The Judicial Expansion of American Exceptionalism

The percolation theory is established as a useful tool in the field of pharmaceutical materials science.It is shown that percolation theory, developed for analyzing insulator–conductor transitions, can beapplied to describe imperfect dc conduction in pharmaceutical microcrystalline cellulose duringdensification. The system, in fact, exactly reproduces the values of the percolation threshold andexponent estimated for a three-dimensional random continuum. Our data clearly show a crossoverfrom a power-law percolation theory region to a linear effective medium theory region at a celluloseporosity of ;0.7

Piercing the Veil: William J. Brennan\u27s Account of Regents of the University of California v. Bakke

Porous nickel oxide films were deposited onto unheated indium tin oxide coated glass substrates by reactive dc magnetron sputtering. These films had a cubic NiO structure. Electrochromic properties were evaluated in 1 M potassium hydroxide (KOH) and in 1 M lithium perchlorate in propylene carbonate (Li-PC). Large optical modulation was obtained for similar to 500-nm-thick films both in KOH and in Li-PC (similar to 70% and similar to 50% at 550 nm, respectively). In KOH, tensile and compressive stresses, due to the expansion and contraction of the lattice, were found for films in their bleached and colored state, respectively. In Li-PC, compressive stress was seen both in colored and bleached films. Durability tests with voltage sweeps between -0.5 and 0.65 V vs Ag/AgCl in KOH showed good durability for 10,000 cycles, whereas voltage sweeps between 2.0 and 4.7 V vs Li/Li+ in Li-PC yielded significant degradation after 1000 cycles.EU GRINDOO

Extinction calculations of multi-sphere polycrystalline graphitic clusters - A comparison with the 2175 AA peak and between a rigorous solution and discrete-dipole approximations

Certain dust particles in space are expected to appear as clusters of individual grains. The morphology of these clusters could be fractal or compact. In this paper we study the light scattering by compact and fractal polycrystalline graphitic clusters consisting of touching identical spheres. We compare three general methods for computing the extinction of the clusters in the wavelength range 0.1 - 100 micron, namely, a rigorous solution (Gerardy & Ausloos 1982) and two different discrete-dipole approximation methods -- MarCODES (Markel 1998) and DDSCAT (Draine & Flatau 1994). We consider clusters of N = 4, 7, 8, 27,32, 49, 108 and 343 particles of radii either 10 nm or 50 nm, arranged in three different geometries: open fractal (dimension D = 1.77), simple cubic and face-centred cubic. The rigorous solution shows that the extinction of the fractal clusters, with N < 50 and particle radii 10 nm, displays a peak within 2% of the location of the observed interstellar extinction peak at ~4.6 inverse micron; the smaller the cluster, the closer its peak gets to this value. By contrast, the peak in the extinction of the more compact clusters lie more than 4% from 4.6 inverse micron. At short wavelengths (0.1 - 0.5 micron), all the methods show that fractal clusters have markedly different extinction from those of non-fractal clusters. At wavelengths > 5 micron, the rigorous solution indicates that the extinction from fractal and compact clusters are of the same order of magnitude. It was only possible to compute fully converged results of the rigorous solution for the smaller clusters, due to computational limitations, however, we find that both discrete-dipole approximation methods overestimate the computed extinction of the smaller fractal clusters.Comment: Corrections added in accordance with suggestions by the referee. 12 pages, 12 figures. Accepted for publication in Astronomy & Astrophysic

Giant magnetic enhancement in Fe/Pd films and its influence on the magnetic interlayer coupling

The magnetic properties of thin Pd fcc(001) films with embedded monolayers of Fe are investigated by means of first principles density functional theory. The induced spin polarization in Pd is calculated and analyzed in terms of quantum interference within the Fe/Pd/Fe bilayer system. An investigation of the magnetic enhancement effects on the spin polarization is carried out and its consequences for the magnetic interlayer coupling are discussed. In contrast to {\it e.g.} the Co/Cu fcc(001) system we find a large effect on the magnetic interlayer coupling due to magnetic enhancement in the spacer material. In the case of a single embedded Fe monolayer we find aninduced Pd magnetization decaying with distance $n$ from the magnetic layer as ~$n^{-\alpha}$ with $\alpha \approx 2.4$. For the bilayer system we find a giant magnetic enhancement (GME) that oscillates strongly due to interference effects. This results in a strongly modified magnetic interlayer coupling, both in phase and magnitude, which may not be described in the pure Ruderman-Kittel-Kasuya-Yoshida (RKKY) picture. No anti-ferromagnetic coupling was found and by comparison with magnetically constrained calculations we show that the overall ferromagnetic coupling can be understood from the strong polarization of the Pd spacer

Law School Libraries 2007

The primary mission of the law school library is to meet the information needs of the faculty and students of the institution it supports. In addition to their role in educating future lawyers, law schools are the major producers of scholarly literature in law and rely on academic law libraries to provide the resources and support needed for research and publication. Beyond support for the core functions of legal education and research, the specific missions of law school libraries vary depending on the size and missions of law schools of different types. Differences among law schools result in differences among their libraries in collection size and composition, staffing and services offered, and additional clienteles served

Wavefunction extended Lagrangian Born-Oppenheimer molecular dynamics

Extended Lagrangian Born-Oppenheimer molecular dynamics [Niklasson, Phys. Rev. Lett. 100 123004 (2008)] has been generalized to the propagation of the electronic wavefunctions. The technique allows highly efficient first principles molecular dynamics simulations using plane wave pseudopotential electronic structure methods that are stable and energy conserving also under incomplete and approximate self-consistency convergence. An implementation of the method within the planewave basis set is presented and the accuracy and efficiency is demonstrated both for semi-conductor and metallic materials.Comment: 6 pages, 3 figure

Ab initio linear scaling response theory: Electric polarizability by perturbed projection

A linear scaling method for calculation of the static {\em ab inito} response within self-consistent field theory is developed and applied to calculation of the static electric polarizability. The method is based on density matrix perturbation theory [Niklasson and Challacombe, cond-mat/0311591], obtaining response functions directly via a perturbative approach to spectral projection. The accuracy and efficiency of the linear scaling method is demonstrated for a series of three-dimensional water clusters at the RHF/6-31G** level of theory. Locality of the response under a global electric field perturbation is numerically demonstrated by approximate exponential decay of derivative density matrix elements.Comment: 4.25 pages in PRL format, 2 figure

Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which in practice never is fully converged. The calculated energies and the forces are therefore only approximate, which may lead to an unphysical energy drift and instabilities. Here we discuss an alternative shadow BOMD approach that is based on a backward error analysis. Instead of calculating approximate solutions for an underlying exact regular BO potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow BO potential. In this way the calculated forces are conservative with respect to the shadow potential and generate accurate molecular trajectories with long-term energy stability. We show how such shadow BO potentials can be constructed at different levels of accuracy as a function of the integration time step, dt, from the minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each functional there is a corresponding ground state BO potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "0th-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Eur. Phys. J. B vol. 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this dynamical framework, where also the electronic degrees of freedom are propagated together with the atomic positions and velocities. The theory is general and can be applied to MD simulations using approximate DFT, Hartree-Fock or semi-empirical methods, as well as to coarse-grained flexible charge models.Comment: 16 pages, 3 figure