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)

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.

Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales

We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: our results seem new and interesting even in the particular cases when the time scale is the set of real numbers or the set of integers.Comment: This is a preprint of a paper whose final and definite form will appear in Journal of Optimization Theory and Applications (JOTA). Paper submitted 17-Nov-2011; revised 24-March-2012 and 10-April-2012; accepted for publication 15-April-201

DC and AC Josephson effects with superfluid Fermi atoms across a Feshbach resonance

We show that both DC and AC Josephson effects with superfluid Fermi atoms in the BCS-BEC crossover can be described at zero temperature by a nonlinear Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS calculations, we find that the NLSE is reliable in the BEC side of the crossover up to the unitarity limit. The NLSE can be used for weakly-linked atomic superfluids also in the BCS side of the crossover by taking the tunneling energy as a phenomenological parameter.Comment: 8 pages, 4 figures, presented at the Scientific Seminar on Physics of Cold Trapped Atoms, 17th International Laser Physics Workshop (Trondheim, June 30 - July 4, 2008

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

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

Hadronic Cross-sections in two photon Processes at a Future Linear Collider

In this note we address the issue of measurability of the hadronic cross-sections at a future photon collider as well as for the two-photon processes at a future high energy linear $e^+e^-$ collider. We extend, to higher energy, our previous estimates of the accuracy with which the \gamgam\ cross-section needs to be measured, in order to distinguish between different theoretical models of energy dependence of the total cross-sections. We show that the necessary precision to discriminate among these models is indeed possible at future linear colliders in the Photon Collider option. Further we note that even in the $e^+e^-$ option a measurement of the hadron production cross-section via \gamgam processes, with an accuracy necessary to allow discrimination between different theoretical models, should be possible. We also comment briefly on the implications of these predictions for hadronic backgrounds at the future TeV energy $e^+e^-$ collider CLIC.Comment: 20 pages, 5 figures, LaTeX. Added an acknowledgemen

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Resolved Photon Processes

We review the present level of knowledge of the hadronic structure of the photon, as revealed in interactions involving quarks and gluons ``in" the photon. The concept of photon structure functions is introduced in the description of deep--inelastic $e \gamma$ scattering, and existing parametrizations of the parton densities in the photon are reviewed. We then turn to hard \gamp\ and \gaga\ collisions, where we treat the production of jets, heavy quarks, hard (direct) photons, \jpsi\ mesons, and lepton pairs. We also comment on issues that go beyond perturbation theory, including recent attempts at a comprehensive description of both hard and soft \gamp\ and \gaga\ interactions. We conclude with a list of open problems.Comment: LaTeX with equation.sty, 85 pages, 29 figures (not included). A complete PS file of the paper, including figures, can be obtained via anonymous ftp from ftp://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-898.ps.