3,031 research outputs found
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
An analysis of the crossover between local and massive separation on airfoils
Massive separation on airfoils operating at high Reynolds number is an important problem to the aerodynamicist, since its onset generally determines the limiting performance of an airfoil, and it can lead to serious problems related to aircraft control as well as turbomachinery operation. The phenomenon of crossover between local separation and massive separation on realistic airfoil geometries induced by airfoil thickness is investigated for low speed (incompressible) flow. The problem is studied both for the asymptotic limit of infinite Reynolds number using triple-deck theory, and for finite Reynolds number using interacting boundary-layer theory. Numerical results are presented which follow the evolution of the flow as it develops from a mildly separated state to one dominated by the massively separated flow structure as the thickness of the airfoil geometry is systematically increased. The effect of turbulence upon the evolution of the flow is considered, and the impact is significant, with the principal effect being the suppression of the onset of separation. Finally, the effect of surface suction and injection for boundary-layer control is considered. The approach which was developed provides a valuable tool for the analysis of boundary-layer separation up to and beyond stall. Another important conclusion is that interacting boundary-layer theory provides an efficient tool for the analysis of the effect of turbulence and boundary-layer control upon separated vicsous flow
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
P2X1 and P2X5 subunits form the functional P2X receptor in mouse cortical astrocytes
ATP plays an important role in signal transduction between neuronal and glial circuits and within glial networks. Here we describe currents activated by ATP in astrocytes acutely isolated from cortical brain slices by non-enzymatic mechanical dissociation. Brain slices were prepared from transgenic mice that express enhanced green fluorescent protein under the control of the human glial fibrillary acidic protein promoter. Astrocytes were studied by whole-cell voltage clamp. Exogenous ATP evoked inward currents in 75 of 81 astrocytes. In the majority (~65%) of cells, ATP-induced responses comprising a fast and delayed component; in the remaining subpopulation of astrocytes, ATP triggered a smoother response with rapid peak and slowly decaying plateau phase. The fast component of the response was sensitive to low concentrations of ATP (with EC50 of ~40 nM). All ATP-induced currents were blocked by pyridoxal-phosphate-6-azophenyl-2',4'-disulfonate (PPADS); they were insensitive to ivermectin. Quantitative real-time PCR demonstrated strong expression of P2X1 and P2X5 receptor subunits and some expression of P2X2 subunit mRNAs. The main properties of the ATP-induced response in cortical astrocytes (high sensitivity to ATP, biphasic kinetics, and sensitivity to PPADS) were very similar to those reported for P2X1/5 heteromeric receptors studied previously in heterologous expression systems
Computational morphogenesis of free form shells: Filter methods to create alternative solutions
p. 536-547Actual trends in numerical shape optimal design of structures deal with handling of very
large dimensions of design space. The goal is to allowing as much design freedom as
possible while considerably reducing the modelling effort. As a consequence, several
technical problems have to be solved to get procedures which are robust, easy to use and which can handle many design parameters efficiently. The paper briefly discusses several of the most important aspects in this context and presents many illustrative examples which show typical applications for the design of light weight shell and membrane structures.Bletzinger, K.; Firi, M.; Linhard, J.; Wüchner, R. (2009). Computational morphogenesis of free form shells: Filter methods to create alternative solutions. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654
Tube Models for Rubber-Elastic Systems
In the first part of the paper we show that the constraining potentials
introduced to mimic entanglement effects in Edwards' tube model and Flory's
constrained junction model are diagonal in the generalized Rouse modes of the
corresponding phantom network. As a consequence, both models can formally be
solved exactly for arbitrary connectivity using the recently introduced
constrained mode model. In the second part, we solve a double tube model for
the confinement of long paths in polymer networks which is partially due to
crosslinking and partially due to entanglements. Our model describes a
non-trivial crossover between the Warner-Edwards and the Heinrich-Straube tube
models. We present results for the macroscopic elastic properties as well as
for the microscopic deformations including structure factors.Comment: 15 pages, 8 figures, Macromolecules in pres
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