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At least 325 records · Page 18

Finite-element time evolution operator for the anharmonic oscillator

The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

Milton, Kimball A.↗

Accounting for crustal magnetization in models of the core magnetic field

The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.

Jackson, Andrew↗

In-Situ Oxygen Isotopic Composition of Tagish Lake: An Ungrouped Type 2 Carbonaceous Chondrite

We have measured the oxygen isotopic composition of several components of Tagish Lake by ion microprobe. This meteorite constitutes the best preserved sample of C2 matter presently available for study. It presents two different lithologies (carbonate-poor and -rich) which have fairly comparable oxygen isotopic composition, with regard to both the primary or secondary minerals. For the olivine and pyroxene grains, their delta O-18 values range from - 10.5% to + 7.4% in the carbonate-poor lithology, with a mean Delta O-17 value of - 3.7 2.4%. In the carbonate-rich lithology, delta O-18 varies from - 7.9% to + 3.3%, and the mean Delta O-17 value is - 4.7 +/- 1.4%. Olivine inclusions (Fo(sub >99)) with extreme O-16-enrichment were found in both lithologies: delta O-18 = - 46.1 %, delta O-187= - 48.3% and delta O-18 = - 40.6%, delta O-17 = - 41.2% in the carbonate-rich lithology; delta O-18 = - 41.5%, delta O-17 = -43.4%0 in the carbonate-poor lithology. Anhydrous minerals in the carbonate-poor lithology are slightly more O-16-rich than in the carbonate-rich one. Four low-iron manganese-rich (LIME) olivine grains do not have an oxygen isotopic composition distinct from the other "normal" olivines. The phyllosilicate matrix presents the same range of oxygen isotopic compositions in both lithologies: delta O-18 from approximately 11 % to approximately 6%, with an average Delta. O-17 approximately 0%. Because the bulk Tagish Lake oxygen isotopic composition given by Brown et al. is on the high end of our matrix analyses, we assume that this "bulk Tagish Lake" composition probably only represents that of the carbonate-rich lithology. Calcium carbonates have delta O-18 values up to 35%, with Delta O-17 approximately 0.5%0. Magnetite grains present very high Delta O-17 values approximately + 3.4%0 +/- 1.2%. Given our analytical uncertainties and our limited carbonate data, the matrix and the carbonate seem to have formed in isotopic equilibrium. In that case, their large isotopic fractionation would argue for a low temperature (CM-like, T approximately 0 deg) formation. Magnetite probably formed during a separate event. Tagish Lake magnetite data is surprisingly compatible with that of R-chondrites and unequilibrated ordinary (LL3) chondrites. Our oxygen isotope data strongly supports the hypothesis of a single precursor for both lithologies. Drastic mineralogical changes between the two lithologies not being accompanied with isotopic fractionation seem compatible with the alteration model presented by Young et aI. Tagish Lake probably represents the first well preserved large sample of the C2 matter that dominates interplanetary matter since the formation of the solar system.

Zolensky, Michael E.↗

K-Shell Photoionization of Nickel Ions Using R-Matrix

We present R-matrix calculations of photoabsorption and photoionization cross sections across the K edge of the Li-like to Ca-like ions stages of Ni. Level-resolved, Breit-Pauli calculations were performed for the Li-like to Na-like stages. Term-resolved calculations, which include the mass-velocity and Darwin relativistic corrections, were performed for the Mg-like to Ca-like ion stages. This data set is extended up to Fe-like Ni using the distorted wave approximation as implemented by AUTOSTRUCTURE. The R-matrix calculations include the effects of radiative and Auger dampings by means of an optical potential. The damping processes affect the absorption resonances converging to the K thresholds causing them to display symmetric profiles of constant width that smear the otherwise sharp edge at the K-shell photoionization threshold. These data are important for the modeling of features found in photoionized plasmas.

Witthoeft, M. C.↗

Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Graphite fiber reinforced thermoplastic glass matrix composites for use at 1000 F

The fabrication and properties of the graphite fiber reinforced glass matrix composite system are described. By reinforcing borosilicate glass with graphite fibers it has been possible to develop a composite whose properties can be compared favorably with resin matrix counterparts. Both high elastic modulus and strength can be obtained and maintained to temperatures of approximately 600 C. In addition, composite dimensional stability is superior to resin or metal matrix systems due to the low thermal expansion behavior of the glass matrix.

Prewo, K. M.↗

Joining and Assembly of Bulk Metallic Glass Composites Through Capacitive Discharge

Bulk metallic glasses (BMGs), a class of amorphous metals defined as having a thickness greater than 1 mm, are being broadly investigated by NASA for use in spacecraft hardware. Their unique properties, attained from their non-crystalline structure, motivate several game-changing aerospace applications. BMGs have low melting temperatures so they can be cheaply and repeatedly cast into complex net shapes, such as mirrors or electronic casings. They are extremely strong and wear-resistant, which motivates their use in gears and bearings. Amorphous metal coatings are hard, corrosion-resistant, and have high reflectivity. BMG composites, reinforced with soft second phases, can be fabricated into energy-absorbing cellular panels for orbital debris shielding. One limitation of BMG materials is their inability to be welded, bonded, brazed, or fastened in a convenient method to form larger structures. Cellular structures (which can be classified as trusses, foams, honeycombs, egg boxes, etc.) are useful for many NASA, commercial, and military aerospace applications, including low-density paneling and shields. Although conventional cellular structures exhibit high specific strength, their porous structures make them challenging to fabricate. In particular, metal cellular structures are extremely difficult to fabricate due to their high processing temperatures. Aluminum honeycomb sandwich panels, for example, are used widely as spacecraft shields due to their low density and ease of fabrication, but suffer from low strength. A desirable metal cellular structure is one with high strength, combined with low density and simple fabrication. The thermoplastic joining process described here allows for the fabrication of monolithic BMG truss-like structures that are 90% porous and have no heat-affected zone, weld, bond, or braze. This is accomplished by welding the nodes of stacked BMG composite panels using a localized capacitor discharge, forming a single monolithic structure. This removes many complicated and costly fabrication steps. Moreover, the cellular structures detailed in this work are among the highest- strength and most energy-absorbent materials known. This implies that a fabricated structure made from these materials would have unequaled mechanical properties compared to other metal foams or trusses. The process works by taking advantage of the electrical properties of the matrix material in the metal-matrix composite, which in this case is a metallic glass. Due to the random nanoscale arrangement of atoms (without any grain boundaries), the matrix glass exhibits a near-constant electrical resistivity as a function of temperature. By placing the composite panels between two copper electrode plates and discharging a capacitor, the entire matrix of the panel can be heated to approximately 700 C in 10 milliseconds, which is above the alloy s solidus but below the liquidus. By designing the geometry of the panels into the shape of an egg box, the electrical discharge localizes only in the tips of each pyramidal cell. By applying a forging load during discharge, the nodes of the panels can be fused together into a single piece, which then dissipates heat through radiation back into a glassy state. This means that two panels can be metallurgically fused into one panel with no heat-affected zone, creating a seamless connection between panels. During the process, the soft metal particles (dendrites) that are uniformly distributed in the glassy matrix to increase the toughness are completely unaffected by the thermoplastic joining. The novelty is that a truss (or foam-like) structure can be formed with excellent energy- absorbing capabilities without the need for machining. The technique allows for large-scale fabrication of panels, well-suited for spacecraft shields or military vehicle door panels. Crystalline metal cellular structures cannot be fabricated using the thermoplastic joining technique described here. If metal panels were te assembled into a cellular structure, they would either have to be welded, brazed, bonded, or fastened together, creating a weak spot in the structure at each connection. Welded parts require a welding material to be added to the joint and exhibit a soft and weak heat-affected zone. Brazing and bonding do not form a metallurgical joint and thus exhibit low strengths, especially when the panels are pulled apart and fasteners require high-stress-concentration holes to be drilled. No equivalent rapid heating method exists for assembling metal panels together into cellular structures, and thus, those parts must be foamed, machined, or investment cast if they are to form a monolithic structure. If the crystalline panels were to be joined using capacitive discharge, as with a spot welder, their bond would be very weak, and the panels would have to be extremely thin. In contrast, the strength of joined BMG parts has been demonstrated to have strength comparable to the parent material. This technique opens up the possibility of using large-scale BMG hardware in spacecraft, military, or commercial applications.

Hofmann, Douglas C.↗

Spatially Resolved Raman Spectroscopy of Thin Carbon Interphase in SiC Ceramic Matrix Composites

A dedicated analysis method is presented to extract the Raman spectrum of an interphase layer thinner than the laser spot size. We focused on spatial correlations between the contrast of optical micrographs and Raman hyperspectral data to predict the constituents of the mixed spectra measured near the interphase. By employing a mapping step size of 0.1 μm, the Raman spectrum of approximately 0.3-μm-thick carbon interphase in a SiC fiber-reinforced SiC matrix composite was extracted from data acquired with a theoretical spot size of about 0.7 μm. Notably, conventional chemometrics procedures were unable to isolate the interphase signal, instead producing a spectrum representing a mixture of interphase and matrix. This study used another composite with approximately 0.9-μm-thick interphase to validate the analysis method, enabling direct measurement of the interphase spectrum. The proposed Raman analysis method has advantages in specimen volume and turnaround time compared to traditional characterization methods, such as transmission electron microscopy. In conclusion, this study also evaluates the applicability of the analysis method to different composite materials and identifies key requirements of the measurements, including the ratio of interphase thickness to spot size and the homogeneity of the surrounding matrix.

ceramic matrix composite↗

Reverse annealing for nonnegative/binary matrix factorization

It was recently shown that quantum annealing can be used as an effective, fast subroutine in certain types of matrix factorization algorithms. The quantum annealing algorithm performed best for quick, approximate answers, but performance rapidly plateaued. In this paper, we utilize reverse annealing instead of forward annealing in the quantum annealing subroutine for nonnegative/binary matrix factorization problems. After an initial global search with forward annealing, reverse annealing performs a series of local searches that refine existing solutions. The combination of forward and reverse annealing significantly improves performance compared to forward annealing alone for all but the shortest run times.

97 MATHEMATICS AND COMPUTING↗

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

cloud droplets↗

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗

Random insights into the complexity of two-dimensional tensor network calculations

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (“not too entangled”) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work, we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at a large bond dimension. Through this statistical-mechanics lens, we argue that (i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, and (ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. Furthermore, these results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Local stress within a granular molecular solvent matrix, a mechanism for individual ion hydration

The activity of water is important in many natural systems and directed processes. To better understand water activity, the hydration of individual ions is approximated for a recently developed speciation-based solution model. Here a matrix of values for hydration of complete salts (anion and cation) was used as source data to calculate individual ion hydration values. Some electrolytes were excluded from calculations of individual ion hydration due to the prevalence of ion pairing and resulting liberation of water upon ion pairing. Evaluation of the periodic trends emerging from individual ion hydration values suggests that ionic volume, relative to the volume of molecular water, dictates both modeled hydration requirements (related to vapor-liquid-equilibrium-derived activity) as well as properties historically described by hydrodynamic radius (ion diffusion and solution viscosity). When water is conceptualized as a granular three-dimensional matrix, solutes may function as substitutional defects (dilation or constriction) inducing local compressive or tensile stress. These results have implications on the mechanism of the Hofmeister series and series reversals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elevated temperature slow plastic deformation of NiAl-TiB2 particulate composites at 1200 and 1300 K

Elevated temperature compression testing has been conducted in air at 1200 and 1300 K with strain rates varying from about 10 to the -4th to about 10 to the -7th/sec on NiAl-TiB2 particulate composites. These materials, which consisted of a B2 crystal structure intermetallic Ni-50 at. pct Al matrix and from 0 to 30 vol pct of approximately 1- micron diameter TiB2 particles, were fabricated by XD synthesis and hot pressed to full density. Flow strength of the composites increased with volume fraction of the strengthening phase with NiAl-30TiB2 being approximately three times stronger than NiAl. Comparison of the light optical and TEM microstructures of as-received and tested samples revealed that reactions did not occur between the two phases, and NiAl-TiB2 interfaces were not cracked during deformation. Additional TEM indicated that the particles stabilize a vastly different microstructure in the NiAl matrix of the composites than that formed in unreinforced NiAl.

Whittenberger, J. Daniel↗

Evidence for Live Cl-36 in Ca-Al-rich Inclusions from the Ningqiang Carbonaceous Chondrite

The short-lived radionuclide Cl-36 decays to either Ar-36 (98.1%, beta(sup -)) or S-36 (1.9%, epsilon and beta(sup +)), with a half life of 3.01 x 10(exp 5) yr. Both the nucleosynthetic and spallation models suggest high initial Cl-36/Cl-35 ratios ((Cl-36/Cl-35)o up to approximately 10(exp -4)) in the early solar system. Previous observed excess Ar-36 in Efremovka matrix has been interpreted to represent a much lower (Cl-36/Cl-35)o ratio of approximately 1 x 10(exp -6). From the observed S-36 excesses in sodalite in calcium aluminum-rich inclusions (CAIs), we report in this study the first direct evidence of the presence of Cl-36 in primitive meteorites. The inferred (Cl-36/Cl-35)o ratios range from approximately 5 x 10(exp -6) to approximately 1 x 10(exp -5).

Lin, Y.↗

Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis.

Bergen, Fred D.↗

Processing and properties of fiber reinforced polymeric matrix composites: I. IM7/LARC(TM)-PETI-7 polyimide composites

A phenylethynyl terminated imide oligomer formed from the reaction of benzophenone tetracarboxylic acid dianhydride, an 75:25 molar ratio of 4,4'-oxydianiline and meta-phenylenediamine and 4-phenylethynylphthalic anhydride as the endcapper at a theoretical number average molecular weight (Mn) of approximately 3,700 g/mol was evaluated as a composite resin matrix. A glass transition temperature (Tg) of 315 deg C was reached after 250 deg C/1 hr annealing of the matrix resin. Unidirectional prepreg was made by coating an N-methylpyrrolidinone solution of the amide acid oligomer onto unsized IM7 graphite fibers. The thermal and rheological properties and the solvent/volatile depletion rates of the amide acid/NMP system were determined. This information was used to successfully design a molding cycle for composite fabrication. Composites molded under 800 Psi at 371 C consistently yielded good consolidation as measured by C-scan and optical photomicrography. The composite's short beam shear strength (SBS), longitudinal and transverse flexural strengths and moduli were measured at various temperatures. These composites exhibited excellent room temperature (RT) longitudinal flexural strength and modulus and RT SBS strength retention at 177 C.

Hou, Tan-Hung↗

Growth of single-crystal columns of CoSi2 embedded in epitaxial Si on Si(111) by molecular beam epitaxy

The codeposition of Si and Co on a heated Si(111) substrate is found to result in epitaxial columns of CoSi2 if the Si:Co ratio is greater than approximately 3:1. These columns are surrounded by an Si matrix which shows bulk-like crystalline quality based on transmission electron microscopy and ion channeling. This phenomenon has been studied as functions of substrate temperature and Si:Co ratio. Samples with columns ranging in average diameter from approximately 25 to 130 nm have been produced.

Fathauer, R. W.↗