Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Interface Microstructures of Si3N4/Fe and Fe-Cr Alloys Joints

Interfaces of solid state bonded Si₃N₄ceramics with Fe and Fe-(5, 10, 15 wt%)Cr alloy interlayers inArgon for 1 h at 1100°, 1200° and 1300°C have beencharacterized by electron probe microanalysis (EPMA) and transmissionelectron microscopy (TEM). Smooth interfaces with no evidence ofreactions products resulted when bonding at 1100°C. However, theinteraction between the ceramic and the metal increased at higherbonding temperatures and Cr-contents. In all samples Si and N fromthe ceramic dissolve and diffuse in the metal interlayer, whereas thesintering additives of the ceramic remain inactive.Low Cr-content (5%) interlayers resulted in the formationof an interfacial zone composed of two sublayer structures; adjacentto the ceramic was a thin one containing the sintering aids ofSi₃N₄ and fine precipitates of Fe₃Si and -Fe₄N in a bcc-Fe matrix. The second was thicker and includedfine Fe₃Si,-Fe₄N and-Fe₂N precipitates in abcc-Fe matrix. The bond region with high Cr-content interlayersincluded three sublayer structures. The first one next to the ceramicwas a bcc-Fe matrix containing sintering aids, fine dispersedFe₃Si and-Fe₄N, and CrN. The secondsublayer was similar but without any segregants from the ceramic. Thethird one, finally had a lamellae structure of Cr₂N/bcc-Fe and the Fe matrix contained also-Fe₄N.The interactionbetween the ceramic and the metal interlayer is believed to becontrolled by the solution rate of N in the alloy foils.     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Resonances in 12C and Their Breakup to the 3α Final State

The breakup of ¹²C states into three -particles is discussed in the context of the continuum three-body problem. New information from the -decay of ¹²N populating 0⁺, 1⁺, and 2⁺ states in ¹²C is presented. The breakup mechanism of the 1⁺ state at 12.71MeV is clarified, the spin of the 10.3MeV state is determined as 0⁺, and evidence for a previously unknown 2⁺ state at 14.1(2)MeV is given.     

Reactive pulsed laser deposition and laser induced crystallization of SnO2 transparent conducting thin films

Transparent conducting SnO₂ thin films with a thickness between 1000–2000 Å were deposited on glass, quartz and silicon substrates using standard pulsed laser deposition techniques with two different targets (Sri and SnO₂) and with three different laser wavelengths (1.06, 0.532 and 0.266 ) from a Q-switched Nd: YAG laser. Tin dioxide films with optical transmission over most of the visible spectrum exceeding 80% were obtained using a Sn target and a background oxygen pressure of 20 Pa. The electrical resistivity () depended strongly on the substrate temperature during deposition, with the lowest values of of about 10^–2 -cm obtained when the substrate was maintained at 400°C during deposition. Using SnO₂ targets, predominantly amorphous phase SnO₂ films were deposited on Si substrates and then transformed into polycrystalline Sn₃O₄ by laser induced crystallization ( = 1.06 m). Whereas these later films were essentially non-conducting as deposited ( > 400 -cm), the electrical resistivity was permanently reduced after laser induced crystallization by a factor greater than 1000 to a value of approximately 4 × 10^–1 -cm.     

Dielectric properties of thin films of chalcogenide glasses

The temperature-frequency dependences of the conductivity (), capacitance (C), and dielectric-loss coefficient () have been measured for metalglass film (composition As₃₀Ge₁₀Si₁₂Te₄₈)-metal structures in an alternating electric field. The glass film was obtained by the method of radiofrequency sputtering in an argon atmosphere, and the top and bottom molybdenum electrodes by thermal evaporation in vacuum. The measurements were made in the frequency range 4·10²–2·10⁴ Hz at temperatures 209–299°K. The relaxation component _r=–_– of the conductivity for T < 240°K and high frequencies does not depend on the temperature (T) and is proportional to ^0.8. At higher temperatures, _r() is described by a complicated curve, which has at low frequencies the behavior ² and goes over to saturation at large values of . In this range of frequencies and for positive temperatures _r exp(E/T), where E 0.45 eV. The frequency-temperature dependences of _r, C, and ' are interpreted on the basis of Fröhlich's model. The calculated and experimental curves are compared. It is assumed that the loss of relaxation type is due to two processes, one of which is governed by carrier hops between localized states near the Fermi level and is predominant at low temperatures. The other is determined by carrier hops between the same states through the valence band and is predominant at positive temperatures.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 35–39, September, 1980.     

New Possibilities of Radioastronomical Diagnostics of the Jovian Magnetosphere Using the Observed Polarization of its Decameter Radio Emission

We discuss possibilities of diagnostics of the Jovian magnetosphere based on the results of measurements of the polarization characteristics of the decameter radio emission. It is shown that the essentially elliptical polarization of that radiation and its generation at frequencies near the local electron gyrofrequency opens new possibilities for radioastronomical diagnostics of the Jovian magnetosphere. The plasma distribution can be studied not only along the radiation path but also in the transverse direction, i.e., over latitudes. Moreover, since the relative position of the source and observer during a decameter noise storm is rather stable, it is possible to perform tomography of the magnetosphere (its diagnostics at different longitudes) using the planet rotation. We present the examples of diagnostics of different regions in the Jovian magnetosphere, such as sources of decameter radio emission, i.e., lower-magnetosphere regions located at a distance of about 1.5-2 R_J from the center of the planet, and the Io plasma torus located at a distance of about 6R_J from the center of the planet. It is pointed out that the number density of the magnetospheric plasma outside the Io magnetic flux tube is small (n 1 cm^-3 at the height of the gyroresonance level f_Be 30 MHz) while it is higher inside this flux tube at the same height: n 3 cm^-3. We estimate the variations in the number density of the plasma along the Io magnetic flux tube (n B, 1-1.8), determine the rate at which the integral plasma density varies over latitudes (d( n dz)/dh 2· 10³ cm^-3), and find the average number density of the plasma in the region where the radiation crosses the Io torus ( n 2· 10³ cm^-3).     

Investigation of Rust Formed on Steel Surfaces and Related Oxyhydroxides

In order to indentity the corrosion products formed on steel surfaces from ⁵⁷Fe Mössbauer spectroscopy, detailed Mössbauer parameters have been determined for various kinds of iron-oxyhydroxides: -FeOOH, -FeOOH, -FeOOH and -FeOOH. ⁵⁷Fe Mössbauer measurements of the iron oxyhydroxides indicate the following results. Fe occupies a single site in -FeOOH, but below the Néel temperature as at e.g., 300 K the Mössbauer spectrum is always broad, showing a distribution of the strength of the magnetic exchange interactions. Its shape depends on the grain-size and synthetic methods of the specimen. Fe occupies 3 sites in -FeOOH. High-purity reagents of -FeOOH always contain small amounts of -FeOOH and their Néel temperatures depend on the synthetic methods of the specimen. Mössbauer spectroscopy of the synthetic -FeOOH shows very broad distribution of the hyperfine magnetic fields.     

Microstructure of single crystals of austenitic stainless steel

Auger spectroscopy and x-ray structure analysis have been used to study the chemical and phase inhomogeneity in single crystals of the austenitic nitrided stainless steel Cr22Ni17Mo3 with various morphologies of the dendritic structure. In single crystals grown in the 100 direction with a classical dendritic structure the interaxial regions are highly enriched with S, N, and C and weakly enriched with Mo, V, and Mn. At the same time these regions have a high density of particles of the type Me₂₃C₆, Me₇C₃, and vanadium carbonitrides, oriented in the growth direction. The axial regions have a subcellular structure, with oxygen-rich subcell boundaries. In single crystals with growth direction close to 110, in which only secondary dendrite axes are formed, the alloying elements, impurities, and second-phase particles are distributed relatively uniformly throughout the ingot.V. D. Kuznetsov Siberian Physicotechnical Institute at Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–6, October, 1992.     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

Nonlocal Monte Carlo algorithm for self-avoiding walks with fixed endpoints

We study a new Monte Carlo algorithm for generating self-avoiding walks with variable length (controlled by a fugacity) and fixed endpoints. The algorithm is a hybrid of local (BFACF) and nonlocal (cut-and-paste) moves. We find that the critical slowing-down, measured in units of computer time, is reduced compared to the pure BFACF algorithm: _CPU N^2.3 versus N^3.0. We also prove some rigorous bounds on the autocorrelation time for these and related Monte Carlo algorithms.     

The lanthanideβ″ aluminas

The entire sodium ion content of sodium alumina (Na_1.67Mg_0.67Al_10.33O₁₇) can be replaced with a variety of lanthanide ions by simple diffusion reactions at moderate temperatures (500–700°C). Lanthanide alumina crystals are hard, clear, chemically stable, and have well-defined crystal structures. The fluorescence spectrum of Nd³⁺ in alumina is similar to that in YAG. The lifetime of the⁴ F _3/2 state of Nd³⁺ in completely-exchanged alumina (350s at 10²¹ Nd³⁺ cm^–3) is about 45% longer than in YAG (240s at 10²⁰Nd³⁺ cm^–3). The lanthanide aluminas may be of considerable interest as new phosphor and laser host materials.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

---

. .

     

Some remarks on braided group reconstruction and braided doubles

The cross coproduct braided group AutC)B is obtained by Tannaka-Krein reconstruction from C ^B C for a braided group B in braided category C. We apply this construction to obtain partial solutions to two problems in braided group theory, namely the tensor problem and the braided double. We obtain AutC) Aut(C) Aut(C) Aut(C) and higher braided group spin chains. The example B(R) B(R) ... B(R) is described explicitly by R-matrix relations. We also obtain Aut(C) Aut(C)* as a dual quasitriangular codouble braided group by reconstruction from the dual category C° C. General braided double crossproducts B C are also considered.     

On the 3+ level in Os186 populated in Re186 Β-decay

The coincidences of the 400–1100 keV gammas with the conversion electrons of the 137 keV transition were measured with the intermediate image spectrometer modified for - coincidences. The e_L 137- 770 keV coincidences were observed. Consequently, in addition to the known 768 keV transition, there is another one with closed energy. For this transition the relative intensity ratioI ⁶³² /I ⁷⁷³ =8±2 was determined. The corrected decay scheme of Re¹⁸⁶ is presented.     

Quantum supports and modal logic

LetA be a quasi-manual with finite operations. Associate to each E = {e ₁ ,..., e_n} A the set _E of modal formulas: (e ₁ ··· e_n), e_i (e ₁ ··· e_i–1 e_i+1 ··· e_n), i=1,..., n. Set _A = {_E|E A}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of _A where the supports are given by {x |A x is true}.On leave from the Department of Mathematics, Pontificia Universidade Catolica, Rio de Janeiro, Brazil.     

The temperature dependence of the refractive index of germanium

The temperature dependence of the refractive index of germanium in a wave-length region of 1·8–5·5 and temperature region of 100–530 °K is given for three samples of single crystal germanium having different concentrations of impurities. The temperature dependence of the refractive index is non-linear. Our results are compared with those of other authors. An attempt is also made to theoretically interpret the observed dependence.

---

1,8–5,5 100–530° K . . . , .

---

---

In conclusion the author thanks Dr. Trousil from the Institute of Technical Physics, Czechoslovak Academy of Sciences, Prague, for supplying the germanium, Mr. Tma for preparing and polishing the prisms, Dr. Tauc from the same institute for enabling most of the measurements to be carried out in his laboratory, and Mrs. ilhavá for help in the measurements.     

A measurement of the neutron-proton differential cross section at extreme forward and backward angles between 45 and 75 MeV

To determine the(¹ P ₁) phase parameter, thenp cross section has been measured from 45 to 75 MeV, by 5 MeV steps, from 6° to 20° at forward angle, and from 168° to 180° at backward angle.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).