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We present a tool that uses a phase field approach to simulate plastic deformation in nanocrystalline materials. It captures the competing grain-boundary and dislocation-mediated deformation mechanisms that govern plastic deformation in these materials. The model is based on a multiphase field approach in which dislocations and grain boundary sliding are represented by means of scalar phase fields described in “The role of grain boundary energetics on the maximum strength of nanocrystalline Ni”, Koslowski, Lee and Lei, Journal of the Mechanics and Physics of Solids, 59 1427–1436, 2011. The tool enables users to quantify how uncertainties in the input parameters (materials properties such as elastic constants, Peierls energy barrier for dislocation glide, and activation barrier for grain boundary sliding) affect the prediction of the yield stress. In addition, it provides a sensitivity analysis that quantifies the relative importance of each input variable. In order to achieve this, the phase field simulation code is orchestrated by the PRISM Uncertainty Quantification tool that enables users to select various state-of-the-art methods for uncertainty propagation

Singular kernels, multiscale decomposition of microstructure, and dislocation models

We consider a model for dislocations in crystals introduced by Koslowski, Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit of the model within the framework of $\Gamma$-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound

The electronic structure of amorphous silica: A numerical study

We present a computational study of the electronic properties of amorphous SiO2. The ionic configurations used are the ones generated by an earlier molecular dynamics simulations in which the system was cooled with different cooling rates from the liquid state to a glass, thus giving access to glass-like configurations with different degrees of disorder [Phys. Rev. B 54, 15808 (1996)]. The electronic structure is described by a tight-binding Hamiltonian. We study the influence of the degree of disorder on the density of states, the localization properties, the optical absorption, the nature of defects within the mobility gap, and on the fluctuations of the Madelung potential, where the disorder manifests itself most prominently. The experimentally observed mismatch between a photoconductivity threshold of 9 eV and the onset of the optical absorption around 7 eV is interpreted by the picture of eigenstates localized by potential energy fluctuations in a mobility gap of approximately 9 eV and a density of states that exhibits valence and conduction band tails which are, even in the absence of defects, deeply located within the former band gap.Comment: 21 pages of Latex, 5 eps figure

The Link between General Relativity and Shape Dynamics

We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity and Shape Dynamics, a theory with fixed foliation but spatial conformal invariance. This streamlines the rather complicated construction of this equivalence performed previously. We use this streamlined argument to extend the result to General Relativity with asymptotically flat boundary conditions. The improved understanding of linking theories naturally leads to the Lagrangian formulation of Shape Dynamics, which allows us to partially relate the degrees of freedom.Comment: 19 pages, LaTeX, no figure

Finite size effects and localization properties of disordered quantum wires with chiral symmetry

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance that reproduces accurately the numerical data for both geometries. However, when the concentration of vacancies increases above a critical value, a transition towards the suppression of the conductance occurs. This is a signature of the presence of ultra-localized states trapped in finite regions of the sample.Comment: 5 figures, revtex

Mixed Atomistic–Continuum Models of Material Behavior: The Art of Transcending Atomistics and Informing Continua

The recent development of microscopes that allow for the examination of defects at the atomic scale has made possible a more direct connection between the defects and the macroscopic response they engender (see, e.g., the December 1999 issue of MRS Bulletin)

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters

Semiempirical orthogonalization-corrected methods (OM1, OM2, and OM3) go beyond the standard MNDO model by explicitly including additional interactions into the Fock matrix in an approximate manner (Pauli repulsion, penetration effects, and core–valence interactions), which yields systematic improvements both for ground-state and excited-state properties. In this Article, we describe the underlying theoretical formalism of the OMx methods and their implementation in full detail, and we report all relevant OMx parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. For a standard set of mostly organic molecules commonly used in semiempirical method development, the OMx results are found to be superior to those from standard MNDO-type methods. Parametrized Grimme-type dispersion corrections can be added to OM2 and OM3 energies to provide a realistic treatment of noncovalent interaction energies, as demonstrated for the complexes in the S22 and S66×8 test sets

Produção, composição bromatológica e extração de potássio pela planta de milho para silagem colhida em duas alturas de corte.

O presente experimento teve como objetivo avaliar as características agronômicas, composição químico-bromatológica e extração de potássio de cinco genótipos de milho para silagem. O delineamento foi realizado em parcelas subdivididas no delineamento em blocos ao acaso, com 3 híbridos (DKB 390, AGX 8517, A-2560) e 2 variedaes (AL-Bianco, Piratininga), em 2 alturas de corte (20 e 40 cm acima do solo) e 4 repetições..

Three-Dimensional Quantum Percolation Studied by Level Statistics

Three-dimensional quantum percolation problems are studied by analyzing energy level statistics of electrons on maximally connected percolating clusters. The quantum percolation threshold \pq, which is larger than the classical percolation threshold \pc, becomes smaller when magnetic fields are applied, i.e., \pq(B=0)>\pq(B\ne 0)>\pc. The critical exponents are found to be consistent with the recently obtained values of the Anderson model, supporting the conjecture that the quantum percolation is classified onto the same universality classes of the Anderson transition. Novel critical level statistics at the percolation threshold is also reported.Comment: to appear in the May issue of J. Phys. Soc. Jp