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Relationship between siderophilic-element content and oxidation state of ordinary chondrites.
The concentrations of Ni and Ir have been determined by neutron activation in a suite of ordinary chondrites for which accurate ferromagnesian-mineral compositional data were available. Although hiatus between the individual groups exist, the trends within the groups are in keeping with the hypothesis that the ordinary chondrites form a continuous fractionation sequence. A significant negative correlation is observed between the abundance of Ni or Ir and the Fe content of the ferromagnesian minerals in the H and L groups, and for Ir in the LL group, as expected if the metal-silicate fractionation and the variation in oxidation states were produced by the same or related processes. The Ir/Ni ratio decreases by a factor of 1.2 between the H and LL groups. This fractionation must have occurred at an early stage in the condensation phase of the solar nebula.
Relationships Among Intrinsic Properties of Ordinary Chondrites: Oxidation State, Bulk Chemistry, Oxygen-isotopic Composition, Petrologic Type, and Chondrule Size
The properties of ordinary chondrites (OC) reflect both nebular and asteroidal processes. OC are modeled here as having acquired nebular water, probably contained within phyllosilicates, during agglomeration. This component had high Ai70 and acted like an oxidizing agent during thermal metamorphism. The nebular origin of this component is consistent with negative correlations in H, L, and LL chondrites between oxidation state (represented by olivine Fa) and bulk concentration ratios of elements involved in the metal-silicate fractionation (e.g., NdSi, Ir/Si, Ir/Mn, Ir/Cr, Ir/Mg, Ni/Mg, As/Mg, Ga/Mg). LL chondrites acquired the greatest abundance of phyllosilicates with high (delta)O-17 among OC (and thus became the most oxidized group and the one with the heaviest O isotopes); H chondrites acquired the lowest abundance, becoming the most reduced OC group with the lightest O isotopes. Chondrule precursors may have grown larger and more ferroan with time in each OC agglomeration zone. Nebular turbulence may have controlled the sizes of chondrule precursors. H-chondrite chondrules (which are the smallest among OC) formed from the smallest precursors. In each OC region, low-FeO chondrules formed before high-FeO chondrules during repeated episodes of chondrule formation. During thermal metamorphism, phyllosilicates were dehydrated; the liberated water oxidized metallic Fe-Ni. This caused correlated changes with petrologic type including decreases in the modal abundance of metal, increases in olivine Fa and low-Ca pyroxene Fs, increases in the olivine/pyroxene ratio, and increases in the kamacite Co and Ni contents. As water (with its heavy 0 isotopes) was lost during metamorphism, inverse correlations between bulk (delta)O-18 and bulk (delta)O-17 with petrologic type were produced. The H5 chondrites that were ejected from their parent body approx.7.5 Ma ago during a major impact event probably had been within a few kilometers of each other since they accreted approx.4.5 Ga ago. There are significant differences in the olivine compositional distributions among these rocks; these reflect stochastic nebular sampling of the oxidant (Le., phyllosilicates with high (delta)O-17) on a 0.1-1 km scale during agglomeration.
A comparison study on peridynamic models using irregular non-uniform spatial discretization
The applicability of peridynamic models to problems with irregular non-uniformly discretized solution domain is critical. In this study, a systematic comparison study on results predicted by eight peridynamic models, including bond-based, ordinary state-based and non-ordinary state-based mechanics and heat conduction models, for three different types of problems, including thermal, mechanical and coupled thermo-mechanical, with irregular spatial discretization are performed. It’s found that for the case of irregular but semi-uniform spatial discretization, all these models yield good predictions compared to analytical local solutions. For the case of irregular and non-uniform spatial discretization, models formulated specifically for this configuration give much better results than the conventional formulations which don’t consider the neighborhood difference among material points in the spatial discretization. As a result for either cases of spatial discretization, the bond-associated correspondence material model predicts the most accurate results.
The Peridigm Meshfree Peridynamics Code
Abstract Peridigm is a meshfree peridynamics code written in C++ for use on large-scale parallel computers. It was originally developed at Sandia National Laboratories and is currently managed as an open-source, community driven software project. Its primary features include bond-based, state-based, and non-ordinary state-based constitutive models, bond failure laws, contact, and support for explicit and implicit time integration. To date, Peridigm has been used primarily by methods developers focused on solid mechanics and material failure. Peridigm utilizes foundational software components from Sandia’s Trilinos project and was designed for extensibility. This paper provides an overview of the solution methods implemented in Peridigm , a discussion of its software infrastructure, and demonstrates the use of Peridigm for the solution of several example problems.
Two-photon coherent states of the radiation field
The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.
Clock model interpolation and symmetry breaking in O(2) models
The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to\infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to noninteger $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with noninteger $q$ has a crossover and a second-order phase transition. We also define an extended-$O(2)$ model (with a parameter $\gamma$) that reduces to the $XY$ model when $\gamma=0$ and to the extended $q$-state clock model when $\gamma\to\infty$, and we begin to outline the phase diagram of this model. These models with noninteger $q$ serve as a testbed to study symmetry breaking in situations corresponding to quantum simulators where experimental parameters can be tuned continuously.
Topological nonmagnetic impurity states in topological Kondo insulators
We examine here the presence of nonmagnetic impurities in a hybridization gap model of a Kondo insulator which has band inversion. The model has been used to predict that SmB 6 is a topological insulator. We show that there are two types of nonmagnetic impurity states in a Kondo insulator. The type of states can be categorized as deep impurity states, similar to the impurity states in an ordinary metal, and impurity states which have energies within the hybridization gap. Unlike the deep impurity states which only form if the impurity potential exceeds a critical value of the order of the conduction bandwidth, the in-gap impurity states form for exceptionally small values of the impurity potential comparable to the hybridization gap. This finding may explain why Kondo insulators are found to be exceptionally sensitive to impurities. We demonstrate that these in-gap states are caused by band inversion and have properties similar to those expected for impurities in a topological insulator.
Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions
The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.
Observational physics of mirror world
The existence of the whole world of shadow particles, interacting with each other and having no mutual interactions with ordinary particles except gravity is a specific feature of modern superstring models, being considered as models of the theory of everything. The presence of shadow particles is the necessary condition in the superstring models, providing compensation of the asymmetry of left and right chirality states of ordinary particles. If compactification of additional dimensions retains the symmetry of left and right states, shadow world turns to be the mirror one, with particles and fields having properties strictly symmetrical to the ones of corresponding ordinary particles and fields. Owing to the strict symmetry of physical laws for ordinary and mirror particles, the analysis of cosmological evolution of mirror matter provides rather definite conclusions on possible effects of mirror particles in the universe. A general qualitative discussion of possible astronomical impact of mirror matter is given, in order to make as wide as possible astronomical observational searches for the effects of mirror world, being the unique way to test the existence of mirror partners of ordinary particles in the Nature.
The Shock State of Itokawa Sample
One of the fundamental aspects of any astromaterial is its shock history, since this factor elucidates critical historical events, and also because shock metamorphism can alter primary mineralogical and petrographic features, and reset chronologies [1]. Failure to take shock history into proper account during characterization can result in seriously incorrect conclusions being drawn. Thus the Hayabusa Preliminary Examination Team (HASPET) made shock stage determination of the Itokawa samples a primary goal [2]. However, we faced several difficulties in this particular research. The shock state of ordinary chondrite materials is generally determined by simple optical petrographic observation of standard thin sections. The Itokawa samples available to the analysis team were mounted into plastic blocks, were polished on only one side, and were of non-standard and greatly varying thickness, all of which significantly complicated petrographic analysis but did not prevent it. We made an additional estimation of the sample shock state by a new technique for this analysis - electron back-scattered diffraction (EBSD) in addition to standard petrographic techniques. We are also investigating the crystallinity of Itokawa olivine by Synchrotron X-ray diffraction (SXRD).
Non-Hermitian topological states in 2D line-graph lattices: evolving triple exceptional points on reciprocal line graphs
Non-Hermitian (NH) topological states, such as the doubly-degenerate nodes dubbed as exceptional points (EPs) in Bloch band structure of 2D lattices driven by gain and loss, have attracted much recent interest. We demonstrate theoretically that in the three-site edge-centered lattices, i.e. the so-called line-graph lattices, such as kagome lattice which is a line graph of hexagonal lattice, there exist three types of triply-degenerate EPs evolving intriguingly on another set of line graphs in the reciprocal space. A single TEP (STEP) with ±1/3 topological charge moves faithfully along the edges of reciprocal line graphs with varying gain and loss, while two STEPs merge distinctively into one unconventional orthogonal double TEP (DTEP) with ±2/3 charge at the vertices, which is characterized with two ordinary self-orthogonal eigenfunctions but one surprising 'orthogonal' eigenfunction. Differently, in a modified line-graph lattice with an off-edge-center site, the ordinary coalesced state of DTEPs emerges with three identical self-orthogonal eigenfunctions. Such NH states and their evolution can be generally realized in various artificial systems, such as photonic and sonic crystals, where light and sonic vortex beams with different fractional twisting can be found. Our findings shed new light on fundamental understanding of gapless topological states in NH systems in terms of creation and evolution of high-order EPs, and open up new research directions to further link line graph and flow network theory coupled with topological physics, especially under non-equilibrium gain/loss conditions.
Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations
Here, this study introduces a general approach for the imposition of local boundary conditions in non- ordinary state-based peridynamics (NOSB PD) to eliminate the displacement kinks near the boundary without a fictitious layer under quasi-static loading conditions. It identifies the underlying reason for the unphysical displacement kinks. Under an imposed linear displacement field, the NOSB PD equilibrium equation is not satisfied near the boundary due to the unsymmetric horizon of material points. However, the equilibrium equation derived by using the PD differential operator is satisfied at such material points. Therefore, the material body is divided into three regions to satisfy the equilibrium equations and to impose displacement and tractions boundary conditions. This approach does not deviate from the original NOSB PD; however, it provides a simple solution to eliminate the displacement kink near the boundary, which leads to unphysical stress concentrations. Its efficacy is demonstrated by considering elastic rectangular and square plates subjected to various types of boundary conditions leading to homogeneous as well as nonhomogeneous deformations. The creep response of a rectangular plate further proves the robustness of the present approach. Also, a quasi-static crack propagation from a pre-existing crack in a square plate under mode-I, mode-II and mixed-mode loading conditions demonstrates its capability for failure prediction based on the critical stretch criteria. Finally, its applicability for 3D analysis is demonstrated by considering a rectangular prism under applied stretch and normal stress.
Bond-associated deformation gradients for peridynamic correspondence model
Non-ordinary state-based peridynamic correspondence material model is known to have issues with material instability, i.e. the existence of zero-energy modes, due to non-unique mapping between deformation states and force states via the conventional peridynamic deformation gradient. In this paper, an alternative approach in which the deformation gradient hence force state are computed specifically for each individual bond is proposed to eliminate the material instability. Bond-associated deformation gradient is calculated based on deformation states of material points within an individual bond’s proximity, termed here as the bond-associated family, rather than a material point’s whole family. This bond-associated deformation gradient can better represent the force state of each individual bond from the deformation states of material points in its proximity, and hence inherently resolves issues of material instability in the conventional correspondence material model. Parametric study on bond-associated horizon size indicates that the optimal size should be no less than the material point’s horizon size but smaller than two times of that value. Comparisons against reference solutions using finite element method establish the validity and accuracy of the proposed formulation.
A position-aware linear solid constitutive model for peridynamics
A position-aware linear solid (PALS) peridynamic constitutive model is proposed for isotropic elastic solids. The PALS model addresses problems that arise, in ordinary peridynamic material models such as the linear peridynamic solid (LPS), due to incomplete neighborhoods near the surface of a body. We improved model behavior in the vicinity of free surfaces through the application of two influence functions that correspond, respectively, to the volumetric and deviatoric parts of the deformation. Furthermore, the model is position-aware in that the influence functions vary over the body and reflect the proximity of each material point to free surfaces. Demonstration calculations on simple benchmark problems show a sharp reduction in error relative to the LPS model.
Peridynamic Model for Single-Layer Graphene Obtained from Coarse Grained Bond Forces
An ordinary state-based peridynamic material model is proposed for single sheet graphene. The model is calibrated using coarse grained molecular dynamics simulations. The coarse graining method allows the dependence of bond force on bond length to be determined, including the horizon. The peridynamic model allows the horizon to be rescaled, providing a multiscale capability and allowing for substantial reductions in computational cost compared with molecular dynamics. The calibrated peridynamic model is compared to experimental data on the deflection and perforation of a graphene monolayer by an atomic force microscope probe.
Short-range correlations in carbon-12, oxygen-16, and neon-20: Intrinsic properties
The Brueckner-Hartree-Fock (BHF) method has been applied to nuclei whose intrinsic structure is nonspherical. Reaction matrix elements were calculated as functions of starting energy for the Hamada-Johnston interaction using the Pauli operator appropriate to O-16 and a shifted oscillator spectrum for virtual excited states. Binding energies, single particle energies, radii, and shape deformations of the intrinsic state, in ordinary as well as renormalized BHF, are discussed and compared with previous HF studies and with experiment when possible. Results are presented for C-12, 0-16 and Ne-20. It is found that the binding energies and radii are too small, but that separation energies are well reproduced when the renormalized theory is used.