Application of Uniform Asymptotics to the Second Painlevé Transcendent

In this work we propose a new method for investigating connection problems for the class of nonlinear second‐order differential equations known as the Painlevé equations. Such problems can be characterized by the question as to how the asymptotic behaviours of solutions are related as the independent variable is allowed to pass towards infinity along different directions in the complex plane. Connection problems have been previously tackled by a variety of methods. Frequently these are based on the ideas of isomonodromic deformation and the matching of WKB solutions. However, the implementation of these methods often tends to be heuristic in nature and so the task of rigorising the process is complicated. The method we propose here develops uniform approximations to solutions. This removes the need to match solutions, is rigorous, and can lead to the solution of connection problems with minimal computational effort. Our method relies on finding uniform approximations of differ ential equations of the generic form as the complex‐valued parameter . The details of the treatment rely heavily on the locations of the zeros of the function F in this limit. If they are isolated, then a uniform approximation to solutions can be derived in terms of Airy functions of suitable argument. On the other hand, if two of the zeros of F coalesce as , then an approximation can be derived in terms of parabolic cylinder functions. In this paper we discuss both cases, but illustrate our technique in action by applying the parabolic cylinder case to the “classical” connection problem associated with the second Painlevé transcendent. Future papers will show how the technique can be applied with very little change to the other Painlevé equations, and to the wider problem of the asymptotic behavio ur of the general solution to any of these equations. (Accepted May 15, 1997)     

The rigid movable inclusion in elastostatics and elastodynamics

The problem of a single rigid movable inclusion is solved both for elastostatics and elastodynamic, using the null field approach. It is also shown how the solution can be obtained as the limit of the solution for an elastic inclusion. Numerical results for scattering by a superspheroidal inclusion are given.     

Nonlinear analysis of multilayered shells

A large deformation theory for layered shells of arbitrarily varying thickness and using a piecewise smooth displacement field is developed. A system of layer coordinates is introduced which allows the results to be presented in a simple compact form analogous to the theory of monocoque shells.     

Time resolved measurements of the flow generated by suction feeding fish

The majority of aquatic vertebrates are suction feeders: by rapidly expanding the mouth cavity they generate a fluid flow outside of their head in order to draw prey into their mouth. In addition to the biological relevance, the generated flow field is interesting fluid mechanically as it incorporates high velocities, is localized in front of the mouth, and is unsteady, typically lasting between 10 and 50 ms. Using manometry and high-speed particle image velocimetry, this is the first study to quantify pressure within and outside the mouth of a feeding fish while simultaneously measuring the velocity field outside the mouth. Measurements with a high temporal (2 ms) and spatial (<1 mm) resolution were made for several feeding events of a single largemouth bass (Micropterus salmoides). General properties of the flow were evaluated, including the transient velocity field, its relationship to pressure within the mouth and pressure at the prey. We find that throughout the feeding event a relationship exists for the magnitude of fluid speed as a function of distance from the predator mouth that is based on scaling the velocity field according to the size of the mouth opening and the magnitude of fluid speed at the mouth. The velocity field is concentrated within an area extending approximately one mouth diameter from the fish and the generated pressure field is even more local to the mouth aperture. Although peak suction pressures measured inside the mouth were slightly larger than those that were predicted using the equations of motion, we find that these equations give a very accurate prediction of the timing of peak pressure, so long as the unsteady nature of the flow is included.     

Large-deformation properties of wheat dough in uni- and biaxial extension. Part II. Gluten dough

Glutens were isolated from flour of three European wheat cultivars which perform differently in cereal products. The rheological and fracture properties of gluten-water doughs were determined in uniaxial and biaxial extension at large deformations and small angle sinusoidal oscillation tests and compared with the mechanical properties of the parental flour doughs. At 25 °C the linear region was in the same range as that of flour dough, while at a higher temperature (45 °C) the linear region was more than an order of magnitude higher. At 45 °C the storage modulus and tan were lower than at 25 °C. Variation in moduli between cultivars was much more pronounced for gluten than for flour doughs.Similarly to flour dough in both uniaxial and biaxial extension the stress () increased more than proportionally with the strain, a phenomenon called strain hardening. The stress at a set strain and strain hardening depended much more strongly on the type of deformation for gluten than for flour dough: was higher in biaxial extension for gluten than for flour dough, but was much higher in uniaxial extension. This indicates that orientational effects in elongational flow are of even larger importance for the mechanical properties of gluten than of flour dough. It is likely that it is the glutenin fraction that, because of its large size, confers these direction dependent properties to gluten and flour doughs. Fracture stresses were much higher for gluten than for flour dough, while fracture strains were in the same range or higher. For gluten dough fracture strains increased less strongly with increasing strain rate than for flour dough. Glutens exhibiting a higher stress at a certain strain had a smaller fracture strain.Our findings confirm the conviction that the large deformation properties of flour dough are mainly governed by the gluten fraction. However, there are also differences. Compared to flour dough gluten dough exhibits (i) a stronger strain hardening, (ii) a larger difference in between uniaxial and biaxial extension and (iii) a smaller strain rate dependency of the fracture strain.     

A phenomenological model of electrorheological fluids

The fundamental assumption of the paper is that the extra stress tensor of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation and length N of the fibers formed by application of an electric field). The resulting constitutive equation for is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of and N on leads to the Bingham behavior for and power law behavior for large shear rates.

Flow-induced structure in a system of nuclear waste simulant slurries

Thixotropy and antithixotropy were characterized in nuclear waste simulant slurries. For the neutralized current acid nuclear waste (NCAW) simulant slurries, NCAW with glycolic acid (NCAW+GA), and NCAW with nitric acid (NCAW+NA) (pH 4), a pre-shear flow at constant shear rate destroys the aggregates in the suspension and reduces viscosity. For the NCAW+NA (pH7–9), a pre-shear enhances the aggregates in the suspension and increases viscosity. With the addition of silica to the NCAW+GA and NCAW+NA slurries, the pre-shear effect tends to promote aggregation due to the formation of a network in the suspension, and hence, the viscosity increases. The macroscopic rheological property variation due to the microstructural aspects of the suspensions associated with the shear-induced effect are addressed.     

Convective heat transfer characteristics of microencapsulated phase change material suspensions in minichannels

A comparative experimental study was conducted in order to investigate the convective heat transfer characteristics of water-based suspensions of microencapsulated phase change material (MEPCM) flowing through rectangular copper minichannels. The hydraulic diameter of the channels was 2.71 mm. MEPCM particles with an average size of 4.97 μm were used to form suspensions with mass concentrations ranging from 0 to 20%. The comparative experiments were performed for varying mass flow rates in the laminar region and varying thermal conditions. The cooling performance of the MEPCM suspensions strongly depended on the mass flow rate and the MEPCM mass concentration. The 5% suspension always showed a better cooling performance than water resulting in lower wall temperatures and enhanced heat transfer coefficients within the whole range of mass flow rates. The suspensions with higher mass concentrations, however, were more effective only at low mass flow rates. At higher mass flow rates they showed a less effective cooling performance than water.     

PopGen: population-based recruitment of patients and controls for the analysis of complex genotype-phenotype relationships

OBJECTIVE: Patient samples used for mapping complex human disease genes are unlikely to be representative of the phenotype spectrum of the respective population as a whole. On the other hand, most ongoing prospective studies are probably too small for evaluating polygenic disease markers. DESIGN: Precise estimates of population-specific genotypic risks can be obtained efficiently through the complete ascertainment of patients in a geographically confined area. The PopGen project uses the most northern part of Germany as a target region for such a pursuit. RESULTS: PopGen currently pursues recruitment, sampling and processing activities in close collaboration with a multitude of clinical partners, covering cardiovascular, neuropsychiatric and environmental diseases. CONCLUSION: PopGen has successfully established itself as a large-scale genetic epidemiological project of international recognition.