1,332 research outputs found
Critical holes in undercooled wetting layers
The profile of a critical hole in an undercooled wetting layer is determined
by the saddle-point equation of a standard interface Hamiltonian supported by
convenient boundary conditions. It is shown that this saddle-point equation can
be mapped onto an autonomous dynamical system in a three-dimensional phase
space. The corresponding flux has a polynomial form and in general displays
four fixed points, each with different stability properties. On the basis of
this picture we derive the thermodynamic behaviour of critical holes in three
different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.
Mechanics of bundled semiflexible polymer networks
While actin bundles are used by living cells for structural fortification,
the microscopic origin of the elasticity of bundled networks is not understood.
Here, we show that above a critical concentration of the actin binding protein
fascin, a solution of actin filaments organizes into a pure network of bundles.
While the elasticity of weakly crosslinked networks is dominated by the affine
deformation of tubes, the network of bundles can be fully understood in terms
of non-affine bending undulations.Comment: 5 pages, 3 figures, final version as publishe
Diffusion-Induced Oscillations of Extended Defects
From a simple model for the driven motion of a planar interface under the
influence of a diffusion field we derive a damped nonlinear oscillator equation
for the interface position. Inside an unstable regime, where the damping term
is negative, we find limit-cycle solutions, describing an oscillatory
propagation of the interface. In case of a growing solidification front this
offers a transparent scenario for the formation of solute bands in binary
alloys, and, taking into account the Mullins-Sekerka instability, of banded
structures
Capillary-Wave Model for the Solidification of Dilute Binary Alloys
Starting from a phase-field description of the isothermal solidification of a
dilute binary alloy, we establish a model where capillary waves of the
solidification front interact with the diffusive concentration field of the
solute. The model does not rely on the sharp-interface assumption, and includes
non-equilibrium effects, relevant in the rapid-growth regime. In many
applications it can be evaluated analytically, culminating in the appearance of
an instability which, interfering with the Mullins-Sekerka instability, is
similar to that, found by Cahn in grain-boundary motion.Comment: 17 pages, 12 figure
Mechanical tension and spontaneous muscle twitching precede the formation of cross-striated muscle in vivo
Muscle forces are produced by repeated stereotypical actomyosin units called sarcomeres. Sarcomeres are chained into linear myofibrils spanning the entire muscle fiber. In mammalian body muscles, myofibrils are aligned laterally, resulting in their typical cross-striated morphology. Despite this detailed textbook knowledge about the adult muscle structure, it is still unclear how cross-striated myofibrils are built in vivo. Here, we investigate the morphogenesis of Drosophila abdominal muscles and establish them as an in vivo model for cross-striated muscle development. By performing live imaging, we find that long immature myofibrils lacking a periodic actomyosin pattern are built simultaneously in the entire muscle fiber and then align laterally to give mature cross-striated myofibrils. Interestingly, laser micro-lesion experiments demonstrate that mechanical tension precedes the formation of the immature myofibrils. Moreover, these immature myofibrils do generate spontaneous Ca2+-dependent contractions in vivo, which, when chemically blocked, result in cross-striation defects. Taken together, these results suggest a myofibrillogenesis model in which mechanical tension and spontaneous muscle twitching synchronize the simultaneous self-organization of different sarcomeric protein complexes to build highly regular cross-striated myofibrils spanning the length of large muscle fibers
Grain Boundary Scars and Spherical Crystallography
We describe experimental investigations of the structure of two-dimensional
spherical crystals. The crystals, formed by beads self-assembled on water
droplets in oil, serve as model systems for exploring very general theories
about the minimum energy configurations of particles with arbitrary repulsive
interactions on curved surfaces. Above a critical system size we find that
crystals develop distinctive high-angle grain boundaries, or scars, not found
in planar crystals. The number of excess defects in a scar is shown to grow
linearly with the dimensionless system size. The observed slope is expected to
be universal, independent of the microscopic potential.Comment: 4 pages, 3 eps figs (high quality images available from Mark Bowick
On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua
Linear combinations of chi square random variables occur in a wide range of
fields. Unfortunately, a closed, analytic expression for the pdf is not yet
known. As a first result of this work, an explicit analytic expression for the
density of the sum of two gamma random variables is derived. Then a
computationally efficient algorithm to numerically calculate the linear
combination of chi square random variables is developed. An explicit expression
for the error bound is obtained. The proposed technique is shown to be
computationally efficient, i.e. only polynomial in growth in the number of
terms compared to the exponential growth of most other methods. It provides a
vast improvement in accuracy and shows only logarithmic growth in the required
precision. In addition, it is applicable to a much greater number of terms and
currently the only way of computing the distribution for hundreds of terms. As
an application, the exponential dependence of the eigenvalue fluctuation
probability of a random matrix model for 4d supergravity with N scalar fields
is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio
Microrheology, stress fluctuations and active behavior of living cells
We report the first measurements of the intrinsic strain fluctuations of
living cells using a recently-developed tracer correlation technique along with
a theoretical framework for interpreting such data in heterogeneous media with
non-thermal driving. The fluctuations' spatial and temporal correlations
indicate that the cytoskeleton can be treated as a course-grained continuum
with power-law rheology, driven by a spatially random stress tensor field.
Combined with recent cell rheology results, our data imply that intracellular
stress fluctuations have a nearly power spectrum, as expected for
a continuum with a slowly evolving internal prestress.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let
Evidence-based entrepreneurship: Cumulative science, action principles, and bridging the gap between science and practice
10.1561/0300000044Foundations and Trends in Entrepreneurship811-6
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