A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

The Formation of Thin Continuous Films from Isolated Nuclei

Formation of thin continuous films from isolated nuclei and effect of electron beam, residual gases, and surface conditions on film growt

Microscopic calculation of the phonon dynamics of Sr2_{2}RuO4_{4} compared with La2_{2}CuO4_{4}

The phonon dynamics of the low-temperature superconductor Sr$_{2}$RuO$_{4}$ is calculated quantitatively in linear response theory and compared with the structurally isomorphic high-temperature superconductor La$_{2}$CuO$_{4}$. Our calculation corrects for a typical deficit of LDA-based calculations which always predict a too large electronic $k_{z}$-dispersion insufficient to describe the c-axis response in the real materials. With a more realistic computation of the electronic band structure the frequency and wavevector dependent irreducible polarization part of the density response function is determined and used for adiabatic and nonadiabatic phonon calculations. Our analysis for Sr$_{2}$RuO$_{4}$ reveals important differences from the lattice dynamics of $p$- and $n$-doped cuprates. Consistent with experimental evidence from inelastic neutron scattering the anomalous doping related softening of the strongly coupling high-frequency oxygen bond-stretching modes (OBSM) which is generic for the cuprate superconductors is largely suppressed or completely absent, respectively, depending on the actual value of the on-site Coulomb repulsion of the Ru4d orbitals. Also the presence of a characteristic $\Lambda_{1}$-mode with a very steep dispersion coupling strongly with the electrons is missing in Sr$_{2}$RuO$_{4}$. Moreover, we evaluate the possibility of a phonon-plasmon scenario for Sr$_{2}$RuO$_{4}$ which has been shown recently to be realistic for La$_{2}$CuO$_{4}$. In contrast to La$_{2}$CuO$_{4}$ in Sr$_{2}$RuO$_{4}$ the very low lying plasmons are overdamped along the c-axis.Comment: 30 pages, 16 figures, 4 tables, 33 reference

Optical conductivity of filled skutterudites

A simple tight-binding model is constructed for the description of the electronic structure of some Ce-based filled skutterudite compounds showing an energy gap or pseudogap behavior. Assuming band-diagonal electron interactions on this tight-binding model, the optical conductivity spectrum is calculated by applying the second-order self-consistent perturbation theory to treat the electron correlation. The correlation effect is found to be of great importance on the description of the temperature dependence of the optical conductivity. The rapid disappearance of an optical gap with increasing temperature is obtained as observed in the optical experiment for Ce-based filled-skutterudite compounds.Comment: 6 pages, 7 figures, use jpsj2.cls, to appear in J. Phys. Soc. Jpn. Vol.73, No.10 (2004

Spatially resolved ultrafast precessional magnetization reversal

Spatially resolved measurements of quasi-ballistic precessional magnetic switching in a microstructure are presented. Crossing current wires allow detailed study of the precessional switching induced by coincident longitudinal and transverse magnetic field pulses. Though the response is initially spatially uniform, dephasing occurs leading to nonuniformity and transient demagnetization. This nonuniformity comes in spite of a novel method for suppression of end domains in remanence. The results have implications for the reliability of ballistic precessional switching in magnetic devices.Comment: 17 pages (including 4 figures), submitted to Phys. Rev. Let

Compact strain-sensitive flexible photonic crystals for sensors

A promising fabrication route to produce absorbing flexible photonic crystals is presented, which exploits self-assembly during the shear processing of multi-shelled polymer spheres. When absorbing material is incorporated in the interstitial space surrounding high-refractive-index spheres, a dramatic enhancement in the transmission edge on the short-wavelength side of the band gap is observed. This effect originates from the shifting optical field spatial distribution as the incident wavelength is tuned around the band gap, and results in a contrast up to 100 times better than similar but nonabsorbing photonic crystals. An order-of-magnitude improvement in strain sensitivity is shown, suggesting the use of these thin films in photonic sensors

Crop Identification Technology Assessment for Remote Sensing (CITARS)

The results of classifications and experiments performed for the Crop Identification Technology Assessment for Remote Sensing (CITARS) project are summarized. Fifteen data sets were classified using two analysis procedures. One procedure used class weights while the other assumed equal probabilities of occurrence for all classes. In addition, 20 data sets were classified using training statistics from another segment or date. The results of both the local and non-local classifications in terms of classification and proportion estimation are presented. Several additional experiments are described which were performed to provide additional understanding of the CITARS results. These experiments investigated alternative analysis procedures, training set selection and size, effects of multitemporal registration, the spectral discriminability of corn, soybeans, and other, and analysis of aircraft multispectral data

Crop identification technology assessment for remote sensing (CITARS). Volume 6: Data processing at the laboratory for applications of remote sensing

The results of classifications and experiments for the crop identification technology assessment for remote sensing are summarized. Using two analysis procedures, 15 data sets were classified. One procedure used class weights while the other assumed equal probabilities of occurrence for all classes. Additionally, 20 data sets were classified using training statistics from another segment or date. The classification and proportion estimation results of the local and nonlocal classifications are reported. Data also describe several other experiments to provide additional understanding of the results of the crop identification technology assessment for remote sensing. These experiments investigated alternative analysis procedures, training set selection and size, effects of multitemporal registration, spectral discriminability of corn, soybeans, and other, and analyses of aircraft multispectral data