equal to 1.00 at all field sizes. A similar procedure was used to find the optimal air thickness required to make a modified Sun Nuclear EDGE detector (EDGEe) which s “correction-free” in small field relative dosimetry. In addition, the feasibility of experimentally transferring k fclin, f msr Qclin,Qmsr values from the SFD to unknown diodes was tested by comparing the experimentally transferred k fclin, f msr Qclin,Qmsr values for unmodified PTWe and EDGEe diodes to Monte Carlo simulated values. Results 1.0 mm of air was required to make the PTWe diode correction-free. This modified diode (PTWeair) produced output factors equivalent to those in water at all field sizes (5–50 mm). The optimal air thickness required for the EDGEe diode was found to be 0.6 mm. The modified diode (EDGEeair) produced output factors equivalent to those in water, except at field sizes of 8 and 10 mm where it measured approximately 2% greater than the relative dose to water. The experimentally calculated k fclin, f msr Qclin,Qmsr for both the PTWe and the EDGEe diodes (without air) matched Monte Carlo simulated results, thus proving that it is feasible to transfer k fclin, f msr Qclin,Qmsr from one commercially available detector to another using experimental methods and the recommended experimental setup. Conclusions It is possible to create a diode which does not require corrections for small field output factor measurements. This has been performed and verified experimentally. The ability of a detector to be “correction-free” depends strongly on its design and composition. A nonwater-equivalent detector can only be “correction-free” if competing perturbations of the beam cancel out at all field sizes. This should not be confused with true water equivalency of a detector.