Finite size corrections to scaling in high Reynolds number turbulence

We study analytically and numerically the corrections to scaling in turbulence which arise due to the finite ratio of the outer scale $L$ of turbulence to the viscous scale $\eta$, i.e., they are due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations \dzm from the classical Kolmogorov scaling $\zeta_m = m/3$ of the velocity moments \langle |\u(\k)|^m\rangle \propto k^{-\zeta_m} decrease like $\delta\zeta_m (Re) =c_m Re^{-3/10}$. Our numerics employ a reduced wave vector set approximation for which the small scale structures are not fully resolved. Within this approximation we do not find $Re$ independent anomalous scaling within the inertial subrange. If anomalous scaling in the inertial subrange can be verified in the large $Re$ limit, this supports the suggestion that small scale structures should be responsible, originating from viscosity either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls)

Financial Transaction Tax: Small is Beautiful

The case for taxing financial transactions merely to raise more revenues from the financial sector is not particularly strong. Better alternatives to tax the financial sector are likely to be available. However, a tax on financial transactions could be justified in order to limit socially undesirable transactions when more direct means of doing so are unavailable for political or practical reasons. Some financial transactions are indeed likely to do more harm than good, especially when they contribute to the systemic risk of the financial system. However, such a financial transaction tax should be very small, much smaller than the negative externalities in question, because it is a blunt instrument that also drives out socially useful transactions. There is a case for taxing over-the-counter derivative transactions at a somewhat higher rate than exchange-based derivative transactions. More targeted remedies to drive out socially undesirable transactions should be sought in parallel, which would allow, after their implementation, to reduce or even phase out financialtransaction taxes

Examples of the Zeroth Theorem of the History of Physics

The zeroth theorem of the history of science (enunciated by E. P. Fischer) and widely known in the mathematics community as Arnol'd's Principle (decreed by M. V. Berry), states that a discovery (rule, regularity, insight) named after someone (often) did not originate with that person. I present five examples from physics: the Lorentz condition defining the Lorentz gauge of the electromagnetic potentials; the Dirac delta function (x); the Schumann resonances of the earth-ionosphere cavity; the Weizsacker-Williams method of virtual quanta; the BMT equation of spin dynamics. I give illustrated thumbnail sketches of both the true and reputed discoverers and quote from their "discovery" publications.Comment: 36 pages, 8 figures. Small revisions, added material and references - Arnol'd's law, Emil Wiechert. Submitted to Am. J. Phy

Mass splittings of nuclear isotopes in chiral soliton approach

The differences of the masses of nuclear isotopes with atomic numbers between \~10 and ~30 can be described within the chiral soliton approach in satisfactory agreement with data. Rescaling of the model is necessary for this purpose - decrease of the Skyrme constant by about 30%, providing the "nuclear variant" of the model. The asymmetric term in Weizsaecker-Bethe- Bacher mass formula for nuclei can be obtained as the isospin dependent quantum correction to the nucleus energy. Some predictions for the binding energies of neutron rich nuclides are made in this way, from, e.g. Be-16 and B-19 to Ne-31 and Na-32. Neutron rich nuclides with high values of isospin are unstable relative to strong interactions. The SK4 (Skyrme) variant of the model, as well as SK6 variant (6-th order term in chiral derivatives in the lagrangian as solitons stabilizer) are considered, and the rational map approximation is used to describe multiskyrmions.Comment: 16 pages, 10 tables, 2 figures. Figures are added and few misprints are removed. Submitted to Phys. Atom. Nucl. (Yad. Fiz.

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Virtual Photon Strucutre Functions and the Parton Content of the Electron

We point out that in processes involving the parton content of the photon the usual effective photon approximation should be modified. The reason is that the parton content of virtual photons is logarithmically suppressed compared to real photons. We describe this suppression using several simple, physically motivated ans\"atze. Although the parton content of the electron in general no longer factorizes into an electron flux function and a photon structure function, it can still be expressed as a single integral. Numerical examples are given for the \eplem\ collider TRISTAN as well as the $ep$ collider HERA.Comment: 16 pages and 3 figures (available from DREES@WSICPHEN as topdraw or PS files); LaTeX with equation.sty; MAD/PH/819, BU 94-0

SUSY signals at HERA in the no-scale flipped SU(5) supergravity model

Sparticle production and detection at HERA are studied within the recently proposed no-scale flipped $SU(5)$ supergravity model. Among the various reaction channels that could lead to sparticle production at HERA, only the following are within its limit of sensitivity in this model: $e^-p\to \tilde e^-_{L,R}\chi^0_i+X, \tilde \nu_e\chi^-_1+X$, where $\chi^0_i(i=1,2)$ are the two lightest neutralinos and $\chi^-_1$ is the lightest chargino. We study the elastic and deep-inelastic contributions to the cross sections using the Weizs\"acker-Williams approximation. We find that the most promising supersymmetric production channel is right-handed selectron ($\tilde e_{R}$) plus first neutralino ($\chi^0_1$), with one hard electron and missing energy signature. The $\tilde\nu_e\chi^-_1$ channel leads to comparable rates but also allows jet final states. A right-handedly polarized electron beam at HERA would shut off the latter channel and allow preferentially the former one. With an integrated luminosity of {\cal L}=100\ipb, HERA can extend the present LEPI lower bounds on $m_{\tilde e_R}, m_{\tilde\nu_e},m_{\chi^0_1}$ by \approx25\GeV, while {\cal L}=1000\ipb will make HERA competitive with LEPII. We also show that the Leading Proton Spectrometer (LPS) at HERA is an excellent supersymmetry detector which can provide indirect information about the sparticle masses by measuring the leading proton longitudinal momentum distribution.Comment: 11 pages, 8 figures (available upon request as uuencoded file or separate ps files), tex (harvmac) CTP-TAMU-15/93, CERN/LAA/93-1

Close-Packing of Clusters: Application to Al_100

The lowest energy configurations of close-packed clusters up to N=110 atoms with stacking faults are studied using the Monte Carlo method with Metropolis algorithm. Two types of contact interactions, a pair-potential and a many-atom interaction, are used. Enhanced stability is shown for N=12, 26, 38, 50, 59, 61, 68, 75, 79, 86, 100 and 102, of which only the sizes 38, 75, 79, 86, and 102 are pure FCC clusters, the others having stacking faults. A connection between the model potential and density functional calculations is studied in the case of Al_100. The density functional calculations are consistent with the experimental fact that there exist epitaxially grown FCC clusters starting from relatively small cluster sizes. Calculations also show that several other close-packed motifs existwith comparable total energies.Comment: 9 pages, 7 figure

Photon and Z induced heavy charged lepton pair production at a hadron supercollider

We investigate the pair production of charged heavy leptons via photon-induced processes at the proposed CERN Large Hadron Collider (LHC). Using effective photon and Z approximations, rates are given for $L^+L^-$ production due to $\gamma \gamma$ fusion and $Z \gamma$ fusion for the cases of inelastic, elastic and semi-elastic $pp$ collisions. These are compared with the corresponding rates for production via the gluon fusion and Drell-Yan mechanisms. Various $\gamma \gamma$ and $Z \gamma$ differential luminosities for $pp$ collisions are also presented.Comment: 22 pages, RevTex 3.0, 6 uuencoded and compressed postscript figures included. Reference to one paper changed from the original preprint number to the published version. Everything else unchange

Aspects of Two-Photon Physics at Linear e+e- Colliders

We discuss various reactions at future e+e- and gamma-gamma colliders involving real (beamstrahlung or backscattered laser) or quasi--real (bremsstrahlung) photons in the initial state and hadrons in the final state. The production of two central jets with large pT is described in some detail; we give distributions for the rapidity and pT of the jets as well as the di--jet invariant mass, and discuss the relative importance of various initial state configurations and the uncertainties in our predictions. We also present results for `mono--jet' production where one jet goes down a beam pipe, for the production of charm, bottom and top quarks, and for single production of W and Z bosons. Where appropriate, the two--photon processes are compared with annihilation reactions leading to similar final states. We also argue that the behaviour of the total inelastic gamma-gamma cross section at high energies will probably have little impact on the severity of background problems caused by soft and semi--hard (`minijet') two--photon reactions. We find very large differences in cross sections for all two--photon processes between existing designs for future e+e- colliders, due to the different beamstrahlung spectra; in particular, both designs with >1 events per bunch crossing exist.Comment: 51 pages, 13 figures(not included