Structure-property characterization of rheocast and VADER processed IN-100 superalloy

Two recent solidification processes have been applied in the production of IN-100 nickel-base superalloy: rheocasting and vacuum arc double electrode remelting (VADER). A detailed microstructural examination has been made of the products of these two processes; associated tensile strength and fatigue crack propagation (FCP) rate at an elevated temperature were evaluated. In rheocasting, processing variables that have been evaluated include stirring speed, isothermal stirring time and volume fraction solid during isothermal stirring. VADER processed IN-100 was purchased from Special Metals Corp., New Hartford, NY. As-cast ingots were subjected to hot isostatic pressing (HIP) and heat treatment. Both rheocasting and VADER processed materials yield fine and equiaxed spherical structures, with reduced macrosegregation in comparison to ingot materials. The rheocast structures are discussed on the basis of the Vogel-Doherty-Cantor model of dendrite arm fragmentation. The rheocast ingots evaluated were superior in yield strength to both VADER and commercially cast IN-100 alloy. Rheocast and VADER ingots may have higher crack propagation resistance than P/M processed material

Irreducible Characters of General Linear Superalgebra and Super Duality

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category \mc{O} of the general linear superalgebra. We also prove the super duality conjecture

A simple mean field equation for condensates in the BEC-BCS crossover regime

We present a mean field approach based on pairs of fermionic atoms to describe condensates in the BEC-BCS crossover regime. By introducing an effective potential, the mean field equation allows us to calculate the chemical potential, the equation of states and the atomic correlation function. The results agree surprisingly well with recent quantum Monte Carlo calculations. We show that the smooth crossover from the bosonic mean field repulsion between molecules to the Fermi pressure among atoms is associated with the evolution of the atomic correlation function

Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step \d \tau in terms of an algorithmic time step \dt. By studying the accumulative multi-step error in Fourier space and controlling the error with arbitrary accuracy, we determine an improved driving scheme \dt=At^{2/3} and confirm the numerical results observed in a previous study \cite{Cheng1}.Comment: 4 pages, late

Haar expectations of ratios of random characteristic polynomials

We compute Haar ensemble averages of ratios of random characteristic polynomials for the classical Lie groups K = O(N), SO(N), and USp(N). To that end, we start from the Clifford-Weyl algebera in its canonical realization on the complex of holomorphic differential forms for a C-vector space V. From it we construct the Fock representation of an orthosymplectic Lie superalgebra osp associated to V. Particular attention is paid to defining Howe's oscillator semigroup and the representation that partially exponentiates the Lie algebra representation of sp in osp. In the process, by pushing the semigroup representation to its boundary and arguing by continuity, we provide a construction of the Shale-Weil-Segal representation of the metaplectic group. To deal with a product of n ratios of characteristic polynomials, we let V = C^n \otimes C^N where C^N is equipped with its standard K-representation, and focus on the subspace of K-equivariant forms. By Howe duality, this is a highest-weight irreducible representation of the centralizer g of Lie(K) in osp. We identify the K-Haar expectation of n ratios with the character of this g-representation, which we show to be uniquely determined by analyticity, Weyl group invariance, certain weight constraints and a system of differential equations coming from the Laplace-Casimir invariants of g. We find an explicit solution to the problem posed by all these conditions. In this way we prove that the said Haar expectations are expressed by a Weyl-type character formula for all integers N \ge 1. This completes earlier work by Conrey, Farmer, and Zirnbauer for the case of U(N).Comment: LaTeX, 70 pages, Complex Analysis and its Synergies (2016) 2:

Long-Distance Contributions to D^0-D^0bar Mixing Parameters

Long-distance contributions to the $D^0$-$\bar D^0$ mixing parameters $x$ and $y$ are evaluated using latest data on hadronic $D^0$ decays. In particular, we take on two-body $D \to PP$ and $VP$ decays to evaluate the contributions of two-body intermediate states because they account for $\sim 50$ of hadronic $D^0$ decays. Use of the diagrammatic approach has been made to estimate yet-observed decay modes. We find that $y$ is of order a few $\times 10^{-3}$ and $x$ of order $10^{-3}$ from hadronic $PP$ and $VP$ modes. These are in good agreement with the latest direct measurement of $D^0$-$\bar D^0$ mixing parameters using the $D^0 \to K_S \pi^+\pi^-$ and $K_S K^+ K^-$ decays by BaBar. We estimate the contribution to $y$ from the $VV$ modes using the factorization model and comment on the single-particle resonance effects and contributions from other two-body modes involving even-parity states.Comment: 18 pages and 1 figure; footnotes and references added; to appear in Phys. Rev.

Modelling Epsilon Aurigae without solid particles

Three components can be expected to contribute to the emission of epsilon Aurigae. There is a primary F star. There is an opaque disk which occults it, and there is a gas stream which is observed to produce absorption lines. Evidence that the disk is not responsible for the gas stream lines comes both from the radial velocities, which are too small, and from the IR energy distribution out of eclipse, which shows free-free emission that would produce inadequate optical depth in electron scattering. The color temperature of the IR excess can give misleading indications of low temperature material. Free-free emission at 10,000 K between 10 and 20 microns has a color temperature of 350 K. Attempts to mold the system are discussed

A BGG-type resolution for tensor modules over general linear superalgebra

We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique maximal submodule of a corresponding reducible Kac module is generated by its proper singular vector.Comment: 11pages, LaTeX forma

SLS Processing Studies of Nylon 11 Nanocomposites

Selective Laser Sintering (SLS) is widely used for rapid prototyping/manufacturing of nylon 11 and nylon 12 parts. This processing technique has not been explored for nylon nanocomposites. This study investigates the technicalities of processing nylon 11-clay and nylon-carbon nanofiber nanocomposites with SLS. Microstructural analyses of the SLS powders and parts were conducted under SEM. Results suggest that SLS processing is possible with the new nylon 11 nanocomposites. Yet the SLS parts built have inferior properties relative to those of injection molding, suggesting that more fine tuning for the processing is required.Mechanical Engineerin