70 research outputs found
Polymer Adsorption on Curved Surfaces: Finite chain length corrections
The structural properties of polymers adsorbed onto a surface have been
widely investigated using self-consistent mean-field theories. Recently,
analytical mean-field theories have been applied to study polymer adsorption on
curved surfaces but all in the context of the ground state dominance
approximation in which the polymer chain length (N) is essentially infinite.
Using an expression for the free energy by Semenov, we determine leading order
(in 1/N) corrections due to the finiteness of the polymer chain length on
surface tension, spontaneous curvature, and rigidity constants.Comment: 24 pages, 7 figures. Accepted for publication in Macromolecule
Depletion forces near a soft surface
We investigate excluded-volume effects in a bidisperse colloidal suspension
near a flexible interface. Inspired by a recent experiment by Dinsmore et al.
(Phys. Rev, Lett. 80, 409 (1998)), we study the adsorption of a mesoscopic bead
on the surface and show that depletion forces could in principle lead to
particle encapsulation. We then consider the effect of surface fluctuations on
the depletion potential itself and construct the density profile of a polymer
solution near a soft interface. Surprisingly we find that the chains accumulate
at the wall, whereas the density displays a deficit of particles at distances
larger than the surface roughness. This non-monotonic behavior demonstrates
that surface fluctuations can have major repercusions on the properties of a
colloidal solution. On average, the additional contribution to the Gibbs
adsorbance is negative. The amplitude of the depletion potential between a
mesoscopic bead and the surface increases accordingly.Comment: 10 pages, 5 figure
A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains
In the first (and abstract) part of this survey we prove the unitary
equivalence of the inverse of the Krein--von Neumann extension (on the
orthogonal complement of its kernel) of a densely defined, closed, strictly
positive operator, for some in a Hilbert space to an abstract buckling problem operator.
This establishes the Krein extension as a natural object in elasticity theory
(in analogy to the Friedrichs extension, which found natural applications in
quantum mechanics, elasticity, etc.).
In the second, and principal part of this survey, we study spectral
properties for , the Krein--von Neumann extension of the
perturbed Laplacian (in short, the perturbed Krein Laplacian)
defined on , where is measurable, bounded and
nonnegative, in a bounded open set belonging to a
class of nonsmooth domains which contains all convex domains, along with all
domains of class , .Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144
Diversified actin protrusions promote environmental exploration but are dispensable for locomotion of leukocytes
Most migrating cells extrude their front by the force of actin polymerization. Polymerization requires an initial nucleation step, which is mediated by factors establishing either parallel filaments in the case of filopodia or branched filaments that form the branched lamellipodial network. Branches are considered essential for regular cell motility and are initiated by the Arp2/3 complex, which in turn is activated by nucleation-promoting factors of the WASP and WAVE families. Here we employed rapid amoeboid crawling leukocytes and found that deletion of the WAVE complex eliminated actin branching and thus lamellipodia formation. The cells were left with parallel filaments at the leading edge, which translated, depending on the differentiation status of the cell, into a unipolar pointed cell shape or cells with multiple filopodia. Remarkably, unipolar cells migrated with increased speed and enormous directional persistence, while they were unable to turn towards chemotactic gradients. Cells with multiple filopodia retained chemotactic activity but their migration was progressively impaired with increasing geometrical complexity of the extracellular environment. These findings establish that diversified leading edge protrusions serve as explorative structures while they slow down actual locomotion
Coupling changes in cell shape to chromosome segregation
Animal cells undergo dramatic changes in shape, mechanics and polarity as they progress through the different stages of cell division. These changes begin at mitotic entry, with cell–substrate adhesion remodelling, assembly of a cortical actomyosin network and osmotic swelling, which together enable cells to adopt a near spherical form even when growing in a crowded tissue environment. These shape changes, which probably aid spindle assembly and positioning, are then reversed at mitotic exit to restore the interphase cell morphology. Here, we discuss the dynamics, regulation and function of these processes, and how cell shape changes and sister chromatid segregation are coupled to ensure that the daughter cells generated through division receive their fair inheritance
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