Shaping of molecular weight distribution by iterative learning probability density function control strategies

A mathematical model is developed for the molecular weight distribution (MWD) of free-radical styrene polymerization in a simulated semi-batch reactor system. The generation function technique and moment method are employed to establish the MWD model in the form of Schultz-Zimmdistribution. Both static and dynamic models are described in detail. In order to achieve the closed-loop MWD shaping by output probability density function (PDF) control, the dynamic MWD model is further developed by a linear B-spline approximation. Based on the general form of the B-spline MWD model, iterative learning PDF control strategies have been investigated in order to improve the MWD control performance. Discussions on the simulation studies show the advantages and limitations of the methodology

Quantum kk-core conduction on the Bethe lattice

Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least $k-1$ neighboring occupied bonds, i.e. $k$-core diluted. In the classical case, we find the onset of conduction for $k=2$ is continuous, while for $k=3$, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupied bond as a random scatterer, we find for $k=3$ that the random first-order phase transition in the geometry also drives the onset of quantum conduction giving rise to a new universality class of Anderson localization transitions.Comment: 12 pgs., 6 fig

Competing Ground States in Triple-layered Sr4Ru3O10: Verging on Itinerant Ferromagnetism with Critical Fluctuations

Sr4Ru3O10 is characterized by a sharp metamagnetic transition and ferromagnetic behavior occurring within the basal plane and along the c-axis, respectively. Resistivity at magnetic field, B, exhibits low-frequency quantum oscillations when B||c-axis and large magnetoresistivity accompanied by critical fluctuations driven by the metamagnetism when B^c-axis. The complex behavior evidenced in resistivity, magnetization and specific heat presented is not characteristic of any obvious ground states, and points to an exotic state that shows a delicate balance between fluctuations and order.Comment: 18 pages, 4 figure

On Vector Bundles of Finite Order

We study growth of holomorphic vector bundles E over smooth affine manifolds. We define Finsler metrics of finite order on E by estimates on the holomorphic bisectional curvature. These estimates are very similar to the ones used by Griffiths and Cornalba to define Hermitian metrics of finite order. We then generalize the Vanishing Theorem of Griffiths and Cornalba to the Finsler context. We develop a value distribution theory for holomorphic maps from the projectivization of E to projective space. We show that the projectivization of E can be immersed into a projective space of sufficiently large dimension via a map of finite order.Comment: version 2 has some typos corrected; to appear in Manuscripta Mathematic

Effects of the Tensor Force on the Multipole Response in Finite Nuclei

We present a thorough analysis of the effects of the tensor interaction on the multipole response of magic nuclei, using the fully self-consistent Random Phase Approximation (RPA) model with Skyrme interactions. We disentangle the modifications to the static mean field induced by the tensor terms, and the specific features of the residual particle-hole (p-h) tensor interaction, for quadrupole (2+), octupole (3-), and also magnetic dipole (1+) responses. It is pointed out that the tensor force has a larger effect on the magnetic dipole states than on the natural parity states 2+ and 3-, especially at the mean field level. Perspectives for a better assessment of the tensor force parameters are eventually discussed