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

Financing North Dakota's Agriculture

Agricultural Finance,

Apparatus for measuring thermal conductivity Patent

Development of apparatus for measuring thermal conductivit

Net solar generation potential from urban rooftops in Los Angeles

Rooftops provide accessible locations for solar energy installations. While rooftop solar arrays can offset in-building electricity needs, they may also stress electric grid operations. Here we present an analysis of net electricity generation potential from distributed rooftop solar in Los Angeles. We integrate spatial and temporal data for property-level electricity demands, rooftop solar generation potential, and grid capacity constraints to estimate the potential for solar to meet on-site demands and supply net exports to the electric grid. In the study area with 1.2 million parcels, rooftop solar could meet 7200 Gigawatt Hours (GWh) of on-site building demands (~29% of demand). Overall potential net generation is negative, meaning buildings use more electricity than they can produce. Yet, cumulative net export potential from solar to grid circuits is 16,400 GWh. Current policies that regulate solar array interconnection to the grid result in unutilized solar power output of 1700 MW. Lower-income and at-risk communities in LA have greater potential for exporting net solar generation to the grid. This potential should be recognized through investments and policy innovations. The method demonstrates the need for considering time-dependent calculations of net solar potential and offers a template for distributed renewable energy planning in cities

A TYPICAL FARM SERIES: DEVELOPMENT AND APPLICATION TO A MISSISSIPPI DELTA FARM

Farm Management,

Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection

In this work we continue the description of soliton-like solutions of some slowly varying, subcritical gKdV equations. In this opportunity we describe, almost completely, the allowed behaviors: either the soliton is refracted, or it is reflected by the potential, depending on its initial energy. This last result describes a new type of soliton-like solution for gKdV equations, also present in the NLS case. Moreover, we prove that the solution is not pure at infinity, unlike the standard gKdV soliton.Comment: 51 pages, submitte

The mean magnetic field of the sun: Observations at Stanford

A solar telescope was built at Stanford University to study the organization and evolution of large-scale solar magnetic fields and velocities. The observations are made using a Babcock-type magnetograph which is connected to a 22.9 m vertical Littrow spectrograph. Sun-as-a-star integrated light measurements of the mean solar magnetic field were made daily since May 1975. The typical mean field magnitude is about 0.15 gauss with typical measurement error less than 0.05 gauss. The mean field polarity pattern is essentially identical to the interplanetary magnetic field sector structure (seen near the earth with a 4 day lag). The differences in the observed structures can be understood in terms of a warped current sheet model

Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schroedinger maps on R^2

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schroedinger flow as special cases) for degree m equivariant maps from R^2 to S^2. If m \geq 3, we prove that near-minimal energy solutions converge to a harmonic map as t goes to infinity (asymptotic stability), extending previous work down to degree m = 3. Due to slow spatial decay of the harmonic map components, a new approach is needed for m=3, involving (among other tools) a "normal form" for the parameter dynamics, and the 2D radial double-endpoint Strichartz estimate for Schroedinger operators with sufficiently repulsive potentials (which may be of some independent interest). When m=2 this asymptotic stability may fail: in the case of heat-flow with a further symmetry restriction, we show that more exotic asymptotics are possible, including infinite-time concentration (blow-up), and even "eternal oscillation".Comment: 34 page