20,246 research outputs found
Single chain properties of polyelectrolytes in poor solvent
Using molecular dynamics simulations we study the behavior of a dilute
solution of strongly charged polyelectrolytes in poor solvents, where we take
counterions explicitly into account. We focus on the chain conformational
properties under conditions where chain-chain interactions can be neglected,
but the counterion concentration remains finite. We investigate the
conformations with regard to the parameters chain length, Coulomb interaction
strength, and solvent quality, and explore in which regime the competition
between short range hydrophobic interactions and long range Coulomb
interactions leads to pearl-necklace like structures. We observe that large
number and size fluctuations in the pearls and strings lead to only small
direct signatures in experimental observables like the single chain form
factor. Furthermore we do not observe the predicted first order collapse of the
necklace into a globular structure when counterion condensation sets in. We
will also show that the pearl-necklace regime is rather small for strongly
charged polyelectrolytes at finite densities. Even small changes in the charge
fraction of the chain can have a large impact on the conformation due to the
delicate interplay between counterion distribution and chain conformation.Comment: 20 pages, 27 figures, needs jpc.sty (included), to appear in Jour.
Phys. Chem
Variational Principles for Lagrangian Averaged Fluid Dynamics
The Lagrangian average (LA) of the ideal fluid equations preserves their
transport structure. This transport structure is responsible for the Kelvin
circulation theorem of the LA flow and, hence, for its convection of potential
vorticity and its conservation of helicity.
Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational
framework that implies the LA fluid equations. This is expressed in the
Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated
for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure
Stretching and folding processes in the 3D Euler and Navier-Stokes equations
Stretching and folding dynamics in the incompressible, stratified 3D Euler
and Navier-Stokes equations are reviewed in the context of the vector \bdB =
\nabla q\times\nabla\theta where q=\bom\cdot\nabla\theta. The variable
is the temperature and \bdB satisfies \partial_{t}\bdB =
\mbox{curl}\,(\bu\times\bdB). These ideas are then discussed in the context of
the full compressible Navier-Stokes equations where takes the two forms q
= \bom\cdot\nabla\rho and q = \bom\cdot\nabla(\ln\rho).Comment: UTAM Symposium on Understanding Common Aspects of Extreme Events in
Fluid
Continuous and discrete Clebsch variational principles
The Clebsch method provides a unifying approach for deriving variational
principles for continuous and discrete dynamical systems where elements of a
vector space are used to control dynamics on the cotangent bundle of a Lie
group \emph{via} a velocity map. This paper proves a reduction theorem which
states that the canonical variables on the Lie group can be eliminated, if and
only if the velocity map is a Lie algebra action, thereby producing the
Euler-Poincar\'e (EP) equation for the vector space variables. In this case,
the map from the canonical variables on the Lie group to the vector space is
the standard momentum map defined using the diamond operator. We apply the
Clebsch method in examples of the rotating rigid body and the incompressible
Euler equations. Along the way, we explain how singular solutions of the EP
equation for the diffeomorphism group (EPDiff) arise as momentum maps in the
Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch
variational principle is discretised to produce a variational integrator for
the dynamical system. We obtain a discrete map from which the variables on the
cotangent bundle of a Lie group may be eliminated to produce a discrete EP
equation for elements of the vector space. We give an integrator for the
rotating rigid body as an example. We also briefly discuss how to discretise
infinite-dimensional Clebsch systems, so as to produce conservative numerical
methods for fluid dynamics
Regularization modeling for large-eddy simulation
A new modeling approach for large-eddy simulation (LES) is obtained by
combining a `regularization principle' with an explicit filter and its
inversion. This regularization approach allows a systematic derivation of the
implied subgrid-model, which resolves the closure problem. The central role of
the filter in LES is fully restored, i.e., both the interpretation of LES
predictions in terms of direct simulation results as well as the corresponding
subgrid closure are specified by the filter. The regularization approach is
illustrated with `Leray-smoothing' of the nonlinear convective terms. In
turbulent mixing the new, implied subgrid model performs favorably compared to
the dynamic eddy-viscosity procedure. The model is robust at arbitrarily high
Reynolds numbers and correctly predicts self-similar turbulent flow
development.Comment: 16 pages, 4 figures, submitted to Physics of Fluid
Geodesic boundary value problems with symmetry
This paper shows how left and right actions of Lie groups on a manifold may
be used to complement one another in a variational reformulation of optimal
control problems equivalently as geodesic boundary value problems with
symmetry. We prove an equivalence theorem to this effect and illustrate it with
several examples. In finite-dimensions, we discuss geodesic flows on the Lie
groups SO(3) and SE(3) under the left and right actions of their respective Lie
algebras. In an infinite-dimensional example, we discuss optimal
large-deformation matching of one closed curve to another embedded in the same
plane. In the curve-matching example, the manifold \Emb(S^1, \mathbb{R}^2)
comprises the space of closed curves embedded in the plane
. The diffeomorphic left action \Diff(\mathbb{R}^2) deforms the
curve by a smooth invertible time-dependent transformation of the coordinate
system in which it is embedded, while leaving the parameterisation of the curve
invariant. The diffeomorphic right action \Diff(S^1) corresponds to a smooth
invertible reparameterisation of the domain coordinates of the curve. As
we show, this right action unlocks an important degree of freedom for
geodesically matching the curve shapes using an equivalent fixed boundary value
problem, without being constrained to match corresponding points along the
template and target curves at the endpoint in time.Comment: First version -- comments welcome
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