Similarity transformations for the two-dimensional, unsteady, stream-function equation

The methods described by Bluman & Cole (1974) are used to derive the infinitesimals of the general invariance group of the unsteady, two-dimensional, stream-function equation for the case where the kinematic viscosity v is equal to a constant and the case where v = 0. The infinitesimals in each case involve ten independent parameters, seven of which appear explicitly and three of which are contained implicitly in three arbitrary functions of time. The various finite groups and similarity transformations which may be derived from the infinitesimals are discussed through examples. Two of the arbitrary functions of time are non-trivial and represent invariance of the stream-function equation under a transformation to a co-ordinate system which moves in a non-uniform irrotational fashion. A general similarity form is derived for which the equations dx/dt = u(x, y, t) and dy/dt = v(x, y, t) for the particle paths may be reduced to an autonomous system. This form is general enough to suggest the hypothesis that, under certain restrictions, the entrainment processes of unsteady flows dominated by two-dimensional large-scale motions may be displayed diagrammatically on a phase-plane plot of particle trajectories

Transition and mixing in axisymmetric jets and vortex rings

A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case

The effects of road commentary training on novice drivers' visual search behaviour: A preliminary investigation

One of the major challenges facing novice drivers seems to be adequately scanning, detecting, and responding to hazards which present during the course of everyday driving; a process that involves ‘reading the road’ and modifying driver behaviour accordingly. Previous studies have indicated that inexperienced drivers tend to utilise only a small proportion of the visual field when driving, and this limited visual search behaviour may play a significant role in the over-representation of young novice drivers’ involvement in crashes. This deficiency in visual search is especially evidenced through crashes occurring at intersections, or other densely populated road environments. More recently, road commentary has become of interest within a number of driver education initiatives, and several current studies have indicated that road commentary indeed improves drivers’ performance in hazard perception tasks. However, relatively little is known about commentaries influence on the underlying cognitive mechanisms responsible for enhanced situation awareness or hazard awareness, and whether such improvements generalize to a broader range of road scenarios. Using hazard perception and eye-tracking measures, we started to examine how road commentary could influence the way drivers visually accrue and process essential road information. First, our data confirmed that commentary training significantly increased the percentage of hazards identified. But additionally, preliminary eye movement data indicated that road commentary may have influenced visual search behaviour of the participants by ‘prompting’ them to allocate extra visual attention capacity to hazard rich areas, as evidenced by an increase of their fixation clusters across the visual field. This could help increase situation awareness, and convert to safer driving behaviour and reduced risk-taking

Rapid Design and Manufacture of Ultralight Cellular Materials

This paper details the design, manufacture and testing of regular metallic lattice structures with unit cell sizes in the range 0.8mm to 5mm and truss elements of 100-500 µm in diameter [1]. The structures were manufactured using Selective Laser Melting (SLM) technology from 316L stainless steel. Compression tests have shown yield loadings of over 3.5kN despite being only 18mm by 18mm by 10mm in height, the results are favourably comparable to current commercially available metallic foams. Software has been developed that creates slice files without the use of CAD software or STL files and is capable of producing lattices within a volume defined by a STL file.Mechanical Engineerin

A numerical study of viscous vortex rings using a spectral method

Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass

High velocity impact resistance of fibre metal laminates

The high velocity impact resistance of fibre metal laminates (FMLs) based on combinations of three different aluminium alloys (6161-O, 6061-T6, 7075-T6) and a glass fibre reinforced epoxy resin have been investigated both experimentally and numerically. A series of perforation tests on multilayer configurations, ranging from a simple 2/1 lay-up to a seven ply 4/3 laminate. High velocity impact was conducted using a projectile gas-gun launcher, operating in the velocity range between 119 m/s and 252 m/s.[1] The impact response of fibre metal laminates samples was characterised by determining the energy required to perforate the panels. A stereoscopic Digital Image Correlation (DIC) method was adopted to measure full-field deformations and strain for FMLs which providing the full field strain history and 3D measurements up to sample perforation. The perforation resistance of the panels was predicted using the finite element analysis package Abaqus/Explicit. A vectorized user-defined material subroutine (VUMAT) was employed to define Hashin’s 3D rate-dependant damage criteria for the composite layers. The subroutine was implemented into the commercial finite element software ABAQUS/Explicit to simulate the deformation and failure of FMLs. Agreement between the predictions of the finite element models and the experimental data was good across the range of configurations. Ballistic limit of those FMLs was obtained from both the experimental tests and numerical approaches

Efficient method for estimating the number of communities in a network

While there exist a wide range of effective methods for community detection in networks, most of them require one to know in advance how many communities one is looking for. Here we present a method for estimating the number of communities in a network using a combination of Bayesian inference with a novel prior and an efficient Monte Carlo sampling scheme. We test the method extensively on both real and computer-generated networks, showing that it performs accurately and consistently, even in cases where groups are widely varying in size or structure.Comment: 13 pages, 4 figure

Admission to psychiatric hospital for mental illnesses 2 years prechildbirth and postchildbirth in Scotland: a health informatics approach to assessing mother and child outcomes

Objective: To identify factors associated with: admission to a specialist mother and baby unit (MBU) and the impact of perinatal mental illness on early childhood development using a data linkage approach in the 2 years prechildbirth and postchildbirth. Methods: Scottish maternity records (SMR02) were linked to psychiatric hospital admissions (SMR04). 3290 pregnancy-related psychiatric admissions for 1730 women were assessed. To investigate factors associated with MBU admission, the group of mothers admitted to an MBU were compared with those admitted to general psychiatric wards. To assess the impact of perinatal mental illness on early child development, a pragmatic indicator for ‘at potential risk of adversity’, defined as a child who was recorded as requiring intensive treatment at any time under the health plan indicators (HPI) and/or who had no record of completing three doses of the 5-in-1 vaccine by 12 months was generated. Logistic regression models were used to describe the association between each variable and the risk of admission between those with a history of prior psychiatric admission and those without. Results Women admitted to an MBU were significantly more likely to be admitted with non-affective psychosis (OR=1.97, 95% CI 1.22 to 3.18), affective psychosis (OR=2.44, 95% CI 1.37 to 4.33) and non-psychotic depressive episodes (OR=1.93, 95% CI 1.42 to 2.63). They were less likely to come from deprived areas (OR=0.68 95% CI 0.49 to 0.93). Women with a previous history of psychiatric admission were significantly more likely to be located in the two most deprived quintiles. Almost one-third (29%) of children born to mothers with a pregnancy-related psychiatric admission were assessed as ‘at potential risk of adversity.’ Conclusions: A health informatics approach has potential for improving understanding of social and clinical factors, which contribute to the outcomes of perinatal mental illness, as well as potential adverse developmental outcomes for offspring