Superlubricity - a new perspective on an established paradigm

Superlubricity is a frictionless tribological state sometimes occurring in nanoscale material junctions. It is often associated with incommensurate surface lattice structures appearing at the interface. Here, by using the recently introduced registry index concept which quantifies the registry mismatch in layered materials, we prove the existence of a direct relation between interlayer commensurability and wearless friction in layered materials. We show that our simple and intuitive model is able to capture, down to fine details, the experimentally measured frictional behavior of a hexagonal graphene flake sliding on-top of the surface of graphite. We further predict that superlubricity is expected to occur in hexagonal boron nitride as well with tribological characteristics very similar to those observed for the graphitic system. The success of our method in predicting experimental results along with its exceptional computational efficiency opens the way for modeling large-scale material interfaces way beyond the reach of standard simulation techniques.Comment: 18 pages, 7 figure

Acceleration and Substructure Constraints in a Quasar Outflow

We present observations of probable line-of-sight acceleration of a broad absorption trough of C IV in the quasar SDSS J024221.87+004912.6. We also discuss how the velocity overlap of two other outflowing systems in the same object constrains the properties of the outflows. The Si IV doublet in each system has one unblended transition and one transition which overlaps with absorption from the other system. The residual flux in the overlapping trough is well fit by the product of the residual fluxes in the unblended troughs. For these optically thick systems to yield such a result, at least one of them must consist of individual subunits rather than being a single structure with velocity-dependent coverage of the source. If these subunits are identical, opaque, spherical clouds, we estimate the cloud radius to be r = 3.9 10^15 cm. If they are identical, opaque, linear filaments, we estimate their width to be w = 6.5 10^14 cm. These subunits are observed to cover the Mg II broad emission line region of the quasar, at which distance from the black hole the above filament width is equal to the predicted scale height of the outer atmosphere of a thin accretion disk. Insofar as that scale height is a natural size scale for structures originating in an accretion disk, these observations are evidence that the accretion disk can be a source of quasar absorption systems. Based on data from ESO program 075.B-0190(A).Comment: 14 emulateapj pages, 7 figures, ApJ in pres

Locked and Unlocked Polygonal Chains in 3D

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D with a polynomial number of moves.Comment: To appear in Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 199

Work-related psychological health and psychological type among lead elders within the Newfrontiers network of churches in the United Kingdom

Building on a series of recent studies concerned with assessing work-related psychological health and psychological type among various groups of church leaders, this study reports new data provided by 134 Lead Elders within the Newfrontiers network of churches in the United Kingdom who completed the Francis Psychological Type Scales (FPTS) together with the two scales of the Francis Burnout Inventory (FBI) concerned with emotional exhaustion and satisfaction in ministry. Compared with other groups of church leaders, Lead Elders within the Newfrontiers network of churches reported lower levels of emotional exhaustion and higher levels of satisfaction in ministry. Compared with other groups of church leaders, there was a higher proportion of extraverts among Lead Elders within the Newfrontiers network of churches. There was only a weak association between psychological type and burnout

Adiabatic Geometric Phase for a General Quantum States

A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems. Furthermore, this new phase is related to Hannay's angles as we find that these angles, a classical concept, can arise naturally in quantum systems. The results are demonstrated with a two-level model.Comment: 4 pages, 2 figure

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

Quantum indistinguishability from general representations of SU(2n)

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-particle configuration space. It is shown how families of such bundles can be constructed from irreducible representations of the group SU(2n). The construction of Berry and Robbins, which leads to a definite connection between spin and statistics (the physically correct connection), is shown to correspond to the completely symmetric representations. The spin-statistics connection is typically broken for general SU(2n) representations, which may admit, for a given value of spin, both bose and fermi statistics, as well as parastatistics. The determination of the allowed values of the spin and statistics reduces to the decomposition of certain zero-weight representations of a (generalised) Weyl group of SU(2n). A formula for this decomposition is obtained using the Littlewood-Richardson theorem for the decomposition of representations of U(m+n) into representations of U(m)*U(n).Comment: 32 pages, added example section 4.

Maslov Indices and Monodromy

We prove that for a Hamiltonian system on a cotangent bundle that is Liouville-integrable and has monodromy the vector of Maslov indices is an eigenvector of the monodromy matrix with eigenvalue 1. As a corollary the resulting restrictions on the monodromy matrix are derived.Comment: 6 page

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior