A computer code for calculations in the algebraic collective model of the atomic nucleus

A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments $q_M$ and are at most quadratic in the corresponding conjugate momenta $\pi_N$ ($-2\le M,N\le 2$). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators $[\pi\otimes q \otimes\pi]_0$ and $[\pi\otimes\pi]_{LM}$. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5)$\,\supset\,$SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.Comment: REVTEX4. v2: Minor improvements and corrections. v3: Introduction rewritten, references added, Appendix B.4 added illustrating efficiencies obtained using modified basis, Appendix E added summarising computer implementation, and other more minor improvements. 43 pages. Manuscript and program to be published in Computer Physics Communications (2016

A review of knowledge: inter-row hoeing & its associated agronomy in organic cereal & pulse crops

The aim of this project was to establish the “state of the art” for inter-row hoeing and its associated agronomic practices in organic cereal and pulse crops. To achieve this a detailed review of literature was undertaken. • To facilitate inter-row cultivation in cereal and pulse crops, some adjustment of row spacing may be required. For cereals, drilling crops in 25 cm rows can reduce yield compared with normal drilling practice, primarily due to greater intra-specific competition amongst the crop (i.e. competition between crop plants). • The yield penalty resulting from widely spaced crop rows can be minimised using a number of approaches, depending on the drill: 1. Reducing the seed rate in widely spaced crop rows can help to minimise excessive intra-specific competition. 2. Band sowing the crop in wide rows can also help to minimise intra-specific competition as the seed is distributed over a greater area. 3. Using a twin-row arrangement can completely overcome the yield penalty. • The recommended row spacing for peas (up to 20 cm) and beans (up to 35 cm) does not require any further adjustment for inter-row hoeing. • Recent developments in automated guidance of inter-row hoeing equipment mean that weeding operations can now be conducted a much higher speeds (10 km h-1). This has highlighted the limitations of some of the cultivators currently used (e.g. ‘A’ blades), as excessive soil throw can occur at this high speed. Rolling cultivators may prove to be the most suitable at high forward speeds. For manually guided hoes working at slower speeds (5 km h-1), ‘A’ and ‘L’ blades offer an effective low cost solution. • In terms of the timing of inter-row hoeing, it is suggested that weeding operations should be conducted at an early stage in the growing season, as the weeds that emerge with or shortly after the crop are the ones that pose the most significant threat for crop yield. Weeding on two occasions can provide better levels of weed control than weeding once, but weeding more frequently offered little additional benefit. Reductions of weed biomass of up to 99 % have been reported as a result of inter-row hoeing, although this has not always resulted in a positive crop yield response. This is probably due to crop damage resulting from inaccurate hoeing, a problem that can be overcome with automated guidance. • There is some evidence to suggest that mechanical weeding operations can mineralise soil bound nitrogen. • The impact of inter-row hoeing on ground nesting birds is uncertain. Early indications suggest that skylarks prefer to nest directly adjacent to or in the crop row rather than between rows. The information contained within this review should enable farmers to make best use of inter-row hoeing in their arable crops. There are a number of areas that require further research and development: • The interaction of seed rate and row spacing needs to be confirmed in organic systems. • Relatively little is known about the mechanisms of weed kill and the detailed interaction between the cultivator blade, the weed and the soil. This is particularly important with the new automated guidance equipment that allows weeding at high forward speeds. • The timing and frequency of inter-row hoeing has received very little attention. The optimum weed control timings are based on small-plot crop:weed competition studies and need to be verified under field scale management with inter-row hoeing equipment. • Finally, the impact of inter-row hoeing and widely spaced crop rows on ground-nesting birds has not been looked at directly, but is of importance. Please see the main report for a more detailed summary before the full text

Homological Error Correction: Classical and Quantum Codes

We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming bound. In the quantum case, we show that for non-orientable surfaces it is impossible to construct homological codes based on qudits of dimension $D>2$, while for orientable surfaces with boundaries it is possible to construct them for arbitrary dimension $D$. We give a method to obtain planar homological codes based on the construction of quantum codes on compact surfaces without boundaries. We show how the original Shor's 9-qubit code can be visualized as a homological quantum code. We study the problem of constructing quantum codes with optimal encoding rate. In the particular case of toric codes we construct an optimal family and give an explicit proof of its optimality. For homological quantum codes on surfaces of arbitrary genus we also construct a family of codes asymptotically attaining the maximum possible encoding rate. We provide the tools of homology group theory for graphs embedded on surfaces in a self-contained manner.Comment: Revtex4 fil

Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers.Comment: 4 pages, 2 figure

On the fundamental group of the complement of a complex hyperplane arrangement

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.Comment: 12 pages, Latex2e with AMSLaTeX 1.2, no figures; this last version is almost the same as published in Functional Analysis and its Applications 45:2 (2011), 137-14

Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density

The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the \emph{``#P-complete''} class, which indicates the problem is computationally ``intractable''. We use exact computational method to investigate the number of ways to arrange dimers on $m \times n$ two-dimensional rectangular lattice strips with fixed dimer density $\rho$. For any dimer density $0 < \rho < 1$, we find a logarithmic correction term in the finite-size correction of the free energy per lattice site. The coefficient of the logarithmic correction term is exactly -1/2. This logarithmic correction term is explained by the newly developed asymptotic theory of Pemantle and Wilson. The sequence of the free energy of lattice strips with cylinder boundary condition converges so fast that very accurate free energy $f_2(\rho)$ for large lattices can be obtained. For example, for a half-filled lattice, $f_2(1/2) = 0.633195588930$, while $f_2(1/4) = 0.4413453753046$ and $f_2(3/4) = 0.64039026$. For $\rho < 0.65$, $f_2(\rho)$ is accurate at least to 10 decimal digits. The function $f_2(\rho)$ reaches the maximum value $f_2(\rho^*) = 0.662798972834$ at $\rho^* = 0.6381231$, with 11 correct digits. This is also the \md constant for two-dimensional rectangular lattices. The asymptotic expressions of free energy near close packing are investigated for finite and infinite lattice widths. For lattices with finite width, dependence on the parity of the lattice width is found. For infinite lattices, the data support the functional form obtained previously through series expansions.Comment: 15 pages, 5 figures, 5 table

Kepler-47: A Transiting Circumbinary Multi-Planet System

We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of the Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5 days, eighteen transits of the inner planet have been observed, allowing a detailed characterization of its orbit and those of the stars. The outer planet's orbital period is 303.2 days, and although the planet is not Earth-like, it resides within the classical "habitable zone", where liquid water could exist on an Earth-like planet. With its two known planets, Kepler-47 establishes that close binary stars can host complete planetary systems.Comment: To appear on Science Express August 28, 11 pages, 3 figures, one table (main text), 56 pages, 28 figures, 10 table

Higher spin vertex models with domain wall boundary conditions

We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.Comment: 14 pages, 12 figures. Minor corrections. Version to appear in JSTA

Error Avoiding Quantum Codes and Dynamical Stabilization of Grover's Algorithm

An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the computational basis. Furthermore, its redundancy is smaller than the one which is achievable with a general error correcting quantum code saturating the quantum Hamming bound. The fact that this code consists of factorizable states only may offer advantages for the implementation of quantum gates in the error free subspace

Prospects for the Characterization and Confirmation of Transiting Exoplanets via the Rossiter-McLaughlin Effect

The Rossiter-McLaughlin (RM) effect is the distortion of stellar spectral lines that occurs during eclipses or transits, due to stellar rotation. We assess the future prospects for using the RM effect to measure the alignment of planetary orbits with the spin axes of their parent stars, and to confirm exoplanetary transits. We compute the achievable accuracy for the parameters of interest, in general and for the 5 known cases of transiting exoplanets with bright host stars. We determine the requirements for detecting the effects of differential rotation. For transiting planets with small masses or long periods (as will be detected by forthcoming satellite missions), the velocity anomaly produced by the RM effect can be much larger than the orbital velocity of the star. For a terrestrial planet in the habitable zone of a Sun-like star found by the Kepler mission, it will be difficult to use the RM effect to confirm transits with current instruments, but it still may be easier than measuring the spectroscopic orbit.Comment: 18 pages, 8 figures, one table. Minor changes. Accepted to ApJ, to appear in the Jan 20, 2007 issue (v655