217 research outputs found
Second variation of the Helfrich-Canham Hamiltonian and reparametrization invariance
A covariant approach towards a theory of deformations is developed to examine
both the first and second variation of the Helfrich-Canham Hamiltonian --
quadratic in the extrinsic curvature -- which describes fluid vesicles at
mesoscopic scales. Deformations are decomposed into tangential and normal
components; At first order, tangential deformations may always be identified
with a reparametrization; at second order, they differ. The relationship
between tangential deformations and reparametrizations, as well as the coupling
between tangential and normal deformations, is examined at this order for both
the metric and the extrinsic curvature tensors. Expressions for the expansion
to second order in deformations of geometrical invariants constructed with
these tensors are obtained; in particular, the expansion of the Hamiltonian to
this order about an equilibrium is considered. Our approach applies as well to
any geometrical model for membranes.Comment: 20 page
Two-colour generation in a chirped seeded Free-Electron Laser
We present the experimental demonstration of a method for generating two
spectrally and temporally separated pulses by an externally seeded, single-pass
free-electron laser operating in the extreme-ultraviolet spectral range. Our
results, collected on the FERMI@Elettra facility and confirmed by numerical
simulations, demonstrate the possibility of controlling both the spectral and
temporal features of the generated pulses. A free-electron laser operated in
this mode becomes a suitable light source for jitter-free, two-colour
pump-probe experiments
Geometry of lipid vesicle adhesion
The adhesion of a lipid membrane vesicle to a fixed substrate is examined
from a geometrical point of view. This vesicle is described by the Helfrich
hamiltonian quadratic in mean curvature; it interacts by contact with the
substrate, with an interaction energy proportional to the area of contact. We
identify the constraints on the geometry at the boundary of the shared surface.
The result is interpreted in terms of the balance of the force normal to this
boundary. No assumptions are made either on the symmetry of the vesicle or on
that of the substrate. The strong bonding limit as well as the effect of
curvature asymmetry on the boundary are discussed.Comment: 7 pages, some major changes in sections III and IV, version published
in Physical Review
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
The prolate-to-oblate shape transition of phospholipid vesicles in response to frequency variation of an AC electric field can be explained by the dielectric anisotropy of a phospholipid bilayer
The external electric field deforms flaccid phospholipid vesicles into
spheroidal bodies, with the rotational axis aligned with its direction.
Deformation is frequency dependent: in the low frequency range (~ 1 kHz), the
deformation is typically prolate, while increasing the frequency to the 10 kHz
range changes the deformation to oblate. We attempt to explain this behaviour
with a theoretical model, based on the minimization of the total free energy of
the vesicle. The energy terms taken into account include the membrane bending
energy and the energy of the electric field. The latter is calculated from the
electric field via the Maxwell stress tensor, where the membrane is modelled as
anisotropic lossy dielectric. Vesicle deformation in response to varying
frequency is calculated numerically. Using a series expansion, we also derive a
simplified expression for the deformation, which retains the frequency
dependence of the exact expression and may provide a better substitute for the
series expansion used by Winterhalter and Helfrich, which was found to be valid
only in the limit of low frequencies. The model with the anisotropic membrane
permittivity imposes two constraints on the values of material constants:
tangential component of dielectric permittivity tensor of the phospholipid
membrane must exceed its radial component by approximately a factor of 3; and
the membrane conductivity has to be relatively high, approximately one tenth of
the conductivity of the external aqueous medium.Comment: 17 pages, 6 figures; accepted for publication in J. Phys.: Condens.
Matte
Hamilton's equations for a fluid membrane: axial symmetry
Consider a homogenous fluid membrane, or vesicle, described by the
Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is
axially symmetric, this energy can be viewed as an `action' describing the
motion of a particle; the contours of equilibrium geometries are identified
with particle trajectories. A novel Hamiltonian formulation of the problem is
presented which exhibits the following two features: {\it (i)} the second
derivatives appearing in the action through the mean curvature are accommodated
in a natural phase space; {\it (ii)} the intrinsic freedom associated with the
choice of evolution parameter along the contour is preserved. As a result, the
phase space involves momenta conjugate not only to the particle position but
also to its velocity, and there are constraints on the phase space variables.
This formulation provides the groundwork for a field theoretical generalization
to arbitrary configurations, with the particle replaced by a loop in space.Comment: 11 page
Nanoscale dynamics by short-wavelength four wave mixing experiments
Multi-dimensional spectroscopies with vacuum ultraviolet (VUV)/x-ray free-electron laser (FEL) sources would open up unique capabilities for dynamic studies of matter at the femtosecond-nanometer time-length scales. Using sequences of ultrafast VUV/x-ray pulses tuned to electron transitions enables element-specific studies of charge and energy flow between constituent atoms, which embody the very essence of chemistry and condensed matter physics. A remarkable step forward towards this goal would be achieved by extending the four wave mixing (FWM) approach at VUV/soft x-ray wavelengths, thanks to the use of fully coherent sources, such as seeded FELs. Here, we demonstrate the feasibility of VUV/soft x-ray FWM at Fermi@Elettra and we discuss its applicability to probe ultrafast intramolecular dynamics, charge injection processes involving metal oxides and electron correlation and magnetism in solid materials. The main advantage in using VUV/soft x-ray wavelengths is in adding element-sensitivity to FWM methods by exploiting the core resonances of selected atoms in the sample
Cylindrical equilibrium shapes of fluid membranes
Within the framework of the well-known curvature models, a fluid lipid
bilayer membrane is regarded as a surface embedded in the three-dimensional
Euclidean space whose equilibrium shapes are described in terms of its mean and
Gaussian curvatures by the so-called membrane shape equation. In the present
paper, all solutions to this equation determining cylindrical membrane shapes
are found and presented, together with the expressions for the corresponding
position vectors, in explicit analytic form. The necessary and sufficient
conditions for such a surface to be closed are derived and several sufficient
conditions for its directrix to be simple or self-intersecting are given.Comment: 17 pages, 4 figures. Published in J. Phys. A: Math. Theore
- …