758 research outputs found
Spectrins in Axonal Cytoskeletons: Dynamics Revealed by Extensions and Fluctuations
The macroscopic properties, the properties of individual components and how
those components interact with each other are three important aspects of a
composited structure. An understanding of the interplay between them is
essential in the study of complex systems. Using axonal cytoskeleton as an
example system, here we perform a theoretical study of slender structures that
can be coarse-grained as a simple smooth 3-dimensional curve. We first present
a generic model for such systems based on the fundamental theorem of curves. We
use this generic model to demonstrate the applicability of the well-known
worm-like chain (WLC) model to the network level and investigate the situation
when the system is stretched by strong forces (weakly bending limit). We
specifically studied recent experimental observations that revealed the
hitherto unknown periodic cytoskeleton structure of axons and measured the
longitudinal fluctuations. Instead of focusing on single molecules, we apply
analytical results from the WLC model to both single molecule and network
levels and focus on the relations between extensions and fluctuations. We show
how this approach introduces constraints to possible local dynamics of the
spectrin tetramers in the axonal cytoskeleton and finally suggests simple but
self-consistent dynamics of spectrins in which the spectrins in one spatial
period of axons fluctuate in-sync.Comment: 18 pages, 4 figure
Helical structures from an isotropic homopolymer model
We present Monte Carlo simulation results for square-well homopolymers at a
series of bond lengths. Although the model contains only isotropic pairwise
interactions, under appropriate conditions this system shows spontaneous chiral
symmetry breaking, where the chain exists in either a left- or a right-handed
helical structure. We investigate how this behavior depends upon the ratio
between bond length and monomer radius.Comment: 10 pages, 3 figures, accepted for publication by Physical Review
Letter
Multistability of free spontaneously-curved anisotropic strips
Multistable structures are objects with more than one stable conformation,
exemplified by the simple switch. Continuum versions are often elastic
composite plates or shells, such as the common measuring tape or the slap
bracelet, both of which exhibit two stable configurations: rolled and unrolled.
Here we consider the energy landscape of a general class of multistable
anisotropic strips with spontaneous Gaussian curvature. We show that while
strips with non-zero Gaussian curvature can be bistable, strips with positive
spontaneous curvature are always bistable, independent of the elastic moduli,
strips of spontaneous negative curvature are bistable only in the presence of
spontaneous twist and when certain conditions on the relative stiffness of the
strip in tension and shear are satisfied. Furthermore, anisotropic strips can
become tristable when their bending rigidity is small. Our study complements
and extends the theory of multistability in anisotropic shells and suggests new
design criteria for these structures.Comment: 20 pages, 10 figure
Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities
The acoustic fields and streaming in a confined fluid depend strongly on the
acoustic boundary layer forming near the wall. The width of this layer is
typically much smaller than the bulk length scale set by the geometry or the
acoustic wavelength, which makes direct numerical simulations challenging.
Based on this separation in length scales, we extend the classical theory of
pressure acoustics by deriving a boundary condition for the acoustic pressure
that takes boundary-layer effects fully into account. Using the same
length-scale separation for the steady second-order streaming, and combining it
with time-averaged short-range products of first-order fields, we replace the
usual limiting-velocity theory with an analytical slip-velocity condition on
the long-range streaming field at the wall. The derived boundary conditions are
valid for oscillating cavities of arbitrary shape and wall motion as long as
the wall curvature and displacement amplitude are both sufficiently small.
Finally, we validate our theory by comparison with direct numerical simulation
in two examples of two-dimensional water-filled cavities: The well-studied
rectangular cavity with prescribed wall actuation, and the more generic
elliptical cavity embedded in an externally actuated rectangular elastic glass
block.Comment: 18 pages, 5 figures, pdfLatex, RevTe
Measure of phonon-number moments and motional quadratures through infinitesimal-time probing of trapped ions
A method for gaining information about the phonon-number moments and the
generalized nonlinear and linear quadratures in the motion of trapped ions (in
particular, position and momentum) is proposed, valid inside and outside the
Lamb-Dicke regime. It is based on the measurement of first time derivatives of
electronic populations, evaluated at the motion-probe interaction time t=0. In
contrast to other state-reconstruction proposals, based on measuring Rabi
oscillations or dispersive interactions, the present scheme can be performed
resonantly at infinitesimal short motion-probe interaction times, remaining
thus insensitive to decoherence processes.Comment: 10 pages. Accepted in JPhys
The Generalization of the Decomposition of Functions by Energy Operators
This work starts with the introduction of a family of differential energy
operators. Energy operators (, ) were defined together with a
method to decompose the wave equation in a previous work. Here the energy
operators are defined following the order of their derivatives (,
, k = {0,1,2,..}). The main part of the work is to demonstrate that
for any smooth real-valued function f in the Schwartz space (), the
successive derivatives of the n-th power of f (n in Z and n not equal to 0) can
be decomposed using only (Lemma) or with , (k in
Z) (Theorem) in a unique way (with more restrictive conditions). Some
properties of the Kernel and the Image of the energy operators are given along
with the development. Finally, the paper ends with the application to the
energy function.Comment: The paper was accepted for publication at Acta Applicandae
Mathematicae (15/05/2013) based on v3. v4 is very similar to v3 except that
we modified slightly Definition 1 to make it more readable when showing the
decomposition with the families of energy operator of the derivatives of the
n-th power of
Vortex and translational currents due to broken time-space symmetries
We consider the classical dynamics of a particle in a -dimensional
space-periodic potential under the influence of time-periodic external fields
with zero mean. We perform a general time-space symmetry analysis and identify
conditions, when the particle will generate a nonzero averaged translational
and vortex currents. We perform computational studies of the equations of
motion and of corresponding Fokker-Planck equations, which confirm the symmetry
predictions. We address the experimentally important issue of current control.
Cold atoms in optical potentials and magnetic traps are among possible
candidates to observe these findings experimentally.Comment: 4 pages, 2 figure
Interface-mediated interactions: Entropic forces of curved membranes
Particles embedded in a fluctuating interface experience forces and torques
mediated by the deformations and by the thermal fluctuations of the medium.
Considering a system of two cylinders bound to a fluid membrane we show that
the entropic contribution enhances the curvature-mediated repulsion between the
two cylinders. This is contrary to the usual attractive Casimir force in the
absence of curvature-mediated interactions. For a large distance between the
cylinders, we retrieve the renormalization of the surface tension of a flat
membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.
On the differential geometry of curves in Minkowski space
We discuss some aspects of the differential geometry of curves in Minkowski
space. We establish the Serret-Frenet equations in Minkowski space and use them
to give a very simple proof of the fundamental theorem of curves in Minkowski
space. We also state and prove two other theorems which represent Minkowskian
versions of a very known theorem of the differential geometry of curves in
tridimensional Euclidean space. We discuss the general solution for torsionless
paths in Minkowki space. We then apply the four-dimensional Serret-Frenet
equations to describe the motion of a charged test particle in a constant and
uniform electromagnetic field and show how the curvature and the torsions of
the four-dimensional path of the particle contain information on the
electromagnetic field acting on the particle.Comment: 10 pages. Typeset using REVTE
Application of the level-set method to the implicit solvation of nonpolar molecules
A level-set method is developed for numerically capturing the equilibrium
solute-solvent interface that is defined by the recently proposed variational
implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf
104}, 527 (2006) and J. Chem.\Phys. {\bf 124}, 084905 (2006)). In the level-set
method, a possible solute-solvent interface is represented by the zero
level-set (i.e., the zero level surface) of a level-set function and is
eventually evolved into the equilibrium solute-solvent interface. The evolution
law is determined by minimization of a solvation free energy {\it functional}
that couples both the interfacial energy and the van der Waals type
solute-solvent interaction energy. The surface evolution is thus an energy
minimizing process, and the equilibrium solute-solvent interface is an output
of this process. The method is implemented and applied to the solvation of
nonpolar molecules such as two xenon atoms, two parallel paraffin plates,
helical alkane chains, and a single fullerene . The level-set solutions
show good agreement for the solvation energies when compared to available
molecular dynamics simulations. In particular, the method captures solvent
dewetting (nanobubble formation) and quantitatively describes the interaction
in the strongly hydrophobic plate system
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