On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

Non-Markovian reversible Chapman-Kolmogorov measures on subshifts of finite type

We consider shift-invariant probability measures on subshift dynamical systems with a transition matrixA which satisfies the Chapman-Kolmogorov equation for some stochastic matrix compatible withA. We call them Chapman-Kolmogorov measures. A nonequilibrium entropy is associated to this class of dynamical systems. We show that ifA is irreducible and aperiodic, then there are Chapman-Kolmogorov measures distinct from the Markov chain associated with and its invariant row probability vectorq. If, moreover, (q, ) is a reversible chain, then we construct reversible Chapman-Kolmogorov measures on the subshift which are distinct from (q, ).     

Investigation of the excitation of nitrogen molecules in the positive column of a discharge in a mixture of CO2 and N2

The absolute populations of the electron states of the nitrogen molecule C³_u and B³_g in the positive column of a discharge in a mixture of CO₂ and N₂ at an overall pressure of 2.5 mm Hg, a ratio of the components of 11, and a current of 60 mA, are determined. An estimate is made of the possibility of exciting the electron state C³_u by direct electron collision and by multistage excitation from the electron state B³_g. It is suggested that the most probable process by which the electron state C³_u is excited is multistage excitation from vibrational levels of the electron state B³_g.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 49–52, October, 1972.     

Interpretation of measurements of π0-meson photoproduction partial cross sections on a6Li nucleus with O+ level excitation

The anomalously large measured values of the cross section of the reaction +⁶Li ⁰ +⁶Li^* (3.56 MeV), which were obtained in two different laboratories, 260–450 MeV -rays, are discussed. It is shown that the disagreement between theory and experiment is due to the background reaction +⁷Li ⁰ + n +⁶Li^* (3.56 MeV), which became possible as a result of the poor isotropic purity of the target. This background reaction is discussed with respect to obtaining data on ⁰-meson photoproduction on neutrons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, 92–96, November, 1991.     

Inequivalent quantizations for non-linear σ model

We compute the homotopy groups ₀ and ₁ of the classical configuration space of anO(3) invariant field theory on ×, where is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications.     

Local energy flux and the refined similarity hypothesis

In this paper we demonstrate the locality of energy transport for incompressible Euler equations both in space and in scale. The key to the proof is the proper definition of a local subscale flux, _t (r), which is supposed to be a measure of energy transfer to length scales <l at the space point r. Kraichnan suggested that for such a quantity the refined similarity hypothesis will hold, which Kolmogorov originally assumed to hold instead for volume-averaged dissipation. We derive a local energy-balance relation for the large-scale motions which yields a natural definition of such a subscale flux. For this definition a precise form of the refined similarity hypothesis is rigorously proved as a big-O bound. The established estimate is _t (r)=O(l _3h-1) in terms of the local Hölder exponenth at the point r, which is also the estimate assumed in the Parisi-Frisch multifractal model. Our method not only establishes locality of energy transfer, but it also clarifies the physical reason that convection effects, which naively violate locality, do not contribute to the subscale flux. In fact, we show that, as a consequence of incompressibility, such effects enter into the local energy balance only as the divergence of a spatial current. Therefore, they describe motion of energy in space and cancel in the integration over volume. We also discuss theorems of Onsager, Eyink, and Constantinet al. on energy conservation for Euler dynamics, particularly to explain their relation with the Parisi-Frisch model. The Constantinet al. proof may be interpreted as giving a bound on the total flux, _t =d ^d r _t (r), of the form _t (r)=O(l _z3h-1), wherez ₃ is the third-order scaling exponent (or Besov index), in agreement with the multifractal model. Finally, we discuss how the local estimates are related to the results of Caffarelli-Kohn-Nirenberg on partial regularity for solutions of Navier-Stokes equations. They provide some heuristic support to a scenario proposed recently by Pumir and Siggia for singularities in the solutions of Navier-Stokes with small enough viscosity.     

Thermometry of an oxy-acetylene flame using multiplex degenerate four-wave mixing of C2

Thermometry of an oxy-acetylene flame using multiplex Degenerate Four-Wave Mixing (DFWM) of C₂ is demonstrated. More than 100 rotational transitions in thed ³ _g a ³ _u (0,0) Swan band of C₂ could be recorded simultaneously by use of a pulsed, broad bandwidth modeless laser. Temperatures were inferred by fitting temperature-dependent synthetic spectra of single- or multiple-shot averaged spectra. The strength and reliability of recorded signals together with the large number of rotational lines observed suggest that multiplex DFWM is a promising technique for minor species detection and for temporally resolved temperature measurements in luminous environments. Factors influencing the accuracy and precision of single-shot thermometry using the technique are discussed.     

Interfacial properties in solid-stabilized emulsions

We prepared concentrated monodisperse oil-in-water emulsions stabilized by solid particles. The osmotic resistance, , of the emulsions was measured for different oil volume fractions above the random close packing ( ). The dimensionless osmotic resistance, /(/R) ( being the interfacial tension and R being the undeformed drop radius), was always substantially higher than the corresponding values obtained for surfactant-stabilized emulsions. It can be concluded that droplet deformation in solid-stabilized emulsions is not controlled by the capillary pressure, /R, of the non-deformed droplets but rather by 0/R, 0 being a parameter characterizing the rigidity of the droplets surfaces. The data can be interpreted considering that the interfacial layers are elastic at small deformations and exhibit plasticity at intermediate deformations. 0 corresponds to the surface yield stress, i.e. the transition between elastic and plastic regimes. We discuss the origin of the surface behavior considering the strong lateral interactions that exist between the adsorbed solid particles. We propose an independent measurement of 0 based on the critical bulk stress that produces droplet fragmentation in dilute emulsions submitted to shear. Finally, the bulk shear elastic modulus was measured as a function of and confirms many of the features revealed by the osmotic resistance.     

Inertia,relativity and cosmology

Starting with the idea that the inertia of bodies is a general property of all kinds of their potential energy, the author arrives at the two fundamental megaphysical equations (I, II)⁰ +c²=0,⁰ =0 where⁰ is the scalar gravitational potential due to the smoothed-out universe,⁰ is its electrostatic potential andc denotes the light velocity in vacuo.The first equation means physically that the cosmic potential⁰ determines uniquely the velocity of light and consequently the pseudo-Euclidean geometry in an inertial frame, in the absence of local gravitational fields. This fact implies the validity of the law of inertia in a non-empty universe only, in full agreement with Mach's principle.If we adopt, for the cosmic potential, that of Seeliger, differing from the Newtonian potential by the exponential factor exp (–r/r_g), we can use Eq. (I) to estimate the lower limit of the range r_g of gravitational interaction within the limits (10¹⁰–10¹²) light years. This suggests a steadystate model of the universe consisting of an unlimited number of finite regions (sub-universes) oscillating independently of each other. Such a superlarge-scale model universe is in agreement with the observed galactic red shift and yet it fulfils the perfect cosmological principle.     

Gas kinetic studies using a table-top set-up with electron beam excitation: quenching of molecular nitrogen emission by water vapour

A table-top set-up for studying gas kinetic processes in dense gases via time resolved optical spectroscopy is presented. The set-up uses low energy electron beams for gas excitation. A thin silicon nitride membrane separating the electron source and the gas cell allows to use electron energies as low as 10–15 keV. The electron source is operated in a fast pulsing mode with a pulse width of 5 ns and repetition rates up to 30 kHz. Light emission from the target gas sample is studied and time resolved photon counting is used to measure decay times and collisional rate constants for specific excited states. The experimental concept is applied to measure the rate constants for quenching of molecular nitrogen in the C 3u state (vibrational levels 0 and 1) by water vapour. Quenching rate constants of (7.1 ±0.7)×10-10 s-1 cm3 and (6.7 ±0.7)×10-10 s-1cm3 were obtained for the C 3u (v = 0) and C 3u (v = 1) vibrational levels, respectively.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Analytical Electron Microscopy Examination of the γ′/γ Interfaces in a Ni-Based Superalloy

The investigation of microstructure and chemical composition of the and phases were performed in a Ni-base superalloy by means of analytical electron microscopy. The distribution of particular elements in the alloy was revealed using X-ray mapping in a transmission electron microscope. The detected concentration profiles of alloying elements at the / interface were relatively sharp in the case of cuboidal shape of the phase while they resembled the classical diffusion profile for the oval phase. The quantitative analysis of the phase revealed much higher content of Al and lower of Ti, W, Co and Mo in the oval precipitates compared to cuboidal ones. This result is attributed to the different solidification paths, which is eutectic for the cuboidal precipitates and peritectic for the oval precipitates.     

Spinors and diffeomorphisms

We discuss the action of diffeomorphisms on spinors on an oriented manifoldM. To do this, we first describe the action of the diffeomorphism groupD(M) on the set =H ¹ (M,Z ₂) of inequivalent spin structures and show that it is affine. We argue that in the presence of spinors the gauge group of gravity is a certain double cover ofD(M) which depends on the spin structure. We explicitly compute the action ofD(M) on whenM is a closed Riemann surface; is seen to consist of exactly two orbits, corresponding to even and odd spin structures.On leave of absence from I.F.T., University of Wrocaw, Poland     

On the electroluminescence of powdered zinc sulphide layers

The experimental study of the dependence of the electroluminescence brightness on the voltage confirms the correctness of the mechanism of electroluminescence, based on impact ionization in parts of the crystal where the electric field is concentrated. A study of the photoluminescent and electroluminescent spectra of phosphors containing two activators (copper and an element of rare earth) permits the determination of the magnitude of the volume of the crystal in which electroluminescence occurs. A study of the influence of the stored light sum on the brightness of electroluminescence and a study of the rate of growth of the variable and constant components of electroluminescence point to the fact that the excitation is transferred from the region of field concentration to the whole volume of the crystal.

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Global properties of conformally flat momentum space and their implications

We consider the global structure of momentum space ^{3, 1} in a field theory which is covariant with respect to the action of global conformal group G. We show that ^{3, 1} is a homogeneous space for G which coincides with (S³×S¹)/Z₂ compact space. The radius of momentum space determines the natural invariant ultraviolet cutoff which may take the form of a Pauli-Vilars form factor in perturbation theory. We demonstrate in the case of the massless ⁴ theory how the conventional ultraviolet divergences which appear in the flat momentum space are regularized in ^{3, 1} global momentum space.     

A method of integration for the inhomogeneous layer

The inhomogeneous layer of an arbitrary index profile is replaced by the conventional multilayer of homogeneous elements. When the number of layers converges to infinity, the solution is performed exactly using the method of rational functions previously described by the author. As a result the reflection coefficient is expressed as the ratio of two infinite power series in (2/)j, the coefficients being defined as multiple integrals of increasing order. The Drude formulae follow as a first approximation. The paper is dedicated to the memory of Dr. A. Vaíek, Professor of the J. E. Purkyn University in Brno, who died on November 16, 1966.     

Rotational distribution of nascent OH radicals after H2O2 photolysis at 193 nm

The rotational distribution of OH(X ²,v=0) radicals was investigated by resonant laser-induced fluorescence (LIF) after photolysis of H₂O₂ at 193 nm. A microcomputer equipped LIF arrangement allowed special shot-by-shot normalization of the fluorescence signal for noise reduction. Using a least-squares procedure we were able to account for all measured line intensities including overlapping lines (blends) and obtain a complete rotational state distribution of the OH(X ²,v=0) state. The rotational excitation shows a Gaussian-like distribution with a maximum atK=12 and with 16% of the total available energy (17,400 cm^–1) appearing in rotation. Only 1% of the available energy is converted into vibration, leaving over 83% for translational excitation. The measured rotational distribution appears to fit a semiclassical theory.     

Roentgenoluminescence of hexahydrate of uranyl nitrate in phosphoric acid solution

The fluorescence (FL) and roentgenoluminescence (XRL) spectra of yellow aqueous solution of hexahydrate of uranyl nitrate phosphoric acid solution have been measured. The XRL spectrum was compared with the XRL of the green alkali alumino-phosphate glasses doped with uranium. It was shown that both the FL and XRL were due to uranyl groups. The radiative transitions are ascribed to³_1u ¹ _g ⁺ .     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Local decay of scattering solutions to Schrödinger's equation

The main theorem asserts that ifH=+gV is a Schrödinger Hamiltonian with short rangeV, L _compact ² (IR³), andR>0, then exp(iHt) _{S L} ² _(|x|<R)=O(t ^–1/2), ast where _S is projection onto the orthogonal complement of the real eigenvectors ofH. For all but a discrete set ofg,O(t ^–1/2) may be replaced byO(t ^–3/2).Research supported by the National Science Foundation under grants NSF GP 34260 and MCS 72-05055 A04