Whirling skirts and rotating cones

Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible, flexible, generalized-conical sheet rotating about a fixed axis. Conservation laws are used to reduce the dynamics to a quadrature describing a particle in a three-parameter family of potentials. One parameter is associated with the stress in the sheet, aNoether is the current associated with rotational invariance, and the third is a Rossby number which indicates the relative strength of Coriolis forces. Solutions are quantized by enforcing a topology appropriate to a skirt and a particular choice of dihedral symmetry. A perturbative analysis of nearly axisymmetric cones shows that Coriolis effects are essential in establishing skirt-like solutions. Fully non-linear solutions with three-fold symmetry are presented which bear a suggestive resemblance to the observed patterns.Comment: two additional figures, changes to text throughout. journal version will have a wordier abstrac

Dipoles in thin sheets

A flat elastic sheet may contain pointlike conical singularities that carry a metrical "charge" of Gaussian curvature. Adding such elementary defects to a sheet allows one to make many shapes, in a manner broadly analogous to the familiar multipole construction in electrostatics. However, here the underlying field theory is non-linear, and superposition of intrinsic defects is non-trivial as it must respect the immersion of the resulting surface in three dimensions. We consider a "charge-neutral" dipole composed of two conical singularities of opposite sign. Unlike the relatively simple electrostatic case, here there are two distinct stable minima and an infinity of unstable equilibria. We determine the shapes of the minima and evaluate their energies in the thin-sheet regime where bending dominates over stretching. Our predictions are in surprisingly good agreement with experiments on paper sheets.Comment: 20 pages, 5 figures, 2 table

Force dipoles and stable local defects on fluid vesicles

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area and volume preserving conformal transformations, which breaks the symmetry between the two points. The volume constraint fixes the distance $S$, measured along the surface, between the two points; if it is relaxed, a second zero mode appears, reflecting the independence of the energy on $S$; in the absence of this constraint a pathway opens for the membrane to slip out of the defect. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. The magnitude of these forces varies inversely with $S$ and so diverges as the points merge; the corresponding torques vanish in these defects. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and in distant regions as a biharmonic quadrupole. Comparison of the distribution of stress with the quadratic approximation in the height functions points to shortcomings of the latter representation. Radial tension is accompanied by lateral compression, both near the singularities and far away, with a crossover from tension to compression occurring in the region between them.Comment: 26 pages, 10 figure

Good Governance: A Step towards Promoting Positive Attitude and Enhancing Productivity in the Civil Service

This is a research about good governance in the civil service. Five federal organizations served as research population: Ministry for Capacity Building, Ministry of Revenue, Federal Civil Service Agency, Ethiopian Civil Service College, and Ethiopian Management Institute. Fifty-six (56) respondents served as research sample. The research was conducted through the use of a research instrument (opinionnaire). Percentage (%) and Chi square (X2) were used as statistical tools. It was found out that reform program pays equal attention to all citizens; financial regulations are violated in Government expenditure; service delivery is poor in the Civil Service; unethical practices do exist in Civil Service; top management system is poor; and Civil Service (HR) is ineffective. Based on the research findings it was recommended that Civil servants need a lot more of education, training and development. African Research Review Vol. 2 (1) 2008: pp. 19-4

Spinor representation of surfaces and complex stresses on membranes and interfaces

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.Comment: 17 page

Yang-Mills theory a la string

A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The theory it defines differs from Yang-Mills theory in that it is a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations describing this surface, introducing a framework which throws light on their relationship to the Yang-Mills equations.Comment: 7 page

Deformations of extended objects with edges

We present a manifestly gauge covariant description of fluctuations of a relativistic extended object described by the Dirac-Nambu-Goto action with Dirac-Nambu-Goto loaded edges about a given classical solution. Whereas physical fluctuations of the bulk lie normal to its worldsheet, those on the edge possess an additional component directed into the bulk. These fluctuations couple in a non-trivial way involving the underlying geometrical structures associated with the worldsheet of the object and of its edge. We illustrate the formalism using as an example a string with massive point particles attached to its ends.Comment: 17 pages, revtex, to appear in Phys. Rev. D5

Open strings with topologically inspired boundary conditions

We consider an open string described by an action of the Dirac-Nambu-Goto type with topological corrections which affect the boundary conditions but not the equations of motion. The most general addition of this kind is a sum of the Gauss-Bonnet action and the first Chern number (when the background spacetime dimension is four) of the normal bundle to the string worldsheet. We examine the modification introduced by such terms in the boundary conditions at the ends of the string.Comment: 12 pages, late

Information provenance for open distributed collaborative system

In autonomously managed distributed systems for collaboration, provenance can facilitate reuse of information that are interchanged, repetition of successful experiments, or to provide evidence for trust mechanisms that certain information existed at a certain period during collaboration. In this paper, we propose domain independent information provenance architecture for open collaborative distributed systems. The proposed system uses XML for interchanging information and RDF to track information provenance. The use of XML and RDF also ensures that information is universally acceptable even among heterogeneous nodes. Our proposed information provenance model can work on any operating systems or workflows.<br /

Geometric Bounds in Spherically Symmetric General Relativity

We exploit an arbitrary extrinsic time foliation of spacetime to solve the constraints in spherically symmetric general relativity. Among such foliations there is a one parameter family, linear and homogeneous in the extrinsic curvature, which permit the momentum constraint to be solved exactly. This family includes, as special cases, the extrinsic time gauges that have been exploited in the past. These foliations have the property that the extrinsic curvature is spacelike with respect to the the spherically symmetric superspace metric. What is remarkable is that the linearity can be relaxed at no essential extra cost which permits us to isolate a large non - pathological dense subset of all extrinsic time foliations. We identify properties of solutions which are independent of the particular foliation within this subset. When the geometry is regular, we can place spatially invariant numerical bounds on the values of both the spatial and the temporal gradients of the scalar areal radius, $R$. These bounds are entirely independent of the particular gauge and of the magnitude of the sources. When singularities occur, we demonstrate that the geometry behaves in a universal way in the neighborhood of the singularity.Comment: 16 pages, revtex, submitted to Phys. Rev.