The Basic Formula Price: Has the Use of NASS Cheese Prices Changed Its Value?

Agribusiness, Demand and Price Analysis,

The Future Viability of the Federated Structure

Agribusiness,

Using constraint preconditioners with regularized saddle-point problems

The problem of finding good preconditioners for the numerical solution of a certain important class of indefinite linear systems is considered. These systems are of a 2 by 2 block (KKT) structure in which the (2,2) block (denoted by -C) is assumed to be nonzero. In Constraint preconditioning for indefinite linear systems , SIAM J. Matrix Anal. Appl., 21 (2000), Keller, Gould and Wathen introduced the idea of using constraint preconditioners that have a specific 2 by 2 block structure for the case of C being zero. We shall give results concerning the spectrum and form of the eigenvectors when a preconditioner of the form considered by Keller, Gould and Wathen is used but the system we wish to solve may have C \neq 0 . In particular, the results presented here indicate clustering of eigenvalues and, hence, faster convergence of Krylov subspace iterative methods when the entries of C are small; such situations arise naturally in interior point methods for optimization and we present results for such problems which validate our conclusions.\ud \ud The first author's work was supported by the OUCL Doctorial Training Accoun

Microwave Scattering and Noise Emission from Afterglow Plasmas in a Magnetic Field

The microwave reflection and noise emission (extraordinary mode) from cylindrical rare‐gas (He, Ne, Ar) afterglow plasmas in an axial magnetic field is described. Reflection and noise emission are measured as a function of magnetic field near electron cyclotron resonance (ω ≈ ω_c) with electron density as a parameter (ω_p < ω). A broad peak, which shifts to lower values of ω_c/ω) as electron density increases, is observed for (ω_c/ω) ≤ 1. For all values of electron density a second sharp peak is found very close to cyclotron resonance in reflection measurements. This peak does not occur in the emission data. Calculations of reflection and emission using a theoretical model consisting of a one‐dimensional, cold plasma slab with nonuniform electron density yield results in qualitative agreement with the observations. Both the experimental and theoretical results suggest that the broad, density‐dependent peak involves resonance effects at the upper hybrid frequency ((ω_h)^2 = (ω_c)^2 + (ω_p)^2) of the plasma

Empirical Study of Simulated Two-planet Microlensing Event

We undertake the first study of two-planet microlensing models recovered from simulations of microlensing events generated by realistic multi-planet systems in which 292 planetary events including 16 two-planet events were detected from 6690 simulated light curves. We find that when two planets are recovered, their parameters are usually close to those of the two planets in the system most responsible for the perturbations. However, in one of the 16 examples, the apparent mass of both detected planets was more than doubled by the unmodeled influence of a third, massive planet. This fraction is larger than, but statistically consistent with, the roughly 1.5% rate of serious mass errors due to unmodeled planetary companions for the 274 cases from the same simulation in which a single planet is recovered. We conjecture that an analogous effect due to unmodeled stellar companions may occur more frequently. For seven out of 23 cases in which two planets in the system would have been detected separately, only one planet was recovered because the perturbations due to the two planets had similar forms. This is a small fraction (7/274) of all recovered single-planet models, but almost a third of all events that might plausibly have led to two-planet models. Still, in these cases, the recovered planet tends to have parameters similar to one of the two real planets most responsible for the anomaly.Comment: 21 pages, 9 figures, 2 tables; submitted to ApJ; for a short video introducing the key results, see https://www.youtube.com/watch?v=qhK4a6sbfO

Space Charge Waves in Cylindrical Plasma Columns

When a plasma is of finite transverse cross section, space-charge waves may propagate even in the absence of a drift motion or thermal velocities of the plasma. Some of the properties of these space charge waves have been investigated by regarding the plasma as a dielectric and solving the resulting field equations. The effect of a steady axial magnetic field is considered, but motion of heavy ions and electron temperature effects are neglected. Waves are found to exist at frequencies low compared with the plasma frequency as well as waves with oppositely directed phase and group velocities (backward waves).Many of the features of these waves have been verified experimentally by measuring phase velocity and attenuation of waves along the positive column of a low pressure mercury arc in an axial magnetic field. Measurements of electron density have been made using these waves and the results are compared with those obtained by other methods. An interesting feature of these measurements, of value in plasma diagnostics, is that they can be made with frequencies which are small compared with the plasma frequency

Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras

The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with a multiparametric co-product action as given by Reshetikhin. Here we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras $U_q[osp(m|n)]$. In this manner we obtain generalisations of the Perk--Schultz model.Comment: 10 pages, 2 figure

Hot Jupiters in binary star systems

Radial velocity surveys find Jupiter mass planets with semi-major axes a less than 0.1 AU around ~1% of solar-type stars; counting planets with $a$ as large as 5 AU, the fraction of stars having planets reaches ~ 10% {Marcy,Butler}. An examination of the distribution of semi-major axes shows that there is a clear excess of planets with orbital periods around 3 or 4 days, corresponding to a~0.03$ AU, with a sharp cutoff at shorter periods (see Figure 1). It is believed that Jupiter mass planets form at large distances from their parent stars; some fraction then migrate in to produce the short period objects. We argue that a significant fraction of the `hot Jupiters' (a<0.1 AU) may arise in binary star systems in which the orbit of the binary is highly inclined to the orbit of the planet. Mutual torques between the two orbits drive down the minimum separation or periapse r_p between the planet and its host star (the Kozai mechanism). This periapse collapse is halted when tidal friction on the planet circularizes the orbit faster than Kozai torque can excite it. The same friction then circularizes the planet orbit, producing hot Jupiters with the peak of the semimajor axis distribution lying around 3 days. For the observed distributions of binary separation, eccentricity and mass ratio, roughly 2.5% of planets with initial semimajor axis a_p ~ 5au will migrate to within 0.1au of their parent star. Kozai migration could account for 10% or more of the observed hot Jupiters.Comment: accepted to ApJ main journal, added one figure and expanded discussion