Transformation completeness properties of SVPC transformation sets

AbstractA set T of permutations of a finite set D is said to be transformation complete if the orbits of 〈T〉, the group generated by T, acting on F(D), the power set of D, are exactly the set of subsets of D having the same cardinality, where the orbit of xϵF(D) is {α(x)|αϵ〈T〉}. This paper studies the transformation completeness properties of suppressed variable permutation and complementation (SVPC) transformations which act on Boolean variables with domain being D = {0, 1}n. An SVPC transformation with r control variables is an identity on the n-cube except on an (n − r)-subcube where the acting is like a variable permutation and complementation (VPC) transformation on n − r variables, 0≤r<n. Let Pnr be the set of all SVPC transformations on n variables with r control variables. It is shown that Pnr is transformation complete for n>r≥1. In particular, it is shown that S2n = 〈Pnn−1〉 = 〈Pnn−2〉 ⊃ 〈Pnn−3〉 = 〈Pnn−4〉 = ⋯ = 〈Pn1〉 = A2n ⊃ 〈Pn0〉, where S2n and A2n are the symmetric group and alternating group of degree 2n, respectively. Pn0, i.e., the VPC transformation group on n variables, is not transformation complete, however. Thus, one control variable is necessary and sufficient to make Pnr transformation complete

Quantum games of asymmetric information

We investigate quantum games in which the information is asymmetrically distributed among the players, and find the possibility of the quantum game outperforming its classical counterpart depends strongly on not only the entanglement, but also the informational asymmetry. What is more interesting, when the information distribution is asymmetric, the contradictive impact of the quantum entanglement on the profits is observed, which is not reported in quantum games of symmetric information.Comment: 5 pages, 3 figure

Vacancy Mediated Desorption of Hydrogen From a Sodium Alanate Surface: An ab Initio Spin-Polarized Study

Ab initio spin-polarized density functional theory calculations are performed to explore the effect of single Na vacancy on NaAlH4(001) surface on the initial dehydrogenation kinetics. The authors found that two Al-H bond lengths become elongated and weakened due to the presence of a Na vacancy on the NaAlH4(001) surface. Spontaneous recombination from the surface to form molecular hydrogen is observed in the spin-polarized ab initio molecular dynamics simulation. The authors' results indicate that surface Na vacancies play a critical role in accelerating the dehydrogenation kinetics in sodium alanate. The understanding gained here will aid in the rational design and development of complex hydride materials for hydrogen storage. (c) 2007 American Institute of Physics

The trade-off between tidal-turbine array yield and impact on flow: A multi-objective optimisation problem

Abstract This paper introduces a new approach for investigating trade-offs between different societal objectives in the design of tidal-turbine arrays. This method is demonstrated through the trade-off between the yield of an array, and the extent to which that array alters the flow. This is posed as a multi-objective optimisation problem, and the problem is investigated using the array layout optimisation tool OpenTidalFarm. Motivated by environmental concerns, OpenTidalFarm is adapted to not only maximise array yield but also to minimise the effect of the array upon the hydrodynamics of the region, specifically the flow velocity. A linear scalarisation of the multi-objective optimisation problem is solved for a series of different weightings of the two conflicting objectives. Two idealised test scenarios are evaluated and in each case a set of Pareto solutions is found. These arrays are assessed for the power they generate and the severity of change they cause in the flow velocity. These analyses allow for the identification of trade-offs between these two objectives, while the methods proposed can similarly be applied to the two key societal objectives of energy production and conservation, thus providing information that could be valuable to stakeholders and policymakers when making decisions on array design

Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States

We present an effective Chern-Simons theory for the bulk fully polarized fractional quantum Hall (FQH) hierarchical states constructed as daughters of general states of the Jain series, {\it i. e.} as FQH states of the quasi-particles or quasi-holes of Jain states. We discuss the stability of these new states and present two reasonable stability criteria. We discuss the theory of their edge states which follows naturally from this bulk theory. We construct the operators that create elementary excitations, and discuss the scaling behavior of the tunneling conductance in different situations. Under the assumption that the edge states of these fully polarized hierarchical states are unreconstructed and unresolved, we find that the differential conductance $G$ for tunneling of electrons from a Fermi liquid into {\em any} hierarchical Jain FQH states has the scaling behavior $G\sim V^\alpha$ with the universal exponent $\alpha=1/\nu$, where $\nu$ is the filling fraction of the hierarchical state. Finally, we explore alternative ways of constructing FQH states with the same filling fractions as partially polarized states, and conclude that this is not possible within our approach.Comment: 10 pages, 50 references, no figures; formerly known as "Composite Fermions: The Next Generation(s)" (title changed by the PRB thought police). This version has more references and a discussion of the stability of the new states. Published version. One erroneous reference is correcte

Hamiltonian theory of gaps, masses and polarization in quantum Hall states: full disclosure

I furnish details of the hamiltonian theory of the FQHE developed with Murthy for the infrared, which I subsequently extended to all distances and apply it to Jain fractions \nu = p/(2ps + 1). The explicit operator description in terms of the CF allows one to answer quantitative and qualitative issues, some of which cannot even be posed otherwise. I compute activation gaps for several potentials, exhibit their particle hole symmetry, the profiles of charge density in states with a quasiparticles or hole, (all in closed form) and compare to results from trial wavefunctions and exact diagonalization. The Hartree-Fock approximation is used since much of the nonperturbative physics is built in at tree level. I compare the gaps to experiment and comment on the rough equality of normalized masses near half and quarter filling. I compute the critical fields at which the Hall system will jump from one quantized value of polarization to another, and the polarization and relaxation rates for half filling as a function of temperature and propose a Korringa like law. After providing some plausibility arguments, I explore the possibility of describing several magnetic phenomena in dirty systems with an effective potential, by extracting a free parameter describing the potential from one data point and then using it to predict all the others from that sample. This works to the accuracy typical of this theory (10 -20 percent). I explain why the CF behaves like free particle in some magnetic experiments when it is not, what exactly the CF is made of, what one means by its dipole moment, and how the comparison of theory to experiment must be modified to fit the peculiarities of the quantized Hall problem

Brane fluctuation and the electroweak chiral Lagrangian

We use the external field method to study the electroweak chiral Lagrangian of the extra dimension model with brane fluctuation. Under the assumption that the contact terms between the matters of the standard model and KK excitations are heavily suppressed, we use the standard procedure to integrate out the quantum fields of KK excitations and the equation of motion to eliminate the classic fields of KK excitations. At one-loop level, we find that up to the order $O(p^4)$, due to the momentum conservation of the fifth dimension and the gauge symmetry of the zero modes, there is no constraint on the size of extra dimension. This result is consistent with the decoupling theorem. However, meaningful constraints can come from those operators in $O(p^6)$, which can contribute considerably to some anomalous vector couplings and can be accessible in the LC and LHC.Comment: Revised version, 20 pages in ReVTeX, to appear in PR

A tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: the structure of PbZr(0.52)Ti(0.48)O3

The perovskite-like ferroelectric system PbZr(1-x)Ti(x)O3 (PZT) has a nearly vertical morphotropic phase boundary (MPB) around x=0.45-0.50. Recent synchrotron x-ray powder diffraction measurements by Noheda et al. [Appl. Phys. Lett. 74, 2059 (1999)] have revealed a new monoclinic phase between the previously-established tetragonal and rhombohedral regions. In the present work we describe a Rietveld analysis of the detailed structure of the tetragonal and monoclinic PZT phases on a sample with x= 0.48 for which the lattice parameters are respectively: at= 4.044 A, ct= 4.138 A, at 325 K, and am= 5.721 A, bm= 5.708 A, cm= 4.138 A, beta= 90.496 deg., at 20K. In the tetragonal phase the shifts of the atoms along the polar [001] direction are similar to those in PbTiO3 but the refinement indicates that there are, in addition, local disordered shifts of the Pb atoms of ~0.2 A perpendicular to the polar axis.. The monoclinic structure can be viewed as a condensation along one of the directions of the local displacements present in the tetragonal phase. It equally well corresponds to a freezing-out of the local displacements along one of the directions recently reported by Corker et al.[J. Phys. Condens. Matter 10, 6251 (1998)] for rhombohedral PZT. The monoclinic structure therefore provides a microscopic picture of the MPB region in which one of the "locally" monoclinic phases in the "average" rhombohedral or tetragonal structures freezes out, and thus represents a bridge between these two phases.Comment: REVTeX, 7 figures. Modifications after referee's suggestion: new figure (figure 5), comments in 2nd para. (Sect.III) and in 2nd & 3rd para. (Sect. IV-a), in the abstract: "...of ~0.2 A perpendicular to the polar axis.

Labour after Land Reform: The Precarious Livelihoods of Former Farmworkers in Zimbabwe

What happens to labour when major redistributive land reform restructures a system of settler colonial agriculture? This article examines the livelihoods of former farmworkers on large‐scale commercial farms who still live in farm compounds after Zimbabwe's land reform. Through a mix of surveys and in‐depth biographical interviews, four different types of livelihood are identified, centred on differences in land access. These show how diverse, but often precarious, livelihoods are being carved out, representing the ‘fragmented classes of labour’ in a restructured agrarian economy. The analysis highlights the tensions between gaining new freedoms, notably through access to land, and being subject to new livelihood vulnerabilities. The findings are discussed in relation to wider questions about the informalization of the economy and the role of labour and employment in a post‐settler agrarian economy, where the old ‘farmworker’ label no longer applies