Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

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     

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 .     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

Hyperfine anomalies and nuclear γ-factors of56Co,57Co and60Co isotopes studied by NMR/ON

The results of NMR/ON measurements on^56,57,60Co isotopes in iron are presented in the paper. To avoid the uncertainties caused by local demagnetizing field inhomogeneities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factors ratios ⁵⁷/ ⁶⁰=1·805(20), ⁶⁰/ ⁵⁶ = 0·761(20), ⁵⁶/ ⁵⁷ = 0·726(20) and hyperfme anomalies^{56 60} = –0·036(10),^{60 57} = 0·017(10) and^{57 56} = 0·018(10) have been calculated from the experimental results.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Intrinsic point defects in niobium: Trapping at100Pd and111In impurities observed by PAC

Radiation-induced lattice defects in high-purity niobium have been investigated in the temperature range of 30K to 540 K by means of - perturbed angular correlation (PAC) measurements using the radioactive probes¹⁰⁰Pd/¹⁰⁰Rh and¹¹¹In/¹¹¹Cd. Both probes were produced within the niobium samples by means of heavy-ion nuclear reactions. At the Pd impurities trapping of defects occurred during heavy-ion irradiation at about 30 K in two defined configurations: defect 1(Pd) withv _Q1=e ² qQ/h=42(±2) MHz, ₁=0 and defect 2 (Pd) withv _Q2=(±2) MHz, ₂=1. Two defects were observed at the In impurities in annealing stage III (around 250 K) after heavy-ion as well as electron irradiations: defect 1(In) withv _Q1=87(±1) MHz, ₁=0 and defect 2(In) withv _Q2=105(±2) MHz, ₂=0.65(±0.02). A third defect (defect 3(In):v _Q3=177(±2) MHz, ₃0.2) appeared above 260 K after heavy-ion irradiation only. The data are interpreted in terms of interstitial trapping at the Pd impurities and vacancy trapping at the In impurities. Information on the microscopic structure of defect 1(In) and 2(In) is obtained from a PAC-single-crystal experiment. For defect 1(In) axial 111-symmetry is found, which leads us to identify this defect with a monovacancy as nearest neighbor with respect to the In probe. Defect 2(In) is the trapped divacancy for which an orientation is found that is consistent with both vacancies being nearest neighbor to the probe but second nearest neighbors to each other.     

Levels in <Superscript>127</Superscript>La fed by the <Superscript>127</Superscript>Ce beta-decay

The low-lying levels in ¹²⁷La have been studied through the -decay of ¹²⁷Ce ( T_1/2 = 29s) produced by bombarding a ^natMo target with a 185-MeV ³⁵Cl beam. Reaction products were on-line mass-separated, and -ray singles and - coincidence measurements were performed. Conversion electrons were also measured and multipolarities of transitions have been derived. The half-life of the 210.9-keV level was determined to be (1.9±0.3)ns by the - delayed coincidence technique. The level scheme obtained has been compared with calculations based on the Nilsson model.     

МЕТОД ОБРАБОТКИ ДВУХ МЕРНЫХ СПЕКТРОВ СОВП АДЕНИЙ И ЕГО ПРИМЕНЕНИЕ К АНА ЛИЗУ γ-γ-СОВПАДЕНИЙ НА Ge(Li)-ДЕТЕКТОРАХ ПРИ РА СПАДЕ155Tb

The method of data processing of two-dimensional coincidence spectra is described and its application for the --coincidence spectra analysis in¹⁵⁵Tb is shown. The existence of levels with energies 86·5; 105·3; 118·0; 235·2; 266·6; 268·6; 286·8; 326·0; 367·7; 427· 4; 451·3; 488·8 keV in¹⁵⁵Gd nucleus is proved on the basis of --coincidences measured in¹⁵⁵Tb decay with Ge(Li)-detectors. Two new transitions with energies of 192 and 163 keV were found.     

Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

The low-temperature phase of Kac-Ising models

We analyze the low-temperature phase of ferromagnetic Kax-Ising models in dimensionsd2. We show that if the range of interactions is ^–1, then two disjoint translation-invariant Gibbs states exist if the inverse temperature satisfies –1^N, where =d(1–)/(2d+2)(d+1), for any >0. The proof involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous-spin system which is suitable for the use of a variant of the Peierls argument.     

Structural state of Cu-Be-Ag alloys in the process of decomposition of solid solution

Investigation of aging Cu-1.5% Be-2% Ag and Cu-1% Be-4% Ag alloys was carried out in this study by the methods of x-ray analysis of monocrystals, and electron microscopy. In the aging process at 218, 300, and 450C, laminar zones of Guinier-Preston, enriched with beryllium and silver atoms were formed. Entry of silver into the zones widens the upper temperature interval of the zone stage to 450C. With the increase of annealing time the metastable-phase was precipitated. The crystals of -phase are precipitated with orientation in the direction (100) in consequence of interactions of the fields of elastic stresses occurring around -precipitations, and periodic structure is formed in the alloy. The stable phase-CuBe and Ag was precipitated in the Cu-1% Be-4% Ag-alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 21–25, August, 1972.     

Derivation and solution of a low-friction Fokker-Planck equation for a bound Brownian particle

The low-friction region of an anharmonically bound Brownian particle is examined using systematic elimination procedures. We obtain an asymptotic expression for the spectrum of the Fokker-Planck operator. Asymptotic means both small anharmonicities and small friction constants compared to the oscillatory frequency . We conclude that Kramers' low-friction equation is generally valid only for 0<0.01 and has to be modified for 0.01 by including phase-dependent terms. From these the nonlinear part of the force field in connection with a finite temperature is shown to shorten the correlation time of the equilibrium velocity autocorrelation function and to renormalize the frequency of the corresponding spectral density.     

Investigation of intrinsic defect-related deep centers in ZnSe

We have studied deep centers in highly resistive ( 10¹² ·cm) ZnSe, containing intrinsic impurities and defects, by means of nonequilibrium photoconductivity, photoluminescence, and wavelength-modulated transmission spectroscopy. We have determined the energy positions of photosensitive deep acceptors with ionization energies of 0.10, 0.18, 0.23, 0.27, 0.34, and 0.47 eV, as well as of radiative and nonradiative recombination centers.ted from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 42–46, March, 1989.The authors consider it a pleasant duty to thank M. K. Sheinkman for his interest in This work and S. S. Ostapenko for his help in PL measurements and helpful discussions.     

Amplitude-distortion factors for the inelastic scattering of an electron at a neon atom in an electric field

Inelastic electron scattering at a neon atom in the presence of an external electric field is considered. The distortion factors of the cross section _M (F) are calculated for a series of 4d and 5d levels. It is shown that the distortion factor in strong fields is a nonlinear and nonmonotonic function of the field. The distortion factors and transition probabilitiesA , are compared. The correlation between the behavior ofA , and _M (F) is explained by the dependence of the mean dipole moment of the Stark state on the field strength.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–110, January, 1996.     

Dynamic transition and hysteresis scaling in Heisenberg ferromagnet

Based on the mean-field treatment and Monte Carlo simulation, we studied the nature of the dynamic phase transition of two and three-dimensional magnetic films in Heisenberg model. The time averaged magnetization components ( mx , my, mz),the average hysteresis-loop area components A for magnetic films with different thickness have been calculated. The dynamic transition phase diagrams from to Q=0 for the 2D and 3D cases have been obtained. The relaxation times for different values of magnetic field, temperature, thickness of the films and the orientation number of spin have been simulated. It is found that the loop area follows the scaling relation, A-A0H0 T-, and the exponents and increase with increasing thickness, while the exponent decreases with increasing thickness. It was observed that the phase boundary line shrinks inward in the H0-T plane with decreasing value of the frequency of the magnetic field and thickness of multilayer film. The phase diagrams were explained by the competition between the relaxation time and the period of the external magnetic field. Moreover, it has been indicated that the dynamical behaviors for 2D and 3D cases derived by both mean-field method and Monte Carlo method in this work are consistent.     

The effects of inkomogeneous center structure on the shape of the ESR spectra of alkali-rich glasses

The paper considers the effect of nonuniform structure in the centers on the ESR spectrum for the case of axial anisotropy in the g factor; it is shown that if (² >² , _¦ >), the model enables one to describe fairly completely the spectrum of a glass containing 33% Na₂O and 67% SiO₂. Good agreement with all experimental evidence is not obtained for potassium silicate glasses.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 86–90, June, 1971.     

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.     

Analytical electron microscopy study of diffusion-bonded multiphase system

This study presents diffusion experiments of NiAl coupled with pure Ni (Ni/NiAl). The couple produces the Ni₃Al-based intermetallic phase ( phase) as an intermediate layer at the interface during diffusion annealing. Analytical electron microscopy is used to examine microstructural features, crystallographic orientation and compositional variations across the interface. Interdiffusivities are measured from the compositional variations. It is shown that the growing behavior of the phase changes between higher and lower annealing temperatures. The growth kinetics of the phase is also discussed.