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

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

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

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:

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

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

The Gibbs free energy of homogeneous nucleation: from atomistic nuclei to the planar limit

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters of a model based on classical nucleation theory can be fit using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the parameters of the macroscopic model are fitted in this way the numerical errors for the final fitted model are smaller and that the extrapolated predictions for large nuclei are thus more reliable

Transport properties for a Luttinger liquid wire with Rashba spin-orbit coupling and Zeeman splitting

We study the transport properties for a Luttinger-liquid (LL) quantum wire in the presence of both Rashba spin-orbit coupling (SOC) and a weak external in-plane magnetic field. The bosonized Hamiltonian of the system with an externally applied longitudinal electric field is established. And then the equations of motion for the bosonic phase fields are solved in the Fourier space, with which the both charge and spin conductivities for the system are calculated analytically based on the linear response theory. Generally, the ac conductivity is an oscillation function of the strengths of electron-electron interaction, Rashba SOC and magnetic field, as well as the driving frequency and the measurement position in the wire. Through analysis with some examples it is demonstrated that the modification on the conductivity due to electron-electron interactions is more remarkable than that due to SOC, while the effects of SOC and Zeeman splitting on the conductivity are very similar. The spin-polarized conductivities for the system in the absence of Zeeman effect or SOC are also discussed, respectively. The ratio of the spin-polarized conductivities $\sigma_\uparrow/\sigma_\downarrow$ is dependent of the electron-electron interactions for the system without SOC, while it is independent of the electron-electron interactions for the system without Zeeman splitting.Comment: 10 pages, 8 figure

Spin fluctuations and superconductivity in a 3D tight-binding model for BaFe2As2

Despite the wealth of experimental data on the Fe-pnictide compounds of the KFe2As2-type, K = Ba, Ca, or Sr, the main theoretical work based on multiorbital tight-binding models has been restricted so far to the study of the related 1111 compounds. This can be ascribed to the more three dimensional electronic structure found by ab initio calculations for the 122 materials, making this system less amenable to model development. In addition, the more complicated Brillouin zone (BZ) of the body-centered tetragonal symmetry does not allow a straightforward unfolding of the electronic band structure into an effective 1Fe/unit cell BZ. Here we present an effective 5-orbital tight-binding fit of the full DFT band structure for BaFeAs including the kz dispersions. We compare the 5-orbital spin fluctuation model to one previously studied for LaOFeAs and calculate the RPA enhanced susceptibility. Using the fluctuation exchange approximation to determine the leading pairing instability, we then examine the differences between a strictly two dimensional model calculation over a single kz cut of the BZ and a completely three dimensional approach. We find pairing states quite similar to the 1111 materials, with generic quasi-isotropic pairing on the hole sheets and nodal states on the electron sheets at kz = 0 which however are gapped as the system is hole doped. On the other hand, a substantial kz dependence of the order parameter remains, with most of the pairing strength deriving from processes near kz = pi. These states exhibit a tendency for an enhanced anisotropy on the hole sheets and a reduced anisotropy on the electron sheets near the top of the BZ.Comment: 12 pages, 15 figure