135 research outputs found
Effective field theory approach to Casimir interactions on soft matter surfaces
We utilize an effective field theory approach to calculate Casimir
interactions between objects bound to thermally fluctuating fluid surfaces or
interfaces. This approach circumvents the complicated constraints imposed by
such objects on the functional integration measure by reverting to a point
particle representation. To capture the finite size effects, we perturb the
Hamiltonian by DH that encapsulates the particles' response to external fields.
DH is systematically expanded in a series of terms, each of which scales
homogeneously in the two power counting parameters: \lambda \equiv R/r, the
ratio of the typical object size (R) to the typical distance between them (r),
and delta=kB T/k, where k is the modulus characterizing the surface energy. The
coefficients of the terms in DH correspond to generalized polarizabilities and
thus the formalism applies to rigid as well as deformable objects.
Singularities induced by the point particle description can be dealt with using
standard renormalization techniques. We first illustrate and verify our
approach by re-deriving known pair forces between circular objects bound to
films or membranes. To demonstrate its efficiency and versatility, we then
derive a number of new results: The triplet interactions present in these
systems, a higher order correction to the film interaction, and general scaling
laws for the leading order interaction valid for objects of arbitrary shape and
internal flexibility.Comment: 4 pages, 1 figur
Contact lines for fluid surface adhesion
When a fluid surface adheres to a substrate, the location of the contact line
adjusts in order to minimize the overall energy. This adhesion balance implies
boundary conditions which depend on the characteristic surface deformation
energies. We develop a general geometrical framework within which these
conditions can be systematically derived. We treat both adhesion to a rigid
substrate as well as adhesion between two fluid surfaces, and illustrate our
general results for several important Hamiltonians involving both curvature and
curvature gradients. Some of these have previously been studied using very
different techniques, others are to our knowledge new. What becomes clear in
our approach is that, except for capillary phenomena, these boundary conditions
are not the manifestation of a local force balance, even if the concept of
surface stress is properly generalized. Hamiltonians containing higher order
surface derivatives are not just sensitive to boundary translations but also
notice changes in slope or even curvature. Both the necessity and the
functional form of the corresponding additional contributions follow readily
from our treatment.Comment: 8 pages, 2 figures, LaTeX, RevTeX styl
Balancing torques in membrane-mediated interactions: Exact results and numerical illustrations
Torques on interfaces can be described by a divergence-free tensor which is
fully encoded in the geometry. This tensor consists of two terms, one
originating in the couple of the stress, the other capturing an intrinsic
contribution due to curvature. In analogy to the description of forces in terms
of a stress tensor, the torque on a particle can be expressed as a line
integral along any contour surrounding the particle. Interactions between
particles mediated by a fluid membrane are studied within this framework. In
particular, torque balance places a strong constraint on the shape of the
membrane. Symmetric two-particle configurations admit simple analytical
expressions which are valid in the fully nonlinear regime; in particular, the
problem may be solved exactly in the case of two membrane-bound parallel
cylinders. This apparently simple system provides some flavor of the remarkably
subtle nonlinear behavior associated with membrane-mediated interactions.Comment: 16 pages, 10 figures, REVTeX4 style. The Gaussian curvature term was
included in the membrane Hamiltonian; section II.B was rephrased to smoothen
the flow of presentatio
How to determine local elastic properties of lipid bilayer membranes from atomic-force-microscope measurements: A theoretical analysis
Measurements with an atomic force microscope (AFM) offer a direct way to
probe elastic properties of lipid bilayer membranes locally: provided the
underlying stress-strain relation is known, material parameters such as surface
tension or bending rigidity may be deduced. In a recent experiment a
pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of
the force-indentation curves. A theoretical model for this case is presented
here which describes these curves in the framework of Helfrich theory. The
linear behavior of the measurements is reproduced if one neglects the influence
of adhesion between tip and membrane. Including it via an adhesion balance
changes the situation significantly: force-distance curves cease to be linear,
hysteresis and nonzero detachment forces can show up. The characteristics of
this rich scenario are discussed in detail in this article.Comment: 14 pages, 9 figures, REVTeX4 style. New version corresponds to the
one accepted by PRE. The result section is restructured: a comparison to
experimental findings is included; the discussion on the influence of
adhesion between AFM tip and membrane is extende
Optimizing end-labeled free-solution electrophoresis by increasing the hydrodynamic friction of the drag-tag
We study the electrophoretic separation of polyelectrolytes of varying
lengths by means of end-labeled free-solution electrophoresis (ELFSE). A
coarse-grained molecular dynamics simulation model, using full electrostatic
interactions and a mesoscopic Lattice Boltzmann fluid to account for
hydrodynamic interactions, is used to characterize the drag coefficients of
different label types: linear and branched polymeric labels, as well as
transiently bound micelles.
It is specifically shown that the label's drag coefficient is determined by
its hydrodynamic size, and that the drag per label monomer is largest for
linear labels. However, the addition of side chains to a linear label offers
the possibility to increase the hydrodynamic size, and therefore the label
efficiency, without having to increase the linear length of the label, thereby
simplifying synthesis. The third class of labels investigated, transiently
bound micelles, seems very promising for the usage in ELFSE, as they provide a
significant higher hydrodynamic drag than the other label types.
The results are compared to theoretical predictions, and we investigate how
the efficiency of the ELFSE method can be improved by using smartly designed
drag-tags.Comment: 32 pages, 11 figures, submitted to Macromolecule
DNA condensation and redissolution: Interaction between overcharged DNA molecules
The effective DNA-DNA interaction force is calculated by computer simulations
with explicit tetravalent counterions and monovalent salt. For overcharged DNA
molecules, the interaction force shows a double-minimum structure. The
positions and depths of these minima are regulated by the counterion density in
the bulk. Using two-dimensional lattice sum and free energy perturbation
theories, the coexisting phases for DNA bundles are calculated. A
DNA-condensation and redissolution transition and a stable mesocrystal with an
intermediate lattice constant for high counterion concentration are obtained.Comment: 26 pages, 10 figure
A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
The motion of a small compact object in a background spacetime is
investigated in the context of a model nonlinear scalar field theory. This
model is constructed to have a perturbative structure analogous to the General
Relativistic description of extreme mass ratio inspirals (EMRIs). We apply the
effective field theory approach to this model and calculate the finite part of
the self force on the small compact object through third order in the ratio of
the size of the compact object to the curvature scale of the background (e.g.,
black hole) spacetime. We use well-known renormalization methods and
demonstrate the consistency of the formalism in rendering the self force finite
at higher orders within a point particle prescription for the small compact
object. This nonlinear scalar model should be useful for studying various
aspects of higher-order self force effects in EMRIs but within a comparatively
simpler context than the full gravitational case. These aspects include
developing practical schemes for higher order self force numerical
computations, quantifying the effects of transient resonances on EMRI waveforms
and accurately modeling the small compact object's motion for precise
determinations of the parameters of detected EMRI sources.Comment: 30 pages, 8 figure
A thermodynamically self-consistent theory for the Blume-Capel model
We use a self-consistent Ornstein-Zernike approximation to study the
Blume-Capel ferromagnet on three-dimensional lattices. The correlation
functions and the thermodynamics are obtained from the solution of two coupled
partial differential equations. The theory provides a comprehensive and
accurate description of the phase diagram in all regions, including the wing
boundaries in non-zero magnetic field. In particular, the coordinates of the
tricritical point are in very good agreement with the best estimates from
simulation or series expansion. Numerical and analytical analysis strongly
suggest that the theory predicts a universal Ising-like critical behavior along
the -line and the wing critical lines, and a tricritical behavior
governed by mean-field exponents.Comment: 11 figures. to appear in Physical Review
Computer Simulations of Supercooled Liquids and Glasses
After a brief introduction to the dynamics of supercooled liquids, we discuss
some of the advantages and drawbacks of computer simulations of such systems.
Subsequently we present the results of computer simulations in which the
dynamics of a fragile glass former, a binary Lennard-Jones system, is compared
to the one of a strong glass former, SiO_2. This comparison gives evidence that
the reason for the different temperature dependence of these two types of glass
formers lies in the transport mechanism for the particles in the vicinity of
T_c, the critical temperature of mode-coupling theory. Whereas the one of the
fragile glass former is described very well by the ideal version of
mode-coupling theory, the one for the strong glass former is dominated by
activated processes. In the last part of the article we review some simulations
of glass formers in which the dynamics below the glass transition temperature
was investigated. We show that such simulations might help to establish a
connection between systems with self generated disorder (e.g. structural
glasses) and quenched disorder (e.g. spin glasses).Comment: 37 pages of Latex, 11 figures, to appear as a Topical Review article
in J. Phys.: Condens. Matte
Attraction between DNA molecules mediated by multivalent ions
The effective force between two parallel DNA molecules is calculated as a
function of their mutual separation for different valencies of counter- and
salt ions and different salt concentrations. Computer simulations of the
primitive model are used and the shape of the DNA molecules is accurately
modelled using different geometrical shapes. We find that multivalent ions
induce a significant attraction between the DNA molecules whose strength can be
tuned by the averaged valency of the ions. The physical origin of the
attraction is traced back either to electrostatics or to entropic
contributions. For multivalent counter- and monovalent salt ions, we find a
salt-induced stabilization effect: the force is first attractive but gets
repulsive for increasing salt concentration. Furthermore, we show that the
multivalent-ion-induced attraction does not necessarily correlate with DNA
overcharging.Comment: 51 pages and 13 figure
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