Application of discontinuity layout optimization to plane plasticity problems

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained

On being the right size as an animal with plastids

Plastids typically reside in plant or algal cells—with one notable exception. There is one group of multicellular animals, sea slugs in the order Sacoglossa, members of which feed on siphonaceous algae. The slugs sequester the ingested plastids in the cytosol of cells in their digestive gland, giving the animals the color of leaves. In a few species of slugs, including members of the genus Elysia, the stolen plastids (kleptoplasts) can remain morphologically intact for weeks and months, surrounded by the animal cytosol, which is separated from the plastid stroma by only the inner and outer plastid membranes. The kleptoplasts of the Sacoglossa are the only case described so far in nature where plastids interface directly with the metazoan cytosol. That makes them interesting in their own right, but it has also led to the idea that it might someday be possible to engineer photosynthetic animals. Is that really possible? And if so, how big would the photosynthetic organs of such animals need to be? Here we provide two sets of calculations: one based on a best case scenario assuming that animals with kleptoplasts can be, on a per cm2 basis, as efficient at CO2 fixation as maize leaves, and one based on14 CO2 fixation rates measured in plastid-bearing sea slugs. We also tabulate an overview of the literature going back to 1970 reporting direct measurements or indirect estimates of the CO2 fixing capabilities of Sacoglossan slugs with plastids

Generic theory of colloidal transport

We discuss the motion of colloidal particles relative to a two component fluid consisting of solvent and solute. Particle motion can result from (i) net body forces on the particle due to external fields such as gravity; (ii) slip velocities on the particle surface due to surface dissipative phenomena. The perturbations of the hydrodynamic flow field exhibits characteristic differences in cases (i) and (ii) which reflect different patterns of momentum flux corresponding to the existence of net forces, force dipoles or force quadrupoles. In the absence of external fields, gradients of concentration or pressure do not generate net forces on a colloidal particle. Such gradients can nevertheless induce relative motion between particle and fluid. We present a generic description of surface dissipative phenomena based on the linear response of surface fluxes driven by conjugate surface forces. In this framework we discuss different transport scenarios including self-propulsion via surface slip that is induced by active processes on the particle surface. We clarify the nature of force balances in such situations.Comment: 22 pages, 1 figur

Environmental behavior of 14C-tagged polyacrylate polymer: Flow tank studies of retention in sand

A highly absorbent consumer-product, polyacrylate polymer material tagged with 14C was dosed to a simulated diaper and buried in a horizontal flow tank containing sand. Two slightly different formulations of the polymer exhibited a mobile fraction, 1.9 percent and 3.48 percent of which was discharged in the tank effluent during the passage of 6 pore volumes. Most of the remainder was retarded along the flow path near the source by the sand. It is expected that more conventional landfill soils would provide even greater retention of the polymer materials studied. The use of a 14C-tagged polymer proved to be a successful method for studying the behavior of these complex materials; pilot-scale studies are planned in lysimeters to determine if microbial decomposition affects the migration of these polymers under landfill conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26930/1/0000496.pd

Isotropic Loop Quantum Cosmology with Matter

A free massless scalar field is coupled to homogeneous and isotropic loop quantum cosmology. The coupled model is investigated in the vicinity of the classical singularity, where discreteness is essential and where the quantum model is non-singular, as well as in the regime of large volumes, where it displays the expected semiclassical features. The particular matter content (massless, free scalar) is chosen to illustrate how the discrete structure regulates pathological behavior caused by kinetic terms of matter Hamiltonians (which in standard quantum cosmology lead to wave functions with an infinite number of oscillations near the classical singularity). Due to this modification of the small volume behavior the dynamical initial conditions of loop quantum cosmology are seen to provide a meaningful generalization of DeWitt's initial condition.Comment: 18 pages, 4 figure

Backward pion-nucleon scattering

A global analysis of the world data on differential cross sections and polarization asymmetries of backward pion-nucleon scattering for invariant collision energies above 3 GeV is performed in a Regge model. Including the $N_\alpha$, $N_\gamma$, $\Delta_\delta$ and $\Delta_\beta$ trajectories, we reproduce both angular distributions and polarization data for small values of the Mandelstam variable $u$, in contrast to previous analyses. The model amplitude is used to obtain evidence for baryon resonances with mass below 3 GeV. Our analysis suggests a $G_{39}$ resonance with a mass of 2.83 GeV as member of the $\Delta_{\beta}$ trajectory from the corresponding Chew-Frautschi plot.Comment: 12 pages, 16 figure

Anomalous Effects of "Guest" Charges Immersed in Electrolyte: Exact 2D Results

We study physical situations when one or two "guest" arbitrarily-charged particles are immersed in the bulk of a classical electrolyte modelled by a Coulomb gas of positive/negative unit point-like charges, the whole system being in thermal equilibrium. The models are treated as two-dimensional with logarithmic pairwise interactions among charged constituents; the (dimensionless) inverse temperature $\beta$ is considered to be smaller than 2 in order to ensure the stability of the electrolyte against the collapse of positive-negative pairs of charges. Based on recent progress in the integrable (1+1)-dimensional sine-Gordon theory, exact formulas are derived for the chemical potential of one guest charge and for the asymptotic large-distance behavior of the effective interaction between two guest charges. The exact results imply, under certain circumstances, anomalous effects such as an effective attraction (repulsion) between like-charged (oppositely-charged) guest particles and the charge inversion in the electrolyte vicinity of a highly-charged guest particle. The adequacy of the concept of renormalized charge is confirmed in the whole stability region of inverse temperatures and the related saturation phenomenon is revised.Comment: 21 pages, 1 figur