Mapping climatic risks in the EU agriculture

Replaced with revised version of paper 11/18/08.Agrometeorological models, climatic risk, European Union, Vegetation indices, Environmental Economics and Policy, Risk and Uncertainty,

Agricultural risk management in Europe

Replaced with revised version of paper 11/18/08Risk management policy, agricultural insurance, calamity funds, ad-hoc aids, natural disaster, Production Economics, Risk and Uncertainty,

Effective sigma models and lattice Ward identities

We perform a lattice analysis of the Faddeev-Niemi effective action conjectured to describe the low-energy sector of SU(2) Yang-Mills theory. To this end we generate an ensemble of unit vector fields ("color spins") n from the Wilson action. The ensemble does not show long-range order but exhibits a mass gap of the order of 1 GeV. From the distribution of color spins we reconstruct approximate effective actions by means of exact lattice Schwinger-Dyson and Ward identities ("inverse Monte Carlo"). We show that the generated ensemble cannot be recovered from a Faddeev-Niemi action, modified in a minimal way by adding an explicit symmetry-breaking term to avoid the appearance of Goldstone modes.Comment: 25 pages, 17 figures, JHEP styl

Two-Qubit Separability Probabilities and Beta Functions

Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of n=4, that is, the two-qubit systems. Making use of the density matrix (rho) parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated integrand in each case is the product of a known (highly oscillatory near nu=1) jacobian and a certain unknown univariate function, which our extensive numerical (quasi-Monte Carlo) computations indicate is very closely proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2, b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case. Assuming the full applicability of these specific incomplete beta functions, we undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and reorganized, with the quasi-Monte Carlo integration sample size being greatly increase

Analysis of new high-precision transit light curves of WASP-10 b: starspot occultations, small planetary radius, and high metallicity

The WASP-10 planetary system is intriguing because different values of radius have been reported for its transiting exoplanet. The host star exhibits activity in terms of photometric variability, which is caused by the rotational modulation of the spots. Moreover, a periodic modulation has been discovered in transit timing of WASP-10 b, which could be a sign of an additional body perturbing the orbital motion of the transiting planet. We attempt to refine the physical parameters of the system, in particular the planetary radius, which is crucial for studying the internal structure of the transiting planet. We also determine new mid-transit times to confirm or refute observed anomalies in transit timing. We acquired high-precision light curves for four transits of WASP-10 b in 2010. Assuming various limb-darkening laws, we generated best-fit models and redetermined parameters of the system. The prayer-bead method and Monte Carlo simulations were used to derive error estimates. Three transit light curves exhibit signatures of the occultations of dark spots by the planet during its passage across the stellar disk. The influence of stellar activity on transit depth is taken into account while determining system parameters. The radius of WASP-10 b is found to be no greater than 1.03 Jupiter radii, a value significantly smaller than most previous studies indicate. We calculate interior structure models of the planet, assuming a two-layer structure with one homogeneous envelope atop a rock core. The high value of the WASP-10 b's mean density allows one to consider the planet's internal structure including 270 to 450 Earth masses of heavy elements. Our new mid-transit times confirm that transit timing cannot be explained by a constant period if all literature data points are considered. They are consistent with the ephemeris assuming a periodic variation of transit timing...Comment: Accepted for publication in A&

A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics

We simulate the vibration of a violin bridge in a multi-query context using reduced basis techniques. The mathematical model is based on an eigenvalue problem for the orthotropic linear elasticity equation. In addition to the nine material parameters, a geometrical thickness parameter is considered. This parameter enters as a 10th material parameter into the system by a mapping onto a parameter independent reference domain. The detailed simulation is carried out by isogeometric mortar methods. Weakly coupled patch-wise tensorial structured isogeometric elements are of special interest for complex geometries with piecewise smooth but curvilinear boundaries. To obtain locality in the detailed system, we use the saddle point approach and do not apply static condensation techniques. However within the reduced basis context, it is natural to eliminate the Lagrange multiplier and formulate a reduced eigenvalue problem for a symmetric positive definite matrix. The selection of the snapshots is controlled by a multi-query greedy strategy taking into account an error indicator allowing for multiple eigenvalues