The evolution of a turbulent vortex

We examine numerically the evolution of a perturbed vortex in a periodic box. The fluid is inviscid. We find that the vorticity blows up. The support of theL ₂ norm of the vorticity converges to a set of Hausdorff dimension 2.5. The distribution of the vorticity seems to converge to a lognormal distribution. We do not observe a convergence of the higher statistics towards universal statistics, but do observe a strong temporal intermittency.This work was supported in part by the Director, Office of Energy Research, Office of Basic Energy Sciences, Engineering, Mathematical and Geosciences Division of the U.S. Department of Energy, under contract W-7404-ENG-48, and in part by the Office of Naval Research, under contract N00014-76-C-0316     

Constrained random walks and vortex filaments in turbulence theory

We consider a simplified model of vorticity configurations in the inertial range of turbulent flow, in which vortex filaments are viewed as random walks in thermal equilibrium subjected to the constraints of helicity and energy conservation. The model is simple enough so that its properties can be investigated by a relatively straightforward Monte-Carlo method: a pivot algorithm with Metropolis weighting. Reasonable values are obtained for the intermittency dimensionD, a Kolmogorov-like exponent , and higher moments of the velocity derivatives. Qualitative conclusions are drawn regarding the origin of non-gaussian velocity statistics and regarding analogies with polymers and with systems near a critical point.This work was supported in part by the Applied Mathematical Sciences Subprogram of the Office of Energy Research, US Department of Energy, under Contract Number DE-AC03-76SF000098     

Algebraic study of chiral anomalies

The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of descent equations.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under contract DE-AC03-76SF00098 and in part by the National Science Foundation under research grant PHY81-18547     

The Poisson algebra of the invariant charges of the Nambu-Goto theory: Casimir elements

The reparametrization invariant non-local conserved charges of the Nambu-Goto theory form an algebra under Poisson bracket operation. The center of the formal closure of this algebra is determined. The relation of the central elements to the constraints of the Nambu-Goto theory is clarified.On leave of absence from Physics Faculty, University of Freiburg, Federal Republic of GermanyThis work was supported by Stiftung Volkswagenwerk, Deutsche Forschungsgemeinschaft and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract De-AC03-76SF0098     

Complex fragment emission from low energy compound nucleus decay to multifragmentation

In the first of these lectures, the experimental emission probabilities of complex fragments by low energy compound nuclei and their dependence upon energy and Z value are compared to the transtion state rates. In the second part, the high energy multi-fragment emission probabilities are shown to be reducible to the single fragment emission probability through the binomial distribution. The extracted one-fragment emission probabilities have a thermal dependence of the formp=e ^–B/T . This suggests that multifragmentation is a sequence of thermal binary decays.Invited lecture given at the International School-Workshop Relativistic Heavy-Ion Physics, Prague (Czech Republic), 19–23 September 1994.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Nuclear Physics Division of the US Department of Energy, under contract DE-AC03-76SF00098.     

Vortex phase transitions in 21/2 dimensions

A phase diagram is mapped out for a 21/2-dimensional vortex lattice model in which vortex filaments lie in a plane, while both the velocity field and the Green function are three-dimensional. Both positive and negative temperatures are considered. Various qualitative properties of turbulent states and of the super-fluid transition are well verified within the limitations of the model; the percolation properties of vortex transitions are exhibited; the differences between superfluid and classical vortex motion are highlighted, as is the importance of topological constraints in vortex dynamics; an earlier model of intermittency is verified.     

The logarithm of the derivative operator and higher spin algebras ofW ∞ type

We use the notion of the logarithm of the derivative operator to describeW type algebras as central extensions of the algebra of differential operators. We also provide closed formulae for the truncations ofW ₁₊ to higher spin algebras withsM, for allM2. The results are extended to matrix valued differential operators, introducing a logarithmic generalization of the Maurer-Cartan cocycle.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76Sf00098 and in part by the National Science Foundation under grants PHY-85-15857 and PHY-87-17155Address after July 1, 1992: Dept. of Mathematics, Yale University, New Haven, CTO6520, USA     

Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation

We consider the Cauchy problem for the two-dimensional vorticity equation. We show that the solution behaves like a constant multiple of the Gauss kernel having the same total vorticity as time tends to infinity. No particular structure of initial data ₀=(x, 0) is assumed except the restriction that the Reynolds numberR=|₀|dx/v is small, wherev is the kinematic viscosity. Applying a time-dependent scale transformation, we show a stability of Burgers' vortex, which physically implies formation of a concentrated vortex.Partly supported by Grant-in-Aid for Scientific Research No. B60460042, the Japan Ministry of Education, Science and Culture     

Relationship between T c and electronegativity differences in compound superconductors

The electronegativity differences, N, between the anions and the cations in suggested resonating elements of some representative high-temperature superconductors with T _c - 10 K are evaluated adopting Pauling's scale. The relationship between N and T _c was found to separate all the examined high-T _csuperconductors onto two curves: One for the cuprate superconductors having two-dimensional layered structures was a straight line, T _c=29.8+4.1N; the other correlation curve representing the remaining compound superconductors including the doped 113 perovskite and the perovskite-related 214 structures was at lower T _c values but also suggested that increasing electronegativity differences was related to increasing T _c.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Solution of lattice models by successive linkage

A linkage algorithm is presented for evaluating the partition function of a union of finite lattice blocks in terms of the partition functions of the component blocks. This algorithm leads to: (i) A fast enumeration method for evaluating the partition function of a finite lattice (for Ising spins in two dimensions, the number of terms needed to evaluate the partition function for a block ofL spins if reduced from 2 ^L to ); (ii) a recursive factorization procedure that accelerates the rate at which quantities evaluated on a finite lattice converge to their thermodynamic limit, and (iii) a scaling procedure that further accelerates the convergence to the thermodynamic limit. The scaling procedure is similar to a method previously used in turbulence calculations.Supported in part by the Applied Mathematics Subprogram of the Office of Energy Research, U.S. Department of Energy, under contract DE-AC03-76SF0098, and in part by the Office of Naval Research under contract N00014-76-C-0316     

Analytic continuation of group representations. III

The connection between the ideas of contraction and analytic continuation of Lie algebras and their representations is discussed, with particular emphasis on the contraction of the Poincaré to the Galilean group.This research was supported in part by the Office of Air Force Scientific Research AF 49 (638)-1440.     

Quantum nonlocality

It is argued that the validity of the predictions of quantum theory in certain spincorrelation experiments entails a violation of Einstein's locality idea that no causal influence can act outside the forward light cone. First, two preliminary arguments suggesting such a violation are reviewed. They both depend, in intermediate stages, on the idea that the results of certain unperformed experiments are physically determinate. The second argument is entangled also with the problem of the meaning of physical reality. A new argument having neither of these characteristics is constructed. It is based strictly on the orthodox ideas of Bohr and Heisenberg, and has no realistic elements, or other ingredients, that are alien to orthodox quantum thinking.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098.     

Search for right-handed currents in muon decay

We report new limits on right-handed currents, based on precise measurements of the endpoint of the e⁺ spectrum from ⁺ decay. Highly polarized ⁺ from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e⁺ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e⁺ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(W_R)>380 GeV, where W_R is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.     

Selfduality and topological-like properties of lattice gauge field theories. A proposal

We introduce for lattice gauge theories an analogue of the Pontrjagin index and a notion of selfduality and antiselfduality. Selfdual and antiselfdual configurations on the lattice have much of the same properties (with some remarkable differences) as the corresponding configurations on the continuum, to which they converge when the lattice spacing goes to zero.On leave of absence from Istituto di Fisica dell'Università di Milano, Via Celoria 16, 20133 Milano, Italy.Research partially supported by Consiglio Nazionale delle Ricerche and Fondazione A. Della Riccia     

Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws

We study the large-time behaviors of solutions of viscous conservation laws whose inviscid part is a nonstrictly hyperbolic system. The initial data considered here is a perturbation of a constant state. It is shown that the solutions converge to single-mode diffusion waves in directions of strictly hyperbolic fields, and to multiple-mode diffusion waves in directions of nonstrictly hyperbolic fields. The multiple-mode diffusion waves, which are the new elements here, are the self-similar solutions of the viscous conservation laws projected to the nonstrictly hyperbolic fields, with the nonlinear fluxes replaced by their quadratic parts. The convergence rate to these diffusion waves isO(t ^–3/4+1/2p+) inL ^p , 1p, with >0 being arbitrarily small.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38     

Mind,matter, and quantum mechanics

A theory of psychophysical phenomena is proposed. It resolves simultaneously four basic problems of science, namely the problems of the connections between:(1) mind and matter,(2) quantum theory and reality,(3) relativity theory and becoming, and (4) relativity theory and Bell's theorem.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract W-7405-EN-G-48.     

How covariant closed string theory solves a minimal area problem

For a given genusg Riemann surface withn0 punctures (n3 forg=0) we consider the problem of finding the metric of minimal area under the condition that the length of any nontrivial closed curve be greater or equal to 2. The minimal area metrics are found for the case of all punctured genus zero surfaces and for many of the higher genus surfaces both with and without punctures. These metrics are induced by Jenkins-Strebel quadratic differentials. They arise from the string diagrams corresponding to restricted Feynman graphs of a closed string field theory action containing classical and quantum restricted polyhedra.Supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

Analytic extrapolation inL ∞-norm: An alternative approach to “QCD Sum Rules”

In view of physical applications (especially to QCD Sum Rules), the following problem, pertaining to analytic extrapolation techniques, is studied. We are considering amplitudes, which are (real) analytic functions in the complex plane cut along=[s ₀, ). A modelF ₀(s) of the amplitude is given through the values ofF ₀(s) on some interval=[s ₂,s ₁] (withs ₁<s ₀) and the values of its discontinuity on. These values are approximate, and are supplemented by prescribed error channels, measured inL -norm (both on and). Investigating the compatibility between these data leads to an extremum problem which is solved up to a point where numerical methods can be implemented.Unité Associée au CNRS n^o040768     

Novel scaling behavior of directed polymers: Disorder distribution with long tails

We study the problem of directed polymers (DP) on a square lattice. The distribution of disorder is assumed to be independent but non-Gaussian. We show that for distributions with a power-law tailP() 1/||¹⁺ , where>2, so that the mean and variance are well defined, the scaling exponentv of the DP model depends on in a continuous fashion.