Investigations into the BFKL Mechanism with a Running QCD Coupling

We present approximations of varying degree of sophistication to the integral equations for the (gluon) structure functions of a hadron (``the partonic flux factor'') in a model valid in the Leading Log Approximation with a running coupling constant. The results are all of the BFKL-type, i.e. a power in the Bjorken variable x_B^{-\lambda} with the parameter \lambda determined from the size \alpha_0 of the ``effective'' running coupling \bar{\alpha}\equiv 3\alpha_s/\pi= \alpha_0/\log(k_{\perp}^2) and varying depending upon the treatment of the transverse momentum pole. We also consider the implications for the transverse momentum (k_{\perp}) fluctuations along the emission chains and we obtain an exponential falloff in the relevant \kappa\equiv \log(k_{\perp}^2)-variable, i.e. an inverse power (k_{\perp}^2)^{-(2+\lambda)} with the same parameter \lambda. This is different from the BFKL-result for a fixed coupling, where the distributions are Gaussian in the \kappa-variable with a width as in a Brownian motion determined by ``the length'' of the emission chains, i.e. \log(1/x_B). The results are verified by a realistic Monte Carlo simulation and we provide a simple physics motivation for the change.Comment: 24 pages, 10 supplementary files, submitted to Physical Review

Station-keeping guidance

The station-keeping guidance system is described, which is designed to automatically keep one orbiting vehicle within a prescribed zone fixed with respect to another orbiting vehicle. The active vehicle, i.e. the one performing the station-keeping maneuvers, is referred to as the shuttle. The other passive orbiting vehicle is denoted as the workshop. The passive vehicle is assumed to be in a low-eccentricity near-earth orbit. The primary navigation sensor considered is a gimballed tracking radar located on board the shuttle. It provides data on relative range and range rate between the two vehicles. Also measured are the shaft and trunnion axes gimbal angles. An inertial measurement unit (IMU) is provided on board the orbiter. The IMU is used at all times to provide an attitude reference for the vehicle. The IMU accelerometers are used periodically to monitor the velocity-correction burns applied to the shuttle during the station-keeping mode. The guidance system is capable of station-keeping the shuttle in any arbitrary position with respect to the workshop by periodically applying velocity-correction pulses to the shuttle

Color separate singlets in e+e−e^+e^- annihilation

We use the method of color effective Hamiltonian to study the properties of states in which a gluonic subsystem forms a color singlet, and we will study the possibility that such a subsystem hadronizes as a separate unit. A parton system can normally be subdivided into singlet subsystems in many different ways, and one problem arises from the fact that the corresponding states are not orthogonal. We show that if only contributions of order $1/N_c^2$ are included, the problem is greatly simplified. Only a very limited number of states are possible, and we present an orthogonalization procedure for these states. The result is simple and intuitive and could give an estimate of the possibility to produce color separated gluonic subsystems, if no dynamical effects are important. We also study with a simple MC the possibility that configurations which correspond to "short strings" are dynamically favored. The advantage of our approach over more elaborate models is its simplicity, which makes it easier to estimate color reconnection effects in reactions which are more complicated than the relatively simple $e^+e^-$ annihilation.Comment: Revtex, 24 pages, 7 figures; Compared to the previous version, 1 new figure is added and Monte-Carlo results are re-analyzed, as suggested by the referee; To appear in Phys. Rev.

Fractional diffusion emulates a human mobility network during a simulated disease outbreak

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.Comment: 26 pages, 4 figure

The Feynman-Wilson gas and the Lund model

We derive a partition function for the Lund fragmentation model and compare it with that of a classical gas. For a fixed rapidity ``volume'' this partition function corresponds to a multiplicity distribution which is very close to a binomial distribution. We compare our results with the multiplicity distributions obtained from the JETSET Monte Carlo for several scenarios. Firstly, for the fragmentation vertices of the Lund string. Secondly, for the final state particles both with and without decays.Comment: Latex, 21+1 pages, 11 figure

Measurement of Birefringence of Low-Loss, High-Reflectance Coating of M-Axis Sapphire

The birefringence of a low-loss, high-reflectance coating applied to an 8-cm-diameter sapphire crystal grown in the m-axis direction has been mapped. By monitoring the transmission of a high-finesse Fabry-Perot cavity as a function of the polarization of the input light, we find an upper limit for the magnitude of the birefringence of 2.5 x 10^-4 rad and an upper limit in the variation in direction of the birefringence of 10 deg. These values are sufficiently small to allow consideration of m-axis sapphire as a substrate material for the optics of the advanced detector at the Laser Interferometer Gravitational Wave Observatory

Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure

Economic Impact of North Dakota Laws that Permit Delayed or Partial Repayment of Agricultural Debt � July 1, 1986

Agricultural Finance,