A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

A new approach to the problem of the anomalous magnetic moment of the electron

A heuristic model for deriving the anomalous magnetic moment of the electron is presented. A term /2 – 0.327(/)² is deduced, in better agreement with experiment than is the QED derivation of /2 – 0.328(/)². The result is strengthened by the recent non-QED account of the Lamb shift by Yu and Sachs.     

Quantum Observables,Lie Algebra Homology and TQFT

Let us consider a Lie (super)algebra G spanned by T where T are quantum observables in BV formalism. It is proved that for every tensor c^... that determines a homology class of the Lie algebra G the expression c^...T...T is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.     

Anomalous diffusion in a random velocity field

We construct diffusions in random velocity fields which present anomalous superdiffusive behavior. The mean square displacement can be made to have any power lawt for 1<2. Higher moments and characteristic functions are also investigated.     

Defect annealing of alpha-particle irradiated n-GaAs

The annealing behaviour of irradiation induced defects in n-type GaAs irradiated at 300 K with 5.4 MeV alpha-particles from an americium-241 (Am-241) radio nuclide have been investigated. The annealing kinetics are presented for the alpha-particle induced defects E1–E5 detected in Organo-Metallic Vapor Phase Epitaxially (OMVPE) grown n-GaAs doped with silicon to 1.2×10¹⁶ cm^–3, these kinetics are compared to those obtained for similar defects (E1–E5) detected after electron irradiation. While defects P1 and P2 were detected after removal of the electron defects E4 and E5, respectively, a new defect labelled P0, located 0.152 eV below the conduction band, was introduced by annealing. The thermal behaviour and trap characteristics of these three defects (P0–P2) are presented. In an attempt to further characterise defects P0 and P1 a preiliminary study investigating the emission rate field dependence of these defects was conducted, it was observed that defect P0 exhibited a fairly strong field dependence while P1 exhibited a much weaker dependence.     

Statistics of the One-Dimensional Riemann Walk

The Riemann walk is the lattice version of the Lévy flight. For the one-dimensional Riemann walk of Lévy exponent 0<<2 we study the statistics of the support, i.e., set of visited sites, after t steps. We consider a wide class of support related observables M(t), including the number S(t) of visited sites and the number I(t) of sequences of adjacent visited sites. For t we obtain the asymptotic power laws for the averages, variances, and correlations of these observables. Logarithmic correction factors appear for =2/3 and =1. Bulk and surface observables have different power laws for 1<2. Fluctuations are shown to be universal for 2/3 <2. This means that in the limit t the deviations from average M(t)M(t)–M-0304;(t-0304;) are fully described either by a single M independent stochastic process (when 2/3 <1) or by two such processes, one for the bulk and one for the surface observables (when 1<<2).     

Experimental survey of the sticking problem in muon catalyzed dt fusion

The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking _s ⁰ (immediately after dt fusion) and for final sticking _s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is _s(0.56±0.04)%, lower than the theory prediction _s=(0.65±0.03)%, at medium density.     

A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.     

On the existence of invariant,absolutely continuous measures

Let (, , ) be a measure space with normalized measure,f: a nonsingular transformation. We prove: there exists anf-invariant normalized measure which is absolutely continuous with respect to if and only if there exist >0, and , 0<<1, such that (E)< implies (f ^–k(E))< for allk0.     

Long-lived fluorescence probes for studying lipid dynamics: A review

A great many studies have focused on the heterogeneous packing of lipids in the bilayer matrix. However, less attention has been directed toward the temporal aspects of these lipid-lipid interactions. Studies of lipid packing fluctuations, or gel-fluid exchange, using fluorescence probe methodologies have been limited. This limitation arises from thesubmicrosecond time scale over which the fluctuations are expected to occur. Traditionally, dynamic studies of lipid bilayers have been restricted to the nanosecond time regime, and the submicrosecond time window has not been explored in any great depth by fluorescence methods, although persistent lipid dynamics has been evident. Probes with long fluorescence lifetimes (several hundred nanoseconds) have the potential to expand this important time window, providing information on gel-fluid exchange rates and insights into how important biological effectors such as proteins, cholesterol, and anesthetics affect or modulate these fluctuations. Using the long-lived fluorescence probe coronene, combined with time-resolved fluorescence methods geared toward microheterogeneity, we present a view of bilayer dynamics in an alternate time domain. Fluorescence probes are expected to inhabit an equilibrium between fluid and gel environments. Some probes remain in their respective environments throughout their excited-state lifetime, while others reside in surroundings that will change (i.e., melt). Long-lived fluorescence membrane probes can provide direct estimates of submicrosecond lipid fluctuation or melt rates. Simple Landau modeling leads to adistribution of melt rates and provides an attractive alternative to a simplercompartmental model where a unique lipid fluctuation of gel-fluid exchange rate is measured. Thedistribution model is probe independent (defined by thermodynamic quantities) and can be applied generally to the rotational motions of fluorescence probes embedded in the lipid bilayer.Abbreviations DMPC l--dimyristoylphosphatidylcholine - DPH 1,6-diphenyl-1,3,5-hexatriene - DPPC l--dipalmitoylphospha-tidylcholine - DSC differential scanning calorimetry - EA fluorescence emission anisotropy - LUV large unilamellar vesicles - SUV small unilamellar vesicles - T_c lipid phase transition temperature     

Phase transformations in Cu-Sn alloys containing Ni,Al, Ge,and In

After quenching from 700C and aging, Cu-Sn alloys containing Ni and Al were found to have a precipitation of-solid solution, with a DO₃ type of ordering, of metastable ,, and phases. It was established that the phase has an 4 type of ordering while the phase has the Cu₃Ti type. Observations revealed that Cu-Sn-Al alloys contained two phases, and, with an identical structure but with different ratios of electron concentration per atom.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–37, April, 1981.     

Antiferromagnetic solid oxygen studied by positive muons

We present a zero magnetic field muon spin rotation study of-O₂ (antiferromagnetic phase of solid oxygen) in the temperature range of 10–24 K. Static magnetic order has been observed below the- transition temperatureB =23.8 K. The temperature dependence of the muon precession frequency exhibits behavior characteristic of a two-dimensional Heisenberg spin-1 system with the anisotropy parameter 10^–2 quite similar to that of antiferromagnetic phase of the high-temperature superconductor parent compounds. A unique local field at the muon site has been determined to beB ₀=1.27(5) kG at low temperatures.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

The room-temperature decomposition of metastable phases precipitated in the Al-Zn alloys at 200 °C

The room-temperature decomposition of metastable phases in the Al-Zn alloys (from 25 to 50 wt. % Zn) was studied by the transmission electron microscopy and X-ray diffraction. Metastable phases, i.e. G.-P. zones, _R-and -phases, were grown at 200 °C and their decomposition into equilibrium -phase at 20 °C was investigated. Ageing times comprised 1 to 999 days.Both the decomposition mechanism and the rate of decomposition of coherent phases were found to be dependent on the particle sizes and their density reached at 200 °C. The local vacancy supersaturation around the -nucleus in a dense system of G.-P. zones leads to an enhanced growth rate of such nucleus and thus to the formation of one large -precipitate at the expense of several neighbouring G.-P. zones. The elastic stress field around this -particle promotes the further nucleation and growth of -precipitates and leads to their gradual spread throughout the matrix. The decomposition of intermediately sized _Rprecipitates results in the development of -precipitates of comparable sizes nucleated on the array of misfit dislocations at the periphery of _R-precipitates. The cooperative effect between neighbouring particles does not influence the decomposition of large _R-precipitated which split then into several smaller -particles. The rate of G.-P. zones or _R to -decomposition increases with the increasing sizes of transition precipitates and with the zinc content of the alloy. The kinetics of to -decomposition was found to be independent both on the annealing time at 200 °C and on the investigated alloy composition. This can be attributed to the constant density of misfit dislocations as nucleation sites for -precipitates along the -matrix interface and to the large mutual separation of -precipitates in all these alloys.In conclusion we would like to express our thanks to Doc. Dr. V.Syneek, CSc. for his valuable discussions and to Ing. V.íma for the preparation of Al-Zn alloys. Our thanks are also due to Mr. Z.iký for his help in the X-ray diffraction measurement and to P.Vyhlídka for the careful chemical analyses of the investigated alloys.     

A Note on the Time Development of Quantum Lattice Systems

The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential . A thermodynamic limit of quantum Gibbs state, a *-algebra and an automorphism group _t for which is a KMS state are constructed.     

A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

A Note on Anisotropic Percolation

We consider an anisotropic independent bond percolation model on , i.e. we suppose that the vertical edges of are open with probability p and closed with probability 1–p, while the horizontal edges of are open with probability p and closed with probability 1– p, with 0 < p, < 1. Let , with x₁ < x₂, and . It is natural to ask how the two point connectivity function P_p,({0 x}) behaves, and whether anisotropy in percolation probabilities implies the strict inequality P_p,({0 x})> P_p,({0 x}). In this note we give affirmative answer at least for some regions of the parameters involved.Mathematics Subject Classifications (2000). 82B20, 82B41, 82B43.     

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