1,665 research outputs found
Importance and effectiveness of representing the shapes of Cosserat rods and framed curves as paths in the special Euclidean algebra
We discuss how the shape of a special Cosserat rod can be represented as a
path in the special Euclidean algebra. By shape we mean all those geometric
features that are invariant under isometries of the three-dimensional ambient
space. The representation of the shape as a path in the special Euclidean
algebra is intrinsic to the description of the mechanical properties of a rod,
since it is given directly in terms of the strain fields that stimulate the
elastic response of special Cosserat rods. Moreover, such a representation
leads naturally to discretization schemes that avoid the need for the expensive
reconstruction of the strains from the discretized placement and for
interpolation procedures which introduce some arbitrariness in popular
numerical schemes. Given the shape of a rod and the positioning of one of its
cross sections, the full placement in the ambient space can be uniquely
reconstructed and described by means of a base curve endowed with a material
frame. By viewing a geometric curve as a rod with degenerate point-like cross
sections, we highlight the essential difference between rods and framed curves,
and clarify why the family of relatively parallel adapted frames is not
suitable for describing the mechanics of rods but is the appropriate tool for
dealing with the geometry of curves.Comment: Revised version; 25 pages; 7 figure
Solution of the Kirchhoff-Plateau problem
The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in
which a flexible filament in the form of a closed loop is spanned by a liquid
film, with the filament being modeled as a Kirchhoff rod and the action of the
spanning surface being solely due to surface tension. We establish the
existence of an equilibrium shape that minimizes the total energy of the system
under the physical constraint of non-interpenetration of matter, but allowing
for points on the surface of the bounding loop to come into contact. In our
treatment, the bounding loop retains a finite cross-sectional thickness and a
nonvanishing volume, while the liquid film is represented by a set with finite
two-dimensional Hausdorff measure. Moreover, the region where the liquid film
touches the surface of the bounding loop is not prescribed a priori. Our
mathematical results substantiate the physical relevance of the chosen model.
Indeed, no matter how strong is the competition between surface tension and the
elastic response of the filament, the system is always able to adjust to
achieve a configuration that complies with the physical constraints encountered
in experiments
Even-Odd Correlation Functions on an Optical Lattice
We study how different many body states appear in a quantum gas microscope,
such as the one developed at Harvard [Bakr et al. Nature 462, 74 (2009)], where
the site-resolved parity of the atom number is imaged. We calculate the spatial
correlations of the microscope images, corresponding to the correlation
function of the parity of the number of atoms at each site. We produce analytic
results for a number of well-known models: noninteracting bosons, the large U
Bose-Hubbard model, and noninteracting fermions. We find that these parity
correlations tend to be less strong than density-density correlations, but they
carry similar information.Comment: 8 pages, 4 figures. Published versio
Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities
Compressive fluctuations are a minor yet significant component of
astrophysical plasma turbulence. In the solar wind, long-wavelength compressive
slow-mode fluctuations lead to changes in and in , where and are the perpendicular and parallel
temperatures of the protons, is the magnetic field strength, and
is the proton density. If the amplitude of the compressive
fluctuations is large enough, crosses one or more instability
thresholds for anisotropy-driven microinstabilities. The enhanced field
fluctuations from these microinstabilities scatter the protons so as to reduce
the anisotropy of the pressure tensor. We propose that this scattering drives
the average value of away from the marginal stability boundary
until the fluctuating value of stops crossing the boundary. We
model this "fluctuating-anisotropy effect" using linear Vlasov--Maxwell theory
to describe the large-scale compressive fluctuations. We argue that this effect
can explain why, in the nearly collisionless solar wind, the average value of
is close to unity.Comment: 11 pages, published in Ap
Hearing the grass grow. Emotional and epistemological challenges of practice-near research
This paper discusses the concept of practice-near research in terms of the emotional and epistemological challenges that arise from the researcher coming 'near' enough to other people for psychological processes to ensue. These may give rise in the researcher to confusion, anxiety and doubt about who is who and what is what; but also to the possibility of real emotional and relational depth in the research process. Using illustrations from three social work doctoral research projects undertaken by students at the Tavistock Clinic and the University of East London the paper examines four themes that seem to the author to be central to meaningful practice-near research undertaken in a spirit of true emotional and epistemological open-mindedness: the smell of the real; losing our minds; the inevitability of personal change; and the discovery of complex particulars
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