A comparison of limited-stretch models of rubber elasticity

In this paper we describe various limited-stretch models of non-linear rubber elasticity, each dependent on only the first invariant of the left Cauchy-Green strain tensor and having only two independent material constants. The models are described as limited-stretch, or restricted elastic, because the strain energy and stress response become infinite at a finite value of the first invariant. These models describe well the limited stretch of the polymer chains of which rubber is composed. We discuss Gent's model which is the simplest limited-stretch model and agrees well with experiment. Various statistical models are then described: the one-chain, three-chain, four-chain and Arruda-Boyce eight-chain models, all of which involve the inverse Langevin function. A numerical comparison between the three-chain and eight-chain models is provided. Next, we compare various models which involve approximations to the inverse Langevin function with the exact inverse Langevin function of the eight-chain model. A new approximate model is proposed that is as simple as Cohen's original model but significantly more accurate. We show that effectively the eight-chain model may be regarded as a linear combination of the neo-Hookean and Gent models. Treloar's model is shown to have about half the percentage error of our new model but it is much more complicated. For completeness a modified Treloar model is introduced but this is only slightly more accurate than Treloar's original model. For the deformations of uniaxial tension, biaxial tension, pure shear and simple shear we compare the accuracy of these models, and that of Puso, with the eight-chain model by means of graphs and a table. Our approximations compare extremely well with models frequently used and described in the literature, having the smallest mean percentage error over most of the range of the argument

Micromechanics of Single Supercoiled DNA Molecules

Abstract. The theory of the mechanical response of single DNA molecules un-der stretching and twisting stresses is reviewed. Using established results for the the semiflexible polymer including the effect of torsional stress, and for the free energy of plectonemic supercoils, a theory of coexisting plectonemic and extended DNA is con-structed and shown to produce phenomena observed experimentally. Analytical results for DNA extension and torque are presented, and effects of anharmonicities in the plec-tonemic free energy are described. An application of the theory to the problem of torsional-stress-induced cruciform extrusion is also discussed. Key words. DNA, molecular biology, statistical mechanics, polymer physics. AMS(MOS) subject classifications. 82D60, 92C05, 92C40

The epizootiology of Lyme disease in upland habitats of north west England

SIGLEAvailable from British Library Document Supply Centre-DSC:D191481 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

The Incremental Bulk Modulus, Young's Modulus and Poisson's Ratio in Nonlinear Isotropic Elasticity: Physically Reasonable Response

An incremental (or tangent) bulk modulus for finite isotropic elasticity is defined which compares an increment in hydrostatic pressure with the corresponding increment in relative volume. Its positivity provides a stringent criterion for physically reasonable response involving the second derivatives of the strain energy function. Also, an average (or secant) bulk modulus is defined by comparing the current stress with the relative volume change. The positivity of this bulk modulus provides a physically reasonable response criterion less stringent than the former. The concept of incremental bulk modulus is extended to anisotropic elasticity. For states of uniaxial tension an incremental Poisson's ratio and an incremental Young's modulus are similarly defined for nonlinear isotropic elasticity and have properties similar to those of the incremental bulk modulus. The incremental Poisson's ratios for the isotropic constraints of incompressibility, Bell, Ericksen, and constant area are considered. The incremental moduli are all evaluated for a specific example of the compressible neo-Hookean solid. Bounds on the ground state Lam\'{e} elastic moduli, assumed positive, are given which are sufficient to guarantee the positivity of the incremental bulk and Young's moduli for all strains. However, although the ground state Poisson's ratio is positive we find that the incremental Poisson's ratio becomes negative for large enough axial extensions.Comment: 16 page

An address delivered at the opening of Portsmouth Academy, on Easter Monday, A.D. 1791, [electronic resource] : by the Reverend John Cosens Ogden, Rector of St. John's Church.

Signatures: [A]p4s B-Dp4s Ep2s (E2 verso blank)Evans,Sabin,Electronic reproduction.English Short Title Catalog,Reproduction of original from British Library

Prevalence and determinants of <i>Cryptosporidium</i> spp. infection in smallholder dairy cattle in Iringa and Tanga Regions of Tanzania

The prevalence of Cryptosporidium spp. infection in a cross-sectional study of dairy cattle, from two contrasting dairying regions in Tanzania, were determined by staining smears of faecal samples with the modified Ziehl-Neelsen technique. Of the 1 126 faecal samples screened, 19.7% were positive for Cryptosporidium spp. The prevalence was lower in Tanga Region than in Iringa Region. The prevalence of affected farms was 20% in Tanga and 21% in Iringa. In both regions, the probability of detecting Cryptosporidium oocysts in faeces varied with animal class, but these were not consistent in both regions. In Tanga Region, Cryptosporidium oocysts were significantly more likely to be found in the faeces of milking cows. In Iringa Region, the likelihood that cattle had Cryptosporidium-positive faeces declined with age, and milking cattle were significantly less likely to have Cryptosporidium positive faeces. In this region, 7% of cattle were housed within the family house at night, and this was marginally associated with a higher likelihood that animals had Cryptosporidium-positive faeces. Our study suggests that even though herd sizes are small, Cryptosporidium spp. are endemic on many Tanzanian smallholder dairy farms. These protozoa may impact on animal health and production, but also on human health, given the close associations between the cattle and their keepers. Further studies are required to assess these risks in more detail, and understand the epidemiology of Cryptosporidium spp. in this management system