On the prediction of structural layout for maximum stiffness

A variational formulation is presented for the problem of predicting the optimal structural system from among a discrete set of possible designs. The development is written for maximum stiffness design of single-purpose structures. The distribution among admissible structural configurations of the prescribed loads is determined as part of the solution. An extremum problem interpretation also provides the basis for evaluating relative efficiencies among locally optimal structural systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45197/1/10957_2004_Article_BF00933027.pd

Tensile Fracture of Welded Polymer Interfaces: Miscibility, Entanglements and Crazing

Large-scale molecular simulations are performed to investigate tensile failure of polymer interfaces as a function of welding time $t$. Changes in the tensile stress, mode of failure and interfacial fracture energy $G_I$ are correlated to changes in the interfacial entanglements as determined from Primitive Path Analysis. Bulk polymers fail through craze formation, followed by craze breakdown through chain scission. At small $t$ welded interfaces are not strong enough to support craze formation and fail at small strains through chain pullout at the interface. Once chains have formed an average of about one entanglement across the interface, a stable craze is formed throughout the sample. The failure stress of the craze rises with welding time and the mode of craze breakdown changes from chain pullout to chain scission as the interface approaches bulk strength. The interfacial fracture energy $G_I$ is calculated by coupling the simulation results to a continuum fracture mechanics model. As in experiment, $G_I$ increases as $t^{1/2}$ before saturating at the average bulk fracture energy $G_b$. As in previous simulations of shear strength, saturation coincides with the recovery of the bulk entanglement density. Before saturation, $G_I$ is proportional to the areal density of interfacial entanglements. Immiscibiltiy limits interdiffusion and thus suppresses entanglements at the interface. Even small degrees of immisciblity reduce interfacial entanglements enough that failure occurs by chain pullout and $G_I \ll G_b$

Band Formation during Gaseous Diffusion in Aerogels

We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides of and react in silica aerogel rods with porosity of 92 % and average pore size of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin sheet-like structures. We present a numerical study of the phenomenon. Due to the difference in boundary conditions between this system and those usually studied, we find the sheet-like structures in the aerogel to differ significantly from older studies. The influence of random nucleation centers and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on request from author

Interfacial layering in a three-component polymer system

We study theoretically the temporal evolution and the spatial structure of the interface between two polymer melts involving three different species (A, A* and B). The first melt is composed of two different polymer species A and A* which are fairly indifferent to one another (Flory parameter chi_AA* ~ 0). The second melt is made of a pure polymer B which is strongly attracted to species A (chi_AB 0). We then show that, due to these contradictory tendencies, interesting properties arise during the evolution of the interface after the melts are put into contact: as diffusion proceeds, the interface structures into several adjacent "compartments", or layers, of differing chemical compositions, and in addition, the central mixing layer grows in a very asymmetric fashion. Such unusual behaviour might lead to interesting mechanical properties, and demonstrates on a specific case the potential richness of multi-component polymer interfaces (as compared to conventional two-component interfaces) for various applications.Comment: Revised version, to appear in Macromolecule

Improved timed-mating, non-invasive method using fewer unproven female rats with pregnancy validation via early body mass increases

For studies requiring accurate conception-timing, reliable, efficient methods of detecting oestrus reduce time and costs, whilst improving welfare. Standard methods use vaginal cytology to stage cycle, and breeders are paired–up using approximately five proven females with proven males to achieve at least one conception on a specific day. We describe an alternative, fast, consistent, non-invasive method of timed-mating using detection of lordosis behaviour in Wistar and Lister-Hooded rats that used unproven females with high success rates. Rats under reverse-lighting had body masses recorded pre-mating, day (d) 3-4, d8, d10 and d18 of pregnancy. Using only the presence of the oestrus dance to time-mate females for 24-hrs, 89% Wistar and 88% Lister-Hooded rats successfully conceived. We did not observe behavioural oestrus in Sprague-Dawleys without males present. Significant body mass increases following mating distinguished pregnant from non-pregnant rats, as early as d4 of pregnancy (10% ± 1.0 increase cf 3% ± 1.2). The pattern of increases throughout gestation was similar for all pregnant rats until late pregnancy, when there were smaller increases for primi- and multiparous rats (32% ± 2.5; 25% ± 2.4), whereas nulliparous rats had highest gains (38% ± 1.5). This method demonstrated a distinct refinement of the previous timed-mating common practice used, as disturbance of females was minimised. Only the number required of nulli-, primi- or multiparous rats were mated, and body mass increases validated pregnancy status. This new breeding-management method is now established practice for two strains of rat and resulted in a reduction in animal use

Quasi-single helicity spectra in the Madison Symmetric Torus

Evidence of a self-organized collapse towards a narrow spectrum of magnetic instabilities in the Madison Symmetric Torus [R. N. Dexter, D. W. Kerst, T. W. Lovell, S. C. Prager, and J. C. Sprott, Fusion Technol. 19, 131 (1991)] reversed field pinch device is presented. In this collapsed state, dubbed quasi-single helicity (QSH), the spectrum of magnetic modes condenses spontaneously to one dominant mode more completely than ever before observed. The amplitudes of all but the largest of the m=1 modes decrease in QSH states. New results about thermal features of QSH spectra and the identification of global control parameters for their onset are also discussed

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure

Formation of Liesegang patterns: A spinodal decomposition scenario

Spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of Liesegang bands. This mechanism yields a sequence of band positions x_n that obeys the spacing law x_n~Q(1+p)^n. The dependence of the parameters p and Q on the initial concentration of the reagents is determined and we find that the functional form of p is in agreement with the experimentally observed Matalon-Packter law.Comment: RevTex, 4 pages, 4 eps figure