8,494 research outputs found
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
The Child Sexual Abuse Epidemic in Addis Ababa: Some Reflections on Reported Incidents, Psychosocial Consequences and Implications
Background: Though child sexual abuse is a universal phenomenon, only reported cases of the incidence are common source of information to get insight on how to understand the problem. Besides, investigating complaints presented by victims themselves would be a stepping stone for designing prevention and rehabilitation programs. The objective of this study was to identify the nature of sexual incidence and experience victims face.Methods: The research was conducted by collecting reported child sexual abuse cases from Child Protection Units of Addis Ababa Police Commission and three selected non-governmental organizations working for the welfare of sexually abused children in Addis Ababa. 64 selected samples of victim children were included from the three organizations. They completed a semi-structured questionnaire and data were analyzed.Results: Of the total reported crime cases committed against children (between July 2005 and December 2006), 23% of them were child sexual victimization. On average, 21 children were reported to be sexually abused each month where majority of the sexual abuse incidence were committed against female children in their own home by someone they closely know. The psychological trauma and physical complaints presented by victims include symptoms of anxiety and depression.Conclusion: It was found out that child sexual abuse cases presented to the legal office was not properly managed. Female children appear to be more prone to sexual abuse than their male counterparts. By virtue of their nature, many children are at risk of sexual victimization by people they truest. Based on the findings, several implications are made, which includes the importance of nation-wide study to formulate a comprehensive policy guideline for protection and criminalization of child sexual abuse in Ethiopia
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
Sufficient Conditions for Apparent Horizons in Spherically Symmetric Initial Data
We establish sufficient conditions for the appearance of apparent horizons in
spherically symmetric initial data when spacetime is foliated extrinsically.
Let and be respectively the total material energy and the total
material current contained in some ball of radius . Suppose that the
dominant energy condition is satisfied. We show that if then
the region must possess a future apparent horizon for some non -trivial closed
subset of such gauges. The same inequality holds on a larger subset of gauges
but with a larger constant of proportionality which depends weakly on the
gauge. This work extends substantially both our joint work on moment of time
symmetry initial data as well as the work of Bizon, Malec and \'O Murchadha on
a maximal slice.Comment: 16 pages, revtex, to appear in Phys. Rev.
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, .
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.
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
Conical defects in growing sheets
A growing or shrinking disc will adopt a conical shape, its intrinsic
geometry characterized by a surplus angle at the apex. If growth is slow,
the cone will find its equilibrium. Whereas this is trivial if , the
disc can fold into one of a discrete infinite number of states if is
positive. We construct these states in the regime where bending dominates,
determine their energies and how stress is distributed in them. For each state
a critical value of is identified beyond which the cone touches itself.
Before this occurs, all states are stable; the ground state has two-fold
symmetry.Comment: 4 pages, 4 figures, LaTeX, RevTeX style. New version corresponds to
the one published in PR
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 , measured
along the surface, between the two points; if it is relaxed, a second zero mode
appears, reflecting the independence of the energy on ; 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 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
Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data
We establish necessary conditions for the appearance of both apparent
horizons and singularities in the initial data of spherically symmetric general
relativity when spacetime is foliated extrinsically. When the dominant energy
condition is satisfied these conditions assume a particularly simple form. Let
be the maximum value of the energy density and the radial
measure of its support. If is bounded from above by some
numerical constant, the initial data cannot possess an apparent horizon. This
constant does not depend sensitively on the gauge. An analogous inequality is
obtained for singularities with some larger constant. The derivation exploits
Poincar\'e type inequalities to bound integrals over certain spatial scalars. A
novel approach to the construction of analogous necessary conditions for
general initial data is suggested.Comment: 15 pages, revtex, to appear in Phys. Rev.
Ideal Basis in Constructions Defined by Directed Graphs
The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. This notion is motivated by its applications for the design of classication systems. Our main theorem establishes that, for every balanced digraph and each idempotent semiring with identity element, the incidence semiring of the digraph has a convenient visible ideal basis. It also shows that the elements of the basis can always be used to generate ideals with the largest possible weight among the weights of all ideals in the incidence semiring
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