Large Parameter Cases of the Gauss Hypergeometric Function

We consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters a, b, c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Krawtchouk, Meixner, etc.), which results are already available and which cases need more attention. We also consider a few examples of 3F2-functions of unit argument, to explain which difficulties arise in these cases, when standard integrals or differential equations are not available.Comment: 21 pages, 4 figure

Fluid flow and heat transfer in a dual-wet micro heat pipe

Micro heat pipes have been used to cool micro electronic devices, but their heat transfer coefficients are low compared with those of conventional heat pipes. In this work, a dual-wet pipe is proposed as a model to study heat transfer in micro heat pipes. The dual-wet pipe has a long and narrow cavity of rectangular cross-section. The bottom-half of the horizontal pipe is made of a wetting material, and the top-half of a non-wetting material. A wetting liquid fills the bottom half of the cavity, while its vapour fills the rest. This configuration ensures that the liquid–vapour interface is pinned at the contact line. As one end of the pipe is heated, the liquid evaporates and increases the vapour pressure. The higher pressure drives the vapour to the cold end where the vapour condenses and releases the latent heat. The condensate moves along the bottom half of the pipe back to the hot end to complete the cycle. We solve the steady-flow problem assuming a small imposed temperature difference between the two ends of the pipe. This leads to skew-symmetric fluid flow and temperature distribution along the pipe so that we only need to focus on the evaporative half of the pipe. Since the pipe is slender, the axial flow gradients are much smaller than the cross-stream gradients. Thus, we can treat the evaporative flow in a cross-sectional plane as two-dimensional. This evaporative motion is governed by two dimensionless parameters: an evaporation number E defined as the ratio of the evaporative heat flux at the interface to the conductive heat flux in the liquid, and a Marangoni number M. The motion is solved in the limit E→∞ and M→∞. It is found that evaporation occurs mainly near the contact line in a small region of size E−1W, where W is the half-width of the pipe. The non-dimensional evaporation rate Q* ~ E−1 ln E as determined by matched asymptotic expansions. We use this result to derive analytical solutions for the temperature distribution Tp and vapour and liquid flows along the pipe. The solutions depend on three dimensionless parameters: the heat-pipe number H, which is the ratio of heat transfer by vapour flow to that by conduction in the pipe wall and liquid, the ratio R of viscous resistance of vapour flow to interfacial evaporation resistance, and the aspect ratio S. If HRxs226B1, a thermal boundary layer appears near the pipe end, the width of which scales as (HR)−1/2L, where L is the half-length of the pipe. A similar boundary layer exists at the cold end. Outside the boundary layers, Tp varies linearly with a gradual slope. Thus, these regions correspond to the evaporative, adiabatic and condensing regions commonly observed in conventional heat pipes. This is the first time that the distinct regions have been captured by a single solution, without prior assumptions of their existence. If HR ~ 1 or less, then Tp is linear almost everywhere. This is the case found in most micro-heat-pipe experiments. Our analysis of the dual-wet pipe provides an explanation for the comparatively low effective thermal conductivity in micro heat pipes, and points to ways of improving their heat transfer capabilities

Improving the Justice System: Victims of Crime Workshop

This report showcases the outcomes of the Improving the Justice System: Victims of Crime workshop in June 2014. This one-day workshop brought together Government and non-Government organisations who work with, and represent victims of crime in NSW to create a clear program of reform for the system to better serve victims of crime

A 6-year-old boy presenting with traumatic evisceration following a bicycle handle bar injury: a case report

We report the case of a 6-year-old boy presenting with small bowel evisceration following a fall onto a bicycle handle-bar. His case is presented, a review of the literature performed and interesting photos pre and post-op are presented

The capacity of people with a ‘mental disability’ to make a health care decision

Background. Based on the developing clinical and legal literature, and using the framework adopted in draft legislation, capacity to make a valid decision about a clinically required blood test was investigated in three groups of people with a ‘mental disability’ (i.e. mental illness (chronic schizophrenia), ‘learning disability’ (‘mental retardation’, or intellectual or developmental disability), or, dementia) and a fourth, comparison group. Methods. The three ‘mental disability’ groups (N = 20 in the ‘learning disability’ group, N = 21 in each of the other two groups) were recruited through the relevant local clinical services; and through a phlebotomy clinic for the ‘general population’ comparison group (N = 20). The decision-making task was progressively simplified by presenting the relevant information as separate elements and modifying the assessment of capacity so that responding became gradually less dependent on expressive verbal ability. Results. Compared with the ‘general population’ group, capacity to make the particular decision was significantly more impaired in the ‘learning disability’ and ‘dementia’ groups. Importantly, however, it was not more impaired among the ‘mental illness’ group. All the groups benefited as the decision-making task was simplified, but at different stages. In each of the ‘mental disability’ groups, one participant benefited only when responding did not require any expensive verbal ability. Conclusions. Consistent with current views, capacity reflected an interaction between the decision-maker and the demands of the decision-making task. The findings have implications for the way in which decisions about health care interventions are sought from people with a ‘mental disability’. The methodology may be extended to assess capacity to make other legally-significant decisions.published_or_final_versio

Uniform Asymptotic Methods for Integrals

We give an overview of basic methods that can be used for obtaining asymptotic expansions of integrals: Watson's lemma, Laplace's method, the saddle point method, and the method of stationary phase. Certain developments in the field of asymptotic analysis will be compared with De Bruijn's book {\em Asymptotic Methods in Analysis}. The classical methods can be modified for obtaining expansions that hold uniformly with respect to additional parameters. We give an overview of examples in which special functions, such as the complementary error function, Airy functions, and Bessel functions, are used as approximations in uniform asymptotic expansions.Comment: 31 pages, 3 figure

Computerized exposure therapy for Spider Phobia: Effects of cardiac timing and interoceptive ability on subjective and behavioral outcomes

Objective: Spider phobia is a common form of anxiety disorder for which exposure therapy is an effective first-line treatment. Motivated by the observed modulation of threat processing by afferent cardiac signals; we tested the hypothesis that interoceptive information concerning cardiovascular arousal can influence the outcomes of computerised exposure therapy for spider phobia. Method: Fifty-three normal healthy participants with high spider phobia scores underwent one of three modified computerised exposure protocols, defined by the timing of exposure to brief spider stimuli within the cardiac cycle: Systole (during afferent baroreceptor firing); Diastole (during baroreceptor-quiescent interbeat interval); Random (non-contingent on cardiac cycle). Outcomes were judged on phobic and anxiety measures and physiological data (skin conductance). Subjects were also rated on interoceptive accuracy. Results: Mancova analysis showed that timing group affected the outcome measures (F(10,80)=2.405, p=0.015) and there was a group interaction with interoception ability (F(15,110)=1.808, p=0.045). Subjective symptom reduction (SPQ) was greatest in the Systolic group relative to the other two groups (Diastolic (t=3.115, ptukey=0.009); Random (t=2.438, ptukey=0.048), with greatest reductions in those participants with lower interoceptive accuracy. Behavioural aversion (BAT) reduced more in cardiac-contingent groups than the non-contingent (Random) group (Diastolic (t=3.295, ptukey=0.005); Systolic (t=2.602, ptukey=0.032). Physiological (SCR) responses remained strongest for spider stimuli presented at cardiac systole. Conclusion: Interoceptive information influences exposure benefit. The reduction in the subjective expression of fear/phobia is facilitated by ‘bottom-up’ afferent signals; while improvement in the behavioural expression is further dependent on ‘top-down’ representation of Interoceptive effects in spider phobia treatment self-related physiology (heart rhythm). Individual interoceptive differences moderate these effects, suggesting means to personalise therapy

Towards an understanding of the burdens of medication management affecting older people: the MEMORABLE realist synthesis

Background More older people are living in the community with multiple diagnoses and medications. Managing multiple medications produces issues of unrivalled complexity for those involved. Despite increasing literature on the subject, gaps remain in understanding how, why and for whom complex medication management works, and therefore how best to improve practice and outcomes. MEMORABLE, MEdication Management in Older people: Realist Approaches Based on Literature and Evaluation, aimed to address these gaps. Methods MEMORABLE used realism to understand causal paths within medication management. Informed by RAMESES (Realist And Meta-narrative Evidence Synthesis: and Evolving Standards) guidelines, MEMORABLE involved three overlapping work packages: 1) Realist Review of the literature (24 articles on medication management exploring causality); 2) Realist Evaluation (50 realist-informed interviews with older people, family carers and health and care practitioners, explaining their experiences); and 3) data synthesis and theorising from 1) and 2). Results Medication management was viewed from the perspective of ‘implementation’ and structured into five stages: identifying a problem (Stage 1), getting a diagnosis and/or medications (Stage 2), starting, changing or stopping medications (Stage 3), continuing to take medications (Stage 4), and reviewing/reconciling medications (Stage 5). Three individual stages (1, 3 and 4) are conducted by the older person sometimes with family carer support when they balance routines, coping and risk. Stages 2 and 5 are interpersonal where the older person works with a practitioner-prescriber-reviewer, perhaps with carer involvement. Applying Normalisation Process Theory, four steps were identified within each stage: 1) sense making: information, clarification; 2) action: shared-decision-making; 3) reflection/monitoring; and 4) enduring relationships, based on collaboration and mutual trust. In a detailed analysis of Stage 5: Reviewing/reconciling medications, adopting the lens of ‘burden’, MEMORABLE identified five burdens amenable to mitigation: ambiguity, concealment, unfamiliarity, fragmentation and exclusion. Two initial improvement propositions were identified for further research: a risk screening tool and individualised information. Conclusions Older people and family carers often find medication management challenging and burdensome particularly for complex regimens. Practitioners need to be aware of this potential challenge, and work with older people and their carers to minimise the burden associated with medication management. Trial registration PROSPERO 2016:CRD42016043506

Processing maps for wrinkle free and quality enhanced parts by shear spinning

An experimental investigation was conducted to study the effects of key processing parameters when shear spinning conical part geometries from both aluminium alloy and mild steel disc shaped blanks. It investigated the effects of feed ratio, spindle speed, initial blank thickness, and thickness reduction on the occurrence of the wrinkling failure, effectiveness of thickness reduction, part springback, surface finish, and strain hardening effects resulting from the process. A design of experiments approach was used to conduct the experimental tests and a multi-variate regression analysis method was applied to obtain processing maps of the key parameters which produced wrinkling free and quality enhanced spun parts. The results showed that the feed ratio was the most critical processing parameter, with higher feed ratios led to the onset of wrinkling failure, less effective thickness reduction, more part springback and rougher part surfaces. The process was shown to result in a significant strain hardening effect in the blank material, which was found to be enhanced when the amount of blank thickness reduction was increased