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Natural frequency bounds for clamped beam with linearly varying compressive load and constant end load by Rayleigh-Ritz, Bazley-Fox second projection and Kato methods
This paper examines the Magsat precision vector magnetometer which is designed to measure projections of the ambient field in three orthogonal directions. The system contains a highly stable and linear triaxial fluxgate magnetometer with a dynamic range of + or - 2000 nT (1 nT = 10 to the -9 weber per sq m). The magnetometer electronics, analog-to-digital converter, and digitally controlled current sources are implemented with redundant designs to avoid a loss of data in case of failures. Measurements are carried out with an accuracy of + or - 1 part in 64,000 in magnitude and 5 arcsec in orientation (1 arcsec = 0.00028 deg).
Two special polyhedra present themselves for the definition of B-splines: a simplex S and a box or parallelepiped B, where the edges of S project into an irregular grid, while the edges of B project into the edges of a regular grid. More general splines may be found by forming linear combinations of these B-splines, where the three-dimensional coefficients are called the spline control points. Univariate splines are simplex splines, where s = 1, whereas splines over a regular triangular grid are box splines, where s = 2. Two simple facts render the development of the construction of B-splines: (1) any face of a simplex or a box is again a simplex or box but of lower dimension; and (2) any simplex or box can be easily subdivided into smaller simplices or boxes. The first fact gives a geometric approach to Mansfield-like recursion formulas that express a B-spline in B-splines of lower order, where the coefficients depend on x. By repeated recursion, the B-spline will be expressed as B-splines of order 1; i.e., piecewise constants. In the case of a simplex spline, the second fact gives a so-called insertion algorithm that constructs the new control points if an additional knot is inserted.
The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.
The biological effects of heavy charged particle (HZE) radiation are of particular interest to travellers and planners for long-duration space flights where exposure levels represent a potential health hazard. The unique feature of HZE radiation is the structured pattern of its energy deposition in targets. There are many consequences of this feature to biological endpoints when compared with effects of ionizing photons. Dose vs response and dose-rate kinetics may be modified, DNA and cellular repair systems may be altered in their abilities to cope with damage, and the qualitative features of damage may be unique for different ions. The nematode Caenorhabditis elegans is being used to address these and related questions associated with exposure to radiation. HZE-induced mutation, chromosome aberration, cell inactivation and altered organogenesis are discussed along with plans for radiobiological experiments in space.
The Surveillance and Test System (SATS) checks the functionality of ATR’s Plant Protection System (PPS). The analogue linearity test checks that the SATS analog and digital conversions are accurate to +/- 61 mVdc. This project analyzes whether this accuracy range can be increased without impacting the uncertainty analysis of the PPS system.
Co3In2S2 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Co is bonded in a distorted linear geometry to four In and two equivalent S atoms. There are two shorter (2.67 Å) and two longer (2.75 Å) Co–In bond lengths. Both Co–S bond lengths are 2.15 Å. There are two inequivalent In sites. In the first In site, In is bonded to six equivalent Co and two equivalent S atoms to form InCo6S2 hexagonal bipyramids that share corners with six equivalent InCo6S2 hexagonal bipyramids and faces with six equivalent InCo6S6 cuboctahedra. Both In–S bond lengths are 3.04 Å. In the second In site, In is bonded to six equivalent Co and six equivalent S atoms to form InCo6S6 cuboctahedra that share corners with six equivalent InCo6S6 cuboctahedra, edges with six equivalent InCo6S6 cuboctahedra, and faces with six equivalent InCo6S2 hexagonal bipyramids. All In–S bond lengths are 3.17 Å. S is bonded in a 3-coordinate geometry to three equivalent Co and four In atoms.
Co3Sn2S2 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Co is bonded in a distorted linear geometry to four Sn and two equivalent S atoms. There are two shorter (2.69 Å) and two longer (2.70 Å) Co–Sn bond lengths. Both Co–S bond lengths are 2.16 Å. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded to six equivalent Co and two equivalent S atoms to form SnCo6S2 hexagonal bipyramids that share corners with six equivalent SnCo6S2 hexagonal bipyramids and edges with six equivalent SnCo6 cuboctahedra. Both Sn–S bond lengths are 2.89 Å. In the second Sn site, Sn is bonded to six equivalent Co atoms to form distorted SnCo6 cuboctahedra that share corners with six equivalent SnCo6 cuboctahedra and edges with six equivalent SnCo6S2 hexagonal bipyramids. S is bonded in a 4-coordinate geometry to three equivalent Co and one Sn atom.
Ni3In2S2 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Ni is bonded in a distorted linear geometry to four In and two equivalent S atoms. There are two shorter (2.72 Å) and two longer (2.76 Å) Ni–In bond lengths. Both Ni–S bond lengths are 2.17 Å. There are two inequivalent In sites. In the first In site, In is bonded to six equivalent Ni atoms to form distorted InNi6 cuboctahedra that share corners with six equivalent InNi6 cuboctahedra and edges with six equivalent InNi6S2 hexagonal bipyramids. In the second In site, In is bonded to six equivalent Ni and two equivalent S atoms to form InNi6S2 hexagonal bipyramids that share corners with six equivalent InNi6S2 hexagonal bipyramids and edges with six equivalent InNi6 cuboctahedra. Both In–S bond lengths are 3.04 Å. S is bonded in a 4-coordinate geometry to three equivalent Ni and one In atom.
Ni3Pb2S2 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Ni is bonded in a distorted linear geometry to four Pb and two equivalent S atoms. There are two shorter (2.82 Å) and two longer (2.84 Å) Ni–Pb bond lengths. Both Ni–S bond lengths are 2.18 Å. There are two inequivalent Pb sites. In the first Pb site, Pb is bonded in a hexagonal planar geometry to six equivalent Ni atoms. In the second Pb site, Pb is bonded to six equivalent Ni and two equivalent S atoms to form corner-sharing PbNi6S2 hexagonal bipyramids. Both Pb–S bond lengths are 3.16 Å. S is bonded in a 3-coordinate geometry to three equivalent Ni and one Pb atom.
LiMo2(PO4)3 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. Li1+ is bonded in a distorted linear geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.85–2.68 Å. There are three inequivalent Mo4+ sites. In the first Mo4+ site, Mo4+ is bonded to six O2- atoms to form MoO6 octahedra that share corners with six equivalent PO4 tetrahedra and edges with two equivalent MoO6 octahedra. There are two shorter (2.13 Å) and four longer (2.23 Å) Mo–O bond lengths. In the second Mo4+ site, Mo4+ is bonded to six O2- atoms to form MoO6 octahedra that share corners with six equivalent PO4 tetrahedra. There is two shorter (1.96 Å) and four longer (2.01 Å) Mo–O bond length. In the third Mo4+ site, Mo4+ is bonded to six O2- atoms to form MoO6 octahedra that share corners with six PO4 tetrahedra and an edgeedge with one MoO6 octahedra. There are a spread of Mo–O bond distances ranging from 1.97–2.22 Å. There are three inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three equivalent MoO6 octahedra. The corner-sharing octahedral tilt angles are 45°. There are a spread of P–O bond distances ranging from 1.49–1.59 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three equivalent MoO6 octahedra. The corner-sharing octahedra tilt angles range from 40–42°. There is one shorter (1.48 Å) and three longer (1.58 Å) P–O bond length. In the third P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with six MoO6 octahedra. The corner-sharing octahedra tilt angles range from 42–55°. There are a spread of P–O bond distances ranging from 1.51–1.60 Å. There are nine inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to one Mo4+ and one P5+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one Mo4+, and one P5+ atom. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to two Mo4+ and one P5+ atom. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one Li1+ and one P5+ atom. In the fifth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Mo4+ and one P5+ atom. In the sixth O2- site, O2- is bonded in a bent 150 degrees geometry to one Li1+ and one P5+ atom. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to one Mo4+ and one P5+ atom. In the eighth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Mo4+ and one P5+ atom. In the ninth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Mo4+ and one P5+ atom.
Cr3Ni2Si crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Cr is bonded in a distorted linear geometry to four equivalent Ni and two equivalent Si atoms. There are two shorter (2.43 Å) and two longer (2.82 Å) Cr–Ni bond lengths. Both Cr–Si bond lengths are 2.80 Å. Ni is bonded to six equivalent Cr, three equivalent Ni, and three equivalent Si atoms to form distorted NiCr6Si3Ni3 cuboctahedra that share corners with three equivalent SiCr6Ni6 cuboctahedra, corners with six equivalent NiCr6Si3Ni3 cuboctahedra, faces with four equivalent SiCr6Ni6 cuboctahedra, and faces with nine equivalent NiCr6Si3Ni3 cuboctahedra. All Ni–Ni bond lengths are 2.48 Å. All Ni–Si bond lengths are 2.25 Å. Si is bonded to six equivalent Cr and six equivalent Ni atoms to form SiCr6Ni6 cuboctahedra that share corners with six equivalent NiCr6Si3Ni3 cuboctahedra, faces with six equivalent SiCr6Ni6 cuboctahedra, and faces with eight equivalent NiCr6Si3Ni3 cuboctahedra.
HgPb2(OCl)2 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. Hg2+ is bonded in a distorted linear geometry to two equivalent O2- and four equivalent Cl1- atoms. Both Hg–O bond lengths are 2.08 Å. All Hg–Cl bond lengths are 3.06 Å. Pb2+ is bonded in a 3-coordinate geometry to three equivalent O2- and five equivalent Cl1- atoms. There are one shorter (2.40 Å) and two longer (2.44 Å) Pb–O bond lengths. There are a spread of Pb–Cl bond distances ranging from 3.34–3.47 Å. O2- is bonded to one Hg2+ and three equivalent Pb2+ atoms to form a mixture of corner and edge-sharing OHgPb3 tetrahedra. Cl1- is bonded in a 7-coordinate geometry to two equivalent Hg2+ and five equivalent Pb2+ atoms.
Ni3Sn2S2 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Ni is bonded in a distorted linear geometry to four Sn and two equivalent S atoms. There are two shorter (2.72 Å) and two longer (2.77 Å) Ni–Sn bond lengths. Both Ni–S bond lengths are 2.18 Å. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded to six equivalent Ni and two equivalent S atoms to form corner-sharing SnNi6S2 hexagonal bipyramids. Both Sn–S bond lengths are 2.91 Å. In the second Sn site, Sn is bonded in a distorted hexagonal planar geometry to six equivalent Ni atoms. S is bonded in a 4-coordinate geometry to three equivalent Ni and one Sn atom.
Tl2Ni3S2 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Ni is bonded in a distorted linear geometry to four Tl and two equivalent S atoms. There are two shorter (2.77 Å) and two longer (2.81 Å) Ni–Tl bond lengths. Both Ni–S bond lengths are 2.17 Å. There are two inequivalent Tl sites. In the first Tl site, Tl is bonded in a distorted hexagonal planar geometry to six equivalent Ni atoms. In the second Tl site, Tl is bonded to six equivalent Ni and two equivalent S atoms to form corner-sharing TlNi6S2 hexagonal bipyramids. Both Tl–S bond lengths are 3.16 Å. S is bonded in a 3-coordinate geometry to three equivalent Ni and one Tl atom.
Ni3Bi2S2 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Ni is bonded in a distorted linear geometry to four Bi and two equivalent S atoms. There are two shorter (2.77 Å) and two longer (2.91 Å) Ni–Bi bond lengths. Both Ni–S bond lengths are 2.18 Å. There are two inequivalent Bi sites. In the first Bi site, Bi is bonded to six equivalent Ni and two equivalent S atoms to form corner-sharing BiNi6S2 hexagonal bipyramids. Both Bi–S bond lengths are 3.03 Å. In the second Bi site, Bi is bonded in a distorted hexagonal planar geometry to six equivalent Ni atoms. S is bonded in a 4-coordinate geometry to three equivalent Ni and one Bi atom.
RbLa9(IrO6)4 crystallizes in the tetragonal I4/m space group. The structure is three-dimensional. Rb1+ is bonded in a distorted linear geometry to two equivalent O2- atoms. Both Rb–O bond lengths are 2.69 Å. There are two inequivalent La3+ sites. In the first La3+ site, La3+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of La–O bond distances ranging from 2.44–2.89 Å. In the second La3+ site, La3+ is bonded to six O2- atoms to form LaO6 octahedra that share corners with six IrO6 octahedra. The corner-sharing octahedra tilt angles range from 0–56°. There are two shorter (2.28 Å) and four longer (2.47 Å) La–O bond lengths. There are two inequivalent Ir5+ sites. In the first Ir5+ site, Ir5+ is bonded to six O2- atoms to form IrO6 octahedra that share corners with two equivalent LaO6 octahedra. The corner-sharing octahedral tilt angles are 56°. There is two shorter (1.95 Å) and four longer (2.04 Å) Ir–O bond length. In the second Ir5+ site, Ir5+ is bonded to six O2- atoms to form IrO6 octahedra that share a cornercorner with one LaO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Ir–O bond distances ranging from 1.95–2.02 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ir5+ atom. In the second O2- site, O2- is bonded in a distorted linear geometry to five La3+ and one Ir5+ atom. In the third O2- site, O2- is bonded to one Rb1+, four equivalent La3+, and one Ir5+ atom to form distorted corner-sharing ORbLa4Ir octahedra. The corner-sharing octahedral tilt angles are 0°. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to three equivalent La3+ and one Ir5+ atom. In the fifth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to three equivalent La3+ and one Ir5+ atom.
Li2(VS2)3 crystallizes in the hexagonal P6_3/mcm space group. The structure is three-dimensional. Li1+ is bonded in a linear geometry to two equivalent S2- atoms. Both Li–S bond lengths are 2.29 Å. V+3.33+ is bonded to six S2- atoms to form distorted edge-sharing VS6 pentagonal pyramids. There are two shorter (2.35 Å) and four longer (2.37 Å) V–S bond lengths. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three equivalent V+3.33+ atoms. In the second S2- site, S2- is bonded in a 3-coordinate geometry to three equivalent V+3.33+ atoms.