Magnetism and cluster growth

The interplay between electronic correlations, magnetism and cluster structure has been investigated by solving exactly a N-site Hubbard Hamiltonian (N ≤ 8) with arbitrary Coulomb-interaction strength U and number of electronsν (1 ≤ ν ≤ 2 N). The calculation of the ground-state energy for all possible site configurations with fixed bond lengths leads to the most stable cluster structure and total spin S for given values of U, ν and N. We discuss the resulting physical behavior together with the built-in limitations of the model.     

Secondary bifurcations in systems with all-to-all coupling. Part II.

In a recent paper Dias and Stewart studied the existence, branching geometry, and stability of secondary branches of equilibria in all-to-all coupled systems of differential equations, that is, equations that are equivariant under the permutation action of the symmetric group S_N. They consider the most general cubic order system of this type. Primary branches in such systems correspond to partitions of N into two parts p, q with p + q = N. Secondary branches correspond to partitions of N into three parts a, b, c with a + b + c = N. They prove that except in the case a = b = c secondary branches exist and are (generically) globally unstable in the cubic order system. In this work they realized that the cubic order system is too degenerate to provide secondary branches if a = b = c. In this paper we consider a general system of ordinary differential equations commuting with the permutation action of the symmetric group S_3n on R³ⁿ. Using singularity theory results, we find sufficient conditions on the coefficients of the fifth order truncation of the general smooth S_3n-equivariant vector field for the existence of a secondary branch of equilibria near the origin with S_n × S_n × S_n symmetry of such system. Moreover, we prove that under such conditions the solutions are (generically) globally unstable except in the cases where two tertiary bifurcations occur along the secondary branch. In these cases, the instability result holds only for the equilibria near the secondary bifurcation points. We show an example where stability between tertiary bifurcation points on the secondary branch occurs.     

Comparison of sensing characteristics of ChemFEC devices based on spin-coated thin films of calix[n]arenes

ChemFECs (chemical field effect capacitors) or EIS (Electrolyte-Insulator-Semiconductor) devices were coated with calix[n]arene macrocycles for cation sensors development. Silicon nitride surface electrodes were spin-coated with p-tert-butylcalix[n]arene molecules for n = 8, 9 and 11. Electrochemical capacitance measurements were carried out to evaluate the sensitivity of the calix[n]arene layers towards specific cations as calcium and copper ions. Sensor responses were due to the “host-guest” specific interaction between the rigid cavity of calix[n]arene receptors (ligand) and chemical ion species. The developed chemical sensors have demonstrated good analytical characteristic in terms of: stability, selectivity and lifetime. In addition, experimental results were fitted using the site binding model in order to determine complex association constants, pK (1.9 ≤ pK ≤ 6.39) and surface density of ligands, N_L (9.10¹⁴ ≤ N_L ≤ 2.10¹⁶). All results obtained in this work were compared with those obtained using silicon dioxide EIS electrodes coated with the same calix[n]arene receptors using both spin-coating and thermal evaporation deposit processes.     

N-particle dynamics of the Euler equations for planar diffeomorphisms

The Euler equations associated with diffeomorphism groups have received much recent study because of their links with fluid dynamics, computer vision, and mechanics. In this article, we consider the dynamics of N point particles or “blobs” moving under the action of the Euler equations associated with the group of diffeomorphisms of the plane in a variety of different metrics. This dynamical system is already in widespread use in the field of image registration, where the point particles correspond to image landmarks, but its dynamical behavior has not previously been studied. The 2-body problem is always integrable, and we analyze its phase portrait under different metrics. In particular, we show that 2-body capturing orbits (in which the distances between the particles tend to 0 as t  → ∞) can occur when the kernel is sufficiently smooth and the relative initial velocity of the particles is sufficiently large. We compute the dynamics of these “dipoles” with respect to other test particles, and supplement the calculations with simulations for larger N that illustrate the different regimes.     

MHD flow and heat transfer due to ecentric rotations of a porous disc and a fluid at infinity

An exact solution of the steady 3-dimensional Navier-Stokes equations and the energy equation is derived for the case of flow due to non-coaxilly rotations of a porous disc and a fluid at infinity in the presence of a uniform transverse magnetic field. It is observed that asymptotic solution exists for the velocity profile both in the case of suction and blowing. Further, it is seen that the velocity boundary layer shows a thickness of 0 (1/) in case of suction and it is of 0 (1/γ) in the case of blowing. While, the thermal boundary layer exhibits a double-deck structure of 0 (1/SP_r) and 0 (1/) in case SP_r − ≠ 0 and single-deck structure of 0 (1/) in case SP_r = = 0. Here a, γ depends on suction S, magnetic parameter N and P_r the Prandtl number.     

Validation and calibration of a lateral confinement model for long-rod penetration at ordnance and high velocities

In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, “How wide should the target be to exert enough confinement?” For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement.

We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius “b” at which σ_r (b) = 0 (σ_r = radial stress component). We did this for three cases: ceramic targets, metal targets, and ceramic targets confined in a metal casing. Generally, σ_r (a) is a decreasing function of “a” (“a” = expanding cavity radius, and σ_r (a) = the stress needed to continue opening the cavity). In the usual cavity expansion problem b → ∞, σ_r (a) = const., R =−σ_r (a) (R = resistance to penetration). For finite “b” we estimate R by averaging σ_r (a) over a range o ≤ a ≤ a_r, (where a_r, the upper bound of the range, is calibrated from computer simulations).

We ran 14 computer simulations with the CTH wavecode and used the results to calibrate a_r for the different cases and to establish the overall validity of our approach.

We show that generally for D_t/D_p > 30, the degree of confinement is higher than 95% (D_t = target diameter; D_p = projectile diameter; and degree of CONFINEMENT = R/R_∞; R∞ = resistance of a laterally infinite target). We also show the tensile strength of ceramic targets (represented by the spall strength P_min) has a significant effect on the degree of confinement, while other material parameters have only a minor effect.     

Dielectric and piezoelectric properties of sol–gel derived Ca doped PbTiO3

Synthesis of Ca doped PbTiO₃ powder by a chemically derived sol–gel process is described. Crystallization characteristics of different compositions Pb_1−xCa_xTiO₃ (PCT) with varying calcium (Ca) content in the range x = 0–0.45 has been investigated by DTA/TGA, X-ray diffraction and scanning electron microscopy. The crystallization temperature is found to decrease with increasing calcium content. X-ray diffraction reveals a tetragonal structure for PCT compositions with x ≤ 0.35, and a cubic structure for x = 0.45. Dielectric properties on sintered ceramics prepared with fine sol–gel derived powders have been measured. The dielectric constant is found to increase with increasing Ca content, and the dielectric loss decreases continuously. Sol–gel derived Pb_1−xCa_xTiO₃ ceramics with x = 0.45 after poling exhibit infinite electromechanical anisotropy (k_t/k_p) with a high d₃₃ = 80 pC/N, ′ = 298 and low dielectric loss (tan δ = 0.0041).     

Performance of transmission dynode photomultipliers in magnetic fields up to 1.5 T

The performance of commercially available photomultiplier tubes with 1, 2, 8 and 16 parallel transmission dynodes is examined in homogeneous magnetic fields B with strengths up to 1.5 T and axial as well as nonaxial orientations. The samples with 16 dynodes allow an operation with gains G ≥ 10³ and time resolutions σ ≤ 230 ps in such strong fields and for tilting angles θ ≤ 50°. The dependence of relative gain G/G(B = 0) and time resolution σ on B and θ is less expressed for the PMs with the smaller numbers of dynodes and a more compact design. The influence of B(θ) on the transit time is discussed qualitatively.     

Three phases in the system Hg1 − xCxBa2CuOy (0.00 ≤ x ≤ 1.00)

Samples of the [Hg_{1 − x}C_x]-Ba₂CuOy system [(Hg,C)-1201] with stoichiometries within the range 0.00≤x≤1.00 were synthesized by a highpressure, high-temperature technique. The sample with X = 0.00 [HgBa₂CuO_4+δ] was non-superconducting with lattice parameters A = 3.8676(2) Å, C = 9.470(1) Å. At low ranges of substitution (0.10≤x≤0.30), the predominant phase was found to be Hg-1201 with identical lattice parameters to those found for X = 0.00. At X = 0.40 the Hg-1201 phase coexists in similar proportions with the phase of mixed [Hg_{1 − x},C_x]-1201 stoichiometry. At X = 0.50, this second phase with lattice parameters A = 3.9271(3) Å, C = 8.676(2) Å is predominant and only traces of the Hg-1201 phase were found. At X = 0.75 the [Hg_{1 − x},C_x]-1201 phase found for X = 0.50 coexists with the CO₃Ba₂CuO_y phase, which is the extreme of the substitution range. This latter was predominant at X = 1.00 with lattice parameters A = 4.0044(3) Å, C = 7.909(1) Å, but at higher pressure than the previous substitutions. This system is constituted of three main phases, HgBa₂CuO_{4 + δ}, Hg_{1 − x}C_xBa₂CuO_y (x ≈ 0.50) and CO₃Ba₂CuO_y, which appear in different proportions according to the percentage of substitution and the applied synthesis pressure.     

The micropolar thermoelastic problem of uniform heat-flow interrupted by an insulated penny-shaped crack

The classical problem of uniform heat-flow disturbed by an insulated penny-shaped crack is solved in the context of micropolar elasticity. The mode II stress intensity factor, K_II is found to depend on two new non-dimensional parameters N and τ − N is a measure of the coupling of the displacement field with the microstructure or the medium (0 N √2) and τ is the ratio of a material characteristic length to the crack radius. K_II remains higher than its classical value when N > 0, τ > 0 and attains the classical value as N and τ vanish. A closed-form expression to K_II is obtained in the physically important limiting case of τ → 0 with N fixed. In this limit the relative increment in K_II, over its classical value, is found to be (1 − v')N² where v' is the micropolar Poisson's ratio.     

Statistical investigation of surface fatigue cracks in large-sized turbine rotor shaft steel

Distribution properties of an initiation life N_i and a propagation life N_p of surface cracks, statistical characteristics of a crack growth rate dl/dN, and a relationship between a scatter of the distributions and a gradient a of S-log N curves in rotating bending fatigue tests were investigated for Ni-Cr-Mo-V steel, using for a large-sized turbine rotor shaft. The distributions of N_i and N_p were expressed as Weibull distributions, and the scatter of them for smooth specimens and for lower stress amplitude σ_a tests were larger than those for notched ones and for higher σ_a tests, respectively. The statistical properties of crack propagation rate were almost similar in both smooth and notched specimens. The relationship between the a and a coefficient of variation η for the distributions of N_i, N_p and a final fracture life N_f was expressed as η = c(a)^−b, where c and b are constants.     

Synthesizing and Physical Properties of GdPr-123 High-Tc Superconductor

Ceramic Gd_1-xPr_xBa₂Cu₃O_7-y (GdPr-123) high-T_c superconductors have been synthesized by the standard solid state reaction method and characterized by XRD, SEM, TGA, and DT techniques in the range of x, 0.0 ≤ x ≤ 1.0 Samples have orthorhombic structure with Pmmm symmetry and there is a small percentage (less than 1%) of the Ba sites occupied by Pr ions in some Pr-rich samples. In these samples a small trace of BaCuO₂ and Pr BaO₃ secondary phases persist with the main peaks at 2θ = 29.3° and 28.9° respectively. Microstructure analysis indicates a uniform grain size distribution with a mean size of 5 μm. No significant change of grain size is shown throughout the range of x studied. The valence of Pr and Cu were determined by magnetization measurements in the temperature range 100 to 250°K. These data reveal a valence of 3.86+ for Pr in all samples independant of x. The similarity of the superconducting and insulating properties in this system to those of the oxygen deficient RBa₂Cu₃O₇ (R-123) (R: Y or rare earth) system implies that the mechanism of superconductivity in high-T_c. superconductors cannot be two-dimensional, even though the superconductive current occurs in two dimensions.     

Correlations between structural and electrical properties of the oxyfluorides observed in the YOF-BiOF system

An investigation of the YOF-BiOF system at 850°C has allowed to isolate an ordered Y_0.75Bi_0.25OF phase and a Y_1−xBi_xOF solid solution (0.52 ≤ x ≤ 0.95).

For x ≤ 0.80 the structure is of fluorite-type and for 0.80 < x ≤ 0.95 it shows a fluorite derived rhombohedral distortion. Correlations between structural and electrical properties are established and compared with those of the analogous Pb_xMO S_8-y solid solution (0 ≤ x ≤ 0.80).     

Comparison between measurements on Rayleigh scattering and form-factor theories for 1 Å ≤ x ≤ 50 Å

From our measured differential cross section of Rayleigh scattering, the form factor for momentum transfers in the range 1 Å⁻¹ ≤ x ≤ 50 Å⁻¹ was deduced. Data for U, Pb, Pt, W, Sn, Cd, Ag, Mo and Cu at energies from 60 to 662 keV and scattering angles ranging from 5° to 140° were used. In addition, for the region 1 Å⁻¹ ≤ x ≤ 50 Å⁻¹ of momenta, experimental data from other authors at higher energies were analyzed. The experimental values obtained were compared with various form-factor theories and limits of validity are established. For the relativistic modified form factor G a good agreement always exists for θ ≤ 65°, independently of energy and atomic number.     

Influence of stress ratio at baseline loading on delayed retardation phenomena of fatigue crack growth in A553 steel and A5083 aluminium alloy

The delayed retardation phenomena of fatigue crack growth following a single application of tensile overload were investigated under the baseline loading with the stress ratio, R = σ_min/σ_max, ranging from −1 to 0.5 for A553 steel and A5083 aluminium alloy. Two different overload cycles were applied; the one is the case that the ratio of peak stress range to baseline stress range, r = Δσ₂/Δσ₁, is equal to two and the other is the case that the ratio of maximum peak stress to maximum baseline stress, σ_2max/σ_1max, is equal to two. The retardation took place stronger in aluminium than in steel. Under the condition of r = 2 the normalized number of cycles, N_D/N_C, (N_D: the number of cycles during retardation, N_C: the number of cycles required for propagation through the overload-affected-zone size) decreased slightly as the R ratio increased from −1 to 0.5, while under the condition of σ_2max/σ_1max = 2 the N_D/N_C-values increased drastically as the R ratio increased from −1 to 0 (or the overload ratio, r, increased from 1.5 to 2) in both the materials. These retardation behaviors were expressed theoretically according to the model proposed by Matsuoka and Tanaka [1, 3] by using four parameters: the overload ratio, r, the exponent in Paris equation, m, the overload-affected-zone size, ω_D, and the distance at the inflection point, ω_B.     

Impact and penetration by L/D ≤ 1 projectiles

Calculations of steel target penetration by L/D ≤ 1 tungsten and tungsten alloy projectiles have been extended to L/D = 1/32 over the velocity range 1.5 to 5 km/s. The ratio of crater to projectile diameter tends to 1 as L/D decreases over this entire velocity range. For impact velocities of 1.5 and 3 km/s, penetration depth normalized by projectile length, P/L, increases with decreasing projectile L/D up to a maximum value and then decreases for still lower L/D. Experiments at impact velocities of 2 and 3 km/s confirm these results. For 5 km/s impact velocity, the calculations show P/L increasing with decreasing projectile L/D over the entire range 1/32 ≤ L/D ≤ 1. The projectile L/D for which the maximum P/L occurs appears to depend on the impact velocity. P/L generally scales with impact velocity as P/L v^f(L/D) where f(L/D) ranges from 0 for a long rod to, we believe, 2 in the limit as projectile L/D approaches zero. The calculations show for 1/8 ≤ L/D ≤ 1/2, P/L v^0.9; for L/D = 1/16, P/L v^1.5; and for L/D = 1/32, the new results give P/L v^1.9.     

Crystal structure of the orthorhombic U2-Al4Mg4Si4 precipitate in the Al–Mg–Si alloy system and its relation to the β′ and β″ phases

The atomic structure of a common precipitate in the Al–Mg–Si system has been determined. It is isotypic with TiNiSi (space group Pnma) and contains four units of MgAlSi in a unit cell of size a = 0.675 nm, b = 0.405 nm, c = 0.794 nm. EDS analyses support the composition. A model was based on the atomic structure of the β′ precipitate, electron diffraction and high-resolution transmission electron microscopy (HRTEM) images. A quantum mechanical refinement of the model removed discrepancies between simulated and experimental diffraction intensities. Finally, a multi-slice least square refinement confirmed the structure. The structural relation with β″ is investigated. A similar Mg–Si plane also existing in β″ and β′, can explain most coherency relations between the precipitate phases and with matrix.     

X-ray analysis of heat-treated titanium nitride films

Titanium nitride films deposited onto steel substrates maintained at 423 K were heat treated in the temperature interval 773–1173 K. Samples were studied by electron probe microanalysis and X-ray diffraction. The high values of the microhardness observed for the as-deposited films decreased after annealing for 3 h at 973 K to nearly bulk values. This decrease is mainly due to the improvement in the microstructure of the films. It is accompanied by strong decreases in strain, stress and the lattice parameter of δ-TiN_x. Growth of the ε-Ti₂N phase at the expense of the δ-TiN_x phase was observed in a film with 34 at .% N when it was annealed for 3 h at 973 K. The lattice parameter and strain in the substrate increased after film deposition, most probably due to a dissolution of nitrogen or titanium atoms in the lattice of -Fe.     

Analysis of interface states and series resistance at MIS structure irradiated under Co γ-rays

In this research, we investigated the effect of ⁶⁰Co γ-ray exposure on the electrical properties of Au/SnO₂/n-Si (MIS) structures using current–voltage (I–V) measurements. The fabricated devices were exposed to γ-ray doses ranging from 0 to 300 kGy at a dose rate of 2.12 kGy h⁻¹ in water at room temperature. The density of interface states N_ss as a function of E_c–E_ss is deduced from the forward bias I–V data for each dose by taking into account the bias dependence effective barrier height and series resistance of device at room temperature. Experimental results show that the γ-irradiation gives rise to an increase in the zero bias barrier height Φ_BO, as the ideality factor n and N_ss decrease with increasing radiation dose. In addition, the values of series resistance were determined using Cheung's method. The R_s increases with increasing radiation dose. The results show that the main effect of the radiation is the generation of interface states with energy level within the forbidden band gap at the insulator/semiconductor interface.     

Impact parameter dependent k-shell ionization probabilities in ion-atom collisions with different asymmetry

We present experimental probabilities P_κ(θ) for target K-shell ionization in 1.26 MeV/u He → Te, Dy; N → In, Nd collisions up to very large scattering angles (θ 170°). The P_κ(θ) are nearly constant for θ > 10°. Groups of collision systems with about the same sum of projectile and target nuclear charge (Z_P + Z_T = united atom system) and collision velocity were s probabilities are within these groups of collision systems nearly proportional to the square of the projectile nuclear charge even up to Z_p/Z_T = 0.7. The calculations in the semiclassical approximation (SCA) by Trautmann et al. are compatible with the experimental results when the recoil effect is included and wave functions of the united atom system are used.