Criticality of the exponential rate of decay for the largest nearest-neighbor link in random geometric graphs

Let n points be placed independently in d-dimensional space according to the density f(x) = A(d)e(-lambda parallel to x parallel to alpha), lambda, alpha > 0, x is an element of R-d, d >= 2. Let d(n) be the longest edge length of the nearest-neighbor graph on these points. We show that (lambda(-1) log n)(1-1/alpha) d(n) - b(n) converges weakly to the Gumbel distribution, where b(n) similar to ((d - 1)/lambda alpha) log log n. We also prove the following strong law for the normalized nearest-neighbor distance (d) over tilde (n) = (lambda(-1) log n)(1-1/alpha) d(n)/log log n: (d - 1)/alpha lambda <= lim inf(n ->infinity) (d) over tilde (n) <= lim sup(n ->infinity) (d) over tilde (n) <= d/alpha lambda almost surely. Thus, the exponential rate of decay alpha = 1 is critical, in the sense that, for alpha > 1, d(n) -> 0, whereas, for alpha <= 1, d(n) -> infinity almost surely as n -> infinity.

Effect of Strain Rate on Evolution of the Deformation Microstructure and Texture in Polycrystalline Copper and Nickel

The evolution of crystallographic texture in polycrystalline copper and nickel has been studied. The deformation texture evolution in these two materials over seven orders of magnitude of strain rate from 3 x 10(-4) to similar to 2.0 x 10(+3) s(-1) show little dependence on the stacking fault energy (SFE) and the amount of deformation. Higher strain rate deformation in nickel leads to weakerh < 101 > texture because of extensive microband formation and grain fragmentation. This behavior, in turn, causes less plastic spin and hence retards texture evolution. Copper maintains the stable end < 101 > component over large strain rates (from 3 x 10(-4) to 10(+2) s(-1)) because of its higher strain-hardening rate that resists formation of deformation heterogeneities. At higher strain rates of the order of 2 x 10(+3) s(-1), the adiabatic temperature rise assists in continuous dynamic recrystallization that leads to an increase in the volume fraction of the < 101 > component. Thus, strain-hardening behavior plays a significant role in the texture evolution of face-centered cubic materials. In addition, factors governing the onset of restoration mechanisms like purity and melting point govern texture evolution at high strain rates. SFE may play a secondary role by governing the propensity of cross slip that in turn helps in the activation of restoration processes.

High-Temperature (1023 K to 1273 K 750 degrees C to 1000 degrees C]) Plastic Deformation Behavior of B-Modified Ti-6Al-4V Alloys: Temperature and Strain Rate Effects

A minor addition of B to the Ti-6Al-4V alloy, by similar to 0.1 wt pct, reduces its as-cast prior beta grain size by an order of magnitude, whereas higher B content leads to the presence of in situ formed TiB needles in significant amounts. An experimental investigation into the role played by these microstructural modifications on the high-temperature deformation behavior of Ti-6Al-4V-xB alloys, with x varying between 0 wt pct and 0.55 wt pct, was conducted. Uniaxial compression tests were performed in the temperature range of 1023 K to 1273 K (750 degrees C to 1000 degrees C) and in the strain rate range of 10(-3) to 10(+1) s(-1). True stress-true strain responses of all alloys exhibit flow softening at lower strain rates and oscillations at higher strain rates. The flow softening is aided by the occurrence of dynamic recrystallization through lath globularization in high temperature (1173 K to 1273 K 900 degrees C to 1000 degrees C]) and a lower strain rate (10(-2) to 10(-3) s(-1)) regime. The grain size refinement with the B addition to Ti64, despite being marked, had no significant effect on this. Oscillations in the flow curve at a higher strain rate (10(0) to 10(+1) s(-1)), however, are associated with microstructural instabilities such as bending of laths, breaking of lath boundaries, generation of cavities, and breakage of TiB needles. The presence of TiB needles affected the instability regime. Microstructural evidence suggests that the matrix cavitation is aided by the easy fracture of TiB needles.

Effect of favorable pressure gradient on transitional spot formation rate

The calculation of the transitional boundary layer requires estimates of the extent of the transition zone, which in turn depends on the rate at which turbulent spots are formed. This rate has been found to scale with local boundary layer thickness and viscosity, and the resulting nondimensional group (called crumble) is a function of the pressure gradient, among other parameters. Available experimental data are analyzed to show that the crumble increases slowly with increasing favorable pressure gradients, being about four times as large as in constant-pressure flow when the Thwaites pressure gradient parameter at the effective origin of the resulting turbulent boundary layer is 0.1 and when transition is driven by free-stream turbulence.

Measurement of the corrosion rate of aluminium in sodium hydroxide using holographic interferometry

The application of holographic interferometry to the measurement of the corrosion rate of aluminium in sodium hydroxide is investigated. Details of the fabrication of the corrosion cell and the experimental procedure are given. Thickness loss of aluminium was found for different dissolution times and compared with the conventional weight-loss method using a microbalance.

Position and Feed-Rate Control for Contouring Numerical-Control Systems

Numerical control (NC) for contouring operations requires precise control of position and feed rate for approximating the contour by linear moves of the cutter. A control scheme, for generating linear moves with desired slopes for the cutter, is described. This scheme provides for nine successive linear moves, and may be either expanded or implemented in succession, for approximating a contour.

Temperature and pressure dependence of 35Cl NQR in NaClO3 and Ba(ClO3)2·H2O

Pressure and temperature dependence of 35Cl nuclear quadrupole resonance (NQR) has been investigated in NaClO3 and Ba(ClO3)2·H2O. NQR frequencies are measured in the temperature range 77–300 K and up to 5 kbar pressure. The torsional frequency of the ClO3 pyramid and its variation with both pressure and temperature are evaluated from the NQR frequencies under the harmonic approximation. In general, the pressure effect on the internal motions is found to be less in Ba (ClO3)2·H2O compared to NaClO3. When the samples are cooled to 77 K the pressure coeffecient of NQR frequency becomes nearly zero in sodium chlorate, whereas it retains a value of 6 kHz kbar−1 in barium chlorate. This behaviour follows from the fact that at 77K, the torsional frequency in NaClO3 is unaffected by the application of pressure while it increases at the rate 12 cm−1 kbar−1 in Ba(ClO3)2·H2O.

Thermal decomposition of zirconyl oxalates I. Barium zirconyl oxalate

Conditions for the preparation of stoichiometric barium zirconyl oxalate heptahydrate (BZO) have been standardized. The thermal decomposition of BZO has been investigated employing TG, DTG and DTA techniques and chemical and gas analysis. The decomposition proceeds through four steps and is not affected much by the surrounding gas atmosphere. Both dehydration and oxalate decomposition take place in two steps. The formation of a transient intermediate containing both oxalate and carbonate groups is inferred. The decomposition of oxalate groups results in a carbonate of composition Ba2Zr2OsCO3, which decomposes between 600 and 800 ~ and yields barium zirconate. Chemical analysis, IR spectra and X-ray powder diffraction data support the identity of the intermediate as a separate entity.

Thermal decomposition of zirconyl oxalates I. Barium zirconyl oxalate

Conditions for the preparation of stoichiometric barium zirconyl oxalate heptahydrate (BZO) have been standardized. The thermal decomposition of BZO has been investigated employing TG, DTG and DTA techniques and chemical and gas analysis. The decomposition proceeds through four steps and is not affected much by the surrounding gas atmosphere. Both dehydration and oxalate decomposition take place in two steps. The formation of a transient intermediate containing both oxalate and carbonate groups is inferred. The decomposition of oxalate groups results in a carbonate of composition Ba2Zr2O5CO3, which decomposes between 600 and 800° and yields barium zirconate. Chemical analysis, IR spectra and X-ray powder diffraction data support the identity of the intermediate as a separate entity.Die Bedingungen für die Herstellung von stöchiometrischem Barium-zirconyl-oxalat Heptahydrat (BZO) wurden standardisiert. Die thermische Zersetzung von BZO wurde unter Einsatz der TG-, DTG- und DTA, sowie der chemischen und Gasanalyse untersucht. Die Zersetzung verläuft über vier Stufen und wird von der umgebenden Gasathmosphäre nicht besonders beeinflusst. Sowohl die Dehydratisierung als auch die Oxalatzersetzung erfolgt in zwei Stufen. Die Bildung einer intermediären Übergangsverbindung mit sowohl Oxalat- als auch Carbonatgruppen wirken hierbei mit. Die Zersetzung der Oxalatgruppen ergibt ein Carbonat der Zusammensetzung Ba2Zr2O5CO3, das zwischen 600 und 800° zersetzt wird und Bariumzirconat ergibt. Die Angaben der chemischen Analyse, der IR-Spekren und der Röntgen-Pulver-Diffraktion unterstützen die Identität der Intermediärverbindung als eine separate Einheit.On a standardisé les conditions de préparation de l'oxalate heptahydraté de zirconyle et de baryum (BZO) stoechiométrique. On a étudié la décomposition thermique de BZO par TG, TGD et ATD ainsi que par analyses chimiques et analyses des gaz. La décomposition a lieu en quatre étapes et n'est pas trop influencée par l'atmosphère ambiante. La déshydratation et la décomposition de l'oxalate ont lieu en deux étapes. Il se forme un composé intermédiaire de transition contenant à la fois les groupes oxalate et carbonate. La décomposition des groupes oxalate fournit un carbonate de composition Ba2Zr2O5CO3 qui se décompose entre 600 et 800° pour fournir du zirconate de baryum. L'analyse chimique, les spectres IR et la diffraction des rayons X sur poudre, apportent les preuves de l'existence d'un composé intermédiaire comme entité séparée.

Continuity of plastic strain rate in stress relaxation tests

Stress relaxation testing is often utilised for determining whether athermal straining contributes to plastic flow; if plastic strain rate is continuous across the transition from tension to relaxation then plastic strain is fully thermally activated. This method was applied to an aged type 316 stainless steel tested in the temperature range 973–1123 K and to a high purity Al in the recrystallised annealed condition tested in the temperature range 274–417 K. The results indicated that plastic strain is thermally activated in these materials at these corresponding test temperatures. For Al, because of its high strain rate sensitivity, it was necessary to adopt a back extrapolation procedure to correct for the finite period that the crosshead requires to decelerate from the constant speed during tension to a dead stop for stress relaxation.

Exotic Physics in the Negative-U, Extended-Hubbard Model for Barium Bismuthates?

We point out possibilities for exotic physics in barium bismuthates, from a detailed study of the negative-U, extended-Hubbard model proposed for these systems. We emphasize the different consequences of electronic and phononic mechanisms for negative U. We show that, for an electronic mechanism, the semiconducting phases must be unique, with their transport properties dominated by charge ± 2e Cooperon bound states. This can explain the observed difference between the optical and transport gaps. We propose other experimental tests for this novel mechanism of charge transport.

Kinetics of ceric ion oxidation of naphthalene and its derivatives. Formation of the radical cation intermediate in the rate limiting step

Ceric ammonium sulfate, CAS, oxidizes naphthalene to 1,4-naphthoquinone in essentially quantitative yield in CH3CN-dil. H2SO4. Stoichiometric studies indicate that 6 mol of CAS are required for the oxidation of 1 mol of naphthalene to 1,4-naphthoquinone. Kinetic investigations reveal that the reaction takes place through initial formation of a 1:1 complex of naphthalene and cerium(IV) in an equilibrium step followed by slow decomposition of the complex to naphthalene radical cation. Kinetic results on the effects of acid strength, polarity of the medium, temperature and substituents are in accordance with this mechanism. Further conversion of the radical cation into 1,4-naphthoquinone takes place in fast steps involving a further 5 mol of cerium(IV) and 2 mol of H2O.

Microstructural features of flow instability in α-titanium cylinders under high strain rate compression at 25°C to 400°C

Cylindrical specimens of commercial pure titanium have been compressed at strain rates in the range of 0.1 to 100 s-1 and temperatures in the range of 25-degrees-C to 400-degrees-C. At strain rates of 10 and 100 s-1, the specimens exhibited adiabatic shear bands. At lower strain rates, the material deformed in an inhomogeneous fashion. These material-related instabilities are examined in the light of the ''phenomenological model'' and the ''dynamic materials mode.'' It is found that the regime of adiabatic shear band formation is predicted by the phenomenological model, while the dynamic materials model is able to predict the inhomogeneous deformation zone. The criterion based on power partitioning is competent to predict the variations within the inhomogeneous deformation zone.