A qq-Queens Problem. II. The Square Board

We apply to the $n\times n$ chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I showed that the number of ways to place $q$ identical nonattacking pieces is given by a quasipolynomial function of $n$ of degree $2q$, whose coefficients are (essentially) polynomials in $q$ that depend cyclically on $n$. Here we study the periods of the quasipolynomial and its coefficients, which are bounded by functions, not well understood, of the piece's move directions, and we develop exact formulas for the very highest coefficients. The coefficients of the three highest powers of $n$ do not vary with $n$. On the other hand, we present simple pieces for which the fourth coefficient varies periodically. We develop detailed properties of counting quasipolynomials that will be applied in sequels to partial queens, whose moves are subsets of those of the queen, and the nightrider, whose moves are extended knight's moves. We conclude with the first, though strange, formula for the classical $n$-Queens Problem and with several conjectures and open problems.Comment: 23 pp., 1 figure, submitted. This = second half of 1303.1879v1 with great improvements. V2 has a new proposition, better definitions, and corrected conjectures. V3 has results et al. renumbered to correspond with published version, and expands dictionary's cryptic abbreviation

Magnetic Properties of Epitaxial and Polycrystalline Fe/Si Multilayers

Fe/Si multilayers with antiferromagnetic interlayer coupling have been grown via ion-beam sputtering on both glass and single-crystal substrates. High-angle x-ray diffraction measurements show that both sets of films have narrow Fe peaks, implying a large crystallite size and crystalline iron silicide spacer layers. Low-angle x-ray diffraction measurements show that films grown on glass have rougher interfaces than those grown on single-crystal substrates. The multilayers grown on glass have a larger remanent magnetization than the multilayers grown on single-crystal substrates. The observation of magnetocrystalline anisotropy in hysteresis loops and $(hkl)$ peaks in x-ray diffraction demonstrates that the films grown on MgO and Ge are epitaxial. The smaller remanent magnetization in Fe/Si multilayers with better layering suggests that the remanence is not an intrinsic property.Comment: 9 pages, RevTex, 4 figures available by fax. Send email to [email protected] for more info. Submitted to '95 MMM proceeding

Transmission Electron Study of Heteroepitaxial Growth in the BiSrCaCuO System

Films of Bi$\rm _2$Sr$\rm _2$CaCu$\rm _2$O$\rm _8$ and Bi$\rm _2$Sr$\rm _2$CuO$\rm _6$ have been grown using Atomic-Layer-by-Layer Molecular Beam Epitaxy (ALL-MBE) on lattice-matched substrates. These materials have been combined with layers of closely-related metastable compounds like Bi$\rm _2$Sr$\rm _2$Ca$\rm _7$Cu$\rm _8$O$\rm _{20}$ (2278) and rare-earth-doped compounds like Bi$\rm _2$Sr$\rm _2$Dy$\rm _x$Ca$\rm _{1-x}$Cu$\rm _2$O$\rm _8$ (Dy:2212) to form heterostructures with unique superconducting properties, including superconductor/insulator multilayers and tunnel junctions. Transmission electron microscopy (TEM) has been used to study the morphology and microstructure of these heterostructures. These TEM studies shed light on the physical properties of the films, and give insight into the growth mode of highly anisotropic solids like Bi$\rm _2$Sr$\rm _2$CaCu$\rm _2$O$\rm _8$.Comment: 17 pages, submitted to J. Materials Research. Email to [email protected] if you want to receive copies of the figure

Selective self-categorization: Meaningful categorization and the in-group persuasion effect

Research stemming from self-categorization theory (Turner et al., 1987) has demonstrated that individuals are typically more persuaded by messages from their in-group than by messages from the out-group. The present research investigated the role of issue relevance in moderating these effects. In particular, it was predicted that in-groups would only be more persuasive when the dimension on which group membership was defined was meaningful or relevant to the attitude issue. In two studies, participants were presented with persuasive arguments from either an in-group source or an out-group source, where the basis of the in-group/out-group distinction was either relevant or irrelevant to the attitude issue. Participants' attitudes toward the issue were then measured. The results supported the predictions: Participants were more persuaded by in-group sources than out-group sources when the basis for defining the group was relevant to the attitude issue. However, when the defining characteristic of the group was irrelevant to the attitude issue, participants were equally persuaded by in-group and out-group sources. These results support the hypothesis that the fit between group membership and domain is an important moderator of self-categorization effects

Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions

We present Monte Carlo simulations of the spanning-forest model (q \to 0 limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show that, in contrast to the two-dimensional case, the model has a "ferromagnetic" second-order phase transition at a finite positive value w_c. We present numerical estimates of w_c and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.Comment: LaTex2e, 4 pages; includes 6 Postscript figures; Version 2 has expanded title as published in PR

Phonon Thermal Transport of URu2Si2: Broken Translational Symmetry and Strong-Coupling of the Hidden Order to the Lattice

A dramatic increase in the total thermal conductivity (k) is observed in the Hidden Order (HO) state of single crystal URu2Si2. Through measurements of the thermal Hall conductivity, we explicitly show that the electronic contribution to k is extremely small, so that this large increase in k is dominated by phonon conduction. An itinerant BCS/mean-field model describes this behavior well: the increase in kappa is associated with the opening of a large energy gap at the Fermi Surface, thereby decreasing electron-phonon scattering. Our analysis implies that the Hidden Order parameter is strongly coupled to the lattice, suggestive of a broken symmetry involving charge degrees of freedom.Comment: 17 pages including figures, updated author institutions and acknowledgement

Structural identifiability of surface binding reactions involving heterogeneous analyte : application to surface plasmon resonance experiments

Binding affinities are useful measures of target interaction and have an important role in understanding biochemical reactions that involve binding mechanisms. Surface plasmon resonance (SPR) provides convenient real-time measurement of the reaction that enables subsequent estimation of the reaction constants necessary to determine binding affinity. Three models are considered for application to SPR experiments—the well mixed Langmuir model and two models that represent the binding reaction in the presence of transport effects. One of these models, the effective rate constant approximation, can be derived from the other by applying a quasi-steady state assumption. Uniqueness of the reaction constants with respect to SPR measurements is considered via a structural identifiability analysis. It is shown that the models are structurally unidentifiable unless the sample concentration is known. The models are also considered for analytes with heterogeneity in the binding kinetics. This heterogeneity further confounds the identifiability of key parameters necessary for reliable estimation of the binding affinit

Exchange Anisotropy in Epitaxial and Polycrystalline NiO/NiFe Bilayers

(001) oriented NiO/NiFe bilayers were grown on single crystal MgO (001) substrates by ion beam sputtering in order to determine the effect that the crystalline orientation of the NiO antiferromagnetic layer has on the magnetization curve of the NiFe ferromagnetic layer. Simple models predict no exchange anisotropy for the (001)-oriented surface, which in its bulk termination is magnetically compensated. Nonetheless exchange anisotropy is present in the epitaxial films, although it is approximately half as large as in polycrystalline films that were grown simultaneously. Experiments show that differences in exchange field and coercivity between polycrystalline and epitaxial NiFe/NiO bilayers couples arise due to variations in induced surface anisotropy and not from differences in the degree of compensation of the terminating NiO plane. Implications of these observations for models of induced exchange anisotropy in NiO/NiFe bilayer couples will be discussed.Comment: 23 pages in RevTex format, submitted to Phys Rev B