8,121 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
Measurement of Thermal Conductance of Multilayer and Other Insulation Materials
Thermal conductance measurements on space suit thermal insulation candidate
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
Alternating groups and moduli space lifting Invariants
Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S
Measurement of thermal conductance of multilayer and other insulation materials Final report
Thermal conductance measurements of multilayer, aluminumized polymeric films for space suit insulation material
Integration of the atmospheric fluctuations in a dual-field optical interferometer: the short exposure regime
Spatial phase-referencing in dual-field optical interferometry is
reconsidered. Our analysis is based on the 2-sample variance of the
differential phase between target and reference star. We show that averaging
over time of the atmospheric effects depends on this 2-sample phase variance
(Allan variance) rather than on the true variance. The proper expression for
fringe smearing beyond the isoplanatic angle is derived. With simulations of
atmospheric effects, based on a Paranal turbulence model, we show how the
performances of a dual-field optical interferometer can be evaluated in a
diagram 'separation angle' versus 'magnitude of faint object'. In this diagram,
a domain with short exposure is found to be most useful for interferometry,
with about the same magnitude limits in the H and K bands. With star counts
from a Galaxy model, we evaluate the sky coverage for differential astrometry
and detection of exoplanets, i.e. likelihood of faint reference stars in the
vicinity of a bright target. With the 2mass survey, we evaluate sky coverage
for phase-referencing, i.e. avaibility of a bright enough star for main delay
tracking in the vicinity of any target direction.Comment: 9 pages, 8 figures, accepted for publication in A&
Two-body effects in the decay rate of atomic levels
Recoil corrections to the atomic decay rate are considered in the order of
Zm/M . The expressions are treated exactly without any expansion over Z alpha.
The expressions obtained are valid both for muonic atoms (for which they
contribute on the level of a few percent in high Z ions) and for electronic
atoms. Explicit results for Lyman-alpha transitions for low-Z of the order
(Zm/M)(Z alpha)^2 are also presented.Comment: 5 pages, 1 table, email: [email protected]
Behavior of self-propelled acetone droplets in a Leidenfrost state on liquid substrates
It is demonstrated that non-coalescent droplets of acetone can be formed on
liquid substrates. The fluid flows around and in an acetone droplet hovering on
water are recorded to shed light on the mechanisms which might lead to
non-coalescence. For sufficiently low impact velocities, droplets undergo a
damped oscillation on the surface of the liquid substrate but at higher
velocities clean bounce-off occurs. Comparisons of experimentally observed
static configurations of floating droplets to predictions from a theoretical
model for a small non-wetting rigid sphere resting on a liquid substrate are
made and a tentative strategy for determining the thickness of the vapor layer
under a small droplet on a liquid is proposed. This strategy is based on the
notion of effective surface tension. The droplets show self-propulsion in
straight line trajectories in a manner which can be ascribed to a Marangoni
effect. Surprisingly, self-propelled droplets can become immersed beneath the
undisturbed water surface. This phenomenon is reasoned to be drag-inducing and
might provide a basis for refining observations in previous work
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